on an Oblate Spheroid. 333 



The position of the point a is at once obtained by writing 



Q 



Z'=0: viz. this gives c=0, b — \, M= p n=0: the differential 



Q 



expressions are ds=Cd<j> ) c?A= t-^<£. Or integrating from = 



A. 



to $= -, we have ^=A.-v^-, A=-^—, agreeing with each 

 other, and giving longitude of «= -r • — \ or, what is the same 

 filing, Z«QB=(l-j)f- 



Writing in the formulas /'=90°, we have c=S, Z>= — > — =0; 



A /i 



7T 



whence JA = 0, or A = const., = — , since the geodesic line here 



coincides with the meridian CB; and moreover s = AE (8, <£); 

 viz. this is merely the expression of the distance from C of a 

 point P on the meridian C B. But we do not thus obtain the 

 position of the point y. 



To find it we must consider a position of V consecutive to C, 



say,/'= — — e, where e is indefinitely small; n is thus indefi- 



nitely large, and the integral II [n } c, <f>) is not conveniently dealt 

 with. But it may be replaced by an expression depending on 



/c 2 \ c 2 



ITf — , c, cf> J, where — is indefinitely small ; viz. (Legendre, 



Fonct. Ellip. vol. i. p. 69) we have 



n(», c, 0-Ffo « + -1= tan- ■■y." t ?ti. -n(J^) 



vu vl- c'siirp \ n / 



where 



«=(i+»)(i+0 



We thus have 



. M f ,,, , x ^\/c 2 + w x . * 7 «tan(f> 



A= — -{ nl(c, <6) + tan" 1 — , , y _ 



w L v Y Vl+n i/l-c 2 sin 3 ^ 



-(cH.)n(^c,^)}, 



c 2 

 where, — being small, 



