Embed Size (px)
Citation preview
No. 9: Part II
Useful Tables from the
American.Practical Navigator
ORIGINALLY BY
NATHANIEL BOWDITCH. LL. D., Etc.
RE-EDITED AND PUBLISHED IN THE
UNITED STATES HYDROGRAPHIC OFFICEBY DIRECTION OF THE SECRETARY OF THE NAVY,
IN ACCORDANCE WITH THE ACTS OF CONGRESS
WASHINGTONGOVERNMENT PRINTING OFRCE
1916
Aitron. tHut.
/
1916. 1930, 1931, 1934, and 1936 •dltloaa of BOvn)ITCH
(Iabl«« in back of bojk)
(1916)Pag« Tabl« Ho. Title
531 2 TraTers* table, degrees
—- • ConTersion of departure into differ^enoe of longitude
IXnot in thete editions -. refer to I
' 19S8 edition. Table 4. page 108)
j
621 8 Meridional parts
634 5B Distance of an objeot by two bear-ings, degrees
... . Time, speed, and distanoe tables^not in these editions - refer to !
1988 edition. Table 18, page 140)
755 42 Logarithms of nvanbers
772 44 Logarithms of trigonometric func-tions, degrees
817 45 Logarithmic and natural haversines
laniel
ureau
)laris;
been
1, the
pages
both
859S62
^^
PREFACE
The following tables comprise Part II of the American Practical Navigator, by the late Nathaniel
Bowditch, LL. D., as revised in 1880 and in 1903, and again in 1914, under the direction of the Bureau
of Navigation, Navy Department.
In the present edition, as in that of 1914, former tables 2SA, 28B, 28C, and 28D, Latitude by Polaris;
37, Logarithms for Equal Altitude Sights; 37A, Bquation of Equal Altitudes near Noon, liave been
omitted; but the former assignment of table numbers and page numbers has not been disturbed, the
pages on which these tables were printed being simply dropped from the book and the tables and pages
not renumbered consecutively. This accounts for the absence of pages 717 to 724 and 734 to 738, both
inclusive; while page 531 is left blank in order to let Table 2 begin on a left-hand page.
IIydrographic Office,
Washinglon, D. C, April, 1916.
3S075°—16 503
359S62
CONTENTS OF PART 11.
Page.
Explanation of the Tables 507
Table 1 . Travetwe Table, Quarter Points 515
2. Traverse Table, Deijrees 531
3. Meridional Parts. 621
4. Length of Degrees of Latitude and Longitude 629
5A. Distance of an Object by Two Bearings, Quarter Points 631—• ~ " " 6345B. Distance of an Object by Two Bearings, Degrees.
Distance of Visibility of Objects of different Heights 640
Conversion of Arc and Time 641
Conversion of Sidereal into Mean Solar Time 642
Conversion of Mean Solar into Sidereal Time 645
Local mean time of Sun's visible Rising and Setting 64S
Reduction of Moon's Jleridian Passage for Longitude 672
Reduction of Quantities from Nautical Almanac 673
Change of Sun's Right Ascension 683
Dip of Sea Horizon 685
Dip at Distances short of Horizon 685
Parallax of Sun 685
Parallax of Planet 686
Augmentation of Moon's Semidiameter 687
Augmentation of Moon's Horizontal Parallax 687
20A. Mean Refraction 688
20B. Mean Refraction and Parallax of Sun 089
21
.
Correction of Refraction for Barometer 690
22. Correction of Refraction for Thermometer 691
Mean Refraction and Mean Parallax of Moon 693
Mean Refraction and Parallax of Moon 693
Variation of Altitude due to change of Declination 702
Variation of Altitude in one minute from Meridian 704
^'arialion of Altitude in given time from Meridian 714
23.
24.
25.
26.
27.
28A.2SB.2SC.28D.29.
30.
31.
32.
33.
34.
35.
36.
37.
37A.38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
Omitted
.
Nautical and Statute Miles 725
Conversion of Metric and English Linear Measure 726
Fahren'neit, Centigrade, and Reaumur Temperatures 727
True Force and Direction of Wind 728
Distance by Vertical Angle 729
Distance bv Horizon Angle 731
Speed Table for .Measured Mile 732
Local Jlean and Standard Meridian Times 733
jOmitted.
Error in Longitude produced by Error in Latitude 739
Amplitudes.' 740
Correction for Amplitude observed in Apparent Horizon 745
Natural Sines and Cosines 746
Logarithms of Numbers 755
Logarithms of Trigonometric Functions, Quarter Points 771
Logarithms of Trigonometric Functions, Degrees 772
Logarithmic and Natural Haversines - . .
.
817
Consolidated table of Altitude Corrections 922
The Longitude Factor 938
The Latitude Factor 941
505
EXPLANATION OF TEE TABLES.
in which
TABLES 1, 2: TRAVERSE TABLES.
Tables 1 and 2 were originally calculate<l by the natural pines talten from the fourth edition of
Sherwin'g Logarithms, which were previously examined, by differences; when the proof sheets of thefirst edition were examined the numliers were again calculated by the natural sines in the second editionsif Hutton's Logarithms; and if any difference was found, the numbers were calculated a third time byTaylor's Logarithms.
The first table contains the difference of latitude and departure corresponding to distances notexceeding 3cX) miles, and for courses to every quarter point of the cf)mpass. Table 2 is of the samenature, but for courses consisting of whole degrees; it was originally of the same extent as Table 1, butbae been extende<l to include distances up to tiOO miles. The manner of using these tallies is particularly
explained under the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V.The tables may be employed in the solution of any right triangle.
TABLE 8: XCEBIBIONAL PARTS.
Thie table contains the meridional parts, or increased latitudes, for every degree and minute to 80°,
calculated by the following formula:
'" =TF log tan ( 45° -r Vf ) — a (<' sin L + J f' sin' L+ ^ f* sin' L + . . . . ),
1©800^the Equatorial radius n = ^ = 3437'. 7467 7 (log 3.5362739);
M, the modulus of common logarithms = 0.4342945;
j^=2.3025&51 (log 0.3622157);
C, the compression or meridional eccentricity of the earth
according to Clarke (1880) =293 4^5
^ 0.003407562 (log 7.5324437);
e=v/ 2c- c" = 0. 0824846 (log 8.9163666);
^ =7915'. 7044558 ( log 3. 8984895)
;
«" = 2.3'.38871 (log 1.3690072);
Ja€* = 0'.053042 (log 8.7246192)
;
iaf«= 0'.000216.523 (log 6.3355038).
The results are tabulated to one decimal place, which is sufficient for the ordinary problems of
navigation.The practical api)lication of this table is illustrated in Chapters 11 and V, in articles treating of the
Mercator Chart and Mercator Sailing.
TABLE 4: LENGTH OF DEGREES OF LATITUDE AND LONGITtTDE.
This table gives the length of a degree in both latitude antl longitude at each parallel oi latitude onthe earth's surface, in nautical and statute miles and in meters, based upon Clarke's value (1866) of the
earth's compression, "oqqT^" ^^ the case of latitude, the length relates to an arc of which the given
degree is the center.
TABLES 6A, 5B: DISTANCE BY TWO BEARINGS.
These tables have been calculated to facilitate the operation of finding the di.-;tance from an object bytwo bearings from a given distance run and course. In Table 5A the arguments are given in points,
m Table 5B in degrees; the first column contains the multiplier of the distance run to give the distance
of oljserved object at seconil bearing; the seconri, at time of passing abeam.The method is explained in article 143, Chapter IV.
507
from which
I
508 EXPLANATION OF THE TABLES.
•/.') . TABt.E G: DtGTANCE OF VISrBILITY OF OBJECTS.
This table contains the distances, in nautical and statute miles, at whicli any object is visible at sea.It is calculated by the formulie: _
d = 1. 15 y/x, and rf' = 1.32 \/x,
in which d is the distance in nautical miles, d' the distance in statute miles, and x the height of the eyeor the object in feet.
To find the distance of visibility of an object, the distance given by the table coixeaponding to ita
height should be added to that corresponding to the height of the observer's eye.Example: Keijuired the distance of visibility of an object 420 feet high, the observer being at an
elevation of 15 feet.
Dist. corresponding to 420 feet, 23.5 naut. miles.Dist. corresponding to 15 feet, 4.4 naut. miles.
Dist. oi visibility, 27.9 naut. miles.
TABLE 7: CONVEBSION OF ARC AND TIME.
In the first column of each pair in this table are contained angular mea.sures expressed in arc(degrees, minutes, or seconds), and in the second column tlu- corresponding angles expressed in time(hours, minutes, or seconds). As will be seen from the headings of cohnnns, the time correspondingto degrees (°) is given in hours and minutes; to minutes of arc ('), in minutes and seconds of time;and to seconds of arc ("), in seconds and sixtieths of a second of time.
