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 scholarsmine@mst.edu.

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

iel'

Read1n~.

To

tal

'2.""

51,<

>f

(st

Sfl

o-f

S

,1h

fm,

QJ' po

/q,.

..,~

Sl

fJJ,

f/,,

~ O

h j!5

' A

ng

le.

~in.

IIr,

M,.,.

E

. w.

E

. w.

SK

ETC

HES

. 5

7

7 5

3

IG 1

2 L

.1~

t 4

8 t

21

00

0 t

Ap

ril

21

,19

17

. 0

2

8 0

0

1 1

0'"

:1.9

48

' 2

0 5

8'

06

8

05

1

9 '-

rt 9

45

t 2

0

55 I

11

.5

8 1

0

1 8t~ 1

9 4

5'

20 5

3'

16

.7

8 1

5

1 7

L ~1

9 4

1'

20

4

8'

21

.5

8 2

0

1 5~ l

Q

39

' 2

0 4

4'

26

8

25

1

4L

~19

34

t 2

0 3

8'

1

31

8 3

0

1 3

,~ 19

31

' 2

0 3

4'

~6

8 3

5

1 2

L ~1

9 2

5'

20

2

7'

41

8 4

0

1 o\

:-1

9 2

0'

20

2

0'

4e

8 4

5

o 5

9'-

"19

13

t 2

0 1

2'

51

8

50

o

58t~ 1

9 0

8'

20

0

6'

56

8

55

o

57

'-~1

8 5

8 t

19

5

5'

ooi

9 .. 0

0

o 51~ 1

8 3

5'

19

26~t

06

9 0

5

o 5

3 '-

~18

42

t 1

9 3

5'

Che

cked

sig

ht

on p

cta

.t.

I ~

loi

g 10

o 51~ ~8

35

' 1

9

26-;t

-· 1

5.6

9

15

o

50

'_ ~1

8 2

0'

19

1

0'

9 1

8

18

7

' t

21

9

20

o

49'~ 1

8 1

3'

19

0

2'

9 2

3

18

06

' \.f

rSt'v

M

I1J"

dr.

26

9

25

o

47

.t -i

s

01

' 1

8 4

8.5

' 9

27

17

5

5'

30

.5

9 3

0

. 0

45

'..:

17

50

' 1

3 se

t 9

33

1

7 4

2'

37

g

35

1

7 3

6'

9 3

7

17

3

0'

I tf;

: IA

rltr

-

, M

:""-...

• f

9 3

7

17

3

0'

41

,9

4

0

o 4

2 '-

!Iao17

23

' 1

8

05

' 9

43

1

7

15

r fU

B

p.11

.

9 4

5

17

9'

9 47

-17

2

' 5

2

g 5

0.5

o 39~ ~18

52

t 1

7 3

1'

57

9

50

(:)

37

!...

~6

31

' 1

7

08t

10

0

3

16

11

' 1

0

05

1

6 0

4'

10

0

8

15

5

5'

11

1

0

10

o 32~ 1

5

40

' 1

5

20

'

--rim

. li

me

2."4

ls

I: S

ho

t 5h

ot

Min

. 1f

t: N

th,

16

1

0

15

10

18

1

0

20

10

2

3

26

1

0

25

3

1

10

3

0

10

3

3

10

3

5

10

3

8

41

1

0

40

4

6

eO

45

1

0

48

1

0

50

1

0

53

5

6

lO

55

1

.5

11

0

0

~ 1

1

03

1

1

05

• 1

1

08

1

1

II

10

1

6

11

1

5

11

1

8

11

2

0

11

2

3

26

1

1

25

3

1

11

3

0

11

3

3

11

3

5

11

3

8

41

11

4

0

50

1

1

45

1

1

53

5

5

58

1

1

59

~i

12

0

0

12

0

3

2 I

Vt2

rnie

r R

eQ

c:/u

7Q

Sl.

qh

fin

v on

fo/

qris

S~AJi/¥

~rJ

;::1

!fhj1!~

-Rlf

tj/f

f 10

f1

nqle

to f

''

'9Ie

to

h/

vi

OC

130

'. ~ 1

50

25

' 1

5

18

t 15

1

0'

14

5

8'

OO26'~ -

14

5

0'

o 2

5 t

,_ ~ 1

4

25

t 1

4 1

7'

14 0

8'

13 5

3'

.,:0

21

'( ~ 1

3 4

6'

o 2

0'-~ 1

3 1

9'

13

1

0'

13

0

2'

12 4

6'

o 16

'~ ~ 1

2 3

8'

o 1

4 t.

