Force in Moving Conductors. 273 



whence ^Trp, or 



a x dy dz 



where p is the volume-density of free electricity. 



Bat with a moving substance the equations usually employed 

 are : 



r = c-r- — 0-77 — 7-' 

 at at ax 



r\ — dz _ dx _ dyjr 



^~ a Jt C dt dy~' 



,, 7 dx dy d4r 



whence 47rp, or ^ — \- -P + - 1 - , becomes, as pointed out by 

 r ' dx dy dz r J 



Professor Niven, 



©!, w 2 , 03 z being the component angular velocities of the 

 substance. But the first two terms on the right-hand side 

 are (as may readily be verified) together equal to 



and would not have appeared if we had taken for our equations 

 -p dy dz d (^dx n dy u dz\ d^ 

 F = c ti- b Tt-a^V^ +a dt +E dt)-dx-' 



That is to say, if we had taken the E.M.F. in the element as 

 if that were at rest and the field moving, a twofold simplifi- 

 cation would have resulted : — 



(1) The E.M.F. would have been made to depend upon 

 relative motion only, as it seems a priori reasonable that it 

 should do ; and 



(2) The symbol ty would have the same meaning in both 

 cases, viz. the potential of free electricity in the field. 



Yours faithfully, 

 Berkswell Eectory, Coventry, H. W. WATSON. 



February 15, 1888. 



