[ 59 * 3 
^thlnk there can be no doubt, but what ^'iVpro-' 
.pofition muft hold good in general. 
Lemma IV, 
Let B D E, bde, and ^ e (fig. 2.) be concentric 
fpherical turfaces, whofe center is C : if the fpace * 
is -filled with uniform matter, whofe particles 
repel with a force -inverfely, as the fquarc of tlie , 
difiiance, a particle placed any where within the fpace 
<C b, as at P, will Joe repelled with as much force in 
^one direition as another, or it will not be impelled 
in any diredion. This is demonftrated in Newt. 
Princip. 'liber I. prop. Ivx. It follows alfo from his 
piemonllration, that if the rcpulfion is inverfely, as 
’fomc higher power of the diflance than the fqiiare, 
the particle P will be impelled towards -the center ; 
and if the repulfion is inverfely as fome lower power 
than the fquarc, it will be impelled from the 
•center. 
L K M xM A V. 
IF the rcpulfion is inverfely as the fquare of the 
dlltance, a particle placed any where without the 
fphere B D E, is repelled by that IJahere, and alfo by 
the fpace B by with die fame force that it would if all 
the matter therein was colleded in the center of the 
* uy the fpace or Bi?, I mean the fpace comprehendeJ 
hvrwccn the fpherical furfaces BDE and or betw^ccfi 
T> D E and by the fpace C ^ or C /3, I mean the fphe.^es 
iw/r or (S'f. 
