Topography for Field Artillery

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'TOPOGRAPHYtor Field Artillery

Departmc!'t of Tactics

Document No.2

1922

This document replaces

Documents 51, 40a, 37b, and 51a.

published

Under the Direction of

THE CHIEF OF FIELD ARTILLERY

by the

TIlE FIELD ARTILLEHY SCHOOL

FORT SILL, OKLAHOMA

I



. Linear measure

. A. .Metric system

B. Conversion between English and metric system'Angular measure

A. Degree system

B. Grade system

C. Mil systemD. Conversion in angular measure

E. Expression of angles by tangents

Table showing accuracy of tangent calculation of angular'values •

F. Gradients

G. Per cent

H. COJ:lversions in tangents and angular measureMeasuring instruments

A. Scales

Metric measuring scaleTriangular scale -"_

Tapes and chains

Testing of edges :.. -:B. Protractors

C. Em~rgency devices .

CHAPTER I.

CHAPTER II.

CHAPTER III

TABLE OF CONTENTS.

. Introduction.

Distance And Direction.

Maps And Scales

Par. 1-5

6-63

,8-14

8-9

10-14

15-53

18-20

21-22

23-29.

30-31

32-45

42

46-47

48-51

52-53

54-75

54-59

55

. 55

57

5860-62

63

The elements of a mapA. Definition . ,B. Classes of maps

C. Map making and map reading1. Map making• 2. ~1ap reading

D. Ground relations

1. Distance2. Direction

3. ,AI ti tude

4. Map essentials J

64-74

64

65

66-68

67

68

69-74

70

71

72

74

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75-83

75

76-83

7778

79-83

84-118

84

85-91

85-86

85

86

87-9188

89-91

92-94 .

95-118

96-99

100-118

100-118

106-109

110,111-118

Distances and scales --------------"7--------~-------------------- .A. Definitions ----------------------------.

B. Scales

1. Representative fraction2., ''lords and figures -------:..---------------------------

3. Graphical scale

~Iap scale problems

A. Classes of problemsB. Simple rules and map scale calculations

1. ~lap to ground --.---------------------------------a. By R. F.

By words and figures scales -------------..:.--------

2: Ground to map '_.a. By R. F. _

b. By words and figures scales

C. Scale conversions

D. Types of graphical scales

1. Construction of reading scales

2. \Vorking scales

a. Strike scalesb. Mounted working scales

c. Interchange of graphical scales

d. Working scale graphs ...

CHAPTER IV. l\Ieasurements Of Slopes And Elevation 119-133

Discussion 119-120

A. Instruments used 120

B. Units in which slopes are expressed -----------------.:..-- 121-1271. Degrees anll minutes 122

2. l\lils ':..___________ 123

3. rercentages 1244. Gradients 125

5. Tangents 126

Type problem 127

C. Slope scale ~_ 128-133

1. Construction of slope scale 129-131

a. For American map .:. -:_ 129

b. For metric map 130-131 .

Degree slope scale ..:.____________ 130

Mil slope scale 131

2 Use of slope ~cale 132-133_

a. in contouring 132

b. In reading slopes .. 133

IIow sho\vnA. Bench ~ai'ks, hachures, and contours

1. Definitions .l

CHAPTER V. , E.levation And Ground 11'orms 13.1.141

134

135-140

135-138

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a. Bench ~rk --:~-----~--------~---------------b. Hachures

c. Contours2. Vertical interval

3. Critical points --:---------------------------------n. ,Logical contouring ----------:--------------------------

CHAPTER VI. Instruments Used In Topographic Operations.

135

136

137.139 .

140

141

142~173

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Description and use 142-173

A. Aiming circles .:.. .:.. :. 142

, n. Battery commander telescopes :.._____________________ 143C. Transit ~____________________________ 144

D. Prismatic compass ..:__________________________ 145 •

E. Peigne' compass ~_:...___________________ 146-150

1. To read bearings 147

2. To plot this direction with the compass 148

3. To plot the direction with a protractor _' 1494. To measure a slope :... 150

F. Plane table ~______________________ 151-152

1. To level the plane table .. . 152G. Alidades 153-161

1. Triangular alidades 153

2. Sighting alidades -' ~_ '154

3. Leveling alidade 155

a. To measure a gradient '_________ 155

b. Laying off directions .:..________ 155

4. Telescopic alidade :. 156-161.

a. To measure distance with the stadia 158b. Horizontal distance 159-161

II. Abney level ~___________________ 162-163

'To use Abney level '______________________________ 163-164

1. Gravity clinometer ... ~________________ 165

J. Levels 166'K. Slope board 167-168

L. Sito-goniometer 169-172 \

1. To measure site and find the minimum range ----.:.--- 170-171a. Site 170

b. Minimum range :.__________ 171

2. To measure angles and deflections .:.._______ 172M. Protractors '_________________________________ 173

• ,.

.

Defi niti on s

Methods of orientation .:. .:.~

A. By a declinated table

1. With a declinatoT unattached

2. With a declinator attached --:..-------------------------

CHAPTER VII. Orientation '174-183

174

175-183

176-177

176

177, .

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,Defini tion -----------------.---------------------------------A. Kinds of traverses .:... ...: •

B. Instruments used :

C. ~ethods of traverse :..

1. Fore sight-back sight method -_--------------------2. Needle traverse' , :..

3., Angle traverse

D. ~feasurernents.

1. Pacing

2. Chaining or taping

3. Stadia readingsE. Special case :. ---------------..:-----.,

F .. Errors in traversing ------,..--------------------------

By a known line:....:---------------.:.:-------------~-----

1. 'Vhen the, plane table is on a station over one of the

known points of a given line ---------..:-------------

2. 'Vhen the plane table is somewhere on the line joining

, two points of known location .:. . ----:..-----

3. By angle traverse ----------------------:..----------

4. When known point on given line' cannot be occupied

5. By resection

'

184-194

184

184

185

186-188

186

187

188

189-192

190

.191192

,193,

194

.

178-183 .. I~

178 :l',

179180. ,'~

181-183

183

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Traverses.

'B.

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CHAPTER VIII.

A,

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.Definition . _.:. . :._..: .:. .:.A. Purpose

B. Accuracy

C. The operation

To locate a point by intersection -----------~---------_:_---'------

Definit ion

Conditions which must be fulfilled if accurate results are to beexpected

~lethod8 of resection

A. Transparent paper method

, B.. Two point method -:..----------------------------------

1. Using a known line ---------~------~--.:.-------.:.---

2. Using the declinator --------------.:.--:..------------

C. .Three point method -------------:..---:..-----------------Triangle of error

1. Operator's posi.tion jnside triangle I

2. Operator's station outside triangle --..:---------:..-----,

a. By inverse triangle method ----------------:..----D. 'Back azimuth method :.. :..

E. Italian resection

;

CHAPTER IX.

CHAPTER X.

Intersection.

Resection.

."

195-198 .~

,

195

196

197

,198 ',

198

199-213 ,.

..199

1

, 200

201-213

201-203

204-205

204205, .

206-208

207-208

207

208

208

209

210-213

-IV-

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1. The process2. The proof, --_-------------..,;-------------------- •

211-212

213

Position and area sketches ----------------------------'-------

A. Characteristics

B. Technique1. Whole to part method :- _' .

2. Determination of critical points

3. Information to be included ---------'---------..:.:..--

4. 'Conventional signs .----------.:..-----------'-~------5. Title .:-6. Border

7. 'Lettering •'Road sketches

A. Characteristicsn. Technique

1. ~fethod oy'sketchin~2. Lateral limits to be considered

3. Information to be in~luded

Characterist ics ,Types of sketches ~---------------.

E8sen ti al s

A. IdentificationB. Information

C. Drawing'

1. Perspective

a. Parallel horizontal lines ------------------.:.-----,

b. Parallel vertical linesc. Parallel lines not horizontal

2. Consecutive crest lines ---------------:.-------

3. Broken lines

4. Ground slope arid form

5. Shading6. Conventional signs

~Jethod of procedure

A. I~quipment ~_

n. Identification and orientation ---------------:..-----::---- •C. Analysis of the fecto~ -----~--~---.:..-------..:.--..:-----~-

D. Selection of reference point and horizontal control

E. Vertical control

F. Drawing in framework. A comparison of methods

1. First method ...

2. Second method _----------------------~-----------

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230-284

230-233

234-236

237-258

238

239-240

241-258

244-247

245

246'

247.

248-249,',250

,251-252 ....

253-254

255-258

259-283

'260

261-264t

265

266-268

269-270

271-274

272

273-274

214-229

214-229

214

215-223

215

216

217

218-220,.

221 ,

'222

223

224-229

224-225

226-229

.226-227 .

228

229

-v-

Ske~ching

Panoramic Sketches.

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CHAPTER XlI.

CHAPTER XI.

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G. Filling in ----.:..---------~----------------.:..-------------

H. Designation of targets and important points

I. SubsketchesMap and panoramic sketch -'---~---.:..---------------------------..

Definitions ----------------------------------.'Visibility

A. Similar triangles ---------------------.:..--..:.---~---------

B. With elastic band --------~-------------~---..:.-----~---

C. 'Angle of site --------------------------------..:---------D. Graphic method ..:. ..:

E. Visibility charts _----------------------- .... Defilade

A. Angle of site

.. , 1. Measured from enemy O. P. ----------'--------------

2.' Measured from covering crest -----------r-..:--------B. o. Profiles.

'C. Trble of defilade ---------------'----------------------D. Type problems

1. First problem ------------------'------------------

2. Second problem

3. Third problem

..,,,,

.1-

l

275-276 ~l'

277-281

282-283

284

285-301

285

286-292

287

288

289

290

291-292

, 293-301

294-295

294

295 I

296

297 ..

298-301

299

300 ')

301.

.......

Visibility And Defilade.'HAPTER XIII.-

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't

302-304 'r-

305-312 .

306

307-309307308

309

310-312

310

311

312

313-327

313314

315-316

317-326

318-322

323-324

325-326

325

326

327

, ,

CHAPTER XIV. l\linimu~ Elevation, Minimum Range And Dead'Space ," ...rGeneral •

.Determination of minimum elevation and range

A. Steps of calculation -..:

B. Effect of Ground Forms ------------.:..-----------------

1. Level Terrain --~--------~---------~:.---------------

2.' Irregular Terrain -----------------'-----~----------

3. Effect of Slopes

'9~ Type PloblemsExample 1

. Example 2

Example 3

Determination of Dead Space -----:----------------------------

\ . Limit of dead space 4_

• Determination of grazing point

Type Problems ------------------:.----.:.'----.,.-------

, Calculation Method 'with Special Chart ------.'.------------------

Preparation of chart

. lJse of chart ---------------------------~-.--------

Type Problems ------------------~--------------'--Example 6

Example 7 ~_,

Dead Space Charts --~-------------------------.:..-----~--------

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-VI-

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Definition

Kinds of projection

A. Mercator's projection .-:------------.:..-------------------

B. Polyhedral projection

C. Conic projection

D. Polyhedral projection

E. Donne projection -------------------:.-----------------

F. Lambert projection ----------------------------------:..

Origin

Coordinates

A. Coordinates of originn. Complete coordinates \

C. Reduced hectometric coordinates

1; Error introduced

D. Plotting points

Convergence of tneredians

Y-Azimuth

CHAPTER XV.

CHAPTER XVI. I

Map Projections.

The Lambert Grid.

328-335

328

329-335

329

330331 ,

332

333

334-335.336-348

336

337-:344

338,339 ..

340-342

341

343-344

345-347

348

CHAPTER XVII. U~e Of Grid In Map Reading And Map Firing.

Advantages of the grid -------------------------~---------:--

A. Method of plotting a p:>int

1. When ruler graduations are longer than the distance

between grid:; -----------.:---------------------

2. When the ruler graduations are too small

n. Method of reading the coordinates of a point :.-----------

1. When the rule is correctly scaled ---------:..-~-------

2. When the scale is too large

3. When the scale is too small

4.' With the right angled ruleC. Plotting directions

1. By Y-azimuth -----------------:..------------------

2. Dy coordinates

a. By auxiliary points'

b. By similar triangles .:.-------------------------

c. Dy reduced similar triangles

d. By reversing direction

D. Detertnination of range and Y-azimuth by coordinates :..--

1. Range by square root

2. Di rection

Eo To locate on the ground a point the coordinates of whichare given

CHAPTER XVIII.

General

The Compass.

----------------------------------------------------

-\ '11-

349-367

349-367350-351

350

351

352-355

352

353

:354

355

356-362

356

357-362

359

360

'361

362

363-365

363

364-365

366-367

368-383 ... ,

368

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~orthAzimuth

~Iagnetic bearing

):-azimuthDeclinationA. Magnetic declination

1. Magnetic variations _.:. ,

2. Use of isogonic chart

n. Compass declination . ..:

.CHAPTER XIX. Laying Guns With A Declinated Instrument.

Using prismatic compass

A. To determine the compass bearing of a target

Off-set method

n. Laying guns with bearing determined

1. Using compass as, aiming point

Using aiming circle or prismatic compass and magic number method

of laying (See Chapter XX). .

CHAPTER XX. Laying The Guns On Dase Line.

Steps' performed in occupation of a sector ---------'-------------

Establishment of base piece on base line -------,;,.---------------- .A. Drill regulation methorl

B. Using topographical methods

Classes of topographical methods

First class. Plane of sight through points located by

coordinatesSecond class. Plane of sight determined by an

established direction

i., Direct ~rientation

a. Using plane table --------------------:...-b. Using aiming circle ------------------.:..

2. Orientation by means of an orienting line

a. Advantages of an orienting line -----.:.--

b. Steps to be performed ----------------.:.

1. Determination of base angle

II. Laying on base line with aimingcircle

First case

Second case

Method ~o. 1.

III. Laying on base line using a planetable

CHAPTER XXI. Topo~raphical Operations In Occupation Of A

Dattery Sector. 418-432

I,

General

, , Gun position

-VIII-

418

419-423

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. "erre!'trial observation '-

Comparison of method3

. A. When coordinates of. gun position can be read directly frommap

n. Wnen gun position cannot be identified on map

1. Using geodetic point2. By resection .:.

3. By an orienting pointBase point or target '-.:.

A. When base point may not be determined .from map

,B. Determination of direction to target or base pointAiming point

. A. Determining direction to aiming point ------:..----------- .

. n. The orienting line ------_-----------------------------

1. Two types of orienting line2. Typical case

I' CHAPTEI~ XXII. Locating Targets.

419

420-423

421

422 •

423

424-425 , t

424.')

425/to

426-432

426

427-432 ,

428-430

431-432 ',,':

{

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433-439

433

434-439

APPENDIX.

Praeticibifity of slopes ---------------"---------------------

Practicable depths of fords ..Strength of ice :

Length of pace on slopes

Appt'ndix J. Slopes. 440-443

440

442

442

443

Appt'ndix II.

Appt'ndix ]11.

Table Of 1\atural Functions:

Circclar Measure.

.444

445-446

Definitions and diagrams ..:

Conve~sion tables

A. Mils in terms of degrees and tangents ------.--------

B. Degrees in terms of mils and tangents

Classes of records

A. ~Iaps and charts1. Battle maps of sector

2. Charts

a. The firing chart ..

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445-446445

446

447-449-

450

451-486

451-468

487-506

487-506

488-501

488

489-501

489.490

Maps And Records.

Reduction Of Stadia ]~eadings.

Azimuth Of Polaris.•

I>efi~itions and Diagrams.

A ppendix VII.

Appendix IV.

. Appendix V.

Appendix VI.

-IX-

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b. Range and deflection fan

c. Position chart -'---------------------------rd. Auxiliary position . --------

e. General system of communication -------.:..--f. Chart of visible and'invisible areas ----------g. Chart of dead space

h. Combined charts

B. Written records

a. B. C. data book

b. Ammunition record ------------------------c. Ta~get sheet

-x-

-1491

492

493

494495

496-497

498-501

502-506

502

503

504

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TOPOGRAPHY FOR FIELD ARTILLERYCHAPTER I. '. "i

INTRODUCTION

nll~OR'rANC~ OF TOPOGRAPHY TO FIELD ARTILLERY ,OFFICERS.

1 . Topography, in general, is "the exact and scientific delineation and

description in minute detail of any' place or region" (Webster's New Inter-

national Dictionary). Military topography delineates and describes all the

physical features of military importance of a place o'r region. The science

is used by every branch of the service in the disposition and maneuvering

of its forces,. both combat and non-combatant .. Topography is especially

important in the' artillery, where it is used not only for maneuvering and

other general purposes, but for the preparation and conduct of fire. For

this purpose a high degree of accuracy is essential, requiring exact methods

not usually necessary in ordinary work.

2. The extensive use of topography in conneCtion with artillery firing

is a development of the late European 'Var. Batteries frequently remained

for long periods of time in fixed positions, making it possible to study theterrain thoroughly and to locate positions and objectives on maps accu-

rately and in great detail. By means of topographical measurements on map

and ground, very accurate data for opening fire could be prepared, and

the first shots dropped close to the target, reducing the labor of adjust-

ment to a minimum, saving much valuable time and ammunition, and gain-

ing an immeasurable advantage by surprising the enemy with a sudden and

effective fire. The advantage of this was especially apparent in crowded

sectors where many batteries were firing at the same time. Unless a battery

could place its first shots close to the target it was difficult for the observer

to distinguish them from those of other batteries. Another important use

l topographical method~ was found in the designation and identification

.of targets for observation, both aerial and terrestrial.

Thus firing with 'data obtained from the map came to be used rather

fr('quently. Even in rapid advances to new positions, much firing was done

em known enemy positions from the map alene, as it was sometimes impos-

..ible to secure observation in the broken and fireswept zones over which

tr.e advance was made. Of course, adjustment always was secured when-

l'ver possible by aerial or terrestrial observation, but with accurate mapsl;nd calibrated guns, fire with considerable effect could be deliveretl almost

immediately on the occupation of a new position, without w~iting for ob-

FoE'rvation. The value of this procedure in harassing a retreating enemy or

. In surprising him at any time is very grea,t.

3, It is by no means to bp. und~rstood that topographical methods of

• preparation and conduct of fire have supplanted the more rapid, but less

. accurate, methods given in Drill and Service Regulations for Field Artillery.

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These methods always will be required in rapid operations at various"

atages during the combat. Wheri) no accurate maps are available terrestrial

observation or open warfare methods must be used. However when oP-..~rations are continued for any length of time in the same territory, surveys

..hotild be made and maps prepared for firing purposes. A good artillery

t'ommander should understand the application of all methods, and take the

fullest advantage of every opportunity to improve the effectiveness of his

fire. To this end a thorough knowledge of topography is essential.

4. Topographical information is recorded chiefly in graphical form,

supplemented by written or printed explanations and reports. TopographicaT

records include maps and position charts, roads and area sketches, pano-

ramic sketches, road and reconnaissance reports, visibility and dead spacecharts, and any other. forms of records which may be necessary to furnish

the required information. The essentials of a good topographical record of.

any kind are: .

First, it must contain all possible information of military value for

the purpose which it is designed to serve, considering first the most im- .

porta nt, and omitting irrelevant matters which cause confusion.

Second, it must be accurate to the degree required for its purpose •.

Third, it must be clear and legible, presenting its information in such

form that it can be readily understood and used.In conveying the desired information on maps and sketches, the to-

pographer or cartographer very largely makes use of a system of conven-

tional signs, which, in reality, are graphs of the thing represented. These

conventional signs are much the same in all services. See Chapter XI.

5. An officer need not be an expert surveyor, draftsman, or artist in order

to make use of topography. The methods used are comparatively simple,

and much of the work can be, and commonly is, done by trained enlisted men.

'Vhere extensive surveys are required they are made by the engineers. . In

training for topography, the practical value of the work should be constantlyemphasized, every step' should be illustrated with practical examples, and'

no subject should be left until its ~pplication is thoroughly understood.

Note:-Where the term artillery.is used in this text it is understood'

that field artillery is meant.

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8. The metric Bystem of linear measure is now used by the artillery of, ", ,'..

practically all nations, including the United States. However, our old ma-

teril is graduated in yards, and many of our maps', manuals, tables, and ", :;''.-'',, ',':,,!

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CHAPTER II.

DISTANCE AND DIRECfION

MEASURE~IENT AND SYSTE:\IS OF MEASURE.

<6. The artillery topographer must be thoroughly familiar with the

-different system's of linear and angular measure used in field artillery, and

must be able to make accurate measurements. Detailed methods will be dis-

cussed later.'7. One of the aims of artillery topography is to save the waste re-

..suIting from inaccurate methods. Hence accuracy should be striven for in

811 work, and every effort made to eliminate sources of error. However, it

is useless to carry either measurements or calculations to a greater degree

of refinement than is required for the use for which the results are intended.

For example, it is possible from an accurate map to calculate site to

minute or a fraction of a mi~. If an accurate quadrant is to be used for

laying the gun, one graduated to minutes o!' fractions of mils, such close cal.

culation is desirable. lIo',vever, with ordinary materiel graduated only to

,even mils, it is useless to calculate closer than the nearest mil. Nor in any

case, is it worth while to calculate closer than the least setting of, the range

scale, or ,quadrant of the particular gun being used. Exceptions to this

may arise where several small calculations are to be combined, the total of

the fractions if taken together making an appreciable amount, but it is a

waste of time to carry a calculation to several decimal places which cannot

be used, especially if there is a possible error .in any of the measurements

on which the calculation is based., The result of a calculation is never more

accurate than the least accurate factor which enters into it.

Again, in measuring ranges on a map, a skilled man can measure

with a good scale to the nearest meter, or even to fractions of a meter OD

large scale maps. But if the map itself is inaccurate, due to .faulty printing,

E'hrinkage, etc., such close measurement would be needless. On the other

hand, in performing resections or other surveying operations on a plane

table with an accurate grid, a high degree of accuracy is possible, and every

measurement should be made with'the greatest care in order to make the

total error of the operations as small as possible.

Each operation should be studied to determine what degree of ac-

(uracy is required, always bearing in mind, first, the use for which the re-sult of the operation is intended, and second, the possibilities of the instru-

ment~ with which the operation is performed.

" ..

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other documents to which the artilleryman must refer use the old English

units of measure. Hence it is necessary not only to know the metric system,

but to be able to convert. r2adiIy, one system into another. It is' assumed

.that the old English system already is well known, so it will not be treatedin detail.

A. METRIC SYSTEM.

. Abbreviations

Latin

prefixes

*Milli-

*Centi-

Deci-

=

=

1~1000 or .001

1~100. or ..Ot.

1~10 or . ~1

mm.

em;

dm.

*:Meter = 1, Base Unit. M. (or m.)

Dm.

Hm.

Kin.Mm.

10 times

100 times

1000 times

10000 times=

=

=Greek

prefixes

1

Deka-

Hecto-

*Kilo-

Myria-

*Units in most common use.

NO"e that the abbrevations of the units larger than the meter

are :apitalized, while small letters are used for the smaller units. The #

standard abreviations for meter is a small "m", but in artillery work a cap-

. ital "M" should be used to distinguish it from the sign ."1/:" for mil.

9. Care should be taken to distinguish the Greek prefix "deka", 10

times, from the Latin "ded';, (pronounced "desi"), 1~10. "Deka" is .some-

times spell~d "deca" (but' pronounced "deka"), especially in France, so the

only certain means of distinction is in the "a" and the "i" and in the pro-

nunciation. These prefixes are used m~re frequently in the grade system of

angular mp.asure than in linear measure.

n. COXVEnSIOX BETWEEN EKGLISH AND l\IETIUC SYSTI~l\IS •.

10. Ease Eqult'alellt: 1 meter = 39.37 inches (practically exact) ..

This is' the 'most. important equivalent to remember, as any conver-

sion can be mE-dethrough it (reducing English distances to inches and met-

ric distances to meters) and any other, desired equivalent can be derived

from it.

11. The length of the standard in'ternational meter has been fixed

with great precision, but the authorities differ slightly as to its equivalent

10 English measure. The above value of 39.37 inches is the legal standard

. equivalent for the United States, by act of Congress, July 28, 1866. The

officir.l British Board of Trade equivalent is 39.370113 inches. Other values

have been determined by different scientists, some larger and some smaller

, than 39.37, but the variation between them is very slight. 39.37 is so close to

the average that it may be accepted as a practically exact equivalent •. It

.. differs from the English standard by only .000113 inch, or a ratio of about

1 unit in 350,000. which is negligible except for the most delicate scientific

measurements.

-4-

.

'



,I.,'" I

.

Note: The standard meter is 1/10,000,000 of the quadrant of the,

,-earth measured along a meridian..

12 Following are other useful equivalents derived from the base equi~-

,alent.

Centimeters to inches: 1 em. = 39.37 in.This is practically exact, being simply 1/100 of the base equivalent.

Inches to centimeters: 1 in. 2.5~ em.

i-raetically exact. Derivation: 1 M. 100 em. 39.37 in.

! in.= 100-+3!).37=2.540005 em.,' or 2.54 within a negligible error.

Meters to yards: 1 M. = 1.09~ yds:

• ,Sufficiently accurate for all artillery purposes. Error amounts to about

, +.00039 yd., or a ra'tio of 1 in 2800 M or 3.6 in 10,000, negligible for artil-

.1ery work. If closer results are desired use 1.0936.

Derivation: 1 M.= 39.37 in. 1 yd. 36 in.1M. 39.37 -;- 36 1.093611 or 1.094 yds.

Yards to meters: 1 yd. .91~ M.

Sufficiently accurate for all artillery purposes. Error amounts to about

-.0004 M., or a ratio of 1 in 2500 M or 4 in 10,000, negligible for artillery

work. If closer results are desired, use .914i.

Derivation: 1 yd. 36 -7- 39.37 .9144018 or .914 M..

Meters to feet: 1 M. = 3.28 ft.

Sufficiently accurate for all artillery purposes. Error amounts to about ,

-.00083 ft., or a ratio of 1 in 4,000 M or 2.5 in 10,000, negligible for artil-'lery work. If closer results are desired, use. 3.2808.

Derivation: 1 ft. 12 in. 1 M. 39.37 -7- 12 3.28083 or 3.28 ft.

Feet to meters: 1 ft. = .305 M.Sufficiently accurate for all artillery purposes. Error amounts to about

+ .0002 M., or a ratio of 1 in 5,UOOM or 2 in 10,000, negligible for artillery ~"

work .• If closer results are desired, use .3048.

Derivation: 1 ft. 12 -+ 39.37 .304800 or .305 M.

13. The foregoing abbreviated values are the' same as those published

as standards for general use by the U. S. Bureau of Standards.Mistakes in making conversions can be avoided by checking all re-

sults by inspection, first deciding which factor to use, and then obtaining an

approximate result by a quick mental calculation.

. For example, in converting yards to meters, the result in meters will

be smaller, because it will take fewer meters to reach the same distance (a

meter being longer than a yard). lIenee use the' smaner equivalent, .914, not

1.094. One of the most common mistakes is in taking the wrong equivalent.

From this equivalent it appears that the result in meters should be about

9/10 of (or1/10 less than) the amount in yards. Thus, .1000 yds.X.914

=914 M., which checks with the approximation.

Again, in converting inches to centimeters, the result will be larger,

because it will take more centimeters to reach the same distance. Hence

use the larger equivalent, 2.54, not .3937. From this equivalent it appears

that the result in centimeteJ;'s should be about 2 1/2 times the amount in

inches. Thus, 2 in.X2.54=5.08 em., which checks with the approximation

U. In order to cultivate facility in thinking and estimating distances in

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= = = =

= = '

= = =

= =

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metric units, it is convenient to bear in mind the following approximate'

rela tions. I

1 meter about 40 inches, which is 4 inches, or' ab~ut 1/10

greater than a yard.

Hence distance in meters is about 1/10 les8 than distance in yards,

(since it will take fewer meters to reach the same distance). To get meters

,'. . from yards, 8ubtract 1/10.

Conversely, distance in yards is about 1/10 greater than distance in

meters. To get yards from meters, add 1/10,

.1 centimeter = about 4/10 inch. .

10 centimeters (1 decimeter) about 4 inches.

1 inch = about 2~ centimeters, or 25 millimeters.

1 foot about 30 centimeters, or 3 decimeters ..1 millimeter = about 2/3 of a sixteenth of an inch.

1 kilometer = about 5/8 mile.

The above equivalents are close enough for rough approximations,

such as estimating distances in open warfare, but for all exact topograph-

ical work the standard equivalents should be used.

ANG ULAR l\IEAS URE

15 An angle is measured by the incl~ded arc of a ci-/cle, the center of

which is at the vertex of the angle. It is immaterial how large the circle

is or how long the sides of the angle are, because angular measure is not

a measure of distance or area, but is an expression of the proportion be-

tween the part of the circle included within the angle and the whole circle.

This proportion remains the same for any given angle, whatever the size of

the circle.

16. By dividing the circle into a convenient number of equal parts, a

system' of angular measure is obtained. This is sometimes called circular

measure, as it is used to measure the relative size of arcs of circles as well

'as angles.' The artilleryman is more concerned with angles than with arcs,

so the term angular measure is preferable ..

In all systems, use is made of the

main divisions of the circle and the clas-

sification of angles based thereon. The

circle is divided into four equal parts'

or quadrants, each of which'is included

within a right angle. I

. Two right angles make a straight

angle or scmicircl~. Four right anglesmake a round angle or complete circle.

C Any angle less than a right angle is an

acute angle. An angle greater than a

. right angle and less than a straight

A- RI~HT.ANGLE,QVADRANT angle is an obtuse angle.' An angle

B . .5TRAI(iliT-ANGLE ,sEMICIRCLE. greater than a strai~ht angle and less, , than a' round angle IS a reflex angle.

C. ROVfJD.AfJGL[ CIRCLE. All forms will be met frequently in

Fig. 1 artillery work.

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IREF'LEX ANGLE~

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A~ DEGREE SYSTEM.

I

-~II

IOBTV.5E:.ANCJl(

Fig. 2.

'/

17. There are three standard systems of angular measure in common

use; the degree system, the grade system, and the artillery mil system. The

mil system is used to a greater or less extent by the artillery of practically

all nations, and in time it probably will replace the other systems entirely

for artillery use, on account of its greater convenience. However, it often

will be necessary to make use of surveys, maps, tables, etc., in which the

other units are used, so the artilleryman must be familiar with all systems

and be able to conver~ readily one form to the other.

-7-

18. Called sex~gesimal because subdivided by 60's.

Base unit: Degree 1/360 of a circle.

• 60" (seconds) =1' (minute'>

60/ =1 ,(degree)=3600"

90° =1 quadrant or right angle

180° =1 semicircle

360° =1 circle=21,600'=1,296,OOO".

This is the old standard system used by the navigators, astrono-

mers, and surve:rors of all nations. In France and other Latin. countries it

has been largely replaced by the grade system, although the old unit still

19 used to some extent. The old system is largely used in the British artillery.

19. Modifications of the standard subdivisions are found in the artillery

of difterent nations.' In the French heavy artillery a unit' of 1/20 degree.

(3'), or 1/7200 of a circle, is used for laying certain types of guns for

elevation. On some German heavy guns 1/16 degree, or 1/5760 of a circle,

is used. .

The notation of seconds (,,) is seldom' used in artille~y, fractio~s of

minutes being indicated by decimals where necessary.

Thus:, 12° 13.8/, instead of 12° 13' 48".

/' 20. In calculating with quantities in the degree system, especially in

making conversions, it usually is more convenient to convert the entire'

quantity into degrcc8 and decimals.

13 48Thus: 12° 13/ 48" 12 +- +-- 12 + .217 + .013 = 12.23°.60 3600

, 13.8Or: 12° 13.8/ 12+-- 12.23°.

60

To re-convert to the regular notation:

12.23°=12°+ (.23X60/) =12°13.8'=12°13'+(.8XGO")=12° 13'48".

.

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.

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= = = =

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The advantage of the other systems, using decimal subdivisions, is

obvious.'

B.' GRADE SYSTEM .

.21. Called centesimal because subdivided by 100's.

Base unit: Grade =1/100 of a quadrant or 1/400 of a circle.

(Sometimes spelled, "grad").

100'" ~seconds) P (minute)

100" 1 g. (grade) 10,000' '\

100g , 1 quadrant

200g 1 semicircle

400g 1 circle 40,000r-=4,000,000"')

The signs for centesimal minutes and seconds are inclined back-

ward to distinguish them from the sexagesimal notations.

Any expression in this system may be handled as a decimal simply

by putting a decimal point in place of the, sign "g". Thus: 3g95i' 30r~-=3.958g.

It must be remembered, however, that the subdivisions are by hundredths, ,

not tenths. lIenee if the figure for either minutes or seconds" is less than

10, a cipher must be put in front of it before pointing off. For this reason .

a cipher should always be put in front of a single minute or second digit

even'in the regular notation. Thus: 3g4> j"'=3.0407g, and sh'ould therefore

be written 3g04) 07"). . I

This is the standard system used by French navigators, astronomers,

and surveyors, although they stH make use of the old degree system to

some extent.

22... The following modifications of the standard system are 'used in the

French artillery:

To indicate wind direction:

1 dekagrade (or decagrade) 10 grades (Abbreviation Dg.)

10 dekagrades 1 quadrant.

40 dekagrades 1 circle.For laying certain types of heavy gun.'J:

1 decigrade 1/10 grade=10> (abbreviation dg.)

1000 decigrades 1 circle.

4000 decigrades 1 circle.

Note carefully the distinction between the spelling and abbreviations

of the two units. I •

('

C. MIL SYSTEM. I

Base unit: Mil=1/6,400 of a circle. Abbreviation "1/L".

1,600'/1=1 quadrant.

3,2001IL=1 semicircle.

6,400'/1=1 circle.

There are no subdivisions of the mil. Fractions or decimals are used j'

where required.

24. The size of the mil unit was determined by taking the angle which

subtends an arc 1/1,000 of the radius. The angle whose arc is equal to the

radius is called a radian. A true mil is therefore 1/1,000 of a r~dian. In

a complete circle there are 2 .". =6.28318, radians. There are, therefore

:l3.

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= = = = = = =

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= 0'0

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, 6,283.18 true mils'in a circle. This is an odd number which cannot be sub-

divided conveniently. The nearest number which can conveniently be sub-

divided is 6,400, and 1/6,400 of a circle was therefore adopted as the

artillery mil.. Its value is so close to that of the true mil that in ordinary

calculation the difference may be disregarded, and it may be assumed that t

the artillery mil subtends .001 of the radius or distance. However, if an

instrument graduated in artillery mils is to be used for stadia measurments

or, other fine work, the exact value of the arc subtended by the artillery' mil

., should be taker. as the basis fbr computing tables or other calculations. This

value is: .

•

I

.628318--'-X.00l=.0009817 of the radius.

6400

25. The Rimailho mil 8ystem takes 1/6,000 of a circle as the workingmil, called the R-mil. Its value is not so close to that of the true mil as

. 1/6,400, and it is little used.

26. The advantage <}f the mil system over others for artillery

work is that angles in mils, within certain limits, can be calculated directly

from linear distances. For small angles, up to 330 mils, the arc 5ubtended

by the angle is practically equal to its tangent, making it possible to use the

tangent, a straight line, in connection with the radius, as a measure of the.

a'ngle, instead of the arc. The great majority of angles requiring such cal-

culation in artillery work are less than 330 mils. For an explanation of the'

reasons for this limit, see par. 37, under Expression of Angles by Tangents.

27. To illustrate the mil graphically, in fig. 3 let OA=l,OOO of any linear

unit, say meters, and arc AB=l meter. Then angle AOB=l mil. Tangent

r ~~-""I~

. I

1: l=~-,;~'~,[TER51

,.METER'"_J._t_

'0 0Fig. 3

AU', perpendicular to 0.1, is practically equal to the arc, and may also be

taken as one meter long. If another mil is added, making the angle AOC, 2

mils, then arc AC or tangent AC' is 2 meters, and 50 on within the defined

limit. If the sides of the angles are extended to 2,000 meters, at D, then arc

DE or tangent DE' of the 1 mil angle is 2 meters, DF or DF' of the 2 mil

W{l60)

L(800)Fig. 4

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angle is 4 meters, and so on, the arc or tangent always having a length of',

1/1,000 of the radius for every mil of the angle.

28., . The mil relation may be expressed in three ways, with which every

artilleryman must be familiar. In fig. 4, let 1/£be any angle in mils within

the limit of 330 mils, L any radius or length, and W any tangent or width,

perpendicular to L. Then:

W 1,000 W

(1) 1ft -l/-I-,O-O-O-L-.sometimes writte,n --L--)

For example, let W=160 meters and L 800 meters.

160 160.

Then1f t

200 mils.(l,l,000)X800 ..8.

. 1hXL.(2) lV 1/£Xl/1,000 L (sometimes wr'Ltten ---)

1,000

This is the most common form, being used constantly in calculating deflection

offsets, deflection differences, site, etc. The other'two forms may be derived

readily from it by transposing the terms. This equation. may be used for

finding the linear width of a target when the angular width can be

measurri or estimated, and for similar purposes. For example, using the

above figures, lV=200X (1/1,000) X800=200X.8=160 meters. •

W. 1,000 W

(3) 1/1,100 L (sometimes written L ---)1/£ 11£

Used pricipally in calculating ranges to targets or other objects of known

linear width whose angular width can be measured, etc.

. . 160For example, 1/1,000 L= =.8, and 1,,=800.

200Some artillerymen prefer the froms given in parenthesis, but most

find.it simpler to use the forms first given, always thinking of L in units of

1,000. Thus, 800 meters=.8,as above; 4,600=4.6, etc.

This method of calculating angles and distances may be' called the

tangent' method, since it is based on the tangent ratio. See par. 32, under

Expression of Angles by Tangents.

29. The same method may be applied;' though less conveniently, to the

Fig. 5

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=

=

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-- =

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= -- =

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degree, grade, or any 'other' angular unit, by taking, instead of '1,000, the ..

length of radius at which the unit considered' subtends a tangent of 1. For

the degree this length is 57.3. Applying this in the same way as 1,000 was

applied for the mil, we have the following relations for the. degree, fig. 5.

(1) Deg. = _'V__ (or 57.3 'V )1/57.3 L L

-11-

D. CONVERSIONS IN ANGULAR MEASURE.

Deg.XL

(2) \V = Deg.X1/57.3 L (or ---)57.3

\V 57.3 'V(3) . 1/57.3 L = -- (or L = ---)

De~ De~

L is thus considered to be divided into unit lengths of 57.3 instead of

1,000. In calculating with grades, use 63.66, the length of the radius at which

1 grade 8ubtends a tangent of 1. To find this length for any angular

\lnit, take the reciprocal of the tangent of that unit.<.,'.'

,

I

, .t.' '.

(

r,".;.'

;

.,.

" ,'l:,.

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..• ••

Tan 17/' .001. 1000..001

Tan 1° .0174551.'

rhus:

1___ 57.2899 or 57.3.

.0174551

1Tan. Ig = .0157093 = 63.6567 or 63.66.

. .0157093

The limits for these forms of calculation are about 14 degrees or 15~ grades.

These limits are somewhat less than the artillery mil limit of 330 mils. For

an explanation of this; see par. 38-39 under Expression of Angles by Tan-

gents. The inconvenience of these forms of calculation as compared with .

mil calculations, using even thousands, is obvious. They are useful, however,

for calculating slopes in degrees or grades directly from distances and alti-'

tUdes, although it is 'practically as convenient to calculate the angle in mils.

and' convert to degrees or grades by means of the equivalents.

Base Equ~valents:

30. 1 Circle=3600=400g=61,007/1.

1 Quadrant=90o=100g=1600l/l.

. Any desired equivalent can be derived from the above, if the sub-

divisions are known,' Following are the special equivalents which will be

found most useful:

Degrees to mils: r=17.7S,/,.Close enough for all artillery purposes.

Derivation: 1°=6400+360=17.777 .•. or 17.781/'.

Mlj[s to degrees: .1,/. .05625° exactly.

Derivation: 17/1=360+6400=.05625.

Minutes to mils 1'=:=.296'/1.

Close enough for all artillery purposes.

. -.• II

.

~

"

.

" \

,.

"

' = -- = = 0 =

---

=



Derivation: 900=5400'=1600,!t, 1'=1600+5400=,296296 .•. or .29611:.

Mils to minutes: 1*=3.375' exactly, or roughly 9 1/9 '.

Derivation: 1,/:=5400+1600=3.375'.

Frequently used in calculating site in minutes. For all ordinary work

it is close enough to calculate in mils and multiply by 3 1/3.

Grades to degree or degrees to grades: 19=.9° exactly.

Derivation: Ig=90+100=.9°. To convert grades to degrees multiply ..

by .9; degrees to grades, divide Ly .9. This is easier and more accurate than

using 1°=1.111. ..... g.

Grades to mils or mils to grades: 19=161/: exactly.

Derivation: 100g=1600, Ig=1600+100=161/z.

To convert grades to mils, multiply by 16; mils to grades, divide by

16. This is easier than using 11/1=.0625g, which, however, is also an exact

equivalent.

The above' equivalents will meet practically all the needs of artillery

work.' Others may be derived in a similar way for special purposes if de-

sired. All angular conversions should be tested by mental approximations

the same as described for linear conversions, par. 13.

31. The following true mil equivalents are given for purposes of com-

parison and for exact conversions from the tangent form' of mil calculation

to other units, the limitations of which are shown in par. 40 and the table,

in par. 42. Such conversions wiU seldom be .necessary in general artillery

work, but occasionally may be required for exact computations.

64001 true mil 1.0186 or 1.02 artillery mils.

6283.186283.18

1 artillery mil .98174 or .98 true mils.6400

360 0'

1 true mil .057296 or .0573 3.438 •6283.18

6283.181 17.4530 or 17.45 true mils.

360

E. EXPRESSIO~ OF ANGLES BY TANGENTS.

32. . ,For some purposes, such as ground slopes, slopes of fall, etc., it is

more convenient to express an angle by its tangent than by angular measure

because the tangent of any angle can be calculated directly from linear dis-

tances, linear distances which depend on the angle can be calculated directly

from the tangent, and the angle can be plotted Rnd drawn quickly and ac-

curately from its tangent.

C

160 METER~

.\ ~OO METER~. B.Fig. 6

. -12-

"

~

= ---- = = ---- =

= --- = = "

° = ---- =

'



"o illustrate the tangent graphically, fig. 6, construct a right tri- .

angle ABC, .of which angle A is the angle of which the tangent is desired.'

The sides of the angle, A B and A C, form the base and the hypothenuse of

the triangle, which is completed by dropping the perpendicular Be from the

hypothenuse to the base at any point. The size of the triangle is immaterialsince the ratios of the sides will remain the same for any given angle. Then

ta~gent A.;IJC, or, in general, consid~ring the two Sid~Sof the ~riangle which

ABform the right angle, the tangent is the ratio of the opposite side o'ver the

adjacent side, or the vertical side over the base. Expressed in linear units,

t he tangent gives the length of the vertical for a l1ase of 1. •

33.' The most common application of the tangent is in calculating'slopes

from a map, where the vertical distance, BC, can be obtained form the con-

tours, and the horizontal distance, AB, measured with a scale. For example

let nC=160 meters and AB=800. meters. Then the tangent of the slope AC"

'\ 160or of the angle A, is =.2, see fig. 6..

800

34 There are three forms of the tangent relation, the same as the mil

relation:

EC Vertical(1) Tan A = --, or Tangent = ---

AB BaseThis form is uscd in calculating the tangent, as illustrated above.

(2) nC=AEX Tan A or Vertical Base X Tangent.

For example, using the above figures, BC=800X.2=160 meters~

BC Vertical(9) , AB = --- or Base = ----

Tan A Tanaent

For example, AB160

, .2800 meters.

C

~ eM.

A IOCM. BFig. 7

3:3. To plot the above angle by its tangent layoff a base' AB of any con-

venient length, say 10 centimcters, fig. 7. At one end, B, erect a vertical,

.Be, the length of which is' cqual to the base multiplied by the tangent,

10X.2=2 ('cntimeters. Draw the hypothenuse AC. The angle A between base "',

and hypothcnuse is then the desired angle which was expressed by' the

tungent. •

2. It must be equal to the original angle from which the tanget was ob-

-13-

•

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;

---

'

=

=--=

'

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" ':



',I I'

tained because the tangent ratio of the sides of the plotted triangle, ...:., has10

been made the same as the ratio of the corresponding sides of the original160

triangle, , making the triangles similar and the corresponding angles

800,

equal. An angle of any size can be' expressed by its tangent and plotted in

this way without the use of the 'protractor.

36. The similarity between the calculation of the tangent and the cal-

culation of mils, degrees, or grades, as described in par. 29, is apparent. The

160

tangent in the illustration, fig. 6, was =.2. The calculated angle in800

'I' 160 'I X h ) . 160ml s IS =200 ml s (1,000, t e tangent ; In degrees,(1/1,OOO)X800 (1/57.3) X800

=11.460 (57.3 X the tangent); in grades, 160 -12.73g (63.66X the. (l/63.66)X800

tangent). The calculation in each case is based on the tangent ratio, simply

introducing the proper factor to convert the tangent ratio into angular units.

37. A Comparison. The reason why the calculation of the angular valuebased on the tangent ratio is limited to small angles, while the tanget it-

self may be used for any angle, is that the angular value is to be used in.

an entirely different way from the tangent value. The angular value ob-

tained .from the calculation is to be used like any other angular measure,

with instruments graduated in a circle, while the tangent value is' to be

used, either in calculation or plotting, as a' ratio between straight lines, in

the same way as it was originally calculated. Angular measure is repre-

sented by the arc of a circle. The tangent is represented by a straight line

tangent to' the arc. The tangent form of calculations can be used forangular measure only within the limits where the tangent is practically

equal to the arc. This is true only for: small angles. As the angle increases

the tangent becomes longer than the arc and cannot be used to represent

angular measure.

38 . To illustrate graphically the relation between the tangent v~lue and

the actual angular value of an angle, construct a right triangle ABF', fig. 8,'

with base AB=l,OOO and vertical BF'=330, divided into smaller triangles as

shown. Then, since the base is 1,000, arc BF and its divisions give the actual

angular measure, and tangent BF' and its divisions the tangent value, in true

mils, of the corresponding angles at A. In angle BAC' the arc Be and tan-

gent Be' are practically equal, both having a length of 10, so the angularj

measure is practically the same as the tangent value, 10 mils. Of course in

reality the tangent is slightly longer than the arc, but the difference for

such a small angle is negligible. In angle BAD' the tangent BD' has gained

perceptibly over the arc BD, but the difference is still slight, only .3 true:

mil. But when angle BAE' is reached, with a tangent value of 250 mils, the

tangent BE' is 5 mils ahead of the arc BE. This, therefore, must be taken'

as the limit for' using the tangent calculation of tru~ mils, or the similar

-14-

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TRVE MILS.,Fig.'S

calculation of degrees, grades; etc., as described in par. 29. In the angle

RAF' the tangent exceeds the arc by 11.3 mils, entirely too great an error .'

for artillery work. Thus it is seen that the tangent calculation gives prac-

tically exact values for small angles, but that as the angle increases the

gain of the tangent over the arc causes an error in the tangent calculation

as compared with the actual angular value which is positive and which in-

(TeaSeS progressively from the start.

:~9. The relation between tangent and angle with the artillery mil, how-

ever, is not the same as with the true mil. The relation shown in the fore-going 'illustration is true only where the angular measure is taken in, the

saltte unit as that on which the tangent calculation is based. In fig. 8 the

tangent calculation was based on a length of 1,000, the exact length at which

a true mil subtends a width of 1, and the arc, representing the ac-,

tual angular value, was measured in true mils. Similar results would' be

obtained if the tangent values had been calculated in degrees on a length

of 57.3, or grades on a l~ngth of 63.66, and the angular values measured in

true degrees or grades. However, if the angle or arc be measured in a dif-

ferent unit from that on which the calculation is based, it is evident that the

relation between arc and tangent will be changed. By taking a unit slightly

smaller than the one on which the tangent calculation is based, ,the error

in that calculation may be offset to a considerable extent for practical

purposes. This is just what is done in using the artillery mil. To illustrate,

construct a triangle BAli', fig. 9, of exactly the same dimensions 'as triangle

AllF' in fig. 8. Measure the arcs, however, with artillery mils ins'tead of

true mils.

40. Since the artillery mill is smaller than the true mil, it will take more

of them to measure a given angle. Hence for the small angles where theangular value in true mils was practically the same as the tangent, 'the

artillery mil value will be greater than the tangent value, and the tangent

ralculation will therefore have' a' negative error at the start, instead of a

positive error as with the true mil. For small angles this negative error is

practically negligible. For angle ABC', with a tangent value of 10 mils the

actual angular value in arWJery mils is 10.2,making an error of -.2 mil in

the tangent calculation. This error increases in the negative direction,

-15-

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£imply because the quantities are increasing" and the increase in the tangent'

f over the arc has not yet commenced to make itself felt, up to angle BAF',

''fhich has a tangent vafue of 145 mils and an actual angular value of 146.8

artillery mils, 'making an error of -1.8. At this point the tangent begins

to gain, and at 237 mils, angle BAG', it overtakes and exactly neutralizes

the negative error, the tangent value and angular value' in' artillery mils

being exactly equal at this point. From here on the error is positive and

increasing, the same as' with the true mil, though to a lesser degree. For

angle BAIl', with a tangent value of 330, the actual angular value in artil- .

lery mils is 324.7, making a positive error of 5.3 mils. 330 mils, therefore"

has been taken as the limit for fairly accurate artillery mil'calculations.(F.

A. Drill Regulations, Par. 1044).

41. . If the angle be measured in a larger unit than that 'on which the tan- ,

gent calculation is based, the effect, of course, will be opposite to that pro- ,

duced with a smaller unit, and there will be an exaggerated positive error

, in, the tangent calculation at the start, increasing rapidly with the. angle.This is the case with the R-mi1 making' it very inaccurate for calculating-

£Ingles abo,Ve 100 mils by the tangent method.

42. It may be laid down as a general rule that for all practical artillery

purposes the most convenient reethod of using, the tangent form of calcula-

tion is always to calculate in artillery mils, and then convert to degrees or

grades by the proper angular equivalents if desired. This saves confusion'

and is close enough for all ordinary uses. For exact results with angles less

than 5°, or 5~g (such as slopes, most of which are small angles), it may be

desirable to calculate in true mils, degrees, or grades on the exact basis, con-

verting to artillery mil,S if necessary. However, it ,is seldom that either the

llccuracy of the measurments of the requirements of the case will justify

such refinements in artillery work.

43. The following table shows the relation between the tangent calcula-

tion and the actual angular value for the degree, true mil, artillery mil, and

R-mil. Values for grades 'may be found by converting either degrees or true

mils by the proper equivalents, as the basis of angular measure and tangent

calculation is the same f')r all three units. .

-16-

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TABLE

Showing accuracy of tangent calculation of angular values.

II Tan. I!Tanllent calc:u-llI lallon of Angle

-II-II 01 I MilSll 01

Actual Angular Value II

\ ~7i: I ~:~~:ii. II

Error in Tangent Calc:nlatioa

1 I True I Art. 1 R.Mila Mila Mill

. I

, .1) Limit for practically exact calculation in true mils, degrees, or

grades.

(2) Limit for fairly accurate calculation in R-mils.

(3) Limit for fairly accurate calculation in true mils, degrQes, or

grades.

(4) Limit for fairly accurate calculation in artiller~' mils.

