( 818 ) 



p',. = k l p, . p',/ =3 / p_,, . p', == ^ p, , . . . . (26) 



passing at tlie same time to .r', y', z', f as independent variables. The 

 final result is 



4rrc^j-" dt' 4:n\d^e' r' '^ dt/' r' '^ öz' r' )' 



As to the formula (18) for the veetor potential, its tiansformation 

 is less complicate, because it contains the infinitely small vector u'. 

 Having regard to (8), (24), (26) and (5), I tind 



4 .T c r' dt' ' 



The field produced by the polarized particle i> now wholly deter- 

 mined. The formula (13) leads to 



and the vector f)' is given l>y (14). We may further use the ecpiations 

 (20), instead of the original formulae (10\ if we wish to consider 

 the forces exerted by the polarized particle on a similar one placed 

 at some distance. Indeed, in the second particle, as well as in tiie 

 first, the velocities u may be held to be infinitely small. 



It is to l)e ren.iarked that the formulae for a system without 

 translation are implied in what precedes. For such a system the 

 fpiantities witJi accents become identical to the corresponding ones 

 without accents; also /• =r 1 and 1=1. The components of (27) are 

 at the same time those of the electric force which is exerted by one 

 polarized particle on another. 



§ 8. Thus far we have only used the fundamental equations 

 without any new assumptions. I shall now suppose that the electrons, 

 which I take to be sphere.-; of radius R in the state of rest, have 

 their dimensions cJtantjed by tlie effect of a translation, the dimensions 

 in the direction of motion becoming k I times and those in perpen- 

 dicidar direction.'^ I times smaller. 



In this deformation, which may be represented b 



•' Ur r 1/ 



each element of volume is understood to preserve its charge. 



Our assumption amounts to saying that in an electrostatic system 

 -2", moving with a velocity //", all electrons are flattened ellipsoids 

 with their smaller axes in the direction of m(ttion. If n(»w, in order 

 to aj»i»ly the theorem of § <>, \\ c subject the system to the defor- 

 mation (/■/, /, /), we shall lia\ e agaiji spherical electrons of ia<liiis H, 



