( 823 ) 



these' sviiiboly iiulicate (lie iiioment, llie coordiiialcs and tlie Iriic (hue, 

 whereas (heir meaning is differen( for (he ni<)\'iiii>' svs(eni, \>\ .1;' , //' , :' , t' 

 l)eiiig here related (o (lie mouieiil \\ the (•()ordiiia(es ,v, y, z and (he 

 general time / in the manner expressed h\ (26), (4) and (5). 



It has already been stated that the equation (27) applies to both 

 systems. The vector b' will therefore be the same in 2' and ^, 

 provided \\q always compare corresjtonding places and times. How- 

 ever, this vector has not the same meaning in tlie two cases. In 2£' 

 it re})resents the elect i-ic force, in 2i" i( is related to this force in 

 the way expressed by (20). We may therefore conclude that the 

 electric forces acting, in ^ and in 2£' , on corresponding particles at 

 corresponding instants, bear to each other the relation determined by 

 (21). In virtue of our assumption h, taken in connexion with the second 

 liyi)othesis of § 8, the same relation will exist between the "elastic" 

 forces; consequently, the formula (21) may also be regarded as 

 indicating the relation between the total forces, acting on corresponding 

 electrons, at corresponding instants. 



It is clear that the s(a(e wq liaxe supposed to exist in the moving 

 system will really be possible if, in J!? and ^' , the products of the 

 mass 7// and the acceleration of an electron ai'e to each other in the 

 same relation as the forces, i. e. if 



-m|(V)3^(^/^ --, _J ,,,,•( V') (32) 



Now, we ha\e for the accelerations 



as may be deduced from (4) and (5), and combining tliis ^vi(ll (32), 

 we find for the masses 



m (^) =: {k% M, kl) m (^') 



If this is compared to (31), it appears that, whate^'er be the value 

 of /, the condition is always satisfied, as regards the masses with 

 which Ave ha\'e to i-eckon when we consider vibrations |)erpen- 

 dicular to the translation. The only condition we have to iuqiose on 

 / is therefore 



dw 



= PL 



But, on account of (3), 

 so that we must put 



d{ku-) 

 dn- 