44. If angular values above the limits for tangents calculation are de-

. sired, or if absolutely exact values are desired for any angle, the tangent

should be calculated and the corresponding angular value found in a tangent

table. ,I '. 45. To Add or Subtract Tangents. In practice, it is frequently necessary'

,to add or subtract angles which are being handl~d by their tangents, as in

applying the angle of site in the proper sense to the angle of fall in order

to obtain the quandrant angle of fall. This can be done by tangents onlywhen the sum of the two angles does not exceed the limits for the tangent

{'alculation of angular values. Strictly speaking, the sum (or difference) of

the tangents of two angles is not the same as the tangent of the sum (or

difference) of the actual values, but within the limits prescribed, the results

are close enough for artillery work. To illustrate the error with angles

beyond the limits, suppose the tangent of the angle of fall has been found

in the range table to be .500, and the tangent of the angle of site has been

calculated from the map to be ~.100. Putting the two together to make the .

quadrant angle of fall, a tangent of .600 is obtained. Now, the actual anglecorresponding to a tangent of .100 is 101.5 artillery mils and the actual angle .

corresponding to a tangent of .500 is 472.3 artillery mils, making the sum

or actual quandrant angle of fall 573.81/1. The tangent of this angle, obtained

from a tangent table, is .631, showing an error of .031 in the result obtained

by adding the two tangents. lienee a tangent table must be used if the

quantities exceed the prescribed limits.

-17-

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46. Certain modifications of the tangent are used in expressing ground

~lopes. The most common are the gradient and the per cent.

Fig. 10.

G. PER CENT.

P. Vertical distance

48. er cent = --------, expressed in the form of per cent;. Horizontal distance

that is, the vertical distance or rise in a horizontal distance, of 100., Thus,

. h 'II ,', Be 160 20u~mg t e same I us~ratlOn as WIth the gradIent; = -- = .20 = --

An 800 100or 20'7c. To obtain the per cent from the tangent or gradient, multiply by

I 100 and affL'{ the per cent sign, which thus becomes simply a substitute for

two decimal places. Thus, .2 or 1/5XIOO=20%. To obtain the tangent

from the per cent, divide by 100~ or point 'off two decimal places. To obtain

the gradient, divide by 100 and reduce to a fraction with numerator 1, thus

20 1

100 549. To plot an angle from the per cent, layoff a base of 100 and a

yertical of the amo~nt in per cent, in any convenient unit., . . . . 'C

ZO

A 100. BFig. 11 .

-18-

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For example, Fig. 11: layoff base AB 100 millimeters and vertical

Be 20 millimeters. Join AC. Thi3 gives the same angle as plotted by the

gradient or tangent.

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100

c

Fig. 12A

50. A common error in expressing slopes

in per cent is to call a vertical drop (that is, a

right angle, or ~OO) a 100% slope, whereas a

450 or 8001/~ slope is really a 100% slope. To

illustrate, fig. 12, layoff a base AB of 100

and n vertical BC of 100, in any unit. Join AC,

100Then, the per cent of angle A is = 100%.

100

that this angle

Its tangent, of

It is evident from inspection

i8 half n right angle or 45°.

. 100 ..course, IS =1, whIch IS the tabular tan-100 •

gent for 45°. The gradient is ~. Above this1

ang-Ie the values increase until at ~OO either the tangent, gradient, or per

cent is infinity.

Fig. 12 gives a good illustration of the fallacy of attempting to cal-

culate angular values from the tangent relation above the limits laid down

100

in I'ar. 40. Calculating in mils, angleA would be ----------1,0001/1.1/1,000 X 100

100Calculating in dcgrees, =57.3°. Since the actual angular_

1/57.3 X 100value is 8001l~ or 45°, the tanget calculation has an ('fror of 2001/~ or 12.3°.

£)1. It is not customary to use the gradient from of expression above 450,

sincc this would make a fraction with a denominator less than 1. For ex-

ample, the angle of 76° has a tangent of about 4, or 400~,. This would

k. 1 1 .. .

ma c a gradient of or -. For angles above 45° It IS customary to

1/4 .25use the straight tangent, giving the rise for horizontal of 1. Among

('ngin<>ers this is commonly stated, "1 to 4." giving the horizontal figure

first instead of the vertical. Thus "Ion or in 4" means a gradient, givin~

the wrtical figure first, while "1 to 4" is merely a form of stating the tan-

~cnt, giving first the horizontal figure, which, for the tangent, is always 1.

H. CONVERSIONS IN TANGEXT EXPRESSIONS AND ANGULAR

MEASURE.

FJ2. It is often desirable, such as when a tangent or gradient is given

without the angular measure, to convert a tangent expression directly to

ang-ulnr measure b;r means of a factor or equivalent without stopping to

plot and calculate the angle. This may be done within the limits laid down

for calculation of angles by the tangent method, and with the same degree

of accurac~', (par. 40 and table, par. 43), as the result of the conyersion is

exactly the same as the calculation.

-19-

I

,

--

--

------

--

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-20-

Ta~gent or gradient to' mils: multiply by 1,000.'

Tangent or gradient to degrees: multiply by 57.3.

Tangent or gradient to grades: multiply by 63.66.

For example, Tangent .2X1,000=2001/1.

. Tangent .2X57.3=11.46°=1l °27.6'.Tangent .2X63.66=12.732~=12~73.' '20,~~"

. In each case the factor or equivalent "is the distance at which the

angular unit considered subtends a tangent of 1; that is, the factor' is the .

reciprocal of the tangent, the same as the factor used in calculating angles

from the tangent ratio, par. 39.

Per cent to mils: multiply by 10 (1%=101/t).

Per cent to degrees: multiply by .573 (1%=.573°).

Per cent to grades: multiply by .6366 (1%=.6366g).

The factors for per cent are simply 1=100 of those for the tangent

or gradient since per cent is 100 times tangent or gradient.

It is also often desired to find the tangent of a given angle for calcu-

lation or plotting. This may be done without a tangent table by means of

the following factors or equivalents, within the prescribed limits.

. .Mils to tangent:' multiply by .001 (the tangent of 1 mil) or point

off three places. For example, 2001/tX.001=.2, tangent.

Mils to gradient: set up a fraction with the given number of mils in

,the numerator and 1,000 in the denominator. Divide through by the num-erator to reduce numerator to 1. This is the same as multiplying by .001

and then converting the result in~o gradient form.

.. 200 1. 2 1For example, 200,/t= , gradient. Or 200,/tX.001=-=.2=- -.

. 1,000 5 10 5

Degrees to tangent: multiply by .0175 (the tangent of 1°).

For example, 2°X.0175=.035, tangent.

DegrOf:s to gradient: set up a fraction with the given number of

degrees in the numerator and 57.3 in the denominator. Divide through bythe numerator to reduce the numerator to 1. This is the same as multiplying

by .0175 and then converting the result into gradient form.

2 1 35 1For example, 2°= , gradient. Or 2°X.0175=.035=-- --.

57,3 28,6 . l,OOO 28.6

Grades to tangent: multiply by .0157 (the tangent of Ig).

Grades to gradient: same as with degrees, except that 63.66 is used,

instead of 57.3.

Mils to per cent: multiply by 1/10, or point off 1 place (11/1=.1%)._

Degrees to per cent: multiply by 1.75 (1°=1.75%).

Grades to per cent: multiply by 1.57 (111=1.57%).

These factors are simply 100 times those for converting to the tan-

gent, sin'ce the per cent is.100 times the tangent.I

53. For angles above the prescribed limits for calculation, a tangent

table must be used for all these operations. If a table is available it should

be u~ed for all angles, as it is more accurate and more convenient than cal- 'culating.

- -- = - =

__ = __ =



MEASUIU~G I!\STRUME~TS

A. SCALES.

U4. All measuring instruments used for exact topographical work should

be the best available, I?ade by reliable manufacturers. No instrument, even

a government standard issue, should be used without being tested.

Scales, rules, or alidade~ may be of wood, metal, celluloid, or. other

durable composition. P~per scales (except graphical scales drawn on maps)

are not' satisfactory,' as they ar~ subject to expansion and contraction from'

moisture. .

55. ,,1 metric measuring scale for artillery work should be 25 or 30 centi.

meters long, and should have two edges, one graduated to millimeters, the

other to half-millimeters. If the scale has only one edge it should be grad-

uated to half-millimeters. An English scale should be a foot long, graduated

on one edge to tenths, on the other to fiftieths of an inch. If it has only one

edge it should show both tenths and fiftieths. An ordinary engineer's (not

, urthitcct's) scale has these graduations. A triangular Bcale is a good form,

since it can be used as an alidade, but it i3 harder to straighten when warped

than a flat scale, and it is seldom that more than two edges will be used

for measuring. A flat scale with folding sights makes a better all-around

instrument and is easier to carrr.

SQ. Bvery measuring Bcale not' known to be standard should be tested

by ('omparing it with a known standard. 'Vooden or metal scales made by

reliable manufacturers may usually be accepted as accurate. All other

scales should be tested by comparison with a good wooden or metal scale.-

~7. Tapes or chains for g~ound measuring should be either all metal or

fabric with wires woven in lengthwise (usually called metallic tapes). Every'

woven tape, and every all-metal tape or chain not known to be standard,

should be compared with some known standard. Any errors discovered

,should be corrected by marks on the tape or by making allowances in measur.

ing. In long measurements where great accuracy is required it is necessary

to allow for stretching, sagging, and expansion or contraction due to heat.

Artillerymen, however, will seldom be concerned with these corrections, as

extensive'surveying usually will be done by engineers. Instructions for mak-

ing 81.1chmeasurements, if desired, may be found in any good engineer's or ,

surveyor's manual.

lJ8. ,Every edge which is to be used for drawing straight lines or for

sightin'g should be tested by sighting along it or by laying it along' an already

tested straight edge or plane surface (as a piece of plate glass or mirror

which gives true reflections). An edge may also be tested by drawing a

line along it with a sharp pencil, then reversing the edge along the other

sille of the Emmeline. If straight it will coincide with all parts of the line.

'A scale may be slightly crooked and still be good for measuring, though it

cannot be used for drawing straight lines. 'Vooden scales are likely to be-

come warped and metal celluloid scales to become bent, so they should be

, handled carefully and tested occasionally even after passing the first test •.

50. The line of sight of an alidade, whether defined by sight or by a

,. f

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,

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straight edge should be tested to see whether is is parallel with the draw-

ing edge. This may be done as follows. Lay the alidade on a piece of paper

fixed on a plane or other flat surface, and sight on some sharp, well-defined

point at least 2,000 meters distant. Draw a fine line with a sharp pencil

along the drawing edge. Examine the line after' it is drawn to see that it

follows the edge exactly, and verify the sighting on the distant point. Re-

verse the alidade, placing the drawing edge carefully along the other side

of the same line. Then, if the line of sight is parallel with the drawing

edge it will again strike the point first sighted on. The process should be

repeated two or three times to make sure of the test. Comparative errors in

angles between lines drawn in any particular operation may be avoided

by placing the alidade so that the line of sight and the drawing edge are

always in the same relative positions, but errors in. orientation; that is, the

relation of lines on the map to corresponding lines on the ground, cannot be

so avoided. Hence if the alidade is inaccurate and cannot be adjusted it

should be discarded for sighting purposes.

B. PROTRACTORS.

60. An acC'urate protractor i; harder to get than an accurate scale. A ;

transpuent celluloid or composition protractor is the most useful type for.

artillery work, though metal protractors are usually more accurate. A pro-

tractor should be as large as can conveniently be used, with a radius of at

least 10 centimeters. A mil protractor should,be graduated to a least reading

of 10 mils, or 5 mils with a large protractor, and a degree protractor to

half, third, or quarter degree, (30', 20', or 15'), depending on the size of

the protractor,' Closer readings are made by eye, if necessary, Circulal'

protractors are sometimes used, but the semicircular type with a linear

measuring scale on the straight edge is better for general use, The sub-

divisions should be numbered clockwise. In a semicircular protractor there

should be an outer row of figur('~, from 0 to 3200~/£ or 1800, for use in the

first semicircle, and an inner row, from 3200,/1 to 6400,/1, or 1800 to 3600 for .

use in the second semicircle, with the protractor reversed.

61. To test a protractor, draw two lines with a tested straight edge in-

tersection at about their centers at right angles, each line slightly longer

than the diameter of the protractor. The lines should be very careful!y

drawn and all the right angles tested with the standard right angle form or

with a scale or compass, Then lay the protractor over the lines so that the

center of the protractor is exactly over the interse<=tion of the lines and the 0and 32001/1 or 1800 marks are on one of the lines. The 1600~/1 or 900 mark

should be on the other line (also the 4800'/1 or 2700 mark with a circular

protractor), If the marks on the protractor do not fall exactly over the

proper lines, it ir.dicates either that the center hole of the protractor is not

at the true center, which is the most common error, or that the grad-

uations are inaccurate. A slight inaccuracy in the position of the center hole.

may be corrected by enlarging the hole so as to make its center coincide

with the true center, If the error is greater than the diameter of the hole,

a new hole should be drilled at the true center, made very small at

~22-

'



first, then tested, and enlarged as desired. A needle broken off at its largest

part, ground flat, then pointed, and fitted with a sealing wax or wooden

handle, makes a good drill. If the new hole runs into the old, the old one

fhould be filled with a hard waterproof cement, such as china cement. If the

, protractor has lines running to the center, these- should be changed, ifI.ecessary, so as to intersect exactly at the true center. Before a point is

l'ccepted as the true center, it should be tested by the middle points and

C)uarter points of the quadrants, the same as above described for the main

quadrant points. Having completed the test, using one of the intersecting

lines as the origin, turn the paper by a full quadrant and repeat the test,

using the other line as the origin, so that any possible inaccuracy in the

drawing of the lines may be detected. The results should be the same using

either line.

G2. While testing the center it may be discovered that some of the grad-

uations are irregular. In that case the center should be located so as to give

correct readings for the greatest possible number of points, especially the

quadrant point and the principal subdivisions. Having established the center,

the accuracy of. the graduations should' be tested as follows. Center the

protractor over the intersection of the two test lines, with 0 on one of

the lines and note whether the other main quadrant points coincide exacf;hr

with the other lines. Then shift the protractor by one of the main suI-

divisions, such as 100'fl or 100, keeping it centered carefully, and note

wht:'ther the corresponding points in all four quadrants coincide with theirproper lines. Continue until the main subdivisions have been tested in this

way. This is usually a sufficient test, as it is unlikely that correspondin~

points in two different quadrants will both have an error in the same direc-

tion. . Another check is' to measure the main subdivisions. along

the edge with a good scale to see whether they are uniform. This, however,

is not an absolute test, because the edge of a protractor may be irregular

and still measure angles accurately, and such a test could not be used with a

rectangular protractor.

C. EMERGENCY DEVICES.

G3. Other Device8. Every artilleryman should know the length of his

shoe, his exact height, and the exact distance between some well defined

lines or marks on his hands, for use -in improvising measuring devices in

rase he should be without a scale. Marks usually can be found on the palm .

or inside the fingers which will give an even number of centimeters or inches.

The measurement should be made with the hand held perfectly :flat without

straining. When needed for use the measurement may be taken from the

hand by marks on the edge of a stick ~r piece of paper. Such measurements,

of courRe, arc not exact, but a fair degree of accuracy can be attained. It is

convenient also to know the span of the fingers, but this is a very rough

method of measuring on account of the difficulty in stretching the fingers

uniformly at different times. The hand and fingers .should of course, be

calibrated for measuring angles in mils, as described in Artillery Drill

Hegu lations.

-23-

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CHAPTER III.

lUAPS AND SCALES.

TIlE ELEl\lENTS OF A l\IAP.

A. DEFINITION.

64. A map is a representation (usually on a flat surface), of the surface

of the earth, or some portion of it, sho'wing the relative size and position,'

according to some given scale or projection, of the parts represented (Web-

ster's New International Dictionary).

B. CLASSES OF MAPS.. ,

65. The map is the most important record of topographical information,

Military Maps may be divided into two general classes, a('('.~Tding to their

ll~es: first, strategical and tactical maps, including staff maps, road and

area sketches, and all other kinds of maps and sketches prepared in advance

or made through reconnaissance for use in the disposition and maneuvering'

of troops; second, technical maps, including artillery battle maps, firing

~harts, plane table sketches, etc., used in the preparation and conduct of artil-

lery fire. Every military map should represent the features of the region.

which it covers with the degree of completeness and accuracy required for its.

use, omitting unimportant details.

C. MAP MAKING AND MAP READING.

66. A thorough knowledge of maps is an essential part of the training

of every artillery officer, and, to some extent, of non-commissioned officers

and other especially trained soldiers. Applied knowledge of maps falls into

... t~o parts, map making and map reading.

(1) Map Making.,

67. For artillerymen there are two phases of map making: first, map;

. . making of an elementary sort, including the making of road, position, and

area sketches, to be used in the conduct of marches and the selection and

occupation of camp sites and artillery position's generally; (all officers, non-

commissioned officers, scouts, and other soldiers employed in reconnaissance-

must be able to make sketches of this kind); second, map making for pur-

poses of exact location and orientation, to be used in the location of gun

positions and targets and in the preparation and conduct of ~ire. All of-'_

ficers concerned with the preparation and conduct of fire must be skilled in .

this kind of map making to the extent required by their particular duties,

and every artillery officer should have at least a general understanding of

the method~ used. Certain non-commissioned 'officers and other soldiers

emplo~'ed in the preparation and observation of fire, such as instrument

sergeants and instrument operators, ~lso should be trained in this work.-'

(2) Map Heading.

(8. Map reading also may be divided into parts, corresponding to the two

general classes of maps: first, strategical and tactical map reading; second,

technical map reading. Eyery artillerman must be able to read intelli-

~.ently all maps which he may be called on to use. A knowledge of map

. making is a yaluable aid to map reading, and at least an elementary' train-

-2.1-



ing in map making is desirable for every Olie who is required to. use maps,

t;ven though he seldom may be called on to make them.

D. GROUND RELATIONS.

(:9. The foundation of every map is a representation of the ground. Other

features of military importance are then added as required. Every pointen the ground has three relations with reference to every other point: dis-'

tance, direction, and altitude. (The term elevation is sometimes used instead

of altitude, but in artillery this should be confined to gun elevation to avoid

confusion.)

(1) Distance.

70. The distance between points as represented on a map is the horizon-

tal distance'.

...•

I

(2) Direction.

71. The direction of one point from another is the horizontal angle be-

tween an established line of known direction and a line joining the two

J:oints.

(3) Altitude.

72. The altitude of a point is its distance vertically above an establi!hed

J<.nownhorizontal plane. Altitude may also be express'ed as the vertical angle

between a horizontal plane and a line poining the two points. Between a

gun and its target this is called the site.

73. By means of these three relations the exact position of every point

{In the ground and the relation of all points to each other, both horizontally

llnu vertically, can be shown on a map. Ground forms are shown by the

altitulles of critical point.:;, supplemented by graphical devices such as contours

or hachures, see pars. 136, 137, Ch. V.' Commercial maps usually show only

the horizontal relations, distance and direction, but for most military pur- ,

po~es it is necessary to show also altitudes and ground forms.

(4) ~Iap Essentials.

74. The essentials of a military map may be summoned up as follows:

1. It must show distances according to a given scale.2. It must show directions with reference to some established line

,of known direction, such as true north, magnetic north, or grid north, or

sometimes, on small local sketches, simply a line between two known points,

1:10 that the direction between points can be determined from the map, and

~o that the map can be oriented with respect to the ground, see par. 179, 179,

Ch. VII.

3. It must show altitudes and ground forms to the extent re-

quired for its use, giving altitudes above an established horizontal datum

plane, usually sea level.. J)JSTAXCES AXn SCALES.

A. DEFINITIONS.

75. Distances are represented on maps by scales, usually conforming to'

a regular system in which the scale is varied to suit the purpose of the

. map.

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B. SCALES.

76. . Any map scale may be expressed in three ways, anyone of which}

may be derived from the others:

(1.) As A I~epresentath.e I.'raction, Abbreviated n~F.77. This is the simple ratio between a given map distance and its hori.

zontal equivalent, expressed in the form of a fraction, whisc numerator is

1one. For example, R. F.,--- , means that. M. D.: II. E. : : 1 : 20,000.

20,000

That is, one unit on the map represents a II. E. of 20,000 of the same units

'. on the ground, and thus every :M. D. is 1/20,000 of the corresponding II. E.

This is no~ a unit of measure, but is an absolute ratio, which can be applied .

to any unit, provided both members of the ratio be expressed in the sameunits. Thus, if the :M. D. between two points measured 1 em., the II. E. be';

tween them on the ground would be 20,000 em. If it measured 2 inches, the r

II. E. would be 40,000 inches. Or if the II. E. measured 20,000 feet, it would

take an 1\1. D. of 1 foot to represent it on the map.

(2.) In 'Vord8 And Figures.

78.. This is a simple statement of the map dist~nce corresponding to

some convenient unit horizontal equivalent, giving the M. D. in small units

used for measuring on the map, and the II. E. in large units used on the".ground. For example,. 3 inches eqllals 1 mile. This means that 3 inches on

the map represents a horizontal equivalent of 1 mile on the ground. To

derive a words and figures scale from the representative fraction, express

the R. F. in some definite unit of measure, and then, convert to other units

. 1 , . .as desired. Thus, if the R. F. is , 1 em., M. D. equals 20,000 em. or

20,000

200 meters II. E., and 5 em. equals 1,000 meters or 1 kilometer. To con.

vert an expressio'n in words and figures into a representative fraction, set

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\'P a fraction with the given 1\1. D. in the numerator and the corresponding

n. E. in the denominator, converted into the same units as the M. D. Divide

hoth members by the numerator to reduce the fraction to a numerator of

1. The result is the R. F. Taking the first example above, 1 mil=63,360

. h . 3 1InC es, hence the R. F. IS = --- .63,360 21,120

(3.) By A Graphical Scale.

70. This is simply a rule or a line drawn on the map itself with divi-

sions marked showing the horizontal equivalents corresponding to the map

distances between the divisions of the scale. The length of any desired

graphical scale may be determined either from the R. F. or the words and

figures scale, as will be shown. The main divisions of the scale should be

large, for measuring the even portion of long distances, with an extra divi-sion to the left of the 0 subdivided for measuring the odd portion of any

distance down to the last reading of the scale, fig. 13.

MIL(-'

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Mf:Tf:R'500 0 500 1000 1500 ZOCO zsoo

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Fig. 13.

80. In measuring between two points, the scale is placed so that the left

hand point is opposite the center of the subdivided portion to the left of the

n, and is then shifted, if necessary, to bring the nearest even mark on the

r.lain scale to the right-hand point. To illustrate, using the meter scale in

fig. 13, place the scale first with the middle or 250 meter point of the sub-

divided part opposite A, then shift to bring the even 1,000 meter point to n,r1aking the distance 1,150 meters.

81. A graphical scale may be made on a separate straight-edge or on the

map itself. Every map should have a graphical scale. The advantage of this

is that if the map expands or contracts accordiingto the moisture in the air,

or if it is enlarged or reduced photographically, the scale goes with it. To

use the scale, take it off on the edge of a piece of'paper or a ruler and apply

to the map, or mark the map distance on the edge of the paper and place it

against the scale. The latter is a convenient method in measuring crooked

(1.'stances, as roads.

82. Where a map bears a graphical Bcale, but the R. F. is unknown, the

n. F. may be determined as follows: Measure the 1\1. D. length of the graphi-

(al srale, or any convenient eVE'nportion of it. Set up a fraction with the

measured 1\1. D. in the numerator and the corresponding II. E. from the

scale in the denominator, converted into the same units as the 1\L D. Divide

looth members by the numerator to reduce to a numerator of 1. The result is

the R. F.

For example, suppose that a photographica1- reduction of a map has

a graphical scale for 5,000 meters which was reduced with the map, with a

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legend showing that the R. F. of the original may was _1 • The scale

20,000

measures 12.5 em. long, 5,000 meters=500,000 em. Then the new i.1. F.

12.5 1 .. .___ = --- , showmg that the map was reduced one-haIr in linear

500,000 . 40,000

dimensions.

E3. When a map bears no scale of any kind, its scale may be determined

by a comparison of measurements between known points on map and ground.

With any convenient scale measure the 1\1:. D. between two points on the

map. Measure the distance between the corresponding points on the ground

reducing it to the II. E. if it is not so actually (see par. 78). This gives at

once a "words and fig'Ures" scale, which can be converted into any units de.

sired. The R. F. can now be found from this as described under, "words and

~gures scale", in par. 78. The points selected shoulJ be such that the hori ••

70ntal distance between them can be measured, and should be as far apart

as conveniently can be reached. The process should be repeated with other

points in different directions, if possible, in order to verify the scale.

For example, suppose the distance between points A and n measureS \

17 mm. on the map, and the horizontal distance between the corresponding'

points on the ground measures 340 meters. Then, the words and figureS

~cale of the map is 17 mm.=340 meters, or 1 mm.=20 meters. 20 meters:::::. 1

20,000 mm. so the R. F. IS ---.

20,000

:\I.\P SCALS PROBLEl\lS. jA. CLASSES OF PROBLEMS.

84. Map scale problems fall into two classes: map to ground (M. D. to

H. E.), and ground to map (II. E. to M. D.). An example of the first class

is in determining- the II. E. for a 1\1. D. measured on the map with an

ordinary scale. A n example of the second class is in determining the M. D.to layoff on a map or sketch for a certain II. Eo measured on the ground,

or in determining the length of a graphical scale to read a certain number'

of units of H. E. In either case the calculation is a simple one of converting'

distances by meanse of the R. F. or the words and figures scale. .l:

B. SIMPLE RULE;S FOR MAP SCALE CALCULATIONS.

(1.) Map To Ground.

85. (a) By the R. P. (1) Multiply M. D. in map measure units by the

denominator of the R. F. The product is the II. E. in the same units. (2)

Convert this II. E. into any desired ground measure units.Example: On a sta~dard American map, the scale of which is 3

inches=1 mile, R. F. , the M. D. from point A to point [J

.21,120 .measures 5.08 centimeters. What is the II. Eo from A to n. in yards? .

Solution: (1) 5.08X21,1~0=107,28!>.G em., II. E.

(2) 107,28!>.Gcm.+2.5.1=42,240 in.

42,240+36=1,173.3 yards, ans .

•or: 107,28!>.Gcm.=1072.8!>G meters.

1072.8!>6Xl.0!)36=1,173.3 yards, ans.

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8G. (b) fly the 1Vordg and figures scale. (1) Find number of ground

measure (II. E.) units represented by 1 map measure unit. (2) Multiply this

by the M. D.

Example: same as under par. 85.

Solution: (1) 3 inches=l mile=1760 ~'ards.

3 inche£=3X2.54=7.62 em.Therefore 1 em.= 1760+7 .6~=230.97 yards.

(2) 5.08 cm.=5.08X230.97=1173.3 )Tards, ans.

Or the II. E. represented by 1 map measure unit may be found from

the R. F.:1 em. on map=21,120 em. on ground.

21,120 em.=211.2 meters.

211.2X1.0936=230.97 )'ards

Therefore 1 em. 1\1. D.=230.97 yards II. E.

This method of finding the II. E. value of 1 map measure unit is

Rimply to express the R. F. in the given map measure units, and convert the,

lI<"nominator into the desired grcund measure units.

Complete the solution as above.

The above example might be worked through in inches instead of

«('ntimeters hy converting the M. D. into inches at the start:

(1) 5.08 cm.+2.54=2 inches, M. D.

3 inches=1 mile=17GO yards.

Therefore 1 inch=1760+3=586.67 yards.

(2) 2 inches=2X586.67=1173.3 }'ards, ans.

Or, obtaining the value in II. E. of 1 map measure unit from the R.}'.

1. inch on map=21,120 inches on ground.

21,120~-36=586.G7 }Tards.

Therefore 1 inch M. D.=586.G7 yards II. E.

Complete the solution as above.

(2.) Ground To 1\lap.

87. Grouucl to map, or II. E. to ~I. D. problems, are simply the reverse

of map to ground, or 1\1. D. to II. E. problems.~8. (u) fly the R. F. (1) Convert the given II. E. into map measure

units. (2) Divide by the denominator of the R. F. The result is the desired

:\1. 1>.

Example: The II. E. from point A to point B on the ground is 1,000

meters. How many inches M. D. must be laid of! to represent this distance

(.n a standard American map, the scale of which is 6 inches= I mile, R. F.

1---?, Or, as a graphical scale problem, what will be the length in inches

10,GGO .

cf a graphical scale of 1,000 meters for this map? .Solution: (1) 1,000 metersX39.3i=39,370 inches.

(2) 39,370+10,560=3.7 inches, ans.

89. (b) By the 'Words and ligures scale. (1) Find number of ground

m<.>asure (II. E.) units represented by 1 map measure unit, the same as in

map to ground problems. (2) Divide this into the II. E. in the same ground

measure units.



Example: Same as under par. 100.

Solution: (1) 6 inches=l mile=1760 yards

1 inch=1760--;-6=293.3 )'ards.

293.3 yardsX.9144=268.2 meters.

Or from the R. F.: 1 inch on map=10,560 inches on.

ground.

10,5GOinches--;-39.37=268.2 meters.

Therefore 1 inch M. D.=268.2 meters II. E.

(2) 1,000--;-268.2=3.7 inches, ans.

90. From the above illustrations, it is evident that any map scale

probl~m can be solved either by means of the U. F. or the "words and

figures" scale. For most purposes the R. F. is simpler, as it uses the.

absolute ratio between map and II. E., and be applied directly to any units of

measure. However, in reading maps with an ordinary measuring scale, the .

, words and figures scale is useful to get the II. E. value of the measured M.

D.'s. The measuring scale becomes a sort of graphical scale when the II. E.

value of one of its units has been determined, though this may not be in a

convenient even amount. Thus, with American maps, as in the above ex-

amples, an inch always equals an odd number of yards II. E. The metric

system, with the corresponding maps having representative fractions in

even thousands, has a great advantag-e over the English system in this. 1

respect. For example, .on a map the R. F. of which is ---, 1 em. M. D.20,000

=20,000 em. II. E.=200 meters II. E. The centimeter scale then becomes

practically a graphical scale, on which each centimeter represents 200

meters, each millimeter 20 meters, and each half-millimeter 10 meters. \Vith

such maps any metric scale may be used as a reading scale, and most

problems can be solved mentally.

91. A convenient rule to remember when using the metric system on any

maps is that 1 millimeter of 1\1. D. equals a II. E. in meters 1/1,000 of the

denominator of the R. F. (because 1 millimeter equals 1/1,000 of a meter).

1 1Thus, on a --- map, 1 millimeter=20 meters; on a --- map, 1

20,000 21,120

1millimeter=21.12 meters; on a --- map, 1 millimeter=80 meters; on a

80,000

__ 1_ map, 1 millimeter=40 mders; etc ..

40,000

C. SCALE CONVERSIONS.

92. The 1\1. D. length of a graphical scale reading in certain units, as

yards, being given, it is sometimes desirable to be able to determine the

length for a similar scale reading in other units, as meters, directly from

the first scale, without calculating through the R. F. or the words and

figures scale. This is the case when the map has a graphical scale but the

R. F. is unknown, as when a map is enlarged or reduced photographically.

Proceed as follows:

93. On the given graphical scale measure with any convenient measuring

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OG.

culated

figures

.

scale, the M. D. length of a convenient number, say 1,000, of the ground

measure units in which the scale reads. Multiply this M. D. by the ratio

between the length of one of the ground measure units of the desired scale .

and the length of one of the ground measure units of the given scale: The

result is the M. D. length of the desired scale, reading the same number

of new units, that is, 1,000, as was taken of the old. The new scale may

then be laid off on the map or made up as a separate scale.

For example, a map is found with a 1,000 yard graphical scale

which measures 3.4 inches. How many inches should be laid off for a 1,000

meter scale for the same map? Any :M.• D. is proportional to the II. E. which

it represents. lIenee the M. D. for a 1,000 meter scale )s to the :M. D. for a

1,000 yard scale as 1,000 meters is 'to 1,000 yards, or as 1 meter is to 1 yard,

or as 1.0036 is to 1 (par. 12). Therefore the :M. D. for the t,OOO meter

Rcale will be l.On6X3.4 in.=3.7 in. (This is the same as was obtained by the

complete calculation'in the example under par. 89.04. The distinction between the conversion of map ~cales a~d the con-

"ersion of ordinary linear' distances from one unit to another should be

noted. In converting map scales, the M. D. representing a given number of

one ground unit is multiplied by the inverse ratio between the units to find

the M. D. corresponding to the'same number of the second ground unit. In

ordinary conversions of linear di~tances the given distance in one unit is mul-

t;plied by the direct ratio between the units to find how many of the second

unit it will take to cover the Bame distance. Thus, distance in yards is to

<1istance in meters as 1 ~'ard is to 1 meter, or as .9144 is to 1, and 1,000 }'ardsX.0144=914.4 meters, using the direct ratio. In the first case the distance

corresponding to a fixed number of units is sought, and the inverse ratio of .

yards to meters or 1.0936 is used; in the second case the number of units

in a fixed distance. In either case mistakes in using the wrong ratio or

equivalent may be avoided by thinking whether the results should be larger

or smaller than the given figure, and gross errors in calculation may be

avoided by making a quick mental approximation of the result.

D. TYPES OF GRAPHICAL SCALES .

. 95. Graphical scales may be divided into two classes, working scales for

map making and reading scales for map reading. Some scales may be used

for both. Stride scales or mounted timing scales are workiing scales. They

cannot be used conveniently as reading scales because they are not graduated

in any standard unit of ground measure. To read a distance with them it

would be necessary to convert e\'ery measurement into standard units by the

prope'r equivalent. A mile scale is purely a reading scale. It cannot be used

conveniently as a working scale because it is impracticable to measure

distances on the ground in miles. A yard or meter scale is both a'l'eading

and a working scale, because it reads in standard units with which measure-

ments can be made on the ground.

(t.) Construction Of Reading Scalt~8.

If no graphical scale is available, horizontal equivalents may be cal-

from map distances, and conversely, from the R. F. or words and

scale. However, if any considerable amount of measuring is to be

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done on the map, a graphical scale should be constructed, determining its

lc'ngth from the R. F. or words and figures scale, as described in par. 97, and

subdivided it as desired. Every topographer should be able to make any kind

of a graphical scale. .

97. For example, to construct a scale to read yards on a 6-inch American

map, the R. F. of which is 1_., Assuming that the scale at hand for

10,560lYleasuring is in inches, first find the M. D. in inches which must be laid off

to represent some convenient even length, as 1,000 yards. Applying the rules

in par. 100:

(1) 1,000 yards=36,000 inches.

(2) 36,000+10,560=3.4 inches M. D. for 1,000 yards.

The next problem is to divide this distance into 10 equal' parts, eacho[ which will represent 100 yarrls. Each 100 yard division will then be .34

inch. If a scale graduated to 50ths of an inch is available, it may be used

17to make the desired subdivision, since .34= inch. This is the most con-

50venient method, and is also the most accurate if the scale is used carefully,

but if such a scale is not available, the subdivisions may be made as follows:

, see fig. 14; ,

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Fig. 14.

Draw line AB the length determined for 1,000 yards, 3.4 inches. At

a convenient angle with AB, preferably not over 450 layoff AC, the nearest

lEngth to AB which can be divi'dcd into 10 equal parts by some even gradua-

tion of a scale say 3 inches~ The length of AC should be so chosen and the

angle BAC so adjusted to make BC about perpendicular to AC if possible

though this is not absolutely necessary. Join BC. Divide AC into 10 equal

parts with the scale by marking every .3 inch. From each of these marks

draw a line parallel to BC intersecting AB, which is thus divided into 10

equal parts by the intersection.:!. The parallel lines may be drawn with a

l'ight triangle and straight-edge, &s shown by the dotted lines. Lay the

triangle with one perpendicular edge' along BC. Then lay the straight-edge

against the other perpendicular edge, holding it firmly as the triangle is

moved aiong in drawing the lines. If no right triangle is available, draw the

parallel lines as follows. Layoff ED exactly equal and parallel to BC (by

the ordinal:y compass method or by measuring two equal ,distances straight

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across), and divide it into ten equal parts, the same as AC. Join the corree

sponding points on A C and BD. The lines so drawn will be parallel.

98. The greatest care must be used in making the measurements and

drawing the lines in order to secure accurate results. One of the divisions

8hould be marked off on the edge of a piece of paper and placed against theothers in turn. Any irregularities should then be adjusted. rr:he dividing

lmes may then be erased and the scale completed as shown, or the, whole

srale may be taken off on a straight-edge or map. To transfer the scale

to a map, prick through the graduations with a needle or' fold the paper

along the scale, place it against the desired line on the map, and take off

the graduations with a sharp pencil. A scale of any desired length may be

made simply by shifting the' divided line along and taking off the marks.

!>9. In making a graphical scale, it is, of course, immaterial what units

the measuring scale is graduated in. A topographer should be able to makeuse of whatever kind of a scale he may happen to have. For example, to

make the above scale with a cer.timeter scale.

1,000 yards=914.4 metel's=91,440 em.

91,440710,5GO=8.6 em.

Or the M. D. could haye been worked out hi inches, as was done,

above, and converted to centimeters for measuring:

3.4.inchesX2.54=8.6 em.

The line would then be laid off with the centimeter scale and divided

fiS above directed. The completed scale would, of course, be exactly the sameleng~h as the one made with the inch scale.

,(2.) "'orkin~ Scale!!.

100. (a) Strule Scales. The most common form of working scale is the ,

f:tride scale.' Every artiller~'man who is likely to be engaged in reconnaise

sance or topographical work" should have a stride scale made for the R. F.

most frequently used. lie should also know the length of his stride so that'

if he is without a scale, he can improvise one if necessary. Using the Ameri- : I :.~

can map system, the most useful R. F. for a scale is 1/21,120 or 3 inches •

to the mile, which is the scale used for road sketches. Using'the French map.~ystem, the most useful R. F. for a scale is 1/20,000, or 5 centimeters to :.:. I

the kilometer, whiC'h is used for road sketches and artillery firing charts. .' '.'

101. To make a stride scale, proceed as follows: ,'.

First: Determine the It:!ngth of the normal stride. To do this, pace Jover a measured course of from 400 to 800 }'ards or meters on ievel ground,:':!

preferably compact turf or dirt road, not a hard road or pavement. The .

('ourse should make a circuit or. double hack on itself so as to offset the effect . <....i'

of any wind which may be blowing. Conditions should be as nearly normal

as possible. It is not well to attempt to determine the normal stride when

, very tired or in a high wind or when the ground is sticky or slippery. Take

a natural stride. It is inadvisa1'le to try to change the natural stride to step

l""cn meters or yards. This can be done for short distanc~s, but not for long

<Hstances. The topographer should not keep steI? with 'or pay' attention' to

anyone else who may be going over the course. Cover the course two

or, threo times on different da~'s. if possible, and take the average. Convert

the length of the couse into whatever units of measure are to' be used for'

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r-.

laying off the scale (inches or rentimeters), and divide this by the average

number of strides taken to cover the course. The result is the length of one

average stride. It is close enough to determine the stride to the nearest inch

'Or the nearest even centimeter, as this will be well within the probable error'Of striding and measuring with the scale.

102. Having determined the normal stride on level ground and made up

the scale accordingly, allowances can be made in using the scale for slopes,

for rough, sandy, or muddy ground, for wind, for the physical condition of

the person, etc. Ability to make these allowances 'comes with experience.

The table in Ch. VIII gives the average allowances to be made for slopes.

However, anyone with much sketching to do should take advantage of every

opportunity to determine his own aIIowances under. different conditions, pac-

ing measured courses both up and down hill, with and against the wind, pac-

ingthe regular course when tired, etc., marking on his scale the allowances

thus determined. After the length of the scale has once been determined, it

should be tested occasionally to see whether it has changed especially on mov-

ing to a different climate, terrain, or altitude.

103. Second: Multiply the length of one normal stride by the total num-

ber of strides desired for the scale, as 500 or 1000. This gives the length of the

scale nn the ground in the units in which the stride was determined, (inches or

centimeters). Multiply this by the desired R. F. The result is the length of

the scale, which may be laid <lff and subdivided as directed in par. 97.

Mark on the scale the name of the maker, the length of stride, and the R. F.

104. For example, to make a stride scale of 1,000 strides with an R. F. of

J/20,000:

Suppose a 500 meter course has been covered three times, in 255,

25!), and 262 strides, respectively, making an average of 258.7 or 25!) strides .

..Assume that the scale is to be laid off with a centimeter rule. Then th~ length

of the stride will be determined in centimeters. Length of the whole course iS

j500X100=50,000 em. Length of one stride is 50,000+259=193 em. Take the

-r,earesteven number, 194 em. The scale is to cover 1000 strides. 1000X194

=194,000 em., length of 1,000 ~trides on the ground. 1/20,000X194,000=

9.7 em., length of scale. Layoff the scale and mark it: Lt. John Smith. Stride

:94 em. R. F. 1/20,000.

105. It is immaterial what unit of measures are used in determining the

length of the scale, whether yards or meters, inches or centimeters, because

the absolute length of the stride is the same, no matter what units it is

measured in, and the length of the scale is determined from the length ofthe stride by "the R. F. In the above problem, if an inch scale it to be used

for laying off the stride scale, convert the length of the course, 500 meters,

into inches instead of centimeters and find the length of 1 stride in inches.

The length of the scale will then be determined in inches. Or work the

problem through i~ centimeters and convert the final result, 9.7 em., into

inches. A course measured in yards might be used instead of a meter course.

In any case the absolute l;ngth of the stride and of the stride scale would

be the same. It should be impressed on men learning the subject that the

'scale when completed is a working scale of strides only, having no relation

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to the system of measure by which it was determined. It cannot be used as

a general reading scale except by converting the strides into some standard

units of measure, nor can it be used as a working scale by anyone having a

different length of stride.

106. (b) Mounted lVorking Scales. For mounted sketching, a timing scale

is most convenient. A stride scale can be made for a horse the same as for

I.l person, and is somewhat more accurate than a timing scale. How-

ever, a timing scale is easier to use, and gives as close results as are usually

required for mounted sketching. ,

1(17. , To make a mounted timing Bcale proceed as follows: ,

First: Find the average distance covered in 1 minute by the horse at

the desired gait under normal c:onditions. To obtain good results, the horse

must have a uniform gait. An ordinary trot is the best gaid for generalwork. Take the horse over a measured course, say 2,000 meters or 2,000

yards, noting the time carefully. Cover' the course two or three times on

<.Jifferent days if possible, and take the average time. Divide this into the

length of the course, giving the average distance per minute~

The course should be the same kind of ground as will, ordinarily be

('overed in actual work, usually a dirt road. The horse should be warmed up

but not tired, and other conditions should be as nearly normal as possible.

Tests' under other conditions should be made later and allowances determined,the same as described for stride scales (par. 102). It is especially imporfant

to determine the difference between traveling light and with packed saddle.

'The scale should be made on th'e time taken with the load usually carried.

.and allowances made when carrying other loads. Separate scales may be

l:lad<,:lfor the different gaits, or the ratios between the gaits may be de-

termined, and the trotting scale used for all gaits, multiplying by the proper

l'atio. For example, the walk is usually about half as fast as the trot, 50

when walking, take half as much distance on the scale as when trotting.

108. Second: Convert the aVE:rage distance per minute into the units ofmeasure (inches or centimeters) which are to be used to layoff the scale.

Multiply this by the desired R. F. The result is the length of the scale for

1 minute. Layoff enough of these to make a scale of convenient length,

say 5 or 10 minutes, with an extra division at the left subdivided to halves,

quarters, and twelfths (5 second intervals). Mark on the scale the name or

number of the horse, the name of the rider, the load carried, the gait, the

!'lIte of speed per minute, and the R. F.

For example to make a trotting scale, carrying packed saddle, R. F.

1/20,000. Say the horse covers 2,000 meters trotting in an average time,

taken from three trials, of 10 min. 15 sec .. or 10.25, min. The average dis-

tance per minute is 2,000+10.25=195 meters. Suppose the scale is to be

measured in centimeters. 195 M.=19,500 em. 1/20,OOOX19,500=.975 em.

length of scale for 1 minute. Take ten minutes, or 9.75 em. for the full

length of the gcale. Lay this off, divide it into ten equal parts, and layoff

.an extra division at the left 8ubdivided into twelfths as above directed. Mark

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the scale: Horse, Bob, No. 278. Lt. John Smith, rider. Packed saddle. Trot

195 :M. per min. R. F. 1/20,000.

109. Using standard American map scales, an ordinary inch scale divided.

into eigths of an inch can be used as a trotting time scale for the average

horse. The average horse trots a mile in 8 minutes. Then if the scale of

the map is 1 inch to the mile, 1/8 inch will represent 1 minute. For other

nap scales take as many as eights of an inch per minuts 'as there are inches

per mile in the scale. Thus, for a sketch on a scale of 3 inches to the mile,

take 3/8 inch per minute. For a walking scale, take. sixteenths of an inch,

as the average horse walks a mile in 16 minutes.

110. . (c) , Interchange of Graphical Scales. Any graphical scale, reading,

or working, made with a given R. F., can be used with any other R. F.'by correcting the readings by the ratio between the original R. F. of the

scale and' the desired R. F. This' can be done very conveniently where the

R. F .'s run in even proportions, as in the American and French standard

'gystem.

For example, to use a 1/20,000 stride scale for a 1/2,000 sketch, as

will frequently be required: The' ratio of the original R. F. to the desired

R. F. is 1:10. Hence consider &11the figures on the scale as if multiplied

by 1/10. Thus, if a distance is covered in 80 strides, it will 'take 800 stride.

divisions on the scale to l'epresent the 80 strides on the sketch.The procedure is similar with reading scales. For example, to use a

1 . I

readmg scale on a 1/21,120 map. The ratio o~ the original R. F. of

10,560

, the scale to the R. F. of the map is 2:1. lienee consider all figures on the

scale as if doubled. Thus, if the scale shows 100 yards between two points,

the distance on the map will be 200 yards.

111. (d) n'orking Scale Gra1)hs. 'Vhere a number of men are to make

working scales of the same kind, the labor of calculating the length of each8cale seperately can be saved by preparing a graph. This can be done for

. any. kind of scale, mounted or dismounted.

112. For example, to make a graph for a set of stride scales of 1,000

strides, with an R. F. of 1/20,000, fig. 15. '

First: Determine the length of the longest scale and the shortest

scale \vhich will probably' be required. .

Say the longest stride is 200 cm. Then the length of the longest

scale will be: 200XI000X1/20,000=10 cm.

Say the shortest stride, is 140 cm. Then the length of the sh~rtestscale will be: 140XI000Xl/20,000=7 cm.

113. Second: Calculate the number of different scales, according to the

l.:nits of measure used, between the longest and the shortest. If the strides

are measured in centimeters, take the scales every other centimeter; that is,

on the even numbers. If measured in inches, take the scales every inch.

This will be close enough, well within the probable errors of measurement,

dc. In this example, the difference between the longest and the shortest

scales is 200--140=60 em., making 30 double-centimeters or even numbered

divisions, see Fig. 15.

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Fig 15.

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116. Fifth: Divide AB and CD each into 10 equal parts, as described in

IJar. 97, each part representing 100 strides. Draw AE equal to 1/10 All

(100 strides) in prolongation of llA. Likewise draw CF equal to 1/10 CD,-

in prolongation of DC. Divide AE and CF each into 10 equal parts, each part '1l'epresenting 10 strides. Draw lines across from EE to FD, joining EF and

BD, and the corresponding dividing points between.

117. Sixth: Through the corresponding division points which were

marked on AC and },IN, draw lines parallel to EB and FD and running from

line EF to line ED. These lines then represent the lengths of the different

scales betw'een EB and FD. Thu~; FD being the scale for a 140 em. stride, the

next line above is the scale for a 142 em. stride, and so on. Number these'

scale lines at the left with the corresponding lengths of stride in centimeters.

118. The portion of each scale line intercepted between AC and BD repre. '.'

sents 1000 strides, divided into 10 equal parts of 100 strides each. The por.

tion of each scale line intercepted between AC and EF represents 100 strides.

divided into 10 equal parts of 10 strides each. These extra subdivided por- .

tions at the left are for making close measurements, as described in par. 79.

To make a stride scale from the graph, apply the edge of the paper or rule

to the line on the graph corresponding to the previously determined length

of stride, and take off the marks with a sharp pencil. If desired the entire

scale may be graduated down to 10 strides by shifting each 100 stride section

in turn opposite the subdivided portion of the graph at the left, taking of!the marks. However, it is very difficult to get all the divisions uniform over

a long scale, especially for men unaccustomed to drawing. It is better to

make the scale in form shown, subdividing one section very carefully, and.

then using the scale in measuring as described in par. 80.

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CHAPTER IV.

l\1EASUHE:\IEJ\T OF SLOPES A~n ELEVATIOJ\S.DISCUSSIOX.

119. Nearly all operations b)" artillery involve a consideration of ground

forms, slopes and elevations, hence, it is important that the artillery officer

1e familiar with all methods and devices or instruments used in the deter-

mination of slopes and elevations, (lither from the map or from the terrain.

A. INSTRUMENTS USED.

120. Slopes or gradients may be determined by means of the transit, thellImmg circle, the battery commander's telescope, the prismatic compass,

levels, clinometers, alidades, the sito-goniometer, and the slope board.

In most instances the aiming circle or battery commander's telescope

will be available. To measure a slope with the aiming circle or D. C. tele-

H~'OlW, 1('n1 the instrument, look through the e~"epiere and sight; upcn the point

the l'levation of whi('h is desired; level the bubble of the reading device

(commonly call(.<J angle of site device) and read the angle.

This is the angle of slope, in mils, from which the angle in degrees,

grlldj('nts, etc., and the actual elevation may be computed.In measuring slopes with any instrument that is not on an actual

levl'1 with the ground, a sight should be taken on an object the height of

-.vhich is approximately that of the instrument being USf?d. On long slopes

the error is negligible but on short slopes a marked error will occur if the

(,bove rule is not followeJ.

For description and discussion of operation of the other instruments

l'numcrated above, see Chapter VI.

n. UNITS IN WHICH SLOPES ARE EXPRESSED.

121. The amount of a given slope JlIa~' be expressed in several different

.ways, each of 1t'hich i8 definitely related to the other. See Chapter II.

(1.) I>e~rl'(,S"And )linutes.

122. The maximum slope of any hill can be only perpendicular or 90°

(plus or ~linus); therefore any measurement made of a slope will read from

o~ to 900•

Fra(.tions of a degree may be expressed decimally as, 5.330, 3.50

, or,

l8Ch dl'gree being divided into GO minutes, fractions of a degree may be ex-

prl'ssed in minutes, as follows; 5° 20', 3° 30'.

(2.) )li1s.

123. Slopes may be given in mils, from 0 to 1600, a perpendicular line

making an angle of 1GOO mils with the horizon.

(3.) Percenta~('s.

124. Slopes may be expressed by the percent of rise in a given distance

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Qn the ground, i. e. the number of feet rise for each 100 ft. of horizontal

distance.

To find the percent of slope; divide the rise by the horizontal dis-

tance. For example, assume a rise of 5 feet in a horizontal distance of 100

feet. Dividing 5 by 100, the quotient is .05 or a 5% slope.

(4.) Gradients.

125. A slope may be indicated by the relation between the rise and the

horizontal distance such as a rise of 5 feet in 100 feet. This expressed as 5

on 100 or 5/100, or 1 on 20, the numerator usually being taken as unity.

~uch an expression is spoken of as the gradient of the slope.

(5.) Tangents.

126. The relation between the side opposite to the side adjacent to an an-gle of a right angled triangle, is the tangent relation of that angle.

Given the horizontal distance and' the degree of slope, look in the

table of tangents for the tangent of that slope and multiply it by the hori-

zontal distance. The result will be the height of the perpendicular of the

right triangle.