~12 O~·

11

58

' 1

1 4

8'

11

3l'

o

11'~ ~ 1

1 2

. t

o 0

9 '-~lO

51

' 1

0 3

9'

10

28

' 1

0 1

1'

o 0

6 t~

1-1

0 0

1'

o 0

31 _

~

9 2

5'

9 1

3'

o 0

3'

8 4

6'

o 0

0'"

, ~

8 3

4'

o 0

2

-~

7 3

6'

7 1

4'

7 0

5'

6 4

5'

o 0

9'

j.tE ~

6 3

9 t

6 3

5'

o 0

9

-~

5 5

2'

Iota

/

f1tJ

l/e

15

"'5

5'

51

16

t

1-1

51"

14

0

7'

13

3

9'

l2

54

· 1

2

20

' i

11

3

3'

11

0

0'

10 0

7'

9 2

8'

8 3

4'

7 3

4'

6 2

5'

5 42

~'

SKE

TC

HE

S.

.Ap

t1l

21

,19

17

.

, •

.. .;.

!Co

"

I1t

IO?t

y'

Che

cked

on

p

oin

t 4 i . f

~"

1ft

1"114

11/,6

1.

l

"

I :c,.

(¢

Til

le.

l,tS

h",

Z".

{ 5

h"t

Min

. Hl

.1 !V

f,;,.

12

0

8

12 1

0

12

12

l~ 15

1

2 1

8

21

i 1

2

20

2

4

12

23

12

26

12

2

8

32

1

2

31

3

5

12

34

1

2' 36~

12

3

8

12

4

0

12

4

2

12

44

1

2 4

6

50

1

2

48

12

. 51

1

2

50

Ih

~.

58

1

1 0

0

10

1

05

1

1"'· G

1 14

1

16

1

18

2

1!

1 2

0

26

1

28

1

38

1

30

~6.5

1.5

i

~8

46

1

45

5

1

1 5

0

.56

1

55

0

1

2 0

0

10

6

2 0

5

11

2 1

0

16

2

15

Ver

n1er

S

lqh

hl1

f 0

17

P"

I"r;

~.

E.

w.

00

16

t l

o 1

6.5

o 2

0'

o 20

t'

o 2

6'

o 3

0'

o 3

1'

o 3

7'

o 3

8'

o 4

2'

8 t~

: o

45

' o

46

' o

48

' o

49

' o

51

' o

52

' o

54

'

Rea

ding

. T

ota

l 51

,-1J

f't11

on

,s

A

ng

le.

E.

.. SK

ETC

HES

. SO

41

' 5

30'

5 1

7 t

4 5

7'

4 3

9'

Eo "'

4 2

6'

4° 1

0'

Ap

ril

22,1

9:},

7.

.-~3

57

' 3

41

.5'

:3 4

6'

3 3

1'

~ ~3

13

t 2

53

' -... 2

4

5'

2 2

4.5

' 2

35

' 2

25

' 2

10

' 1

57

' 1

44

' 1

31

' ~ ~1

18

' o

52

' o

58

t

o 2

7'

o II'

-~O

O·

o 2

' o

32

' E

-~

1 8

' 1

QQ

t

1 2

4'

!

1 3

7'

1 5

0'

f-+

2 2

' -

2 2

0'

2 5

7'

~ ~

2 5

7'

3 3

5'

3 1

1t

-~

:3 2

5'

<"" ~

~ ~@

: ~

~~:

-~

5 0

2'

5 4

7'

t-I-

5 4

0'

6 2

6'

-4'

6 0

7'

6 5

5'

'f--

e 4

2'

7 3

1t

-~

7 0

9'

8 0

0'

f--

7 4

3'

8 3

5'

Che

cked

on

p

oin

t

-~

8 0

9'

9 0

3'

I '" CIt

I

Tim

e.

12114

Sh

.. "

l$f.

Sh

ot.

Min

. H

r. M

in.

22

.5

2 2

0

26

. 2

28

3

6.5

2

30

41

2

40

46

2

45

52

2

51

57

2

55

01

3 00

07

:;

05

11

3

10

1

6

3 15

21

3

20

2

6

3 2

5

31

3

30

3

6

3 3

5

II

:3 4

0

52

3

50

5

6

3 5

5

01

I 0

0

07

4 0

5

12

4 1

0

16

4 15

21

4

20

26

4

25

3

1

4 3

0

36

4

35

4

45

4

50

~

4 5

5

Ver

nie

r S

I9h

f ,,,'3

on

P

olar

is

E.

w.

