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7
TABLE
-FOR-
FINDING THE HOUR ANGLE
WITHOUT LOGARITHMS.
Entered according to Act of the Parliament of Canada in the vear .898. bv P. J. Lekch
at the Department of Agriculture. ■ . r. j. LthtH.
Copyrigrht applied for in the L'nited States. ,
PREFACE.
This Table was prepared for the use of Surveyors in
Canada, to enable them to find the Hour Angle from a morning
or afternoon altitude of the sun without the use of Logarithms,
with sufficient accur;icy to determine the Azimuth of Polaris at
any time without waiting for an elongation (a Table for which
is in preparation).
This Table, however, gives the Hour Angle so close that
it is available for Navigators, the error varying from o to 4
seconds, the greatest error occuring where the Declination is
o, the Latitude 58 and the Altitude 28° 45'.
It can be used in the Northern or Southern Hemisphere
between the Latitudes 40° and 6o\
EXPLANATION OF THE TABLE.
The column headed Alt. contains the altitudes of the sun's
centre corrected for Parallax and Refraction.
The column headed H. A. contains the Hour Angle corres-
ponding to the Altitude which is on the same line, and to the
Latitude and Declination which is above it.
The column headed D. gives the variation of the H
Angle for one minute of Altitude.
our
The Table is computed to the nearest second for every
Degree of Declination from o to 24 N., for every degree of
Latitude from 40 to 59 N., and for every 30 minutes of Altitude
within limits of four degrees.
Bessels' Refractions from Altitude 24° to 44° will be found
on page
METHOD OF USING THE TABLE.
(1.) On the day of observation the observer shall note the
Declination of the sun. and consultinj,^ the Table, shall time his
observation, so that it shall fall within the limits of the Altitudes
for that degree of Declination and those of the one following'.
Having: taken his Altitude and corrected it for Refraction.
Parallax and Semidiameter. he shall take from the Table the
Hour Angle due to the next lower Altitude, next lower Latitude
and next lower Declination. Multiply the minutes and seconds
of the corrected observed Altitude by the number under D. and
apply it to the Hour Angle with the sign minus.
Multiply the difference between the Hour Angles due to the
two successive degrees of Latitude between which lies the
Latitude of the place, by the minutes and seconds in the latter
and apply to the Hour Angle with the sign minus. Call the
result A.
Proceed in the same manner, but using the next higher
Declination, and call the result B.
Subtract A from B. multiply the ditrerence by the minutes
and seconds of the Declination, add the product to A. The
result will be the Hour Angle.
N.B.-The result of each of those multiplications is seconds
of time.
The following examples will illustrate the method :
(3)
EXAMPLE 1,
Corrirlid Alliliidc 41 4S 20 ..r 41 4^.}^
F,iitilu(le of placi' 46 27 10 " 46 27.17
I )f(,'n correct I'd for 1,011 u) 23 j.S " 19 2{.()}
ll. 111. MV.
Tahiiliir Hour .\nt,'lc, F)cc. 19" j 17 y
M'l:.
18.33x6 =io<j.97 = — I 50
27.17 ■ 1.83 -:r 49.72 = — 49.7
Tiilnilar Hour .Anj^Ic, Dec. 20 ^ 21 22
M'l-.
1S.33 y 6 :-- 109.97 ^ _ , 30
27.17x1.62= 44.01 = —. 44
H .\ --
siv.
H A -4.31 which nuilliplicd liy 23.63 gives 101.9. . , -
Adding to A gives Hour Angle
ll. 111. sec.
3 14 29.3 = A
3 18 48 .-H
4 1X.7
I 41.9
3 16 II. 2
EXAMPLE 2.
Corrected Altitude 39 14 50 or 39 14.83
Latitude of place 57 12 40 " 57 12.67
Dec'n corrected for Lon .... 22 9 20 " 22 9.33
Tabular Hour Angle, Dec. 22
Nl'l\
14.83X7.9= II7.2
12.67 X 3
38
h. m. sec.
3 25 32
= — • 572
h. ni. sec.
= — 38.0 3 22 56.8. A
Tabular Hour Angle, Dec. 23
sec.
14.83x7. 8 -115.7
12.67x2.65 - 33.6.
6.62 X 9.33 = 61.8.
3 32
« 557
33-6
Adding to A gives Hour Angle
(4)
3 29 33-7 = B
6 36.9= B-A
— I
1.8
3 23 58.6
(2.) If the minutes of the Observed Altitude when corrected
lie between ,5 and 30. or between 45 and (k>. and the minutes of
the Latitude and Declination are each ^rreater than 30. or if any
two of those three quantities fulfil these conditions, take out
the Hour Anjfle due to the next hi^Wier Declination. Latitude and
Altitude. Proceed as in ( 1 ) but usinj. the si^ni plus where minus
is mentioned, and subtracting from instead of addinj^Mhe final
result to A.
The following example will illustrate the method:
EXAMPLE.
Corrected Altitude ^. ,,
Lalitiule ,
5" J4 40
I )ec'n corrected ("or Loll . ^
HourAnyle, Dec. 6, Lu,. 57, Alt. 26. . . 3 ,x 36
12 40 '.r i2.7.S.X=nI;8 = ^ i 51.X
25 2oor 25.3.5.4=Hj.8 .,= ,. , ^^ ^^
3 22 21. 6^ A
n..ur Anyle, Dec. 5, Lat. 57, Alt. 26. , . 3 10 44
"•'^^^•'^■^ = ^ . 54-3
25.3x4.9 .24.0 ^ ^ ^ ^^
3 14 42.3 H
r 39 3 A n
7.6x23.8 180.9- 3 0.9
A ^-=3 22 21.6
Hour Annie. ...
3 J9 20.7
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BESSEL'S REFRACTIONS.
Alt.
o
24.
25-
26
27.
28..
30
32
34
Iv-'fu. Alt i> r
2 cS.9 .... ." ' "
^ j5 I 22.3
" '^ 36 , ,9.3
' 57-8 ^,7 , ,65
' 5^'^ 3S , ,3.8
• '*^- 39 , n.2
59-7
25-4
The Parall;
IN
"iny l)e taken as 7" throughout.
ERRATA.
I'lij^c 5, line i6, for 25.3 ■- 5.4 rmcI 25.3 •, 4.5
I ., » ' in s 111 s
II, L;il. 5.S, Ah. 27 30 r,,r 21 5S mid 21 15
12,
" 4',
t (
33 30 •
'63-
6 30
14,
" 50,
**
30 30 •
' 59 49 '
' 59 39
•5,
' 50,
t 4
27 30 '
' 21 40 " 21 48
16,
6.7 5.7
^•7 5-7
40, 32 10 34 f,,r 6.7 mid 5.7
6.S 5.8
6.8 5.8
111 ^ 111 s
" 26 30 lor 54 16 read 56 16
" 28 30 •' 46 30 " 46 36
" 40 " 6 13 " 6 15
40, " 36 30 •• 38 8 " 38 28
31 30 Id 32 30 Inr 7.0 read 7.1
111 S 111 s
" 3''^ 30 lor 35 ^^ read 35 S3
45, " 44, " 3^ jJ " 40 43 " 4« 43
" 26,
" 50,
" 30.
" 53.
" 35.
" 45.
" 57,
" 40,
' 42,
' -54,
' 43, '
' 42,
J
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