Fundamental Law of Electrical Action. 365 



It can be easily proved that 



for the points a* and # are rigidly connected. Accordingly 



Let ^p (j>' d£l = <&. 



Then X-^ d f"d®\ 



~dx drYbwi) ' 



To evaluate <3> we need only find out the value of the 

 integral 



Introducing the Lorentz-transformation, in which the axis 

 of motion of the cylinder (13) becomes the new time-axis, 

 we have now 



(Y pW^ 



I 



over the volume 



(f-&) I + fo-<»o) s +(r-S>) , <r J ; 



and E' is expressed in terms of the new-coordinate system. 

 Let (£', t/, f, v') be the new coordinates of B. 

 Then 



R ,2 =(f-r) 2 +(^-v) 2 ^(?-?o 2 +(^-^) 2 



>1(^P)<+WK'+(MW'+M^ 



where (w>i", w 2 ' ! , w 3 ", wl') are the direction cosines of the 

 axis of B in the new system. E' is therefore of the form 



+ 2F7 7 / f , + 2Uf + 2VV + 2Wf / + D. 



Let (E) be the same function of (f , 7705 So)» *• *• & is now 

 the perpendicular distance of the centre of A from the 

 axis of B, 



Then it can be proved that approximately 



gri- (2 -<v + ...1. 



1=^1 



