( 428 ) 



§ 3. We shall iippl} these equations to ;t svstein ul' bodies, 

 having a common velocity of translation p, uf constant direction 

 and magnitude, the aether remaining at rest, and we shall hence- 

 forth denote by i', not the whole velocity of a material element, 

 but the velocity it may have in addition to p- 



Now it is natural to use a system of axes of coordinates, which 

 partakes of the translation p. If we give to the axis of ^- the direc- 

 tion of the translation, so that p^ and \\~ are 0, the etjuations 

 (la)— (Va) will have to be replaced by 



Blrii = n , (lb) 



iJiv.^^ — ^), (lib) 



3 .5- 3 .n,/ , , / 3 3 \ 



3 «. _ 8ft ^ ^ ^ / 3 __ 3 ^ J 



d~ 3^ \dt d^i'J ' 



dS^;f d-tc . , , / 3 3 N 



*-''"|-3-^^37J = -'^--'' 



€• = 4 .T F- b + [ V . Jp I + [ Ü . •') ] • • • • (^'1') 



In these formulae the sign Dir, applied to a vector ?l, lias still 

 the meaning deHi\ed by 



n- ..3 31. 3 -Jl,, 3 31. 



() X d 1/ OS 



As has already been said, » is the relative velocity with regard 

 to the moving oxes of coordinates. If d =- 0, we shall speak of a 

 system at rest; this expression therefore means relative rest with 

 regard to the moving axes. 



