EXPLANATION OF THE CONSTRUCTION AND USE OF 
THE TABLES 
DEVELOPMENT OF THE FORMULAS 
Let us consider the astronomical triangle MPZ (fig. 1) 
projected upon the plane of the celestial horizon. 
Where P is the elevated pole, 
Z is the observer’s zenith, and 
M is any celestial body. 
Then the side PZ is equal to the colatitude; 
the side PM is equal to the codeclination; 
the side ZM is equal to the coaltitude; 
the angle at P is equal to the local hour angle, and 
the angle at Z is equal to the azimuth of the 
heavenly body. 
Now, let fall a perpendicular ZD from the observer’s 
zenith upon the circle of declination. Call this perpendic- 
ular a. This will divide the astronomical triangle into two right spherical tri- 
angles and the side PM into two parts which we shall call b and B respectively. 
It will also divide the azimuth into two angles Z’ and Z’’. 
In the upper or “time triangle” (Napier’s rules) 
N_ Co.Lat. 
Sinvad—COsPiaisinvi mia wae aoe oe ee ee Se (1) 
Marie = CO bs la: COS" aa sa ow oa tap hate esters fa ee cece ae (2) 
CG Zi itn ai Gea a at oe (3) 
In the lower or ‘‘altitude triangle’’— 
Sint 0) — COSI COSu baw eae ea ne oe ae a ae eee (4) 
CoteZ/ Seine: COW Bessa ee Booed oe eee ae see ee (5) 
Now, since B is equal to (90°—d) minus b=90— (d+), equaticns (4) and (8) 
become 
Binh — Cosraysime(GoD) a ee oe eee asec eee ae (6) 
cot 7/= sin astans (ds) es ee eee ea ee eae (7) 
Inverting equations (6) and (7) they become— 
cosee ;— sec a-cosee (da-U) eos. Je aL eee (8) 
tan 7 —ICosec acon (G20) ae ee ee eet eee (9) 
It is apparent that Z’ plus Z’’ is equal to Z, the body’s azimuth. This azimuth Explana- 
is always reckoned from the elevated pole east or west from 0° to 180° and 3 
marked in the conventional manner depending on the sign of the latitude and Hon 
whether the body is rising or setting; i. e., east or west of the meridian. of the | 
CONSTRUCTION OF THE TABLES Construc- 
Table I.—For every degree of latitude from 0° to 65°, and for every degree of tion and 
local hour angle from 1° to 90° there is tabluated four columns headed b, A, C, Use of 
and Z’. Tables 
Column b is the value of the side 6 (fig. 1) in degrees, minutes, and tenths. ; 
It is found from equation (2). 
Column A is the log secant of side a (fig. 1) multiplied by 10° power. The 
value of a is found from equation (1). 
Column C is the log cosecant of side a, to three places and multiplied by 10° 
power. It, too, is found from equation (1). 
Column Z’ is the value of the angle Z’ (fig. 1) to degrees and tenths. It is 
found from equation (8). 
67 | | 
SE nT eee EY Se 
