( 437 ) 



wlieiKT we cui'-elucle that the e(iuatiuiis will be tsatisfieil In vahics 

 of .0 'j , p'yj 'P';, S'x, 5'y, As, which are likewise in both case« the saiiie 

 t'unetions of .c', //', z\ t'. By what has been said at the beginning 

 of this §, not only a', but also the total electric force will be the 

 same in »S'o and .S', always provided that corresponding ions at cor- 

 responding times (i. e. for ecjual values of t') be considered. 



As to the molecular forces, acting on an ion, they are conHned 

 to a certain small space surrounding it, and by what has been said 

 in § G, the diftereiice of local times within this space may be 

 neglected. Moreover, if equal spaces of this kind are considered in 

 Sg and <S, there will be, at corresponding times, in both the same 

 distribution of matter. This is a consc(|uence of what has been sup- 

 posed concerning the two motions. 



Now, the simplest as&umption we can make on the molecular 

 forces is this, that they are not changed by the translation of the 

 system. If this be admitted, it appears from the above considerations 

 that corresponding ions in >% and (S will be acted on by the same 

 molecular forces, as well as by the same electric forces. Therefore, 

 since the masses and accelerations are the same, the supposcil motion 

 in *S' will be possible as soon as the corresponding motion in N,j can 

 really exist. In this way we are led to the follow^ing theorem. 



If, in a body or a system of bodies, without a translation, a system 

 of vibrations be given, in which the displacements of the ioas and the 

 components of 5' ii"<l -'3' are certain functions of the coordinates and 

 the time, then, if a translation be given to the system, there can 

 exist vibrations, in wliich the displacements and the components of 

 5' and -p' are the same functions of the coordinates and the loail 

 time. This is the theorem, to which I have been led in a much 

 more troublesome way in my ,,Versuch eiuer Theorie, etc.", and by 

 which most of the phenomena, belonging to the theory of aberration 

 may be explained. 



§ 8. In what precedes, the molecular forces have been supposed 

 to be conhned to excessively small distances. If two particles of 

 mutter were to act upon each other at such a distance that the 

 ditt'erence of their local times might not be neglected, the theorem 

 would no longer be true in the case of molecular forces that are 

 not altered at all by the translation. However, one soon perceives 

 that the theorem would again hold good, if these forces were changed 

 by the translation in a doKnite way, in such a way namely that 

 the action between two quantities of matter were determined, not 

 by the simultaneous values of their coordinates, but by their values 



