Infinite Series . 
1 63 
or affirmative; or fraaion, of which the numerator is odd; 
then the preceding refolution will be phyfically juft , for in 
this cafe, if the attraaion on one fide of the particle be affir- 
mative, the attraaion on the other will mathematically be 
negative, that is, phyfically oppofite : but if n be an even 
number, or fraaion, of which the numerator is an even and 
denominator an odd number, the mathematical folution will 
not agree to the phyfical ; for in the former the force on both 
fides will be affirmative, in the latter the forces will be oppo- 
fite, and therefore phyfically the force in this cafe will vary as 
L+ H, and not as L-H, which is the force in both the cafes 
when A is greater than t and - 1. The fame may be applied to 
the more general refolution. 
1 Let ABCD (fig. 4.) be a globe, of which the diameters AB 
and CD are fituated at right angles to each other, and AHBL be 
a fpheroid generated by the revolution of an ellipfe on its axis 
AB, to which let HL nearly equal to CD = AB be the conju. 
gate, and P a point in the axis BA produced ; to find the attraaion 
of the ring contained between the globe and the fpheroid on the 
point P, on the fuppofition that the force of any corpufcle in 
the ring on the particle P varies as the magnitude of the cor- 
pufcle direaiy, and the »th power of its diftance from the 
corpufcle inverfely. 
Let AB = CD = 2/, CD = HL(m) + aCH = .2c+2tf, and 
confequently OH = c = t~e, where * has a very fm all ratio 
to t, *P = A, fo=x, and pM parallel to CD=y; then, by 
the preceding lemma, the attraaion of the circle whofe radius 
; and in. 
0—— r * 
is pu on the point P will be 
b-iPM 
like manner the attraaion 
of the circle, 
Z 2 
whofe radius is pm, 
will 
