MATHEMATICAL SECTION. 59 
Referring to the attracted particle as origin let (a,, 6,) be the 
corner nearest and (a,, b,) that farthest from the particle; then 
Ba: “ 
a CaAXL 
vg = mdr SoS ce ob y)? 
Q, 
b, 
= mot y dy ((a, = yy? — (a? + )) 
| b+ (at +52)? b+ (a2 +5) 
= mor] 4 WEA Ee A 
b, + (a? +67)" b+ (a? + b,”)° 
and a similar expression for Y by exchanging the a’s for the b’s. 
(2) 
If in this we place a, = b, = 0 then X= moro. 
This is taken by Price to be infinite; yet, since the thickness t 
must be taken infinitesimal, this is an entirely unfounded conclu- 
sion, 
At first, however, I did not suspect this result, and when Mr. 
Woodward found an infinite attraction of a circular disk on a point 
at its circumference, which result I checked, it seemed to be possible 
that the attraction of a finite mass could be infinite. Yet neither 
Mr. Woodward nor myself was entirely convinced. To settle this 
question I then resolved to determine the attraction of a right 
‘prism and also of a right circular cylinder ona particle at mid- 
height, which, being then moved to the surface and taking the 
height infinitesimal, would give the attraction of a plate on a par- 
ticle in a position at which an infinite attraction had been found. 
For a right rectangular prism we have, 2A being its height, 
By ha h 
dr 
x= a hay: adx Serer! 
° a, ~ 
b, 
2Qhadx 
wed J. WerpetyTr Si 
° a, 
Comparing this with (2), putting 2h = t, we readily see that 
these values are by no means identical, for (2) is of the form 
tf, (a,, @,, b,, b,) while (8) is <f, (a,, a,, 6, b,,7). Here f, is independ- 
ent of z while f, is not. 
