sg o Mr. Knight oh the Attraction of such Solids 
aff(a'+ r+ f) Ti = 2ndf(a , rT+rT’+~) t. 
It' therefore we solve Prop. 32, on this supposition of density, 
we have for the equation of the curve pr, fig. 15, when the 
solid has the greatest attraction, 
xL (ry v/x 2 (1 + 1 2 ) y 2 ) — xL >/ x* + f -f C (x'ry ry 5 
Now, when r is infinitely small, we shall have, by neglect- 
ing all the higher powers thereof, 
L [ry + v/F+"(i + r 2 )y) = L s/T+f + ; 
by substituting which our equation becomes 
— - * — ^ C (x 2 -\- y 2 ), or a^x — (T'+y 2 ) 3 = 0, as we shewed 
a priori must necessarily happen. 
I shall just remark here, that, as the results of Prop. 32, are 
not altered by conceiving the density any function of a and T, 
such is also the case with respect to Problem 31, if T there 
represent the distance of any particle from a plane passing 
through the attracted point and the axis of the cylinder. This 
the reader may easily convince himself of. 
The proposition just mentioned (31) is only a particular 
case of the following very general one. 
Prop. 34. 
Let uvv'u', fig. 15, be a rectangle, whose plane is perpen- 
dicular to the line pm, and its centre in that line. Let this 
rectangle move parallel to itself, in the direction pm, and vary 
in such a manner, that the middle points r and r' of its sides 
may continually touch two different curves. 
