212] ELECTROMAGNETISM. 415 



are the same. Hence the dimensions of the quantity I/ A are accord- 

 ingly the same as those of a velocity. All that has been said of 

 course applies to any absolute system of units, and has no re- 

 striction to the C.G.S. system. If the units of length, mass, and 

 time are given, we can by definition immediately obtain the 

 unit of electricity in either the electrostatic or electromagnetic 

 system, and by experiment determine the number of electrostatic 

 units contained in one electromagnetic. If the unit of mass is 

 now changed, and we define our electrical units as before, the size 

 of both units of electricity has changed, but in the same ratio, 

 so that the number of one kind contained in one of the other 

 is the same as before. If, on the other hand, we change the 

 unit either of length or time, the two electrical units change, 

 but in different ratios, so that the numeric expressing the number 

 of one kind in one of the other is changed from its former value. 

 It has, however, changed in precisely the same way that the 

 numeric expressing any given velocity has changed, so that we 

 may say that the number I/ A represents a certain definite velocity, 

 which is totally independent of the units chosen. When the units 

 of mass, length, and time have been settled upon, the numeric of 

 this velocity may be given. This velocity will be denoted by v. 

 It is to be noticed that the determination of the quantity v 

 depends upon the determination of a certain numeric, the units 

 being settled upon, and that there is nothing of the nature of an 

 actual velocity involved. We shall, therefore, not as yet be under- 

 stood to speak of v as a velocity, but merely as a quantity whose 

 numerical expression changes like that of a velocity, with any 

 change of units. The quantity v is thfc most important electrical 

 natural constant. Numerous determinations of its value have 

 been made, the first by Wilhelm Weber* and Rudolf Kohlrausch, 

 in 1856. The number now generally accepted is 

 v=3 x 10 10 cm./sec. 



Electrical and magnetic potential are defined in terms of 

 work, so that 



(8) [eV] = [mCl] = [ML*T- z l 



which agrees with the other possible definition 



Weber, Elektrodynamische Maassbestimmungen iv. 1856 ; Werke, Bd. in. p. 609. 



