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Scholars' Mine Scholars' Mine
Bachelors Theses Student Theses and Dissertations
1917
Simple methods and tables for determining true meridian Simple methods and tables for determining true meridian
Howard Jones Teas
Follow this and additional works at: https://scholarsmine.mst.edu/bachelors_theses
Part of the Civil Engineering Commons
Department: Civil, Architectural and Environmental Engineering Department: Civil, Architectural and Environmental Engineering
Recommended Citation Recommended Citation Teas, Howard Jones, "Simple methods and tables for determining true meridian" (1917). Bachelors Theses. 113. https://scholarsmine.mst.edu/bachelors_theses/113
This Thesis - Open Access is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Bachelors Theses by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected].
SIl\l1'LE I.~ETEODS and TABLES for DETEPJ'IIINIIJG TRUE L:ERIDI::..:'~.
By
Howard J. Teas.
A.
THESIS
Submitted to the fa.culty of the
UN IVERS ITY of MISSOURI SCHOOL of MINES and T\~ET.hLLURGY
In partial fulfillment of the work required for the
Degree of
BACHELOR of SCIENCE in CIVIL ENGINEERII;Q."_·.:
Rolla., r,Fo.
1917.
TABLE of CONTENTS.
PAGE.
1. LIST of ILLUSTRATIONS. 1.
2. INTRODUCTION. 3.
3. O~MON METHODS of DETERrvTINING the MERIDIAN
WITH A SURVEYORS TRAlTSIT. 5.
a. SOL.AR OBSERVATION WITH EXAMPLE. 50
b. OBSERVATION on POLARIS at CUI1~~INATION. 10.
c. OBSERVATION on POLARIS at ELONGATION. 11.
d. MISCELLANEOUS METHODS. 14.
4. PROCEDURE FOLLOWED in OBSERVATIONS. 15.
5. REC~ENDATIONS ror FURTHER S~]DY. 18.
6. TABLES. 19.
a. AZn~UTH Of POLARIS at ELONGATION. 20.
b. LOCAL MEAN ASTRONaLICAL T1UEof UPPER
CUlMINATION. 21.
e. ANGLES BETWEEN URSA MINOR and and
ltELATlVE BEARING of POLARIS.
7. BIOGRAPHY.
8. INDEX.
9. DATA.,
10. CUltVES.
- 1 -
22.
27.
28.
29.
37.
LIST of ILLUSTRATIONS.
PAGE. DIAGRANI. SHOWING PATE ot STARS. 9.
DIAGRAM SHOWING RELATIVE POSITION of STARS. 12.
PHOTOGRAPH SHOWINGf\ll OUNT IN G of the Tru~.NS IT. 14a •
..,: 2 -
fNTRODUCT ION:
The ordalnary methods of determining the true
Ineridian by observation on either Polaris or the sun
are so tedious to calculate that most surveyors and
students dread making them. Observation on Polaris at
either elongation or clumination require less calcula
tion and are much simpler, but this simplicity is off
set by the fact that they must be taken at an exact
instant. It a cloud cresses the sky at that time, the
surveyor has to wait Q~til the next night. Then again
the observer must know the date, exact longitude and
latitude and correct time tor making the observation,
and these are not always known in the field.
The method described herein was suggested ,.,' ~;
by Professor Harris. Briefly, it consists of taking a
complete sunset to sunrise set of observations of the
total angle between Urser Minor Polari8 and Urser Minor
p and the corrosponding angle between Polaris and the
kn 0 Vin t be r:l er 1d ian •
These angles were plotted to a large scale and
connected up with a smooth curve. Then the table shown
on page l.2l) was constructed from this chart.
Determining the meridian by the use or this table
pORsesses several very distinct advantages over the c~
men methods-
-3 -
First, the table may b~ used independant of the date,
time of night, or longitude of the observer.
Second, with the tabl., the meridian may be determined
without any calculations whatever. This fact makes
this method particulary adapted to railroad surveying
and topography, mining, geology and exploration reaping.
- t -
SiJRVr;YORS TRA~JS IT.
SOLAR OBSERVATION.
Precedure.
FIRST. :et the transit up over a point where
shadows will not interfere, sometirre between 9and 11
A .r.:. or 2 and 4 P.M. and s ig:t:t on Lt referenc e po in t
with the verner set at zero.