For Complete Conversion Tables see Appt'ndix III.

127. Typical Problern: Assume that with a slope board, or other slope

mea~uring device, the slope of a given hill has been determined to be 4°. It

il': desired -to change this into mils, percent, gradient, or. tangent values.

Refering to Appendix III the following values are found; (For a discussion

of values see Chapter II).

1°=17.78 mils or 1.75% and 1%= a gradient of 1/100 hence the

equations:

4X17.78=71.12 or 4°=71.12 mils.

4X 1.75= 7.00 or 4°=7%.

l%=gradient 1/100 then 7%=7Xl/IOO or a gradient of 7/100=1

on 14.28 or 4°=gradient of 1 on 14.28. From the tables, 4°=a tangent of

.06993.

Assume now that the point to which the slope has been read was

the top of a cliff, to the base of. which, it is possible to measure or pace .

off the horizontal distance. The height of the cliff is desired. .

Assumed horizontal distance=400 (60 inch) strides, GO in.=5 feet.

Then 400 strides=400X5 or 2,000 feet.

From Appendix III the tangent of 4°=.OG003. (The horizontal dis-

tance times the tangent gives the altitude of a right triangle). Therefore

2000XO.06993=130.86 or the height of the cliff in feet.

C. SLOPE SCALES.

128. A slope scale is a scale by which the slope between the contours may

be refld or which can be used in map making for locating the relative posi-

tions or distances between contours.

For American or other maps where the V. I. is directly proportional

to the scale of the map, a slope scale may be constructed that is applicable

to all such maps irrespective of the scale; i. e. if .65 in. is the M. D. between

contours for a 1° slope on a map, the scale of which is 3 inches to the mile, .

.



with u V. I. of 20 feet; it follows naturally that .65 in. is the 1\1. D. for a

10 slope on u map, the scale of which is 6 inches to the mile, with a V. I. of

10 feet, etc.

(1.) Construction Of Slope Scale.

12!). (a.) For American maps. To ascertain the M. D. between contours

\\ hen the degn\e of slope is known, the following formula applies:

. R. F.XV. I. (in feet)XG881\1. n. hctwcen contours:..:-:;-------------

Number of de(!'rees of sloDe(il-'H ht.ing- the numlwr of inches horizontal distance necessary to give a rise

of 1 foot on a 10 uC'gree slope.

l'roo! : .

10 slope=l ft. rise in 57.3 feet (or G88 inches) horizontal distance.

For G in. map 10

slope=10 ft. rise (the vertical distance between con-tours) 'in 573. ft. horizontal di5tance. But 6 in.=l mi1c. Then G in.=52~0

ft.~ alHI 573 ft.=G73/il280 of G in.=.G;, inch=:\1. D. betw('en countours for 10

fo;lope.

Similarly it may he. ~hown that the 1'1. n. for a 1 0 ~Iope with the

1 in., 3 in. and the 12 in. maps i~ .65 in.

For small ang-les it is npproximately true that the amount of rise

('ompan'<1 to the horizontal distance keeps pace with the degree of the ang-le.

Thus if a horizontal distance of 573 feet is required to g-ivc a rise of 10

f(.(.t on a 10

slopt', a similar rise would be f('cur('d in half that distance on a2° 'slope.

Or if .Gr>in. is the map distance between contours on the American

maps of 10 slope, thcn the map distance between contours will be half .65

m, or .325 in., for a 2° slope.

Solutions for various degrees of slope for American maps give the

following:

.(if) inch M. D. (between contours) for 10 slope,

.:~~;, inch M. n. for 2~ slope,

.22 inch 1\1. D. for 3° 810pc,

.1G inch M. D. for 4° slopc,

.13 inch 1\1. D. for 5° slope.

Draw a line subdivided into the abo\'e units (use a ruler dividcd into

d<>cimal parts of an inch, if possiblc, for accuracy). This scule pasted on a

trillng-ulnr ruler or aliJade can be used in contouring and will prove of yalue,

('spt\('ially in road sketches.

130. ([).) For metric maps. To construct a deg-ree slope scale for the

1/20,000 map with a [) metcr contour interval proceed as follows:

For a 10 ~lope a rise of 1 meter is equivalent to a horizontal dis-tnnee or 57.3 meters. A rise of [) meters (the distance between contours) will

he (.quivalent to a horizontal distance of 5X57.3l\1=28G.5:\1=28G50cm. On a

J /20,000 scale, 2~G50 cm. on the ground corre!'ponds to 1.4325 em. on the

mnp.

131. To ('onstruct a slope (lO,jl slope) for the 1/20,000 map with a 5

ruder contour interval proc('ed as follows:

For a 10,!1 slope a rise of 5:\1 corre~ponds to a horizontal distance of

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500M. On the 1/20,000 map, Imm.=201VL Therefore a distance of 500M on

the ground corresponds to 500+20=25mm. on the map.

A 20/ll slope would have a M. D. between contours of half the above,

or 12.5 mm., and a 100/lt slope would require a M. D. of 1/10 or 2.5mm.

(2.) Use Of Slope Scale.

J32. (a) In Contouring: Only when a slope is absolutely uniform can a

~lope scale be used for plotting contours accurately; However it can be used

with sufficient accuracy' for all practical purposes of the military sketcher.

Assume that in making a road sketch a slope of 3° is measured from

the base of a hill to its crest, but by observation it is seen that the slope at ,

the base is gradual, and the slope towards the crest is steeper. Then by

measuring the number of times the interval for a 3° slope will go into thedistance as laid off on the map representing the hill, the number of contourS

crossing the road for the distance will be known. If, in this manner, it is

found that 8 contours will cross the road, the total distance is divided ipto

8 parts, intervals near the base of the hill being wider than those near the'

top after which the contours are drawn through the points of division.

If the slope is uniform the contours will be equally spaced.

133. (b.) In reading slopes: Place the slope scale on the map near the

slo!J~ which it is desired to measure. Move the scale around until one of the

,divisions on the scale corresponds to the M. D. between 2 adjacent con.

tours and so on with the next contours until the slope has been measured J'

for the distance de~ired. This gives the slope between adjacent contours only.'

, To get the slope between several con~ours the total of the slopes

measured may be averaged, thus getting the average slope of any given

ground; or the slope between the top and bottom of the hill may be read

and ~vepaied. This should be done only where the difference in slopes be.

tween contours does not exceed 1 or 2 degrees.

• Avetages should be taken only for plus or minus slopes, never for'both combined.

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CHAPTEn Y.

ELEVATIO:\S A~n GHOUNI> I"ORl\IS.

1I0W SIlOW~. .134. A map is a picture of a portion of the earth's surface, usually drawn

(,n a flat piece of paper, and gives a view of the earth similar to that pre-

Sl'n1('d to an observer in the car of a balloon. As a balloon rises an ob-

server gradually loses sight of some of the details. He will, however, see the

surfa('c of the E'arth in relicf, and will be able to distinguish' all the undula-

tIOns of the ground. As he rises higher the country will look flat and he will

fin(l difficulty in distingouishin~ valleys from hills. In such a circumstance

the view from a balloon exactly res('mbles the picture which the map maker

('n<!('(lvors to r<.>produce.

It is n('('essary, hr)\\,evcr that elevations and ground forms be shown

el l the map. This is accomplished by several methods. Those most generally

w,;('d are the ECllch .1101'1,;,lIarhurcs and Contours.

A. BENCH ~IAltKS, IIACIIURES A~D CO~TOURS

----ig. 16.

Contour lines on the map are

(1.) Ih'finitions.

1:!5. (a) A Delich .1Iurk is' a p('rmanent object or marker, the cxact loca-

tion and ('lcvation of which, with respect to sea level, are known. Usually

only the elevation is marked upon it, thus, llG7.7 would, on an. American

1,1Up,mean that the hench mark in question is 1167.7 feet above sea level.

.] ;jG. (lJ) I!arhurcs, The appreciation of the form of an obj<."Ct results

from the diffen'nee of light awl shadow on its various sides, ~o an illusion

",f solidity may be procured by a suitable arrangocment of shading. Themeans of doing this in topography is

ealled l/achuriIlU. In the absenee of

CO/ltou1'8, which are diseusscd in the suc-

ce('dingo paragraphs, relief or elevations

on the ('l1rth's surface may be indicated

by h(£chu1'c8, which are short parallel, or

. slightly divergent lines, running in the

l1ir<>ction of the st<'cpest !'lop<.>.IIachures

should be u!';eu only to indicate areaswhkh pres('nt slopes ste('p cnou~h to

offer ('over or become obstacles. The use

of Iwrhur(,8 is illustrated in fig. 16.

137. (c) Confow's. A contour line is

an imaginary line joining points of

('(lual elevation on a gi\'en ground form .•

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lines joining points of equal eleyation above a known datum plane, usually

Ela level, see fig. 17.

MovNTAI Nand CoNTOVR0

Pra.S9,nt' .5'2.Q La-va. I.

Fig. 17.

Imagin~ a submerged mountain with the o'cean receding, thus bring.ing the mountain peak up out of the water. The water around the mountain

leaves a series of water marks as it recedes. These water marks may be

likened to the contour lines which are drawn on the map representing eleva.

tlOnS above sea level. A contour line, then is a line, each point of which

ras the same elevation. Contour lines never. cross except in the case of

<'ver-hanging cliffs, see fig. 18.

PROflL£ MAP

to ~~\~~~ :~--. ' . ..../"% ".

Fig. 18.

Valley contours go in pairs; that is, there is always one contour of

the same elevation' on each side of the valley. They form a V which opens

~ut in the direction of water flow, the point of the V being upstream. Con.

.

"COO

Fig. 19.

t0ur lines take the form of a U for spurs with the curve of the U at the

ridge crossing, see fig. 19.

138. (d) A countour has no en,d. If it enters a map it must leave it; the

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two ends joining somewhere off the sheet. A contour is a line without a

break, a dosed circuit. A contour which closes within the limits of the map

indicates either a sllmmit or a depression. Contours alwa~'s are at right

lmgles to the Jines of the steepe'st slope, see fig 17. The spacing of the con-

tours indicate the steepness of the slope; the closer the spacing the steeperbeing the slope.

(2.) Yt'rtical Inlen-at.

130. \'('rUeal Interval is the differerlee in elevation between adjacent con-

tours. Iri American maps, the Vertical Interval (abbreviated V. 1.) changes

with the scale of the map in a regular progression. A simple rule for

American maps made prior to the "'orld "'ar is that GO divided by the

seale of the map (inches to the mile) will give the V. 1. in fee't. For the

later maps, divide the denominator of the Representative Fraction b~T 1000;

thig g'ives V. 1. in feet. For more detailed explanation, ~ee A. R. 100-15.

(3.) Critical P()inl~.

1.10. Critical ]'oil1ts. :\0 map can show e\'ery change of form of the

g-roun<l. 1t is necessary only to know the critical points of the master lines

or the g'round. Su(.h points are the heads of valleys, the changes in direction,

l'nd the chang-es in slope of the drainage lines; the tops, the changes in

direction, and the changes in slore of the ridge lines; and the points at which

a sin'am ('niers awl leaves the area being mapped. These critical points

rmst IJe locat('d an<l their clev3tions determineJ.

B. LOGICAL COXTOURIKG.

141. Logical COl/touring. When the critical points and the drainag'e net

1:I1ve },l'('n established as above described, the sketcher can intl~rpolate be-

tWl'l'll th(\sc mast('r critical points and draw in all contours hy taking into fiC-

('ount the log-ical felation of ground forms, see figs. 20, 21, 2~, 23.

The importance of mUl'h practi('e on these drainage skeleton can not

he over-estimated.

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870y t./

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87Z x

-v.'" /t

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'" f870

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88'j'X "-870

I xII \ 805

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Fig, 22.Same An'a Partl), ('ontour('d b)' Intt'rpolalin~ behH't'n Critical Points.

Fig. 23.

Same Art>a with all Contours Drawn.

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t42.

143.

144.

145.

14G.

CHAPTEU VI.INSTUUl\1ENTS USED IN TOPOGUAPlIIC OPERATIONS.

DESCRIPTION A~D USE.

A. AIMING CIRCLE-See Hand Book.

B. BATTERY COl\ll\'lANDER TELESCOPES-See Hand Book.

C. TRANSIT-See Engineer Manual.

D. PRISMATIC COMPASS-See Hand Book.

E. PEIGNE' COMPASS.The Piegne' compass is used for topographical reconnaissance. It

allows the topographer to measure bearings and slopes. The distances arc

measured by stride or steel tape.

The Peigne' compass comprises a box in the bottom of which a grad~

uated dial is set. The magnetic m~cdlc swings on a pivot standing in the

center of the box. It may be' damped by means of a lever and a milled

lnob. The line of sight is defined by a slit sight and two wires extended in

the slot of the lid. InsiJe of the lid a mirror is inlaid.

One side of the box is beveled and engraved with a millimeter scale.A plummet rotating on the pivot of the needle gives the slopes in mils.

(1) To I{ead Bearings.

147. The lid is kept npen by means of the slit sight. The sketcher hold~-

the compass in his left hand, using his right index finger to release or clamp

the needle as needed. The point is sighted and the image of both needles and

graduated dial are observed in the mirror. By means of the lever, the,

sketcher may check the vibrations of the needle. He then screws the milled.

hrlob with his right thumb. The bearing may then be read. It is better to

Jepeat the operations two or three times and take the mean of the readings:!

(2) To Plot This Din'ction With The Compass. j148. On a sheet of drawing paper attached to a board draw a few parallel

lines in the direction of magnetic north (these lin~s making an ang'le with~

true north equal to the declination of the compass) near the point represent:;1

ing the place at which the bearing was read. Lay the box, entirely opened,:

(,n the table and pivot the bevel about the station point until the axis of thc1

I.eeelle is parallel to these lines. Draw a ray along the bevel. This ra:}

Il'presents the ~lirection as obtained with the ('ompass. .

(3) To Plot The Din'dion With A Protractor. i149. Use a protractor the graduations of which are the same as those oli

the dial. Layoff a line through the station point in the direction of maw~

netic north. Rotate the protractor about the station point until its zero linet

loincides with the line on the paper representing magnetic north. Mar~ of!

a point on the paper that will coincide with the angle as read from the com,':

rass. Connect this point and station point. This gives the line of knowll

direction. I

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. PLANE: TABLE:.Fig. 24.

o

(4) To Measure A Slope.

~50. ~Iold the box vertically, and sight" the point in question. Keep the

ox .vertIcal and note the image of the graduation which is seen in the mir-

for ~n conjunction with the plummet. This gives the ~alue of the slope.

F. TilE PLANE TABLE.-The plane table consists of a drawing board fastened to a trip~d of

three adjustable legs, by means

of a large hand screw. The

drawing board mayor may not

contain a compass inlaid near

one edge of the board. The

plane table revolves on the qead

of the tripod and can be held in

a fixed position by tighteningthe head screw. The plane table

should be level when in use, fig.

24.

(1) To Level The Plane Table .•

152. This is accomplished by

placing two of the legs firmly

on the ground and by adjust-

ing the third by bringing the

surface of the plane table on

a plane of sight in accord with

a distant horizon. When one

, 151.

edge is parallel with the hori-

zon, level the edges perpendi-

c?lar to the first edge in aelm'lI ar manner, by using one

?f the other legs as the adjust-

Ing leg. Repeat to make sure

the other side has not been

thrown out by the last adjust-

ment. The board may be level-

ed more accurately in the same

~anner by means of a level-

Ing alidade or spirit level.

Tho declinator mayormay not be attached to theboard, fig. 25.

. The plane table is used

In connection with topographi-

cal work for run'ning traversesme . '. asurmg angles, and otherlIke operations.

P ER.S PEe T IVE:.

.OECLINATOR-

o 0 0

~----3o 0 0

. PLAN"Fig. 25.

,

-49-,

. o

0

o

'



:,

G. ALIDADES.

(1) Triangular Alidade.

153. The triangular alidade is a box wood rule which has a triangular

~rossection. All three edges of the alidade must be parallel to one another.In using this alidade one lower edge is placed along the line drawn, or to be;.

drawn, while the sighting is done along the top edge. ,'I

(2) The Sighting Alidadt>.

154. The sighting alidade or F. A. plotting scale is a flat ruler about

~5 centimeters long with two beveled edges. One edge is calibrated in milli-.

J(,eters and the other graduated to a 1/20,000 scale. On the face are placed '!two folding up-rights, one at each end, so that the line of sight passing

through the slits in each one is parallel to the edges of the scale. This alidade :can be used only for laying off directions and plotting points. In laying off'

directions either edge is placed along the line drawn, or to he drawn, and

the sighting is done by lining in the object with the line of sight passing

through the up-rights. The slit with the crosshair should be placed farther

from the eye.

(3) The Leveling Alidade.

155. The leveling alidade, sfJmetimes called a French alidade, ma~r be ..

used in laying off directions, plotting points, and measuring gradients, fig.::

-----_. ---- . -- -- _.- •._-- .- _._- -

If

ALlOAO[. :1Fig. 26. j

26. It consists of a ruler 20 to 25 centimeters in length on which are sup~

ported a level and 2 hinged standards. It al~() contains two eccentrics for

leveling the alidade. The rear standard contains three eye holes. The front /

standard forms an open frame including a horse hair sight. One side of the.!frame bears a graduation numbered upwards, the other side hears a grad"'l

uation numbered downwards. Each graduation consists of 40 divisions, ench..

division being equal to 1/100 part of the distance between the two stan'~dards, or 10 mils. I

.t,I

I

I

~



By construction, when the standards are' fully raised and the level

shows the bubble between its ma1"ks:

1. The lines of sight are horizontal. These lines are defined by:

The bottom eye hole and the bottom zero division.

The intermediate e}Oeholeand the division 20 of the 2 graduations.

The top eye hole and the top zero division.

2. The horse hair stretched across the front standard is vertical.

The edges of the alidade bear a graduation in millimeters and a scale

of cotangents. .•

(a) TIJ measure a gradient: To measure the angle of elevation or

depression to a point, the alidade must be absolutely level. This is accom-

phshed by bringing the bubble between the respective marks by means of

the eccentrics which raise or lower one end of the alidade, as desired. In

measuring elevations to points higher than the point at which the plane'ta?le is set up, use the bottom eye hole and the rising gradient, and for

~OJi1ts lower, use the top eye-hole and descending graduation.

(b) In laying off directions or finding direction use the alidade the

same as the sighting alidade. .

(4) T(']es("opic Alidade.

,156. This alidade consists of a flat metallic straight edge on which is

~ountcd a telescope (similar to an ordinary surveyors transit) with a level.

t m.ay or may not contain a dec1inator. In the latter case onc generally is

~nrTl~d in the same box. This telescopic alidade may be used for determin-

In?, .dlrections, slopes and stadia readings. For measuring slopes and deter-

mlnlng directions it is used similarly to the other alidades. To use in

measuring slopes the telescope mu~t first be placed in a level position.

157. To measure distances with the telescopic alidade, a stadia rod is

llsed.

t On the stadia rod are graduations subtending different known dis-

anl]ces as read by the telescope. By means of cross hairs in the telescope,

('a ed stadia h . . dTh I aIrs, a certam length subtended on the rod may be rea .. e ength read on the rod required to produce an image of fixed size

In .the telescope, is directly p;ooortional to the distance of the rod from the

POlnt over which the telescope .is set, see figure 27. .

t The length of the rod as read, therefore, may, .by means of table~,

)~ reduced at once to distance on the ground. The distance mellsured is

O?g the gradient and this in turn may be reduced to the horizontal, if

cSlred, by means of tables, diagrams or stadia slide rule.

Elevation is read by taking a level sight on the rod with the telescope

bn~ measuring on the rod the vertical distance from the ground to the

POlnt Where the line of sight cuts the rod. The elevation of the telescope

~Love the ground must be taken into consideration in determining the dif-

, erence in elevation between .stations.

The degree of precision of the stadia method may be enhanced by

Using it for traverses under ROO feet, using a telescope the magnifying

rov:er of which is 15 to 25, with cross hairs that are fine as possible, and by

tl\kmg readings during the cooler portions of the day, since excessive tern ..

Perature causes refraction.

-51-

I~

~



158. (a) To measure distance with the stadia. The distance to any point

i~ read by observing either the angle subtended by a known length, or how

many divisions of the stadia road are intercepted by a known angle.

1st Process .. The stadia rod, Be, is provided with two sighting

marks the distance of which, h, is constant and generally equal to 2 meters ..

If the stadia rod is standing perpendicular to the line of sight, see fig. 27, ,

hD---• Tan a

A

Fig. 27.

The micrometer of the instrument used may consist of a scale giving

distance, D, instead of angles a. When the micrometer is graduated in mils,

2037

and the stadia rod is 2 meters long, D meters .a mils

, The numerator of this equation takes. into account the relations of

. . 6400 (artillery mil to the true mIl; that IS, 2X see par. 24 and 31).

. 62832nd ProceS!l. The stadia rod is graduated in centimeters. The angu-

lar distance between the upper and the lower horizontal wires of the tele-

scope is known and is generally equal to 1/100=10 mils or 1/200=5 mils.

In the first case (1/100) the number of divisions intercepted on

the stadia rod gives the distance in meters. In the other case (1/200) thereading on the stadia rod must be doubled.

159. (b) Horizontal distance. Distances on the map are the representa-

tion of horizontal distances. Therefore the readings taken ~n sloping ground

are to be corrected before they arc plotted. \

J

__---_0 ,0

Fig. 28.

160. If the stadia rod stand'3 perpendicularly to the line of sight, read-ings on it give actual distance on the slope. fig. 28.

= ---

0

--- _

- _

0



The slope measured is angle CAB=i. Then the horizontal distance

An AC X Cos i

.= DXcos ii

• This equation may be written D' = D D (2 Bin' -).

2It also is applicable to the distances measured along the slope with chain or

read on a stadia rod vertically.

161. When the stadia rod is not provided with a peep-hole, the rod-man

~annot easily stand it perpendicularly to the line of sight. Then he stand!

lt vertically and it is read with the line of sight inclined up or down, fig 29.

The intercept is CG instead of CF,=CG cos i. If D" is the distance

"<>authen A C=D=D" cos i and D'=A n=A C cos i = D" cos' i.

The equation may be written D'=D" cos' i = D" (l-sin'i) ,

=D" D" sin' i

f Tables in appendices give the correction D" sin' i to be subtracted

rom uistance read on stadia rod standing vertical.

---------0'------- -------'"

I.

IG2.

11. TilE ABNEY LEVEL.

This level or clinometer is an instrument adapted for measuring grad-

Fig. 30.

.-53-

= -

-



ients, fig. 30. It has the horizontal plane indicated by a spirit level. The

above level consists of a tube, with a graduated vertical. arc fastened to it

and a level tube with attached arm revolving about a horizontal axis through

the center of the vertical arm. The base of the sight tube is a 'plane

parallel to the line of sight. Under the center of the level tubeis an opening

in the sight tube inside of which is a mirror occupying one half the width of

the sight tube and facing the eye end at an angle of 45° wIth the line of

sight. A horizontal wire extends across the middle of the sight tube in front

of the mirror. When the bubble is brought to the center, its reflected im~

age seen from the eye-end appears to be bisected by the wire.

The central position of the bubble indicates that the level tube is

horizontal, and the reading of the index arm upon the arc is the angle be-

tween the axis of the level tube and the line of sight. This reading should

be 0° when these lines are parallel. The vertical arc is graduated each way

from 0° at its middle point. The index arm has a double vernier whose

smallest reading is 10° of an arc. Gradients of more than 45° are difficult

to measure on account of the foreshortening of the level tube as reflected

in the mirror.

'Vhen the vernier is set at 0°, the instrument may be used as a hand

level to locate points at the same elevation as the eye. The graduation~ on

the inner edge of the vertical limb correspond to the ordinary Ifractional

method of indicating slopes at 1 on 2, 1 on 10, etc. This scale should be read

on the forward edge of the index arm, or in some forms on special index

marks on a shorter part of the arm.

163. To use Abney level, steady it by resting against some object as a

tree or fence post, sight through the eye-piece bringing the cross hair upon

the o.bject to be measured, level the bubble with the left hand (its reflection

being seen in the small mirror). When level read the angle of slope.

164.' The level tube is made parallel to the sight tube by the adjusting

l:;crews. To test and correct the adjustment, place the instrument on a smooth

surface, the more nearly horizontal the better, and mark carefully the posi~

tion of one side and one end of the sight tube. Center the bubble by moving

the index arm, and read the vernier. Reverse the instrument, bringing thel

other side and end of the sight tube to the marks. Center the bubble by

J'YIovingthe index arm and read again. Note and record for each reading

its .direction from 0°, whether, toward or' away from the eye end of the sighttube. Note and record also the location of the eye end in each pORition with

respect to some fixed object, so that the instrument can. be replaced in the

first position or second position at will.,

If the first and second readings are the same, the adjustment is cor~

l'ect. If they differ, take the mean of the two and set the vernier at that

l'eading on the side corresponding to the first reading. Place the instrument~

in the first position and bring the bubble to the center by means of the

graduating screws. For a check, set the same readings on the side corres~ponding to the second reading and place the instrument in the second posi-

tion; The bubble should come to the middle. .

'

' '



1. THE GRAVITY CLINOMETER.

165.. The gravity clinometer consists of a circular case in which fs a grad-

u~ted circle controlled by a pendulum, fig. 31. The line of sight is through :1

Fig. 31.

~~CP ,and glass covered opening. The zero line is engraved on the glass.

th mIrror near the center reflects the scale back to the peep. Looking

th rolugh the instrument the object is seen on the zero line, and at one end of

r.t eth~tter graduation of the scale is visible. The graduations are from zero

te horIzontal, each way to 45°, the graduations and numbers for eleva-

Ion b .. ,emg m red and those for depression in black.

t 11 A sliding bar on the outside of the case u~locks the spring con-

rOded stop. which, when pressed, frees the pendulum and graduated circle,

an when r 'I d', e ease stops them agam.

th I f To use, ~ove the locking bar to free the stop; hold the instrument in

, e

h

. e t ha~d wIth the forefinger on the stop; depress stoP;. bring line of

BIg t on obJect and read.

J. LEVELS.

1~6'1 The engineer's level is an instrument that does n~t give the angles

~t 8 ope, but is used in connection with a graduated rod and by successive'

}e.P8 (~ith back and fore sighting) the actual elevation or depression of an

o )Ject 18 .'I ' measured. The process is slow but accurate and seldom used In

mI Itary sk t h' I I' . t h Ic mg. ts use for locatmg dramage mes In renc es, emp ace-

mcnts, etc., is common.

. In the use of the level great care must be ex~rcised to see that it is

properly leveled at each set-up.

A type of hand level designed for slope readings is now generally

P~eferred to the clinometer. This level has horizontal lines on the object

go a8~, either reading degrees or percent. With the percent graduations it is

i~SsIble to obtain differences of elevation without the necessity of using

a >les of degrees for differences I)f elevation, see Abney level, par. 162.

-55-

\

~

'

"

"

"



, ,

. K. SLOPE BOARD.

167. The determination of gradients by the plummet line is quicker alldmpler, but less precise than with the clinometer, though exact enough :fO~<:rdinary purposes. If a line of sight be taken along the edge of a board alii

a line drawn perpendicular to' the sighting edge, this ~ine when the board ~'

Fig. 32.

held in a ver,tical plane, will make the f;ame angle with the plumb line th

the sighting edge makes with the horizontal; or in other words, will indicgl

the slope, fig. 32. ":JThe scale may be constructed by drawing an arc with the center

the intersection of the perpendicular and the sighting edge. 'From the pet

. pendicular layoff each way on the are, chords equal in length to 1/51

c.f the radius. It is convenient to take a radius of 5.73 inches or 5~

~cant, when the chords will be 1/10 of an inch, or to use a radius of 7 3/inches, when the chords will be 1/8 of an inch. :

, Short radial lines drawn at the ends of the chords form a graduati,

in degrees. The scale may be drawn on the lower edge of the board by pt

longing the radial lines. The plumb line is suspended so that when the Si

mg edge is horizontal it coincides with the zero line on the board.

!68. In use, the board is held so that the plumb line swings freely b

very close to the board. The sighting edge is directed to the object and wh

the line is steady the board is quickly. tilted so that the line draws acro;

the edge. The board is then turned in5:~orizontal position or nearly so, "

'

"

inCh

gl

l



the reading taken; or, when the line is steady, it may be pressed against

~he board with the finger and held in place until the reading is taken. It

IS. better to take two or three readings and use the mean.

L. SITO-GONIOMETER.

169. The sito-goniometer, intended primarily for the light artillery, is a

pocket instrument for rapid approximate measurements during a reconnais-

sance, or at any time when more accurate instruments are not available ..

. The instrument is contained in an aluminum case. On one face tnere

1~ a table of parallaxes. A handle is provided, which also serves as a point

o attachment for a chord. •

It is used for:

(a) Measuring the sight and determining the minimum range

which will clear the mask.

1 (b) Measuring angles in mils and transfering them into terms of

p ate and drum. .

(1.) To Measure The Sight And Find The Minimum Range.

;~O. ~a) Site. Hold the instrument, edge to the front, at the height of

e eye, In such a manner as to see the site bubble, and also external objects

the right side. Incline the iristrument to the front or rear so as to center

e bubble. Read the graduation seen on the height of the objective, fig. 33.

171.. (b) Minimum Ra"-nge. At the gun position, again hold the instru-

ment as if to measure a site. Select a point A on the mask of the same site

:~ the objective. Move the instrument so this point is seen ~o the left. Bring

: .zero of the scale to the height of the point selected, and then read the

~Inlmum range at the summit of the mask. This can on!}. be used for dig-

~n('es from the mask not greater than 300 meters and with the normal

(. nrge, (French 75), fig. 33.

-57-

~~



(2.) To Measure Angles And. Deflections ..

172. Hold the instrument horizontally, edge to the front, close to th:3

1ight eye so as to see the deflection scales and at the same time see distant

objects over or under the instrument.

Bring one or the other of the indices at PI. 0 on the objective, the

lower o~e if the aiming point is on the right of the objective, and the upperone if the aiming point is on the left of the objective. The deflection is

then read at the aiming point in terms of plate and drum, fig. 34.

If an angle is to be measured, look over the upper edge and use the

encircled figures with the 0 on the left.

M. PROTRACTORS.

173. A protractor is an angular scale of equal parts used for plotting

and reading angles. Protractors may be semi-circular, rectangular, or

circular in shape; made either of metal or transparant organic substances;graduated in mils, degrees, or grades; in a clockwi.se or counter clockwise or

both, while the size will depend upon the purpose for which the protractor is

to be used. .



175.

CHAPTER VII.ORIENTATION.

DEFINITIONS.

174. A plane table or map is said to be oriented whe~ all the directions

~:l the map correspond to the respective directions on the ground; i. e., when

.rUe north on the map points to true north, etc. It is evident, therefore, that

: plane table is oriented when all the lines on the board are parallel to the

re~pe.ctive lines on the ground and points 'on each line are in the same

e atlve positions as on the ground.('0 A plane table is said to be declinatcd when the declination of the

brtnpass needle is known and recorded, so that when the compass needle is

OUght opposite its index, the table becomes oriented.

o . An instrument is said to be oriented when the zero is on true north

r the Y-north depending on which is used as an origin.

( An instrument is said to be declinated when the declination of the

iOtnpass needle is known and recorded, so that when the declination constant

b'i se~ off and the needle is brought opposite its index, the instrument will

e onented.

METHODS OF ORIENTATION.

There are two general methods of orientation; viz.

First. By ,means of a'declinated instrument, or plane table, and,

not b Second. By means of a line of known direction, which mayor may

e established in advance.

A. BY A DECLINATED TABLE.

t (1.) With Declinator Unattached.

P76. ,Draw a line on the board making an angle with true north in the

o~ofe.r d~rection equal to the declination of the compass. Place the declinator

phis hne and rotate the board so that the compass needle coincides or is

tl~rallel to this line. Lock the board and verify by repeating the same opera.

On.

1 (2.) 'Vith Declinator Attached.

t 77. 'Place the map or gridded sheet upon the plane table so that the

prue north line makes an angle with the zero line of the declinator which is

()qual to the compass declination. Rotate the board until the compass needle is

Pposite its index. Lock the board. Verify by repeating.

i Note: For a discussion of the process of orienting with a declinated

n,strument, see Chapter XX.

( B. BY A KNOWN LINE.1.) When The Plane Table h On A Station Over One Of The I\:nown

178 Points Of a Given Line.r' Let the capital letters designate the points on the ground that are

ePresented respectively by the same small letters on the map or plane table ..Assume A to be the point on the ground at which the plane table is.

'

'



.. . .

ABenchMarK.

to be set up' and B a point of know location which can be seen from A, fi

35. .. , '

Set up 'the board over A and bring's~::c.~f\e a level position. Place the alidade

. .. the' line ab with the point a near'

.-'-- ':.",-, and b farther away.

. If the point B is so far fro

A that the two points cannot bepl<

ted on the same sheet, it will be

sary, only to have a line from a

-35- the direction of b.

Rotate the board until the point B falls directly in the line of sig

when sighting over the alidade. Lock the board and verify by again sightil

over the alidade. The board is then said to be oriented because ab of

plane table corresponds in direction with An on the ground.

The orientation may be verified by sighting one or more ot

points in a similar manner. If the alidade is placed onAC the point C sho

fall exactly in the line of sight and if on ad the point D should fall

in t"le line of sight. If this does not occur then the error lies either in

point or points being improperly plotted, poor sighting, or because the pI

table is not over station A. Make the necessary corrections and

I,eat.

(2.) When The Plane Table Is Somewhere On The Line Joining Tw

Points Of Known Location.

179. The plane table may be on

line ab extended, in which caset

point farther away, will be

on, fig. 36.

Fig. 36. Fig. 37.

Set the plane table up on an imaginary line joining the two

A and B. Placing the alidade on the line ab and with the plotted point a

farthest away, rotate the board until the point A falls exactly in the

of sight when sighting over the alidade. Lock the board. Verify. Leavl

the board locked, walk around to the opposite side of the table and si

over the alidade on point B. B should fall exactly in the line of sight withl

moving either the plane table or alidade. If this does not occur either

sighting was poorly done or else the board is not on the line An. The lat

generally is the case. Make the necessary corrections and repeat the op

tion.

\

' __-~ '

.

nec

exac

sigh

poir



. Note: The process is simplified when the direction is materialized

on the ground as in the case of a road, see fig. 37.

(3.) By Angle Traverse (See Chapter VIII).

180. Orienting by an angle traverse involves the principle discussed

llbove. The last leg of the traverse is the line of known direction.

J8 (4.) When Known point On A Given Line Cannot Be Occupied.

U 1. The case sometimes occurs when the station A cannot be occupied.

I' nder these 4lircumstances the plane table is set up near point A and a

Ine of known direction from this new position is established on the board.

~A\

\\

Fig :l8.

su (a) Let x be the point at which the plane is set up and x' its as-

med location, fig. 38. .'

th, '1' After the plane table is set up, orient it approximately and, pivoting

t

ea rldade around a, sight on A. Draw the ray from a. Measure the dis-

an('e ro A0' tf m to x and lay off ax' equal to ax, which gives the approximate

n(a 1m of the plane table. pivoting the alidade at x' sight on fl, draw x'D.

e fO})1 a perpendicular from b to the line x'B. Let this be bb'. Draw line ay'

qua to x'b' At ., d' 1 h 1" 1,1' D . y erect a lme yy perpen ICU ar to t e me ay and equa to

d

,), 1 raw ay. At x', erect a perpendicular. The intersection of this perpen-

leu ar 'th' WI the line ay determines the point x which the plane table oc-

U}>Jcs. Orient the board by using x as one point of the known line.

lR2' (b) A much simpler but less accurate method than the one above

n ay be used for. quick work. Place the table near A and orient approxi-t,lately. Place the alidade on d and dra~ a ray towards A. Set off the sta-

t~n point x' at the measuerd distance from A, reduced to scale. While x is

i e true plotting of the position which the plane table occupies, orie:nt us-

nR' x as the station point.

lR (5.) By Resection •

., 3. If more than two points are available orient approximately and re-

Oc(,t S 1 h . ..' • 0 ve t e tTlangle of error and proceed as above when OCcup),jng a

lOlnt on a line of established dirE:Ction.

-61--

' ' '

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~; • 'W" i""

,

CHAPTER VIII.

TRAVERSES.

DEFINITIONS •

. . -.184. ,A Traverse is the process of determining a route for, representation

(,n a map or sketch by actually proceeding over it, making the necessarymeasurements on the 'ground.

A. KINDS OF TRAVERSE.

Tra~erses are of two kinds, open and closed. A closed tra~erse' is one

which returns on the starting point or ends by passing through a known

point. An open or unclosed traverse fulfils neither of these requirements.

For the sake of 'an accurate check, a closed traverse should always be made

in any topographical work i~volving traverses, see fig. 39. I

UNCLOSE:D TRAVf.f1~f: .

A~

. c I

d

" XUnkown POint.

.A

CLO~E:D TRAVER-,E,s.,

b

Fig. 39.

. , I

B. INSTRUMENTS USED. I

185. Instruments 'U8ed in 'T-raversing ~re either a declinated instr~ment

or plane table. The declinated 'instrument may be used either in a needle

or angle traver8e described below, or in an ordinary survey., The plane

table is the usual method of recording traverses on a, map or sketch,

in which event a working scale is used to layoff on the table the distances

measured on the, ground. ,

C. METHODS OF TRAVERSE.

(1.) The Foresight.Back~ight Method.'

186. Methods 01 Traversing include the foresight-backsight meth'od,

needle traverse and 'angle traver8e. The foresight-backsight method is des~"

cribed as follows: Set up plane table at A,' the starting point. Cla'mp th~,

board and plot A on the sheef. Call the plotted point a. Pivot the alidadeat a until the ~cond station, n, is, sighted. Draw a ~ight r~~ ~he fU~1length

"

, , /

t

.

l



of the alidade, fig. 40.' Pick up the plane table and pace the distance be-

tween A and B in the dIrection of the ray already drawn. Arrived at B

layoff, on the ray already drawn, the distance ab corresponding to the

distance AB. Orient the board by laying the alidade on the ray ab and turn-

ing the board until A is sighted over the alidade, fig. 41. Clamp the board.

'

-----KC

Fig. 41.

"11TABL[.oN. B

II

f-AFig. 40.

for:esighton 8

rB

/ I'TABLLOVERAI

mTABLrOv[R.C

Pivot the alidade about b until the 3rd station C is sighted over the alidade.

Draw a light ray be, etc., proceeding by this method until the entire traverse

is completed, see figure 42.

(2) Needle Traverse.

187. ..1, Needle Traverse may be made in

order to save time over the fore sight-back

sight method. Alternate stations may be BY.-._

occupied and sights taken with a dec1inated

instrument, to stations not occupied. A

rodman may be used at the unoccupied

stations (in case these stations have no

sharply defined point to which sights may

be taken. First read the bearing from the

,first occupied station to the unoccupied

station; measure the distance; thence pro- \

,ceed to the second occupied station, mea- \

suring that distance. Plot the position of \

the unoccupied station from the direct~on Fig. 42. ,~ D

and distance first measured. Set up at the second station and read the

hearing to the unoccupied station. Draw a ray through the unoccupied sta-

tion with the bearing last read, plus or minus 3200ljl (back azimuth), and

on this ray plot the second occupied station at the measured distance.

(3.) Angle Traverse.

188.' A ngle Traverses sometimes are of value when it is desired merely

to orient at another point and the matter of distance is not important. In

such a case the orientation of the first known point is merely carried for-

Ward to the other known point.To do this, set up the table or instrument at the first point, A, and

-63-

, -

, ')

;

.' '

.

'"

--

'

-

,



tJrient. Take a shot at a second point, B, and draw the direction ab, on the

table, as in the case of any other traverse, fig. 40.

Proceed to the second station, B, and set up the bo~rd. Do not pause

to measure the distance. At B orient by a back sight on the line just drawn.

~ight on a third station, C, and draw line in this direction across the lineab. Proceed to C and repeat the operation.

Continue until the desired point is reached. The point will be reach-

ed with an oriented board which is what is desired.

In this operation, as in other traverses, the number of legs must be

lImited, otherwise the ~umulative error will be so great that the orientationrnnnot be accepted.

D. MEASUREMENTS.

180. Traverse. Distances p~ssed over may be determined by the stride of

man or horse, by the time taken by a rated horse, by the revolutions of ?'wheel, by chain or tape, and by stadia. Distances not' passed over may be

determined by estimation, by stadia, or by intersection.

(1.) Pacing.

190. Accurate measurWlent by pacing depends on the skill of the operator

In maintaining a uniforr •• length of pace, or of stride (a stride equals two

paces), on the care taken in determining the length of his pace, and theaccuracy with which the working scale is made and used.

Good pacing should not be in error by more than 3% on distances

up to 600 yards. On long traverses it is better to use an~ther method in order

to avoid a large error. It will be noticed that strides always are shorter

on sloping ground both going up and down grade than on horizontal grou~d.

This is due to the fact that the effort of moving upward shortens th: strIde

While in moving downward the operator checks himself, thus shortenmg the

stride. The length of the stride, moreover, is not the same when moving up

a given slope as when moving downward on the same slope.

The following table applies for an op-er~tor taking 100 paces up or

down slopes of 5 degrees and greater. The table indicates the number of

paces to layoff with the working scale for any given slope. On slopes less

than 5 degrees, and for distances on such slopes not greater than 200 yards,

J:O calculation is necessary and ground distances may be taken as the base.

In most instances errors resulting from this procedure are 'compensating.

5°

-~'P- ' I~~~.~

-----\,._-100 ;

PACES,9(J.4'\ 95.6

10° I 15° 20°-----l'~ ,I DOW:-.l 1. ~p I~ _P :D?~_~

78.7 91.5 i 69.3 87.4 58.81 80.8

25° 30°,-- _.

LP 'DOWN UP DOWN

4-9~~1-;~;-35.8 51.4 ,

TABLE OF PACES.

The above takes in;o c~nsideration both the slope of the ground and

the difference in the length of pace due to the slope. See Appendix 1. When

pacing count the number of paces between stations ,apply the working scale,

nnd layoff the proper length of the traverse on the map.

--- ---- ------- " ,.,

1 J



(2.) Chaining Or Taping.

:191. Having set up at a given station and .having oriented the board or

plane table, take a sight to the next station and draw a ray along the alidade

"'hile thus sighted. Send out chain or tape men who will measure the dis-

tance between stations. Keep these man lined in:by sighting over the alidade.

Apply the Representative Fraction of the map in question and layoff the

proper length of the leg of the traverse on the map. For very accurate work

the expansion or contraction of the steel chain or tape, tue' to the temparat-

ure, and its sag, are calculated and the measurement thus corrected.

~3.) Stadia Readings •.

192. This is a rapid method of obtaining measurement of distances es-

pecially over rough terrain where the pace, chain, or tape methods are likelyto cause large errors. The apparatus consists' of a transit or telescopic

alidade and a stadia rod operated by an assistant, see Ch. VI.

E. SPECIAL CASE.

193. When l'-"irstStation Cannot Be Occupied. (See fi'g. 43).

Fig. 43

Set up and level the plane table at B, a point not necessarily known,

but from which the point C is visible. Orient with a compass and plot the

Point a, the point (represented on the ground by A) which cannot be oc-Cupied. Sight on A. Through a draw ray am. Pivot the alidade on a and sight

the point C. Draw this ray ao. Pace or otherwise measure the distance B-C.

This distance, laid off to scale on the ray ao, gives point o. Move to C. set

up, level and orient the table with compass as before. Through a draw an

tOward C. From 0 draw. a line parallel to am. This intersects an at the de-

sired point c, the station last occupied, thereby giving the map distance ac

Which was what was desired.

I'

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F. ERRORS IN TRAVERSING.

194. ~'he rermissible error in traversing is 5% of the entire Je~lgtit of the

traverse. This limit applies only to the ordinary traverse. No such amount

. of error is permitted in surveys. In making a closed traverse there probablywill be an error of closure. Fi.~re 44 indicates the method of correcting

this error for a closed traverse which returns on the starting point. The

procedure is the ~ame for a traverse closing on any known point.

o

l-I

// ....

/

/

/I

/........//

I"..../!'-.....

/

/1. .. . . .. ..

B/.........

A__//

/

8~---\\

7/-//

6~--\

\

5\-:.-

(ORR(CTING [RROR Or CLO,5VR[

ORIGINAL'TRAvERSE.CORRECTED' TRAV[RSE.

Fig.,44.

roint A' should be at A, but due to errors in traversing does not so P~i)t

On a straight line O-A laYoff from 0 in succession, the lengths of the

(;ourses A.1, 1-2, 2-3, etc. From the end of this line lay off, perpen~icular

to A-O, the line A-B equal to the error in closure, A-A'. Connect Band O.

Now from each Succeeding station on the line O-A, draw a line parallel tothe line A-B.

Referring to the traverse, draw through each plotted station, a line

parallel to the final closure lin(' A'.A. On each such line layoff its respec-

tive offset length, as determined ahove, giving new positions for each st~t.ion.

Connect these new stations and the traverse is adjusted .. Erase the or~gmaltraverse from the sheet.

~

-

-----



CHAPTER IX.

INTERSECTION.

DEFINITION.

195. Intersection is tha.t topographical operation by which a point on the

ground is located on the map by the intersection of rays, from two or more

l\n~'Yn points drawn in the direction of the unknown point.

A. PURPOSE.

196. Intersection is used to determine a point without occupying it, and

often is the only method which can thus be employed. It may be used to

lOcate a point behind the enemy's lines, a tree on the opposite side of a

~tream, a mountain peak in the distance, etc.

The method may also. be used to check up the accuracy in angles

and distances of a traverse, in the following manner: Before starting,

select an object on the ground that can be seen from at least three places

along the route to be followed, preferably at the "set-up" stations. While

making the traverse, after orienting the board, draw rays toward the select-

ed Point from known positions. The three or more rays should intersect at

One Point, if th~ work is correct.

B. ACCURACY.

l~7. Accuracy may be expected when the angles between at least two

of the rays is not less than 500 mils; nor more than 2700 mils, as the bad

x~/ "-/ "-

// "-/ \

/ "-//

/.//

//

//

\

\

"\\

Fig. 45.

~ffect of erratic sighting becomes smaller and smaller as the angles at the

Intersection of the rays approach right angles.

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".c. THE OPERATION •.

To Locate A Point By Intersection.

198. A and B are two known points, accurately located on the map (or .

grid). It is desired to locate a third point, C, a church steeple, which can

he seen from both A and B. Process: Occupy A, and orient board accurately.

With a on the map (or grid) as a pivot sight on C on the ground, and.

through a draw a rayon the map toward C on the ground. Occupy B, orient

:-oard, a~d with b on the map as a pivot, perform the sa~e operation. The

mtersectIon c of the two rays will be the location of the pomt C on the map ..

If there is a third point' of known location on the' map, the location' of c

can be checked by repeating the operation at D on the ground. The three

lays should meet at one point. If they form a triangle, an error has been

made in sighting, orienting the board, or in plotting the location of A, B,or D.



CHAPTER X.

RESECTION.

DEFINITION.

199. Resection is that topographical process (the reverse of intersection)

by which a point of the map, corresponding to the sketcher's position on the

ground, is located by the intersection of rays drawn from points on the

ground through corresponding points on the map, after the map has beenoriented. .

CONDITIONS WHICH MUST BE FULFILLED IF ACCURATE RESULTS

ARE TO BE EXPECTED.

200. 1. , Known points must be plotted accurately.

2. Points chosen must be so located that the angles of intersection

of any of the rays drawn from them must be more than 500~t and less tban

27001;lt: also so that the points selected and the point sought should not

lie on the circumference of the same circle. .

3. The plane table must be level.

4. All rays should' be drawn on the same side of the alidade.

5. Lines should be fine and drawn with a hard pencil.6. Sighting should be accurate. After a ray is drawn it should be

checked by resighting. , . .

7.. Allowable error. The. error in the location of the point sought

mUst not exceed one millimeter of the true position no matter what scale

of map is used. Thus, on a 1 to 20,000 map this error would not be greater

than '20 meters, on a 1 to 10,000, this error would not be greater than 10

meters, and on a 1 to 5,000 map, this error would not be greater than 5meters. .

:METHODS OF RESECTION.

A. TRANSPARENT PAPER METHOD.

201. The operator is at point P which he wishes to determine on the map

~r grid. Points a, b, and c, exactly located on the map or grid, are visible

rom this position. The plane table is set up and leveled. A piece of trans-

pa,rent paper is fastened to the board which is locked fast without being

oriented. A needle is struck in the center of the sheet. This represents p.

t With the needle as a pivot, A, B, and C on the ground are sighted in

urn, rays .being drawn toward each. The rays are labeled. The transpar-~~t. sheet is then taken from the board and placed over the map or the grid.

th IS next moved about until the rays drawn toward A passes through a on

T~ map, while that to B passes through b, and that to C passes through c.

th e hole in the paper made by the needle, now is over the point p which is

th~ map representatio? of the point P on the ground. By pricking through

IS hole the point is recorded on the map.

-G9-

. ,

',

'

,



'202. The proof of the above is found in the fact that the rays drawn on -

the paper from the pin toward the various points from angles which c~rres-

pond exactly to those actually on the ground, and that these rays can mter-

. sect only in one point, which is the location sought (unless, of course, all J.

points on the circumference of the same circle). .

203. In using the transparent paper method, it is well to ~emember that

any errors made do not show in the final result. Thus, because no error

appears, the operator must not conclude that there is' none. If accurate re-

sults are sought with this method, a fou~th point should be used as a check

after the point p has been determined on the map.

B. THE TWO POINT METHOD.

204. This method requires careful orienting. Thus, a very se~sitive declin-

ator or a line of known direction is necessary. This method is suitable for

sketching but should not be used in careful topographical operations.

\

\

\

\\

Fig. 47.Fig. 46.

I/

(1.) Using A Known Line.

The operator is somewhere on a line of known direction which is

represented on his map, such as a railroad track. He wishes to find hisexact location.

First, he sets up his board on the track and, placing his alidade on

the map representation of the track, sights along this line, turning ~is boarduntil the map direction corresponds with that of the track itself, fIg. 46.

From this position. he notes a point 'en the terrain which he can

identify on the map. Through a, on the map, he sights on this point A, .on

the ground, and draws the ray. The intersection of this ray with the lme

representing the railroad track is the exact location of p, which is t~e maprepresentation of the point P.

Note: The railroad is used

not only to orient the map but also

as one of the rays drawn in aknown direction through the pointsought. I •

~.

. "

(2.) Using The Declinator.

205. The declinator is used to orient the board after which two points,

identified on the map and visible from the point in question, are selected,

fig. 47. With a, andbon the map as pivots, draw rays towards

Aand

B.on

the ground. The intersection at p will be the location on the map of the pomt

i

~ ~



C. THREE POINT METHOD.

206. Let A, Band C be three known points on the ground which are

located on the map or plotting board, fig. 48. Orient the board as well as

Possible. With a, b, and c on the map as pivots draw rays towards A, B, and

C on the ground. If the orientation of the board is exactly correct the three.

rayS will intersect at one point, p, on the map which is the location of theplane table.

Triangle Of Error •

. If the orientation is not c.orrect a Htriangle 'of error" will occur, fig.

49. This triangle'may be solved in several ways. .

,'.,

.' .

I

I

II .

C Fig. 48

.B

----

. I,I/

I

Ie • Fig. 49.

. :

c

I

I

../

.1

.

207. (t.) If The Operator's Position Is Inside The Triangle On The Ground,

The Vertices Of \Vhich Are A, B, And C.

