[ 6i6 ] 
is not improbable but fome part of the cylinder 
may be undercharged. 
Lem m.a VII. 
Let AB (fig. 10.) reprefent an infinitely thin 
flat circular plate, feen edgeways, To as to appear 
to the eye as a ftraight line ; let C be the center of 
the circle; and let DC paffing through C, be per- 
pendicular to the plane of the plate ; and let the 
plate be of uniform thicknefs, and confifl; of uniform 
matter, whofe particles repel with a force inverfely as 
the n power of the diflance ; n being greater than 
one, and lefs than three : the repulfion of the plate 
, DC DC 
on a particle at D is proportional to ; 
provided the thicknefs of the plate and fize of the 
particle D is given. 
For if C A is fuppofed to flow, the correfponding 
fluxion of the quantity of matter in the plate, is pro- 
portional to C A X CA; and the correfponding fluxion 
of the repulfion of the plate on the particle D, in the 
direftion DC, is proportional to — — — X ryr, = 
^ ^ iP — . for D A is to C A : : C A : D A ; the va- 
DA” 
DC 
riable part of the fluent of which is • 
^ n — I X D A 
whence the repulfion of the plate on the particle D 
. , DC DC 
is proportional to 
DC 
DC 
n — I X D C 
1 
n — I xD.V 
or to 
DC 
— 1 
DA 
n — I 
C O R O L- 
