396 ON THE GEOMETRICAL THEORY OF SOLAR ECLIPSES. [474 
if for a moment G denotes the distance between the centres of the Sun and Moon. 
We have therefore 
tan A = , 
*JG 2 -{k' + ky 
or since 
this is in fact 
G 2 = (a' - of + (&' - bf + (c' - c) 2 , 
tan A = 
k' + k 
p + p — 2a 
where p, p, a signify as before; and thus X Q , F 0 , Z Q , tan A are all of them given 
functions of a, b, c, k, a, b', c, k', and consequently of the before-mentioned astronomical 
data of the problem. The form is substantially the same as Bessel’s equation (3), 
Ast. Nach. No. 321 (1837), (but the direction of the axes of X, 7 is not identical 
with those of his x, y); and it is therefore unnecessary to consider here the application 
of it to the calculation of the eclipse for a given point on the Earth.