William David Pence.

A manual of field and office methods for the use of students in surveying online

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utes mean solar time. The time from Upper Culmination to
Lower Culmination is 11 hours 58 minutes.

Astronomical time, or Local Mean Solar time, is the time
that would be kept by the mean sun and is obtained from
Standard, or railroad time, by adding or subtracting 4 min-
utes for each degree of longitude that the place of obser-
vation is east or west of the Standard Meridian. The As-
tronomical day begins at noon of the civil day of the same
date, and is reckoned from zero to 24 hours. i

The Hour Angle of Polaris is found by subtracting the
correct Local Mean Solar time of Upper Culmination
(Table A), from the Local Mean Solar time of observation.

The Time Argument used in entering Table B is the Hour
Angle of Polaris, or 23 hours 56.1 minutes minus the Hour
Angle of Polaris, for the given year. Table B is used as
followH: 'Find the "hours'* of the time argument in the
left hand column of either page of Table B, following,



y Google



124



THE TRANSIT.



Table B. Azimuths or Polaris at Any Time. .



STAR ANo AZIMUTH


POLARIS ABOVE THE POLE..


W.ofN. when hour angle fa
hss than II'' S8'"-


To determine th* true f4eridian the azimuth


win be laid off to the tast when the hour


L. of N. when hour an^e Js
qreaierfhan 11*^ SS"^


on^le Is leas than ll^saz ond to the Vi^at


when greater than ll'^SS'^ The hour anglee


TlmeArgument^ the Star's hour
angle (or ZS^SSJ-^mihue itm


are expressed in Mean Solar Time


A period after an azimuth indicates that


altar's hour angle), far ^yean "■


It is as 'greater than printed.


1


1


%


^


1


J.


Azimuths roR Latituoc .


30


32.


^-


56





40


4Z_


44


46


ii.





A


m


m


m


m.


m


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1


1


1


/


/


/


/


/


/


/














o








































s


S


5


s


5


z


2


2


2


z


z


z


z


2


2.


2.




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9.


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10


3.


3.


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4


4


4


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4.


4.


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m.


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s.


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6


6


6


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7


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a.


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9


9.




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24.


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29


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14




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34


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IS.


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39


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44


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PROBLEMS.



125



Azimuths


or


Po


LAR


IS


At Any TiMt fCoNTb)






STAR ANo AZIMUTH


POLAR.! S Bciow THL POLE


W.ofN. when hour angh is
/ess ihan //* Se^


To ek^rmine the Ih/e t^eriehan the azimuth


Witt be laid off to the Last tvhen the hour


C.G/'A/. y¥hen hour angh h


anyle is iess than It^Sa'^. andiothe hkef


when greater than tt'^SS'^. The hour an^es


TJme Armument fhe s^r's hour


are expressed in f^ean Solar 77'me.


angte (or ZS^SSf^mmus the


^period after an azimuth indicates


sfar:$ hour angle), fbrthe yror-


that it is 0.6 'greater than printed.


1


1


1


1


1


1




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riTu


oc 1


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tas


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81.

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83.

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126



THE TRANSIT.



and the "minutes" in the column marked with the cur-
rent year. On the same horizontal line with the "minutes"
the "azimuth" will be found unider the given latitude. Thus
for 1901, time argument 2 hrs. 6 min., latitude 40°; find 2 hrs.
on the left hand page, and under 1901 find 6 min. in the
second line un-der the second heavy horizontal line, and on
the same line with the minutes under latitude 40° is azimuth
0°51\ For hour angles greater than 5 hrs. 55 min., find
the azimuths on the right-hand page. If the exact time
argument is not found in the table, the azimuth may be
found with sufficient accuracy by direct interpolation. Azi-
muths for latitudes between values given in Table B may
be found by direct interpolation. The nearest whole degree
of latitude is usually sufticiently accurate. The time used
tn making observations should be correct to the nearest
minute. If accuracy is desired.

Table A, "Local m-ean (astronomical) time of the upper
culmination of Polaris, computed for longitude 6 hours.
(90°) west of Greenwich," was computed by the authors
from data given in the Nautical Almanac.



