56 
ON LAPLACES METHOD FOP THE ATTRACTION OF ELLIPSOIDS. 
dF % *JR / 7 y\ \iy 
~jz ~ -T— = № + hr l + c 0 % 
da 
dF 
dl 
dF 
dk 
I \ , ( 1 
-f- la ( — 
L s/R 
~(a% + b v + c O + 2X 2 2l/*jR)\’ 
= (a£ + br) + eg) 
y/R 
- 1 \ 
V R 
P \ 
1 
2VÆ 
values which give, as they should do, 
7 dF dF dF j dF 
l —jy + mi -y— + n —j— -j- k 7/ — 0. 
at dm dn dk 
Hence forming the values of the different parts of the first equation, 
7 (dV dF\ Tr „ 7 dF dF dF 
— jfe -== TT ) + V-F-l- Tr -mi-, n -j— 
\dk dk 
dm dn 
IyJR kl 
= “r-2ül + ( “^ i, + tf) rT + 
y/R k 
V-RJ ’ 
(dF . \ , 7 /dF D \ , /dF / f- , ; , ^ i Æ ) 
U- 4 ) + 6 U _iî ) + c (*- c )= Of+fc! + <*){ £ -vsp 
./ dF 7 dF dF\ 
“ 2 rs + i 36 +c To)- 
_ I sJR kl 
D 2L \/R ’ 
which satisfy the first equation. 
And in like manner for the second equation, 
-<•'+»•+*•>£-2)—<•'+*'+•’> tan *>•' * *■+••>« *■>+« ,71 
c /dF 
n Vdc 
-(7 
= (ttf + + eg) 2 - (a 2 + b 2 + c 2 ) (af + bv + eg) ^ 
(a^ + 617 + eg) (2x2 + 2L 2 y/Il) ” 
, (a dV b dV c dV\ . , , . 
Hi Æ+m ^ +« *H a +6 ' +c ''2Tvs- w ^^2Z’ T 2Zv 
f-S-S= -(«i + 6, + o^ 2 - I L 5 + (a> + ^ + o>)(aï. + 6, + C ?) 2 -i s 
+ (a{ + + cf) H, + 2£»./&/ ’ 
[173 
which satisfy the second equation