The table will be especially convenient in dealing with longitude and liour angle. The method of
ita employment is best illustrated by examples.
E.X.\MPLE I. ! EXA.MPLE II.
Requireil the time corresponding to 50° 31' 21".
50° 00' 00" = 3" 20'° 00'
31 00 = 2 0421 = 1?*
50 31 21 =3 22 05.4
Required the arc corresponding U) 6'' 33"° 26*.5.
6" 32" 00» = 98° 00' 00"
1 24 = 21 002:':l= 37.5
(3 33 26.5 = 98 21 37.5
TABLES 8 AND 9: SIDEREAL AND MEAN SOLAR TIMES.
These tables give, respectively, the reductions neces.sary to convert intervals of sidereal time into
those of mean solar time, mid intervals of mean solar into those of sidereal time. The reduction for anyinterval is found by entering with the number of hours at the top and the number of minutes at the side,
adding the reduction for seconds as given in the margin.The relations between mean solar and sidereal time intervals, and the methods of conversion of
these times, are given in articles 289-291, Chapter IX.
TABLE 10: SUN'S RISING AND SETTING.
This table gives the local nie:m time of the sun's visilile rising .'in<l setting—that is, of the appearanceand disappearance of the sun's u|iper limb in the umibstructed horiz.m of a pei-son whose eye is 15 feet
above the level of the earth's surface, theiitmospheric cunditiims beinir normal.The local apparent times of rising and setting were determined fiom the formula for a time sight,
the altitude employed being —0° 56' 08", made up of the following terms: Refraction, — 36' 29"; semi-
diameter, - Hi' 00"; dip, —3' 48"; and parallax, -! 9".
To ascertain the time of rising or setting for any given dat« and place, enter the table with thelatitude and declination, interpolating if the degrees are not even. In the line R will be found the time
of rising; in the line S, the time of setting. Be careful to choose the page in which the latitude is of
the correct name, and in which the "approximate date" corresponds, nearly or exactly, with the
given date.
This table is computed with the intention that, if accuracy is de.sired, it will be entered with thedeclination as an argument—not the date—as it is impossible to construct any table based ujion dates
whose application shall be general to all years. But a.-* a given degree of declination will, in the
majority of years, fall upon the date given in the table as the "approximate date," and as, when it
does not do so, it I'an never be more than one day removed therefrom, it will answer, where a slight
inaccuracy may be admitted, to enter the table with the date as an argument, thus avoiding the neces-
eity of ascertaining the declinatiim.
Example; Find the local mean time of sunset at Rio de Janeiro, Brazil (lat. 22° 54' S., long.
43° 10' VV.), on January 1, 1903 (dec. 23° 04' S.).
Exact method. Approximate metlntd.
Lat. 22° \ p. .o„ Lat. 22°.. \ ,ii. 4«m
Corr. for + 54' lat +02 Corr. for + 54' lat +02Corr. for + 04' dec 00 Corr. for 1 day -01
I,. M. T. sunset ti 50 I.. M. T. sunset 6 49
EXPLANATION OF THE TABLES. 509
TABLE H: KEDUCTION FOB MOON'S TRANSIT.
This table was calculated by proportioning the daily variation of the time of the moon's passing themeridian.
The numbers taken from the table are to be added to the Greenwich time of moon's transit in westlongitude, but subtracted in ea^t longitude.
TABLE 12: REDUCTIONS FOB NAUTICAL ALMANAC.
This is a table of proportional part* for rinding the variation of the sun's right ascension or declination,
or of the equation of time, in any number of minutes of time, the horary motion being given at the top ofthe page in seconds, and the number of minutes of time in the .side culumu; also for finding the variationof the moon's declination or right a.«cension in an v number of seconds of time, the motion in one minutebeing given at the top, and the numbers in the side column being taken for seconds.
TABLE 13: CHANGE OF SUN'S RIGHT ASCENSION.
This is a table that may lie employed for finding the change of the sun's right ascension for anygiven nmnber of hours, the hourly change, aa taken from the Nautical Almanac, being given in themarginal columns.
TABLE 14: DIP OF SEA HORIZON.
This table contains the dip of the sea horizon, calculated by the formula:
D = 58".8 v/F,
in which F = height of the eye above the level of the sea in feet.
It is explained in article 300, Chapter X.
TABLE 15: DIP SHORT OF HORIZON.
This table contains the dip for various distances and heights, calculated by the formula:
D = ? fZ + 0.56.514 X ^,
in which D represents the dip in miles or minutes, d, the distance of the land in sea miles, and h, theheight of the eye of the observer in feet.
TABLE 16: PARALLAX OF SUN.
This table contains the sun's parallax in altitude calculated by the formula:
par. = sin ; X 8". 75,
in which : = apparent zenith distance, the sun's horizontal j)arallax being 8".7.5.
It is explained in article 304, Chapter X.
TABLE 17: PARALLAX OF PLANET.
Parallax in altitude of a planet iw found by entering at the top with the ]>lanet'8 horizontal parallax,and at the side with the altitude.
TABLE 18: AUGMENTATION OF MOON'S SEMIDIAMETEB.
This table gives the augmentation of the moon's semidiameter calculated by the formula:
jr = c «' sin ft -f J c" .«' sin^ ft + J c" «',
where ft = moon's apparent altitude;
s = moon's horizontal semidiameter;X = augmentation of semidiameter for altitude ft; and
log c = 5.25021.
TABLE 19: AUGMENTATION OF MOON'S HOBIZONTAL PABALLAX.
This table contains tlie augmentation of the moon's^ horizontal parallax, or the correction to reducethe moon's equatorial horizontal [larallax to that point of tin- earth's axis which lies in the vertical ofthe observer in any given latitude; it is computed by the forniulie:
^ ' v/(l — c sin'L)
where a = equatorial horizontal parallax;L= latitude;
c = eccentricity of the meridian; log e* = 7.81602; andA T = augmentation of the horizontal parallax for the latitude T,.
510 EXPLANATION OF THE TABLES.
TABLE 20A: MEAN BEFRACTION.
This table gives the refraction, reduced from Bessel's tables, for a mean atmospheric condition in
which the barometer is 30.00 inches, and thermometer 50° Fahr.
TABLE SOB: MEAN BEFBACTION ANTt PATtAT.T.AX OF STTN.
This table contains the correction to be applied to the sun's apjiarent altitude for mean refraction
and parallax, lieing a combination of the quantities f(ir the altitudes given in Tables Iti and 20A.
TABLES 21, 22: CORRECTIONS OF REFRACTION FOR BAROMETER ANDTHERMOMETER.
The.se are deduced from Bessel's tables. The iiiethud of their employment will be evident.
TABLE 23: MEAN REFRACTION AND MEAN PARALLAX OF MOON.
This table contains the correction of the moon's altitude for refraction and parallax corresponding
to the mean refraction (Table 20A), and a horizontal parallax of the mean value of 57' 30".
TABLE 24: MEAN REFRACTION AND PARALLAX OF MOON.
This table contains the correction to be applied to the moon's apparent altitude for each minute of
horizontal parallax, and for every 10' of altitude from 5°, with height of barometer 30.00 inches, andthermometer 50° Fahr.
For seconds of parallax, enter the table abreast the approximate correction and find the seconds of
horizontal parallax, the tens of seconds at the side and the units at the top. Under the latter andopposite the former will be the seconds to add to the correction.
For minutes nf altitude, take the seconds from the extreme right of the page, and apply them as
there directed.
TABLE 25: CHANGE OF ALTITTTDE DUE TO CHANGE OF DECLINATION.
This table gives the variation of the altitude of any heavenly body arising from a change of 100" in
the declination. It is useful for finding the equation of equal altitudes by the approximate methodexplained in article 324, Chapter XI, and for other purposes.
It the change move the body toward the elevated pole, apply the correction to the altitude with the
signs in the table; otherwise change the signs.
TABLE 26: CHANGE OF ALTITUDE IN ONE MINUTE FROM MERIDIAN.
This table gives the variation of the altitude of any heavenly body, for one minute of time from
meriilian jiassage, for latitudes up to 60°, declinations to 63°, and altitudes between 6° and 86°. It is
based upon the method set forth in article 334, Chapter XII, and the values may be computed by the
formula:1".9635 cos L cos d"~
sin (L-rf) '
where a= variation of altitude in one minute from meridian,
L = latitude, andd = declination—positive for same name and negative for opposite name to latitude at upper
transit, and negative for same name at lower transit.
The limits of the table take in all values of latitude, declination, and altitude which are likely to
be required. In its employment, care must be taken to enter the table at a place where the declination
is appropriatelv named (of the same or op[)(>site name to the latitude) ; it should al.so be noted that at
the liottom of the last three pages v:dues arc given for the variation of a body at /oiccr trsuisit, which can
only be observed when the declination and latitude are of the same name, and in which case the reduc-
tion to the meridian is subtractive; the limitations in this case are stated at the foot of the page, andapply to all values below the heavy rules.