SECOND. Foc'tls the image of the sun and the cross
hairs on the back of the note book or on a white card
as shown below.
l,Ji
Shot
Before noon il.fter noon
THIRD. Make two successive shot.s, once with the
transit normal and once inverted, not over five ~inutes
apart and. record the exckt time, horizontal and vertical
angles of each. ~fter each shift bring the bubble on
the telescope to zero and read the vertical verner.
Record the data as shown in the followine example.
FOURTH. Average the results obtained as shown
in the example.
- 5 -
FIFTH. With the loneitude of the place and the
local tirrle of observation known, change the local time
of the observation to Greenwhich time b~T adding algebra
ically to the former the differenoe in time between the
place and Greenwhlch. This procedure may best be ex-
plained by the following example.
SIXTH. Correct the average vertical angle by
subtracting the correction for refraction from it.
This c orre c t ion is equal to 55 U t ilne s the cot. of the
vertical angle.
SEVENTH. Calcul¢e the bearing of the. time from
the instrument to the point .bserved by the fell.wing
formula.
Sin D. N L Ces .A· ---- a •• eN X aes .L - Tan.· Tan.
Where D= Declination of the aun.
~., lbr Corrected altitude et the BUll.
It-=Latitude .r the ebserver.
The sign or the first term in the second half
of the equat10n will be minus if the declination 1s
south, and the second term .111 be plua if the latitude
18 south. It the a.s.A is plus, the azimuth 1s between
o and 90 as measured from the north; if minus, it is
between gO and 180.
- & -
EXAMPLE.
Observations made do the afternoon of March 9,
1917 by H. J. Teas. Transit set on pointX on the track
sighting at transit point in north window of jy.m.
helcl rlotllS.
Tel sUn Horizontal Verner Vertical verner/nate & Time.
On mark On sun On sun Bub. at o Mar. 9 1917
~ ()
00' 0
35' 36°35' 0"01' Norm 00 85 2: 34p:r.~.
lnv. ..t- OO~ 00 ' 87Q
25' 35" 24 J 0"01*' .... 2: 44P:M.
Av. + 00· 00 t 86° 30 t 35tr
59* 0" OIl' 2: 39P;M.
Av. Vert. angle corrected for bubble 36c
OO' 45 ft
KNOWN Latitude of Rolla 37° 57' 15 n N.
" Longitude of Rolla 92 w. FROV: the CURRENT SOLAR EPHElJIERIS.
Apparent Deolinational Greenwhioh noon.
Difference for one hour. 58.56 11
Equation of' time to be added to apparent time 10'45.75"
Difference for one hour.
CALCULATIONS.
Time at Rolla 2&39'
Correction for Long. 6'ft 08 '
Time corrected 8h
47'
Hourly change· 58.56 lt
- !] -
Change for 8° 47' 58.56" x 8.783 tf -= 8 t 34"
Decl. at Rolla Decl. ~tt Greenwhich x change for
correc ted time 4 Q 36 '15 ftx8 r 34"::; 40
44' 49 1t
Correction for Refraction~ -Cot. Vert. angle x
55"::--Cot.36°00' 45 ft X 55 ft :=- l'15.67 ff
Vertical angle corrected 36 OOt45n~ _0"1'15.67" o
35 59' 29.33"
Cos. A. Sin Decl.!.-- _ Tan Lat x Tan Alt. Cos Lat x Cos Alt.
(1) (2)
_- S:I.n 4" 44 '49" -Tan 370
57 '15 nxTan 35;;> 59 '29 .33 ft
Cos 37~57t15ttx Cos 35°59'29.33"
( 1)
Log Cos 37°57'15"
Log Cos 35°59'29.33"
Log Sin 4"44'49 1f
Log (1)
( 1)
Log Tan 35" 57 '15"
Log Tan 37~59'29.33u
Log (2)
(2)
-8 -
9.896802 - 10
9.908019 - l{j
.1:'9.804821 - 10
19.917793 - 20
9.804821 - 10
7'0.112972 -.l<:i'
-0.12971
9.860530 - 10
9.892676 - 10
.~.753206 -J:O
-0.56651
-0.12971
- 0.69622
Nat Cos i ...
A
-0.69622
450
52 '29"
Av. Horiz.~
,"6° 29' 60 n
45° 52' 29 11
40 0 37 t 31 n
~. ~ ~r
'-t.o;--'" '--~--"'"
- Sa -
\rI E.IDn~atl"n
Instrl/menf
- ~
By OBSERVATION ~n POLARIS at CUI1IJ~ INATION •
PROCEDURE.
