applied to Statical Electricity. 21 



or 



Ydr^e^dr, (126) 



where F is the resistance and dr the motion. 



If the body £ 2 be small, then if r is the distance from e 2) equa- 

 tion (123) gives 



r 

 whence 



e \"c. 



%=W-2; 



F=_E 2 ^; (127) 



or the force is a repulsion varying inversely as the square of the 

 distance. 



Now let 7j l and tj 2 be the same quantities of electricity mea- 

 sured statically, then we know by definition of electrical quantity 



(128) 



ViVz, 



r* 



and this will be satisfied provided 



fl7i=Ee,andi7 9 =E* 2 j .... (129) 

 so that the quantity E previously determined in Prop. XIII. is 

 the number by which the electrodynamic measure of any quan- 

 tity of electricity must be multiplied to obtain its electrostatic 

 measure. 



That electric current which, circulating round a ring whose 

 area is unity, produces the same effect on a distant magnet as a 

 magnet would produce whose strength is unity and length unity 

 placed perpendicularly to the plane of the ring, is a unit current ; 

 and E units of electricity, measured statically, traverse the 

 section of this current in one second, — these units being such 

 that any two of them, placed at unit of distance, repel each other 

 with unit of force. 



We may suppose either that E units of positive electricity 

 move in the positive direction through the wire, or that E units 

 of negative electricity move in the negative direction, or, thirdly, 

 that -JE units of positive electricity move in the positive direction, 

 while ^E units of negative electricity move in the negative direc- 

 tion at the same time. 



The last is the supposition on which MM. Weber and Kohl- 

 rausch* proceed, who have found 



JE~ 155,370,000,000, .... (130) 

 the unit of length being the millimetre, and that of time being 

 one second, whence 



E = 310,740,000,000 (131) 



* Abhandlungen der Konig, Sdoksiaoheii Gesdlsohaft, vol. iii. ( 1 857), p. 2CU, 