Up



a 30

0'*3
O 33
9 10
9 21
9 30



O 37

e 30

O 37
9 17
9 26
9 37



ocTEf tMirva- ON Of TBU : Mcn dian sy

Owb RRIinic McofiSa HourAn taknulli Crror
Obs lorllma gle of of RbI^ of
|of Ob». Rjloris jtVof N Obs
h m
9 It
9S4
9 31

9 51

10 02
10 II



I O?^ 't.O

0.0

~I.O

tajo

tl.0

±££-



to.'s

10



50.0
3hjO
49.0
45.0
42.0

Allom^ 2r^ar
Colculotion
LohtuOe 40*oe' Longituete eO'lS'W
M«p« Solor Time Upper Culminotion ^
Astrenon'TimcOC FbktnsApt^J3,t90l 23-fS7
ftettuchon to Apr Zl. - 3.94 X5' -19.7
Aitronomicat ( local Mean 3olar ) ^ ^
nme UC n>lans. Apr 21, /90I 25 2C
Hour Arty/e of f^ffUfm 'A'tean Soimr TTme
Of C^9 f24*'00'^- f^ean 3efar r/me
UC f^/arfjf2j''2if'"J
Time A/i^umenf - fiour on^fe of ^^f^r/s

for e3 ^3^1" -houran^/e J
Asfronemico/ T/rrre ( Lacaf A^ean So/arJ
. nrecltonee/ from /c" o 'c/eck Afoon Onfhe
\ ^tvil cfay of Ahe Some cfate



/{prtf il ,/SO/r^ArsJC/earAWarm
OuffttBan^r Transit Ate 5, 2ianfern3
fiuta,dflat^ake3,ptaftk3<>">i4'x2\4-
0effMnfs,Mmtch3et tokeejf ffai/rooel
or JtonaOfa Timej a»e.
Set Tbansit oner huk of 6:15 F*M;
J)l^/ea af fh/an's, ateipresMa tele>-
cepe onef cjfoMsttea larfet 300ft
from mftn/ment, fhe ^onM ^as
p7ace*f of n^t an^/es to tine and
natiea ro a stoke efrtt^en af each
ena,
3er vertica/ hair on 3far,nofoa fime,
f/he



te/eacope ancf
markea /meon
fanfet wifhpiencil
Apn/2Z,l90lf2kr3}
f^et^jcea okservu-
fwns using Aci -
nwrh Tbb/es
Lakf off Atimufh
to the £asfanef
measurma Ang/e
with true MerMf/art




y Google



PROBLEMS. - 127

Table B, "Azimuths of Polaris at any time/* was com-
puted by the Authors and was checked by comparing with
data given in Appendix No. 10 U. S. C. & G. S. Report, 1895,
and is believed to be without error. The azimuths for 40*
were taken the same as in the "Land Survey Manual" and
the corresponding hour angles for the different years were
computed. The azimuths for the different latitudes corre-
sponding to the given liour angles were then computed. A
period occurring after an azimuth indicates that its value
is 0.5' greater than printed.

The observations should be made as near elongation as
possible for the reason that Polaris is moving most rapidly
in azimuth near culmination and errors in observing the
time and using the table are then a maximum.

With careful work the range of 6 reduced observations
should in no case exceed V of arc. Record the data and
make the calculations as in the accompanying form.



J^.



(a) (bj

Fig. 23a.

PROBLEM D16. DETERMINATION OF TRUE MERIDIAN
WITH SOLAR TRANSIT.

(a) ^QfMtpmewf.— Complete transit with solar attachment,
reading glass, solar ephemeris, axe, hubs, tacks.

(b) Pro&^cm.— Determine a true meridian *vith a solar
transit

(c) Methods, — (There are various forms of solar attach-
ments, to transits, among which are the Saegmuller, (a),
and the Buff and Berger, (b), Fig. 23a; the former is the



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128



THE TRANSIT;



best known. The theory of all solar attachments in gen-
eral use is the same, and is as follows: In order to bring
the image of the sun into the center of the solar telescope,
when the line of collimation of the solar telescope makes an
angle, with the line of collimation of the main telescope
equal to the sun's declination corrected for refraction, and
the line of collimation of the main telescope is elevated at
an angle equal to the co-latitude of the place of observa-
tion, it is rigidly necessary that the line of collimation of
the main telescope lie in a true meridian as shown in (b)
Fig 23a.

The elementary lines of a solar attachment are: (1) The
polar axis; (2) the line of collimation of the solar teles-
cope; (3) the attached level line. These lines should have




Fig. 23b.



the following relations: (1) The polar axis should be per-
pendicular to the line of collimation of the solar telescope
and the horizontal axis of the main telescope; (2) the line
of collimation of the solar telesco'^e and the attached level
line should be parallel. The methods of making these ad-
justments are obvious.

