OF ELECTRO-DYNAMIC FORCES. 519 



tro-dynamics be compared with the fundamental principle of 

 electro-statics mentioned at the commencement, we see that each 

 estimates a force which two electric masses exert upon each other; 

 but that in the cases hitherto considered, one of the two forces 

 disappears each time, whence the other only requires consi- 

 deration. This occurs ^r5^ in all cases which belong to electro- 

 statics, because here the force determined by the new principle of 

 electro-dynamics always disappears ; but it also occurs, secondly, 

 in all cases belonging to electro-dynamics which have yet come 

 under consideration, where relations are constantly pre-supposed 

 to exist, in which all forces estimated by the principle of electro- 

 statics are mutually checked. 



Thus the two principles are complementary to each other, and 

 hence they may be combined to form a general fundamental 

 principle /or the whole theory of electricity, which comprises both 

 electro-statics and electro-dynamics. 



By the fundamental principle of electro-statics, a force 



_ ^^ 

 ~ RR 



was found for two electric masses E and E' at the distance R ; 

 if this force be then added to that yielded by the new principle 

 of electro-dynamics, 



_ __a_a EE 

 ~ 16' R 



we obtain, as the general expression for the complete determina- 

 tion of the force which any electric mass E exerts upon another 

 E', whether at rest or in motion, 



R /<^R- _oT? ddR \ 

 R \dt^ " dt^ )' 



EE 



R V 16 • <;r^ "^ 8 dt^ )' 



R 



For a definite magnitude assumed for the purpose of measuring 

 the time, in which a = 4, this expression becomes 



EE'/ dR'' ddR\ 



RRV-ll¥-^^^~di^)- 



d R 

 Moreover, supposing that both R and —j— are functions of t, 



consequently that -j— is to be regarded as a function of R, which 