TABLE 27: CHANGE OF ALTITUDE IN GIVEN TIME FROM MERIDIAN.
Tliis table gives tlie ]>rodnct of tlie variation in :iltitndo in one minute of a hoaveidy body near the
meridian, bv (he s(iuare of the number of minutes. Values are given for everj- half minute between
C" 30" and 26 " 0', and for all variations likely to he employed in the method of "reduction to the
meridian."The fornmla for computing is:
Red. = <( X t\
where <i — variation in one nunute (Table 26), and( = number of miiuites (in units and tenths! from time of meridian pasi>age.
The table is entered in the coluum of the nearest interval of time from meridian, and the value
taken out corrresponding to the value of n found from Table 26. The units and tenths ar>' picked out
separately and combined, each Ix-ing corrected by interpolation for intermediate intervals of time.
The result is the amount to be applied to the'observed altitude to reduce it to the meridiau altitude,
which is alwavs to be added for upi)er transits and subtracted for lower.
EXPLANATION OF THE TABLES. 511
TABLE 28, A, B, C, D: LATITTJDE BY FOLABIS.
[Omitted.
TABLES 29, 30, 31: COITVEBSION TABLES.
These are self-explanatory.
TABLE 32: TKTJE FOKCE AND DIBECTION OF WIND.
This table enables an observer on board of a moving vessel to determine the true force and direction
of the wind from its apparent force and direction. Enter the table with the apparent direction of thewind (number of points on the bow) and force (Beaufort scale) as arguments, and pick out the direc-
tion relatively to the shii)'s head and the force corresponding to tlie known speed of the ship.
E.xample: a vessel steaming SE. at a speed of 15 knots appears to have a wind blowing from threepoint.s on the starboard bow with a force of 6, Beaufort scale. What is the true direction and force?
In the column headed 3 (meaning three points on lx)w, apparent direction) and in the line 6(apparent force, Beaufort scale), we find abreast 15 (knots, speed of vessel) that the true direction is 5points on starboard bow, i. e., S. by W., and true force 4.
TABLE 33: VEBTICAL ANGLES.
This table gives the distance of an object of known height by the vertical angle that it subtends at
the position of the observer. It was computed by the formula:
tan a = -,,
where « = the vertical angle;h = the height of the observed object in feet; andd = the distance of the object, also converted into feet.
The employment of this method of finding distance is explained in article IXK chapter IV.
TABLE 34: HOBIZON ANGLES.
This shows the distance in yards corresponding to any observed angle between an object and thesea horizon beyond, the observer being at a known height.
The method of use is explained in article 139, chapter IV.
TABLE 35: SPEED TABLE.
This table shows the rate of speed, in nautical miles per hour, of a vessel which traverses a meaj^uredmile in any given number of minutes and seconds. It is entered with the immber of minutes at the topand the number of seconds at the side; under one and abreast the other is the number of knots of si)eed.
512 EXPLAXATION OF THE TABLES.
TABLE 36: LOCAL AND STANDARD TIMES.
This table contains the reduction to be applied to the local time to obtain the corresponding timeat any other meridian whose time is adopted as a standard. The results are given to the nearest minuteof time only; being intended for the reduction of such approximate quantities as the time of high wateror time of sunset. More exact reductions, when required, may be made by Table 7.
TABLE 37: LOGARITHMS FOB EQUAL ALTITUDE SIGHTS.
[Omitted 1
TABLE 37A: EQUATION OF EQUAL ALTITUDES NEAR NOON.
[Omitted.]
EXPLANATION OF THE TABLES. 513
TABLE 38: EFFECT TJPON LONGITTTDE OF ERROR IN LATITUDE.• Table 38 shows, approxiiTiately, the error in longitude in miles and tenths of a mile, occasioned byan error of one mile in tin- latitude.
Tliua, when the sun's altitude is 30°, the latitude 30°, and the jwlar distance 100°, the error is
eight-tenths of a mile.
The effect of an increase of latitude is as follows:
In TT>i< longitude, ( K:\at \ of meridian, the f decreased 1 except where marked f increased \the body being \ West ) longitude is \ increased J
' by *, when it is \ decreased i
'
In East longitude, / East \ of meridian, the / increased \ except where marked f decreased \the body being \ West j longitude is \ decreased /
' by *, when it is \ increased J
'
A decrease of latitude has the contrary effect.
The direction of error may readily be seen by drawing the Sumner line in a direction at right anglesto the approximate bearing of the body.
TABLE 39: AMPLITTTDES.
This table contains amplitudes of heavenly bodies, at rising and setting, for various latitudes anddeclinations, computed by the formula:
gin amp.=sec Lat. Xsin dec.
It is entered with the declination at the top and the latitude at the side.
Its use is explained in article 358, Chapter XIV.
TABLE 40: CORRECTION FOR AMPLITUDES.
This table gives a correction to !>e applied to the observed amplitude to counteract the verticaldisplacement due to refraction, parallax, and dip, when the body is observed with its center in thevisible horizon.
The correction is to be applied for the sun, a planet, or a star, as follows:
At Eising in N. Lat. ) , ^v *• * »i • i,x •
Setting in S. Lat. r^^'^y*^® correction to the right.
At Rising in S. Lat. 1 i ^u i- » lu i r..
Setting in N. Lat. | *??'>" ^^^ correction to the left.
For the moon, apply /i'i//the correction in the contrar;/ manner.
TABLE 41: NATURAL SINES AND COSINES.
This table contains the natural sine and cosine for every minute of the quadrant, and is to beentered at the top or bottom with the degrees, and at the side marked M., with the minutes; thecorresponding numbers will be the natural sine and cosine, respectively, observing that if the degreesare found at the top, the name sine, cosine, and M. must also be found at the top, and the contrary if
the degrees are found at the bottom. It should be understood that all numliers given in the tableshould be divided by 100,000—that is, pointed off to contain five decimal places. Thus, .43366 is thenatural sine of 2-")° 42', or the cosine of 64^^ 18'.
In the outer columns of the margin are given tables of proportional parts, for the purpose of finding,
approximatelv, by inspection, tlie proportional part corresponding to any number of seconds in theproposed angle, the seconds being found in the marginal column markol M., and the correction in
the adjoining column. Thus, if we suppose that it were required to fincl tlie natural sine correspondingto 25° 42' 19", the difference of the sines of 2.'>° 42' and 25° 43' is 20, being the same as at the top of theleft-hand column of the table; and in this column, and opposite 19 in the column 1\1., is the correc-tion 8. Adding this to the aliove number .43366, because the numbers are incrraning, we get .43374 for
the sine of 25° 42' 19". In like manner, we find the cosine of the same angle to be .90108—4=. 90104,using the right-hand columns, and subtracting ht^c2LnsB the numbers are decreasing; observing, however,that the number 14 at the top of this column varies 1 from the difference between the cosines of 25° 42'
and 25° 43', which is only 13; so that the table may give in some ca.ses a unit too much between theangles 25° 42' and 25° 4.3'; but this is, in general, of but little importance, and when accuracy is required,the usual niethod of proportional parts is to be resorted to, using the actual tabular difference.
TABLE 42: LOGARITHMS OF NUMBERS.This table, containing the common logarithms of numbers, was conipareil with Sherwin's, Button's,
and Taylor's logarithms; its use is explaine<l in an article on Logarithms in Appendix III.
TABLE 43: LOGARITHMS OF TRIGONOlttETRIC FUNCTIONS, QUARTER POINTS.
This table contains the logarithms of the sines, tangents, etc., corresponding to points and quarterpoints of the compass. This was compared with Sherwin's, Hutton's, and Taylor's logarithms.
514 EXPLANATION OF THE TABLES.
TABLE 44: LOGARITHMS OF TBIGONOMETRIC FXTNCTIONS, DEGREES.
This taVjle contains the common logarithms of the sines, tangents, secants, etc. It was comimredwith Shervviii's, Hutton's, and Taylor's tiibles. Two additional columns are given in this table, whichare very convenient in Jj^nding the time from an altitude of the sim; also, three columns of jiroportional
parts for seconds of space, ami a small table at the bottom of each page for finding the proportional parte
for seconils of time. The degrees are marked to 180°, which saves the trouble of subtracting the givenangle from 180° when it exceeds 90°.
The use of this table is fully explained in A])pt^dix III in an article on Ixigarithms.
TABLE 45: LOGARITHMIC AND NATXTBAL HAVERSINES.
The haversine is defined by the following relation:
hav. A=J vers. A=J(1—cos A)=sin- JA.
It is a trigonometric function which simplifies the solution of many problems in nautic.il a.stronomy
as well as in plane trigonometry. To afford the maximum facility in carrying out the processes of
solution, the values of the natural haversine and its logarithm are "set down together in a single table
for all values of angle ranging from 0° to ot>0°, expressed both in arc and in time.
