ACTING INVERSELY AS THE SQUARE OF THE DISTANCE. 173 
finite quantity varying continuously within the space under con- 
sideration, which quantity we will call B. Thus the integral 
da 
me: 
2 3+ be 
(+n) et"hBde , rp dB 
Sam aes ar cts 
The conclusions in the preceding article may be applied to 
the second integral immediately, and to the first after a slight 
2 
ae d ge resolves itself into the two following : 
: 1 
transformation. If we call ae m, p' == 0, or p =o”, then that 
integral becomes 
Bho'mdc 
= (m+ Daag @—2) a 
It is manifest that this integral also has an infinitely small 
value, only so long as the integration is extended no further 
than from 0 to an infinitely small value of ¢; whereas for each 
finite value of o the coefficient of do receives the same value, 
within an infinitely small difference, whether x be taken = 0, 
or as infinitely small. This holds good likewise of the whole 
integral if extended from « = 0 to ¢ = ea pl. 
There is only one case in which our conclusions lose their 
validity, if ~ is not of the same order as any power of g, as, for 
; g 
ite : : 
example, if — is of the same order as in this case, as 
g 
log — 
the point O approximates infinitely to the surface, Q increases 
beyond all limits ; and the same would be true for X also, if this 
relation existed not merely for some particular values of 6, but 
forall. It is, however, unnecessary at present to proceed further 
in this development, as we may exclude this particular case from 
our investigation without any disadvantage. 
17. 
Employing the same suppositions and notations as in Art. 15, 
we proceed to the consideration of the quantity Y, of which 
hbd t ; 5 
A ae is an indefinite element. As 7= y (6? + c? + (a—~2)?), 
and consequently 
