334 Prof. Cayley on the Geodesic Lines 



n (£ c > *) = f(i+ £.«> «*)•!=»* 



J(l sm 2 </>W<£ - , N , 



v,:,„„.; -(-a^ti^fr. 



And expanding also the tan -1 term, we thus have 



_(c»+»)[(i- J)lfe*>+ £»(**)] } 



-H(* 2+ |)_ f(c ** ) -( i+ 3 e ^^ 



which, in the term in { } neglecting negative powers of n, becomes 



' A= ^{y»| + b*F{c, <£)-E(^ c^-cot^l-c^in 2 ^}. 



C 1 



We may moreover write c = S, 6= -r-, <£ = 90°— A', n=-2,M = e, 



A. € 



M 

 and therefore — = e. so that the formula is 

 n 



A = s^l | +&*F(c,9O°-\0 - E(c, 90°- V) - tan \Vl-c 8 cos 8 \'J 



= |-e{tanV v / l-c 2 cos 2 V + E(c, 90°-V)-& 2 F(c,90°— V)}, 



/ C 2 C 

 where I retain c, Z> as standing for \f l--^,-r respectively. 



Writing herein \' = 0, we have 



A=|-€(E / c-^F / c), 

 where the coefficient 'E t c—b 2 F l c is 



IT 



1-6' 2 V 



7T 



• v/l-^sin 2 ^ 

 cob* OdO 



Vl-c*sm*0 