The declination of the sun (see Fig. 23b for explanation
of astronomical terms) for the place of observation 1?



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PROBLEMS. 129

found by adding, algebraically, the hourly cuange multi-
plied by the number of hours since Greenwich mean noon
(6 A. M., 90th Meridian) to the declination of the sun, as
given in the solar ephemeris for Greenwich mean noon for
the given date. The setting (apparent declination) is found
by taking the algebraic sum of the refraction correction and
the declination of the sun obtained as above. The refrac-
tion is always plus; the declination is plus when the sun
is north and minus when south of the celestial equator;
and tne hourly change in declination is plus when the sun
is moving north and minus when moving south.

The "Pocket Solar Ephemeris and Refraction Tables for
Use with Saegmuller's Solar Attachment," may be obtained
from G. N. Saegmuller, Washington, D. C, price 10 cents.
The true local mean solar time should always be used, and
may be obtained from standard or railroad time by adding
or subtracting four minutes for each degree that the place ,
of observation is ea^ or west of the standard meridian.)

(1) Calculate the apparent declination (setting) of the sun
for several difterent times, varying by 15 minutes, between
8 and 10 o'clock A. M. and 2 and 4 o'clock P. M. (2) Set the
transit over hub, level up very carefully with the attached
bubble, and very carefully adjust the main transit and
solar attachment Determine the index error of the vertical
circle, and either correct it or apply it to all vertical an-
cles with its proper sign. (3) Level the transit very care-
fully with the attached bubble. Bring the line of collima-
tion of the main telescope and the ime of collimation of the
solar telescope parallel by sighting on a distant point, an5
point the main telescope south. (4) Set off the apparent
declination (setting) with opposite sign on the vertical
circle, i. e. dip the telescope when tha declination is plus
(north), and elevate the telescope when the declination is
minus (south). (5) Level the solar telescope by means of
its attached bubble. (6) Set off a plus vertical angle on the
vertical circle equa^ to the co-latitude of the place. (7)
get the A vernier at zero and sight at a point on the true
meridian. (8) Unclamp tho upper motion, turn the main
telescope about its upper motion and the solar telescope
about lis polar axis until the image of the sun is brought
to the center of the cross lines in the solar telescope at the
time for which the dec! nation was computed, and clamp



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130



THE TRANSIT.



DE ERMII lATION



Time
DfObs

900
9 13
9^50
RM,

2 30
B^5

3 OO



True
Allowkbfc ^ror =U



tion
fl9'3i3

wyj'j



t/9JAl



tt9Xf ta 6



tO.J



J tS H9ie'i^ fO'h fl9'j9L0 ^e'lt'

3 30yf9*3d^i-0.'7 f/9*SSie ££l£3L

2d lOlS

Azimtlfh of ^ne ee'/OJ)

£iYor ■ O.'S



OF TRUE MERIDIAH

Sethng
Cor MppOn;) mufh
tO.7 1i$y5'3 £d'll*
tl9yX3 <?^ V

tdjb t/9iir ££'I0'

tols tf9'3V ed'l3'

to.'s t/9'3^ ee*n



f/9'3e:^t0'3 t/9'3a.'5 t£'09'



f/330JO £B*09'



CokukiNon of Setting ^AppOecl) ^^A^Xm.
Latitude -40*06' A^j Longihjae S6'/3 'iV
A^ Dgclinahon Ormentvtch MeanJ^aorr
(6 *'07'"AM here ), May£0, /90/,t/9'3Jl^
Correct/on for £^£3'"mR4)(a33. f O/lS
Deettnatiort of Jon at e*^30'Af1 •f/9*34a
ffle fraction Cor - J ''■30'" before no on t (17
Apparent Oect at a^JO*^ A f^ - tJsf^XS
App. Dec/ f3ethn^) for ffre other f/mes
was calcu/oteet in /ike manner



Obseryerjfii^

WITH SOLAR TRANSIT
MoyC0,/90f. (4ftr3 ) Oearpnamrm

OuffAOefgeti TrunsifffoS with Soe^-
mutlcr 3o/or Attachment, huhs, axe,
watch ^ettofree^ ^ptfrvad 7ime,'3o-
fmrCphemens fOeoAfStte^moffer, Ifkat
in^ron, D C -^fchet 3ofar fpheme, 19

one/ He/roction 7iih/es )

Teitee/ Tnanaitanet Jolar Arutchment and
founaboth in perfect adjustment.

