( 442 ) 



arc in S^^. If therefore the required agreement is to exist with 

 regard to the vibrations parallel to OX^ the ratio of the masses of 



the ions in S and S^ should be — ; on the contrary wo find foi' 



k 

 this ratio — , if we consider in the same way the forces and the 



accelerations in the directions of OF and OZ. 



Since k is different from unity, these values cannot both be 1 ; 

 consequently, states of motion, related to each othcu' in the way we 

 have indicated, will only be possible, if in the transformation of'% 

 into S the masses of the ions change; even, this must take place 

 ill such a way that the same ion will have different masses for 

 vibrations parallel and perpendicular to the velocity of translation. 



Such a hypothesis seems very startling at first sight. Nevertheless 

 we need not wholly reject it. Indeed, as is well known, the effec- 

 tive mass of an ion depends on what goes on in the aether ; it 

 may therefore very well be altered by a translation and even to 

 different degrees for vibrations of different directions. 



If the hypothesis might be taken for gianted, Michelson's expe- 

 riment should always give a negative result, whatever transparent 

 media were placed on the path of the rays of light, and even if 

 one of these went through air, and the other, say through glass. 

 This is seen by remarking that the correspondence between the two 

 motions we have examined is such that, if in S^ yve had a certain 

 distribution of light and dark (interference-bands) we should have 

 in S a similar distribution, which might be got from that in 'S',, by 

 the dilatations (6), provided however that in S the time of vibration 

 be kf times as great as in 'S,. Thi^ necessity of this last difference 

 follows from (9). Now the number k s would be the same in all 

 positions we can give to the apparatus; tlierefore, if we continue 

 to use the same sort of light, while rotating the instruments, the 

 interference-bands will never leave the parts of the ponderable 

 system, e. g. the lines of a micrometer, with which they coincided 

 at first. 



We shall conclude by remarking that the alteration of the mole- 

 cular forces that has been spoken of in this § would be one of the 

 second order, so that we have not come into contradiction with 

 what has been said in § 7. 