TABLE 46: CORRECTIONS TO BE APPLIED IN ORDER TO FIND THE TRUE ALTI-TUDE OF A STAR AND ALSO OF THE SUN FROM THE OBSERVED ALTITUDEABOVE THE HORIZON.
This is a consolidated table in which the tabulated correction for an observed altitude of a star
combines the mean refraction and the dip, and that for an observed altitude of the sun's lower limbcombines the mean refraction, the dip, the parallax, and the mean semidiameter, which is taken as16'. A supplementary table at the foot of the main table takes account of the variation of the sun's
semidiameter in the different months of the year. '
TABLE 47: THE LONGITUDE FACTOR.
The change in longitude due to a change of 1' in latitude, called the longitude factor, F, is given in
•this table at suitable intervals of latitude and azimuth. The quantities tabulated are computed fromthe formula
—
F=sec. Lat. Xcot. Az.
When a time sight is solved with a dead-reckoning latitude, the resulting longitude is only true
if the latitude be correct. This table, by setting forth the number of minutes of longitude due to eachminute of error in 'atitude, gives the means of fin<ling the correction to the longitude for any error that
may subsequently be disclosed in the latitude used in the calculation.
Regarding the azimuth of the observed celestial body a.« less than 90° and as measured from either
the North or the South [wintof the horizon towards East or West, the rule for determining whether thecorrection in longitude is to be applied to the ea-^tward or to the westward will be as follows: If thechange in latitude is of the same name as the first letter of the bearing, the change in longitude is of thecontrary name to that of the second letter, and vice versa.
Thus, if the body bears S. 45° K. and the change in latitude is to the southward, the change in
longitude will be to the westward; and, if the change in latitude 's to the northward, the change in
longitude will be to the eastward.The convenient applic^ition of the longitude fa<-tor in finding the intersection of Sumner lines is
explained in article 389.
TABLE 48: THE LATITUDE FACTOR.
The change in latitude due to a change of V in the longitude, called the latitude factor, f, is givenin this taljle at suitable intervals of latituileand azimuth. The quantities tabulated, being the reciprocals
of the values of the longitude factor, are computed from the formula
—
f=T?=,—
—
[ „x w ,—r— =cos. Lat. Xtan. Az.r sec. Lat.Xcot. Az.
When an ex-meridian sight is solved with a longitude afterwards found to lie in error, this table, byBetting forth the number of minutes of latitude due to e.ach V of error in longitude, gives the meansof finding the correction in the latitude for the amount of error in the longitude used in the calculation.
Ilegarding the azimulh of the observed ceUsti:d body a." less than 90° and ai> measured from either
the North or the South point of the horizon towards Kast or Wet^t, the rule for determining whether thecorrection in latitude is to be applied to the northward or to the southward is as follows: If the changein longitude is of the same name as the second letter of the bearing, the change in latitude is nf thecontrary name to the first letter, and vice versa. Thus, if the body bears S. 14° K. anci the change in
loiigitu<le is to tlie westward, the change in latitude will be to the southward, and, if the change in
longilude is to the easlw;ird, the I'hunge in latitude w ill be to the northward.Tin: convenient atiplication of the latitude factor in finding the intersection of Sumner lines is
explained in article ;J90.
Page 616]
Page 518]
?fc«52»
Page 522]
Page 524]
Page 526]
Page 528]
Page 630]
Page 532]
Page 534J
Page 536]
Page 538]
1
Page 540]
Page 542]
rPage 546]
Page 548]
1
Page 550]
Page 552]
Page 654]
Page 556]
Page 558]
Page 560]
Page 562]
Page 564]
Page 566]
Page 568]
Page 570]
Page 572]
Page 574]
Page 676]
«
Page 578]
Page 680]
Page 582]
Page 584
Page 586]
Page 588]
Page 690]
Page 692]
Page 594]
Page 596]
Page 698J
Page 600]
Page 602]
Page 604]
Page 606J
Page 608]
Page 610]
Page 612]
Page 614]
Page 616]
Page 618]
Page 620
Page 622^
Page 624]
Page 626]
Page 628J
Page 630]
Page
Page
Page 636] TABLE
Page 638] TABLE 515.
Page 640
Page 642] TABLE s.
Page 644]
1
Page 646] TABLE I*.
Mean Solar into Sidereal Time.
Page 648]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 649
Page 660]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 651
a z
c ,3
S •§
o c
a
xoJd^Y Q"^ 0!xaadMin«aiKcci«cfiPStDMcn'McriaicB «maiMMM«cnOSai Mm«aJPSd«m«cn«
&
SSSS3SSSSS
feiOoicoSoooi.'iO'coinoiO'-.iOi-tii
s^'^S'"'^^'^'''^"-^ "'
SSSSoK^irtSS
ciMSiMaSOTe^xaiM^SaioSaiaatnsSMaJujoSwMcoajtnMaiaiaJalm^
Page 652] TABLE 10.
Mean Time of Sun'e Visible Rieing and Setting.'
J .
3^ 3 M^^^Meoeo
o-ar,.c;a:o:(Ka:xa:x'a:a:e;xo;xc!»:ci:DD ciwKaieicccsxBStt c::xc£xB:x'ex3:x
r •© ^ iS T" u^ "T" ic ^TiS^riO^u
i95 ISSSS S8!S8s?8!?8Sg teS^SSS;
5'-rS^O^S-?'A'«f'o5o'^o5©^G
6' r- f t^ ^ O "T * ^ O >-t hs t5 u5 ^ lit o i-t c "^ '* -^ !- :c r
s!Sg'5SS2;252 ?S3n52S!2?!2te25SSSg£§S S:
:;£?£S2 ?52l?l:fS2S£S2 g8g5S?;£??!3?}
E"St5?S5S525!2te2!;SS2gSS2 S8RaSSSS;!??3 SSSagasSSS
-Mt>.g«.-«0 3RSSS gSffi^SSSSSSi^SSSSSSSSa
2 1
5 a
g«25!2S!853SS|sSS?iRSSaS3S'sSSSS3?iSSS«!sgSSSSSaaS
e9;:9;^$!is;s;;s^ sssssKsss;:: f:;SnnS»^s;;ss vss^s^ssssjs
E^aSSISSSSSS 3SS%8SSS;SS3g »^S3S^^.S^% 5n7.~S^^7S'S.^ l0 10 to lo lO ie lA <o to to iomotoA<oi^to*ott iioto^ tf >C(OkQ toic to tc<e<£^>ctDo<ctA(0
,^<A<oto<o>atDiO(Oie«
sSSRSSSSSS?s|ss?SSaSS5SSla5S«aSS525'i::^2S=J2S=3
ESSSS'^SSSSSS SS8S83S5a'-5 SSa^aSSSSS £S2S =SS8Sg
^fdtDintoioto«e«DtQ«»o<otewiO<e*ato*0(Oie«iid«o<o<ot/twiAt^iiCr«<Ar«teN*et^>or«
eSSSSS383R!9 a532aS822SfcS££28SSSS 88Sgg282S£
E"S35SS?a3RSa5 asas83£22SpS2823S88S SSSSS=S23S^iCtOtO(oiO(Oia<ototD;>o«ototo>ow>oto>otoy:ttiAr->er»«ftr-tcr-tcr-tot«^r*^r>^r
39S;S$a$SS c3SS2!::S£K23'=o88&S8SS2 SS&2£2S8Sri
ESJSSSSasas 2S2S: =E2S2S SS888SS =S2 S2S2SS5S5
E'a«S!;892Z!::3 2S2S=S8S&S|38SSS=&=X2 S2Sf:$S5R?S
e»$89SS2SSZ SSSS&8S8SS 8SS2S222S2 !;s3S?RSSSS
(OJ^
e232$S3£!S;S3{S£8SS8oSSS|SS:;2sS
i^
itiViSSSR
QfDOfiCoOfitfCDCCOQtfX
Page
TABLE 10. [Page 655 1
Mean Time of Sun's Visible Rising and Setting. 1
Page 656] TABLE 1(1.
Mean Time of Sun's Visible Riring and Setting.
^3==^ 3 £ S
eSlSSiXBiXBSCESia caaoBaiBSxaj3:s:a;iaa:axe!!r.o!xaaosceaxa;xaT.
?3 I
5 I
^ I
s 5
5 s
o 8
Esssssss; 1 SSS2S238SS^£5SS5!S5gSS SSSS3S£S=S8
E"gS§S8SgS2?:]:2S2E?J2S2SS'5gSS?S?525lSSS52SE:2tf
ESSSSSSgggRSc :£E:2S?32S$8gS3?e2; :SS8S?g?
