[ 1 
Lemma X. 
If we now fuppofe all the matter of the plate to ba 
colleifled in the circumference of the circle, fo as to 
form an infinitely (lender uniform ring, its repulfioa 
on the column DC wdll be lefs than when the matter 
is Ipread uniformly all over the plate, in the ratio of 
3 — « X A C’ 
AC"' 
DA'" 
to DC3-'’4- AC3- 
D A 3 -«. 
For it was before faid, that if the matter of the 
plate be fpread uniformly, its repuilion on the column 
will be proportional to DCs— "-pAC 3 ~” — DA3— 
or may be exprelfed thereby ; let now A C, the femi- 
diameter of the plate, be increafed by the infinitely 
fmall quantity Acj the quantity of mattor in the 
plate will be increafed by a quantity, which is to the 
whole, as 2 A c to A C ; and the repulfion of the 
f)late on the column, will be increafed by 3 — nx. 
Acx AC^-” — -^CX^X3 — =3 — n 
X A c X A C X — ^ — : therefore If a quan- 
AC"-' DA"-‘ . 
tity of matter, which is to the whole quantity in the’ 
plate, as 2 Ac to AC be colletffed in the circum- 
(erence, its repulfion ob the column DC, wfill be to 
that of the wdiole plate, as 3 — 7zxAcxAGx 
iH, toDC3-'4-AC3-«— DA 3 -'q and 
AC”~' DA"-* 
confequently the repulfion of the plate when all the 
matter is collected in its circumference, is to its re- 
K 2 pulfi’::!! 