Set Transit oifer hob, /e^t/eat^trry eare-
fu/// with /onf bubble , founa tnOett Cr-
rar of ¥er/ica/ Orc/e • Zero,

3et off - 19'33'5 (-f^ Oec/Jen Vertical
circ/e ona /eve/ee/ 3o/ar Te/exop^ by
means of its a/hacheet bubble

Setoff i'49 '54 ' (Co -Lat.l en Vertical
circle • 7efejc»pepointeel south both hmex

3etA vernier at zero amf Sf^hte4t at
Station J with lower mot/on.

i/ncfan'^ec/ Ujpper mohon,meuea Than-

sit on Vtrticalayis andjolar on its

po/ar axis, one/ brought tma^e of

Sun into center ofjofaraf a^jCAM.

Mean 3olar TTme/ffS Time 'fiff Titite*^
'Reail Aximuth, ffepeatmtt until fO ifolues

were determineef f3Ati.andSf*M /



the upiper motion. The line of collimation of the male
telescope will then be in the meridian. (9) Read the hori-
zontal plates. The reading will be the azimuth of the line
first sighted on. (10) Repeat, using the setting correspond-
ing to the time of observation, until ten values are ob-
tained. If possible make five determinations in the A. M.
and five in the P. M., about the same time from noon. The
mean of these observations will eliminate instrumental
errors. The most favorable time for making observations
with a solar transit is from 8 to 10 A. M. and 2 to 4 P. M.
(11) Determine the true azimuth of the given line. The error
of the determination of the meridian should not exceed one
minute. Record as in the prescribed form.

PROBLEM D17. DETERMINATION OF TRUE MERIDIAN
BY DIRECT OBSERVATION ON THE SUN.

(a) Equipment. — Complete transit, reading glass, hub, axe,
colored eyepiece or colored shade to fit over objective, good
watch set to keep standard time, solar ephemeris.



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PROBLEMS.



131



Telescope



Direct Of.
Rev*d ~b



flMfl



WnzonM^HIL



Observation,



1



I do* so 00
0' 30' 00"



m'^Q' Qr



rc/cRc^(?l'gS
On Sun



/OCT 41' 00"
Z5d 47 30"



100' 44' 15"



VerficalCircle
Readings



45' 39" 00"
46' or 00'



4(f Qi' QQ"



Date and TirrK,



May 15 1901

3 AM.
MeorrSohrJme



Computation.

Declfnafm at Greent^/ch Noon ^6 AM. 6t'dT/nre 90"^/^ =16*45' jChT
Hourly Change = 35'!6 Chani^e forjhrs '3Sox5 - f'4r4'N

Declf/7affof?at9AM i8r4745yN

Average yert/ca/Ar?gJtdy0^serMfhn^ 46*03' 00\
Correction for Refractio/? ^ 00 34'
True Altitude ^^ 46*02' 26"

JLatftude of (Haerratoiy Uofl = 40' 06 00'
^tatiofT /OO ft Nor fir - 00"

Latitude of 3tatior? ° 40'0^0{f

ras^PZsA I S/n-i-5)c5in(-i5r-Fo/e D/stT
^ ^ V S//?Co-A/tix3inCo-lat

where 6 ^f^/e Dist -h Co -Alt. -t- Co -Lot
PokDist « 7/' 12' 16"
Co- Alt « 43' 37' ^4"
Cff'laf = 45rS4 00
5 = /6S'00'S0'

fs = S2'jr3:r

Po/e Dist = 7/' /2' 1 6'
iS-Po/e Dist= ir 19' 39'




Log.^irf 82*32'00'^ 3.99630

n '». 11* f9'39l'- 9.293 IB

C0-l0gS/?45'3r34''^ 0.15853

m / '. 49'S4'00"m 0. 11638

2//^j644l

Log CosiPZS = 9. 78220

^ iPZ3 = SS'^5'39'

P25 ^105' 27' to'



Azimut/TOfSun

from North 'lOf 27 tcr
Angle JKlwcenSim and

fiarK ^80'03'43'
Arrgk fromNorrtf
station to Mar Kites' 32^

Error of Ofisayatioir = 45'



(b) ProftZem.-— Determine a true meridian by a direct ob-
servation on the sun with a transit.

(c) Methods. — (1) Set the transit over a hulj and level up
very carefully with the attached bubble. (2) Test the ad-


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