358 
Mr. Ivory on the Attractions 
da z / * ^ db z 
and hence it is easy to infer, that 
(^) + ($) + ( 
ddA \ 
~dc r j 
0. 
Substitute the series for A in this last equation, and let the 
coefficients of the several powers of a be equated to o ; and 
there will be obtained 
A (3> 
Al5)= i. 
4-5 
A<7) 
&C. 
j_ f f ddA 
2-3 * 1 V db z 
f f ddA t 3) 
db* 
_L ( ( 
• \ \ db z 
M 
W 
)+( 
ddA 
dc z 
(1) 
(3) 
ddA 
dc z 
ddA ($) 
dc z 
)} 
)} 
)}• 
Thus, all the other coefficients depend upon the coefficient of 
the first term, being derived from it by a repetition of the 
same operations: and when the general expression of AT 
shall be determined, the whole series will become known. 
Resume the formula (4) 
and let 
2 x . dy . dz 
x* + — J') 2- Hr- j 
9 
jr 
2 
x = R cos. A 
b — y — R sin. A cos. q 
c — % = R sin .p sin. q, 
then will R =1 j x 2 + (b — yp + (c — zp express the line 
drawn from the foot of a to the point in the surface of the 
ellipsoid, of which x,y, z are the co-ordinates ; p will be the 
angle which R makes with a ; and q the angle which the plane 
drawn through R and a , makes with the plane of y and x. In 