ES?ggZgsa8S 8?SSaSSJ!5££ SrSSRi^SSS ss$$s?gsss
SS5g^555SSS2S3SSS8SSa'SS8S 5SSS5;SSS5$
E§SS?S!;S;$55lE;?SSKS«f?SaSS8SS?;222zt =S£a8S3a3
SSSS 5!$5355?5gS'SS?SS8R8; ^SSS
^5gSSS3SS3SS SSSSJS1S55!;? 5Si'SSSE88S S5S?— Ol-^-r xo
sssssaseggss'sssssos ISSS8S2S
Essasssssss sssEs?ssssg,gS5; : Z^S£9;;jS^£>S
E2SS23SaS?:S SSRg?!SSSSSlS2S3Sg?S5!5 4555!S?Si'RSS
E££H3£22rg2 ?JggSSS5SSS,SSS8aSSSS:j I
e22223I;2SS£ 2S2aSsa^S3S aSSSSSS5g58|3SaSRSS25!S
Egg2?!3SE!S22'S2£S2S2222 aa!5S?32SSSS BSS83gS8S5
E8C;SR8a8a8s'2gS{:j:;?;SSS2'22EE2S2£S5]?)2aSSgBSa8
E3S!SS3S8gSS'Ba£SgK;S?.2ahs2a2?J3S2S's22S225£?J2
esss^gsgrt8s's8sasass88lsa8agagR2s|=a232s=?i2n
6SSSSSSSSSS8|8S5SSSgRgs|sa3SSrtSSSa]8JSgSBSSSg?i
63?353??3??S5]S3E?S;)SSJS5!S5SSSS8S8g=SSS3SgKgS
ES?S?S$S5S5 353?35353!; 5i;3S:3SSS3S SSS5S5S5B;
6S28S3SS?Sg2 SSS3SS?S.'?SS S?2S3SSSS!S?S SSSSSi'Si'SJ:'
6!;KS;£5S535S5S!;S5S!;SSS'SS3aS3SS!SS'«S*S5?*858
1" "i'^x'sr^ "S'lr'i""!"^
TABLE 10.
Mean Time of Sun'g Visible Rising and Setting.
[Page 657
CO BiwBSmcimXmpiaam'BBirnctaiOi'DOi^iCii^aiaipivJcixBi'BlaiaiaiaiBixiA'^Bi^tiai
& ^s;
£o--to — O'-HO'-HO'-t o3of-<or-io3o3
^ a
^OfNOcSoiMOC
-<i-lt-iriO^OMO C-»OrJOMO?JOc5ih
« Sh
Stti
„ 2 0.C lOiib OibOiAOT
eScoi^tcoi'/jciwaM'aJaJeiaJBiMiBitBBJto eJoiBiaiaJmaima; aa:}!£aiaitBC£aiBi'eXo
Page 658] TABLE li>.
Mean Time of Sun'e Visible Rising and Setting.
o^SiSS^a^S^SSS s £ 'eg £; s
a^3Qai3Qaix:^ccXx0^ri:iftfxa2xaSxa£cc,^x«xs±x9<x— xpiccaiaQ^fx^xQ^x
^ 3M >
S "5
s s
I
"
f 3o^ a
a
tea
Eg2S232S2SS^5SS88g8S5S;SSSgSgsS2S2SSS2S2S2S^ (O « --O O O O %D O O 'O j^ O O tJ> '-S « O O -O "O |-i3 '-D "J "O -J '^ '.3 « <S O "J O "O » » O tO O '^ O
52S252SSS=;2 2S2g23333SS3£3
i^s: I S Z S — o — 3 ^ s ;S232SSS SS23282g2S
ekfiic.i^»w':t>*^r-'0-£> t--.pr-i-'^i'-i5XiO»'T 5»-r7i^^30ri— 5» ^ — ri'-TiowOMa*
EJ:Si:S2S2S28 23S3?§=:§SSli^SS:J5S3l5S?:S,SS^2SSSS5S
s2'^2555^s=53 ?is?i3?3S?i3?:o '^.S'=^SS2^5S£ ?ss^2^as;:?ss
£c:3?J3?iS?i3?;S plocio'^S^StiaS S25£S5^S;3:3 w3*^3??333^S
So^to'r^&^Si^Stli-oSofiidJuOMiSMiiScSooSOTSjWifcMiOOTfiOQTS?
SggS3SS?:8SS;SSgaȣ33?*i3 33S3S3SSS3 S3g53:;??5!5
ES:3SSISSS3i$K|S&iJ3S3SS2SS^SSS%2i;39?.?$^$:$?$3$3
?ioSSooS90tamtS|n!^o6ASSoOM!)mtA-MS'<r-v7-v^-^» kO O O to tQ to tO
^ -D lO 13 lO ts iC « u^ '-o >c to ^ -J -It-i ^t -J -': %» i.'s ]'**.'; -^
^?s^v:^S'?s3;;:gi35n
s3'iiS3!5SSS3S3SS?
Ea3g5?«y?3?l'45!;35SS?S3S!3a5SE3SSsSS3's>l35SE: = ;
Ea?5«:;55;!S3pS5S2a3335 s;?!E?;3SS?;3?!,SSB;;S£a322^co>Ato>Rto>4t0tAto*aNo>/^'.d>cotatotOtoo»tacotOtoi/3r«kai'«*a[t^oi-«tar>«ar*tac«ka
<tf>/S(0tO%3in(OOtOtA UiA'0>':tO>AtO<AiOiA|«U?0>/St^tSr->Sr^iOJt<-iAI'>*Or>Ot^tOr*0
dOt0iAttt'3(OiCtcdtOtntao;00«9tnto^r>kr:r>>nr>kOr*oli'«tcr«inr«<cr>vr*«
5?i5?;5a«ai'-;s32S23SSiil3?28SSSSSSS|2E2g2323?]S
S!S«^!;2$BS£,28SSSS5£32jSS3!;^?£;£S
KaQOSoQaiaDXaDflfia KwUafiooaSciiaSvaSadaStnMasafiaDafic&aiaQaSQc aCxaSoBtfxaeaoefiad
"TTI
TABLE 1(1. [Page 659
Mean Time of Sun's Visible Rising and Setting.
Page 6601
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 661
S^ 53 a S S S
aJodoSxiSaJ«x"«m«ai«t»«cBiaco«coUM«a;«ajoSooBioO|SSMa;aiBSMasa!ajai
em?lMC^'^o*^5^T
3 It oicoico>cS.o«: 3ii
2 -3
if ftocoooooooc
y^; . :^a:^XJ:.^xX-jJX-^\£i^S!irnXa2!^ic;:iU2\XxXauXcD;iicaa^\Oiaaaiu^X^Ci'J2aita
Page 662] TABLE 10.
Mean Time of Snn'e Visible Rising and Setting.
•^ -^ ^ SSliC « .C i tclio iC ic £
oSoisiodBiaiaiaosiaijiixaiadtfccSodcix 3:cc3:xa:xXffie^cc
ESgSSSS3S?5gS;??j; I 58SSSS o^ "^ g^ :« .-.c ;SSSS
?.aSSS£i =£S
gS5Sg?ia?5?:'S?i SS?.?ig55!z:?S SSSo8SSS2!S 2
s £>Si^iccSRSSSS a2?-i$S§5S£ SSS52?SSag
^ 6o*coSo-ro-; !!::gK:SSSSSR5 S?!S2S£3 =?g ZSSS5:?S2::?
rSi*;-!KadbiiT
saSSSIiSSSgE S5£!5252S2S,£SS«aSSSS8 K2524SSSSS
tSSSSSSSSS 8SgSSSg!S25'2?2K2S?358R g5S8S£?! = !;S
E!SS5BS?Si'§2e 3ISSK838SSS g!S=?S5ESSS S«?;S;;?iSSS2
^ ^Eg!;q:£5 = 52!£ =pSSSaS3gg5'528S83SSS£ =SS5!EsSS?:S
ES?.SSSi?t::?£i;Z!g£:!;2SSs$2SSSS88SSSiSSSS:
ES??.3?;S?5R?lgS f2g$S$35ES £SgES2S32S
E8s«?i5;ss«isa,s?3sass55s iSS8:SS2SSSS!S
J I>2S? =SSXSE8
S5?:SSSaS?5va.S!8?2!?t:5:2g:
ja^a; SSSRSSSSSS saKg8SSSSSlRSSS3S5!?J58
e2!;2$S5s5?:? ?55Sv?:;!S?aS 8SRSaS?!SK!?'5?SSSSsS5?S5
e2SE:SES28SS 2¥258!;s!;s5 S«a5S5fi5SS! S5SSSS8SSS.e to tA« tC tC tO <C iC *C tC W >C «0 (ft tc (C «C tC «0 *0 (O iC «0 (O «0 (fi W (C (C •£ to iC (C .C *C <C (fi •/> tt tC
E"2l2=S33 =3£S 2S2g2SSSES9tAtOtA«O<C«*CtC>C«>CtO<CU:>C«etAt0i<
2:S:S£S£S2Sp£3C:2t:2£S236=8=8=S=22S 222S25:
ESSSSSSSSSS{SS8S888SSS'2g2S2S2o = o{=s =o=8^8SS^«««to«V}ie«««oSowts<o«to«to<04o|«w««««>«to«ew<otow««e<o<ooio
e8S£S£S£S'<SS 8SSSSSS58S'iSSSSSS88S 888S8&8&8&
B82g2g2g2S2g2gSg2o252s2oSo2s=E=;SZ8=8=8£8£.^to««tt tf to tt«toto to<o (Oto «o<o leiow io«to«<e<ote«<e*o ioio(oto« «tD*ototo
eeaDBCodOficdoiaoBScd aCosoCaotf edoCoDOCtc ttaQOSaoBfiaotfcnoeaoAecdQiaDtf octtccaecn
TIT" "TTITXXITTxtttt-
TABLE 10. [Page 663
Mean Time of Sun's Visible Rising and Setting.
