io8 Appendix to Preliminary Propositions 



reason the deficience of fluid in the trial plate will bear very nearly the same 

 proportion to that in the jar, &c. as it would if it had been placed at an infinite 

 distance from it. 



It is plain that if the plates had been placed at such a distance from the jar 

 that the quantity of fluid in them had been considerably less than if they had 

 been placed at an infinite distance, still the quantity in the large circle would 

 bear very nearly the same proportion to that in the two small ones as it would 

 if they had been placed at an infinite distance. 



189] Secondly, it is plain that in trying the large circle, the repulsion of 

 that circle increases the deficience of fluid in the trial plate, and the attraction 

 of the trial plate increases the redundance in the circle. Now the repulsion of 

 the plate Ee on the canal mMNa, and the attraction of the trial plate T on 

 rRSA (supposing mMNa and rRSA to be infinitely continued beyond a and A) 

 are by [Cor. IV, Art. 183] very nearly the same as if the redundant fluid in Ee 

 and the deficient fluid in T were both collected in the centers of their respective 

 plates, and the quantity of redundant fluid in Ee may be considered as equal 

 to the deficient in T, and consequently the repulsion of Ee on mMNa is very 

 nearly equal to the attraction of T on rRSA. Moreover, the repulsion of Ee 

 on its own canal rRSA must be equal to the attraction of T on mMNa, as the 

 jars with which they communicate are both equally electrified, and therefore, 

 by Cor. [IV], the quantity of redundant fluid in Ee will be increased in very 

 nearly the same ratio as the deficient in T. 



190] In like manner, in trying the two small circles, the quantity of re- 

 dundant fluid in them is increased in very nearly the same ratio as the deficient 

 in T, for as half the distance of the two circles never bore a greater proportion 

 to em than that of 18 to 72, the repulsion of the two circles on the canal mMNa 

 will be very nearly the same, and the deficience of fluid in T will be increased 

 in very nearly the same ratio as if all the redundant fluid in them were collected 

 in e, the middle point between them. 



The quantity of redundant fluid in Bb indeed will be increased in a rather 

 greater ratio, and that in Cc in a rather less ratio than if it was placed at e, 

 but the ratio in which the quantity of fluid in Bb is increased must very nearly 

 as much exceed that in which it would be increased if it was placed at e as that 

 in which Cc is increased falls short of it, as the attraction of T on the canal 

 fRSA exceeds that on rRSA by nearly the same quantity as its attraction 

 gRSA falls short of it, and therefore the quantity of redundant fluid in both 

 circles together is increased in very nearly the same proportion as that in a 

 circle placed in e would be, and consequently the redundance in the two circles 

 is increased in very nearly the same ratio as the deficience in the trial plate. 



191]* The attraction of the trial plate on the canals fRSA and gRSA and the 

 repulsion of the circles Bb and Cc on the canal mMNu is very nearly the same as 

 if the deficient or redundant fluid in the plates was collected in the center of their 

 respective plates, and therefore the repulsion of the circles Bb and Cc on the canal 



* Memorandum relating to the second article. 