FIRST. C.ltlplete the exact tirne .r cUlmination
by reference to the table given en paBe ( 20).
SECOND. Get th~ exact 18cal time fr.m the
tele~raph station.
THIRD. Set up the instrument over &. station
about 20 minutes before the calculated time of
cUlmination for that date.
FOURTH. Start rellowing Pelaria with the
tangent screws a oc1nute or 80 before this time.
FIFTH. Clamp the inatrument at the EXACT
calculated tim ••
SIXTH. Check the Gbserv~.ti.n by DlMEDIATELY
lowering the telescope and sighting en eithe~
Cassl.pela Delta <tr Ursia Major Zeta. These two
stara are 1n the same vertical plane with PolarIs and
the pole at culmination. (F0r the relative pesition
of these star., see page ( 12) ).
SEVEnTH. Depress the telescope and set a tack
in [:1 stske a. hundred feet or more away.
Then the line from the plumb beb to this point
1. the true meridian.
- 10 -
By OBSERVATION en POLARIS at ELONGATION.
PROCEDURE.
FIRST. Find the bearing of Pelaria at .longatien.
This may be reund by imterpulat1ng the table en page
(19 ) er by 8ub8tltuting in the fell.wing forn.ula.:
Sin. F.1ar18 Dist. of Star S1ft. Stars True Bearing~ ____________________ __
Cos. Latitude of Observer
The mean polar distance or l.lari8 ~.r the .ext
rour year. 18 shown in the r.llowing table.
MEAN POLAR DIST. of FOLARIS.
Year Mean Pe1a.r D1at.
1917 1° 08 ' 16.45 t
1918 1" 07 57.94
1919 10
07 3Q.45
1920 1" 07 20.98
EXAM.PLE. Fer Rella. (Lat. 370
57' 15 ft) in 1917.
Sin True Bearing of Pelaria- Sin 1 0 08' 16.45 11
- C8.3'0 57' 15"
:: J"2-bf
38"
SECOND. Find aut the apprexlmat. time er ea.stern
or western elengation. This may be do •• either by look
lag up frem the table on page (20) the time or culmin
ation and either adding er subtracting 5 hra. 55 t fer
e •• tern er .estern .1.R~ation er merely .bserTi., the
stars eft the night b.r.re. At either e1engatlen,
Pelar18, ur.er Majer Zeta and Casai.peia Delta are at
the same altitude.
- 11 -
~ \1\ ...... ~
" ~ ~ ~
\t) ~ ,..... ...... (:)
~
5
.,:
.- Po'"
Uy,So. Hfno!'"
* * *p *T'
H Urso. jor '* ;5 *e 6
*'1
P".si lion of C on:;fe//",fIIllI1S w..)t'IJ Po loris /..1 or
Upper Ci//m;"nafio/J.
- 12 -
s::: ~
'1--1
(J c::t\ t: ~ l&...i
t ~ '" <::os ~
-Ieee
-i',
'Icy
THIRD. Set up the transit over a point where a
cl~ar vi~w Qf the sky tQ the north may be obtained
abeut thirty minutes before elongat1oa. Sight on P.larls
wIth the vertical eres8-aalr and fellow along it with
the cre.8 metlen until Pelaria appears to move either
dewn .r up the cress-hair without changiag ita azimuth
~.r five minutes or .e.
FOURTH. Depress the telescepe and •• t a tack in
a stake about a hundred t •• t fr.m the instrument.
FIFTH. Cheek the point by anether Bight eft lelaria, with transit l'ele5C. o pe I""~rtd.
This is pessibl. because P.lar18 apparently dees not
change ita az1r:tuth fer abeut ten er fift.en minute.
at elon&ati.n.
SIXTH. Sight en the point just •• t wIth the verner
at zero and tura et'£ the azirriutll ef relarll ebtained
abevs te the east or west by the fell_.ing rule.
When Pelaria ia at •• at elengatien, (the dipper
in the east), turn the angle er the azimuth t. the
east t. l.eate true n~rth.
When Pelaria 18 at east elengatiGn,(the dipper
in the weat}, turn the aagle of the azimuth te the west
to I_cat- true north.
- l~ -
M ISCELANEOUS METHODS.
There ar~ several Gther methods of more 0r lesa
accuracy which are sOffiatimes used, but none .t them
are of' any ir:lportance. AnHJng these are observations
GU Pelaris at any time, which are made and calculated
like .~lar ebservations; observations er the sun,
P.larla~ er Ie •• other prominent star at equal altitudes
near culmination; etCe These methods are seldom. used
and wl11 n.t be d •• crlbed her ••
The •• lar tela.cope methed is not diacussed as
it requires additi~nal apparatus •
.. 14 -
PHOTOGRAPH SHO ING ~ . OUNTING of the SIT.