Page 664]
Page 666] TABLE 10.
Mean Time of Sun's Visible Rimnf! and Setting.
i s
t I
s i
0:xcdxtf:dcCxtfccpadQSa3CESQdtfx3£a6a:xs^x0^ccQiQQC£aDC£QQB:cdcC0GCCxfl''#''>'r/ft'r#^»*r*^fv•f»iWn
SSSSoSo'^o'vo 5SSSSSSSS SSSsriSsgSt:^;
^ lA iC (C ^ >a <£ u; I/: I
2, I 6?g5!S = Sg:e53
6SS5S?S?gSSS SSaSS3gSSS;t;SSSag?32S= S22SS2£2i^ to tx; ic I/) US lA tc ic ^ >o tfi tn< <a>c tctc <fitci0 tfi <otit u tc (o is wtc te tO w ^ to tA tc tc ts u:
l8SS'agSSaSSSag S222J;2££ = e;
3SS33S SSSSSSSgs58 ssggSSSSas SS22U;;:22:
SS2|SS??S55.'gg2gS?;S8'^saS?;3S38SS8S2g£ =S2S:
I£3SS9SS£;;^^s:;sss;:S^SSEs;s'2SSS8S5'^S
E$9S9SS&3%S 3SSZ^S:«SSEJf3SSS!;8SSSS ?:3SS?:8SS2SS2
ES5SSSSRSSS!?SSSggSSsSJSSS!iSa8R5Sg;S8SSSSSSS'=2S
ESgiSSSSSSKS|SgS8Si33SSS|SSSE8SSgS8[RSSSgagSSriS;iS
;^S5?SoSg88S3SS
h e;3?s$ss ;2feSS;?SS 3SSESSS3SSg S8SSSgagt;gt;5
E9S5SCSSSSS gSSSSJRSSS'SSSESESSSS ggS38SS8o?.gjiS
ES!SS!S5lS5S?i"iSSgSS3S3SSSSS3?SESSSS!sS8S?S385!o«o-g^ tO U5 >0 iC tO >/
ess3S9z?s9s|;:;323:7s;::;s:? ss!;%KESEiSS $S3^^s;;ggsi^
E?g?S5g9S5SJS!SS!3?25aSS|?a?g38gESESS!KaSSSS?SSffS';:S
E5S?S5g?35S5353335:S?SteS5SSSSBSESE?5SIS.'5S5Sv^35
E5K«SS3«S«3p3;S?«5£5S5SS!SSJS5JE5!E3E5SS5?5 = .s=3,^ieift>CkOtog?ietfttOkOiAkOintc>f:tCia>oiAtAic>oie>o>c<«iAiCiO>AteiOio>etfttitw-tCk'. •':•-': o
ES3!*3SSSaS2i93«3SSSS?S! ;S = S;S5S5SI5E5K:;Ei;E5!S«i!
E9S3S3S9iS9Sb£!;S!;:S!;S!;%'!;s^S!;:t?!;St;s'$SS:!;$s^$3?:i:f'?:^
2, E3X99;3S3S3SpS$S%s;%£$:S$S9S9S9S$SpS$S$S$s:9S$S
rojnd $00 etmeimXaeiiKeiaaaiaacimXmaiiiXm BttiBimeiietiw^tBameiaa tf ODQAadatfcnafix
TABLE 10.
Mean Time of Sun'8 Visible Rising and Setting.
[Page 667
Page 668] TABLE 10.
Mean Time of Son's Visible Rising and Setting.
S I
S 3
°-!
* 5
.« c
3 I
c2 B
I
Kx'ttaoPfxSxttaQjctfuaSxKmKafex.oiKeixBixItficBSEc 3:xB:x«ai«aa:i]T
e5S2a2S2S8?,g?S5SS96;S §£S5S2?!S£g gggiSSgSiS;:^
^sssss;
:a,ssss8sssg; ssssssssssg ssssgggRsig
Eg8S85S?Jg5E; i;£:.'£S?JSSg?S SSJSSS^S^gE SS5g?ig£ = 6?3
eSSSS58SS?38 28SS2S22S?) gggSSSSSSS 5;5Sg8g?:S5 =
ESSSSSSaSSS SSSS28222S g2gS5SESSS 5S5SSgSgRS
E:;&gSSSS2SS SSSSS!33S&!:S ZS=^gSS?:8S :SSZ&SS;!;3S
E"!g«55S55SSS:':rtS52S2Sg?5S SS^ =Z-SEBc^ SSZasSSS??
esssss?53K3S 5S!Ss;;y!;ss !;ss:;rsssgsgte;£8g:;i:2£22
isnsm^.StiSti S^SS99^SfS^\^^^^^:?.^SsS ^SSSS&SSi.
• IESSSS;g55gS«2S?g5-SS5:sS?S!55:5!S55SS|5SSSgSSSR5
68agasagSSS|SS5S8SiS;?:<S;!?S5?gS?555«;i?5S5SSS53S!S
E22S;S = ?:2?!8S 55g?SfiagSg« 8aS5KSSK5?S ^?555S£55g
^1*- wr*r»« :sfc?;=f!2agS£S gssrig;?=?:"8-Isfi5B»«g^g5
E?J3SS8£222KSS22£9 = «2S!laS=r'58?55V.£ri:5S3ag88SSS
E§ =§=a232aS|?iSc;£?;SaC22 22E8£SSfi2g!2a=S8RS8SS
EsS8S5gS2a='E-,=K::a:;s2fiz[?;£n2fJus282 2g2sE?i£az?:
EasSSSSSfeSS J?SK£S£Sgg2lg!2g=5:Jt;:iS2 S5=S£S2?Jl:?i2
ES8S8SSSS3S;3|!;3!?SS8^S^8{^8^&3&;SS!;S|SSS2s2g = S;S
e9898983S9o SS9S?o7g7g,?83gS83SSS g3S3SSS;8!;S
eCxaeu£c£xa£»dx|a^xBSxa£xciaxoCxfiSaL'ae»aeadGe 00^06^00
,.
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 671
-2 £
^ i
J a
a 18 I
I
s ^
SKo S S S S^ o s
ficicntf oQCtiaDoinpciaip^coOiiaipiQQtfdpijoQ a;m pi cri p:i of tf ccd oq o^odtfGca^odpiHCQtf
SSSSfSc
£mSc5c
fiO'-<aot».-<i-^'T.-ir-oOr-i'*"*c
3cioc3oMicSiOMi
Jp-foa01-^w^~>'^2|QO<-'OOlWr-
OuSoSooS
'xojody ^^ oiwCAc6^t:6Xi^pd':a
21594°—
M
36
300 — MaOOJC^iO^C
BSoiOaiaiaiBiccaiiQ «03«aiCiSaiS5a:«ai BScdcSaJMcoJsSoiWa
Page 672]
Page 674J
Page 676]
Page 678J TABLE 12.
For finding the Variation of the Sun's Right Asceneion or Declination, or of the Equation of Time, inany number of minutes of time, the Horary Motion being given at the top of the page in seconds,and the number of minutes of time in the side column. Also for finding the Variation of theMoon's Declination or Right Ascension, in seconds of time, the motion in one minute being givenat the top and the numbers in the side column being taken for seconds.
TABLE 12. [Page 679
Fur finding tlie Variation of tlie Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side colunm. Also for finding the Variatior of theMoon's Declination or Eight Ascension, in seconds of time, the motion in one minute being givenat the top and the numbers in the side column being taken for seconds.
Page 680]
TABLE 12. [Page 681
For finding the Variation of the Sun's Right Ascension or DecHnation, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,and the number of minutes of time in the side cohimn. Also for findmg the Variation of theMoon's Declination or Righi Ascension in seconds of time, the motion in one minute being givenat the top, and the numbers in the side column being taken for seconds.
