Middle of the Nineteenth Century. 227 



and 



fd z r\ z d z r , c?r <Fr 



__ = u * __ + 2uu --?-, + u 2 -j-7- 

 df <fo* dsds ds* 



By aid of these and the similar equations with the suffixes 3 , 3 , 4 , 

 the equation for the ponderomotive force may be transformed 

 into the equation 



d?r\ f dV 



I nt 



A A' tl&rtst' \ \ ///z /, \ ///* / 



F = 



But this is the equation which we should have obtained 

 had we set out from the following assumptions : that the 

 ponderomotive force between two current-elements is the 

 resultant of the force between the positive charge in ds and the 

 positive charge in ds', of the force between the positive charge 

 in ds and the negative charge in ds t etc. ; and that any two 

 electrified particles of charges e and e', whose distance apart 

 is r, repel each other with a force of magnitude 



* l & 



Two such charges would, of course, also exert on each other an 

 electrostatic repulsion, whose magnitude in these units would 

 be eec'/r 2 , where c denotes a constant* of the dimensions of a 

 velocity, whose value is approximately 3 x 10 10 cm./sec. So 

 that on these assumptions the total repellent force would be 



ee'c z f rr r* 







* The units which have been adopted in the above investigation depend on the 

 electrodynamic actions of currents ; i.e. they are such that two unit currents flowing 

 in parallel circular circuits at a certain distance apart exert unit ponderomotive 

 force on each other. The quantity of electricity conveyed in unit time by such a 

 unit current is adopted as the unit~eharge. This unit charge is not identical with 

 the electrostatic unit charge, which is definedHqbe such that two unit charges at 

 unit distance apart repel each other with unit poniieiQmotive force. Hence the 

 necessity for introducing the factor c. 



Q 



