Testing large ami small circles by trial plate 1 07 



187] Let DE be an uniform canal of incompressible fluid infinitely con- 

 tinued towards E, and let A and B be given points in a right line with D, and 

 let AB be bisected in C; the force with which any particle of fluid repels this 

 canal (supposing the repulsion to be inversely as the square of the distance) 

 is inversely as its distance from the point D, and therefore the sum of the forces 

 with which two equal particles of fluid placed in A and B repel this canal is to the 

 sum of the forces with which they would repel it if both collected in the point C, 



I I . _2_ 



* AD + BD : CD ' 

 or as C> 2 : CZ> 2 - CB*, 



CB* 



or as i : i - =-^ . 



188] Let us now examine how far the proportion of the quantity of fluid 

 in the large circle and the two small ones in Experiment V [Art. 273] Fig. 18, 

 bear to each other will be affected by the circumstances mentioned in [Art. 276], 

 supposing the plates to be connected by canals of incompressible fluid. 



First it appears from Cor. [VII, Art. 186], that the quantity of redundant 

 fluid in the large circle, and also in the two small ones, will bear very nearly 

 the same proportion to that in the jar A as it would if it had been placed at an 

 infinite distance from A, for the distance of the plate from the jar was in neither 



Fig. 18. 



experiment less than 63 inches, and neither the length nor the diameter of the 

 coated part of the jar exceeded four inches, so that the repulsion of the jar on 

 the canal connecting it to the plate could not differ by more than ^ part from 

 what it would be if the canal was infinitely continued, and would most probably 

 differ from it by not more than J or ^ part of that quantity*; for the same 



* The repulsion of a globe 4 inches diameter on a straight uniform canal of 

 incompressible fluid extending 63 inches from it differs by only ^ part from what 

 it would be if the canal was infinitely continued, but the repulsion of a Leyden 

 vial of that size on the same column differs probably not more than J or J of that 

 quantity from what it would be if infinitely continued. 