(a) Solution by using perpendicular bisectors of the sides of the triangle

of error, fig. 50.~.\

\.0

/II

y /

'~¥~~~Z~/ \ \.\

lj '

./Fig. 50.. Fig. 5L

Draw perpendicular bisectors of the triangle of error. These meet

at a point p, which is the location of the operator. Check by resighting.

-71-

\ .

I

~'

{

~

~



208. (2) If The Operator's Station Is Outside The Triangle On The Ground

The Vertices Of 'Vhich Are A, B, And C.

(a) By the inverse triangle method'

. Label the intersection of the rays to A and B as x, to Band C as 1/,

and to A and C as z. Next twist the board slightly and draw new rays to

A, B, and C as before .. If the intersection is at one point, then, that point is

the correct location of the operator, and the twist has oriented the board.

(Note: Usually the point sought will be found opposite the long side. of the

triangle of error, and the twist'should be' in that direction.) If the board

has been twisted far enough it will have moved past the true point and an

inverse triangle of error will have been formed. Label'the intersection of

the new rays to A and B as x', to nand Cas y', and to A and C as z', fig 5.1.

Next connect x and x', y and y', and z and z'. The three lines wIllintersect in a point p which' is the location of the operator on the map.'

(Note: The two opposite triangles of error must be quite small to get good

results. This is because the points of intersection of the corresponding rays

do not move in straight lines during the shift from one side of p to the other,bu t ra ther swing along arcs.)

D. BACK AZIMUTH METHOD. ,

209. In using the Back AZl~uth Method, it is essential that the compassdeclination be known, par. 378, Ch. XVIII.

Pick three points A, n, and C which can be seen from the operator's

position, P, and which are located accurately on the map or grid. Through

each of these points on the map, draw a true north-south line, fig. 52.

toA.....

.........

\

\ to C

Fig. 52.

With the decl!nated instrument take the bearing to A, n, and C and

reduce each to azimuth. Add 32001f~ to the results, which will give the "backazimuth" readings. With a protractor laYoff these respective readings,

using as an origin the true north lines drawn through the respective points .

. The three rays will intersect at one point, p, which is the lucatiqn .of

the pomt, P. If a triangle of error results, some part 'of the work is In-

accurate and should be repeated. ,

. No~e: The Point may be located in th~ same manner if the lines

through A, B, and C are drawn in the direction of magnetic north, grid

north, or the north of the particular compass used. See par. 383, Ch. XVIII.)

The value of this method lies in the fact that it may be performed

'

~



\

I

in the field without a map. It is necessary only to read and record bearings,.

after. which the actual work of res~ction may be performed in the plotting

room, or the dug-out. .

'C)(

xC

l:l)(

)Co.

E. ITALIAN RESECTION. (Bessel's Theorem)

210. The first part of Italian resection is, in reality, merely a method of

orienting the board, hence the name "Italian orientation" might well be ap-

plied. The last steps are those of the ordin'ary two or three points resection.

The orienting, however, is so exact that no triangle of error results.

(1.) The Process.

211. Three points A, B, and C are selected as in the three point method.

The corresponding points on the map are a, b, and c. The point C (c) should

be the point farthest away, fig. 53.

e.?'-,I

II

!

Fig. 53. Fig. 54.

No attempt is made to orient the board. The sighting alidade is laid

with its edge on ab. Assuming that the operator is at a, he sights from a to

B over b; and locks the board, fig. 54. . .

With a' as a pivot C is sighted at, and the corresponding ray is

drawn, calling it CloThe board is then unlocked.

N ext, the alidade is laid along ba, and, assuming that he as b the

operator sights from b to A over a, and locks the board. With b as a pivot

he sights on C and draws the ray C2, fig. 55. \

e)C

A'\,\\

Fig. 55.

Fig. 56.

-73-

,



The two rays, C1 and C2~ intersect at a point, d.

From d the operator draws a ;ay to c. The point sought is some-w~ere along this line.

Unlocking the board the operato~ lays the alidade on the line de and

~ights from d to Cover c. This orients the board which then is locked inposition, fig. 56.

To find the location of the point p, on the line dcC extended, it is

necessary only to piv~t the alidade about a and b in turn, sighting on the cor-

responding points on the ground and draWing the rays across deC. The inter-section of the three lines is the point, p.

212. The location of p may be checked by sighting on a fourth point. In

fact, it is always advisable, if possible' to check any resection in this man-

ner. In Italian resection, if the points ~re plotted falsely, a perfect resection I

may result, no triangle of error being evident, and yet the point will be

quite false. A fourth sight will check this error.

c

(2.) Geometrical Solutio~.

213. Let A, B; and C be the known points i

on the ground, represented by a, b, and c o~the map. Let P (1') be the operator's POSI-

tion which is to be determined, fig. 57.

Through a draw the line ad making with ab

the angle x (BPC) and through b, the line

bd, making with ab the angle y (A PC) ,

cutting the line ad at d. Through a, d, and

b pass a circle and through c and d draw, . t. a line cutting the circumference agam a p.

The point p is the operator's position from

which the angles x and y were drawn.

. For p must lie in the 'circumference

through adb by construction, otherwise an-

"gle abd would not be equal to apd, and as

they are both measured by the same arc ad,

. they are equal. The same holds for angle x.

Also the line pd must pass through c, other-wise the angle ape would be greater or less

than angle y, which cannot be. The point p

Fig. 57. is therefore on the line cd, and also on the

circumference of the circle adb, whence it is at their intersection.

This demonstration is valuable as showing when this ~ethod fails to

locate, and when the location is poor. For the nearer the point d comes to c,

the more uncertain becomes the direction of the line cd and when d falls at c,

that is, When p is on the circumference of a circle through a, b, and c, thesolution is impossible, inasmuch 3S p may be anywhere on that circumferencewithout changing the angles z and 1/.' ,

_



CHAPTER XI.'

Sl{ETCHING.

POSITION .AND AREA SI{ETCHES.

A. CHARASTERISTICS.

.. '1

I .• I

/' .

,(,

,'-. i!,

-. \ .'

/O/l.

.998

990

1006

985

975

J<:"... .

\ Maq.

,\1'Iorth.I

I X98~l

Fig. 58.

,

x 10/4,

995

993

214. Position and area sketches are of the same nature, including, a

traverse upon which, as a framework, the sketcher makes a map showing all

the details of military value contained therein. ,

Such sketches must be drawn to scale; distances on the ground must

b~ ,represented in proper relationship on the map, directions must be in-dicated in reference to the True or Magnetic North, and where ground forms

are d value, the vertical relations must be properly represented.

A map must be capable of orientation. Thus, unless directions are

properly indicated, the sketch has little valu.e.

, Accuracy and,reasonable speed are required in making such sketches.

(The time usually is limited).

However accuracy must not 1095be sacrificed for speed. The

sketcher should be careful at

first to be accurate. Speed

"'in come with pr~ctice and

experience.

D. TECHNIQUE.

(1.) Whole To Part Method.

215. The simplest and best

lnethod of making an area

sketch is known as, the

"whole to the part" method,

, and consists in making a tra-

Verse around the whole area,

after which the'details of the

interior are located and put

on the map.

In traversing locate;

(a) every drainage line

crO!sed or running generally

Paranel to the line traversed

and note the direction of

drainage; (b) every building

and easily identified feature

n~ar the route' (c) the high

Points or ridg~ lines crossed

by the traverse. Determine

,,'

-75-

'

.

"

\ ,- J ~

'



\ Mag.

. \ NorthFig. 59.

."/'X9B5/OJ!.

1/* 9901027X

998

lOll

\ Mag

\Notth.Fig. 60.

the elevations of all these

points, without putting in 1095

any contours, see fig. 58. I X 1014

This is the first step,

or . sketching the "whole."The next step is the' locating

of all the critical points,

within the area, from which 985

the completed sketch can be

ma~e, see fig. 59. The final 993

step is the drawing in of

these details, completing the

drainage lines ,and filling in

the contours, fig. 60. (See

Ch. IV.) mFor complete sketch

see fig. 61.



,100

Fig. 61.

~~g.

'. \orth.

Scalrt

6 in.="nil~:R.F 1t&oVi loft.. VD S

, , I I I (

() tOO too ,xl() 400 $

il

.

':

(2.) Determination Of Critical Points.

2.16. The following are ~riti('al points from which ground forms can' be

fIlled in; (a) junctions of stream lines, (b) sources of streams, (c) entrance

a?d egress ~oints of streams, (d) points of high elevation such as crests or

rIdges (e) road crossings or road junctions, (f) points where there is a

hlarked <1ifference in the degree of slope.

-77-

,

= =

"

'



T

The location of these different points may be determined by travers- ,

ing through the area in one or more directions, or by intersection. If the

area be small, one traverse usually will suffice, the critical points being de-

termined by intersection as the traverse proceeds across or into the area;'

but if the area be large or one with such natural features that the view

is materially obstructed, then it will be necessary to traverse in several dif-

ferent directions. These traverses may be branches from a main traverse

through the area, or they may enter the area from different points. .

. [n making the traverse of the "whole," as many.'of the interior

critical points should be -located by intersection as is possible. With the

critical points established the contouring of the area can be done readily.See Chapter V. .

(3.) .Information To Be Included.

217. In the above'description of the makin~ of an area sketch, only ~he .

determination of the' natural. features has been considered. In an area

sketch. as intended for military purposes, all features' that have milita:yvalue must be shown. The exact purpose to which the sketch is put Will

determine what features may be omitted and what must be included.

The artillery is concerned with an area sketch as it applies to ar-

tillery, and therefore all details must be included that will permit the ar-

tillery to Use feasable roads, or routes, lines of communication, and in fact

every thing that wilI enable the artillery commander to properly dispose of.his different elements. '. , . .

(4.) Conventional Sign~.

218. The conventional si~s used by the American service in military

sketches are illustrated in this chapter. See Plates I to IX.

~ •

-

I

-



Canal or Ditch .• :.: :

Aqueduct or Waterpipe :.,' {

Aqueduct Tunnel ......................•.•. )= ==,~-(,-

',:,"

.~

,.'.

.1

Wagon Roads

Canal Lock (point up stream) .....•..••....••

r

Metaled .

Good ======================

I Poor or Private ~==~============I

L On small-scale maps .....

I

,,'

i,

I'

l~' I

.!I

-,

............................ -----------rail or Path

nailroads

( Railroad of any kind ..... 1 I I I I I

I

(or Single Track)

Double Track =*==*=*=*=*=+=*==*==~;;:

I Juxtaposition of I I I I I

I

i {I I I I I I I I I 1 I , I I I I I I II I I 1 I

IElectri'c .

IIII1I11111111I11111111I

ISta.am L/rletrlC..

In Wagon Road or Street ==X:::::I;;C' ':x====:Z;:LTunnel •.........................•.......... I I I I -(I I 1 I 1 I

:Railroad Station o~ any kind ..........•..•... I I I I I._ I , I I I 1-+

f

Symbol (modified below) .. T T T T T T T T

T I Along road .

e egraphLine

....•..•• I Along road.............. 'J

I (small-~cale maps) • .

L Along traIl -r-,--,-r I--r-r-r

Electric Power Transmission Line ............• ---.--:--e---e---._Plate I.

-7\)-

• I'

, I,,'

,

~ ========

~~-:=-~:~~= __

-.

:

~,,

~

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I ;.

(

I General Sym1x>1 1I I

I Drawbridges (on large scale ... tI chart. leave ~h~nnel QP~n). r

.•...... Truss (W, Wood; S, Steel) ..

I Foot .Ii Suspension .

I Arch ......•....................

l Pontoon .

(........................................ )

rGeneral Symbol .(or Wagon and Artillery) .

. . .'. . . . . . . Infantry and Cavalry ..

1 Cavalr}' .

.............................................

Bridges

Ferries

Fords

Dam

Streams in General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..

-Intermittent Streams ............................•.

"" .

Lake or Pond in General .

(with or without tint, 'waterlining, etc.)

Salt Pond (broken shore line if intermittent) ........•

Intermittent Lake or Pond ......•..................

Spring ..•........................................

Falls and Rapids

_.- .. .-- ...._-----

~

~ ~

" --

~

~



•uildings in General ....•.......................•• 0

RUins••••• I •••••••••••••• I •••••••••••••••••••••••

Church .......................................•..•

I-Iospital .........................................•

Schoolhouse ...................••..••.•••••••••• : ••

Post Off' .Ice .•..........••...••.•.....•••••••.•••••

Telegraph' Office ................................••

'Vater Works .......•..•

\V indn:dll .........................................•

I.!.•-

+or 6• HOS.

• P.O.

• WW.

.

City, Town, or

Village .

(small-scale m.aps)

City, own, or Village ..............................•

City To V'll ( l' d), wn, or I age genera l.ze .......••........

r

l'apital .

County Seat .

Other Towns .

. L •Cerneter .

y ...•...............•.•..........•.....•..

Mine Or Q f k' d ( t)uarry 0 any In or open cu .

Prospect.

Shaft

.. , .

1fine Tunn I . (Opening : .e •..... i

Showing direction .

o

ICfAiorifl.. ] u ..

X

f!I

•• II •••••••••••••••••••••••••••••••••••••

Plate III.

-81-

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>. ,

, .

Oil Tanks (abbreviation, OT) .

Coke Ovens .

-::••o~A••• ••• t:a.

FencesjFe~c: ;:a:;Yfe~;e~

Stone

......... Worm

I . .Barbed S"'ooth

I \Vire ~-x-x-x-x-~-.-o-o-o-o

lHedge =="',,=

County Line .

Civil ownship, District, Precinct, or Barrio

Reservation Line _._.~._._

Land Grant Line...............................

City, Village, or Borough .

Cemetery, Small Park, etc • • .• ...

........... _- _ _--

( ,[ownship-Section. and Quarter Section Lines ... 1

(anyone for township line alone, and any (

two for township and 8ectio~ lines).

Township and Section Corners Recovered .......•.

_+~ _+ __+_.'Boundary Monument •.•••••.•.•••.••.•.•.••••••. ... _-:--

Triangulation Station ..........•................

Bench Mark ...........................• .

u. S. Mineral Monument ._•....•......•........•.

8MX

:Z.32.

.

------------------

~ ~

_

__ _ '

~

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. "",'" .~v

.f CO;::":: b;l~;")"""""""""Glaciers....... . . .1-I

'l'Form Lines showing flow .

IIill Shap(.s . rORM-UN ES.1-jACHUR£.SSTJPPl.[OR'OTHER-"HADIN~.

Contour System .. L •••••••••••••••••••••••••••••••••

Depressio"n 'Con~ours, 'if otherwise

ambigous, hachured thus .

L --'

('~I:Rocky (or use contoura) .

/.I

• L ."••• L.. I"

, I.

:' :l:'Other than rocky (or use contours).

Bluffs

Sand Dunes •• " . . • . . . . . . . . • . . . . . . . . . • .. .. .. . .. .. • . flil~ltLevee ....••.... ".: •....•.....•.•...•...••••...••••.

Plate V:

~,\WII\'III\II¥IIJHI~~'I"\'IIl\'!.'!/Jlliunm::

,-83~

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Marsh .

Salt .

. Wooded ...........•.............

.................

...........................................

Cypress Swamp

Palm

Marsh in general (or Fresh Marsh)

Pine Jor Narrow Leaved Trees) •.....•...........

Woods or any kind (or Brood Leaved Trees)

Woods of any kind (in green) (or as shown below)

~



Palmetto

Orchard .... .•••••••••••••••••••••••••• II ••••• II II

Mangrove

...... ................................. .

••••••••• ', •••••••••••••• II •••••••• II •••• II

• II ••• II •••••• II

Bamboo

Cuetus

Banana

Grasslan .d III general

Plate VII.

'rull Tropical Grass . . . . . ... . . . ... ............ . ...

-85-

0 •

••••• II .. "

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Sand .

.

,

I-

~i'l"~

j

7''''' 'f11'1'''(' l'I 1'r.- T 1'1'rr.' ;1' T1'fT\~"''1' 1'1' 'I

'l' .. 'r ' l' rl' l' 'r1'TITl' 'i'~m I T'f\~'l' f I 'IT I

Surveyed .....

Unsurveyed

Shoreline {

~hores and

Low-Water lines.

Tidal Flats of Any Kind

(or as shown below) .

Cultivated Fields in general .••.•.••.•••••••••••..•

Cotton .. ',' ..•....••.......•....•.....•...•..••••.

Sugar Cane ..•..•••..•..• .••.••....•.•..•...••...

Corn ..........•..••••...•..•...•...•.........•••.

Rice .......•...•..••......•...•.....•....•.......

,

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-

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Mud .

Gravel ~nd Rocks .

:oral Reefs .

+ .$

* ::~(f; P. D

l~l1~:<c4iiE1........................................

.............................................

:el Grass

.elp

ihores and

'OW-Water Lines( continued)

,ock under water .

.ock awash at any stage of the tide .

~ockwhose position is doubtful .

,ock whose existance is doubtful .

Vreck of any kind (or Submerged Derelict) .

'reck or Der,elict (not submerged) .........•......•

able (with or'Without lettering) .......•...........

verfalls and Tide Rips

Limiting Da~ger Line

hirlpools and Eddies

.............. ,

.............. '. : ,

urrent, not tidal, velocity 2 knots .

Flood, 1 knots _'.. ,

idal

u rren ts .

Ebb, 1 knot .

Flood, 2d hour or • ., II.

Ebb, 3d hour .

o bottom at 50 l<'athoms .

Plate IX. -87-

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219. In practical sketching, if it is more difficult, or requires more time

to make the conventional sign than it does to write what is meant, the ex-

perienced sketcher will write the description. A sketch is made primarily

to convey information. If what is meant to be conveyed is not clear the sketch,

is of no use. Again, if it takes a commander too long to read a sketch h~

will blame the sketcher, and as his time probably will be limited he may not. be,

able to take time to read it. It is well to remember that the sketch is bemE"

made to be read; that the convenience of the reader is sought, not that of th~

sketcher; and that is useless to put a mark on the sketch unless that mar~has a meaning which the reader will understand.

It is desirable that the conventional' signs shall picture what they

represent as nearly as possible, so as to be easily interpreted; that they he

simple in construction, so that they may be made rapidly; that they do nottake too much space on the sketch; and that they be so clear as to be readilyunderstood and not be mistaken one for another. .

220. The adaption of the convenional signs to the size and scale of the'

map is accomplished, in part by varying the boldness of the pen stroke, and

in part by wider spacing of them. The strokes never must be so small as,

to render the signs illegible and never larger than can be made easily with.

a medium pen. The object is to produce a reSUlt, which, While distinct

to conventional meaning, shall not be so heavy in general tone as to catcb.the eYe, or, What is more important in military maps, to obscure any ad"

ditions which may be made. Topographical signs should bee perfectly clear

twhen looked for, but not obtrusive. .

. Practice in rapid work has developed many short cuts in making CO""

ventional signs. These convey the same information as the standard signs,

I'ut with fewer pencil marks, and probably greater clearness;

It should be noted that the cross marks on a railroad, the signs in',

dicaling the different kinds of fences, the marks along a road indicating atelepraph line, and the T representing a telegraph line across country, should

not be put close together. This is done principally for the sake of clearness/~.although a great deal of time is saved by it. It is, however, an excellent rule,

never to put a mark on a Sketch, no matter how small, that is not necessary.

A culvert or bridge, less than 10 feet long, (road length) should be

n'presented by two V'S at right angles to the road with the point of the V'.~

opposite each other. Dimensions need not then be given as in a larger

bridge, but the material and the condition, if poor, should be noted: "Bric1(,Poor," or "Wood, bad." . .

Roads are conventional signs, but where Possible should be drawn to

8cale. The road lines should stand out clearly and distinctly with no lin,gS

or other conventional signs crossing the roads. Fence and telegraph syrl1-

bols are placed on the road lines. A hedge fence may be represented ..'._

drawing II's across one of the road lines at the same intervals as the fen C

signs. Fence or hedge signs are the only marks which ever sho~1d appe:between the road lines.

Stone and Wood fences, may be indicated quickly in sketching .writing in "Stone" or "Wood" along a line drawn to represent the fenc

'

as.

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or if along.a road, on the road line, with marks indicating the limits of the

stone or wood fence. A marginal note is simplest and easiest.

Signs for single trees are dra\\'1l oblong or roughly circular in shape.

They should be spaced sufficiently so as to blue print readily. It is not

necessary to show individual trees. The sign indicates trees in that locality.<?ften it is better to draw a ragged border about the timbered area and

Write, "Wooded" therein.

Houses are represented by blocks which are made square and large

~nough to be set in the roads at the scale being used. Black blocks indicate

stone, brick, or concrete houses; and hollow blocks represent frame houses.

A row of houses occupying a certain distance along a road need not be in-

dicated individually, but house signs covering the scale distance occupied by

them should be shown.

In order to proportion the signs to the scale used, it is convenient to

hlake the lines that go on or along a road, of the same length as the width

of the road. This refers to such signs as those for telegraph llnes, barbed

wire, cuts, fills, bridges and culverts.' .

. A dry watercourse should be indicated by a broken line, which should

be wavy so as not to be mistaken for the trail sign; the latter being a broken

~traight line. If there is a small town along the road, it is not advisable

In a road sketch to show the individual streets, alleys and houses.' A town

sign covering the area of the town, and its name, is sufficient.

Where a conventional sign or written words can not be put in at the

Dlace desired without excessive crowding, write a (1) at that place and in-

sert the description in a marginal note opposite a (1) on the margin. Carry

~hese marginal notes by serial numbers. On a road sketch start them at the

ottom of the margin and run up. On other sketches start at the top of the

l)aper and number them down.

Break contour lines on each side of a road, or of a conventional sign,

Or of an abbreviation (as a description of a bridge).

. It sho~ld be remembered that a sketch, when finished, should be readyfor blue printing without tracing; therefore all signs should be destinct

enough for this purpose. All lines should be firm and clear cut.

(5.) Title.

221. Every finished sketch should have a descriptive title setting forth;

(a) the character of the sketch, (b) its locality, (c) the sketcher's name and

rank, (d) its date, (e) its linear scale, its contour interval and its datum

Plane, fig. 62.

Titles should be adapted in size and boldness to the size and import-ance of the sheet. They should be divided into lines following mainly the sub-

diVisions given above. The middle letter of each line should fall on a line

drawn vertically through the middle of the space alloted to the title. Lines

~hoUldbe alternately long and short. All items of the title should be weighted

oth by size of letter and the space between adjoining items so as to em-

PhaSize their relative importance. See sample title, Fig. 62.

t' Sometimes the magnetic north direction is indicated in the title sec-

Ion but usually it is found in the body of the map. .

-89-



'(6.) Border.

222. The sketch or drawing sh~uld be enclo'sed in a I'ect~ngle, pref~r~bl

with its ~ides N. and S, and E. W.. The .bo~der consis'ts of two para1l4

Jines, the inner one medium fine, the ~ute~' one medi~m heavy, with a spac

between them equal to th~. heavy line, see fig. 61~ .

POS/770N 8KETCH

MarOLD POST -rORTS/LL O)(LA

ByJOhn Doe" SgrBrry 'F "'/YFA.

12rebi:E.

RF~y2oooo V/~20Fl'

Yord3~Of.w f ( "1' 1 '1 :r '7 -r Ip

Fig. 62.

(7.) Lettering.

223. All lettering on ~Pposit.e sketches should be w~itten so as to read, fro

the south edge. In place sketches the lettering should be so located as

be read from the sketcher's position with the sketch oriented. In outpo

sketches the lettering is read facing toward the enemy. In road sketche

jhe lettering should be made so that it may be read by anyone followmg tll

route of the sketcher, with the sketch oriented.. . .. As a rule names and figures relating to points on the map are ma

parallel to one side. Names and figure~ relating to extended features,.

large areas, are disposed along the feature', or across the area, in straigllor curved lines.

Ornamental lettering should be avoided. A good general I'ule to folIo

is to use inclined letters for all names and words on the map which relates

water and upright letters for these which do not. In case the sketcher is n

expert in both upright and inclined letters, it is netter to. use the inc1in,

letters entirely. The type of inclined letter to be used is the Reinhardt lette:,

which is uniformly used by engineers through out our country fo~ gener,'lettering. See fig. 62 and Plate X.

~ ~

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LETTERING

Names of natural land features, vertical lettering;Names of natural water features, slanting lettering.

Thiclfness, of letter 1/7 of height.

Slope of letter :1 parts of base to 8 of height.

'AUTHORIZED ABBREVIATIONS

, A. Arroyo L. S. S. Life Saving Station.abut.

Abutment L. H.Lighthouse

A. Arch Long. Longitude

b~ Brick Mt. Mountain

B. S. Blacksmith Shop Mts. Mountains

bot. Bottom N. North

llr. Branch n.'f. Not fordable

br. Bridge p. Pier

C. Cape pk. Plank

... cern. Cemetery P. O. Post Office

con. Concrete Pt. Point

cov. Covered q. p. Queen-post

Cr. Creek R. River

cuI. Culvert R H. Roundhouse

D. S. Drug Store RR . Railroad

E. East S. South

Est. Estuary s. Steel

f. Fordable S. H. School House

Ft. Fort S. M. Saw mill

G. S. General Store Sta. Station

. giro Girder st. Stone

G. M. Grist Mill str. Stream

i. Iron T. G. Toll Gate

I. Island Tres. Trestle

Jc. Junction tr. Truss

k.p. King-post W. T. Water Tank

L. Lake W.,W. Waterworks

Lat. Latitude W. West

Ldg. Landing W.' Wood

Plate X.

-91-

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ROAD" SKETCHES.

A. CHARACTERISTICS.

224. Road sketches differ from area sketches in that they show the na

tural and military features on and in the immediate vicinity of the road only.They consist of simple traverse~ that follow the direction taken by the road

In drawing road sketches speed must be acquired as they should be

made at a rate of 2~ miles an hour if dismounted, or 3 to 5 miles if mounted.

225. Road sketches commonly are made. on a scale of 1/20,000. The sket-

cher should familiarize himself with a few of the common and frequently

used units of measure so that he will not have to apply his scale in locating

every detail on the map. He should, with practice, learn the graphical repre-

sentations of 100 and 200 yds., and the M. D. (between contours), for-la, 30,

and 5° slopes. He should practice estimating the degrees of slope of va~ied

terrain, checking against the reading of an accurate instrument. In this way

the sketcher can locate accurately and speed;ly the position of buildings,

streams, railroads, etc. on the map. He also will be able to give a better ideaof slopes of the adjoining terrain.

B. TECHNIQUE.

(1.) Method Of Sketching.

226. The sketcher must provide himself with the following: sketchingboard, alidade (or triangular ruler), slope measuring instrument (or slope-

board), pencils' and erasers, compass, working and slope scales. These latter

two scales should be pasted on the alidade for convenience. The board may be

mounted upon a tripod (becoming a plane-table) if desired.

227. Proceed to the place of beginning, and set up the plane table, or, ifusing a board, set it on a fence post, stonp., or on the ground. Place the

board so the general direction to be taken will correspond with the long side

of the board. Place the compass on the board and draw a line, in one cornet

of the paper, parallel to the needle. Mark this line to indicate the magnetic

north. This mark or arrow can then be used for orientation.

Having indicated the magnetic north, place a dot on the paper torepresent the point of beginning. Insert a needle in this dot. Place the

alidade against the needle and in the direction of tnwerse. Sight along the

edge of the alidade toward the point at which the next set-up will be made,

using the needle as a pivot, and swing the alidade until it is in direct line

with the direction to be taken (without disturbing the original position of

the board). Steady the alidade and draw a light ray in the new direction,

fig. 63. Measure the slope to the new point. Note all features in the vicinity.

Place them on the sketch and tr.en porceed to the new point just sighted.

Again set up the plane table. Measure off, on the ray just drawn, the

distance just traversed, orient the board by backsighting or with compasS.

Place the needle in the new point, -swing the alidade in the new direction tobe taken, and proceed as from the beginning.

Continue until the entire road distance has been covered, using the

same methods. Check the orientat~on frequently with the compass.At each new set-up, after the first, all the data observed, noted or

measured, "'ill be indicated on the sketch; and contours will be. drawn in



Where they cross the road, as well as in the vicinity of the road. Especial

attention must be given to noting all details that have military value.

Maq.\

l'iortht

[ /'

I!l/~'

~.WOOd',

\'~."" 0

L~~t'\ill

ROAD StrETCH fj SJVICINITY Or W.vON£S a 0

Jca/eJ" 'mila

Fig. 63.

o

t Time must not be wasted in actually pacing dist~nces to buildings off

he road or in measuring the distance between them. Nor must time be.

~Pent in measuring the exact size of cultivated fields, nor the distance that

Hre d .d" ams,. telephone or telegraph lines are from the roa . EstImate these

lstances and locate their positions approximately.

t .' Points of importance, such as hills, villages, etc. will be located by in-

~rsection as the traverse proceeds. If their location is beyond the limits

o the sketch their direction will be indicated. . .

A more rapid method of making a road sketch is to run the traverse

entirely with the compass needle. In all sketches the needle should be used

as a check to prevent gross errors or orientation.

-93-

=



(2.) Lateral Limits To' Be Considered. .

228. The lateral limits of a road sketch are; perforce, limited to what can'

be seen readily from the road. The limits usually considered are 400 yardon each side.

The lateral limits extend beyond this only when the additional infofmation has a military value, and then the salient points are drawn in, th

intervening details being. omitted in. whole or in part.

(3.) Information To Be Included.

229. A road sketch should be so complete that the military commande

can see at a glance all features of value. He must be able to tell the kind 0

road; its slope. and particability for his troops; if the road is fenced;

flanked by cultivated fields and if.tbey are fenced, also the type of fence; If

lhere are Woods near the road, or other cover and concealment; if hills

h.igh point~ of observation ~re visible; if there is cover so that in~antr~ can

jire effectively on troops on the road (effective range 600 yds.) If artIllery

positions are within view (this may include up to several miles); if there are

lines of communication, villages, buildings, water for men and animals along

the route; if the ground is level on both sides of the road; the location and,.

type of buildings. In short aU. information of military value must be sho\\:l

ln a road sketch. Minor and unimportant details should be omitted to aVOIdconfusion and to save time.

~ or



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CHAPTER XII. ::

PANORAM'ic" SKETCHES., CHARACTERISTICS.

'., ,:

;, l

",I., :.••

.. :.

,. ;.

230. A panoramic sketch is' not a land-scape sketch. It has been 'called'

a vertical map, but it is more than a map. In addition it is a military.retord'

containing information of value to the higher commander; and' also- data for

Use by the officer conducting 'fire.: ;; . I •• ; :" ,'", ',:

231. Ever'y' 'artili~ry "officer is famiiiar with the' term ':'Re~~~mai~'s~n~~(

and Occupation, of, a ,Position":' Customarily ;,ho~ever ,~"th~.o'fffcer: thinks.' ofthe reconnaissance and occupation of a position chiefly, with',respe~t, to~'his',

own position, whereas it,: is just as important that he reconnoiter: ~n~:(fani-'

iliarize himself, with the enemy.position, (in'the sense that' he. secure'

the same information that the e'nemy has). This l~st is absolutely 'necessary' if '

the officer is to make, an intelligent estimate of the situation .. Irifact it is' a

fundamental of military operations that he, who would outguess the enemy"

must place himself, in ,the enemy's. position 'and, reason from ,the same prem-

ises adopted by the enemy. Hence, the need of the reconaissance of th~

enemy's position, so far, as is possible from a distance ..The absentee occupa-

tion of the enemy position may be accomplished by systematic observation of

the hostile terrain and of the enemy's movements, and by the careful record-

ing of the data thus obtained. Here it is that the panoramic sketch plays its

, part, the sketch being part of the attempt to occupy the enemy's position.

232. The meaning of the above may be illustrated better by citing a simple,

instance at certain field maneuvers. In the middle distance, as seen, from

the friendly O. P., was a ridge. Beyond the first ridge was a second one con."

taining a notch, appearing about, on a level with the top of the first ridge,

see fig.64. At a certain hour the offi~er in charge' of the O. P. noted the

second ridge, but the

..

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glimpse was so brief and the visibility so poor that he could not determine

the direction of the movement. A study of the map indicated that there

were suitable battery positions for the enemy both in front and behind the

second ridge. He noted the appearance. of the fleeting target on the sketch

but was unable to record any definite data for the target. Shortly afterward

the heads and shoulders of two men were noted on the hill to the left of

the notch and the officer concluded that the enemy observation post was to

be located on that height. As yet he had nothing to indicate the batteryposition.

Sometime later in the morning the observer saw a dismounted man

proceed up the hill to the right of the notch. He drew the line' of travel on

the sketch from the point of first appearance to the point where the ridge

was crossed, and noted the time. Immediately afterward a horseman came

in sight more to the right and rode in a diagonal direction up the same hill.The facts were again noted on the sketch. Then, taking his map, the ob-

server plotted the lines of travel of the horseman and the dismounted soldier

and prolonged them u~til then intersected in the valley in front of the

second ridge. The observer reasoned that the intersection of these two

lines was the battery position of the enemy. Accordingly he prepared a

sketch showing the enemy position, and O. P., which, with the panoramic

sketch, was furnished his commanding officer. The observer was credited

with a solution of the problem, for the enemy battery was located as he had

reasoned, and zone fire' in the area indicated would, undoubtedly, havesilenced the enemy guns.

233. . As just indicated the function of the panoramic sketch is to supple-

ment the topographical map, to aid in the identification of objects on the

map, to furnish information of the situation within the enemy lines, and

also to provide data for the artillery. So detailed and exact should this in-

formation be that the battery commander may rely on the sketch and openfire without using any other data.

TYPES OF SKETCHES.

234. The panoramic sketch may be made in a few minutes by one of the

scouts in warfare of movement; or it may be made by a scout or other ob-

server from a permanent observation post, in warfare of position, in which

case an abundance of time will he available. Whoever makes the sketch must

Lear in mind that the sketch is to be used by another person, either by the

higher commander in his study of the sector or by the battery commander

in his conduct of fire; hence certain fundamentals as to identification, infor-

mation and technique must be observed. .

235. The tYPe of ketch that is to be made will depend upon the time

{'lement. In so called "open warfare", time is likely to be the all im-

.portant element, since the sketch must be available by the timp. the battery

commander is ready to open fire; hence rapid methods of calibration of the

paper with regard to the landscape will be employed. In warfare of position

the sketcher will use instruments in making measurements of all deflections

and of all angles of site and will, accurately, place the points'so measured

on the paper, according to some adopted horizontal and vertical scale. SuchII. sk:t:-h will be almost photographic in its exactness.

""

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• I

ESSENTIALS.

236. . The French make a distinction between the sketch made deliberately

with exact instruments and covering all of the terrain visible from a given

O. P., and the sketch made by the scout during the reconnaissance of a posi-

tion. The former is called the panorama. The latter is known as the per-

spective sketch. The American service makes no such distinction in momen-clature, for there really is no distinction, one sketch grading into the other

according to the time' employed on it. The blank sheets furnished the

8ketcher by the field artillery, iig. 65, may be used for either type of

sketch. These sheets contain a series of parallel vertical lines and a series

of parallel horizontal lines. By adopting a certain scale for the space be-

, tween the vertical lines; e. g., 100 mils, it will be possible to make a series

of sketches all to one scale, which, when pasted together end to end, will

give the sketcher a complete panorama. On the other hand the lines on the

Paper lend themselves to the more hurried methods of calibration as will be

explained later.

237. What are the essentials of a good panoram.ic sketch? There are two

Which stand out with particular prominence; first, clearness of identifica-

tion; second, information furnished. Accuracy is another essential. Draw-

ing ranks last in the list.

A. IDENTIFICATION.

238. As to the matter of identification, the sketcher must remember that,

if the person using his sketch cannot identify the terrain respresented, then

his work is valueless. Hence the sketcher must neglect nothing that will

add to the ease of identification. Of course the horizon line is likely to be,

the greatest aid to identification of the sector and hence should not be omitted

although the objects thereon may be far out of artillery range. Ohjects in

the mid-distance and fore-ground also should be included when they will aid

in this step although they may have no particular military value. Lastly

the data to be entered at the bottom of the page, showing the place wherethe sketch was made and indicating the orientation, are essential to the iden-

tification of the sector.

B. INFORMATION.

239. Of course'the object of the sketch is to convey information. Hence,':" ,

although the sketch may be a work of art; and although the one who picks

it up may have no difficulty in identifying he sector; if that sketch does not

contain military information, and, in particular: information of use to the

artillery officer, the sketch is valueless and the sketcher might better not

have waisted his time on it. . . .

240. That the in/orm.ation furnished should be accurate is self evident

<Jtherwise the sketch loses much of its value.

C. DRAWING.

241. .. While drawing is not so important as'some other things in sketching,'

the officer must remember certain fundamentals. First, the sketch must be

..clear to the point of bareness. That is, the important features must be em-

phasized at the expense of the' unimportant: In other words the sketch be-

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-Comesa~caricature of the landscape. Hence it is just as important to know

What to leave out as it is what to 'put in. Whatever is done the sketcher

must not attempt to show the 'sector by a mass of shading such as would

b'i! employed by the ordinary sketcher. Such a procedure will hide essential

details rather than emphasize them. The fewer lines that can be used to

Convey the desired idea, the better it is.

242. However, the subject of drawing need not prove troublesome. Any

man who can handle a pencil well enough to make a map or area sketch can

, make a satisfactory panoramic sketch,. regardless of whether or not he has

any of the instinct of an artist. More often than not he will make a more

, valuable sketch that the trained artist because he. will not be tempted to

make a pretty picture and so hide military information.

~43. Since the sketch must enable the user to identify the sector quickl~',

'It should convey to the eye a rough picture of the terrain as it actually is

seen. To secure this ~icture few technical' devices should be employed.

(1.) Perspective System of Parallel Lines.

, 244. First of these technical devices is the principle of perspective. This

is a means of making use of the fact that distance to the eye is indicated

by the angle which an object of given height subtends at the eye. The

greater the distance the smaller the angle and hence the smaller the object

appears to the eye. Thus a row of objects of 'a given height extending into

the distance apparently will grow. smaller as the distance becomes greater

Until they finally vanish into a point on the horizon: In order to get theSame effect of distance or depth in a sketch,' the following principles of

Perspective should be applied.

245. (a) Any sy stem of para llel horizontal lines in a plane not parallel

to the plane of the observer, tends to come together or vanish at a point on

the horizon, called 'the vanishing point .. Such a system of lines is shown in

fig. 66. The lines" of the house which are parallel and which fulfill the con-

ditions enumerated, if prolonged, will meet in vanishing points, VP1 and VP2,

on the horizon. .

Perhaps the commonest example of vanishing of parallel lines to tobe found in the track of a railroad, a line of telegraph poles or the sides of a

road, as indicated in fig. 67.

246. (b) Any system of vertical parallel lines no matter in what plane,

will rem,ain parallel. In fig. 66 all vertical parallel lines remain parallel.

247. (c) A ny system of parallel lines not horizontal, in a plane not par-

allel to the plane of the observer, vanish in a point above or below the

horizon. In fig 68 the'lines joining the top and bottom of the picket fence

form the system of parallel lines fulfilling the above conditions. The section

.of the. fence All, is inclined downward and hence would vanish at VP 2• below

the horizon. The section Be, being inclined 'Upward, vanishes at VP 1 above the

horizon. . ,

(2). Consecutive Crest Lines.

24ft The effect of distance can be given in a mechanical way by varying

the weight of line. Since objects seen' close at hand are large and clear

and decrease in size and ciearness as. they recede from the observer, this

principle must be applied to sketching~ The nearest features must be the

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largest and the heaviest of line, while they should become smaller and

lighter of line until the sky line is reached, which must be the faintest of all.

249. Figure 69 illustrates this principle. The successive crests recede fromthe observer in the order A, B, C, D.

The crest A therefore, should 'be the heaviest' line, and the lines

should decrease in intensity to the borizon D, wbich should be the faintest

line in the sketch. Tbe road, following tbis principle and the principle of

perspective, decreases in weight and tends to vanish in a point during its

Successive meanders. No lines should be so faint as to be indistinguishable.

(3.) Broken Lines.

250. By refraining from actually joining intersecting crest lines, as A',

fig. 69, a further technical means is employed of giving effect of depth

to the sketch. This gives the effect of haze found on distant slopes.

(4.) Ground Slopes And Form.

251. One of ihe fundamental requirements of a good sketch being clear-

ness, it is essential that all useless details be omitted. On the other hand

the general slopes and configurations of the ground are of military im-

portance and the question arises as to how to show this ground form with

out detracting from the clearness of the sketch. This is effected by using

the natural and artificial features that exist on the ground, drawn to con-form to the principles ~f perspective.

252. In figure 70 the position and shape of the road indicates a rise overthe crest in the foreground, a gentle dO\Vllward slope to the turn, and finally

a gradual rise to the crest, Where it disapuears. The telegraph line brings

out the same facts as does the line of single trees. The featnres represented

are of military importance and therefore must be shown, but, by means of

these features the configuration of the ground' also is indicated without

introducing useless lines or detracting from the clearness of the drawing.

In the same way the form of the hills is brought 'out by a few lines flowing

in the direction of the .lope. In the case of the Wooded hill the lines are short

and irregular, representing the tops of trees, while in the bare hill tbe

lines are smoother. The necessity for showing the form of these hills arises

primarily for easy identification and from the fact that targets, reference

Points, etc., may be located in a particnlar position on the hills which can

be indicated only from their.' relation to the ground conformation. If the

drawing of a wooded hill is diffiCUlt, smooth lines may be uscd and the hilllabeled, "Wooded."

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(5.) Shading.

253. The tendency of the average sketcher, upon completion of his sketch,

is to attempt to add to the general artistic effect by introdUcing shading of

various descriptions. This course cannot be too strongly criticised, for the

only result accomplished is to detract seriously from the dearness of the

work. It should be borne in mind that the panoramic sketch is not a land-

scape draWing, but is a skeleton chart, devoid of everything of no military

value, in which clearness is one of the prime essentials sought. Therefore,

unless the sketcher is thoroughly familiar with shading and its use, it ShOUld.be eliminated. ,

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254. Shading is, however, essential for one purpose; namely, contrast.

When it is necessary to. distinguish between features that are adjacent or

superimposed, simple shading is permissible and should be used. .

. In fig. 71 the consecutive groups of trees are partially superimposed;

and in order, to distinguish them quickly, alternate groups are shaded by

simple parallel lines. Thus groups, A, B, C are quickly distinguished and

if a target should be located in or between these groupS this fact could be

indicated clearly. When it is necessary to distinguish adjacent cultivated

fields, simple horizontal shading should be used in checker-board fashion.

Objects of military importance can thus be clearly.located in field E or F.

(6.) Conventional Signs:' .

255. Since simplicity and clearness is the key-note o~ a good sketch, the

simplest possible symbols to represent natural and artificial' features should

be used. For' this reason conventional symbols' or, signs are used that are

easily and quickly made, and which, by slight variations, represent and iden-tify features found in any given locality. One consideration shouldl govern.

For the purpose of rapid identification of features depicted, it is necessary

to make the conventional signs look as much like the features they representas possible.

Fig. 72.,

256. For example, fig. 72, (a), is a group of pure conventional signs

representing from left to right, a tree, a house, a church and tree in their

relative position. They tell nothing of the actual appearance of those objects,

and if this group were closely related to other groups of similar objects it

would be impossible to identify it. By makinig these conventional signs more

nearly like the particular objects they represent, still keeping'them equally

simple, a result as in fig. 72 (b), is obtained. The group now emerges from

the general to the particular; identification is assured; ,and yet the sketchhas lost nothing in simplicity or clearness. ,

257. Possibly the features most commonly met in a lands~ape are tree

groups. They should be represented by an iregular line for tbe lops and

a more or less straight line for the near edge, shaded or not, as required, as

in fig 73. Care should be taken to make the irregular line' very irregular.

Fig. 73.

to prevent its confusion with the lines of the sketch such as h.iI!s. crest li~es.etc. "

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260. It

articles:

1.

2.

3.

4.

5.

258. Figure 74 illustrates in' a' conventional way some of the most common

features. No attempt shoul<f,ba made to draw, 'accurately villages or close

groups of houses. It is ~;uffici~nt to indf<;ate a general outline showing very

~imply the trend of the roofs. Different kinds of trees should be shown

Where necessary to aid identifi~atio~, :' "".:'". .

METHOD OF. PROCEDURE.

259. The inexperienced' sketcher examining, a landscape is confused by

the mass of details that meet his eye. Important and unimportant features

are so numerous and mixed together that it"seems a hopeless task to pick out

and recognize the simple frame-work on ,which the whole is built. It is

nece~sary, therefore, that' the. ~ye' be, trained to separate a landscape into

its main mass groups, disrE~ga~ding,details, and bounding these' masses by

single lines so that the relative position and size of the masses, both vertical-ly and horizontally, shall from the frame work of the whole. The lines bound-'

ing hills, mountains, crests, an'd tree groups, and their intersection with

each other, form such mass grou:gs;' aiId once having recognized these main

boundary lines, and having plotted' them in their relative horizontal and

vertical relation, the sketcher has a frame work that is complete, after which

important details may be inserted quickly in their correct positions. A simple-

. method of recognizing these mass groups is to half close the eyes and ex-

amine the counry, when h~s~ groups will become immediately apparent.

. .,.... .'A. EQUIPMENT.

is nec:ss~ry that' the .s~etcher. be equipped with the' following

Compass ..

Field Gla'sses.,

B. C. Ruler.

Penknife:

1 medium hard (2h)anci i mediu~ soft" (2b) pencil. Colored pen-

cils may be used.

6. Eraser. ,

7. A map of the terrain to be sketched, from which the names of

villages, destination or roads and railway lines, names of rivers, streams

and mountains may be obtained, and ranges to prominent features measured

by scaling. ,

8. Sketching pad of smooth paper. This paper preferably should be

ruled in faint lines in some convenient manner as a guide and aid to the

~ketcher. '~

The first step necessary. is, to determine, by actual inspection, the

limits of the sector. If the sector has b~en plotted on a map previously it is

necessary for the sketcher to orient himself and determiine the sector limits

accurately from the map. Having located the limits of the sector, the sketcher

measures it with a B. C. ruler, or some other instrument for ~easuring

horizontal angles. Since the panoramic sketch is drawn to a definite hori-

zontal scale it is necessary to determine this scale before proceeding. The

artillery sketching pad is divided into eight vertical zones between the two

limiting vertical lines. Hence, if the sector measures 800 mils, the distance

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between any two adjacent vertical lines, will represent 100 mils; if the sector

is 400 mils, the distance between adjacent vertical lines will represent 50

lllils, etc. For a pad ruled in any similar convenient manner the scale of

'the sketch may be determined.

B. IDENTIFICATION OF THE SKETCHER'S POSITION AND THE

ORIENTATION OF THE SKETCH.

261. It is essential that this be done immediately, for the important rea-

son that unless this information is shown, the sketch' is of slight value to

anyone else attempting to use it.

Casualties among sketchers and observers are frequent and it should

be mandatory on all sketchers to complete th~se data,' as soon as the sector

to be sketched has been determined. The sketch thus becomes valuable at

once to others as soon as any military information appears on it, and in-('reases in value jn proportion to the completeness and accuracy of. this in-

formation.

262. Just as a map must, in order to make it of any value, have indicated

upon it the points of. the compass, so must a panoramic sketch have some

indication of direction. In the latter case this indication is only an approx-

imation and serves more for identification of the country than a correct

designation of direction.

263. An examination of fig. 65 will show that, at the bottom of the sketch,

and opposite the word, "Place", there is a cross mark o'n' the center verticalruled line. It is'through this mark that the arrow indicating the magnetic

north is drawn. Its direction is determined in the following mam1er.

As shown in fig. 75 turn the sketching pad into a horizontal posi-

tion. Sight along any vertical line at or near the center until this line, if pro-

longed, will pass through the exact point on the landscape through which

it passes in the sketch. The sketch is 'now oriented.

Holding the pad in this position place a compass on it and allow the

needle to come to rest.

Through the cross-mark on the center vertical line draw an arrow

parallel to the compass needle. Note, in the spaces indicated, the place from

'Which the sketch is made, the name of the sketcher, date, weather, as re-

{Jards 'visibility, and the hour of the day.

264. This last is important as the visibility changes from day to day and

from hour to hour, hence, unless indicated, an officer who was using a sketch

of a particular sector might imagine that he was in the wrong area unless

he knew that the conditions of visibility had changed. If time permits a

sketcher may choose the hour of the day when the visibility is best for the

area before him. Thus the early morning is best for a sector to the east

While shadows of late afternoon will serve to bring out successive ridges in

an area to the west.

C. ANALYSIS OF THE SECTOR.

265. Before proceeding further, examine the sector with and without glas-

Ses. The ground should be studied in an effort to get a clear mental picture

of its formation and to separate it into its fundamental mass groups; the

foreground mass or defilading screen, successive crests, the background or

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orizon. Glasses often will disclose crests, hollows, etc., capable of hiding

argets which otherwise might be overlooked. A little study will separate

he important from the unimportant details and the sketcher then is ready

o proceed, along definitely through-out lines, to conform to the object of the~keteh

, ;. SELECTI~N OF REFERENCE POINT AND HORIZONTAL

CONTROL.

~26: In order to ~ake the hori~ontal scale of practical value,'an origin of

i oflzontal measurement must be selected from the terrain and must be plot-

;ed and indicated on the sketch. A, sketch without a clearly indicated re-

~~rence point is more ,useless than a map without means of indicating direc-

I Ion. The reference point maY'i>r may not be in the sector included by the

~ketch. It should pre~erably, if possible, be in the sector, but owing to the

act .that the reference point must be a distinct, easily identified point, it isossible' that a given sector may be devoid of any point that could fulfill

t~ese conditions. In this case such a point should be selected as close to

,either limit, of the sector' as possible and an arrow should be drawn im-

mediately above the sketch pointing in the direction of this reference point,

~n.d should be so labeled. The point selected should further be described

rlefly as, "Reference point, lone pine tree on sky line", etc. Under normal

Conditions a suitable point can be chosen in the sector and indicated directly

on the Sketch. Since it is the origin of horizontal measurements, its angular

~esignation will be zero, a fact which further identifies it.67. In the selection of a reference point, the following considerations

;hoUld govern: (a) it should be easily seen and identified even under un-

avorable conditions of visibility, hence,' not too far away (as a distant

'lllountain_peak on the horizon); (b) it should be of such a character that it

cannot be entirely destroyed by artillery fire. ',.

<l' Owing to the prevalence of conditions of poor visibility, especially

urlng the winter months, in western Europe, the most suitable reference

~oints during the late war were found in the middle listance, and preferably,

f~atures of the terrain, such as; a small hill of distinctive shape, a well-de-

t lne? cross-roads or road fork, the point, where a road crossed a crest, or

the Intersection of a stream with a road or railroad, etc. These were found

o satisfy all conditions better than houses, towers, chimneys, trees or dis-

tant mountains. .' , .

268. By means of the plotted reference point and the vertical guide lines,

a ,baSis of horizontal control is established. By actually measuring with the

mI~ ruler the horizontal deflection of important points from the reference

POInt, these points may be plotted horizontally on the sketch in their true

I'elation.

In fig. 76 the farm is 200,mils from the reference point; the inter-

section of crests, A,' is 1l0inils, the peak, C, is 300 mils, etc.

