394 
ON THE GEOMETRICAL THEORY OF SOLAR ECLIPSES. 
[474 
and thence 
p = (1 - sin 2 k), 
r sm z p 
p = (1 - sin 2 k), 
r Sin 2 j3 
a = -r > [cos A cos A' + sin A sin A' cos (h' — h) + sin k sin k\ 
amp smp J 
P = fsin A (x cos h + y sin h ) + z cos A }, 
Sin]9 1 
P' = . ^ . i sin A' (x cos b! + y sin li) + z cos A'}. 
sm p 1 
Moreover, if the right ascensions of the Moon and Sun are a, a respectively, and 
if the R.A. of the meridian of Greenwich (or sidereal time in angular measure) be 
= 2, then we have 
/i = 2-a, h! = t-oi. 
It is to be observed that h—li, A, A' are slowly varying quantities, viz., their 
variation depends upon the variation of the celestial positions of the Sun and Moon ; 
but h and h' depend on the diurnal motion, thus varying about 15° per hour; to 
put in evidence the rate of variation of the several angles h, h', A, A' during the 
continuance of the eclipse, instead of the foregoing values of h, ti, I write 
A '={ £+ ( i+ ¥M ir - 
where t is the Greenwich mean time, E, E x are the values (reckoned in parts of an 
hour) of the Equation of Time at the preceding and following mean noons respectively, 
taken positively or negatively, so that E, E 1 are the mean times of the two successive 
apparent noons respectively; whence also 
A=j.E+(l + ^ 1 ^)iJ 15° -a + a'; 
and moreover 
a = A + m (t — T), 
a = A + to' (t— T), 
A = D + n (t—T), 
A' = D' + n' (;t-T), 
if T be the time of conjunction, A, A, D, D' the values at that instant of the 
R.A.’s and N.P.D.’s ; to, to' and n, n' the horary motions in R.A. and N.P.D. respectively.