w k r' — 



/• ir 



( 8i7 ) 

 k 1 



x4- 



l c 



dr' 0/ 



x^4-yv- 



0.« O// 



0/ 



units of time. In tliis last expression we may put tbr the differen- 

 tial eoefücients their values at the point A. 

 In (17) we have now to replace [9] by 



[?] + f^-' ~. X 



1? 



0^ 



+ 



k 1 



or' dr' dr' 



Xv- + yr- + Z — 



0.*^ otj dz 



L 



do- 



> 



, . (25) 



where 





relates again to the time f^. Now, the value of t' for 



which the calculations are to be performed having been chosen, this 



time tg will be a function of the coordinates ,1; y, z of the exterior 



point F. The value of \_q] will therefore depend on these coordinates 

 in such a way that 



d[9] _ /• 1 dr' rd^n 



by wdiich (25) becomes 



etc., 



«' RpI / öfp] d\o 





Again, if henceforth we understand by r' what has above been 



called ;•'„, the factor - must be replaced by 

 ?* 



so that after all, in the integral (17), the element f? >S' is multiplied by 



d x[q] d ylQ] d z[q] 



d.c r' 





K>/ 



dz 



This is simpler than the primitive form, because neither r' , nor 

 the time for which the quantities enclosed in brackets are to be 



taken, depend on ,i', y, z. Using (23) and remembering that lQdS=0, 



we ffet 



4:.tc'r'idt J 4-r |ö.i- r' "^ Ö/y r' '^ dz r' j' 

 a formula in which all the enclosed quantities are to be taken for 

 the instant at which the local time of the centre of the particle is 



t' . 



c 



We shall conclude these calculations by introducing a new vector 

 p', whose components are 



Proceedings Royal Acad. Amsterdam. Vol. VI, 



54 



