( 4^0 ) 



Siiir(! those oqiiatioiis d) no Idiin'or nxplicitly coutnin tlio volocity 

 V, , tlu'v will hnlil, without ;iny chniio'C! o!' form, lor ;i syslom that 

 has no translation, in wliirh easo, ol' rourso, /' wouM hf the sanio 

 tliino' as tlio nnivcrsal tiino i. 



Y(>t, stiicth speakinti-, llicro would ho a sliti'ht diflViviioc in the 

 foiiuulao, whoii applied to tho two oas(>s. Tn tho systoni without a 

 translation a,,, af,, a, would bo, in all ])oints of an ion, tho sanio 

 funotions of t', i. e. of the universal time, whereas, in the niovina; 

 systoni, these compouents would not depend in the same way on t' 

 in difterent parts of the ion, just booause tlioy must evorywhero 

 bo the same functions of /. 



However, we may ignore this differonco, of the ions are so small, 

 that we may assign to each of them a single local time, applicable 

 to all its parts. 



The equality of form of the electromagnetic equations for the two 

 cases of which we have spoken will serve to simplify to a large 

 extent our investigation. However, it should be kept in mind, that, 

 to the equations (Id)— (IVd), we must add the equations of motion 

 for the ions themselves. In establishing these, we have to take into 

 account, not only the electric forces, but also all other forces acting 

 on the ions. We shall call these latter the molecular forces and we 

 shall begin by supposing them to be sensible only at such small 

 distances, that two particles of matter, acting on each other, may 

 be said to have the same local time. 



§ 7. Jjot us now imagine two systems of ponderable bodies, the 

 one -S' with a translation, and the other one >% without such a 

 motion, but e(]ual to each other in all other respects. Since we 

 neglect (juantities of the order p^r-/!'", the^ electric force will, by §5 

 be the same iu both systems, as long as there are no vibrations. 



After these have been excited, wo shall have for both systems 

 the equations (Td) — (IVd). 



Further wo shall imagine motions of such a kind, that, if in a 

 point (x\y',z') of .S'o wo find a certain (]uantity of matter or a 

 certain electric charge at the universal time /', an equal quantity 

 of matter or an equal charge will be found in the corresponding 

 point of S at the local time f'. Of course, this involves that at 

 these corresponding times we shall have, in the point (.r', y\ z') of 

 both systems, the same electric donsiiy, the same displacement a, 

 and equal velocities and accelerations. 



Thus, some of the dependent variables iu our equations (Id) — (IVd) 

 Avill be represented in Sq and *S' by the sanio functions of .c', //', 2;', <', 



