( 440 ) 



Tliu.sc fuiiiiiilao will alrio liuW lur a sysitcm williout translation ; 

 iiiilv, in this case we must take /:= 1, and we shall likewise take 

 i =r 1, thou.oh this is not necessaiy. Thus, j", y'', 2" will then be 

 the coordinates, /" the same thiut;' as <, i. e. the universal time, n" 

 the displacement, u^^' the electric density, -0" and A" the magnetic 

 and electric forces, tins last in so tar as it is due to the vibrations. 



Our next object will be to ascertain under what conditions, now 

 that we retain the terms with \>x^iV~i two systems H and .b'o, the 

 first having' a translation, and the scc^ond iiaving none, may be in 

 vibratory^ states that are related to each other in some definite way. 

 This investigation resembles much the one that has been given in 

 §7; it may therefore be expressed in somewhat shorter terms. 



To begin with, we shall agree upon the degree of similarity there 

 shall be between the two systems in their states of equilibrium. In 

 this respect we define ,S' by saying that the system S^ may be 

 changed into it by means of the dilatations indicated by (6); we 

 shall suppose that, in undergoing these dilatations, each element of 

 volume retains its ponderable matter, as well as its charge. It is 

 easily seen that this agrees with the relation (8). 



We shall not only suppose that the system *% nuaj be changed in 

 this way into an imaginary system <S', but that, as soon as the trans- 

 lation is given to it, the transformation reallij takes place, of itself, 

 i. e. by the action of the forces acting between the particles of the 

 system, and the aether. Tluis, after all, iS' will be the «fl)»6Mnatcrial 

 system as *S'. 



The transformation of which I have now spoken, is precisely such 

 a one as is required in my explication of Michel.son's experiment. 

 In this explication the factor i- may be left indeterminate. We need 

 hardly remark that for the real transformation produced by a trans- 

 latory motion, tlie factor should have a definite value. I see, howe- 

 ver, no means to determine it. 



Before we proceed further, a word on the electric forces in .S' and 

 S(^ in their states of equilibrium. If « ^ 1, the relation between 

 these forces will be given by the equations of § 5. Now e indicates 

 an alteration of all dimensions in the same ratio, and it is very 

 easy to see what influence this will have on the electric forces. 

 Thus, it will be found that, in passing from S,^ to N, the electric 

 force in the direction of OX will be changed in the ratio of 1 to 



-, and that the corresponding ratio for the other components v/ill 



1 



be as 1 to — . 