TABLE 13. [Page 683
For finding the Sun's change of Right Ascension for any given number of hours.
Page 684] TABLE IK. |
For finding the Sun's change of Right Ascension for any given number of hours.
TABLES 14, 15, 16. [Page 686
Page 686] TAHLE 17.
Parallax in Altitude of a Planet.
Page 638]
Page 692]
Page 694]
1
Page 696]
Page 698] TABLE 24.
Page 700]
Page 702] TABLE 25.
Page 704]
TABLE 20. [Page 705
Variation of Altitude in one minute from meridian passage.
Pag
TABLE 26. [Page 707
Vajiation of Altitude in one minute from meridian passage.
Page 708J TAHLK _'.;.
Variation of Altitude in one minute from nieridian passage.
Page 710J
TABLE 2(!. [Page 711
Variation of Altitude in one minute from meridian passage.
Page 712]
Page 714j
Page 716]
Pag 726J TABLE 3n.
Conversion Tables for Metric and English Linear Measure.
• iteiric to Engtith.
Page 728] TABLE 3l>.
To obtain the True Force and Direction of the Wind from ita Apparent Force and Direction on aMoving Vessel.
Page 732] TABLK ;;:..
TARLE :;s. [Page 739
Error in Longitude due to one minute Error of Latitude.
Page 740]
TABLE 39. [Page 741
Amplitudes.
Page742J
TABLE 39. [Page 743
Amplitudes.
Page 744] TABLE 3H.
Amplitudes.
TABLE -iO. [Page 746
Correction of the Amplitude as observed on the Apparent Horizon.
Page 746]
Page 748]
Page 760]
Page 762]
Page 754J
1Page 753J
Page 760]
Page 762]
Page764j
Page 7661
Page 768]
Page 770J
TABLE 43. [Page 771
Logarithmic Sines, Tangents, and Secants to every Point and Quarter Point of the Compass.
Page 772
f-
Page 774]
Page 776
Page 778j
Page 780]
Pag-e 782]
Page 784]
Page 786]
Page 788]
Page 790j
Page 792J
Page 794]
Page 796]
Page 798J
Page 800J
Page 802]
Page 804]
Page 806]
Page 808]
—
-
Page 810]
nPage 812]
Page 814]
Page 816]
Page 818] TABLE 45.
Page 820]
Page 822] TABLE 45.
Page
Page 826]
Page 828]
Page 830]
TABLE 45. [Page 831
Haversines.
i^1 Page 832]
Page 834]
Page 836]
Page 838]
T.VBLE 4.-.. [Page 839
Haversines.
Page 840]
+ 1'
5
6
7
+ 2'
9
+ 3'
+ I«'
«» 25^ 36° 15'
Log. Ilav. Nat. Ilav
.09678
.09680
.09683
.09684
.09686
.09689
.09691
.09693
.09695
.09697
.09699
.09701
.09704
.09706
.09708^09no.09712.09714.09717
.09719
.09721
.09723
.09725
.09727
.09729
.09732
.09734
.09736
.09738
.09740
.09742
.09745
.09747
.09749
.09751
.09753
.09:.7.'»
.0975;
.09760
.09762
.09764
.09766
.09768
.09770
.09773
.09775
.09777
.09779
.09781
.09783
.09786
.09788
.09790
.09792
.09794
.09796
.<I979»
.09801
.09803
.09805
.09807
8.98,578
.98.587
.98597
.98606
8.98616.98626
.98635
.98645
8.98655.98661
.98674
.98684
8.9869:!
.9870.i
.98712
_^98722
8.98732.98741
.98751
.98761
8.98770I
.98780 t
.98790
.98799
8.98809.98818
.98828
_ .98838
8:98847.98857
.98866
_^98876
8.98886.98895
.98905
_^98915
8.98924.98934
.98943
.989.53
8.98963I
.98972
.98982 I
.98991
8.9900r'.99011
.99020
.99030
'8.99039
.990-19
.99058
.99068
8.0907S.9<M1S7
,
.99097
_J»9106 '
8.99116.99121!
.99135 ,
_^99145
!
8.99154,
nl^.W"
Sh 26^ 36° W
TABLE 4.5.
Haversines.
?* iT" 36° 45'
Log. Hav. Nat. Hav
8.99154.99164
.99173
.99183
8.99193.99202
.99212
.99221
8.99231
.99240
.99250
.99260
8.9U269.99279
.99288
.99298
8.99307.99317
.99327
.99336
8.99346.99355
.99365
^993jjl^
8.99384
.99393
.99403
.99412
8.99422.99432
.99441
.99451
8.99460.99470
.99479
.!l!ll.'^9
.!)!I5|)S
.99517
_ .99527
"8.99536
.99.516
.99556
.99565
8.9957.5
.99.584
.99594
.99603
8.99613.99622
.99632
.99641
¥.99651.99f;60
.99670
.99679
8.99689.99i;9.S
.99708
.99717
8.99727
.09807
.09809
.09811
^09814
.09816
.09818
.09820
.09822
.09824
.09827
.09829
.09831
.09833
.098:t5
.09837
.09S1(I
'.09S42
.09S44
.09846
.09848
.09850
.09853
.09855
.09857
.09859
.09861
.09863
.09866
.09868
.09870
.09872
.09874
.09876
.09879
.09881
.09SH3
.n9ss.-.
.09s^SJ
.09890
.09892
.09894
.09896
.09898
.09900
'.oooai
.09905
.09907
.09909
V09911.09913.09916
.09918
.09920
.09922
.09924
.09926
.09929
.09931
.09933
.099.%>
.09937
f /* SSm
Log. Hav.I N'at. Hav. Log. Hav. Nat. Hav
8.99727 I
.99736 1
.99746
.99755
8.9976.5I
.99774
.99784
.99793I
8.99803.99812
1
.99822j
.99831
8.99841.998.50
.99S60
.9!/s;i8
.99907
8.99917.99926
I
.99936
.99945
8799955
.99964
.99974I
.99983
8.99993,
9.00002'
.00012
.fHH12!
9.()oo:'.l
.0(K)40
xm\\'.\
(KKIMI
9,(101 .i,s
.(MKCV
.000^7
.(HHHIT
9.001(111
.001 1 (;
:
.00125 I
.(Xii:r.
9.(KI14I
.00151
.(KH63
.(HI 172
'9.(H11,S2
.(X)191
.00201
.00210
9(H)2J0.00229
.(H)2;19
.(H)2IX
9.{KI25S
.(KI2(i7
.(KI27(;
.002Si;
9.0(1295
.09937
.09939
.09952
.09944
.09946
.09948
.09950
.0995:i
.09955
.09957
.09959
.09961
.09963
.09966
.09968
.09970
.09972
.09974
.09977
.09979
.09981
.09983
.09985
.09987
.09990
.09993
.09994
^09996
.09998
.10000
.10003
.1000.5
.10007
.10009
.10011
.10014
.1(1016
.10018
.10020
.10022
.1002.'.
.10027
.100'»9
.10031
.10033
.1003.1
.I003S
.10010
.10042
.10014
.10046
.10049
.1 00.1
1
.10053
.100.S5
.10057
.100.19
.10062
.10064
.10066
.IOn6S
il>> .?."> :?/* M"
ill fSm 37° 15'
Log. Hav. Nut. Ha
9.00860.00869
.00878
.008SS
9.00897.00906
.00916
.00925
9.00935.00941
.0095:;
.O0<)6:4
9.00972"
.00981
.0099
1
.0I(HX1
9.01009
.01019
.0102^
.0lo:>:
9.01047.OI0.5(i
.ou)(;5
.01075
9.010SI
.01091
.0110:i
J)11129.01122.01131
.0114(1 '
.01150
9.01 15m
.oiii;s
.oii:>
_oiis:9.01196
I
.01206I
.01215
.01224
9.(I12:!4
.0124:1
.012-52
_.01262
9.01271
.01280i
.01289 I
.01299
jr.0130S
.01317
.01327
_0I336901315.01:1.55
.01364
_^01373
9.013S:;
.01:192
.014(11
.01411
9.01421)
.10200
.10202
.10204
.10206
.10209
.10211
.10213
.10215
.10218
.10220
.10222
.10224
.10226
.10228
.10231
.10233
.10235
.10237
.10240
.10242
.10244
.10246
.10248
.10251
.1025.3
.10255
.10257
^10259.10262.10264.10266.10268
.10270
.10273
.10275
.10277
.10279
.10281
.10284
.102SG
.10288
.10290
.10'J93
.10295
.10297
.10299
.10301
.10304
.10.306
.10308
.10310
.10312
.10315
.10317
.10319
.10321
.10323
.10326
.10328
.I0:«0
.I0.%32
Page 842]
Page 844] T.\BLE 4:..
Ilaveryinw.
Page 846]
Page 848] TABLE 45.
Haversines.