E. VERTICAL CONTROL.

269. Vertical control, while not so important as the horizontal must be

~?nsi<lered by the sketcher if he would avoid distortion. Thus, unless some

lIne of vertical control is adopted a sketcher often will enlarge the vertical

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ale of one side of his sketch, due to the amount of detail which appears

ere, while the other side, being without military features, may be com-

ressed, Usually it is customary for the sketcher ,who. is not using in-

,truments to choose a vertical control line to which he will'refer all other

l.leva~ions,he referenc~ being wholly by eye. Since the sketcher is concern-

, d chIefly with military features at mid-artillery range, it is customary to

'hoose a line at about the level of the eye and at mid-distance, such as the

l~pf a prominent ridge, the top or bottom of a line of trees, as line AB,

Igures 77, 78, 79. . .

70. In choosing the vertical control line for the sheet it is well to remem-

er t~at the targets at artillery ranges are the ones with which the artillery-

flan IS concerned and' hence this line should be placed so as to leave the

:..greater part of the area of the sheet for the showing of these mid distances.

ro properly portray the various horizontal lines of the ordinar. y terrain and

~hemass of detail, a certain amount of exaggeration of the vertical relationss desirable, otherwise successive crest and tree lines will be so crowded as

:llto make the pictur~ obscure. Ordinarily the sketcher who has' adopted a

Iv:rtical control line need not concern himself with the need of exaggeration,

SIncehe will, unconsciously, exaggerate in the course of his drawing.

If, however, the sketch is to be a true panorama in which the site of

tach target is desired, the vertical relations of the several points to be

1noted may be obtained and the points plotted on the sheet in theeir proper

'I. relation according to a determined vertical scale. Some schools advocate

a vertical exaggeration of two to one. This amount is excessive and thesketcher should be cautioned against too great an exaggeration, lest he

Il:'ake his sketch grotesque an? add to the difficulty of identification.

c •• F. DRAWING IN FRAMEWORK. A COMPARISON OF METHODS.

, ./l.'Vith the horizontal and vertical control established, there are two

methods of drawing in the framework of the sketch. .

1h Assume that fig: 78 shows the terrain in which the sector occurs and

"hat the points represented. under the arrow-heads indicate the limits of

e sector. . .

By measurement it is found that the'sector is 800 mils ,in width

and consequently the distance between vertical lines on the pad will repre-

Sent 100 mils. The reference point indicated in the figure is selected be-

cause it is a sharply'and clearly defined point. Horizontal control is now

'established. , .

For vertical control, the horizontal line established by the crest

and tree line AB, gives a well marked base line, and since this line runs ap-

i~OXimatelY through the center of the sector, the center horizontal line of

e Pad will represent it.. Figure 79 shows only that. part of the ruled' sketching pad within

WhIch the sketch must be drawn both vertically and horizontally.

27 (1.) First Method.

~. This method consists simply of plotting a few important or critical

POInts by means of the horizontal and vertical control. 'Vith these points

~tab1ished, the framework can then be drawn in through them by reference

the terrain.

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Since the reference point is slightly to the left of the center of the.

sector it is plotted slightly to the left of the center of the sketch, and at

such height above the line AB as the eye estimates it. to be above the

imaginary line AS in the sector. This Point must be plotted first. By mea

Surement the chimney of the house is found to be 100 mils to the right 0

the reference point. It is also slightly below the imaginary line AS, fig. 78

Using the pre-determined scale of the sketch, measure off 100 mils to the

right of the plotted reference point, and, moving vertically. downward below

the line AS, plot in the location of the chimney such a distance below this

line as to be relatively correct, fig. 79.' In a similar manner, enough critical,

points are plotted to the right and left of the reference point to. establish

the framework of the sketch. A few such points are indicated.in fig. 91

by crosses. Typical critical Points are crests of hills, intersections of crests,

houses, limiting points of roads, limits of tree groups, etc. Through these

plotted points draw the outline of the terrain. , , ,

This method is the most accurate but is slow on account of the con-stant necessity of identifYing the plotted points with the points in the terrainthey actually represent. .,

. .(2.) Second Method ..

273. By holding the sketching pad vertically in front of the eye and look-,

ing ove: the top of the pad at the landscape, and at the same time moving

the pad, to or from the eye, a point will be reached at which the two

. limiting vertical ::nes of the pad will intersect, if prolonged" the corresponde

. ing limits of the sector. Figure 80 shows the pad in this position for the

landscape and sector shown in fig. 78. Holding' th~ pad here' the' sketcher

draws in lightly, in the one inch space at the extreme top of the sheet, the,

sky line and as many other important points. as possible, comparing the

outline'directly with the country as he glances over, the top of the pad.!,

This procedure automatically locates the framework horizontally. When,

completed, the pad is lOwered into a comfortable horizontal position and the.

framework so drawn is carried' down into its proper position on the sheet,'especial attention being given to locating the framework correctly by means,of the vertical control. '. ". .

,This method is much more rapid than the other and after 'a little:practice equally accurate result. can be obtained with it. It has the advan-

tage of eliminating constant identification of plotted points with correspond-ing grounds Points, and the consequent loss of time.' ..

274. The frame work drawn by either method should be done lightly with'

. a hard pencil. If time permits it can be gone over later and corrected where,.

nceSsary. More attention can then be paid to characteristic shapes and for-"

mations, and to relative vertical relations:. The principles of perspectivealso should be applied., , . ',' , . , , i.

.N otel: By using a sheet of transpar~nt celluloid, the same sizeas the sketching pad blank, ruled in the Same manner as the blank and,

a.ttached at rig?t angles to the pad, the sketcher may calibrate his sketc?, J!sImply by looking through the celluloid, and nOting on which line or m

which space each feature falls. It is a simple matter, then, to sketch 'these.

features in the same areas on the paper. ", ,",.:'. -. '. . . ;

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Note 2: Another mechanical device, the most rapid and accurate of

all, consists of two mirrors arranged in a small hood, two or three inches r~

wide, and two or three inches long, very similar to the hood of a trencr

periscope. Instead of being placed parallel the mirrors are set at an angh

or 22~O to each other so that the image seen through the peep hole appearf-

1

on the sketching pad placed below and in front of the device. In order that

the sketcher may see the pad and his pencil, and so trace the image of the

landscape, the lower mirror is made semi-transparent by a series of fine .

lines cut through the mercury back. The degree of vertical exaggeration

desired to secure by inclining the sketching pad away from the plane par-

allel to the lower mirror. Calibration of the sketch may be secured by amil scale on one of the mirrors.

G. FILLING IN.

275. With the framework established it is a comparatively simple opera-tion to fill in with those details, the importance of which is governed by tbej.

purpose of the sketch. Time being a factor, and the object being to locate

targets, the framework is sufficient and no time should be spent on filling j'.

in, while the framework itself should be only a rough approximation. Hence

time and the object sought govern the amount of detail shown, and it is

here that the knowledge of wbat to omit makes itself manifest. This last canbe gained only by actual experience.

276. Speed and simplicity are gained in locating details by plotting

limiting points on the frame work and then drawing in the details between

these points. Points where roads, telegraph lines, fences, etc., appear and

disappear over crests, horizontal limits of tree groups and settlements, are

features that can be located this way. Simple points may be located by refer-

ring them to points on the sky-line under which they are vertically situated.

With the soft pencil the sketcher should go over the drawing and

vary the weight of the lines in it, bearing in mind that the weight of line

. and size of objects decrease uniformly as they recede from the .observer, the

lightest lines being the objects seen farthest away. No time should bewasted on the foreground. A simple heavy line showing its general con-formation is sufficient.

II. DESIGNATION OF TARGETS AND IMPORTANT POINTS.

277. In order that the sketch may be of value to others beside the sketcher

points. of identification must be indicated and data provided as to these

points. First in importance of the targets is the ridge line which will afford

shelter for the enemy, and on which the artillery officer is likely to fire.

Next in importance will come roads Where they cross such ridges, roads and

routes of travel, battery and battalion areas, tree lines, streams, and in-

dividual targets. As fast as such a target is plotted on the sketch the data

concerning deflection and range, as well as the target designation, should

be entered in an appropriate place on the sheet. This must be done so that,

should the Sketcher be interrupted, his sketch will be valuable so far as hehas gone.

2i8. In identifying targets they are referred to the reference point as to

deflection, and to the sketcher's position for range. Figure 81 shows the

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method of accomplishing this. Vertical lines' are drawn from the top of t

sheet and terminate in an arrow head in the exact point on the sketch whe

the point in question is located on the ground. Directly at the top of t

line the description of the point so located is written diagonally, so that

can be read with the sketch held in a normal position. Conventional si! '

for targets should not be used. They serve only to add unecessary de

to the sketch and destroy clearness. Since, in the artillery, the right of t

target is the point on which firing data are computed, the vertical line sho?

indicate the loeation of the right of the target, and if further identificatl ;

is necessary, its width in mils may be indicated. This would mean then, tli

lhe arrow-head locates the right of the target, and that the target exte~to the left of this point so many mils. '.

279. Simplicity in designation' of targets can be accomplished by usjil;

definitely understood abbreviations; e. g., "I" for infantry deployed, "A" rartillery in position, etc. The reference point always should be indicated

such and may further be given its correct name if known. For quick iden

fication the line to this point may be made' heavy or doubled. Accordir

to the jUdgement of the sketcher and the purpose of the sketch, any inforIl1I

tion may be shown, such as names of hills, mountains, farms, villages, de

tination of roads and railroads, location of bridges, trestles, culverts, et

The sketcher is governed only by consideration of the relative military iportance of the poirt:s shown or omitted. I

280. On the artillery sketch, directly under the description of the indicat

point or object, should be shown its range. The range is either estimate

or measured. If the latter, it is unde~'lined. By reference to fig. 65 it

~een that at the top of the sheet. are five horizontal zones marked at t

left, DE', DD, Sf, KR, alld .nN. These zones are solely for firing data a

these data are filled in before and corrected after firing. The firing dat '.

referring to any particular target, should be written across the vertical Iidesignating the target, and be in the correct zone. j

It is evident, therefore, that a third range Occurs. This ran~e, aft

aclual firing and correction, is the gun range to that particular point. Hen

on the complete sketch there will be shown estimated ranges, measur;,:

ranges determined by instruments, or from the map, and gun ranges d~termined by actual firing.

281. Immediately below the five horizontal zones for recording firing

data, fig. 65 is a one-inch Space before reaching the upper horizontal limit

of the sketch proper. This space is used solely for rec:>rding angular deflection)The deflection in mils of the particular point indicated, right or left of the

reference point, is placed directly on the vertical reference line, as indicated

in fjg. 81. The' deflection of the reference point is, of course, zero, which

further identifies this point. With a reference point within the sketch, de-

fl~tions will increase to the right and left of it. 'Vith the reference P()j[Wllhout the sketch, deflections will increase throughout the sketch to t~ .

left or right, depending on where the reference Point is, to the right or ~el •

of the sector. Deflections are habitually indicated to th~ nearest multlp

of five, as no closer measurement is possible with a mil ruler.

.

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, I. SUBSKETCHES.

:82. In certain cases the sketcher may wish to show the terrain sur-

~Unding any particular point in more det~il than is possible on the ma.in

'8etch. This may be done by means of a subsketch, see A, fig. 8l.

, 3. In conclusion the sketcher must remember that he is busied in mak-

~g a map, a military record which is to be used by others. Therefore he

h?uld ask himself constantly the question, "What value has this sketch at

'hIS moment to another person"? With this question before him the sketcher

I ould be able to resist the temptation to draw unessentials, and so put,

,own only data of value, recording such items in turn according to their im-

ortance.,

MAP AND PAI\ORAi\HC SI{ETCH.

~84.. Plate Xl is a section of the military reservation of Fort Sill, Okla.

n It is marked a sector to be sketched from a given point, A. Fig. 82 is the

:noramic sketch made of this sector from the desired point. A study of

:he map and an examination of the sketch will show the comparison between

.e two and also will indicate the immense value of a sketch for showing

...vw the ('ountry actually looks from the customary point of view. No matter

ow great the topographer's knowledge or ability to read a map, it is im-

~~.ssible for him to get an accurate men.tal picture of the countr~ si~pl>:

." un a study of the map. The sketch brIdges the chasm between Imagma-

:101\

and1

C'ality; and with both at hand, intelligent and exact action may:l(: planned e':en though the country is entirely new and strange.

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287.

Lelow.

CHAPTER XIII.

VISIBILITY AND DEFILADE.

DEFINITIONS .

. • 285. In the discussion of this subject no attempt will be made to expl~

'any methods other than tho,", pertraining to Topography. The term, "vi

ibility", is used ordinarily with reference to our own or the friendly q

servation posts. "Invisible Area" the.n is the area invisible from theo. P. . , .'

The term, "defilade", relat~s primarily to what may be seen, fr

the enemy observation posts or lines, with a view to obtaining conc.ealm ffrom the view of the enemy. However the term also is used in conneclIon w~shelter from the enemy fire. . ,]

Defilade is given, usually in yards or meters in order to determI~

at once what kind of defilade is obtainable, i. e., materiel, dismount~. mounted, flash, dust, smoke, etc.

.

VISIBILITY. .286. There are several methods by which visibility may be determine(the more common of which will be considered below.

.A. SIMILAR TRIANGLES.

The first method to be considered is that of similar triangles give

Find from the map the elevations of the observation post, of t

point considered in the enemy'S lines, and of the intervening crest suspect

the

Fig. 83.

The line of sight from the observation post falls 30 feet in 50

}.ards. The intervening crest is 3000 yards away. By proportion, 5000: 300

: :30 :x. Solving, it is found that the line of sight at the crest will pa

through a point 18 feet below" the level of the O. P. In other words, the Iir.

of sight at the crest will have an elevation of 1112 feet. Since the crest h

un elevation of 1120 feet the line of sight between the O. P. and the enemY

line will pass 8 feet below the top of the crest. Hence the enemy positiocannot be seen.

friencJ'

~

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10 . 1"angle of site or the intervening crest is +3=-11/t, approXImate y.

3line of sight to the objective considered, therefore, has a. ste~pe~ d?w~,,:.

slope than the line of site to the crest. Therefore the obJectIve IS mVIS

The opposite is true'in case both crest and objective are above the elevatof the observation post.

D. GRAPHIC METHOD.

290. The question of visibility also may be settled by means of proff

To construct a profile apply a piece of cross section paper, or any ot

paper which has horizontal lines equally spaced upon it, to the line joining'

O. P. and the point considered in the enemy's line, see ray B, fig. 85. On

edge of the paper mark with its elevation each point where a contour cros

ihe line. Number the horizontal lines of the paper to correspond to the ele'thus of the several contours crossing .the line between O. P. and the targ

From the points on the edge of the paper drop perpendiculars to the corr,

'ronding horizontal lines. (Note. It may be more convenient to use a straiji

<:dge an', a right angle triangle and so drop the perpendiculars directly fr(

the ma) to the p! ~per parallel line, without bothering to plot points onmargin ')[ the paper.)

Consider th2 points plotted on the parallel lines as Ii'11',tir';~ pr,i,

of the p,ofile desireu. Join these points with a smooth ('ur'/e, takin6" i!'

account the character of the ground forms as shown on the map. The fsuIt will be a vertical cross section of the terrain between the O. P. and tpoint in question. See Profile B, fig. 85.

On the profile draw a straight line from the observation' post, ta

gent to the intervening crest. If the point considered is below this line it VI

l,e invisible, and all terrain between the crest and the point where the line'sight tOllches the ground, also will be invisible. •

In this method the horizontal scale of the map must be preserve

While the vertical scale generally is much exaggerated in order to bringmore clearly, the ground features. ,

It must be remembered that if the observer is placed on an 'obser~:

tion tower, or in a balloon, the line of sight must be drawn, not from

ground elevation of the O. P., but from a point SUfficiently above, accordilj

to th.e vertical scale of the profile, to maintain the proper relation bctwe1Observer and objective sought. ,

, .'E. VISIBILITY CHARTS.

2!H. In preparation for the occupation of a position, a chart called tb

Vi8ibilit~ chart is ~repared, showin~ all area~ i~visibIe and visib~e from

observatIOn posts lIkely to be occupIed. The mVIsIble areas of dIfferent

P's., if appearing on the same chart, are marked in different colors. It mu

be remembered, however, that no matter how carefully this chart Is Pl~

~ared from the map, it must be verified b~ a careful .stndy of the terra~Itself, as soon as the observation post can be occupied.

292. This chart is prepared on a transparent sheet from profilesfollows: .

Place the sheet of transparent paper on the map. From the observ81

tion post draw a series of radiating lines, A, B, and C, fig. 83, through thj

-

o' " t

'

'



....

1000

bil

\ .

transfer the points to the chart. After marking all the ra}1S on the map in

,this manner an irregular area or areas will be indicated by the dots. See

Points x', y', and z' of ray A, and x"~ Y",'and z" of ray C. Connect these dots

.

,',1

,..;

"

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:lnd hatch the area enclosed with diagonal parallel lines, using different

'Colors or cross hatching to distinguish between invisibility caused by ground

forms and that due to masks, such as trees, buildings, etc. Objects situated

in invisible areas, the tops of which are visible, also should be indicated by

"ringing in" with a different color, see the smoke stack indicated in fig. 85.

This last is important as it often happens that a line of trees or telephonepoles projecting Upward from an invisible area will indicate the presence ofa road or other objective for the artillery.

These charts, as constructed above, are prepared for each observa-

tion post or auxiliary observation post and transmitted to superi~r com-

manders where they are consolidated and used in assigning missions to the

various batteries, and in assigning the various observation posts. of a par-ticular sector. See Appendix No.7.

DEFILADE.2?3.. A~ in the case of visibility, defilade may be computed by means of j

SimIlar tnangles, by angle of site, and graphically. .

.A. ANGLE OF SITE. \

, (I) Measured From The Enemy O. P.

294. Obtain from the map the elevations of the enemy O. P., the covering

crest, and the proposed route or position; also the ranges between the dif-

ferent elements. With these data compute the angles of site to the crest, and

to the position, as mea:sured from the enemy observation post. Subtractalgebraically the angle of site of the crest from the angle of site of the

position, and multiply the result by the distance, in thousands of yards or

kilometers, from the enemy O. P. to the position or road. The result willhe the defilade in yards or meters, see fig. 86.

lIf,O-tr---t--~~-;---2.5~. ~ tMYOP.

I I "Ii '/"\ ~iJf\l"..,!,t '11~~')f/l ,f:t:.~~1 I

~I .... \, ,,-,IF Ir-~,~R(~t~:, ,'or ,~,;!'~it~ ID(F1lAD(i7;5YO~ ,;~~liJh! ;--I:,::\;W;!"~~ ,,~~!~~Z; '1100

P05ITIO ---1- -j_1/'00 f-4 4(100 YD~-

._- -.50()()yo~- '---4

Fig. 86.

1160-1100=60 feet=20 ~.ardsthe difference in elevation between theO. P. and the position.

1160-1130=30 feet=10 ~.ards=the difference in elevation between

the O. P. and the crest.

The angle of site of the Position=20+5=-41!1.

The angle of site of the crest=10+4=_2.51!1.-4-(-2.5)=-1.5111. ,

l.!illl X5=7.5 yards=defilade of the position.

(2) Measured From Covering Crest.

295. The amount of defilade also may be found from the map, by the

same caltulation generally used when it is possible to occupy the position and

the ('fest with angle measuring instruments. ,

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_ - -- - __

- - - - - - -



From the map determine elevations and ranges as before. With this

data compute the angle of site of the enemy O. P. measured from the crest,

and the angle of site of the crest measured from the gun position or the

road. The amount of defilade is obtained by subtracting the site of the. ob-

servation post from the site of the crest, and multiplying the remainder by

~he distance, in thousands of yards or in kilometers, from the position to the

crest, see fig. 87.

1160-1130=30 feet=lO yards, or the difference in elevation between

crest and O. P.

1130-1100=30 feet=10 yards, or the difference in elevation be-

tween the crest and the gun.

10-7-4=2.51/t=the site of the O. P.

10-7-1=10,/t=the site to the crest.

10-2.5=7.5//1. .

7.5X1=7.5 yards= amount of defilade at the position.

B. PROFILES ..

. 296. Defilade also may be determined by means of profiles, as follows:

From the enemy observation post draw a profile or series of profiles

of the terrain including the proposed position or roadway. The method of

construction is the same whether visibility or defilade is sought .

. Draw a straight line, representin.g the line of sight from the observa-tion post, tangent to the covering crest, see fig. 88. At the position measure

the vertical distance from the surface of the ground to the line of sight, ,

?rawn as above. This distance, according to the vertical scale of the profile,

IS the amount of defilate of the position.

1140

1130

IlZO

II If,

Fig. 88.

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Defilade I75mm.

155 mm.-:_- --~~~sh ---.---. -----,

--4 meters

8 meters-------- -----,----Smoke

I8 meters

15 meters

c. TABLE OF DEFILADE.

297. Although usually determined by a personal inspection of the terrain,

the following kinds of defilade may be determined from the map:

Materiel Defilade, where the materiel is just below the plane of de-filade.

Dismounted Defilade, where the level of the ground is 2 yards be-low the plane of defilade. .

Mounted Defilade, where the level of the ground is 3 yards belowthe plane of defilade.

Dust Defilade, where the piece is far enough b~low the plane of de-

filade that the dust, caused by firing, will not be visible from the enemy

position. This last varies with the weather and the terrain and is difficult

to obtain except in swamps, along watercourses, and by wetting down theposition.

A convenient table showing amounts of defilade required for smokeand flash defilade in light and heavy artillery is given below:

.D. TYPE PROBLEMS.

2!:l8. Types of problems concerning defilade and methods of solution, us-

ing the principle of similar triangles, follow. Any of these types may be .

solved using either of the other methods explained for computing the amount \of defilade of a position.

(I) }~irst PrOblem.

299. To compute the amount of defilade of a position. Having found fromthe map. the elevations and ranges, as shown in fig. 89, eonstruct and solve l

the triangles indicated. The line of sight which falls 40 feet in 4000 yards

will fall 50 feet in 5000 yards. Since the difference in elevation between

the enemy's observation post and the position is 60 feet, it follows that the

line of sight will pass 10 feet above the' position, or the position will have10 feet of defilade.

j 1.



-r--= =--r-=~~~D~~~~(l -:=;ri'~OMY OP

I ~ . "W~' .t'

u.. <to 'N1/C .. .--- "v

'f M 'l-~~ . ._____ ,~@\h/

I IIIO~ '''/\:.:1\''/''.

1100. :/' ,.~ .:'llr' 7. . ~C 'r'(',qi(T=,;}d:'-;,'I>

ptt f 'ON'''' Fig. 90.

5000: 4000:: 60 : x.

x=48 feet.b 1160-1110=50 feet=the amount the ground level at the crest is

clow the enemy O. P.50-48=2 feet=amount the mask must be raised to reach the line of

'(2) Second Problem.

300. To find the amount by which a mask must be 'raised to secure con-

Cealment from the enemy's view.Find from the map the elevations and ranges as shown in fig. 90.

Construct and solve the triangles indicated. Since the line of sight passes

48 feet below the level of the enemy's observation post and the top of the

Inask is 50 feet below, it follows that the mask must be raised 2 feet, plus

the amount necessary to secure the kind of defilade required; i. e., the amount

nf:cessary to give 6 feet for dismounted defilade, 9 feet for mounted de-

Ilade, etc.

sight.

40 6 feet at th~ position will "gi~e dj~mounted defilade. 6.: x::. 50~0:

'do00. x=4 4/5 ft., dIstance above lme of sIght at the crest, WhIChWIll gIVe

t Isrnounted defilade. Therefore 2+4 4/5=6 4/5 ft., the height necessary

o raise the mask.

(3) Third Problem.

301. To find the height to which an observation tower or balloon must be

raised to ovei'come the defilade of an enemy's position. Find from the map

~he elevations and ranges as shown in fig. 91. Construct and solve the

Indicate triangles. The line of sight from the enemy's position passes over

t~e crest at a height of 30 feet above the enemy position. Since this is the

flse in 1000 yards, the line of sight will rise 150 feet in 5000 yards, to which

height it will be necessary to raise the observer. But since the ground at

the observer's position is 40 feet above the enemy position it will be neces-

Sary only to raise the tower or balloon by the difference or by'150-40=110

feet. .'

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/

/

1000: 5000:: 30: x.

X=150 feet. -.'

150-40=110 feet=height balloon or tower must be raised above theround.

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CHAPTER XIV.

MINIlUUM ELEVATION; MINIMUM RANGEAND DEAD SPACE.

GENERAL.

~02. . Mlinirnum elevation is the least quadrant angle of elevation at

which the trajectory will clear the covering mass or mask. It is a range

~cale or quadrant setting on the gun.

Minirnum range is the actual range to the point of fall for the

~inimum elevation. It is a measurement on rnap or g'round of the shortlimit of fire.

Dead space is ground which cannot be reached by fire. It is caused

by: first, the covering mass or mask immediately in front of the battery

~\Vhich also fixes the minimum elevation); second, obstructions beyond the

Immediate cover which may protect the enemy from artillery fire.

The first class of dead space begins at the crest of the immediate

COver, under the ascending branch of the trajectory, and extends to the

lninimum range. Its limits are determined,' in connection with minimum

E:levation and range. The second class of dead space is usually under the

descending branch of the trajectory, and must be -determined separately.

303. Accurate information as to minimum elevation, minimum range, and

dead space is of the highest importance to the artilleryman. The executive

and gunner must know the minimum elevation at which they may lay the

gun~, but need not know the minimum range, except so far as the term

"range" may be applied to the range scale setting. The battery commander

must know both the minimum range and the minimum elevation, because he

must know both the short limits of fire on the ground and the elevations tobe given the guns for targets at those limits. Higher commanders must

I know the minimum ranges and the boundaries of all other dead areas for

reference in assigning targets to batteries.

In an open warfare situation, the minimum elevation and range are

determined immediately on occupation of a position by measurements made

On the ground (F. A. Drill Regulations Par. 1168-1176; Art. Firing, Par.

56-58). Dead space of the first class is determined in connection with the

Process. Dead space of the second class cannot be determined without a map,

Unless the ranges, elevations, and slopes of protected enemy terrain are

accurately known from previous reconnaissance.

In a stabilized situation, as soon as the location of the guns has been

determined, and often' before the actual occupation of the position, all this

information is determined from the map, and tables and charts are pre-

Dared showing it in detail, for the use of the various commanders.

304. Every fixed obstruction of any considerable size which may stop

Or divert the passage of a projectile or cause it to explode is taken into con-

Sideration in determining minimum elevation" minimum range, and dead

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~pace. Thus trees and buildings may be obstructions, as well as hills and

ridges. Tables and charts should show the nature of the obstruction by

notation or by some graphical device. It is assumed to be ground unlessotherwise noted.

A. STEPS Of' CALCULATION ..

HETEIUIINATIOX OF l\1II\"BIUl\fELEVATION AND RANGE.

305. In a stabilized situation a table should be prepared showing the

minimum elevation for each gun for at least every 200 mils of the sector

from the right limit to the left limit. If the covering crest is very irregular,

closer intervals must be taken. Minimum range is determined at the same

time. It may be recorded in special columns in the minimum elevation table

or in a separate table, and it will also be plotted on the dead space chart.

Separate tables must be made for each different projectile, charge, and fuso

wherever there is an appreciable difference in the trajectory.

The object of any calculation of minimum elevation and range is,first, to find the minimum elevation to clear the crest, and then to find a

point on the ground be~Yond, such that' the quadrant elevation required to

strike it is equal to the minimum elevation. This is the actual point of fall

for the minimum elevation. Methods differ in their details, but all are based,

!'ubstantially on the above principles. The following is the usual procedure. ~,

range.

306. 1. Determine th" minimum elevation in angular measure (mils or

degrees and minutes, etc.) to clear the crest as follows: Find from the

range table the elevation for the range to the crest, and add to this the

f;ite of the crest, calculated from the map. This is the quadrant elevation

for the crest. If the guns are close to the ('rest (within 300 yards with

the French 75, n~rmal charge), the drop in the trajectory is negligible, and

the site may be taken as the minimum elevation. The minimum elevation

Ehould be recorded in the table in angular measure as calculated, and the

corresponding range Betting (not map range), in yards or meters should alsobe entered if a range scale is used on the guns.

2. Find from the range table the map range corresponding to the

minimum elevation. This gives the range to the horizontal point of fall,

whert> the projectile would strike if the ground were level with the guns.Call this the first trial range.

3. Find from the map the altitude of the ground at the first trial

If it is the same as the altitude of the guns, the trial range is the J"

actual minimum range. (Example 1.)

If it is higher than the guns, the actual minimum range is short ofthe' first trial range. (Example 2.)

If it is lower than the guns, the actual minimum range is beyond thefirst trial range.

4. Where the altitude of the ground at the first trial range has

been found to be different from that of the guns, a further calculation is

necessary to determine the actual minimum range. In such calculations two _

things must be taken into consideration: first, the general altitude of the..

ground .t first trial range; second, the form of the ground, whether level'l

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uniformly sloping, or irregular. The methods of calculating under different

circumstances will now be taken up in detail.

B. EFFECT OF GROUND FORMS.

(1) Level Terrain.

307. With the ground at first trial range level, or approximately so, (al-

titude either higher or lower than guns) find the actual minimum range as

follows:On the map select a second trial point, the range to which is de-

termined by subtracting algebraically the site of the first trial point from the

minimum elevation, and taking from the range table the map range corres-

ponding to the resultant elevation. The second trial point is the minimum

range if the quadrant elevation to hit this point is equal to the minimum

elevation. (Example 2).If it is not equal to the minimum elevation find the difference be-

tween the two elevations and make a further range change in the proper

<lirection equal. to the range value of this difference. The second range

change wiII usually give the actual minimum range, but it should be tested

by its quadrant elevation, and a still further change made if necessary. .

(2) Irregular Terrain.

308. With the ground at first trial l'ange sloping or irregular, (the gen-

eral average altitude being either higher or lower than guns) the actualminimum range cannot be found by a range change corresponding to the val-

ue of the site, because the site of the ground at the new range would not be

the same as at the first trial range where the site was calculated. The

quadrant elevation of any point depends on two things, range and site. Both

are changed when the l'ange is changed on irregular or sloping ground.

lienee the effect of both must be taken into consideration in calculations on

such ground. Proceed as follows. Example 3: .

Make a l'ange change of some convenient even amount, say 50 or 100

yards, in the proper direction. Call this new range the second trial range.

Calculate the quadrant elevation to hit the ground at this range. If it is equal

to the minimum elevation, accept the range as the actual minimum range.

If the quadrant elevatio~ to hit the second trial point differs from'

the minimum elevation, the actual minimum range will be found between the

first and second trial points when the quadrant elevation of these points

differs from the minimum elevation in an opposite sense. (See (e) Example

3).When they differ f'rom the minimum elevation in the same sense, the

actual minimum range will lie beyond the second trial point in the direction

first trial point-second trial point. (See (d) Example 3).

It is rarely possible that the quadrant elevation of the first or even

the second or. third trial point will be exactly equal to'the minimum elevation, .

therefore if one trial point is short (over) of the minimum range select an-

other trial point at some convenient range change, say 50 or 100 yards, that is

lover (short) the minimum range. By narrowing the bracket thus obtained,

the point of fall for the minimum elevation may be determined as accurately

as is desired. (Example 3):

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7.4 'II

40 'It

The degree of refinement to which calculations should be carried

depends on the accuracy of the map, the accuracy of the measurements and

the least setting of the guns. For practical purposes within 25 ~!ards is con-sidered sUfficiently accurate.

(3) Effect Of Slopes.

309. In making range changes on slopes, it should always be remembered

that if the ground at the point of fall slopes upward from the guns (opposite

to the trajectory), a smaller range change will be required to make up fi

given difference in elevation than if the ground is level, because the change

in site effects the elevation in the same sense as the range change. Thas is

an Upward slope works with the range change in changing the quadrant

(.levation. If the ground slopes downward from the guns at the point of

fall (in the same direction as the trajectory), a greater range change will

be required than if the ground is level, because the change in site affects

the elevation in the opposite sense from the range change. That is, a down-ward slope works against the range change in changing the quadrant ele-

vation. These statements are true whether the general altitude of the ground

is higher or lower than the guns, and whether the range change is madeforward or backward.

Type Problems.

310. Following are typical examples of minimum elevation andI'ange calculations.

Example 1.

Point of Fall on Level 'Vith Guns.

75mm. gun, H. E. Shell. MK. IV, Fuse MK. III (Long),

Range to crest 500 yards. Altitude of guns at muzzle, 400 feet.Altitude of crest 460 feet.

(a) Elevation for range of crest, 500 yds.

(from range table)

60 20Site of crest = 20 yds.

3 5

Minimum elevation (quadrant elevation of crest) 47.4 111

(b) Corresponding horizontal range (from range table

by interpolation) 2423 yds.

Layoff this range on the map. It is seen that the ground

at the point of fall has an altitude of 400 feet, the same as the

guns. The actual minimum range is therefore 2423 yards.

Example 2.

311. Point of fall on level ground higher (lower) than guns.

Other data same as example 1.

(a) Minimum elevation, same as example 1, 4i.4 'II

(b) Corresponding horizontal range, 1st trial range, 2423 yds.

(c) From the map altitude of the ground at the first

trial range is seen to be 430 feet, or ten yards above the guns.

S. h' . 10Ite at t IS pomt =+4.1 'II.

2.42

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47.4 'f£ (minimum elevation) minus 4.1 * (Site of First trial

Point) 43.3 1fr

(d) Corresponding horizontal range 2265 yds.

~, Layoff this second trial range on the map. This is minImUm

range if the quadrant elevation to hit the ground at this point is equal to

47.4 m, (the minimum elevation). If it differs from the minimum elevation,

proceed as in example 3.

Example 3.

312. Point of fall on irreg'lllar terrain, the average altitude of which

differs from that of the guns.

Other data same as example l.

(a) l\1inimum elevation; same as example. 1. 47.4 1ft-(b) Corresponding horizontal range, 1st trial range, 2423 yds.

(c) From the map the altitude of the ground at the first trial range

is seen to be 430 feet, or ten yards above the guns. Therefore the quadrant

elevation of the first trial point is greater than the minimum elevation and

the actual minimum range will be short of the first trial range.

(d) Let us try a point 100 yds short.

Elevation for range 2323 yds (2423-100) = 44.8 1ft

From the map the site of the ground at the second trialrange is found to be = 3.5 'fe

= 42.2 1fl

= 4 'fl

Quadrant elevation to hit ground at second trial range, 48.3 1/1

As 48.3 is greater than the minimum elevation it is possible to hit the

second trial point, and the actual minimum range will be found short of the

second trial point.(e) Try a third trial range 100 yds less than the second.

Elevation for range 2223

Site of ground at third trial range

== 43.5 1ft

4.1 *

Quadrant elevation to hit ground at third trial range = 46.2 'fl

As this is less than the minimum elevation it is not possible to hit

the ground at the third trial range, and a fourth trial range must be

selected at a greater range than the third.

(f) Try 50 yards more.

Elevation for range 2273

Site of ground at fourth trial range

Quadrant elevation to hit ground at fourth trial range = 47.6 1!1

As this is greater than the minimum elevation it is possible to hit the

Rround at the fourth trial range. Therefore the actual minimum range must

lie somewhere between' 2223 yds., and 2273 yds. Take the middle of the

bracket and call 2248 yds., the minimum range. In this case the difference

between the actual minimum range and the assumed minimum range of 2248

yards cannot exceed 25 yards, which is accurate enough for all practical

. Purposes. A greater degree' of refinement may be obtained by narrowing

the bracket to 25 yards, or smaller if desired.

~137-

=

.



Determination of Dead Space.

313. Dead Space of the second class, under the descending branch of the

trajectory, begins at the point at or near the top of the obstruction where

the slope of the ground first commences to be steeper than the slope of the

fall. This is called the grazing point, where the projectile will just graze

and go over. The dead space extends to the point of fall of the projectile on

the ground below. Every point beyond the grazing point, the quadrant eleva-

tion of which is less than the quadrant elevation of the grazing point isdead space. (See (b) Example 4).

Determination of the Grazing Point.

314. To determine' the grazing point, select on the' map a trial grazing

point, at or beyond the top of the obstruction, where the steepest part of the

slope begins. Calculate the quadrant elevation of this trial grazing point.

The test whether this is the grazing point, calculate the quadrantelevation of points both short and over the first trial point. The actual graz-

ing point is the point which requires the greatest quadrant elevation for

the projectile to clear. The distance that the other trial points arc selected

from the first trial point depends on the slope of the ground in the vicinityof the first trial point.

When the slope is steep, the trial point may be taken every 50 yards,on a gradual slope 100 or 200 yards. . .

Having obtained a bracket on the grazing point, that is when a point jof greater quadrant elevation has been enclosed by two trial points of less ,

<juadrant elevation, one short of and one beyond the point of greater elE!va-,

tion, the actual grazing point may be located r..s accurately as is desired bynarrowing the bracket, (See (d) Example ,4).

Type PrOblem.

315. The fOllowing is a typical example of locating the grazing point.

Example 4.

75 mm gun, H. E. Shell. MK. IV, Fuse MK III (Long), Range to first trial

grazing point 3000 yard3. Altitude of guns at muzzle, 400 feet. Altitude of

first triaI grazing point 445 feet. (The highest point on the crest in ques-tion).

(a) Elevation for range of first trial point, 3000 yds., (from

range table) 64.2 1/t

Site of crest at first point,45 15

:: 15 ~"ds. 5 1ft3 3

Quadrant Elevation of first' trial graze point :: 69.2 1/t

(b) Select a second trial grazing point 100 yards beyond the first.

From the map the altittude of the ground at this point is found to be '415eet.

-138-

- - _



Elevation for range of second tr"ial point, 3100 yards = 67.2 1il

Site of crest at second trial point,

15 5'- = 5 yds.

3 . . . 3.1 1.6 1/l.Quadrant Elevation of second trial grazing point. = 68.8 1/1

As this is .5 * less than the quadrant elevation of the first trial point, it is

impossible to hit the ground at the second trial point, therefore the second

trial point is in dead space, and is not a grazing point.

(c) Select a third trial grazing point halfway between the first and

! second. Altitude of the ground at this point is found to be 440 feet.

Elevation for range of trial point, 3050 yards 65.7 1/1

Site of crest at 3rd trial point,40 . 13.3_ == 13.3 yds. == 4.3 1it

3 2.05

Quadrant Elevation of third trial grazing point . = 70.0 1/1

As this is greater than the' quadrant elevation of the first trial

Point, the first. trial point. is not a grazing point, as it is possible for a

projectile to pass over it and hit the third trial point.

(d) Test the quadrant elevation of points 25 yds., short and 25 yds.,over the third trial point. A point 25 yds. over is found to have a quadrant

elevation of 69 1/1. A point 25 yds., short has a quadrant elevation of 70.4 1/1.

Therefore the actual graze point is located 25 yards' short of the

third trial point. If greater accuracy is desired this bracket of 25 yards may

be narrowed.

316. The far limit of dead space of the second class is found in exactly

the same manner as is the minimum range to clear the mass or mask im-

mediately in front of the battery. In Example 4 (d) above dead space of the ~,

second class begins at the grazing point and extends to a point on the ground

beyond, such that the quadrant elevation required to strjke this point is equal

to the minimum elevation to clear the crest, which in this case is the quadrant

elevation of the grazing point or 70.4 mils.

Calculation Method 'Vith Special Chart.

. 317. The work of calculating the minimum elevation, grazing point, and

minimum range may be greatly simplified and much time and labor savedby the use of a special chart. By means of this chart it is possible' to read

directly the quadrant elevation required to hit a point when the map range

and difference in altitude between the gun and point are known. Also the map

range may be found corresponding to any quadrant elevation.

318. To prepare such chart proceed as follows:

On a piece of 'cross' section paper rule two vertical lines about eight

inches apart. The exact distance between these lines is not important, four

inches or more may be used, but the farther the lines are apart the closerthe chart may be interpolated.

-

=

= --

-



f.

-.-.

-'f, . _. ..

-'-;.~+--

I....~ i-

II

II

i.5

I

+-

..•-,:-

.1,

-, 1:- .,.-

.t- 12 -

-;-1--''1---- '.f1--. -:-!-

,'f- I .~'I ~,

r 'l~'1-- ~jJi;,11 -L LJi.- p

-+ r ,1 -t'-.: + ';;i1 -++1---+ -t !~'- I.:IT -' .-+~"1- L-. .::::-!-

I') 'f 'r.<

',-~Hc +-<+:.. 'r:>iJij,

'r .:+- "-,'! .•

'L~L .... ".'1":

:.. t- ~ , , .. I- --I-i-

t ~--'''.I-l;;, f- +- + ,+ - - ~'f-- I-Y -~'lirJ..

J-i- --+........ r-l-- ~i-- r-+- .;.. -h-(~f~ +- . ~-'v1 ~R'- I~~_

I iP~ -1 ...... +-.+ 1+I=";I"rJ-- +. ~-H-I'1t;;~lL in

I i- rL .. ;- ---t- .: ~il- H-~~j".,~ , . hr.::' : t:~. +. -t-' r

I t r~ 'k, 1- -t. + j-.1 rt +H-- l' rt Lt ._ .j_

f f- lit'~ ,--1-.-.~ -1- -t-H- --~f-t i++. -t- rf ~i-

,'t-- tit, H+~ ..+ ~ -t- +H -'H'I-'f-

I r-'~'~~ +~H+ f.-',i. --t- .t--+ H+ ,+[r +-) -f' ~+._ f +---f-f-' .+- -+ _

!i- ~. 1- + -f ;- + i:- t-- '+ i- +., __b'

I' --, i.t 1'- t + H- T- -+ + + i Ij- ,;,j_ ,I~ ... h

l!- rt:. t-.i t t j ....+ -+- f- __ .

i j-!;;; 4-. I -1- .. t- ;- -l-- '-~f-r -; .. ..L. k .•

t.. f.-t..- : ; l+'-!-i+.4 -t - '.I-j

I f- r 'H- t~-+H + E1t1t~12:t +r j,; II.~ -~-'- -~H.H++H ~, _

~ - -ir r- :tl -+- ,-r-~- :-t+f -+1-1+ I

r t- -t T +Ji:.t "': +1++-- +t'1"1,..+ --H+H- I : +++~:

! :) J" !--i-++ -+ '7-~H-- -t-H----8'. :'t.-

F--t-+- -t- t- -, J •.q_~: -n + f4-,,'L.rl' "I I ~4'L- b.L ..i.J I I .;:-J--.L' 1,,1,

Plate XII.

-140--

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1

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~

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---

~

--

1

-- . ~~ -

-~-

--

~ __

J •.

--

~ -I __ _

~ ~

j ~





Use of the Chart.

323. The main advantage of the chart lies in the fact that it is

Possible to read directly the quadrant elevation necessary to hit or clear any

Point when its map range and elevation are known without the necessity

of calculating the site, or taking the elevation from the range table.'

324. To find the quadrant elevatio'n of any point:

Take from the map the range and difference in altitude between the

. gun and the point in question. Place a straight edge on the chart in such a

manner that it will pass through the Points corresponding to this range and

difference in altitude. When the straight edge cuts Line "B" will be foundthe desired quadrant elevation.

Example VI.

325. To find the quadrant elevation of a point.

Range to crest 500 yards. Altitude of guns 400 feet. Altitude of<-rest 460 feet. The crest is therefore 60 feet above the guns.

Place a straight edge through plus 60 on line "A", and through 500

on range curve, and read 47+ mils Where the straight edge cuts line B.

This is the Same result as was obtained in Example 1 by calculating tbe siteand taking the elevation from the range table.

Example VII.

326. Given the minimum elevation to determine the mInImum range.

Point of fall on irregular terrain. Other data same as example l.

(a) To determine f.rst trial range place straight edge through 47.4

mils on line "B", and through zero on line "A", and on range curve read2425 yards.

(b) From the map, the altitude of the l:rround at this range (2423

Yds.) is seen to he 430 feet or 30 feet above the guns. Therefore the actualminimum range will be short of the first trial range.

(c) Try a point 100 yards short.

From the map the elevation of the ground at this point is foundo be 424 feet.

Place straight edge through plus 24 on line "A" and 2325 on rangecurve and read 48.5 mils on line "B".

(d) Proceed as in example 3 until the minimum range has beenlocated I1S aCcurately as is desired.

B. DEAD SPACE CHARTS.

327. The prohlem in determining dead space is to find the grazing point

and the point of fan, near and far limits, along several rays drawn on

the map from the gun Position, through each obstruction. The first ray is

drawn through the steepest slope of a ridge or through the highest point of

a vertical obstruction, such as trees or bUildings, and the limits of the dead

Space are determined and marked on this ray. Other rays are then drawn

successively on either side of the first, and the dead space is determined for

each, until a ray is found on each side where there is no dead space. The

more irregular the ground, the closer must be the rays. Some slopes will

require rays every ten mils; some only every hundred. The corresponding

points marked on the different rays are. then connected with a smooth

-142-

'"



~urve, completing the boundary of the dead area, Plate 13. The

irea should be hatched lightly with a colored pencil. Dead space

~aused by ground may be hatched in red, that caused by trees in

Penci1.Dead space caused by ground may be hatched in red, that by trees in

freen, that caused by buildings or other constructions in blue. The hatchings

or diff~rent kinds of obstructions should run in different directions so that

they. can be distinguished in case they overlap. If no colored pencils are

~vailable the direction of the hatching will be sufficient distinction. \Vhere

ead spaces for different changes are shown on the same chart, the area

or the greater charge will always cover and exceed the area for the lesser

eharge. The two areas may be distinguished by making all the hatchings for

~ne charge heavier, by double-line or broken-line hatching, or by cross

atching.

A legend explaining the hatchings and any other graphical devices

sed, and showing the charges, p'rojectiles, etc., for which the dead spaces

.1)ATH~Y:X=

. NOP\MAL' CHMGE. tz2Z8

. ~r:DV(tD(tiAI\CjE' WillD

Plate 13.

'Were determined, always should be put on the chart. The chart is usually

~ade on transparent paper laid over the map, but may be made on the map

• Self. If not made on the map reference should be made to the map used.

-143-

~=

"



CHAPTER XV •

.MAP PROJECTIONS.

DEFI:\'ITIO~.

328. As has been' stated elsewhere, a map is a representation, to scale, 0

a certain portion of the earth's ~urface. Its purpose is to afford information

Therefore maps are of varied sorts depending on the information desired

Moreover a map usua'lly is a plane or flat surface while the surface of th!earth is in the shape of a spheroid. i

It will be seen, therefore, that certain difficulties are met by thecartographer, in the course of map making, when projecting a certain portio

Jlof the earth's surface, reduced in scale, upon a 'flat sheet of paper. The

means by which this is done is called projection. There are many types of

projection involving different formulae in spherical trigonometry. It is not

the purpose of this text to work out these formulae but rather to show the

application of the various methods and to point out the value of each forcertain definite uses. ,

The cartographer will choose the method of projection which willleast affect the accuracy of the work in hand'.

KI~DS OF PROJECTION.

A. MERCATOR'S PROJECTION. f

329. The oldest form of projectio~ is the Mercator Projection, and is em'

plo)'ed in making Navigator's charts. In this method the surface of the

earth is projected outward to the surface of an -enclosing cylinder which is

tangent to the 'globe at the eqnator. Because the line on the cylinder and

the globe coincide at the equator, distances along the equator on a map made

MERCATOR-S pgOJEITION

40 cO 0 ZO,

,~

R.c

-- I

'" I11'17':.

I I)

I

II/

/, I /

"" ,,--, ""'-- CYUNOC.... ~",-, ....::.... _... .,TA}-{~E:NT MER.DIAN Of LCNq TVDE. !

TO qLOBE: AT EQVATOR.

Fig. 92.

with this projection are exact, but, beginning i~mediately north and sout?,

a distortion is encountered as the poles are approached. At the poles thIS

is the greatest, for the pole has been projected outward in all directionS

'

~ ~ -

~-



Until it becomes a line, represented by the circumference of the top of the

cYlinder, and is as great as the equator itself.

Thus the Mercator projection creates noticeable distortion in maps

of North America and Asia.. The navigator however is concerned only with the latitude and long-

~tude and therefore can use the projection above described. This would note satisfactory for the person who was measuring land areas, nor for the

artilleryman who wishes to measure angles and distances with precision.

Figure 92, above, shows the projection of the globe outward to the

~urf~e of the cylinder; also the map formed when the cylinder is slit

OWnone side and unrolled.

POLYHEIl\AL PROJECTiON

M[RIDIAN.S OF lON~ITVDE.

Fig. 93.

B. POLYHEDRAL PROJECTION.

~30. The Polyhedral is a common form of protection which may be used

In mapping siege areas and cities, since only limited areas are involved. Inthis system each small area mapped is represented by an isosceles trapezoid.

the parallel sides of which are

equal in length to the arcs of the

corresponding parallels, while the

oblique ones are equal to the arcs

of the meridians comprised be-

tween these parallels.

The accurate assembling of

these small areas into a largerwhole is impossible. It only can

be done approximately by the play

of the paper, see fig. 93.

C. CONIC PROJECTIONS.

331. The most common form of projection is the Conic of which there are

various types. In this, a cone is passed tangent to the surface of the globe

and t.he surface underneath the cone is projected outward to the surface of

the cone. At the point where the cone is tangent to the globe, the distanceso~ the map will correspond to those on the globe. Elsewhere the distortion

:"111increase as the line of tangency is left behind. This distortion is min-

Imized by the application of certain mathematical formulae. The formula

~o be applied will.vary,. according to the purpose to which the map will

e applied. Figure 94 shows the cone tangent to the globe, also the same

cone a,fter being split down one side and flattened out to form a map.

D. POLYCONIC PROJECTION.

332. The Polyconic Projection is a modification of the conic projection. It .~as devised by Ferdinand Hassler, the first superintendent of the U. S.

Oast and Geodetic Survey, and has been applied to maps of the United

.;)tates.

h. In it a series of cones has been passed tangent to the globe, the cones

aVIng their apexes on the prolongation of the axis of the earth. Segments

?f the cones, each with its central parallel, when unrolled, form a map which

IS satisfactory along a north and south area in the vicinity of the common

tneridian of origin; while the distortion east and west of the meridian in-

-145-

~ '



creases with the distance from it, due to the increasing divergence of th

~everal segments. Such a map causes an error as great as 6~% on t

Pacific Coast of the United States, while a map 'of the United States on th

PROJECTION

Fig 94.

Lambert projection wou"ld show. a maximum distortion north and south of

only 2'!c. The figure on the left, fig. 95, shows the centres (K, KI, 'K2,

K3) of circles, on the projection, that represent the corresponding parallels

on the earth. The figure 0"'\ the right shows the distortion at the, outermeridian due to the varying radii of the circles in the polyconic develop'ment.

POlYCO!\JIC

PROJ EeTION

'K :K..t " " .. " " "~. I I

• I I

. oK. 'K.

• I

I

Fig. 95.

E. BONNE PROJECTION.

333. British and Belgian battle maps in the recent war were made using

the so-called Bonne Projection, another of the conic systems. The origin of

this projection for these maps was Brussels. The earlier French battle maps

were also made using this projection taking the'town of Aurillac, Lat. 450

North, to the south of Paris, on the Paris meridian, as the origin.

In this projection, the meridian through the origin is a straight line.

All other meridians are curves, the curvature incr~ases with the difference

in longitude. The parallels are represented b'y concentric circles, with centreSat, S, north of the pole, p, the distance between th.e concentric circles being'

o



equal to the lengths of the arcs of the. meridians upon the globe. See fig.

96. In this projection areas are preserved near the initial parallel and mer-

idian; angles and distances along the initial parallel and meridian are pre-

served in their exact relation; but departure from them brings distortions

which, at the edges of the map of France, reach a value of 18' for angles and

1/379 for lengths. These distortions are too great for use in computations

for artillery fire.

s

BONNE PROJECTIONp

/' .

