104 Appendix to Preliminary Propositions 



For the force ! may be divided into two parts, namely 



PA- B pA+ B 

 P+p " P+p 

 PpA + pB PpA + PB 

 P+p P+p 



(pA + B 

 PpA + PB 



\ f 

 I P + p 



, has no 



tendency to alter the redundant fluid in AB, but the first part, or the force 

 PA -B 



P + P (CG in direction CG 



- PpA + pB a ' 1 (EM in direction EM ' 



or - 



P + p 



{ -PA + B 

 P + P 



(CG in direction GC 



- PpA + pB a ;1 (EM in direction EM 



to i. 



P + p 



(GC -PA + B 

 as they are to the repulsion of H on j ^ as -- to H, 



or as (- PA + B) J^-^ to S, 



increases the redundant fluid in the ratio of 



B- PA i + p 

 S P + p 



180] COR. I. If the lengths of the columns CG and EM are such that the 

 repulsion and attraction of AB and DF on them are not sensibly less than if 

 they were of an infinite length, the attraction of DF on CG will be very nearly 

 equal to its attraction on EM, and therefore, if the forces with which N repels 

 the columns CG and EM are very nearly equal to each other, the quantity of 

 redundant fluid in AB will be very little altered thereby. 



N.B. If the size of H is much greater than that of AB, it is possible that its 

 distance from the glass may be such as to exert a very considerable repulsion 

 on EM, and yet that the action of AB and DF on CG shall be not sensibly less 

 than if it was of an [infinite length], 



181] COR. II. Let the bodies H and L be of the same size and shape and 

 at an infinite distance from the glass, and let the fluid be in equilibrio. Let 

 now an equal quantity of fluid be taken from H and L, the quantity of redundant 

 fluid in AB will be very little altered thereby. 



For the repulsion of the whole quantity of fluid in L on the canal EM will 

 be as much diminished as that of H on CG, so that it comes to the same thing 

 as placing an overcharged body N in such manner that its repulsion on CG 