- .14a -
PROCEDURE FOLLOWED in OBSERVATION.
A transit base was first mounted in the north
window of room 11 of Jackling Gymnasium. A transit was
then set up on a point X near the running track and a
solar observation made to determine the bearing of the
line from X to the transit pOint. A stake was then set
about 200 ft. up the road from the window and a tack
set in it to give the true north. This pOint was then
checked by two independent observations on Polaris at
elongation as described above.
On the night ot April 12, a set of observations
were made oovering a period of s1x hours beginning at
dusk. The p*ocedure was as tallows: A light was first
set up on the merid1an point and the transit sighted on
this point verniers at zero. The oross-hairs were 1l1um
inaeed with a. light from a reading lamp. Polaris was then
sighted and the VBrnier read and the reading recorded,
showing wether it was east or west. Then Ursa Minor Beta
was sighted, its bearing recorded and the d1fference in
time between the two shots noted. This was repeated every
five lflinutes. Sighting on Polaris and Ursa M Inor Beta
alternately and recording the time of each observation.
On the night ot April the 21, a complete set of observations
were made tram dusk to daylight. The procedure was the
same as before, except that whBn ursa Minor Beta was:·
near its upper culmination observations were taken on 1~.
- '15 -
every two minutes. as it was changing its azimuth so
rapidly that less frequent shots would not give enough
pOints to plot a smooth curve.
This data was then plotted to a large scale on
coordinate paper, with the vertioal scale of 1/10
inch equal to one minute of time, and the horizontal
scale of l/~O inoh equal to one minute of angle. This
large horizontal soale was made possible by plotting
sections ot the curve two degrees in length at a time.
A smooth ourve was drawn thru the points. Next the bear
ing of Polaris tor even degrees an4 minutes ot total
angle between Ursa Minor Beta and Polaris was taken
from the chart with a scale and the values tabulated.
See page (21).
In making the observations, a good deal ot diffi
culty was experienced in locating and recognizing the
stars quickly enuf 80.:';8." not to allow any appreciable
time to elapse between any pair of shots. Polaris is
eompartiTely easy to recognize because ot its brilliancy
and also because of a amall star about a half a minute
away which appears in the field of the transit at the
same time that Polaris is sighted. It was much more
difficult, however, to locate and recognize Beta because
of the proxhnlty of Gamma which forms the lower outer
corner or the little dipper. Thru the transit, these
stars are Tery d1frlcult to distinguish one trom the other,
- 1.6 -
especially when Beta is near culmination. It is there
fore advisable to make the observation as early in the
evening as possible.
- 17 -
REC~~lENDATIONS for FURTHER STUDY.
On account of the authors having to work alone
and because of a long series of cloudy nights, the
table is not complete, and has not been thoroughly
checked. The author therefore suggests that a further
study be made, and to facilitate efficient work
offers the following reoommendations as the result of
hid exper1ance.
FIRST. That the subjeot be takeb up by two or
three invest1gatirs lnsted of one.
SECOND. !hat the meridian used be checked by
every known method so that the investigators wIll be
sure that it is as accurate as can be looated wIth a
transit.
THIRD. That two transits be used tor the
observa~1on8. They shou14 be mounted in two ad'aDent
windows, so that the7 w111 not Interfere with each other.
One observer should. be stationed at each instrument
and each tollow with the trans1t,,',one star continuously.
In this way siroeltaneous readings can be taken, which
w1l1 permit the using of a much smaller vertic •• scale
tor plating the results. It 1s of course needless to
say that the instruments should be in the best of
adjustment before use.
FOURTH. Tha~ the observations be made early in
the year. 80 that as long as a set ot read-ings as
possIbly may be made.
.. 18 -
1'ABLES.
