Ponderomotive and Electromotive Forces. 273 



The result is 



n 1= =n+G l3 (28) 



n 2 =n + G 2 , (29) 



whereby equations (24) and (25) are changed into the fol- 

 lowing, 



B(n + G t ) d (-bu\ . 



^-dt 

 5 ( n + ft 2 )_d/jny ■ 



2 B<e dt\^dx)' v ' 



B c¥ 



which in conjunction with (13) are very convenient for com- 

 parison of the results of the three fundamental laws. 



The electrodynamic potential function of a closed current 

 (or system of currents) above introduced, and denoted, in its 

 three forms corresponding to the three fundamental laws by 

 II, U ly and II 2 , is readily perceived to be very different from 

 that potential function of which the differential coefficients 

 occur already in Ampere's theory of the ponderomotive forces, 

 and which in a previously published analysis* I named the 

 magnetic potential function of the closed current, and denoted 

 by P. This latter is obtained when, in the well-known man- 

 ner, two magnetic surfaces are imagined to be substituted for 

 the closed current, and then Green's potential function is 

 formed for the quantities of magnetism present on those sur- 

 faces; accordingly its obvious signification is that it repre- 

 sents by its differential coefficients with respect to x, y, and z, 

 taken negatively, the components which fall into the directions 

 of the coordinates, of that force which the closed current 

 exerts upon a unit of magnetism conceived as situated in the 

 point x } y, z. It can only serve indirectly, and with the aid 

 of special theoretical considerations, for the determination of 

 the ponderomotive force exerted upon a current-element and 

 of the electromotive force induced in it. The electrodynamic 

 potential, on the contrary, which can be used directly for the 

 determination of the force exerted upon a moved unit of elec- 

 tricity ', needs only to be applied to the electricity in the con- 

 ductor in order at once to determine the ponderomotive and 

 the electromotive force. 



* Die mechanische Behandlung der Electricitat, Abschnitt VIII. p. 211. 