DISTANCE: BETWEEN pARALLEL"(QUAL TO ACTL'AL DI,srANCE oN qLOBE

Fig. 96.

BONNE: PROJ[CTION Of HEMISPHERE

O(lvG.lopment of cone taM<;)ent o.l"n9 pa.ralla.{4SoN

.'

F. LAMBERT PROJECTION.

334. Because all projections, heretofor: described, admitted too great a I'

distortion in angles and linear measurements, the French were forced to re-

-147-

-

.



IJ.. t

'surrect another projection at the beginning of the World War. The Lam.~

bert Conformal Conic Projection was found to be satisfactory for artillery.

purposes due to the fact that angular and linear distortions were practically,

negligible in any of the mapped areas likely to be used by artillery of any Icalibre. ", ... i

This projection was evolved by JOhann Heinrich Lambert, an Alsa- f',tian' (1728-1777). Lambert was a noted cartographer and mathematician who:

worked out another projection which bears his name. The one used in French ~<

battle J1'1apsis known as the Lambert Conformal Conic Projection. •

For a base map covering a zone 500 kilometers in wtdth, or 250 kiI-,

ometers on either side of the parallel of origin, 490 30' (=55 grades) north

latitude, this projection shows a degree of precision which is unique, and,

which answers every requirement as to orientation, as to direction and dis-;

tance, and quadrillage (system of kilometric squares). It is admirably'

adapted to a region of predominating east and west dimensions, hence with;

it, all the northeastern region of France, as well as Belgium and part of

Germany, can be presented on one map. It can be extended ,east and

west as far as desired, the projeceion remaining conformal throughout.

The angular distortion is so small as to be negligible and the linear

distortion is no more than .05 per cent (1 meter in 2000 meters) which is

nearly negligible. It is to be borne in mind however that this is only true'

within the base map, north and south limits of which, are indicated above.

. In this conic projection, the cone is secant to the globe instead of

being tangent to it; that is, the cone cuts the globe in two places, see fig. 98~

These two places at which the cone cuts the spheroid or globe are,

for the French battle map, along the 53 and 57 grace parallels as shown in

the figure. The O1'igin of the projection is taken at 6 grades east of Paris

(called -6 grades longitude, since longitude east of Paris is minus and that

west is plus), and at 55 grades north latitude. Meridians are straight lines

,perpendicular to the arcs representing the parallels, see fig. 98.

Obviously along the parallels of 53 and 57 north latitude, distances

on the map will correspond to those on the globe. The arc or sector of the

globe between these parallels is somewhat distorted in flattening it down

to the surface of the cone" Two formulae may be used in caring for this;

distortion, one ,of which is exact while the other is approximate. (See "Man- .

u'al for Orientation Officer", "W. D. Doc. No. 648", also "The Lambert Con-

formal Conic Projection" by Deetz, Special publication No. 47, gOY:printingoffice.) .

335. , In summing up, the L~mbert conformal conic projection preserves

angle3 and distance; with negHgible distortion within a belt whose north'

and south dimension is limited to the battle area of France and Belgium, but

whose east and west dimension is not. This is the only projection "as yet.

devised giving these relation of the earth's surface on a plane surface or

map in sufficient exactness for use in modern artillery warfare. Such a

projection is well suited for' mapping the United States where the greatest.dimension is east and west. .

Below is appended a chart showing the Lambert conformal conic pro-jection, .a~ applied by the French in the recent war, to France, Belgium and

'

~

'

'

~





rj German) •. See Plate XIV. It will be noted that a portion of the grid sys-

.~ tem is also shown near its origin (which coincides with the origin 'of the pro-

.:1 jection). In the (.hart the grid is not shown to scale, the lines being ap-;

LAM5ERT'.s CONfORMALCONIC PROJECTION.

Fig. 98.

proximately 4 kilometers apart in place of 1 kilometer.

This grid system is discussed in Chapter XVI.

-149-

~





.~eans of the subdivisions on that X line made by the intersection of the Y

Ines. Similarly distances on any Y line from the 0 of the system are re-

~r~ed by means of the subdivisions on that Y line made by the intersecting

. lInes. A point is always designated by taking the value (XY) of the

~outhwest corner of a kilometric square, then reading to the right or east

rorn that point, thence up or north to the point itself. Complete coordi-nates are given in six figures for each axis, the X always being given first,

See fig. 99.

..

~.

X-LINES

I

POINT-AX-50,,200

Y-2.95300

0'000o 0' C 0

~g(3~U")

to lO It')

PORTION Of LAMBERT GRID

ADJACENT TO lTj ORIGIN

Y-L'NE.s~

0

0

0

0,0RIGI N

00

00 A

a .~-00

00-

. - '""0 ,.... 0 0 0 0

30400

30300

30200

30100

3000

2990

2980

?'970

2960

g g a0" 0 0

0' 0 0

V" lC) 10

Fig. 99.

C. REDUCED HECTOMETRIC COORDINATES.

~O . For convenience in designating targets, a system of reduced hecto-

etric . coordinates is employed. This system is sufficiently accurate for

~~rposes of identification and has the advantage of reducing the number of

19ures which must be sent over a wire, or which must be sent down from

an airplane.

d Since heetometric coordinate means coordinates expressed in hun-ureds of meters, the heetometric coordinates of the point A in the above fig-

re 'Would be; X=5022, Y=2983. --1 But even this abbreviation calls for the use of more digits than

I;Cessary; and the above may be further reduced as follows. A glance at any

~heth~ ordinary battle maps will show that there will be no duplication of

1 fIgures in the hundreds of thousand's and the tens of thousand's

(,'0 urnns on anyone sheet, hence these digits may be dropped. Further, there

-151-



100

Fig. 100

will be no duplication of the digit in the thousand's column nearer th'

10,000 meters,' and this is a di3tance great enough that it should cause

('onfusion. Thus, in the above figure, it is seen that the lowest figure {

the Y value.is 296,000, the figure 6 being the value in the thousand's colum

There is no duplication of the figure 6 for the Y value in the limit shov.1

the other digits in the thousands column being 7, 8, 9, 0, 1, 2, 3, 4. Similar

there is no duplication of the digits in the thousand's column for the X w

ues found below nearer than 10,000 meters, the figures running 5, 6, 7,9, 0, 1, 2, 3, 4, 5.

Therefore, if the above digits are used as the identification nUll

bers of a set of coordinates, the point can be recognized just as readi

as if the complete coordinates were used (within the limits of the sing

sheet). The hectometric coordinates for the above point, A, reduced in th

manner, will change from X= 5022 and Y=2983. to X=22 and Y=83.

However the reduced hectometric coordinates will not be separate-

as to X and Y values but will be written thus: 2283.

(1.) Errors Introduced.

341. As indicated above the use of hectometric coordinates brings int

being a certain amount of error, since the point is read to the nearest hur.

dred meter subdivision. The' maximum error so introduced is 71 meter.

which is within the dispersion of the ordinary field piece. An error of thi.

size Occurs only when the point in question is located at the center of l

hundred meter square, or in other words, when the point is 50 meters re

moved from both axes. The error introduced then is ~50~ +-f>O~:= 71, se

fig. 100, in which P is the true position of the point and P' is the point aCcording to its hectometric coordinates.

For actual map firing the coordinates must be readdown to the last meter.

342. In some areas of France both the Lambert and the

Bonne projection maps are used, with grids printed upon

them, each using the origin of the projection as the orig- C

in of the grid. These are cases where complete surveys

for the Lambert projection have not been completed,

hence an allowance must be made, in using the grids,

for the joining of maps of the two systems.

D. PLOTTING POINTS.

343. The above discussion has referred to reading the coordinates of 8

point. In plotting points to the nearest meter great care must be given to the

plotting with a metric scale, or scale which is divided into 100 units of anYsort. The X should be measured carefully in two places on the grid, at least

one grid square apart and a line drawn joining the two points.

Similarly it is best to measure along the Y lines in two places, at

least one square apart and' join these two points with a line. The inter-

section of the two lines will determine the point which is to be plotted, seefig. 101. .

344. For example, in the figure below it is desired to plot point B the CO'

ordinates of which are X=484,247,Y=307,751. Measure 247 meters ove!

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~

~



trom the 484,000 line at (1) and agai~ at (2). Draw a fine light line between

(1) and (2) thus establishing the X coordinate of the point (B). Similarly

~easure 751 meters from the 307,000 line upward, and plot (~) and (~). The

~ntersection of the lines (1)-(2) and (3)-(~) will determine B. Outline the in-

. ersection by heavy lines in soft pencil, as shown in the figure, leaving the

:~tual intersection untouched so that the point may be pricked with' a

~rp needle. .

PLOTTING A POINT

308000Q-

0\

(3) ._~ ..

.a..,

....._! J2.. ._. - _. - ... - ..X(4)I

306000

8C")

co'\t

ogIr)

co"\t

Fig. 101.

h Note: In drawing the lines a hard pencil sharpened to a chisel edge

B ould be used.

3 CONVERGENCE OF MEIUDIANS.

45. On most battle maps based on the Lambert projection there are

al'l'~Ws indicating the relation ~f magnetic north and true north with the Y

iLambert or Grid) north. Since all direction on firing charts is reckoned

t~orn Y north, such direction being known as the Y azimuth of the point,

e relation between grid north and true north or between grid north and

1l1agnetic north must be known. In case the map does not indicate this, use

1l1ust be made of the formula AD=(M-Mo) sin Lo, in which AD is the

:ng1e of convergence (sometimes called angle of divergence); M is the longi-

.ude of the point in question; Mo is the longitude of the origin of the pro-

Jection (likewise of the grid since they are identical for French battle maps),

an? Lo is the latitude of the origin of the projection (likewise that of the

. ~rl~). Mo is -6 grades (being east of Paris), and Lo is 55 grades north

atItude as discussed in Chapter XV on projections. The formula then be-

-153-

~



tomes, Angles of Convergence= (M-(-6» sin 55 grades. The sine of 6

grades is .76. The formula in its final form, then is AD=(M+6) . 76, whi(

~hould be noted in all artillery field notebooks. A simple discussion of an

a figure showing this relation between true north and grid north, as aboexpressed, is appropriate here.

346. By a theorem of spherical trigonometry, the qivergence of the me}dians from the north pole to the equator is a function of the sine of Uangle of latitude.

Fig. 102.

PARALLEL

'- Of ~5.9'\

, ANGLE.5 OFCONVER<qtNa1\

90"=100.9'

rQVATOR

For example, in the left hand part of

fig. 102 are shown two meridians converging at

the poles. Figure 103 portrays a development

of these same meridians showing that the an-

gIe between them is greatest at the pole. At the

pole the angle of latitude is 90° or 100 grades

(see right hand portion of fig. 102) and the

sine of 100 grades=l, its greatest value.However at the equator the meridians

are parallel. At the equator the angle of lati-

tude is 0 and the sine of this angle is O. Hence

the meridians, being parallel, form no angle.

The amount of the angles formed by meridians

may thus be seen to be a function of the sine

of the latitude at any given parallel, such as 55

grades, the one used in the formula.

347. The divergence of the true north andgrid north is identical with that for meridians,

since the Y axis coincides with the meridian of

origin. This divergence, then, is the measure of

some definite angle; that is, the angle between DEVr.LOPMf.NT OF

the meridian of origin (-6 grades), and the Tt-IRE.E. MtRID/AN.:>

point in question, M. Fig. 103.

Assume for example, that the point on the map in q'lestion is 3 grades

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-



east of Paris. Applying the formula, Ad=(-3+6) .76=3X.76=2.28 grades,

See fig. '"104.

ANGLE" or CONVER6[NCE

39 4«3 5~ 69

303

30,

301

30qooo

299

ME:

---ORIGIN OF' GRID

AND PROJ eTloN

298

•

('t')

C-\A.

I

--.Jooa-

Fig. 104.

3 Y-AZIMUTH. ,

48, A direction from grid north is called Y-azimuth and is measured in

a clockwise direction from the Y line. This is done by means of a protractor,!lee fjg, 105.

Y-AzIMVTH

/Y-LlN(S~

Fig. 105.

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CHAPTER XVII.

USE OF GRID IN l\IAP READING AND l\fAP FIRING.'

ADVANTAGES OF THE GRID.

349. As indicated in the preceding chapter, the grid offers a precise at

('onvenient method of designating and locating points on a map or grid shec!

I n addition it also is possible to determine the direction of one point froP

another, or the range from point to' point by comparing the coordinates all':, .'tlaking a few simple mathematical calculations. In all of this work WI

the gridded sheet, the artilleryman, who is to do map firing, should be 1I~

adept. Often he will find that the grid sheet and the rules used are nC;of the standard dimensions, in which case he will have to adopt some one 0'

the expedients indicated below. ;

A. METHOD OF PLOTTING A POINT.

350. (1.) When the Huler Graduatio)ls are Longer Than The DistanC/Ilt>tWt't'n Grids •.

To plot a point P, the coordinates of which are;

X=25,400 Y=55,400.

57,000

56,000

pc'

a' :)5,000

C 0 a0

~' af")

r-'...,C'-'

N

Fig. 106.

Place the zero of the scale on one grid line, 25,000, and the 10 of

multiple of 10 on the adjoining grid line, 26,000, see fig. 106.

Layoff the necessary unit, a'=400. Repeat by holding the ruler j!1

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,

~



same manner but above or below this position. Layoff the same unit, a.

0ln a and a'. This line determines the X-coordinate.

lh . In similar manner lay of~ the Y -coordinate, and c', joining them by

e hne, (}-c'. The point P is determined by the intersection of lines, a-a'

~ndc-e'. Show point as in diagram by drawing four rays with a soft pencil,

~one of which should pass through the point. Prick the point with a fine1eedle:

'1" Note: This method of using intersecting lines should be used for

~l accurate plotting, as it at once discloses any gross errors in the use of

e rule while small errors are averaged together.

3 '(2.) When The Ruler Graduations Are Too Small.

5~. Determine the number of units on the rule that the scale lacks of

l.elng equal to the distan.ce bet~een two adjace~t ~rids. Let this be equal to

Say that the X-coordmate IS 25,400. Then It' IS necessary to allow for

400/1000 of l)=S in laying off, a. This may be done by laying the zero ofhe ruler S distance from the grid before starting measurements, fig. 107, or

else laying the zero on the grid and adding S to 400, fig. 108. The point, p,

l11ustbe determined by the intersection of rays, a-a' and c-c', as in fig. 106,

abOve.

25000

ooo'0N

55000 2.6000lJIVIo

g

o

UIG"-o

oo

Fig. 107. Fig. 108

III Example: Let the point to be plotted be, X=25,400; Y=55,500. To

loot the X,coordinate, let the distance between the grids be equivalent to

00, plus 50 units of the rule. Then 1050 units are equivalent to 1000

~eters or 1 meter is equal to 1050/1000 of one unit. To layoff 400, al-

.owance must be made for the proper portion of the 50 extra units, which

18 equal to 400/1000 of 50 or 20. This may be done either by setting the zero

~f the ruler 20 units from the grid, or else by laying off 400 plus 20 units'1420) with the zero on the grid. The Y-coordinate is established in a sim-

1 ar manner taking into consid<!ration 500/1000 of 50 or 25 units, or 525

'\lnits.

3 B. METHOD OF READ1NG THE COORDINATES OF A POINT.

152. Reading the coordinates of a point is the reverse of plotting a point.

it is essential at all times to keep in mind that the distance between adjoin-

ng grid lines is equal to 1000 meters, and that it is necessary only to find

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f;ome means to interpolate or divide this distance up in the required numberd equal parts.

(1.) When The Rule Is Correctly Scaled.

Lay the zero of the ruler on the grid line and read the units to thl

point. Add these units to the thousands of the grid. For instance, the grid

line on which the zero is laid is marked 35,000, and the number of units to tbl

point from the grid line is equal to 475. Then that complete coordinate woulC

be equal to 35,475. The same applies for the reading of the other coordinate.

(N ote: When the grid is used to 10 times .the scale for which it was

originally intended, then the distance between grid Iines=lOO' meters. ThiS

('ase often arises when using a 1/20,000 grid for a 1/2,000 chart. Mallethe proper allowance in this case).

(2.) \Vhen the Scale Is Too Larg-e.

353. Bring the edge of the ruler opposite the point and at the same tinleturn it so that the 0 and 10 coincide with their respective grids. Read the

number of units and add to the thousands of the grid. If the ruler is toO

mu('h oblique, care must be used to get the exact value, see fig. 106.

(3.) When The Scale Is Too Small.

354. Determine the number' of units on the rule that is equal to the dif,

ference in length between the rule and the distance between grid lines. Let

this distance equal 1, see fig. 108. 1000+1= total number of units betweel1

grids. Let m= the units read from the grid to the point. Then the truCdistance, el, may be expressed as follows: d= [m-;-(lOOO+l)] 1000. Add the

value "d" to the thousands of the grid to the left and this will give one of

the ('omplete coordinates. The other coordin'lte is obtained in a simila1manner.

Bxample: Assume the point "P" lies between the grid lines 25,000

and 26,000; that the distance between the grids is equal to 1000 units of tM

rule +50 units. In other words, there are 1050' units of the rule betweeTl

adjacent grid lines. These 1050 units are equivalent to 1000 meters. As-

sume that from the grid line of 25,000 to the point there are 420 units. Then

420. .the distance in meters would be equal to -X1000, which is equal to 400.

' 1050

Therefore the X-coordinate =25,400. The other coordinate is obtained ina like manner.

(4.) With Hight Angled Rule.

355. A more rapid method for plotting and reading coordinates i5 indicated

in fig. 109. The right angled ruler enables one to read both coordinates at

one operation, but does not give as exact results as the operations des-tribed above.

This method is close enough for reading and plotting abbreviated

hectometric coordinates, also for preparing firing data in some types of maPfiring.

C. PLOTTING DIRECTIONS.

(1.) By Y-Azinwth.

356. The Y-azimuth of a line is the angular distance measured clockwise

-158-



from grid north or the Y-line. Therefore, in order to plot a line, given its .

Y-azimuth, it will be necessary to establish the direction of grid north by

Il.

Fig. 109.

means' of a line through'the point f~om ~hich the direction is determined.

Placing the center of the protractor at this point, with the zero line of. the

protractor in the direction of grid north, layoff the clockwise angle equal

to the Y-azimuth. .

tl

w

19

\0

()

II

=-10 .. ;-

II :6 I

7 I

I

5 I':-- <} :io.OOO,

l.I ,

0- ••..I.I

Il I~

,"':

. ,'-'.

,

(2.) By Coordinates.

357. A line may b~ determined by two points on it; therefore, if the <:,0-

.ordinates of two points are drawn and plotted and these points joined, the

line is then established. Drawing a line through one of the points parallel to

the Y-grid line and measuring the clockwise angle from this line, the Y-

azimuth of the line is determined. Note: If the line between the two points

intersects a Y-line of the grid, ~s is usually the case, the Y-azimuth may beread directly without further work ..

It sometimes ~rises that both points cannot be plotted on the same

grid, because the map distance between the two points is greater than the

size of the gl'idded sheet or map.

358. Take a case when working on a grid with a 1/2,000 R. F. If the

distance between the two points is 250 centimeters and the greatest distance

-159-

~

~



available on tbe grid i. 30 centimeter., it i. evident tbat point a and point b •

.cannot be plotted, fig. 110. Let point a be the station point; let b be the

254-

Z5qao

2.532.5(J,700

Z52.l5C>,GOO

2.51

25Q500

R

o 0

COo'... « )

In ' It'''

Fig. 110.

point, (250 centimeters on the map or 5000 meters on the ground from a),

which is to be sighted on in order to orieOnt the board. The direction to thispoint ma~' be continued in three ways.

Let a=X=425,500, Y=250,400.

'\. b=X=428,500, Y=254,400.

559. (a) By Auxiliary Points. The grid may be renumbered on a 1/20,-

000 scale for the time being and the two points plotted, a' b'. The V-azimuth

can then be determined from the line connecting a' b'. Through a on the

1/2,000 scale draw a line parallel to a' b'. This will give the direction to 0,see fig. 110.

360. (b) By similar triangles. From'the coordinates it will be seen that

the point, b, is 3000 meters east and 4000 meters north of a, fig 110. Then

with a scale laYoff 3000 units (say 3 inches) east and 4000 units (say 4inches) north, and the point x is determined. Joining a and x the direction

of the line, ab, is determined, since similar triangles have been constructedand x is in the same direction from a as b, see fig. 111.

361. (c) By Reduced Similar triangles. Or by a comparison of similar

-1GO-

~~ ~

~ ~-

~ ~

°



triangles a point, p, may be established that lies on th~ line, ab, near enough

to a,' so that a and p may be plotted; and in this manner the direction of

line, ab, is determined, see fig. 111 below.

3000 : 4000:: 150 : Y ,

600,000=3000 Y 1Y=200Then the coordinates of point pare:-

X=425,500+ 150=425,650.

Y=250,400+200=250,600.Next plot point p and join with a, and the direction of the line, ab, is deter-

mined. .

.362. (d) By Reversing Directions. It sometimes will happen that the

point a is near one edge of the paper and the point b lies off the sheet. By

revolving the direction ab, through 3200 mils,. or in other words by plotting

a point b, which differs in its coordinates from a, in the same direction andby the same amounts as a differs from b, the direction, b'a, which is the same

as ab, is established.Since a is 3000 meters west and 4000 meters south of b, the point b'.

will be 3000 meters west and 4000 meters south of a, see fig. 112.

8

13000-----.,

Fig. 111.Fig. 112.

SubtracUng 3000 meters from the X-value of a, and 4000 meters

from the Y-value of a, the coordinates of b' are found to be, X=422,500,

Y=246,400. This point is plotted and the direction determined, see fig 112.

D. DETERMINATION OF RANGE AND Y-AZIMUTH BYCOORDINATES.

(1.) Range By. Square Root.

363. The coordinates of a point not only determine its location on a grid

.but also determine its distance and direction from other points. The dis-

tance may be found in a mathematical way by finding the east and 'west,

and north and south differences between the two points. Take into consider-

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~

~

~---



ation the problem stated above, see fig. 110. The two legs of the right angle

triangle are found to be 3000 M. and 4000 M. respectively The distance

a'ii or the range fron a' to 1/ i~ equal to.-V 3~;-+ 4~-OOO~===25,000,000SOOOM.

(2.) Direction.

364. (a) The direction at a line given by two points may be determined by

a brief calculation without plotting the points, when the direct;on

does not lie more than 390 mils off either the X or the Y axes,

'Vhen angles are formed greater than this, the difference between

the mil and the tangent relation tends to give inaccurate results,fig. 9.

Example:

Given the coordinates of a, as X=25,000 Y=50,OOO

b, as X=25,500 Y=55,OOOb is 500 meters east and 5000 meters north of a. Figuring the

angle by dividing the distance subtended, by 1/1000 of the range

the angle. of 100 mils is found. This is equal to the Y-Azimuthof the line ab, fig. 113.

Q.

Fig. 113.

I .

, \ , I

\ \ , I ,

\, / I

'I" '.... ,,/ /

~ J?oo.t--,.,,,, /~ ","

'...... ...,"........

xFig. 114.

Example:

Given the coordinates of c, as X=30,000 Y=60,000

d, as X=24,OOO Y=58,800d is 6000 meters west and 1200 south

of c. The angle made with the x-axis A-I,ZOOis equal to 200 mils. (1200+6) The

Y-azimuth is equal to 4800-200 or4600'1'.

365. (b) When the direction lies

more than 330 mils from the X orthe Y axis.

When this situation ari~es the

. Y-azimuth may be determined accu-

rately by comparing the coordinates

to determine the tangent of the angle

considered, and then by consulting

the table of natural tangents (Appen-

dix . II. Determine the corresponding

angle.

Example:

Consider the direction ft ' b', fig 110. The perpendicular side opposite

the angle, b' a' R, is 4000M. The side adjacent to the angle b' a' R is 3000M.

The tangent of the angle then is 4000/3000, or 4/3 or 1.333. From the

table.it is found that this corresponds to an angle of 53°8'=955111.

The Y-azimuth is reckoned from the Y-line or vertical line. There-lore the Y-azimuth will be 16001/1-9551/1=6451/1.

-1~2-

~ =

~ - ---

~



E. TO LOCATE ON THE GROUND A POINT THE CO.

ORDINATES OF WHICH ARE GIVEN.

~66. Let p= the point to be determined on h~ ground. Plot this point 011

the plane table or map. By examination of these coordinates and coordi.

nates of nearby control points, make an estimation of where this point would

be on the ground. Set the plane table up at this point (called x), fig. 115.-

/p....-'"....-

;"

Fig. 115.

Determine by accurate resection or other means the location of x on the

plane table. Measure the distance on the plane between x and p and de.

termine the relative distance on the ground. With the plane table oriented

and the alidade on x p, p being the point farthest away, line a man in with

the alidade at the required distance. This should be the point. Verify and

make the necessary corrections.367. It sometimes happens that brush or a crest intervenes between P

and x, fig. 116. If such a case arises it will be necessary to run a two (or

,P(

-I

I

I

I

,I

,~------ - .~. .~

-------~

Fig. 116.

more) legged traverse, determining another point y on the plane table and

ground. Proceed from y in the same manner as x in the preceding problem.

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CHAPTER XVIII.

THE COMPASS.

GENERAL.

f,

'-'i!368. In modern artillery practice the compass needle plays an important.,

part since it affords a convenient and reawnably accurate method of deter-

mining directions, of making traverses, of intersection, resection, and if lay- ,

ing guns for direction. Other things being equal the longer the needle the.

greater the accuracy of the direction determined. Even with a long needle

some sort of sighting device and some method of reading the subdivisions.'.j

of the angle set off is needed, in order to do satisfactory work, hence the

prismatic compass, the aiming circle or similar instruments only, can beused with a satisfactory degree of accuracy.

NOI{TH.

369. Because the artilleryman is dealing with three different norths-

True North, Magnetic North and Grid North (Lambert or Y-north)' it is-

convenient to designate horizontal angles measured from these various direc.tions by different names.

370. Azimuth. Thus in this. publication the horizontal angle, measured

dockwise from true north around to a given direction will be spoken of as .the azimuth of that direction.

371. The Magnetic bearing or bearing of a given direction will be used to-

designate the horizontal angle measured clockwise from magnetic north.

372. The Y-Azimuth of a direction is the horizontal angle measuredclockwise from Y-north or Grid north. .

Note: Actually Azimuth is any angle measured horizontally in a

clockwise direction from a given vertical plane. In some engineering man-uals and in the air ~ervice, the term is used to designate the horizontal

angle measured from magnetic north, the same angle which, in this text,will be termed bearing.

Bearing on the other hand in some texts is confined entirely to mea.

surements within a certain quadrant as "North North East" and alwayssu('h bearings are less than 90 degrees.

DECLINATION.

A. MAGNETIC DECLINATION.

373. The north magnetic pole is situated south of the north pole and in

the western hemisphere. Therefore the magnetic meridians and the true

meridians generally do not coincide. Magnetic Declination is the angle at

any given point between these two meridians or between true north andmagnetic north. .

Since the compass needle points toward the magnetic pole it is evi-

de.nt -that, except at a few localities it will not point toward the north pole.

-164-

.

i

-

"

_



.At certain parts of the earth's surface it will point east of the true no~th

giving an easterly declination and at others it will point west giving a west-

tlrly declination.

374. In America there is a westerly declination in the eastern part of the

Continent and an easterly declination in the western part of the continent.

The amount of declination varies with the locality. The amount of declina~, tion may be determined from an isogonic chart, such as that included in this

chapter, plate XII, which, for the epoch noted, gives, by curved lines con-

?ecting points of equal declinations, the approximate declination for points

ln the area represented.

. . Note: "Isogonic, of, pertaining to, or noting equal angles." Hence

lsogonic lines are imaginary lines joining points on the earth's surface at

'Which the-magnetic declination from the true north is the same.

At no 'point is the magnetic declination a constant. It is subject to

a number of different variations.

(1.) Magnetic Variations.

375. There are innumerable variations in the lines of magnetic force of

the earth very few of which can be computed. Following are the more im-

Portant variations to which the compass needle is subject. Of these, the

first two only, usually are considered.

(a) The daily variation, consisting of a swing from the. extreme

easterly position at about 8 :00 a. m. to the extreme westerly position about

1:30 p. m.; the mean position occuring about 10 :00 a. m. and 6 :00 p. m. Thisvariation is from 5' to 15', and the exact amount to be expected for any

hour of the day, and the months of the year may be obtained from tables

~hat have been computed. This often is called the diurnal val'iation.

. (b) The secular variation, a long slow iwing, covering many years.

In the United States both east and west declinations now are gradually in-

creasing at varying rates depending upon the locality.

(c) The annual variation, which is very small (less than l' per year)

and need not be considered .

. (d) The lunar variation, which is still smaller.(e) Irregular variations, caused by so-called magnetic storms, un-

certain in character and not to be predicted. Such variations are sometimes •

large.'.'

(/) Local attractions. These may greatly disturb the needle, and

often. 'come from unknown sources. The observer should have them con-

stantly in mind and endeavor to keep all magnetic influences, such as mag-

netic bodies, electric wires, steel helmets, etc., at a distance from the in-

strument when the needle is being read. Experiments indicate that a tran-

sit compass needle is not materially affected by large masses of metal atdistances greater than fifty feet.

Compass Error.

(g) The geometric axis of a needle may not coincide with its mag-

netic axis, hence the readings of two compasses at the same point may differ

slightly. This last, is known as a compass error. Any variation due to

faUlty construction of the compass itself is a compass error.

-165-

-

-

-

-

-



. (2.) Use Of Isogonic Chart. .

376. When the artillery officer is called Upon to run a direction or to la1,

his guns, and the declination of his compass needle is not known, and can',

not be determined in the time allotted, he will be compelled to use the ,data

W-J0-

~o

~t'"l-0

-::s.~

cCo(b

(0.

00g

"-,-0'0

furnished by his isogonic chart and by the tables of diurnal variation, in,

determining the magnetic declination which he will Use. The following prob-lem will indicate the method of procedure. I

-166-



AMOUNT AND VARIATION OF' THE MAGNETIC NEEDI.E FROM ITS

MEAN DAILY POSITION.

The letters E and W indicate which side of the

mean position the needle points.

sea.son and P.OSition\ 1 ~~cal:ea~ t,ime~._~_o_~ningH~~~~

in Latitude. 6 h. I 7 h.! 8 h.1 9 h. 110 h. 11h. !12h ..

--~~~~~-;::--;:b~,~~-.-~-.~~' Min~1 Min. I Min~1 Min~: Min. -~.-IMin ..Lat., 25° to 37° O.IW I O.IE: , l.OE j2.0E 2.2E 1.1E 0.5W

. Mar., Apr., May, ILat., 25° to 37° \ 1.6E 2.8E, 3.3E 2.6E. l.IE 0.6W l.9W

Jun., Jul., Aug. I iLat., 25° to 37° ! 2.,4E I 4.0E I 4.2E 2.9E: 0.5E 1.6W 2.8~

Sept .. Oct., Nov., I I ILat.,_2.~0 ~~_.~70_'.' ~''''_'-'_'.'-' _~9_~, 2.IE I 2.6E 2.1E I 0.6E 0.9E 2. IW

Local mean time: Afternoon Hours.

Season and Position ,.------in Latitude h \ h i--h-I---:I---'---~hT;;-

: _~_1_. :_~_1_3_._~~ .. :__Dec., Jan., Feb., I M n. Min. I Min. \ Min, \ Min. Min. \ Min.Lat., 25° to 37° : 0.5W 1.5WI1.8WI1.6WIl.OW 0.4W\'0.lW

Mar., Apr.. :!\Iay, i ILat., 25° to 37° 1.9W 2.6W,2.8W

I2.4W 1.6W 0.9W 0.5W

Jun., Jul., Aug., iLat., 25° to 37° "1 2.8W 3.2W,' 3.1W i 2.4W 11.5W 0.8,WIo.4WSept., Oct., No\'.,Lat., 25° to 37° ! 2.1W 2.3W1.9WI1.2W 0.7W 0.4Wl02W

(From' .Tracy's Surveying)

Latitude of Fort Sill is about 34°-40'.

=:--:.-:-:-~-:-. ,. ::---- -_ .. :--.. ,--"._ .. -_:~ .._---...:..-=-:-:..::.-:--=-""':::"""::-=-.- ._-=-=-.--=-::-.:...;-:-:.:..:.: _.- ---~:_::_~":..:-:.:...,:=.

377. Assume the officer is located at Ft. Sill, Oklahoma, and that he ex- .

, pects to use his compass needle at 3 o'clock on the afternoon of May 1, 1919.

From his map or from the isogonic chart he finds that on Jan. 1, 1915, the

magnetic declination at Ft. Sill was 10 degrees 4 minutes east. From the

isogonic chart, Plate XII he notes that the line of secular change of 2'

east per year is north of Ft. Sill and that of 3' is south of the same place.

By interpolation he finds that there should be an annual increast of easterly

declination at Ft. Sill of 2.6'. Since Jan. 1, 1915, four and one third years

have elapsed. Therefore the easterly declination would. have increased in

. that time by 4 1/3X2.6' or 11.26'.From the table of diurnal variation he finds that at 3 o'clock in the

afternoon in the monih of May the needle will show a variation of 2.4' west

of its mean position. He adds the variations and secures the total of 10"

12.8G' or a variation of 181.581ft=1821ft east.

-167-

. ----

_ _

I'

"

j __ __

__ ~ '

1

1

1

j

--- -- -- - - =-- -





Magnetic declination as given in isogonic chart 100

4.' E

Secular change in 41/3 years .............................•.. 11.26' E

Total ...........................•..•...... 100

15.26' E

Less Diurnal variati~n for 3 p. m. May 1 2.4' 'V

Total ; 100

12.86' E

10° 12.86'=181.58'lt=182'1t.

B. COMPASS DECLINATION.

378. ,Compass Declination includes the magnetic declination, the mag-

netic variations, and the error of the compass itself. Naturally it will be

different for each compass.

Since all" of these are difficult to compute, and since the magnetic

declination and 'the variations generally are not subject to any suddenchanges of great size in a given locality, the most satisfactory method of

procedure is to determine the compass declination by a topographical opera-

tion and to' use the value so obtained for a limited period of time.

(1.) Comparison Of Azimuth And Bearings.

379. Determination of the compass declination may be secured in the fol-

lowing manner, see fig. 117.

Select a position to work from, which is clearly marked on the mapand from which can be seen at least three distant objects, widely separated

if possible, which also are clearly marked on the map. When selecting this

position, it is important to see that no metal is near which might have an

effect on the needle of the compa!'!!!.

Draw a line through the selected point on the map parallel to the

true north-south line found on the map.

Mark the selected point carefully on the line and draw rays from it

to the three indicated objects already selected.

Place a circular protractor on the map with its center on the point

where the rays meet, zero toward the north, 50 that the 0-3200 diameter

roincides with the true north-5<?uth line drawn on the map.

Read off the number 'of mils at which the rays to the three distant

objects cut the edge of the protractor; in other words, read the azimuths to

these objects, making a careful note of each in turn.

Set up the prismatic compass at the position on the ground from

which the azimuths have been read on the map, and read carefully the

magnetic bearings to the three distant objects, making a careful note of each

in turn as before. The average of difference between bearings, and azimuths

will give the mean compass declination.

In figure 117 is shown a map on ~hich a protractor is laid, 'giving

the azimuths to a schoolhouse; a church, and a windmill, all taken from a

turn in a main road.

A compass is set up at this turn and the magnetic bearings to these

three objects are read. The results are tabulated ~s follows:

-169-

~ -

' '



AZIMUTH MAGNETIC BEARING COMPASSREAD WITH PROTRACTOR READ WITH COMPASS DECLINATION

Schoolhouse. 450 mils 775 mils 325 mils \V

Church 5670 Ie 5985 315" W

Windmill 3880 .. 4185 .. 305" W

Total 945 WMean declination 315 "w

This mean declination can be taken as the compass declination of the

compass used for the experiment. If this is compared with the magnetic

declination computed for the particular locality and particular time, the

error of the compass can be ascertained and marked on the back for futureguidance in this locality. .

It is important to take at least three bearings to guard against per.

sonal error, and desirable to select objects as distant as Possible.

(2.) Declination Constant.

,380. The Declination Constant, is the reading which must be set off on an

instrument in order that, When the compass needle is brought opposite itsindex, the instrunlent will be oriented.

For a clockwise instrument the declination constant is the same as

the compass declination if the compass declination is east. If the compass

declination' is west, the declination constant is equal to 6400-the compasseclination.

,381. Y.Declination, fig 118, is the angle which magnetic north makes with

grid north. If the Y.Declination is used in orienting the instrument the

'declination constant is spoken of as The Magnetic Number. In this case the

",era of the instrument, When oriented will point toward Y-north

..

Fig. 118.

•

North,

Convu~~nc.~ .

-170-

"

' "



USE OF COMPASS AND MAP.

A. TO FIND A MAGNETIC BEARING ON A MAP WITH A

PROTRACTOR.

382. Draw a true north-south line through the point on the map, fig. 119,

from which it is desired to take a magnetic bearing.Place a circular pl'otractor on the map,'with its center on this point,

zero toward the north, so that the 0-3200 diameter coincides with the true

north-south line.

Mark off on the map by a light pencil mark, the exact number of

mils that the compass in use varies from the true north; clock-wise, if the

variation is east, counter-clockwise, if it is west.

Join this mark to the point at the center of the protractor, and the

line so made is the magnetic north-south line through the point from which

bearings are to be taken ..IPlace the protractor on the map with its center on the same point

as before and with the 0-3200 line coinciding with the magnetic north-south

line just drawn. ,

Keeping the protractor in this position, by means of a piece of fin~

string attached to the center, magnetic bearings can be read to any object

on the map across which the string is stretched, by noting the number of

mils where the string cuts the edge of the protractor.

B., MAGNETIC RESECTION (BACK AZIMUTH).To Use A Compass And A Protractor To Locate A Positio.n On The }\fap.

383. When selecting a position, it frequently happens that its situation on

the map, obtained by a study of the surrounding country, is not sufficiently

€:xact. In order to obtain accurate bearings and ranges to objectives, it.

is very important to locate precisely, on the map, the position selected .

. . ' "11-



Fig. 119.

-172-



-173-

"



map. In fig. 120, P is a position ;Vhich it is desired to fix exactly on the

Set up the compass at PaRd read the magnetic bearing to a

prominent distant object, as W, a windmill which also is marked on the map.This bearing proves to be 4410 mils.

Draw the magnetic north-south line through TV to agree with themagnetic. variation of the compass used~ and place the protractor with its

center on the Windmill, wIth zero to the north on the magnetic north-southline just drawn.

Make a pencil mark at A on the map close to the edge of the pro-trictor, at 4410. mils, the magnetic bearing of TV from P.

Draw a line from A to TV and produce in the direction of P.

Repeat this process for another object, as C, a church to which themagnetic bearing is 5660 mils.

Draw the magnetic north-south line as before through C, lay theprotractor on it and make a pencil mark at B, on the map close to the edgeof the protractor, at 5660 mils.

Draw a line from B to C and produce in the direction of [J untilit cuts the other produced line, A W.

The intersection of these two lines is the point from which were read

the bearings to the windmill and church, and is therefore the position" whichit is desired to locate. .

Note: The above process is the same whether the operator works

with the true north and magnetic declination or with Y-north and y. declina-tion, fip' 52, par. 209.

-Ji4 -



CHAPTER XIX.

I~AYING GUNS WITH A DECLINATED INSTRUl\IENT.USING PRISMATIC COMPASS.

384. In laying the guns for direction with a compass there are two steps:

First, the determination of the bearing of the direction, gun-target

Qr the direction gun-base point, and

. Second, the laying of the guns with the bearing determined ..

A.. TO DETERMINE THE COMPASS BEARING OF A GIVEN TARGET.

The bearing of the target or base point may be determined. in two

'Ways:

(1) If an accurate map is available, on which both gun and target

positions are shown, the bearing may be read directly from the

map with a protractor, as described in Ch. XVIII, or the azi-

muth or Y-azimuth may be read from the map, and the bear-

ing computed. .

(2) If the. map is not available the battery commander must com-

pute the bearings by the offset method, analagous to the

parallel method of computing firing data, described in DrillRegulations. .

The Offset Method.

385. Assume that the target is net visible from the gun position, but that

there is an elevation near at hand from which the battery commander can

, See both the target and the directing gun.

From this elevation he takes the bearing of the target and the bear-

ing of the gun.

The battery commander also measures or estimates the distance be-

tween the compass and the gun position, and the distance between the gun

Position and the target.

With these data he computes the angular offset for the gun position

and modifies the bearing of the target, read from the B. C. station, by the

amount of the offset. Since magnetic north is the same for both the gun

Position .and the B. C. station there is no offset to be computed for that

direction, (corresponds to HP" in parallel method). iThe bearing as determined by the battery commander is sent to the

<'xecutive who lays the guns accordingly.

386. The following problem will illustrate the steps taken by the battery

<:ommander in computing the bearing of the. target.

Let C be the compass position.

Let G be the gun position.

Let T be the target position.

The distance from gun to target is 4000 meters.

The distance from the compass to the gun is 400 meters.

The battery commander reads the bearing to the target and finds

-175-

c.



that this is 1400 mils, see fig. 121. He also reads the bearing to the directing

gun and determines the bearing of the direction, compass-gun, to be 3800mils.

The difference of these two bearings will give him the value of the

nngle TGG. If this angle is equal to 1600 mils the line gun-eompass is approxI-

mately normal to the line gun-target. It not, there will be an obliquity factorto' be applied. The battery commander subtracts 1400 mils from 3800 mils

!'IN

Fig. 121.

and finds that the angle TeG. is equal to 2400 mas. In other words it is 800

mils greater than the normal angle, he~ce the obliquity factor of .7 will besed.

At range 4,000 (the distance to the target) a base of 400 meters be- .tw,-en the gun and the compass would subtend 100 mils if the b"e werenormal to the gun-target line.

In this case an obliqUity factor of .7 must be applied as determinedabuve, hence the angle subtended at T will be 100X.7==70 mils. The offset

then, is 70 mils. 1400-70==1330 mils which is the bearing of the target

as viewed from the gun position' and this is the bearing sent to the ex-cutive.

n. LAYING TIlE GUNS WITII THE BEARING DETERMINED.

3H7. In laying the gun~ with the bearing iust determined by the battery

commander, the executive should have a compass which reads the same as

that. of the captain, or at least the declination of both compasses should be

known' in order that any differenee in their readings may be eonsidered.

In the above ease assume that the battery eommander is using a('ompass with a declination of 180'lz east, While that of the executive has a

reading of 1701/z east. Should the battery commander therefore, send down a

bearing of 1330,/, for a particular target, the executive would modify that

bearing by the amount of 10,/, applied in the proper direction, or he would

add 10", to 1330,/, making 1340"., which would be the bearing he would usein laYing the guns, see fig 122.

-176-



'T

MAQNETIC DECLINATION

'N <'~A

TG

On the other hand, suppose that the battery comm~nder should send

down the Y-azimuth of the\ target as measured, from the map. Assume this

to be 1320,11. Knowing the Y-declination of his instrument, for that Dartic-

ular locality, the executive would apply this in the proper direction and lay

accordingly. Assume that the Y-declination of the /executive's compass is

201ft west. The magnetic bearing with which he would lay the guns wouldtherefore be 1320+20 or 13401//, see fig. 123.

N MN OF EXeCUTIVE 0COMPA55

MN OF f>.C.'0

COMPA5510",

Fig. 122. Fig. 123.

Several methods may be used by the executive in laying the guns

With the compass, the methods varying with the time available and the ac-

Curacy desired.

Using Compass As Aim~ng Point.

388. Ordinarily when the guns are laid by compass, the executive sets up

the instrument in the vicinity of the' guns, but distant enough that the

masses of'metal do, not affect the needle, and after he ha's made his com-

Putatio'ns,,' the g~nners lay for direction using the compass as an aiming

Point.

Let G be the gun position, C that of the compass and T the target.

The executive already knows the bea,ring of the target, angle A,

Fig. 124. He reads the bearing of the gun, angle B. He subracts the bearing

of the target from the bearing ,'of the gun. This gives the angle

D, one side of which contains the line of sight from the gun through the

compass and the other side of which contains the line of fire to the target.

This angle is the clockwise angle from the target, T to the aiming point, C.

If the sigLt was graduated from 0 to 6400 mils, the angle would be 3200 mils.

greater, or the angle TGC measured clockwise from T. But since the plate

of the American panoramic sight is divided into two semi-circles, each grad-uated from 0 to 3200 mils, the angle D is the deflection announced. If the

executive is laying a French 75mm gun, the' deflection must first be trans-

formed to, plateau and drum readings.

The above steps may be expressed by the following equivalent

formula:

. Bearing of gun minus bearing of target equals the deflection B-A

:::::'D.

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~ "

'

- -



Fig. 124.

Fig. 125.

-178-

r



If the bearing of the target is greater than the bearing of the gun,

a multiple of 3200 must first be added to the bearing of the gun before sub-

tracting the bearing of the target.

389. An examination of four cases below, arising as the compass is

placed in each of the four quadrants with respect to the gun position, will

establish the validity of the formula. In each of the cases considered:

let G be the gun position,

C 'the position of the compass,

T the target position,

A the bearing of the target,

n the bearing of the gun.

D be the deflection.

390. First Quadrant, Fig. 125.

Assume that A = 1200 1f t and that n = 3600 III 3600 1200

2400 mils = deflection D.

391. Second Quadrant, fig. 126,

. Assume that A = 1200 111 and that n 5500 111. 5500 1200 =4300 111. Since 4300 mils cannot be set off on the sightg, the setting will be

4300-3200 = 1100 mils, which is the desired deflection.

-179-

- _

= -





Assume that A=1200t!1 and that B=800t/z. 800+3200-1200=2800

. =- Angle D == required deflection.

393. Fourth Quadrant. Fig. 128.

Assume that A=1200,!z and. that B=2500,/1 2500-1200=1300//1.

T MN

r'

o

Fig. 129.

394. In figure 129 assume that A=6100,/1 and that B=750,/1 750+6400-

6100=1050=angle D= required deflection.

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CHAPTER XX.

LAYING THE GUNS ON THE BASE LINE.

STJ<;PS PERFORMED IN THE OCCUPATION OF A SECfOR.

395. In the occupation of a battery sector the battery commander:

First, Lays his guns on the base line with a well defined sheaf(uS\lally a parallel sheaf);

Second, Determines the lateral limits of fire and the maximum andminimum ranges;

Third, Lays his guns for the normal barrage;

. Fourth, Computes the data for other targets, objectives, and bar-rages in the order of importance.

396. The establishment of the battery on the base line will be done either,

rapidly with approximate accuracy, or with accurate methods, according to

the circumstances; but the establishment on the line never must delay theopening of fi'.e.

lf the Opt!ration is roughly performed, it must be improved as soon

as possible both by firing and by performing new topographical measure-ments.

397. In placing the battery in observation on the base line, there are twosteps:

First, The laying of the base piece on the base line, andSecond, Formation of the sheaf.

Note: Both of these operations may be performed by rough field

methods, by computation, or by exact topographical operations and measure-ments from the map.

This text will not discuss the formation of the sheaf which more pro-perly belongs under the subject of fire control.

ESTABLISIDIEXT OF THE BASE PIECE ON THE BASE LINE.

398. The operation of laying the base piece on the base' line or the target,falls into two general classes:

"First, Field method of measuring angles and calculating offsets fromthe B. C. Station;

Second, Topographical methods.

, 399.

A. USING AN AIMING POINT, AN ANGLE MEASURING INSTRU-

MENT, AND COMI,UTATION OF OFFSETS FROM THEBATTERY COMMANDER'S STATION.

This method is discussed in drill regulations.

B. USING TOPOGRAPHICAL METHODS.

400. Quick and accurate fire on a given point demands careful prepara-

tion. The required data for opening fire: deflection, range, and site, may be

read off the map, after the gun, the target, and the plane of sight, aimingdirection or aiming point, have been plotted.

-182-



The accuracy of these data depend on four things:

First, The accuracy of the map itself; .

Second, The care with which the topographical operations have been.Performed; . .

Third, On the precision of the subsequent measurements;Fourth, Additional errors may also be expected if measurements are

1llade from the map, due to the contraction and expansion of the paper.

'l'hese

last errors, however, may be minimized by the use of the firing board.

. If the battle map is used, the original errors due to the construction

()~the map itself may be disregarded. If the plotting board is employed the

distortion of the map, due to weather conditions, may be overlooked.

. There remains then, .the consideration of the errors' likely to arise

In locating and plotting .points, and in measuring distances and directions

. flso the consideration of the methods to be followed which will be leastIkely to involve error.

CLASSES OF TOPOGRAPHICAL METHODS.

401. In general there are two classes of topographical methods of layingthe, base piece on the base line: .

First, That in which the plane of sight is established by two pointsWhich have been located by their coordinates;

t . Second, That in which the plane of sight is determined by an es-abhshed direction.

PIRST CLASS. PLANE OF SIGHT THROUGH POINTS LOCATED BY

COORDINATES.

I 402. The simplest of all cases involving computation of firing is that

"'herein the position of the gun, the target, and the aiming point all are defi-

nitely known. A reading scale may

then be used to determine the range,

a portractor employed to compute the

IZOO deflection, while the site may be com-

puted by determining the difference

in elevation of the gun and target

as shown by the contours of the

map, and dividing this difference by

thousandths of the range, expressed

in the same units as the difference in

altitude.

In fig. 130 let G be the gun

position, P, the aiming point which is

visible from' the gun position and T,

the target position, all of them beingllOints accurately plotted on the map. Draw the lines, GT and GP. With

a, Protractor measure the angle, PGT. Assume this to be 950 mils. The

:~ring angle of deflection for the American sight ~hen will be 6400 minus

vO or 5450. Measure the distance GT. Assume tll1S to be 2500 meters. T

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" "



is situated on contour 1200 and G is located at an elevation of 1225, giving

a difference of 25 meters. This elevation, 25, divided by the range in kilo'

Ometers gives a site of minus 10. The data obtained from the map then be'come:

Deflection

Site

Range

54501/1,

290'11,

2500M.

SECOXU CLASS. PLAXE OF SIGHT DETEIUIINED BY AN

f:STABLISIIED DIRECTION.

r

:} p

Fig. 131.

r///

LL__G

(1.) Hired Orientation Of The Directing Piece 'Vithout The Use Of

An Orienting Line.

403. (a) Using (t l)[ane table. Plot the gun position, g, on the board and

the (lirection gun-target or gun-base point. Orient the plane table in the,

vicinity of the gun position, either by resection, by a short traverse, (not.

more than three legs) or by use of the magnetic needle (the dcclinatio~

constant of which has been determined previously). Wjth the aljdade pivoteabout g, sight G (the panoramic sight of the gun) and draw the directioJ1

GgP. l\Ieasure with a pro'

tractor clockWise from ~h:base line the angle WhlC

this line makes witb

the base line, GT. Let thiS

be th~ angle A. In the case

illustrated in fig. 131, the

angle A, is the firing angle

which, with the deflectioJ1

eon stant added, is the angle.

To convert into the defleC

tio~ (see note) given the

gunner. 'Vith this defleetiO~

on his sight the gunner ne~

lays for direction, using as a:

aiming point a pencil hel

vertically on the point, P, o~the plane table. The operation should be repeated once or twice on accou

l1

of the displacement of the gun sight during the process of laying, the gU,J1

h('ing moved slightly until this is accomplished. When the gun finally 1;laid on the GT line the gunner refers the piece (reads the deflection to.1'o

more distant aiming point) and records the deflection. If the angle Ii IS

greater than 3200 mils, the firing angle is A-3200 mils.

