60 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
Placing a, = b, = o or supposing the attracted particle at the 
edge of the prism we have - 
1 
adx 
X = 2moh ne yee E 
0 0) 
b, Vaptyt h? 
Var tyre 
z2—h 
1 
= auth faol aes 
Verh 
Vap+y, +R 
z2—h 
mo fal Ve rm = | (4) 
Vet 
This form nets clearly that X vanishes with h; therefore the 
attraction of a rectangular plate on a particle at one of its corners 
is not infinite, but, on the contrary, it is infinitesimal. 
Similarly the attraction of a circular plate on a particle at its 
circumference may be found by considering the plate a vanishing 
cylinder. Using cylindrical co-ordinates to a vertical line through 
the attracted particle as axis we have, if p = horizontal radius 
vector, v = vectorial angle, for the attraction of a cylinder, radius 
r, density 0, ona particle at midheight h and distance d from axis 
of cylinder where 
My shah lees ; 
COS V = Qpd 
; 1 “tid BA ESe, ¢ 
and sin v= 9g VIE + 
d+r v h 
Aja mo fp? dp { cos vdv FFA “ a Ht 
d—r —v _ 
d+r 
2h - 
a a7, br ies AGES Biarclil TEIN 
= mo fp de * 2smv. PV OLE 
d—r 