0°5

5'

o 5

7'

o 5

8'

1 0

1'

1 0

2'

1 0

4'

1 0

5'

1 0

6'

1 0

7'

1 0

8'

1 0

9'

1 1

0'

1 II'

1 1

3'

1 1

4'

.. 1

15

' 1

16

' 1

17

' 1

18 t

1 1

9'

1 1

9.5

1

1 2

0'

1 2

1'

1 2

1'

1 2

2'

1 2

3'

1 2

4'

25

' 1

25

'

Rea

diuJ

ts.

To

tal

-S

f9h

tm9

_

on

;3

A

ng

le.

Ap

ril

22

,11

17

.

I w.

E

. i

-E--

8° 5

1t

go 4

6'

-~

9 0

6'

10

03

' .. ~

10

1

4'

11 1

2'

-~

10

3

2'

11 3

3'

~ ~

11

02

' 12

0

4'

- ~

11

30

' 12

34

' of

-~

12 0

0'

13

05

' .- ~

12 lS

' 1

3 2

2'

-E---

:12

22

' 1

3

29

t

- ~

12 4

0'

13 4

8'

<-I-

13

3

2'

14

42

' -~

1

3 4

8'

14 5

8'

<:~

14

16

' 15

2

7'

-~

14 3

4'

15 5

7'

~I-

15

1

9'

16

33

' - ~

15 4

1'

16 5

6'

~ -

16

01

' 17

1

7'

-~

16 0

8'

17 2

5'

t I--

16

37

' 1

7 4

5'

-~

16

41

' 18

00

' 4-I-

17

01

' 1

8 2

0.5

.-~

17

1

1'

18 3

1'

.f-

17

29

' 18

50

' -~

17

4

0'

19

01

' 0f-

f--

17

5

3'

19

1

5'

-~

18 0

4'

f-I- H- - -t'~

'7iin

e:-

7//

41

8

2.,...

,t/ s

A"

t It

sf

6h

.",r

Mn

'f,

If"

!11-

*' '7

sa

7 '!J

7 3

2

32

3

5

33

.5

41

.5 7

40

4

8.5

4

6

54

.5

52

B

0.5

5

9

9 8

8.5

1

7.5

6

19

23

8

21

.5

32

8

31

36

.5

35

41

.5

40

46

4

5

51

.5

50

S 5

6.5

8

55

9

01

9 0

0

: g

06

9 0

5

g 1

1

9 1

0

I Ie

1

5

21

20

2

6

25

3

1.5

a

30

3

8

8 3

6.5

4

1.3

8

40

46

a

45

5

2.5

8

40

5

6

8 5

5

1 9

0 6

9 5

11

.5 9

1

0

16

9

15

21

g

20

2

6.4

9

25

3

1

Q

30

3

5.5

9

35

4

1

9 4

0

46

9

45

VerJ

1le

r R~ac/lyJqs

Sf""f

,,,, q

d

l' /?#

f4"'

~ 5

"t?

IJ-'

fiIJ'

I"

0»

F'

J:

.~

W

6 -

W/

b f

1 2

1.5

-~18

°14.

5 1

23

.51

~18

22

' 1

24

-~

18

26

.5

1 2

4'

-~18

38

15

1

24

.5.1

fi.1

8 4

9'

1 24

18

86

' 1

22

.5'

19

5.5

1

21

' 19

1

5.5

1

20

.5'

19 2

6.5

1

20

' 19

28

.5

1 1

9'

19 3

6'

1 1

8'

19 3

1'

1 1

7.5

' 1

9 4

3'

1 1

6'

19 4

51

1 1

5'

17 4

7'

1 1

4'

19

48

.5

1 1

3.5

' 1

9 4

9'

1 1

2'

19 5

0'

1 II

' ~9

40

' 1

10

' 19

48

' 1

07

.5'

19 4

7'

1 0

8'

19'f4

5 '

1 9

' 1

9 1

7.5

,.

1 8

' 1

9"'

45

' 1

8'

19

42

' 1

6'

19

41

' 1

4.5

' 1

9 3

5'

1 2

.5'

19

32

' 1

2'

1Q

28

' 1

O·

19

2

31

o 5

9'

19 1

5'

o 5

8'

19

1

1'

o 5

7'

19

2

1'

o 5

5'

18

56

' o

54

' 1

8 4

6'

o 52

1 18

·3

9'

o 5

1'

18

27

' o

49

.5'

18

18

'

T:;

fa(

/lJ1y

r/e-

19

°39

' 1

9 4

5'

19

50

.5'

20 0

2.5

t

20 1

3.5

' 20

2

0'

20

2S

' 20

36

.5'

20 4

6.5

' 2

0 4

8.5

' 20

5

5'

20 5

7'

21 0

0.5

' 21

0

1'

21 0

2'

21

0

2.5

' 21

0

2.5

' 21

0

2'

21

0

0'

20

5

8'

20

5

6.5

'

20

5

5.5

' 2

0 5

3'

20

5

0'

Ap

bil

2

J 1

91

7 •

"F

rt(

'3-,

'f/

7

1"11

17

deda

nD

f LA

'>Pc

/,

• (Ill

at

•

I

7/11

1&

4II

fl!4

/5

1

HIH

1I

r.