-lQ -
FORM B. 109-10-15-5000
MISSOURI SCHOOL OF MINES
Lat. Year f
N. 13I7 i i9 18 19I9 1920 0 0 m a n< ... .. '"
5 I 8.5 I 8.2 I 7.9 1 7.6
10 I 9.3 I 9.0 I 8.7 I 8.4
12 fJ.7 9.4 9.T S.8
15 11.0 10.7 10.4 IO.I
18 11.8 11.5 11.1 10.8
20 I I2.6 1 I2.9 I II.Q I 11.6
22 13.8 I3.4 13.1 I2.7
24 14.8 I4.5 14.1 13.8
26 Ie.O 15.7 15.3 I4.9
28 17.4 17.0 16.7 I6.3
30 I 18.9 I 18.5 I I8.2 I 17.g
32 20.5 20.1 19.8 IQ.4
34: 22.4 22.I 21.7 21.3
~& 24.5 24.I 23.8 23.4
~8 25.8 25.4 2f5.0 25.6
40 0 I 29.2 I 28.8 I 28.4 I 28.0
42 32.0 3I.e3 31.I 30.7
44 35.0 34.6 34.1 33.6
45 38.4 37.g 37.5 37.1
48 42.2 41.8 4I.3 40.8
50 I 46.3 I 4:5.9 I 45.4 I o:44.g
52 51.0 50.5 50.0 49.5
54 58.3 55.8 55.2 54.7
5e 2 02.2 2 1.7 2 1.1 2 00.5
58 g.O 8.4 7.8 7.2
I. p.~2 CcJ 2 Ie.e 2 re.o 2 15.3 2 14.7
PAGE .. _ ..• _._ ..... _
- 10"-
PAGE .............. .
MISSOURI SC,~O{)L .,OF.MI"N~S
LOCAL MEAN ASTRONOV1 leAL TIME of UPPER CUI.N INATION of POLARIS.
19I7 1918 19IQ I920 {)iff. ("Dr
[)ate. 1. Oay
Hr Min. Hr. Min. Er ~ Min. Hr ~ Min 'M in.
Jan. I e 45.e 6 47.0 6 48.4 43 4Q.Q 3.95
Jan. 15 5 50.3 5 51.7 5 53.1 5 54.6 3.95
Feb. I 4 43.2 4 44.e 4 48.0 4: 47.5 3.QS
Feb. I5 3 47.g 3 4g.~ 3 50.7 3 52.2 3.94
Mar. I -.2 52.5 2 54.1 2 55.5 2 53.0 3.94
Mar. 15 I 57.4 I 58.9 I 00.3 I 57.7 3.g3
Apr. I 0 50.6 0 52.1 0 53.5 0 5O.g 3.93
Apr. IS 23 5I.0 23 53.1 23 54.e 23 52.0 :5w92
14ay I 22 48.9 22 50.3 22 51.8 22 49.~ 3.g2
Mal 15 II !54.0 21 55.4 2I 5e.9 2I 54.4 3.92
Ju. I 20 47.2 20 4,8.0 20 50.1 21 47.8 3.9I
June 15 19 52.4 19 53.8 IQ 55.:5 I9 52.8 3.91
J.ll I 18 49.8 18 5I.2 IS 52.7 18 50.2 3.9I
Ju1l 15 I7 55.1 17 5&.5 17 58.0 17 55.5 3.92
Aug. I I& 48.5 It) 49.9 Ie> 51.4 Ie 48.9 3092
Aq, 15 15 53.7 I5 55.1 15 56.6 15 54.I 3.92
Sept. I 14 47.0 14 48.5 !4 49.9 I4 47.4 Z.g2
Sept. 15 13 52.1 13 53.8 13 55.0 I~ 52.5 3.Q;S
Oct. I 12 4g.3 I2 50.8 12 52.2 12 4Q.7 ~.93
Oct.. 15 II 54.3 II 55.8 II 57.2 II 54.7 3.Q3 - -Ii -
Ney. I 10 ,.,.s 10 4g.0 IO 50.4 10 '7.g 3.94
.ev. II {I 62.4 9 53.9 g 55.3 Q 52.8 :5.94
Dec. I 8 ,g.2 a 50.7 8 82.I S ,g.e 3.g4
Dec. Ie 7 54.0 7 55.5 7 58.9 7 54.4 3.94
FORM Sa J09-S0-J5-5000 F. P. ~ S Co.
TABLES SHOWING ANGLES BETWEEN URSA MINOR f£
andp? and CORRESPONDING BEARINGS of POLARIS.
DIRECTION for USE of TABLE.