~ote: The "deflection constant" is the deflection which causes th~

plane of sight to be parallel to the plane of fire. It is plateau 0, drum 10

for the French 75mm sight and 0 for guns equipped with the Americatlpanoramic sight.

404. (b) Using the aiming circle (French). The battery commander first

-18-1-

~ '



measures on the map or computes from the coordinates, the Y-azimuth ofthe base line or gun-target line.

'. The Battery commander knows the Y-azimuth of magnetic north or

(declination constant) (magic number) of his instrument (the reading which

~U8t be set off in order that, when the needle is brought opposite its index

• 'Y the general motion, the instrument will be oriented). He sets this on the

~s~rument and orients. This brings the zero of the horizontal scale on the

-lIne. With the lower motion clamped, he sets off a reading equal to the

~-aZimuth of the base line. His line of sight is now parallel to the base line,

ut he wants the zero of his instrument on this line. He picks out some

~asi1y identified point on this line of sight or sets a stake on this line .

.ext he sets his instrument at zero, unclamps the lower motion and again

~Ights on his stake. The instrument then will be laid so that the line of sight

~ill be parallel to the base line when the reading on the lower (red) scaleIS Zero.

With" this line established parallel to the base line it is necessary

O?ly to turn the line of sight, using the upper motion, to the sight of the

dIrecting gun, note the readings, and announce it in terms of plateau and

~rum. The gunner sets off the announced deflection on his sight and

ays on the spindle of the aiming circle as an aiming point .

.405. A modification of the above method sometimes spoken of as the

magic number method is given below. Let L be the declination con-

. Iltant (magic number) of the given instrument. Let V be the Y-azimuth of

' ~ h e base line. The deflection of the base line from magnetic north then, is.

d-'V or 6,400 plus L-V if L is less than V. Set the aiming circle at the value• etermined and proceed as before.

106. The following problem will illustrate the above method, fig. 132.

The Y-declination is found from the map to be 250 mils west. This

rnakes the Y-azimuth of magnetic north equal to 6150 mils. In other words

~e magic number (declination constant) for a clockwise instrument is 6150.

rrom the map the Y-azimuth of the target, T measured from the gun posi-Ion, is found to be 2000 mils.

6150-2000=4150 which is the firing angle from magnetic north

Whichwill place the gun on the GT line. Setting 4150 on the instrument the

tleedle is brought to its index whereupon the line of sight is in the direction

. C1", parallel to the GT line. Note: When operating an aiming circle use the

s~owmotion screw rather than the rapid motion if accurate results are de-Illred.

. The line of sight is then swung around to the gun, G. The angle

l'ead is T'CG, measured clockwise. Assume this angle is 1900 mils. In laying

a. French 75mm gun the plateau and drum readings are read directly on the

:Itning circle. In laying guns equipped with the American panoramic sight

3he

deflection announced is the angle T'CG, if the reading is less than

• 200 mils. If the reading is greater than 3200 mils, the deflection an-

~~unced is the reading minus 3200 mils. In fig. 132 the actual firing angle

aId by the gunner is xGC, measured clockwise, which (by geometry) istlqUalto T'CG, measured clockwise.

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~



Fig. 132.

407. Since there is a variation in the compass readings of different iJ11

l>truments, and also daily and seasonal variations it often is of advantage

to materialize either the line, CT', or the line, CT, on th~ ground as a check

on the future laying of the piece. In this case the materialized direction bel

comes a true orienting line.(2) Orientation Of The J)irectin~ Pi{'ce By )Ieans Of An Orienting Line.

403. (a) Advanta{jes of an orienting line. In using an orienting line theartilleryman will find several advantages;

First, The orienting line, being established, permits of rapid deterl

mination of firing angles since it is necessary only to set up the plane table

or aiming circle at any point on the line and read the angles to the variouspieces:

Second, It is a convenient method in close country where distant ai}111ing points are not visible;

Third, It is permanent and affords a convenient way of checkiJ1g'

deflections or of re-Iaying the guns if they are moved a short distance;

Fourth, Since the orienting line may be common to two or more bat;

teries or even to two or more battalions, the advantages of a parallel shea

within a hattery can be extended to more than one battery.

409. (b) Steps to be performed. The establishment of a battery on the

base line, making use of an orienting line consists of:

First, The determination of the base angle or the angle between the

-186-

"



base line and the orienting line measured in the same direction as the sightgraduations;

, Second, The establishing of the base piece on the base line;

Third, The establishing of a parallel sheaf or a sheaf of other welldefined relation., .

The last two operations usually are performed successively or sim-

Ultaneously. '. ','

A battery with an extended field of fire often uses several base

POints. The object of this is, in shifting fir~, to avoid the errors incident to

llleasuring large angles. Consequently, if a shift will carry the line of fire

!last a base point other than the one being used, the piece should be es-

tablished on the new base line. ,

J. Determination of the base angle.

410. . Plot the base piece and the base point on the firing board or map

by means of their coordin'ates.

Draw the base line joining the two points.

The orienting line having been materialized either by battalion or

Lattery orienting ~fficer, plot the orienting line on the firing board by its

Y'azimuth or by coordinates taken from the plane table.

\Vith a protractor measure the base angle. .

Lun"Ight .

. Fig. 133.

II. Laying on the base line using an aiming circle.

411. If the orienting line passes thr~ugh the sight of the base piece, the~rienting line is used directly in laying for direction.

. If the orienting line does not pass through the sight of the base

PIece, an aiming circle or other angle measuring instrument, or plane table

ll1ust be set up on the orienting line and used. .

. If the orienting line has not been previously established and material-

~zed,th'e base piece is established on the base line by means of a declinated

Instrument, see pars. 404-406 and the line is afterward materialized.

412. First Case. Orienting line passes through' sight of base piece. In

this case the plane of sight is taken as coincident with the orienting line

While the firing angle becomes the same as the base angle, providing the

aiming point i~ to the right, see fig. 133.

. Convert the firing angle

Into deflection by adding the

deflection c'onstant of the par-

ticular gun used.

Lay for direction with

~his deflection, using the orient-

Ing line (extended to the right t--

for sights graduated clockwise)

as an aiming 'direction.

Refer the piece to another aiming point and record the new defIec-tion.

1 When the marker of the orienting line which is to be used as an aim-

ng point is Close to the gun, care must be used to insure that the base

lliece is not thrown off the orienting line while laying for direction. To

-187-

'



this end it is well to establish a supplementary marker on the orienting linenear the gun.

413. Second Case. Orienting line does not pass through sight of base piece.

. In this case an angle measuring instrument or a plane table is se~

up on the orienting line, so that the sights of the several guns are visible,

and the firing angles are determined. There are a number of different meth-

ods of doing this, the order of measuring the angles usually being dependen;

en the manner in which the one doing the work visualizes the relations 0the angles he desires.

414. Method No.1. Using- an aiming circle, laid parallel to the base line.

One favorite method is to set up the instrument on the orienting line

with the zero of the instrument pointing in a direction parallel to the baseline and then lay the guns by a process analagous to reciprocal laying.

Establish the aiming circle on the orienting line.

Set the instrument at. the base angle.

Using the general motion, point the aiming circle along the orienting'

1': . T'Be13~ Point.

L

Fig. 134.

line to' the right (the right as one faces the base point). The zero of the

inst,rument is then on a line parallel to the base line, fig. 134.

415. The aimingcircle or" director being established parallel to the base

line, to lay the base piece on the base line, using the aiming circle as an~.ming point.

With the zero of the instrument laid in the direction, CT' or parallelto the base line take the reading to the sight shank of the base piece. Let .Abe the reading so obtained.

If the panoramic sight and the aiming circle are graduated in thesame direction, the firing angle for the piece is:

A mils, if A is less than 3200 mils:. . .

. A-3200 mils, if A is greater than 3200 mils. See figs. 135, 136, 131,

138. for the four quadrants, below, the first and fourth occuring when the

orienting line is in front of the battery, and the second and third when theorienting line is in the rear of the guns.

~



o

. ,-"t..QVAORANT.

L

o

.2 ndQvAORANT

Fig. 136.

-189-

T'



o

7'

Fig. 137.

r

4t;Q

Quadrant

r' ,T

l

0

Base A"..:J1e

L

Fig. 138.

-190-

I



piece.

In' each of these figs., OL is the orienting line;

G is the gun position.

C is the aiming circle position."

GT is the baseline.. : .

CT' is a line parallel to the base line;

A is the angle measured from the base line to the panoramic sight of'the gun. . ". . .

Having determined the firing angle' in each case it may be converted'

into deflection by adding the deflection constant for the particular type of ,

panoramic sight used. .

After the base piece has been laid on the aiming circle it will be re-

ferred to some other aiming point and the deflection recorded.

III. Laying on the base line using a plane table.

416. The orientIng line and the base line should be drawn the full length

of the plane table.

Set up the pla~e table over the orienting line. .

Orient the table by sighting on a distant point of the orienting line.

\Vith the alidade pivoted about g, the plotted position of the gun, sight at G,

the sight shank of the base piece, and draw the line Gg. the full length of

the rule.

With the protractor measure the angle between the base line and the

line Gg. measured in the same direction as the sight graduations.

This is the firing angle which is converted into deflection by adding

the deflection constant, see fig. 139.

Fig. 139.

With this deflection, lay the gun for direction, using as an aiming

point a pencil held vertically at any point on the line Gg.

Repeat this operation until the 'sight no longer moves in laying the

Refer the piece.

Record the base deflection.

Cases in the other three quadrants will be solved in' a like manner.

~191-



417. Note: In all of the above methods it is better to determine' the base

deflection after the guns are in position. The method of marking the posi-

tion of the gun sight with a stake and sighting on that stake from a near-

by point, or of setting the aiming circle over this stake and computing the

deflection, should not be used if time permits the establishment of the piece.If used, the piece should be moved until the deflection read on the sight

checks with that previously determined, or should be checked in some othermanner, and the corrections made.

-192-



\ ~ ..1

\

\

CHAPTER XXI.

TOPOGRAPHICAL OPERATIONS IN OCCUPATION OF

A BA1YfERY SECTOR.

GENERAL.

418. Topographical operations to be performed in the occupation of. a

battery sector are dependent on:

First, the time element;

Second the instrument available for use;

Third, the accuracy of the map used;

Fourth, the proximity of geodetic points or points of general con-

troI.

The object of the topographical operations is to determine the initial

elements of fire. These operations are performed, partly during rcon-

naissance, and partly after the position is occupied.

The topographical steps may be performed: (1) entirely by the bat-

tery commander or his reconnaissance officer; or, (2) by the battalion

reconnaissance officer who locates the orienting line and place marks for all

batteries, followed by the battery commander who completes the work for

bis particular battery.

GUN POSITION.

(A) WilEN COORDINATES OF GUN POSITION CAN BE READ

DIRECTLY FROM THE MAP.

419. The simplest operations arise when the battery is located at a point

which may be identified on the map so that the coordinates may be taken

directly from the sheet.If the base point or the target also can be identified on the map the

base line, or the direction to the target, may be taken from the map, as ..

may the range, while the site may be computed by using the map elevations.

In such a case a line of sight may be established through a distant.

aiming' point, or along a line of established direction, and the guns laid ac-

cordingly; or, the direction to the base point having been determined, the

guns may be laid. with a declinated instrument on the base line, see Ch. XX.

B. WHEN THE GUN POSITION CANNOT BE IDENTIFIEDON THE MAP.

420. In the majority of cases the position of the guns cannot be identified

on the map.

Since the position of the guns must be known before any firing data

may be computed from the map, the first topographical step is the de-

termination of the battery location. This may be accomplished in a number

of different ways.

-193-



(1) Using A Geodetic Point.

421. If the battery is close to a geodetic point the coordinates and eleva-

. tion of the gun position may be determined by a short traverse.

(2) By Resection.

422. If the battery is in a position from which two or more control points

can be seen, the position may be determined by resection.

(3) By An Orienting Point.

423. If neither of these conditions hold, it will be necessary to establish

an orienting point" which will be used as the starting point for further

topographical operations. The guns are located, in this case, by running

a traverse from the orienting point.

If the topographical operations are performed in advance of the ar-

r!val of the guns, it is customary to establish a place mark near the bat-tery position. The coordinates and elevation of this place mark will be

recorded and when the battery does arrive, the exact location of the guns,

hori"ontally and vertically, may be determined, either by traverse, or by

determining how much east or west, how much north or south, and how

much above or. below the place mark, the gun position may be.

BASE POINT OR TARGET.

A. WHBN THE POSITION OF THE BASE POINT. OR OTHER TAR-GETS MAY NOT BE DETERMINED FROM THE MAP.

42.1. (see Ch. XXII.)

B. DETERMINATION OF DIRECTION TO TARGET OR BASE

POINT FROM THE MAP.

425. \Vith the gun position and the target position determined by coordin-

ates, the direction or Y-azimuth may be read directly from the map by

means of a protractor, or the direction may be computed directly by a com-

parison of the two points, see Ch. XVII. /

AIMING POINT.

A. DETERMINING DIRECTION TO AIMING POINT.

426. The direction to the base point or target being known, it is neces-

sary, before the guns can be laid, that a plane of sight should be determined.

This also may be done topographically.

The desired direction may be determined by using a distant known

aiming point, see Ch. XX; by using a declinated instru~nt, see Ch. XX,or by making use of an orienting line.

B. THE ORIENTING LINE.

427. The orienting line, as the name implies, is a line of known direction

usually materialized on the ground by means of which the battery commander

can orient his guns. Magnetic north, as used in connection with a declinated

instrument, is such a direction, and if this direction is materialized on the

~round, it becomes a true orienting line. The direction, Gun-aiming Point,

if materialized on the ground, also becomes such a line.

-1~ t--

"



(1) rfwo Types Of Or\enting Lines. (See cuts, Appendix No.6.)

428. In general there are two types of orienting lines, viz;

(a) Those established through a known point or points, and

(b) Those established with a known direction.

Magnetic north, if materialized, is of the last type. In some cases it

is easier and more accurate to establish an orienting line by direction ratherthan to run it through known points. If such a line is established it is not

necessary to determine the coordinates of any points on the line. The line

may be run through the gun position, or in front or rear of it, and in any

direction, and the guns speedily laid by means of a plane table or angle

measuring instrument set up on it at any place visible from the guns.

42~. 'Vhere the orienting line is established by direction it still is neces-

sary for the battery commander or reconnaissance officer to take the topo-

graphical steps necessary to determine the coordinates of the battery.

On the other hand where the orienting line is run through an

orienting point which has been occupied in the work, the two sets of opera-

tions may be performed simutaneously and the reconnaissance officer will

reach a point in the vicinity of the battery with all control elements

determined.

T

Fig. 140.

.430. The orienting line should be established by means of a set of con-

spicuous stakes or markers set up at such intervals that, from anyone stake

.at least two otherg will be visible. This affords a check on direction and

-103-

'



alignment in case a stake is destroyed. Usually the stakes or markers ofeach battalion will be of a distinctive type. .

(2) A Typical Case.

431. Assume that the battalion has been assigned a sector, that the gen';

eral location of gun positi-;'ns and of objectives is known, and that there istime enough for the compl~tion of the topographical operations.

In such a case it is probable that an orienting line and place marks

would be established by the .battalion orienting officer after which the bat-tery commander would continue the work.

Assume that the battery positions are so situated that no controlpoints are visible therefrom, fig. 140.

. From the hill-top, P, the battalion orienting officer identifies three

control points, A, fl, and C, which he uses in making an Italian resection and

so establishes an orienting point, P. The battery positions cannot be seen

from the hill so the orienting officer runs a traverse pxy, and arrives at 'J/,

the coordinates and elevation of which he computes and records.

From y he notes a distant church steeple in the direction of the gun

positions and so decides to run the orienting line through that object. He

measures the Y-azimuth of the direction from y to the steeple and finds thatit is 2450'1&. This is recorded.

Starting from y, the orientin~ officer then runs a line with a Y.azi-

muth of 2450'/& past the battery positions, establishing his markers, and de-termining coordinates and elevations of one or more place marks in thevicinity of the batteries, see fig. 140.

432. All data secured is recorded, and the battery commanders are

furnished rough sketches showing the Y-azimuth of the orienting line and

the coordinates of the place marks in the vicinity of and visible from their

battery positions. 'Vith these data they then proceed to establish their gunson the base line.

I!II; .



....

CHAPTER XXII.

LOCATING TARGETS.

'JTERRESTRIAL OBSERVATION.

433. While the airplane and the areal photograph afford means of locat.

ing new targets, terrestrial observation continues the most important obser-

\'ation method, hence the battery commander, to secure the most effective

llse of his advantages must be familiar with all methods of securing the

coordinates of the targets in his sector. If a target is visible he may de-

termine the range and azimuth by registering on it and then swinging his

fire to a registration mark, the range and deflection of which are known.

With the range and azimuth so determined he then may plot the target it

l:lestion on his firing board or battle map. It frequently is possible, by

the employment of a few simple topographical operations, to accurately lo-

cate objectives in the battery sector, thereby saving time and ammunition

l'equired for the attack. Therefore all possible use of topographical methods

should be made in the determination of the coordinates of new targets~

COMPARISON OF METHODS.

434. The most common method of locating objectives is by intersection,

and where two observation posts both are accurately located, and are some

distance apart this method is quite satisfactory. It is necessary only to take

the Y-azimuth of a given objective as seen from the two stations and to plot

the direction on the firing board. It usually happens, however, that where

the observation posts are some distance apart they are unable to pick up the

, same objective. An auxiliary O. P. may be established near the first station,

but usually in such cases the base is so short that an intersection will show

a considerable error in range. Therefore it is better, where it can be done,

to determine the value of the angle subtended at the desired point by a base

of given length and thus determine range by use of the mil relation. There,

are a number of different methods of approaching such' a problem.

Case I.

435. Given an O. P. at A, fig. 141, a reference point at T, and a target'

'Which it is desired to locate, at some unknown point, T', From A, the ob-

server erects a perpendicular base to B. Assume this to be 100 meters in

length. The observer knows the distance to the reference point. Assume this

distance, AT, to be 2500 meters. The angle x subtended by the base of 100

meters is then 40 milc:;. At A the observer measures the angle a. Assume

this to be 110 mils. Proceeding to B the observer measures the angle, b.

Assume this to be 120 mils. By geometry a+x=b+y. Therefore a+x-b=y.

or 40+110-120=30 mils. An angle of 30 mils will subtend a base of 100

meters at a distance of 3333 meters, which is the distance to T'.

If the angular distance between T and T' is great, this method will

not be accurate.

-19i-

,



1

100

Fig. 142.

A 100 f)

Fig. 141.

T'T'

j

T T

T

J-j

j

Case II.

436. When T' is in line with T, aLlseen from the observation post, A, fig.

142. Layoff the base AB. Again assume this to be 100 meters. From B

measure the angle y between T and T'. Assume this to be 10 mils. Having

a known base, All, and a known distance, AT, the angle, a, is commputed.

Assume this to be 40 mils. By geometry a=x+y. Then a-y=x or 40-10

=30. If x equals 30 mils and AB equals 100 meters then the distance AT'equals 3333 meters.'

Case III.

437. Layoff a base, AB, from the O. P., fig. 143. Let this be 100 meters.

Assume the angle, a, to be equal to 1600 mils. At B take a back sight and

measure the angle, b. Assume this to be 1570 mils. By geometry a+b+x=

3200 mils. Therefore x= 30 mils. Therefore the distance to T equals .3333meters.

"Case IV.

438. From A the observer reads the bearing or the azimuth to the target,.

T, fig. 144. Assume this bearing, a, to be equal to 350 mils. Proceeding to

B, 100 meters distant, he reads the bearing to the point, T. Assume this to

Le 300 mils. By geometry a-b=x or 350-300=50 mils. Therefore T is2,000 meters distant.

Case V.

439. In any of the above cases where, because the obesrvation post is

under fire, it may be impossible to layoff a perpendicular base. It often is

possible in such ~ases to run a traverse down a trench line to B, fig. 145, and

by plotting this point determine the perpendicular distance, A'B, after which

the value of the angle x may be determined as. before.

-198-

_

-



,

/"\N

III

"I. I .

I.\

IIa

-199-

"A. Fig. 145.

","

"

"

" \



APPENDIX I.SLOPES.

2111 .







. 444. Natural sineR and tangents to a radius 1:

Arc. Sine.i

Tang. Cotang. Cosine. I,

---_. .

--0--";-o 00 .. 0000000 .000000 Infinite . 1.0000000 ! 90 000 .0029089

.002908 '343.7737 .9999958 500 .0058177 ~005817 /171.8854.9999831 400 .0087265

.008726 114.5886.9999619 30

0 .0116353 .011636 85.93979 .9999323 200 .0145439 .014545 68.75008 .9998942 101 00 .0174524 .017455 57.28996 .9998477 89 000 .0203608 .020365 49.10388 .9997927 500 .0232690 .023275 42.96407 .•9997292 400 .0261769 .026185 38.18845 .9996573 300 .0290847 .029097 34.36777 .9995770 200 .0319922 .032008

31.24157 .9994881 1000 .0348995 .034920 28.63625 .9993908 88 000 .0378065 .037833 26.43160 .9992851 500 .0407131 .040746 24.54175 .9991709 400 .0436194 .043660 22.90376 .9990482 3040 .0465253 .046575 21.47040 .9989171 200 .0494308 .049491 20.20555 .9987775 103 00 .0523360 .052407 19.08113 .9986295 87 000 .0552406 .055325 18.07497 .9984731 500 .0581448 .058243 1716933 .9983082

40

0 .0610485.061162 16.34985 .9981348 300 .0639517 .064082 15.60478 .9979530 20

0 .0668544 .067004 14.92441 .9977627 1000 .0697565 .069926 14.30066 .9975641 86 000 .0726580 .072850 13.72673 .9973569 500 .0755589 .075775 ! 13.19688

.9971413 40. 30 .0784591 .078701' 12.70620 .9969173 300 .0813587 .081629 12.25050 .9966849 200 .0842576 .084558 11.82616 .9964440 1000 .0871557 .087488 11.43005.

.9961947 8:; on0 .0900532 .090420 11.05943 .9959370 500 .0929499 .093354 10.71191 .9956708 400 .0958458 .096289 10.38539 .9953962 300 .0987408 .099225 10.07803 .9951132 200 .1016351 .102164 9.788173 .9948217 1000 .1045285 .105104 9.514364 .9945219 84 000 .1074210 .108046 9.255303 .9942136 500 .1103126 .110989 9.009826 .9938969 400 .1132032 .113935 8.776887 .9935719 300 .1160929 .116883 8.555546 .9932384

200

.1189816 .119832 8.344955 .9928965 107 00 .1218693 .122784 8.144346 .9925462 83 000 .1247560 .125738 7.953022 .9921874 500 .1276416 .128694 7.770350 .9918204 400 .1305262 .131652 7.595754 .9914449 300 .1334096 .134612 7.428706 .9910610 200 .1362919 .137575 7.268725 .9906687 10

--II ..... ---.,--'- -_ .osine.( Cotang. Tang. Sine.

Arc.

-204-

--- __

----- - --



r.

!

Natural Sines and Tangents-Continued.

-I .

Arc. Sine. I Tang.' i Cotang. Cosine.

.. .. --i------------

, 8 00 .1391731.140540 7.115369 .9902681 82 00

10 .1420531 .143508 I 6.968233 .9898590 50

i 20 .1449319 .146478 6.826943 .9894416 40

t

30 .1478094 .149451 6.691156 .9890159 30

40 .1506857 .152426 6.560453 .9885817 20

50 .1535607 .155404 6.434842 .9881392 10

9 00 .1564345 .158384 6.313751 .9876883 81 00

t 10 .1593069 .161367 : 6.197027 .9872291 50

20 .1621779 .164353 6.084438 .9867615 40,'

30 .1650476 .167342 5.975764 .9862856 30

40 .1679159 .170334 5.870804 -.9858013 20

t50 .1707828 .173329 5.769368 .9853087

10

10 00 .1736482 .176327 5.671281 .9848078 80 00

rI 10 .1765121 .179327 5.576378 .9842985 50

20 .1793746 .182331 5.484505 .9838808 40

30 .1822355 .185339 5.395517 .9832549 . 30

40 .1850949 .188349 5.309279 .9827206 20

50 .1879528 .191363 5.225664 .9821781 10

11 00 .1908090 .194380 5.144554 .9816272 79 00

10 .1936636 .197400 , 5.06G835 .9810680 50

r20 .1965166 .200424 4.989402 .9805005 40

t. 30 .1993679 .203452 4.915157 .9799247 3040 .2022176 .206483 4.843004 .9793406 20

I

50 .2050655 .209518 4.772856 .9787483 10

12 00 .2079117 .212556 : 4.704630 .9781476 78 00

10 .2107561 .215598 I 4.638245 .9775386 50

20 .2135988 .218644 i 4.573628 .9762215 40

30 .2164396 .221694 4.510708 .9762960 .30

40 .2192786 .224748 i 4.449418 .9756623 20

50 .2221158 .227806 : 4.389694 I .9750203 10'

13 00.224%11 .230868 : 4.331475 .9743701 77 00

10 .2277844 .233934 : 4.274706 .9737116 50

20 .2306159 .237004 4.219331 .9730449 40

30 .2334454 .240078 'j 4.165299 .9723699 30

40 .2362729 .243157, ! 4.112561 .9716867 20

50 .2390984 .246240 : 4.061070 .9709953 10

'14 00 .2419219 .249328 ; 4.010780 .9702957 76 00

10 .2447433 .252420 3.961651 .9695879 50

20 .2475627 .255516 3.913642 .9688719 40

.30 .2503800, .258617 I 3.866713 .9681476 30

40 .2531952 .261723 3.820828 .9674152 20

50 .2560082 .264833 3.775951.. 9666746 10

15 00 .2588190 .267949 3.732050 .9659258 75 00

10 .2616277 .271069 3.689092 .9651681 50

20 .2644342 .274194 3.647046 .9644037 40

30 .2672384 .277324 3.605883 .9636305 30

40 .2700403 .280459 3.565574 .9628490 20

50 .2728400 .283599 I 3.526093 .9620594 10

1:--Cosine. -T-~ot~~;'-!- T~ng:

-r---' -- - - 1------Sine. I Arc.

i

-205-

~

-- -- ~ ____ __ ' '__

~ ~ ' j

~ '

~

'

-~ I

i

!

j

! -

~



'


(Tang. . \ Cotang. -r Cosine. \

Arc. Sine.

--0---'--- ---_ -------, ._--_ .. _-_.-16 00 .2756374 .286745 i 3.487414

.9612617 74 000

.2784324 .289896 3.449512 .9604558 500 .2812251 .293052 : 3.412362 .9596118 400 .2840153 .296213 3.375943 .9588197 300 .2868032 .299380 , 3.340232 .9579895 200 .2895887 .302552 : 3.305209 .9571512- 1017 00 .2923717 .305730 : 3.270852 .9563048 73 000 .2951522 .308914 ; 3.237143 .9554502 500 .2979303 .312103 I 3.204063 .9545876 400 .3007058 .315298 ; 3.171594 .9537170 300 .3034788 .318499 I 3.139719 .952838220

0 .3062492..321706 : 3.108421 .9519514 1018 00 .3090170 .324919 3.077683 .9510565 72 000 .3117822 .328138 I 3.047491 .9501536 500 .3145448 .331363 ; 3.017830 .9492426 400 .3173047 .334595 2.988685 .9483237 300 .3200619 .337833 2.960042 .9473966 200

.3228164/ .341077 2.931888 .9464616 1019 00 .3255682 .344327 2.904210 .9455186 71 000 .3283172 .347584 2.876997 .9445675 500 .3310634 .350848 2.850234.9436085 400 .33380691 .354118 2.823912 .9426415 300 .3365475 .357395 , 2.798019 .9416665 200 .3392852 .360679 ; 2.772544 .9406835 1020 00 .3420201 .363970 2.747477 .9396926 70 000 .3447521 .367268 ! 2.722807 .9386938 500 .3474812 .370572 : 2.698525 .9376869 400 .3502074 .373884 2.674621 .9366722 300 .3529306 .377203 , 2.651086 .9356.t9!) 200 .3556508 .380530 2.627912 .9346189

10 •\

I

21 00

!.3583679

.383864 : 2.605089 .9335804 69 000 .3610821 .387205 2.582609 .9325340 500 .3637932 .390.554 2.560464 .9314797 400 .3665012 .39.'3910 2.538647 .9304176 300 .3692061 .397274 2.517150 .9293475 200 .3710079 .400646 2.495966 .9282696 1022 00 .3746066 .404026 2.475086 .9271839 68 000 .3773021 .407413 2.454506 .9260902 500 .3799944 .410809 ! 2.434217 .9249888 400 .3826834 .414213 i. 2.414213 .9238795 300 .3853693 .417625: 2.394488.92'27624 200 .3880518 .421046 ! . 2.375037 .9216375 103 00 .3907311 .424474 I 2.3558.52 .9205049 67 000 .3934071 .4279!2 i 2.336928 .9193644 500 .3960798 .4313;)7 i 2.318260 .9182161 400 .3987491 .434812 i 2.299842 .9170601 300 .4014150 .438275 I 2.281669 .9158963 200 .4040775 .441747 2.26373.5 .9147247 10

Cosine. Cotang. Tang. Sine. Arc.

-206-

- f -

" --

'

~ -

r

-

I

'

-




Arc. Sine. { Tang. \ Cotang .. \ Cosine.

I--------(--

24 00 .4067366 .445228 2.246036 .9135455 66 00

10 .4093923 .448718 2.228567 .9123584 5020 .4120445 .4522171 2.211323 .9111637 40

30 .4146932 .455726 2.194299 .9099613 30

40 .4173385 .459243 2.177 492 .9087511 20

50 .4199801 .462771 2.160895 .9075333 10

25 00 .4226183 .466307 i 2.144506 .9063078 65 00

10 .4252528 .469853 2.128321 .9050746 50

20 .4278838 .473409 I 2.112334 .9038338 40

30 .4305111 .476975 I 2.096543 .9025853 30

40 .4331348 .480551 ! 2.080943 .9013292 20

50 .4357548 .484136 ! 2.065531 .9000654 10

26 00 .4383711 .487732 2.050303 .8987940 64 00

10 .4409838 .491338 : 2.035256 .8975151 50

20 .4435927 .494954 I 2.020386 .8962285 40

30 .4461978 .498581 2.005689 .8949344 30

40 .4487992 .502218 1.991163 .8936326 20

50 .4513967 .505866 1.976805 .8923234 10

2700 .4539905 .509525 1.962610 .8910065 63 00

10 .4565804 .513195 1.948577 .8896822 50

20 .4591665 .516875 1.934702 .8883503 40

30.4617486 .520567 1.920982 , .8870108 30

40 .4643269 .524269 1.907414 .8856639 2050 .4669012 .527983 1.893997 .8843095 10

28 00 .4694716 .531709 1.880726 1 .8829476 62 00

10 .4720380 .535446 1.867600 .8815782 50

20 .4746004 .539195 1.854615 .8802014 40

30 .4771588 .542955 ; 1.841770 .8788171 30

40 .4797131 .546728 : 1.829062 .8774254 20

50 .4822634 .550512 1.816489 .8760263 10

29 00 .4848096 .554309 I 1.804047 .8746197 61 00

10 . .4873517 .5.581171.791736 .8732058 50

20 .4898897 .561939 . 1.779552 .8717844 40

30 .4924236 .565772 , 1.767494 .8703557 30

40 .4949532 .569619 1.755559 .8689196 20

50 .4974787 .573478 1.743745 .8674762 10

30 00 .5000000 .577350 I 1.732050 .8660254 60 00

10 .5025170 .581235 1.720473 .8645673 50

20 .5050298 .585133 1.709011 .8631019 40

30 .5075384 .589045 : 1.697663 .8616292 30

40 .5100426 .592969 ! 1.686426 .8601491 20

50 .5125425 .596908 : 1.675298 .8586619 10

31 00 .5150381 .600860 i 1.664279 .8571673 59 00

10 .5175293 .604826 1.653366 .8556655 50

20 .5200161 .608806 1.642557 .8541564 40

30 .5224986 .612800 1.631851 .8526402 30

40 .5249766 .616809 1.621246 .8511167 20

50 .5274502 .620832 1.610741 .8495860 101-- ----\--------:-----'-- - . --I--~~c. -

osine. Cotang.! Tang. I Sine.

-207- .

-

1

_

\

' i

~ ~



Xatural Sines and Tangents-Continued.

L~ ....___ Tang~_.Irc.

Cotang. Cosine. I,----0. 0,.

32 00 .5299193.624869 1.600334 .8480481 58 000 .5323839 .628921 i 1.590023 .8465030 500 .5348440 .632988 1.579807 .8449508 400 .5372996 .637070 1.569685 .8433914 30

;]40 .5397507 .641167 1.559655 .8418249 200 .5421971 .645279 1.549715 .8402513 10

33 00 .5446390 .649407 1.539865 .83867C6 77 00'10 .5470763 .653551 1.530102 .8370827 50'0 .5495090 .657710 1.520426 .8354878 400 .5519370 .661885 1.510835 .8338858 30' .0 .5543603 .6660761.501328 .8322768 20,0 .5567790 .670284 1.491903 .8306607 10.

34 00 .5591929 .674508 1.482561 '.8290376 56 00- -10 .5616021 .678749 1.473298 .8274074 500 .5640066 .683006 1.464114 .8257703 400 .5664062 .687281 1.455009 .8241262 300 .5688011 .691572 1.445980 .8224751 20 .-0 .5711912 .695881 1.437026 .8208170 1035 00 .5735764 .700207 1.428148 .8191520 55 00'0 .5759568 .70455J 1.419342 .8174801 50-20

.5783323 .708913 1.410609 .8158013 400 .5807030 .713293 1.401948 .8141155 300 .5830687 .717691 1.393357 .8124229 20'0 .5854294 .722107 1.384835 .8107234 10-36 00 .5877853 .726542 '1.376381 .8090170 54 00'0 .5901361 .730996 1.367995 .8073038 500 .5924819 .735469 1.359676 .8055837 40-30 .5948228 .739961 1.351422 .8038569 300 .5971586 .744472 1.343233 .8021232 20O .5994893 .749003 1.335107 .8003827 10

37 00 .6018150 .753554 1.327044 .7986355 53 00'0 .6041356 .758124 1.319044 .7968815 500 .6064511 ..762715 1.311104 .79,51208 400 .6087614 .767327 1.303225 .7933533 3040 .6110666 .771958 1.295405 .7915792 200 .6133666 .776611 1.287644 .7897983 10

38 00 .6156615 .781285 1.279941 .7880108 52 000 .6179511 .785980 1.272295 .7862165 500 .6202355 ,,790697 1.264706 .7844157 400 .6225146 .795435 1.257172 .7826082300 .6247885 .800196 1.249693 .7807940 20 J50 .6270571 .804979 1.242268 .7789733 10'

39 00 .6293204 .809784 1.234897 .7771460 51 000 .6315784 .814611 1.227578 .7753121 500 .6338310 .819462 1.220312 .7734716 400 .6360782 .824336 1.213097 .7716246 300 .6383201 .829233 1.205932 .7697710 200 .6405566 .834154 1.198818 .7679110 ______Q_--'--,----------------osine. Cotang. I Tang. ISine.

IArc.

-208-

------- __-~--

" .

"

:.

---



Natwral Sines and Tangents-Continued.

Cosine.otang.

---;~175; I~~604441.184737 .7641714 501.177769 .7622919 401.170849 .7604060 301.163976 .7585136 201.157149 .7566148 10

, 1.150368 .7547096 49 001.143632 .7527980 501.136941 .7508800 40

1.130294 .7489557 301.123690 .7470251 201.117130 .7450881 10

1.110612 .7431448 48 001.104136 .7411953 501.097702 .7392394 401.091308 .7372773 301.084955 .7353090 20

1.078642 .7333345 10

1.072368 .7313537 47 001.066134 .7293668 501.059938 .7273736 401.053780 .7253744 30

1.047659 .7233690 201.041576 .7213574 10

1.035530 .•7193398 46 00

1.029520 .7173161 501.023546 .7152863 401.017607 .7132504 301.011703 .7112086 20 .1.005834 .7091607 10

1.000000 .7071068 45 00 I

Cosine. --~~~-I--~~~~~-)---~ine. Arc.

Arc. Sine. Tang.

I40 00 .6427876 .839099 I

10 .6450132 .84406820 .6472334 .. 849062

30 .6494480 .854080

40 .6516572 .859124

50 .6538609 .864192

41 00 .6560590 .869286

10 .6582516 .874406

20 .6604386 .879552

30 .6626200 .884725

40 .6647959 .889924

50 .6669661 .895150

42 00 .6691306 .900404

10 .6712895 .905685

20 .6734427 .910994

30 .6755902 .916331

40 .6777320 .921696

50 .6798681 .927091

43 00 .6819984 .932515

10 .6841229 .937968

20 .6862416 .943451

30 .6883546 .948964

40 .6904617 .95450850 .6925630 .960082

44 00 .6946584 .965688

10 .6967479 .971326

20 .6988315 ., .976995

30 .7009093 .982697

40 .7029811 .988431 ,

50 .7050469 .994199

45 00 .7071068 1.000000

-209-

I ~~-~~



APPENDIX III.

(~IRCULAR MEASURE .

. 211-



445.

CONVERSION TABLES.

360 degrees=400 grades=6400 artillery mils.

1 degree= 17.781/~. 1 grade=16 mils.

1 degree=l.l1 grades.

A.' MILS IN TERMS OF DEGREES AND TANGENTS.

446.

n. DEGREES IN TERMS OF MILS AND TANGENTS.

~~gTeesJ_. Mils .. _Tangent:! I~e~r~~,-I Mils I Tange~ts1 I 17.777 .0175 40 1- -71[ff1 ---1 -.8391 -.

, .,' 2' ".,=- 35.555-~ 1.- ~, .0349,~ , 45 .. ", '~800.00' I 1.000 -,.

_3 ~_I 53.333,,_1 ".0524 50 .._,1_ 888.889~1--- . ,.

4, I 71.111 I .0699 /60 I 1055.555 r--, -'-.-, -, .,5 ,,-, .. 88.889' I .0875 '\" 70 .- I 1233.333 -'I' ..

_.JJ~;:;;;-=--J.:-_~~~~~,==~g-.}I:~~:~~J~-00__8 I 141.111 1.1405 I 100 I 1777.777 I

'---9----'- 159.9!19' ,---- .1584 "-200---0['35'55.555--1-----

-= ~g=+'~~~:~~~::..:~~~~~~g: ~~~~:~~3.-.1. -_-:-:~(j-'!i33.333-r-.!i774-'-1 ---,-- --.---- ,--,--

-212-

,

_ r

- ~ _ ~- -__

-- - -- --

-

-



\

. APPENDIX IV.

REDUCTION OF STADIA READINGS.



447. Table I.

000t.,)- ....

<I:> 'D "'"DOe.&>CO(.O(C(.J:)CQ(,C)(,Ql:OCC

Co t.o ",,:.0 U, f.o '.c tD (0 Co~~~~~~~~~<t:>'"

............................................

:..:.en~"'Q,~~~~~:-... 'D ~, 0 ... 00 1-:; Q)

.........~<I:>'D~"'<I:>"'OOOf,,:)CO""'(,CtOtO':.OOOO

<:> <c <c <c;.:><c <c 0 0 0<t:>"'000

---0 (0 X> 00:'1 en Crt. .. . 01COw -a--:nO ... :o

.........................................

0000000000

0000000000

00000000000000000000

Qo

-------_. -'.- _ .. .

...... CO~(O<oceCDCOt.OC:>(otO<0<0<1:><0<0<0<0<0<0<0 tOco~t:>tOtO('ocotOc.o :::OCOfDCO(OCCCQCOCQCOf,C<O<O<O<O<O<O<t:> "'<0<0 (0 COtOCQCO to CDCQ c,oc.oO:', Oo~~~~<c<c<c<c<c<c (o~t.L,(o~~~Q:>(O~ (O<O~(O(OCoto(ou,(oIlOC/t 00 OC C,Q to co 0 0 0 l~t.;ll.:l w <N w ........ l:/1 C/1C/1C/1a>a>a>a>~~~

0oOCoOCoOCoOCoOCoOCoOCoOCoONN NNNNNNNNNN N NN NN . .. .. .. .. .. .. .. .. .. .o~o .. A.e-,~~~:.....oo(or.o oo~:..:.~~Q,a,~~~ ~~~oou,to~oo:....CoOt-:l ec~-.a ......cno ... ;X) 1. )- -1 . .. .C11 co CN -.a t..;, <:n 0 ... :x w - .a . .. .. c:.nr.c .. ':.IOI'W(7)O~

--_ .._---- .. ----_ .._- -_._--

co co co co to co <0 co (0 co •0 co co (0 tOtO co co ... :> ( :) co<0<0 <0 'D <0 <0<0 <0<0 :::0<0<0<0<0"'<0<0<0<0<0

"'<0<0<0"'<0<0"''''<0"'<0"'<0<0<0<0"'<0<0NO:':' ~~:..:.:..:.~:..:.:..:.:..:.:..:.:..,:..:. ~:":'CoboooOoOoOoOoio 00000000~~00000000nocn "'. Q) Q)-J -:10000 tD co 0 0 ..........~ N '4. .. .. .. c :.nQ1<:ncn- .a -.a- :aoo

Ncncnc:nC11 ............. .,. ...................

....CoOCoOCoOCoOCoOCoOCoOCo>w000 N:-:.....O(OfDOOOO:..:.~~ en a. A. ;~;...:- 0 o(o<OOo:":':":'entnCn~Il"W -.a C,l'. (C 00 I":' en ... . c:.n(,:'l CN OC tv 0 .. 00 C4-.a

.... <:i\O~OONcnOCJ1(Q

----.- .- ..._----- ---------_._-----_. ---_.- .. _._---~~~~~~~~~(Q (Q(Q~~(Q(Q(Q(Q(Q(Q

(Q(Q(Q~(Q~(Q(Q(Q(Q(Q (Q(Q~(Q(Q~(Q(Q(Q~ ~(Q(Q(Q(Q(Q(Q(Q(Q(Q

~~~.~~~~~(Q(Q O-N~~~~~~~ ~OO~(Q(QQ~~~~

~~~a>~~~~a>a>~ ~~a>~~~~~cn~ cncn~~~~~C/1~~

~~~~~~~~~i~~Q~OO~~-~o~~ ~~-~(Q.~I~~O ~~~~N~Q~~~

:::o:'

o

(Q~~~(Q(Q~~~~~ ~~(Q(Q(Q=~~~(Q ~(Q~~~(Q(Q(Q~(Q

"'<O~~~"'<O"'~~'" "''''<O<O~'''<O~<O<O ~<O<O<O<O<O~~<O<O

~~~~~(QO_~~~ ~~~OOOO(QO-~~ ~~~~~~(QO~_

~~~~~~~~oo~oo

en en A. i~ r~ ; .. . ; . .. <:> :.= C o :.0 0, :';1 ::.. t -: J ; .. .: - <:> (0:JJW .... -"'O .... OOI .... -J_ l:I1(Q .. :.t:Jt~~-:.r.~c..a OC'r~c:nO-:ll(Q~-.aI.:c:n

"""

..- .. --- ....00000000"'<0'" <O<O~"'~~"'~~'" ~<O"'<O~OO~OO~OO

:""W Ni~:":'" 0 ~~~;., :....:..:, b,A. ~C4i.:. N;"'O ~(c Oc::x,:...0 .. :Cl1~-.a-",O .... :cW -a- -:l1 :> ... ::,()W -a- w\ O~ OOW-a_ c.nO ...

(Q~~(Q(Q~~~(Q=(Q ~~~~~(Q(Q(Q(Q~ (Q~~~~(Q~~~~

OO~~~~XX~~(Q(Q (Q~(Q(Q(Q(Q(Q(Q~(Q (Q(Q~(Q(Q~~(Q~(Q

~~~~~~~~;...~~~~~c:n-.aOO~O_~ ~CJtc:n-.aX(QO_~~ l:I1~-.a~(QO_~~~

~(Q(Q(Q(Q(Q~(Q(Q(Q(Q (Q~~~(Q(Q(Q~~~ (Q(Q(Q(Q~(Q(Q(Q(Q(Q

OO~~OOX~OO~XX~ OOOOOOOOXOOOO~~~ ~~::,()OOOO~OO~OO~

-~~~~~O_~~~ -JX~_~~~~~~ O-N~~~~~O~

.... - ..~-... _----~ I~ .. .-

;... f.o ~OO:'l~ <:nOt:r.O .... OOWr,)~,...~O ... f,Qw

...._------- ..---------0... c..., ~;~;.....:.... <:> 0:.0-.a I~ 0 CD X I~ :f')

...... - ........ - ..... --000000000

~~:"l~~~o-.c.n~~-Q1(,Q~;X)l-:J-.a,...~O

Q'l

o

-214-

------- ----------- ------

'" '" '" '" '" ~ '" ~

~ ~ -

"''''''''''''' ~ ~

- - - --- -- -

~ _ -~ ~

~ ~

---

'" ~ ~~ ...... ~

~ ~ ~ ~ ~ - ~ ~

- -

~~~~~~~~~~~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~ ~~~~~~~~~~

~

~~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~

~~~~~~~~~~~ ~~~~~~~~~~~

~~~~~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~ - - - - - - -

~~ ~ '" ~



=i CtN""'CIO~:==: ON "llf'coaoON..,UtClO ON.,."'OO=N""Utao~ >t:lO>t:l..

NNNNN~MMMM ~'l)W')W')....,C'O r-:~~

...e"-1r-C"-IOO~aoC":)OO~~ --1"c:n~otOotOotO...-4 fJ:) .-t t :: > . .. .. to ':'J r- Co) r- C"1 t- r-C"l0>

..c:n~OO""''''''C'JC'JC''?C'?

~~tOtDtDr-r-OCOOQ) c:nOO .......... C'JC'JC"':)C"':)~'III:f"

~C'!C'-!GI "';"':e-ie-iNNNe-ie-ie--i c-i~e-iC'ie-iC'ie-ie-ie-iN e-i~MMMc?c?c?et5c?c?0 > C'lC\lCNC'lC\lC'JC'JC'JC'JC'J C'IC'IC'IC'IC'IC'IC'IC'IC'IC'I C'JC'lC'JC'JC'JC'JC'lC'JC'JC'JC'I

M.-4

....,..c:Df..C'III:f" ..... c:DCOC"?.-( OOCDC"':lO OOtOC'J Or-'" Nc:Dte..,. .....Of.DMOr-lQ C"lr--..CJ?~~~~~r--:~r--:I-: tDtDU'>c.etOtOtOtO~'III:f" ~C"?MC"':)C"?C'JC'JC'JC'J~"'" r-:~~

Q .;.~..,;~~~.;~~..;. ~';'';'';'';'..,;..;.';''';'.;.';'

=: 'III:f"""""~""''''''''''''''''''1'''''0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0>0>

--_.~- ..._- _." -"-- .. -'.- .'. -_._-_._--

t!..,.c:n~OtOOU'> ..... tO ..... r-C'-1t-C"?ooC"?oo~aa"" c:DtOOl.OOU> ..... U) .....-e:-1 CO C'I to-

~~~~~~~t-:r--:~ OOc:nc:nOO .......... C'JC'JC"? ~:;~~:::::::;::: ~C"!C"!

GI 0000000000OOO....:....;~....:,..:,..;....:

0 > C'JC'JC'IC'JC'J::'.JC'JC'JC'J:'-I C'1C'JC"JC'JC'JC'JC'\IC'lC'lC'J CNC'JC'\IC\lC'lC'lC'JC'JC'JC'\IC'J

N

OOtOC ""' ..... a::tDC? ... c:,Df,D ..,. ..... CD CD ""'1' C'1 c:n r-..,. C'I c:n t- ""1' IN 0) t- ""'1' e"1 0) r-..,. ..,OCC'l.. CO<QCDtDtOU:tOtO""'1'...,. ~~MC"?C"?C"?C'JC'JC\lC'J ...............0 OOOCD Cf)c:n ~o:C'!Q

tr.iu':itr.i~uo;ll:itr.itr.iU-;;..;tr.ilr,jtr.i.r;;Lti,~tr.itr.itr.iLti ,r,; IQ u-;; U; tr.i L"; tr.i .;. .;.

=: 0> 0> 0>0> 0> 0>0>Q'l 0>0> 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0>0>

_.__ .. _. _.- _._---- _._---- .._--

~OO..,.(7)lt:)OlO.....,CQ ..... r_ e'J00 M oc : . ., . 0) 0 lQ O~ . ... . C'Oe_Jr _e_JOCMOO~ >t:lOlO

.. r-r-OCOCCDOO .......... C'JM M ...,. lt:> '0 c.e r- r- O O O O (7 ) c n OO . . . . .. . . . .'Jt'J~ ~~C'!

GI ~~:~~~~~~~ aiaiaiaiOOOOOOO0

....................'lC'lC'JNNNC'.

.-4- .,. ~I 0) r- M ..... 00 tD ""'1'!Ncnr-.t:)~OlX)c.eC'o? C) to . ., .c... r- lQ (:'1 0 00 C"lI>':N

.. C":)~C"':)C\lC"Je"oJe"olC\J""''''' .....0 00 00 cn(7)) CDooCCooOOr-r-r-r-r-~ ""':~='!Q cDu)tDtOeDtDtDcDcDtC tOtDcDtD~tD~LO~LO ~.~~~~U-;;~~,~,~lfi

=: cn~cncncncnQ')cncncn cnO)cnCDQ)cncncncncn 0>0>0>0>0>0>0>0>0>0>0>

_. ,.- ..

o U) . .. .toO C'1

r- MOO"" c:')l.~OtD .... c.eC'J r-MOO~ C) 'Of1' 0 ...... D . ... . r- e"ol00 C"')

::~~.. .. .. .. .. C \I e:--I ( , M ..,. lQ lO CQt-t-COOOCDCDOO ..... ....t'lC":)M...,.~lO..oc.ec.er-

GI ~,.;r-..:r-=l..:r-..:~I'.:r...:t..: ~~~~:::~~~~~:,.. ...............................................

0.-4 .. 00 "'.c.,. ':'-J00 to ~NO 00 c.e C'1 0 00 ..,. C'J 0 r-lr.> C"? .. .. r- It:) C"1 0 00 tD .,.OC'"

Q ~~~~~~~~~oc: t- r- r- r- t- c.e CQ c.e CQ c.e lOlOlt:>Lt)~..,..,....,.~C":)C":) r-:~C'!

=: c.e'-CtDt.:lCDtOtDCQcDt.O tDtDcDtD~tttDtD~eD tOtDtDtDtDtDtDtDtDcDtD0> 0> 0> 0> -0> 0> 0> 0> a> 0> cncncnc:ncncncncncncn 0>0>0>0>0>0> o>o>c> 0> 0>

--_._-------------------------_ •._.-_._.

t!1t:> .... c.e C"1r- 00 ..,. en't:> o tD .... r- C'J OC M O ': l . .. .. 0 ,~ ..... t D e"oJr- MOO"" cn L~ 0

lOll':> CD CD r:- r- 00 00 en o O - ..... C'lC '1 C "C """'L O lOc.ec.er-r:-OOOCcncnO .....C' 1c,c . ... .