51

9

56

9

1 1

0

0 1

0

11

. 1

0

16

1

0

21

1

0

26

1

0

31

1

0

37

1

0

42

10

4

6.f

10

5

2

10

5

6

11

1

11

9

11

ll

.f 1

1

16

1

1

21

1

1

26

1

1

31

1

1

36

1

1

41

1

1

46

1

1

51

1

1

56

1

1

01

1

2

06

1

2

ll.f 1

2

16

.e 1

2

21

1

2

2&

12

3

1.f

12

1

2

41

1

2

41

12

?h

Qf

HI'

n.

50

5

5

0 5 1

0

15

2

0

25

3

0

35

4

0

45

5

0

55

0 6

10

1

5

20

25

3

0

35

4

0

45

5

0

55

0 5

10

15

2

0

25

3

0

35

4

0

40

Ver

nIe

r R

eb

dln

q5

;

S 1

9 hf/l

1f{

0 n

f" f4

.Y"I

s 5,

'11,

fll1

,9'

. ~~

P

Ii"

W

I:

w

, 0°

119

t ~

lB0

5 t

o 4

6'

A I

--7

56

'

t og

.+,'y\

· r

,,\f

.lV

rl/l

. .Y

(I

'{

'~

'J.~t

J. \

SKET

CH.

Ap

ril

13,1

91.7

.

o 4

5'

- ~ 1

7

40

' o

43

t ,/:

. I-

17

3

0 I

o 4

1 t

-~ 1

7 1

3'

o 4

0 r

<:; '* 1

7

l'

o 3

8 t

-~ 1

6 4

3'

o 3

6' ~ 1-

--16

30

I o

34

.5~

f-:-1

6 1

0'

I-0

32

.5-'

~ 1

5 5

6'

o 3

1'

- ~ 1

5 3

0'

o 2

9' ~ I--

15

1

9 r

o 2

8 t

-~ 1

4 5

0'

o 2

5.&

'" 1

4 3

9'

o 2

4'

-~ 1

4 1

3'

o 2

1'

4 I--

13

5

2'

o 2

0'

-~ 1

3 2

6'

o IS

' k

f-1

3

9'

o 1

7'

-~ 1

2 4

0 t

I o

16

' ~ v

1

2

22

' I

o 1

3'

-~ 1

1

51

t o

11

' +

1---1

1 3

1'

o 1

0'

-~ 1

0 5

9'

o 7

5'

.. I-

10

39

tt,

0 6

' -\

->9-1

0 7

' 0

3.5

1 ~

9 4

4'

0 2

t -

b>

9 1

5'

o O

· 0

0'

.L,,;I

~ 8

49

' A

pr 1

1 1

4,1

9 1

7 •

o ,t

.-!'?"

8

10

' o

4'

k I-

7 4

8'

o 5

.5'

-I-'>

7

15

' o

7.5

' ~f-'

6 4

9'

o 9

' -~

6 0

6'

Lu

nch

F

irst

C

ours

e.

o 1

3'

""I-

-5

8'

o 1

3'

-~5

8'

I r c..

Q')

I. T

7n

-?d

-a.t:

!.5h"

f 1~

"'Sh

dr

N,n

. /f

r.

MIT,

51

.5

12

50

6

6

12

56

1 1

a 6

1 is

a 1

10

16

.8

1 15

2

1

1 I(

] Ie

1

25

3!

1 30

3

6

1 :5

5

~Y"n

/~"'

" Readll'?~.5

S/91

J77H

~ C

J J?

Po

ltrrl.

5 S

'f'1

rt I J

;'1'T

() n

/"

S W

-E

hi'

" 0°

17

' ~f-

50

8'

o 1

9'

- .,

. ~ I

32

' o

20

' t:

. 2

51

' o

23

' a

24

' o

24

' -,

. 1

35

' "-

-o

1&'

-71>

1

18

' o

27

' 4

: -

·)0

St!

' o

30

' 7-

o 1

0'

o 3

1'

o 3

8'

o 31

' o

56

'

Po.tll

. \o\D

f l,

.A$r

~ /11

f\ll

\~(

CIJ

I' II

~·

Ap

ril

14

,lm

7.

C,URVES.

- 87 -