also; but to fix the ideas we may assume that the mass is finite. And the pre 
potential and its derived functions vary continuously with the position of the attracted 
A MEMOIR ON PREPOTENTIALS. 
330 
[607 
but here, 2^ + 1 being negative, the term 8 2 ? +1 Q does not disappear : the formula has 
to be treated in the same way as for q = — and we arrive at 
viz. the formula is of the same form as for the potential case q = — Observe that 
the formula does not hold good in the limiting case q = — 1. 
17. We have, in fact, for q = — 1, the potential of the disk 
whence 
since, in the complete differential coefficient « 4- 2« log «, the term « vanishes in com 
parison with 2« log «. Then, proceeding as before, we find 
1 dW , 1 dW" -8<T!) S 
/ _7/"h // I // J // 1 \ 
8'log 8' ds + 8" log 8" ¿8" r(i S -l) P; 
but I have not particularly examined this formula. 
18. If q be negative and > —1 (that is, — #>1), then the prepotential for the 
disk is 
and it would seem that, in order to obtain a result, it would be necessary to proceed 
to a derived function higher than the first; but I have not examined the case. 
Continuity of the Prepotential-surface Integral. Art. Nos. 19 to 25. 
19. I again consider the prepotential-surface integral 
in regard to a point (a,.., c, e) not on the surface; q is either positive or negative, 
as afterwards mentioned. 
The integral or prepotential and all its derived functions, first, second, . &c. ad 
infinitum, in regard to each or all or any of the coordinates (a,.., c, e), are all finite. 
This is certainly the case when the mass J p dS is finite, and possibly in other cases