A DYNAMICAL THEOEY OF THE ELECTROMAGNETIC FIELD. 569 



Measurement of Electrostatic Effects. 



(80) The quantities with which we have had to do have been hitherto 

 expressed in terms of the Electromagnetic System of measurement, which is 

 founded on the mechanical action between currents. The electrostatic system of 

 measurement is founded on the mechanical action between electrified bodies, 

 and is independent of, and incompatible with, the electromagnetic system ; so 

 that the units of the different kinds of quantity have different values according 

 to the system we adopt, and to pass from the one system to the other, a 

 reduction of all the quantities is required. 



According to the electrostatic system, the repulsion between two small 

 bodies charged with quantities fy, 77, of electricity is 



where r is the distance between them. 



Let the relation of the two systems be such that one electromagnetic unit 

 of electricity contains v electrostatic units; then ij l = ve l and ty, = ve a , and this 

 repulsion becomes 



eP^.A^! by equation (44) .................. (45), 



whence k, the coefficient of "electric elasticity" in the medium in which the 

 experiments are made, i. e. common air, is related to v, the number of electro- 

 static units in one electromagnetic unit, by the equation 



k = 4vv* .................................... (46). 



The quantity v may be determined by experiment in several ways. Ac- 

 cording to the experiments of MM. Weber and Kohlrausch, 



v = 310,740,000 metres per second. 



(81) It appears from this investigation, that if we assume that the medium 

 which constitutes the electromagnetic field is, when dielectric, capable of receiving 

 in every part of it an electric polarization, in which the opposite sides of every 

 element into which we may conceive the medium divided are oppositely elec- 

 trified, and if we also assume that this polarization or electric displacement is 

 proportional to the electromotive force which produces or maintains it, then we 



VOL. I. 72 



