594 ELECTRICAL UNITS. 



610. RELATIONS BETWEEN THE Two SYSTEMS OF UNITS. In 

 order to establish a relation between the corresponding units, we 

 may compare their dimensions, or equalise the numerical expression 

 of the same quantity as a function of each of them. Consider, for 

 instance, the different expressions for the same quantity of energy W ; 

 we shall have the equalities . 



Vf = eq =EQ, 

 W = *V =E 2 C. 



From this we deduce the constant value a, 



These being the ratios between the numerical values, we shall 

 have for the ratios of the corresponding units (604) 



__ 

 RTF! 



The constant a denotes then the number of electrostatic units 

 [q\ of electricity which there are in an electromagnetic unit [Q]. 



Since the electromagnetic resistance R is a velocity, and the 

 electrostatic resistance r is the inverse of a velocity, the ratio 



- or p=-^ is the square of a velocity. As this ratio is equal to 

 r [KJ 



# 2 , it follows that the constant a is itself a velocity. 



A great many experiments have been made in order to deter- 

 mine the value of this constant. There are clearly as many methods 

 as there are quantities which can be measured in electrostatic as 

 well as in electromagnetic units. All the results obtained range 

 about the number which expresses the velocity of light in air. It 

 is probable that this is not an accidental coincidence, and that 

 the equality of the two numbers arises from a correlation in the 