Set the instrument up on a clear night where
there 1s an unobstructe4 view of the north sky- Locate
and recognIze Polaris and Ursa Minor Beta by the use
of the chart on page (12), and note the approximate
position, 18 wether near upper culmination or
elongation, ete. Sight on Beta with the vernier at
zero, turn to Polaris and plant the instrument, not
ing the difference in time between the shots. Kead
the ver1ner and correct the angle read tor the
.1tterence in time between the shots. Take from the
proper table t~e bearing ot Polaris corresponding to
the angle rea4. Turn this angle off east or wsat as
shown 1n the table. Set a stake and. tack: about a hundred
teet trom the instrument. Th8 line trom the taok: to the.
instrUMent 1s then the true meridian.
- 23 -
Iofa f I1n"le Corre~fO~n./ll7j
fr"m « to# /!J1rIR fy""" 0( ; .. '
i East Ttl IY/~Yidfll"
1bfal I7h'flt C ",.re sf""d /IIf
fy6t)1 qC f. ~ flJ1g/e {","m ~ East 1" Aet-1dltf4
20 4 58 I" 10' 3<J 19° 45' O· 54' 2d'
56 , 9 15 40 54 00 l'
54 :.; 8 20 35 53 10 ~:
52.'. 7 40 30 52 25 ~ ~
50 " 7 00 25 51 45 ~.
48 1 6 25 20 51 00
46 5 50 15 50 30 " ...
44 5 15 ~ 10 49 50
42 4 45 5 49 20 ~
20 40 1 4 20 ~ lQ 0 0 47 30
38 4 00 .~ "
18 55 0 48 00 ~
36 3 30 ~ q, 50 47 30 a....
34 3 00 ,'I) .... 45 45 50 ··f
~ .a..
32 2 30 ~ ~
30 1 2 00 \..., 0
40 46 00 ~ ~
35 45 40 ~~
28 1 1 45 ~ ~
.~ 26 1 15 ~ 24 1 00 ~
~
30 45 10 :~
~
~ 20 44 5 ~
~ 10 43 00 \j
20 22 0 30 ~ ~
18 ( 0 42 Op
20 1 j. 0 ~
~ 17 50 0 41 30
15 0 59 0 40 0 40 00
10 0 58 20 30 38 40
5 0 57 30 20 58 00
20 0 0 56 45 10 37 00
19 55 0 56 00 17 0, , ~5 io
50 55 15 16 50 34 45
tdtq/ f!rtgj Cor ~~f'o~IIYJf /fJet"qe",., . .,.. f f/111/e ('row< pC
Ii
E i"~r~rh () (
16" 40' 0° 33' 45
7;"f0. ( f/"'1le Corr( .$/'011 cltny
fro", 0( fd f9 ;flly-Ie f'r,~ oC
[; ~"fckq" 120 sa 0° 13{ 46 -
30 32 4G 10 12 50
20 32 00 12 0 0 12 20
10 31 00 11 50 11 40
1e; 0 0 30 00 40 11
15 50 0 2Q . 20 30 10 30
40 28 30 20 10
30 27 50 10 9
20 25 45 11 0 0 8 40
10 25 00 10 50 8 .~
" 15 0 0 25 00 ~ 40 7 15
14: 50 0 24- 30 t 40 23 45 ,~
'"
.~
30 6 50 t :\:
20 P 6 15 ~ ,~
:SO 23 00 . ~ 10 5 30 t\.
20 22 15 ~ ~
10 21 20 \)
t. 10 0 5 ~ ~ 50 4r 20
~ '..J
14 0 0 20 50 40 3 50
13 50 20 00 30 3
40 19 20 20 2 30
30 18 30 10 2
20 18 00 g 0 0 1 20
10 17 8 50 1
13 00 0 1& 15 40 0 30
12 50 0 15 30 8 30 0 0 0
40 15
30 1.4 15
,. 25 ...
BIOGRAPHY.
The following books were freely consulted in
the preperation of this work;
Breed and Hosmer. Ptinciples and Practice or Surveying.
Hosmer - Text book of Practical Astronomy.
Coal Miners Hand Book.
• 27 -
INDEX.
Angles between Ursa Minor G:- and' Relative
Bearings of Polaris.
Azimuth of Polaris at Elongation.
Biography.
Common Methods of Determining the Meridian.
Curves.
Data.
Introduction.
Local Mean Astronorr.ical Time of Upper
Culmination.
Miacelaneous Methods.
Observation on Polaris at Culmination.
Observation on Polaris s.t Elongation.
Procedure ~ollowed in Observations.
Recommendations.
Solar Observation.
Tables.
-28 -
22.
20.
27.
5.
37.
29.
21.
14.
10.
11.
15 ..
18.
5.
DATA.
Ti;;
'~
Tim
e
Vem
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