GI ~~~~~~::::::~::: :::~~~~~~~~:::: -:-:~0

lQ M ':"1 0 00 c .e . ., . M ..... en r- lQ M .....cn 00 to .. ,. e-l 0 00 to..,. C'1 0 00 to..,. ':'1 C 00.. lQlQlt:lQ.,....,...,."",...,.M C":>C":)C"":lMe-JC'J:"JC'JC'JC'1..........000000')

.,.0>'"Q r..:t.:r..:.....:~~r...:t..:r..:r..: ....:r...:r--=r-..:r...:r...:....:....:~.....: .....:.....:.....:.....:....:.....:.....:r..:""':""':u:i

=: O)a-~O)~C')aaa')O)~Q) c:nQ')O)Q')cnO')O')~Q)O) c:nO')~O')Q):r..Q)cnc:;)Q)O) l:~~

-_ .. _._,--- .. . .. .. .. .

OO.,.O)It:)....-ltOC'Jt-C'l?oo "'11' 0 It:) ..... c.e C"Jt- 0)01O....-ltOe--Jt-C"':)OO""Olt)

::;~~. t-oooocnOO....-l ...... C\IC\I C":)...,....,. 1010 to tOt-r:-CO Q)o)OO ......C\J"'C"":>~~

GI ~~~~..,;.~..;...;.~~ :::::::::: ~:~~~~~~~~~0

:,.. ...-t....-l ~_ ....-l

00

.. . to'~ .....0 00 t- 10 M C"1 OOCr-lt)C"lC'lOOOCOlt) M ...... O)OOU'''''1'N ..... cnr:-lt)

.~~~00000>0>0>0>0> 0> 00 00 00 OC 00 00 t- t- t- t-t-CDCDCQtOCDCQlJ:)lQlQ

QOOOOOOOOOO~r..:r..:r--:r--: r..:.....:r..:t--=r..:~r..:r..:r..:r--: ~~.....:~r..:r...:r--:r--:r..:....:~

=: 0> go. a> 0> 0> 0> Q> 0> 0> 0> 0>0>0>0>0>0>0>0>0>0> 0>0>0>0>0>0>0>0>0>0>0>

CN~~~ON~~~ OM~~~CN~~~CNNNNNMMMMM .~ •••

---_._---------------------------

NOo>r-CO.,.C"l_OooCO

C'\IC"J....-l_ ....................... OO

ooooooaOaOaOaOoc~oooo0>0>a>a>0>0>0>a>0>1j;0>

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t!GI0

:,..

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-215-

.........

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--- - --- -- _

~ ~

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---

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...... .... ~ ...........

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~~~~~~

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,-

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;;:=:::~QDCft"'NC a::(;10C11 CQl)~"N=QoO\""N=

(X.O) N=CXlO \_NC

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.APPENDIX V.

AZIMUTH OF POLARIS.

-219-



Lat. 51°-53°, 6/10

Lat. 56°_57°, 7/10 ,

Lat. 53°-59°, 8/10

Lat. 60°-6p, 9/10

.~

450. The table below sh~ws the azimuth of Polaris in different positionS

. with respect to the pole. Epoch 1911; polar distance 70'. Latitude 00 to18° north. This table n.ay be used until 1930.

Fig. 146.

Clock Readini ' 0(. Azim- Clock Readini' 0(. Azimuth Clock. Reading of. Azimuth

5 Z uth 5 Z of 5 Z of

Cassio- Ursae of Cassio- Ursae Polaris CassiJ- Ursae Polarispeia Major Polaris peia Major peia Major

XII :30 VI :30 18' IV:30 X :30 0 49' ~~Il II 358059'

I VII 35 V XI 35 IX III 358 50

~VII:30 49 V:30 XI:30 I 18 X IV-- 358 59

II I Vf!~ 61 VI :30' XII :30 359 42 X:30 359il!_II--IJ~-- }--L~~~~ ~I V --?~£IV X 61 VII:30 1:30 1359 11 XI:30 V:30 359 42

'\. For higher latitude add to the small azimuths or subtract from thelarge ones, as follows:

Lat. 19°-30°, 1/10

Lat. 31°-37°, 2/10

Lat. 38°-42°, 3/10

Lat. 43°-46°, 4/10

Lat. 47°-50°, 5/10

It is well to keep track of the position of Polaris by noting it fre-

quently and taking the corespondence clock time. Then if on a cloudy night

a glimpse of Polaris is had, the observation may be taken even though thOother stars can not be seen.

-220-

'1

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,

APPENDIX VI.

DEFINITIONS AND DIAGRAIUS.

-221-



Fig. 147.

-222-

TO ,sTEEPLE:(3. KiloS)

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Fig. 148.

-223-





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Fig. 150.

-225-

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fig. 151.

-22~

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451. Adjusting Point. The point used for the adjustment of the elements

of fire is called an adjusting point. It is the particular part of the objective

on which the guns are adjusted.

Note: Terms used in .this chapter are illustrated graphically in

figs. 147, 148, 149, 150 and 151.

452. A iming Point. An aiming point is the point in which the gunner~ights when laying his piece for direction.

453. Base Angle. Tpe horizonal angle between the base line and the

orienting line, measured in thl~ same direction as the sight graduations,

is termed the base angle. It is a clockwise angle for the American panoramic

sight.

454. Base Deflection. Base Deflection is that deflection, which if used in

laying the base piece will direct the plane of fire of that gun on the base

Point, and for any other gun is the deflection that will direct the plane of

fire of that piece on a line parallel to the base line.

455. Base Line. The base line is the line joining the base piece and the

base point. It is always continued across the orienting line if an orienting

line exists, to form the base angle. It is used as an origin for direction from

the gun position.

456. Base Point. A base point is a well defined point of the terrain

Usually situated in the battery. sector, which, as one of the points defining

the base. line, is used as an origin for direction from the gun position. It

is generally shown on the map and it is desirable that it be plainly visible

from the observation post. It is advisable that a base point be chosen which

Inay be fired upon, so as to check the laying of the battery on the base line.

One base point may be common to several batteries.

A battery may have several bae points in which case they

are determined as "Base Point No.1, "No.2", etc.

457. Battle M'ap. A battle map is a large scale map showing the enemy

.works and occassionally the friendly works.

458. Eventual Zone. (Usually eventual zones Nos. 1 and 2). Zones with.

in the objective zone, but outside the normal zone, within which the bat-

tery may be called upon to fire under certain contigencies are termed

eventual zones. .

459. Control Point. A control point is a geodetic point or other point

\ the coordinates of which are known, that may be used in topographical

operations~

460. Control Sheet. A control sheet is a sheet containing a list of control

points for use by the battery reconnaisance officer, battery commander, or

battalion orienting officer, in the location and development of the position"

461. Datum Point. A datum point is a clearly visible point of knownlocation selected as an adjusting point. It is either shown on the battle map

or is a point that may be accurately plotted ..

462. Declinatinu Point. A declinating point is a point used for the declina-

ting of instruments. It is a point through which pass several lines, all ma.

terialized upon 'the ground, the azimuth of Y-azimuths of which lines are'

known. .

-227-

'



.,463. Deflection Constant. Deflection constant is the deflection setting

which must be set on the sight to bring the plane of sight parallel to the

plane of fire. For the American sight it is 0 and for the French 75 itis 100.

464. Directing Piece: The gun for which the initial data is computed,also called Base Piece.

.465. Field of Observation. The angle between the right and left limits

of observation either with the naked eye or with an instrument, is known

as the Field of Observation. Usually the field of observation is limited

by the location of the observation post. The O. P. should be located so that.

the entire objective zone is included in the field of observation.

466. Firing Angle. The firing angle is the horizontal angle between the

plane of fire and the direction of sighting measured in the same direction asthe sight of graduations.

467. Firing Board. The firing board is. a board of wood, or of wood and

zinc on which is mounted the firing chart or battle map, preparatory to the

measurement of the elements of fire.

468. Z.'iring Chart. A grid sheet, or the battle map itself on which are

shown the elements used in the computation and preparation of the firin~

data is termed a firing chart.

469. Limits of Fire. Limits of fi~e are lines marking limits of areas on

which fire can be delivered. .470. Ma-rker. The term marker is applied to'~ metal or wooden stake

three or four feet in height used in materializing an orienting line. The

markers used in staking out an orienting line should be distinctive for eachbattalion. .

471. Normal Zone. The normal zone, is the zone within the objective zone,

for which a battery is normally responsible, and within which its normalfire is directed.

472. Objective Zone. The objective zone includes the areas beyond the

friendly lines and within the lateral limits of fire. .

473. Observation Post (0. P.). An observation post is a post selected for

the observation and conduct of fire, for the observation of a sector, for the

study ,of objectives,. and for the purpose of securing information of the

enemy and his activities. Observation posts are classified as firing O. Po's

Command O. P's and Intelligence O. P's. .

474. Observer Displacement. The observer displacement angle is the

angle at the objective between the observer and the battery.

475. Observing Line. An observing line is the line joining the observerand the adjusting point.

476. Observing Sector. An observing sector is the sector subtended by the

objective as viewed by the observer. It contains the observing line.

477. On the Base Line. A battery is said to be on the base line when the

plane of fire of the base piece is directed on the base point and when the

planes of fire of the pieces are parallel.

478. Orienting Line. An orienting line is a line of known direction, ma4

terialized upon the 2Tound, and located on the map or chart, bi reference to

which the guns are laid for direction.

-228-



479. .Orienting Point. An orienting point is a point of known location

from which it is possible to orient.

480. Origin Line,. An origin line is a line selected near the center of the

. field of observation to which angular measurements are referred. If the sec-

tor is very extended several origin lines may be used. Usually the origin line

is .the line extended from the obsrvation post to the base point.481. Place Mark. A place mark is a point materialized upon the ground

and exactly located on the map, with known coordinates ana known eleva-

tion, by reference to which the guns may be located, on the ground and upon

the map, both horizontally and vertically.

482. Position. The position, strictly speaking, is the Gun Position, al-

though actually the position includes the battery organization for combat,

-or all elements outside the objective zone which may be used in the com-

putation of data, the observation and conduct of fire.

483. Range Deflection Fan. A range deflection fan is a graph composedof rays and arcs, showing range and' deflection, and drawn on the firing

~hart, the battle map, or separate transparencies, for the determination of

firing data. The fan is usually drawn for the directing piece, sometimes

for the observation post, and sometimes for both. In many cases the de-

flection arcs only will be shown and the ranges will be measured by a range

.arm.

484. Reference Point. A reference point is a prominent point on the ter-

rain by reference to which objectives may be identified. .

485. Referring Point. A referring point is an auxiliary or individualaiming point used by the gunner in referring his piece.

486. Witne88 Point. A witness point is a point clearly visible on the

ground, but not necessarily located accurately on the map which is used

for obtaining an adjustment preparatory to delivering fire on an unseen ob-

jective. The method consists of two adjustments; the first usually by aerial

-Observation on the objective, the other immediately afterward on the witness

point. The relation between the adjusted data for the witness point and the

-objective holds for subsequent firing. For such subsequent firing it is

necessary only to adjust on the witness point and calculate data for the<>bjective.



APPENDIX VII.

MAPS AND RECORDS.



CLASSES OF RECORDS.

487. One of the important duties of the battery commander is the com-

pilation of exact records, the elaborateness and exactness of which, depend

.Upon the stability and importance of the battery position to which theypertain. .

Records are kept of all battery activities and of all data affecting

the battery's functioning in combat, such records being for permanent use in

the battery position, either by the original battery commander or by his

Buccessors. Briefs of these records are made, from time to time, for trans-

mission to battalion, regimental and higher commanders.

Data pertaining to the artillery sector fall into two general classes;(1) maps and charts, and (2) written records.

A. MAPS AND CHARTS.

(1.) The Battle !\lap Of The Sector •

. 488. There should be kept at the observation post and at the command

post a battle map, of the latest edition, constantly kept up to date by the

aid of additions and revisions published by the topographical section.

(2.) Charts.

489. Among the several charts usually ~repared are the following:

(a) The firing chart: a great saving of time and ammunition can be

effected by making use of a suitably prepared firing chart, to be used forthe computations and measurements incidentto~ the preparation of fire.

A complete chart of the. Typical. Battery Sector would show:Preliminary topog7'aphical operation8;

The Sector, which is the area enclosed by the lateral limits of fire,

the maximum range and minimum range of the battery;

The Objective Zone, which is the area beyond the friendly line withinthe sector;

The Position, which means strictly the Gun Position,' but includesbattery organization for combat, or all outside the objective zone which is

used for the. computation of data, the observation and conduct of fire.

490. The following method of preparing a firing chart has been found

satisfactory. A sheet of drawing paper is mounted on a flat surface, a

wooden board or zinc sheet. Squares are drawn upon it, the sides of which

are 5cm. long. The lines are numbered to correspond to the grid lines of

the battle map of the sector considered. Upon the gridded sheet are plotted

the elements necessary to the calculation of map data for the conduct of

fire. No topographical detail is really essential on a firing chart, for it al-ways can be obtained from a corresponding battle map. However it is usualto draw, or paste on, the enemy organizations.

The grid system should be drawn first with a hard sharp pencil

and, after checking, with ink. It is essential that its construction be precise.

The error should not exceed .2 mm. in a 5 em. square. The following methodof procedure is suggested, fig 152.

-232-:-



Co

... ,/ .

"-

, /

/\\

a A 8 b

I

'. /

" "

"- /'......

d

Fig. 152.

1. Draw the major axis,ab, approximately in the middle of the

paper.

2. Draw the minor axis, cd, perpendicular to ab, see par. 72•

.3. Draw arcs with centers on the axes. The radii for the arcs from

each axis should be in multiples of the distance between the lines of the

b'Tid (5 em. on a 1/20,000 map) and the arcs should be tangent to the

proposed outer lines of the grid.

4. Draw tangents to these arcs. They will be parallel to the axes.

5. Commencing at axis cd, by means of a carefully graduated ruler,

determined points at 5 em. intervals on the axis, ab, and its two parallels.

Join successively the set of three points, lining the paper in the direction of

ca.J. In the same way the paper may be lined parallel to ab.

7. Place numbers on the grid lines representing the metric coordi-

nates of the portion of the battle map to which the firing chart corresponds.

The grid may be checked by drawing a diagonal through two inter-

sections. This diagonal should pass through all corresponding intersections.

The battle map is somE:times used as the base of the firing chart.

When the map is mounted upon the board by pasting, considerable angular

error may occur, due to the irregUlar expansion and contraction 'from wet-

ting. This error may be confined within a small area by cutting and mount-

ing the map in sections. This, however, is a slow process and requires

great care. :

491. (b) The Range and Deflection Fan. To rapidly determine angular

relations, and map ranges to certain points or targets within the sector, a /

-233-

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range and deflection fan may be prepared on transparent paper, or on the

firing chart itself. Hays are drawn usually every 50 mils, to include the

width of the field of observation when used at the observation post or the

width of the limits of fire when used for the directing piece, fig. 153. With

the middle ray as zero, the rays are numbered to the right arid left in mul-

Fig. 153..

tiples of 50. With the O. P. or the base piece as the center, arcs are drawn

over the rays at ranges of, usually, every 500 meters to include the extreme

, range of the gun. These are numbered properly.

-234-



Another method, which has been found satisfactory, is the use of the

range arm. An arc is constructed upon the firing chart with a radius of

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-235-

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the extreme range of the gun and is graduated to five mils, with zero at

the intersection of the base line with the are. The range arm, made of some

non-shrinkable material, is graduated to ten meters and includes the extreme

range of the gun. The range arm is placed upon the chart with zero at the

. gun position and its edge passing through the target. The range is read

from the arm and the deflection, right or left, is determined by the pointwhere the edge of the arm intersects the deflection arc, see fig. 154. I

Although it is desirable to keep the firing chart free from unecessary

lines, there is an advantage in placing the range and deflection fan upon

the chart itself. The error due to contraction or expansion is in this way

VJZ4000

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<'1iminated since the fan expands or contracts with the chart. The deflec-tion rays need not be continuous, only their intersection with the range arcs

need be shown. It is desirable, however, before placing the fan upon the

('hart permanently, to ch~ck its accuracy by actual fire upon an adjustingpoint.

492. (e) Po~ition Chart. This is a chart showing the organization of the

gun position in detail. Preferably it is made on a scale of 1/2,000 and

. -236-

"

~

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usually shown:' (1) the position of each gun, its coordinates and elevation,

referred to the place- mark; (2) the orienting line; (3) aiming stakes for

day and night, and the direction and designation of aiming point or auxil-

liary aiming point; (4) avenues of ingress and egress" with notes on hours

for their use; (5) command post, deep shelters, telephone stations, latrines,

Kitchen, etc., fig. 155.

493. (d) Auxiliary Positions. Diagrams and _ charts are _ also prepared

showing au~iliary positions with routes thereto, and coordinates and eleva-

tions of place marks therefor.

494. (e) General System of Communication. Charts are required showing

the general system of communication between elements of the battery, with

other units, and with higher command posts.

495. (I) Chart of Visible and Invisible areas. The zones, visible and in-

visible, from the observation post should be accurately indicated, either ona special map posted at the observation post or charted to scale on trans-

parent paper which may be. superi~posed upon the firing chart or battle

maps of the sector. Copies of this chart are prepared for use by the bat-

talion and higher commanders. The method of preparing the chart has been

considered in Ch. XIII.

Areas that are invisible frorr( one O. P. may be visible from another.

By dividing the area included in the field of observation into small squares,

the possibilities of observation from auxiliary O. P's.,' on areas invisible

from any particular O. P., may be -indicated. The number -of numbers ofthe auxiliary O. P's. Which can be used are placed in the square in question,

fig. 156. .

496. (g) Chart of Dead Space. The study of the possibility and the ef-

fectiveness of fire on reverse slopes and on heavily wooded areas within a

. sector is purely topographic and its value depends upon the degree of ac-

curacy of the battle map. In no case, however, should the study be neg-

lected, for all topographlcal conditions capable of affecting the ,precision of

fire must be ascertained as far as possible. Such charts are particularly

important for the fire of guns with a flat trajectory. The chart of dead. areas is prepared to scale, either on a special map or on transparent paper

which may be superimposed upon the firing chart or battle map of the sector.

Copies of this chart are prepared for use by the battalion and higher com-

mander. The methods of computing dead space have been considered in

Ch. XIV.497. The possibilities of fire by neighboring batteries upon the dead

areas of a particular battery should be indicated upon the chart of dead

space of that battery. This may be accomplished by dividing the field of

fire into small squares, either 1cm. or 2.5 em. on a side; inserting the num-ber of the neighboring battery within the squares indicating the areas upon

which it can deliver fire. The correct squares may be determined by a study

of the chart of dead space of the "neighboring batteries, see fig. 157.

498. (h) Combined, Charts of Higher Commander. The topographical

records of the battalion and higher organizations comprise information trans-

mitted by the batteries, together with that secured form other sources. These

records consist of information relative to the organization of the gun posi-

-237-

-

'





,. ,,\

J~1/

\\ "S" I

It:W . I....

.\ ~y /~,k$I

/'~V I

I,

(;E J--

A--ahU c.. ,:'

Ii;'\,.." I~\. I

f:'.

\ .-to\. :+-''I!l.

.~

-- /1\ /

L '1

\i" ;- .J (l\ -

~~\!!Y C!I!Jc '\t::J ,.~ CE~-d::-

-239-

~ ~~

~

~ ~ ~

~ ~ ~~ ~ ~ ~

~ ~

~ ~ ~

~ ~ ~ ~ ~

--

~ ~

~

~



is enabled to pass. along, without difficulty, all information that his succes-sor may need.

499. The artillery commander, in order to direct properly the fire of his-.-

artillery, needs to have a map so arranged that he may see instantly thepossibilities of fire of each battery.

There are various methods of preparing such a map. Among. the

most simple and most practical, may be mentioned that one that consists.

of sticking into the battle map, (fastened to a board or to the wall), pins

or needles at each emplacement of the batteries of the command. A colored

thread, indicating the caliber, attached to each pin, carries a mark cor-

responding to the limits of the range of the battery. It is, therefore, easily

seen whether a target may, be reached, and if so, by what batteries.

500. . To prepare plans of fire concentration, the following system may be-

used. Cover the battle map with a sheet of tracing paper marked off into-:.

Rquares of 2.5 cm., one fourth of the ordinary square, see fig. 158. Construct .

the field of fire of battery A, drawing an are, BC representing the range

corresponding to the maximum elevation. Indicate the dead areas within the-

field of fire. Mark in each square, or fraction of Rquare that can be'

reached by fire, the number of the battery which can fire on the square,

such as, 171. Repeat the operation for each battery. The result will be a

very' simple and clear document enabling anyone to make up .without

difficulty, a plan of fire concentration of the command. .

501. A document may be prepared in a similar manner to indicate areas.

visible or invisible from any observation post of the sector. Such a chart.

offers a convenient method of rapidly determining the most suitable obser-

vation post to use, in adjustment of fire within any particular area.

B. 'VRITTEN RECORDS.

502. (a) The B. C. Data Book. The written records of a sector consist

of the B. C. data book and certain subsidiary documents. The n..C. databook contains the record of all accurate data pertaining to the preparation

and occupation of the position and its subsequent activities, including initial

elements of firing data and tactical and technical problems concerning the'sector and position. It is a permanent record of the position and is turned

over to,the relieving battery commander. If the position is abandoned, the'

hook is forwarded to the chief of artillery of the sector concerned, and, i~case of clOReattack, it is destroyed.

5U3. (b) The battery commander keeps an Ammunition Record and a

Gun Diary for each gun, which diary remains with the gun throughout its'life. .

r04. (c) A Target Sheet is kept at the observation post upon which is.

~ntered, data concerning new targets discovered, and corrections on the lo~a-tkn of targets previously reported.

505. The batter~' commander transmits, from time to time, reports on the

general enemy activity on his front, sometimes including exact records o( .

enemy artillery fire, reports on new targets discovered, and corrections on

the location of targets previously reported.

506. 'Vith reference to records, it is important to remember that the ef-

ficient battery commander will not permit himself to become a slave to forms.

-2-i0-

-

- _



32.

31

30

35

34

33

2.9

25

2.7

2.6

2.5

2.4

23

2Z

ZI(0

II II

. and schedules. The elaboration of records is valuable only in the exact

. measure that it facilitates the tactical and technical work of the battery

. and increases the efficiency of the battery's fire.

(9 30 31 32. 33 "34 35 36 37Fig. 158.

-241-



408

308

197

7

16

451

162-164

340

338

INDEX.

A..Abney level

Abbreviated coordinates _~ ---- ---------------------------Absissae

Accuracy

Computation of minimum range and elevation --------------Inter~ection

Topography

Acute angle

'Adjus~ng point ----------------------------------------------.Advantage of

Orienting ]ine

.AimingCircle 142, 404-407, 411-415Direction 426-432Point 452, 426-432

Alidade 54, 153-156French 155

Leveling 155Sighting 154

Telescopic 156

Tests of' 59

Triangular 153

Al titude 84

Ammunition record 513

AngleAcute 16

Base 410, 454Definition '-_________ 15

Expression of-, by tangents 32-45Firing .______________ 466-499

--Of divergence ~_______________________ 345-347, 427-429

-of observer 'displacement. 474, 507

-of site 289, 294, 319, 295I~eflex 16

Round 16

. Straight 16

To plot-using gradient 47

, To plot-using percent 49

To plot-using tangent 35--traverse 188

Angular measure 15-29

Base equivalents 30

-243-

/

_ _

_ _ _

_



467

167, 168

333

502

222

502

506505

457

425, 427

399-400

384-386

382 .

134, 135

207

Conversions. in- ~_________________ 30, 31

Definitions ---------------_______________________________ .16

Systems --------------______________________________ 17

. Annual variation -------------________________________________ 375

Area sketches -------------__________________________________ 214-223

Border ---------------__________________________________ 222, 238Conventional signs ---------_____________________________ .218-220

Information ----------__________________________________ 217

:Lettering --------------_________________________________ 223

Title -----------------__________________________________ 221

Artillery sector ------------__________________ 451-486, 487-506, 395-397Auxiliary position

Chart of -------------___________________________________ 493

Azimuth -'______________ 369, 370, 372

Back-, resection by 209, 383

of Polaris ~____________________________ 451

Used to determine compass declination 379

Y ----------------_______________________________ 348, 369, 372

B.

Back azimuth, resection by --------____________________________ 209, 383

Band, elastic, visibility by means of ---_________________________ 288

Base

Angle ---------------------_____________________________ 410, 453

Deflection ---------------------_________________________ 454

.Equivalents ---------------------________________________ 10, 30

Line -------------------------__________________________ 455, 477

Point ---------------------_________________________ 424, 425, 456

Battery commanderData bookRecords

Reports

Battle 1\f aps :. .Bearing

Determination of compass declination by means ofOf target

To find a bearing with a protractorBench lllark

Bisectors, perpendicular .

BoardFiring

Slope

Donne projection

Dook, B. C. data

Border, position and area sketcheg

-244-

-,;j

------------

-------------

-----

-----------

-

~~ _ _ _

__ _ ~__

_ _ _

~ _ _ _ _ _

_ _

:



c.

\

500

331

44

13, 30

43

57

191

, 284

271-274

36

37

3

378-381

379

375

369-372

146-150

145388-394

384-394

383

--------------------------------------------------orth

Peign~

Prisma tic:...-

Used as aiming point .Usc"d to lay gunR

Used in magnetic resection

Concentration fire, plans of :..Conic projection

Constant

Calculation

Angular values above limits

Mental- in conversIons

Using tangent -----.-------------------------------------hainsChaining

ChartAuxiliary position 493

Combined 498, 499, 501Dead space 327

Firing 46~ 48~ 490

I General System of communication 494Invisible areas 495, 501

Isogonic ~_________ 374, 376, 377Position 492

Special- for dead space calculations 317-326Visible areas 495, 501

Visibility . 291, 292Circle 16

Aiming; See aiming circleCircular measure .16

Table for conversion "Appendix III

Clinometers .Abn~y 162-164

Gravity 165

Combined charts .:.. :..___________________________ 498, 499, 501

Communication, general system of . 494

ComparisonOf map and panoramic f'k~tch .:..

Of methods of panoramic sketchingOf bngent and mil calculation :..

01' t'tngent ratio and tangent0: ..~rfare methods

CompassDecl ina ti on

Determination of

Error

-245-

_ _ _

--------

_ _ _ _

--------------------------- ----

------------------------------------

_ " _

----

__ ------------------------

_ ~ _

" _ _



266-268

459

46Q

259, 270

4

255-258

218-220

4

345-347 .

Declination --------------__________________________ 380, 406, 407

Deflection ---------------_______________________________ 466

Construction of

Mounted timing scale -------______________________________ 107-109

Profiles ---------------_________________________________ 290

Reading scale -------------_______________________________ 96-99Slope board -------------_________________________________ 167

Slope scale ~_ 129-131

Special cKart for dead space ----___________________________ 318

Visibility chart ------------_______________________________ 292

VVorking scale ------------_______________________________ 101-105

VVorking scale graph -----________________________________ 111-118

Contours --------------____________________________ 134, 137, 138, 215Contouring, logical ---------__ 141

ControlHorizontal

Point

Sheet

Vertical

Conventional signsDefinition

. For panoramic sketches .

For position and area sketchesUse of

Convergence of meridian

Conversion

Angular measure -------------------______________________ 30, 31

Circular measure .. .. 30, 31, Appendix III

Gra(lients --------------------__________________________ 46, 52

Linear measure ------------------_______________________ 10, 12-14

Mental calculations in- ... 13, 30

Of degrees and minutes to decimals ----____________________ 20

Of angles above prescribed limits -----_____________________ 53Per cent ------------------------_________________________ 48, 52

Table of slope --------.:.---------- Appendix I

Tangents ~_________ 36, 52, 53

True mil equivalents ---------------_______________________ 31Coordinates

Abbreviated ----------------________________________ 340

Corn plete ---------------------__________________________ 339

Definition ---------------------_________________________ 337

Geographic ---------------------________________________ 337Ilectometric -------------------_________________________ 340

Lambert grid -----------------~---_______________________ 337

Location of point on ground by means of -__________________ 366, <367

Method of reading --------.:.------_____________________ 339, 352;-355

Method or plotting point3 by --------_____________ 343, 344, 350, 351

or origin --------------------____________________________ 383, 420

-246-

-------------

_ _ _ _ _ _ _ _

--------- -----

-----------

-------------------

-----

.



!

..

Range, determination by --------..:---------..:---------------

Reduced hectometrico measure

To plot direction byUse of

, . Y -azimuth, determination by means of ----------------"""----

CorrectionErrors of closure

Of inaccurate protractor

Crest lines . .:

Critical points ..:

Determination of

D.

363

340, 422

352-355

357, 358

350-367

364, 365

194

62

248, 249

137, 140

216, 232

455

285

285, 297

293-296

294, 295296

298-301

297

298-301

Daily variation .:___________________ 375

Data book, B. C. 502Datum point 461

Dead space 313-326

Accuracy of determination .:.____________ 308Chart 327

Limits of 313

Methods of determining :..._______________________ 313-326

Calculation 314-316

Comparison of angles of fall and ground 313Special charts 317-326

Problems 815, 325, 326

Decagrade 22

Decigrade 22

Dec1inated plane table; Orientation by 176, 177Declinating point .___________________________________________ 462

DeclinationCompass 378-381

Constant 380, 406, 405

Magnetic 373, 374y---- 381

Decl inator 152

U sed in resection 205, 206

DefiladeDefi ni tionKinds of

. Method of determining .Angle of site

Profiles.

Similar trianglesTable of

Type problem~

Deflection .

Base

-247-

. \ .

-------------------------------------- _ _ _

_ _ _ _ _

-

__

_ _ _ _ _ _ _

~ ~ _



463

172

20

29,39-4219 •

18-20

19

122

277-281

, II

Constant

To measure, by sito-goniometer

Degrees .Conversion for use

Limit of calculation by tangent ratio ..:.Sixteenth ofSystem

Twentieth of ..:.

U sed to express slope

Designation of targets :.

Devices

l\Ieasuring ---___________________________________________ 63

Technical, in panoramic sketching 0________________________ 243-258Diary, gun -----:- ~_______________________________ 503

Directing piece ---____________________________________________ 464~

Direction ------_____________________________________________ 71

From grid north -_________________________________________ 372

From magnetic north -____________________________________ 371, 453

From true north ------____________________________________ 370, 452 .'

Plotting-- ---------_____________________________________ 356-362

Director in laying gun ----___________ 404-407, 411-415

Displacement, angle of observer .:. _"_ 474

Distance -----------_________________________________________ 70

Expression on map . 75

lIorizontal ~_______________________ 159

~Iap .:. ~____ 75

Drawing

On panoramic sketches -------_____________________ 241-258, 265-286

E.

ElevationIIow shown

,Minimum--

Engineer's level

l~ngineer's scale

Equipment

Panoramic sketching •Itoad sketching

EquivalentBase

llorizontai

True mil

ErrorAllowable in resectionCompass

Explanation of, in tangent calculationIn closure

In traverse

134

I

302 'I66

55

260

226

10, 30

7531

200

375

40

194

194

-248-

~

_ _

~ _ _ _ _ _ ~

~ _

__

------- -

------------

-----------------

_ _ _ _

~------------- _ _ _ _ _ _ _ _ _ _



200

32-45

33

36

.37

28

Maximum, by using reduced hectometric coordinates 341. Triangle of 207-208

Error

Allowable in resection -----'------------------------------

Essentials ofMili tary map :..___________________ 74

Panoramic sketch _= _ 261

Eventual zone 459

Exaggeration in vertical control 237, 290, 314

Explanation of error in tangent calculation 40

Expression ofAngles by tangents

Applica tion

Comparison of tangent and mil calculation

Comparison of tangent ratio and tangentMil relation

F.

.fan, rangoe deflection .: 483, 491, 528

Field of the observation 465

FireConcentration, plans of '- . 600Limits of 469

Possibilities of 497

FiringAngle 466

Board 467

Chart 468, 489, 490

Fords 441

Foresight-backsight traverse \ ..:. ~__ 186

Form~, ground. See ground form")Functions, table of natural Appendix II

G.

Geodetic point; Use of

. Geographir. cOQrdinates

C;oniometer, sito

Grade system

Limit of calculation by tangent ratio

Tangent method applied toGradients

Conversion

Limit of use

Tc measure .

To plot an angle using

Ured to express slope ~_

Gr~ph, dead space

VVorking scale

-249-

459, 421

337

169-172

21, 22

29, 39-42

29

46, 47

46, 5251

155

47

125

327

111-118

_ _

------------

--------------- _

__

_ _ _

--------- ~ _ _

_ _ _ _

- _ _

~ _ _



290

79-82

110

95

165

Graphical method; VisibilityGraphical scale

Interchange of .Types of ,

Gravity clinometer

Lambert. See Lambert grid.

Ground forms

Effect on minimum range and elevation 30'7-309

Methods of indicating 73, 134, 251, 252Ground relations 69

'Altitude -_______________________________________________ 72

Direction .71Distance , 70

Use of-- 73

Ground slopes; Panoramic sketches 251, 252

GunDiary 503

Position, location of 419-423

H.

I-Iachures

Heetometric coordinates ------.Horizon tal control

Hori zon tal equ ivaI ent ~_.:.

I.Ice

Identification; Panoramic sketch

InformationArea sketch

On map

On panoramic sketchOn road sketch

Title~of sketch

InstrumentsDec Ii nated

~feasuring

Oriented

U sed in t ra versing

Intersecting, arcs in solution of triangle of error

IntersectionAccuracy

Defin ition

LocatiC'n of targets by .:...Operation

Purpose

Interval, vertical

134, 136

340

266-26875

442

238

217

74

239, 240229

221

17~

54-62

174

185

208, I

195-198

197

195

434

198

196

139

-250-

_ ~ _

- _ _

'

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _



Irregular variation . 375

Isogonic chart 374, 376, 377

J.

K.

Known lineOrientation by •

l.!se of, in two point resection ---------------------------"--

L.

178, 179

"204

223

29, 39-42

313

469

51

Lambert grid 336-348

Convergence of meridian _-------------------------------- 345-347Coordinates 337-342

Description 336

Divergence 345-347

Origin 336, 418

Use of 349-367

Y-azimuth 348

Lambert north '______________________ 74, 369, 372

Lambert projection 334, 335

Lateral limitsFire 469

Latitude ..:___________________________________________ 329, 334, 336

Laying gunsCompass as an aiming point 388-394

Dec1inated instrument ...:_ 384-394

Prismatic compass . 384-394

LetteringPosition and area sketches

Level

. Abney ~--------------------_-_------------ 162-164Enginee~s 166

Limits

Calculation of mils by tangent method

Dead spaceire

Gradient form of expression

. LineBa~e 455, 477

Broken 250

Crest ~_ 248,249'Observing . 475

Orienting ~____________________________________4 78, 427-432Origin ~_____ 480

Parallel 244-247

Linear measureConversions in .___________________________________ 10," 12, 13, 14

-251-

--------

--------------------------

_ "

--------

" _

---------------------

---------------------------------------------- _ _

" ~



I

I

I

Location of unknown points byComputation of angles 433-439Intersection -___________________________________________ 195-198

Resection 199-213

Traverse' 184-194

Logical contouring 141

Longitude ---___________________________________________ 329, 334, 336

I...unar variation ~______________________________ 375

M.

487-506

65

64

75

74

74

66

174

328-335

68

75-79

128-133

369, 371

382373, 374

383

375

,

481, 423

470

300

54-62

54

59

57

55

56

60. 61, 6262

61

54

57

54

55

56j

.J

-----------------------------------------------

-----------------------------------------------

-252-

Magic number ----_______________________________________ 381, 406, 407

MagneticBearing

Bearing from map with protractorDeclination

Resection

Variation

Maps

Artillery sector, of the !.

Classes of

Defini tionDistance

Essen tialsInformation

Know ledge requiredOriented

!'ro jections

Reading

Scales

Slope scales •

MarkPlace

~Iarker

Mask; Amount to be raIsed to secure defilade~Ieasuring instruments

Alidades

Test

Chains

Metric me1suring scaleTest

Protractor

Correction

Test

Specifica tionsTapes

Tests

Triangular scales "-

Test

_ _

_ _ _ _ _

_ _ _

_ _ _

-- _ _

~------------ _ _

~ _ _ _

~ _ _ _

_ _

~ _ _ _ _ _





System

1Jse of

Vsed to express slope

.M inimum elevation and range. Accuracy.

Determina ti on

Effect of ground formsProblems

Steps of calculation

~finutesCentesimal

Sexagesimal

Mounted timing scale .Construction of

N.

17, 23-29

17

123

305-312

308305-312

307-309

310-312

306

. 21

18

106

107-109

~eedle traverse 187

Normal zone ~________ 471

North -------------_______________________________ 74, 369-372

Grid ---------_______________________________________ 74, 369, 372

Lambert -----___________________ 74, 369, 372

Magnetic -----__________ 74, 369, 371True -------_________________________________________ 74, 369, 370

Number; Magic ----______________________________________ 381, 406, 407

O.

Objective zone

ObservationOf enemy's movement

Of hostile terrainTerrestrial

Observation post

Visibility charts ...:.

Observation tower, height of

ObservationAngle of-displacementField of the

ObservingLine

Sector

Obtuse angle ., Occupation of position

Of sector

Operations, topographical. See topographical operations.Ordinate .

Orientation~fethods of _

-254-

472

231, 232

231, 232

433-439

473291, 292

301

474

465

475

476

16

231

395-417

338

175

_ _ _ _

~ _ _ _

~ _ _ _ _ _ _

--

_

_ _ _ _

~~ _ __

_ _ _ _ _ _ _ _



::

By angle traverse 180

By declinated plane table 176, 177

By known line :. ..:_ 178, 179

By resection .;.. ..:._______________ 183

, Panoramic sketches 261-264

When known point or given line cannot be occupied 181, 182Orienting line 478, 427-432

J\dvantages of ~___________ 408

Determination of 427-432

Kinds of _.:.. :.._ -428Selection of 427-432

Use ofTo lay guns on base line :_ .. 408-417

Using aiming circle . 411-415

Using plane table ,:,_______________'416'Orienting point 479

To locate gun position 423

,Origin; 'Lambert grid 336

Coordinates of .___ . 338 .

Origin lineDefinition '. 480

. P.

Pacing 190

Length of pace ~___________________________________ 447

Panoramic sketchesCharacteri.<:;tics .:.____________________________ 230-233Essentials 237-257

n1ethod of procedure _~___________________________________ 259-283

Subsketches 282-283

Types of sketches 234-236

Parallel lines .:.. ..:_____ 244-247, 268-271

Per cent ~___________________________ 48-51Calculation ~_________________ 48

Common error 50

Conversion . 48, 52

To plot an angle, using ..:. . 49

Used to express slope 124

Perpendicular bisector _~_____________________________________ 207 .•

Solution of triangle of error 207Perspective 244-246

Place markDefinition 481

Determination of ::. . 423

Plane tableDeclinated 174

Description 151

Oriented 174

-255-

~ ----------

~ ~ ~ -

~ __~

------

~~ ~ -

~



9

473

299493

492

482

419-423

231

214-223

222

218-220

?17223

221

497

To level --------------___________________________________ . 152

tJse -----------------_______________________________ 151, 403, 416tJsed in traverse ~_______________________ 185

Plotting directionsBy auxiliary points ..:_____ 359By coordinates -__________________________________________ 357, 358

By reversing directions 362

By similar triangles 360-361 .

By Y-azirnuth -----_______________________________________ 356

Plotting points by coordinates ~-----------7----------- 343, 344, 350, 351

PointAdjusting ---___________________________________________ 451

Aiming ------______________________________________ 452, 426, 432

Base ------________________________________________ 456, 424, 425

. Control ---______________________________________________ 459

Critical ---____________________________________________ 140, 216Datum -________________________________________________ 461

Declinating -____________________________________________ 462

Geodetic --------________________________________________ 459, 421

Important--:, Designation of 277-281

Location of-, by coordinates 366, 367

Method of plotting -______________________________ 343, 344, 350, 351~Iethod of reading ~___________________ 339, 352-355

. Orienting ---___________________________________________ 479

Reference -------------______________________________ 26C-268, 485

Referring ~____________________ 485

VVitness -------------------------_______________________ 486Polaris; Azimuth of :.___ 450

Polyconie projection ----------------__________________________ 332

Polyhedral projection ----------~-_____________________________ 330

Position

Amount of defilade, problemA uxil iary-, Chart ofChart

Defin itionGun

Reconnaissance and occupation of

Posit:on sketchesBorder

. Conventional signsInformation

Lettering .Title

Possibilities of fire

Posts. Obscrvat~n

. PrefixesLat'n and Greek

-256-

ffI•

1

i

t

-

~

-----------------

-------------------

' _

~ _ _ _ _

~------------- _ _

~-------------_ _ _ _ _ _



Prismatic compa!'!s

Compass as aiming point

Compute bearing of target -~-~---------------------:"------'

Laying guns with

ProblemsComputation, minimum range and elevation

Conversion of slo~es

Dead spaceefilade

Laying guns on base line with aiming circle

Laying guns with compass as aiming point

Locating targets by topographic means

~ap scales

Profile

Construction ofTo determine defilade --------..:-------------------.

To determine visibility

Projections, map ----------------------------------.

Bonneonic

Definition

Lambert~ercator's

PolyconicPolyhedral

Protractor

Corrections for inaccuracy

Descri pt ion

Testse of

Use of in finding magnetic bearing from map

Purpose of intersection

145

388-394

384-386

387-394

310-3.12127

315-316

298-301

411-415

390-394

435-439

82-91

290296

290

328-335

333

331

328

334, 335

329

332330

61, 62

60, 173

61

173

382

196

Q.

Quadrant, circular measure ..:. ~_____ 16

R•.

RangeDeflection fan ..,;______________________________________ 483, 491

Determination by coordinates ~!..- - ------------------ :..- - 363

Minimum

Accuracy 308Definition 302

Determination 305-312-

Effect of ground forms 307-309

To measure, sito goniometer .:..______________________ 171, 168

Steps of calculation ..:._.:._______________ 306

Reading of points ..:____________ 339, ~52-355

-257- '

------------------------------------------------

--------------------------------------------

--- ----~--------------------------

----------------------------------------

---------------

--------------------------------------

-----------~-------------------------------- _ -----------------

----------------

--------------------

----------------------------------------------

-------------------------------------------

--------

------------------------------------

----------

-------------------------------------------------- _ ----------------------------------------------

_ _

------------------------

-------------~------------------

---------------------------------------------

--------------------------------------------------- _ --------------

----------------------------------------

~

__ __



231

232

231

75

38, 42

42

.89-42

41, 42

139

505

77200

199-213

209, 383

199

210-213

383'

183

200

206422

201-203 .

204, 205

16

224-229

224, 225

229

Reading scales ------------------__________________________ 79, 80, 96-99

Construction of ----------------__________________________ 96-99.lJse of ~____________ 80

Ueconnaissance of

Enemy position'Example

Position

Records

Ammunition -----------_________________________________ 503

Artillery sector -----------_______________________________ 487-506

Classes of -----------------_______________________________ 487

Elaboration of ------------_______________________________ 506

.~faps and charts --------_________________________________ 487-501

Topographical .________ 4Written ------------_________________________________ 487, 502-506

Reduced hectometric coordinates 340

Reduction of stadia readings ----______________________________ 158, 477

Reference point -------------~________________________________ 484

. .. D.csirabl~. considerations -------__________________________ 267

Selection of ------------------____________________________ 266-268

lJse of --------------------______________________________ 268

.~ Referring point ------------:.---______________________________ 485

Reflex angles -----------------_______________________________ 16nelatio~ of

~. D. to II. E. _

Tangent computation and true angular valueTangent computation and degrees

Tangent computation and artillery mil

Tangent computation and R-mil .:.v. I. to scale of the mapReport of B. C.

Representative fraction

Requirements for accurate results in resectionResection

Back azimuth

DefinitionItalian

~fagnetic

Orientation by

Requirements for accurate results. ":"Three point method

To locate gun positions byTransparent paper method

. Two point methodRight angles

Road sketch

Cha racterist ics

InrGrm~tion

-25h

..

-----~-------------

~ _ _ _

---------

"

_ _ _ _ _ _ _ _

~~ _ ~ _

_ _

_ _ _

~ ~ _ _ _ _ _ _ _

~----------- _



Lateral limits

Method

228

226, 227

s.

21

18

I

214-223

222

214

294, 295

287

169-172

170-172

24

265

487-506

260

395-397

375

253, 254

82-91

92-94

79

76-79

55

106

95

139

128

55

95

80

78

95

111.118

Scales

ComputationsConversions

Graphical

~ap _

Metric measuring .

Mounted timingReading

Relation to V. I.

Slope ------------------r-------------------------------riangularTypes of

Use of

VVords and figures

VVorking

VVorking-graphs

SecondsCentesimal

Sexagesimal

Sector -----------------------------------------------------.nalysis of

. ~aps and records

Measurement of; Panoramic sketchOccupation of

Secular variations ..Shading

SheetControl 360

Target 504

Signs, see conventional signs 4, 218-220, 255-258

Similar triangles .To determine visibility 287To plot direction by .________________________________ 360, 361

Site~ngle of, used to determine defilade'

~ngle of, used to determine visibility -'-Sito-goniometer

Use ofSize of mil _

Sketch

Panoramic, see panoramic sketchPosition and area .

Border

Cha raeter isti cs

-2G9-

-------------------_ _ _ _ _ _ _ _

~ _ ~ _

~ _ _ _ _

~ _ _ _ _ _ _

_ _ _

~ _

__ _

------------------



.... ..

)

" i'tf, ,

121

313-321" ,

298-301

82-91

305-312''207-208 .

.

122

125

12~

124

, 12&

18-20

49B'

21, 22

328-335

23-29'

218-220

216

217 ,

223

215, 216

221

Conventional signs

Cri tical po intsInformation

:Lettering .. :.

~ethod of makingriUe

Road, see road sketch

SlopeBoard 167, 168

Construction .________________________________ 167

,Conversion of slope, problem 127Ground 251-252

Practicability of' :.. ~__________ 440

Scale ~____________________ 12&Construction 129-131

Use of ~_______________________ 132-133

, To measure :.. ~__ 150, 155, 12~

Units of expressionDegrees and minutesGradient'

~Iils

Per cent

Tangent

SolutionConversion of slope, problem :.:. __'Dead space

. Defilade

Map scale, problems _,;.

~inimum Range and elevationTriangle" of erro~

Space, dead (see ,dead space)

Stadia rod"o measure distances ~_______________________ 157, 158, 160, 161, 192" l

. Reduction or readings 447'

Straight edge tests _~ :____ 58'

Systems \_Degree or sexagesimal -:.

General communication ~_

Grade or contesimal -:. :.._~ap projections

~il

T.

, TablesAzimuth of polaris , ,(50

Conversion,- of :..' App:' III.

,Defilade 297 ..

Len21h of strida ,(43:'

-260-

- ~ "

'

'

_ _ _

~ _ ~ _

_

~__

~ ~__ _ _ _ _ _ _

~ ~ ~ _ _ _ _

~ ~ _

"

" ~ _

~ ~ _

_



38

39

57

172

157

171

58

59

5.1

61

56

206

221

395-417

404-407

399

408-414

403

152

51

45

36, 52

126

28

29

39-42

384-386

277-281

433-439

504

486

143

156

433

App. 11.

417

190

440

..Natural functions

Reduction of stadia readings.

Slope corrections

Slope practicabil ity

TangentsAbove 45 degrees

Addition and subtraction

Conversion ------------------------------.--------------

Used to express slope

Tangent methods .---------------~----------------------------Applied to degrees and grades

Tangent ratio, limits of calculation b}' 29,

Tangent valuesRelation of, to actual angular values --------------:.-------

Relation of, to artillery mil

Tapes

TargetBearing of

Designation ofLocation of 424, 425,

Sheet

VVitnessTelescope, battery commander's

Telescopic alidade

Terrestrial observation

Test~EdgesLine of sight of alidade r----------------. Measuring instruments ---------:---------------------------

Protractors

ScalesThree point method, resection by

Title, position and area sketch

'1'0 lay guns on base line

Aiming circle method

Aiming point method

Orienting line method

Plane table method

To level plane table

To locateAiming point or direction 426-432

Base point or target 424, 425Gun position _:--- 419-423

To measureAngles and deflection, sito-goniometer

Distance, telescopic alidade -----------------------------'-- ....

Minimum range, s:to-goniometer ------------------------.

Slope

-261-

-------------------------------------

------------------------------

----------~---------------------------------------------------------------------

---------------------------------------------------------------------------

------------------------------------

----------------------------

-------------------------------

------------------------------------------------------

----------------------------------------------

-------------------------------------------

--------------------------------------------------

--------------------------------------------------------------------------------

------------------------------------------------------------------------------------

--------------------------------- --------------~

--------------------------------------------

--------------------------------------------------------------------------------

--------------------------------

------------------------------------

------------------------------------

------------------------------------

------------------------------------

-----~---------------------------------

------------------------------------------

~ ---------------------



..

---------~-------------------------_. 343, 344, 350, 351

Leveling alidade

Peigne compass

Sito- gon iometer

To plot

Coordinates

DirectionCoordinates

Piegne compass ...Protractor

TopographyAdvantages

Defini tionUses of

Topographical information, how recorded ...:Topographical methods \

TopogTaphical operations

. Laying guns on base line .=.

Locating aiming directionLocating base point

Locating gun position :. ...:Topographical records

Essentials

TransitTraverse

Angle

Orientation byClosed

Definition

Errors in

Foresight-backsight

Instruments used : .

~feasurement of distance~Iethods

~eedle

Open

'friangle of error

Solution of

Intersecting arcs. .,

Perpendicular bisectors

Triangles, similar

To plot direction by, Visibility by

Twentieth of a degree

Two point method, resection by .:

.155

150

170

356-362

148

149

2

1

14

5418 .

395-417

426-432

424, 425

419-423

4

4

144

184-194

188

180

184

184

194

186

185

189

186-188

187

184

206-208

207-208

208

207

360-361

287

19

204, 205

u.

Unknown points

Location by

Computation of angles -----------__________________ 433-439

-.262-

_ _ _

_ _ _

_ _ _ _ _ _ _ _

~__ _ _ _ _ _ _ _ _ _ _ _

__ _ _ _ _ _ _ _ _

~ _ _ ~ _

_



Intersection

Resection

Traverse

----------------------------------------------------------------------------------

-------------------------------------------

195-198

199-213

184-194

Use of

Abney' level ~_________ 163, 164

Aiming circle -----------------0--- 404-407, 411-415Declinator 205, 206

Elastic band 288

Engineer's level -:..._____________ 166Gradient 47, 125

Graphical scale 80

Gravity clinometer 165Grid ~_________________ 349-367

Ground relations ~____________________________ 74Isogonic chart .:.___ 376, 377

Known line .:.._________________________ 178, 179, 204

Orienting line ..:____________________________________ 410-416

Origin line 480Panoramic sketch 233

Panoramic sketch pads 236, 263

Peigne compass 147, 148, 150

Plane table 151, 403, 416

Prismatic compass 384-394Profiles -:_______________________________ 290, 296

Right angled rule 355

'Similar triangles 287, 299, 301 ,

Sito-goniorneter 170-172

Slope board ~_ 16S

Slope scale .:. 133

Special chart, dead space .:..________________ 388, 389Stadia ~_________________________________ 158, 160, 161, 192

Telescopic alidade 157

Visibility chart 292

v.Variation, magnetic 375

Vertical control 269, 270

Exaggeration 270, 290

Vertical interval 139

Visi bili ty 285-292

Charts ,________________________ 495, 501, 291, 292Construction ~________________________________ 292

Definitions and limitations 285

Methods of determining 286-290

Angle of site ._________________________________ 289

Elastic band 288 .

Graphic method 290

Sintilar triangles 287

I

:.-263

I •

'

------------------------------------

~

------------

~ '

~

-



...... -

w.

215

22

'Vhole to part method

'Vind direction .

_ _