f,44 rr.OFESSOU G. IT. DATJAVIX OX ELLIPSOIDAL HAILMOXIC AXALVSIS. 
This mav be reduced to the form —/3 Sy 2,_2 A ("/’+I)d--I/S Syor -2 / (>’) ; u’hich by (92) 
" j ‘ " 1 ■ 
W. 1 2/3 I + l ! , t + l ! 
and (93) becomes-^,— - -ZT:' 
The term ofThe second order is 
/3- %y2,—2.t (^’+T) 
o 
'fins is reducible to 
( 4 /-- 1 ) , iV +1 
Srlr-I)"^ 4/- '2(; 
1 ) 
+^Vo/ {-) (i“o+TiV./ )• 
T^"%..v- 2 /('‘+t)+ 4 ^f ^2 ( /_4) ^^yo; which becomes 
1 
1./30 .„_:L 
2/+1 • /-i: 
—-,v/30./-4)j^;+4./3^-b/. 
-1 :• 
Therefoie 
=47^1 ^4' -/3+i^^)+ 'P : m+w u- 1 >]. 
Introducing for G its value (79), ve find M or 
rhTT 
J> (c,- 
, 2 t>\-/l +/3 2 rfli + ll 
COS 6 
‘'>^=47477^ 
1 -i^+ri6^4r-i4+4) 
i+i: 
+ 77 M 
7 —I ' 
I:+ 7) j. 
d(T. If this be added to 
But ill ( 74 ) v-e have L>((!rd)~ [(PBB-fPd 
' L \ cos-^ > A 
the result just found the term which has not l /(2i+l) as a factor is anniliilated, and 
7 27ri\I 14-1! 
c- 0'o- = 27 + 1 '7:41 
I +\li (3/+1«) + sA/S- (20r + 1 34/-t-;184) 
Now from (37) the square of the factor for converting (T' into C' is 
— (cos) =1-^/3-{■ gV^'X/ - 8). 
There foi'c 
rD 
fXnP.‘C4^rn=A^iXY['+4^4+0+444(29r+74/+48)]. 
'fhese last two conqfiete the solution for .s”]. 