Page 850]
TABLE 4->. [Page 851
Havereines.
Page 852 j TABLE 45.
Ilavereines.
Page 854]
Page 856]
Page 858]
Page 860]
Page 862]
Page 864]
Page 866]
Page 868]
Page 870]
Page 872] T.VBLE 4.5.
Haversinea.
TABLE 45. [Page 873
Haversinea.
Page 874]
Page 876] TABLE 45.
Haversines.
Page 878]
Page 880]
Page 882] TABLE 45.
llaversinea.
Page 884]
Page 886]
TABLE 45.[Page 887
Si.
5" 30' 6* 23'" 95° 45' I 6^ 2-i"'- 96° 0'
.73878
.73881
.54792
.54796
.54800
.54803
.54807
.54810
.54814
.54818
.54821
.54835
.54828
.54832
9.74044.74047
.74049
.74052
9.74055.74058
I
.74061
.71064
9.74067.74069
.74072
.74075
9.74078.74081
.74084
.74087
9.74089.74092
.74095
.74098
9.74101.74104
.74106
.74109
9.74112.74115.74118
.74121
9.73676.73679
.73682
.73685
9.73688.73691
.73694
.73697
,54521
.54524
.54528
.54532
.54535,54539.54542
.54546
.54550
.54553
J4557.54561.54564
.54668
.5*571
,54575
.74015
_J4018^9.74021.74024
.74027
.74029
"9^4032
,74035
.54894
,54897
,54901
.54904
,54908
,54912
,54915
M919^,54923
,54926
,5:930
.5^3,54937
,54941
,54944
,54948
,54955
,54959
^4963.54966
,54970
.54973
.54977
T549S0.54984.54988
_^4991_
754995.54999.55002
^5006.5.5009
9.74124.74126
.74129
.74132
9774135.74138.7414174144
9J4146.74149
.71152
.74155
9774158"
.74161
.71163
.74166
9^74169,74172
.74175
.74178
iKTilSl",74183
,74186
.74189
i7h 39m37"^
9.74192.74195
74198
_74200_9.74203.74200
.74209
.74212
9.74215
.55009
.55013
.55017
^020..15024
.55028
.55031
^55035
.55038
.55042
.55046
^55049.55053
.55056
.55060
.55064
"7550«.55071.55075.55078
"7;55082
.55085
.55089
^,55093
.55096
.55100
.55103
.55107
":55iir|
.55114
.55118
^55122
.55125,55129
.55132
^65136
.55140
.55143
.55147
^5150.55154.55158.55161
^5165^7,55169.55172.55176
^55179
.55183
.55187
.55190
J5194.55197
.55201
.55205
_^208.55212.55216.55219,55223
,55226
9.74215.74218
I
.74220
^74223_1
9.74226 I
.74229
.74232_jl235^
^774237.74240
.74243
^742469.74249.74252
.74254
.7425'
9.74260.74263
.74266
.74269
"97427^
.74274
.74277
.74280
9774283.74286
.74289
_J42919.74294.74297
.74300
_743039.74306.74308
.74311
.74314
9.74317.74320
.74323
.74325
nh SO'171'- 3.-,
Page 888]
Page 890]
Page 892]
TABLE 45. [Page 893
Havereines.
Page 894]
Page 896!
Page 898]
Page 900]
Page 902] TABLK 45.
Ilavcreine.-.
Page 904] TABLE 45.
llavereines.
Page 908]
Page 910]
Page 912] TABLE 4:..
TABLE 45. [Page 913
Page 914] TABLK -i:..
IIav,T-in,--.
Page 916] TABLE 4.5.
Page 918] TABI>F> l."
Ilavcrsincs.
10* 5im 163°
U.*:. lluv,
9.99041.99043.9!l(H4
.!i!»(M(;
9, 9904 S
.99(l.=)0
,990.'iL'
.991l.i4
9.990."i(;
.990.1S
.99().'.9
.99(»lil
9.990(i:i
.99(10.5
9.990()7
iiit. llav
l.97»15
.9;si9
.97824
.97M281.97832
.97*J6
.97»41
.97H4.5
1.97843
.9785:{
.97858
.97862I.978fi6
.978701.97874
Lot'. IlaT^N
9.99 111 0.
.991.'iL': .
.9yi.=>4; ,
.99150 i ,
9.9910SI0,
.991.59\
.
.991(,1I
,
.9910.5: ,
9.99105I0.
.99100' ,
.99l0.-> ,
.99170 1 .
9.9917:; i 0.
.9917:5 ,
9.99175I
0,
164°.1. 11.H
98063HS06798071.98075
.98079
.98083
.98087
.98091
.98095
.98099
.98103
,98107
.98111
,98115
.98119
/(>" 41'
9.9«70;y
.98706
.9K708
.987109.9K712
.98714
.98717
.98719
9.98721
.9872:5
.98725
.98728
9.98730.98732
9.987:54 I 0.
160^97a;997064970699707497078970839708S9709397098971039710897113971179712297127
JO'' .v.i" 163° Kih .i:
9.9.<977
.9.-^979
9.9.V9S1
9.99009.99071
.99072
.99074
9. 99(170
.9907.S
.990^0
.99(l>-2
9.990VI.:i9(l>5
.99(1^7
.99(».S9
9.9:11191
.9!MI9:5
9.9909.5,
l7ih
0.97879.97883.97887.97891
0.97895.97899.97904.97908
0.97912.97916.97920.97924
0.97929.979:W
0.97937
9.99177.99179.99180.991K2
9.991.S4
.99180
.991S7
.991S9
9.99191
.9919:;
.99194
.9919(i
9.99I9•^
.99200
9.99201
J64'1.98123
.98127
.98131
.981351.98139
.98142
.98146
.981501.98154
.98158
.98162
.981661.98170
.9HI74
1.98178
Klfi .it;n
9.9S,so:5
.9KS(;5
.9SS07
.98S099.9,XS71
.9S,S7:5
.9SH75
.9SS77
9.9SSS0.9SSS2
.9S,SSI
.9s><s(;
;90
161°
0.97416.97421
.97425
.974300.97435.97439.97444.97448
0.97453.97458.97462.97407
0.97471.97476
0.97180
/.11 l.i'i
9.9:i2o;iI
0.
.99205 ,
.99200 '
.
.992081
,
9.99210j
0,
.99212 ,
.9921:5 ,
.99215
9.99217 0.
.9921s, .
.99220 '
.
.9!i222
9.!i!'22:i 0,
164°
,98182
,98185
,98189
,98193
,98197
,98201
,98205
,98209
,98212
,98216
,98220
.98224
.9S228
.9S232
.9S236
i~. -1
/(/I J.fm 160"'
I 'i^Ti.'l 0.97204'i-~
. I .97209
.97211-
. .97219
0.97221'1 .97ri8'- M .97233
>7238.m; 0.97213,-- .97217,:in .»72.VJ
.'.' .972.);
ril 0.97202'" .97266:'N .97271">! 0.»;27«i
I'ih i,;m'
tiih 47"! 161°_
9 9,^S'|| 0.9748,>9SVI0 .97490'isyis .971919-<900 .97499
9 9s'ili2 0.97.>03!Is:hii .97508'is'iiir, .975129VIIIS !I7.-,17
9.990121.99014 I
.99010 I
.99018I
9.9!t020
.99022
.!l9024 !
.99020
9.99027.)'9n29
.990;!1
.99o:t.i
9.99(i:ri
.9:io:'.7
9 ! 9041
162^
0.97751.97755.97760.97761
0.9776S.97773.97777
.977810.97785.97790.97794
.977980.97802.97807
.97811
0.97815
lil'>
.
9.991249912099127.99129
9.991:51
.991:1:5
991:5,5
.991:50
9.991:58
.99140
.99142
.9914:5
9.9914.5
.99147
.99149
9 991.51
|_163°
I
0.9.S002
.98007
.9.8011
.980150.98019
9,8023
.98027
.98031
0.98035.98039.9H0I3.98047
0.9,8051
.980.S5
.980590.98063
lOli :i9''>
9.99229I
.9!I2:50
.992:52 I
.992:54'
9.992:55 '
.992:57j
.992:59
.99210
9 99242.99244 '
,99245
,99247
9.99249.99250
.992529 99251
164°
;982:».98243.98247
.98251
.981M
.98'^58
.98262
.98266
.98270
.9S274
.9S277
.98281
,98285
.98289
,98293,98296
Page 920]
Page
Page 924]
Page 926]
Page
Page
Page
Page 934j
Page 936]
Page 938J
Page 940J
Page 942]
Page 944]
e)
'>
14 DAY USERETURN TO DESK FROM WHICH BOWIQWED
This book is due on the last date stamped below, oron the date to which renewed.
Renewed books are subject to immediate recall.
TU tlbM^
AAfrKoMOMir-
iWRAiir
;z_
