272 Dr. H. W. Watson on the Electromotive 



Now c -~- — b -^ differs from — -j- (determined as suggested) 



d/ F dx + G di + R ck\ gQ that ^ E#M>F> in tWg 

 J dx\ dt dt dt) 1 



to be consistent with the preceding, should be 

 dy , dz d-ty-' __ d-ty 

 dt dt dx dx 

 where , , _. dx ,„ dy TT 



The interpretation of this ty' was given by Dr. Larmor in 

 a paper on induced currents, in this Magazine, January 1884; 

 viz. if in the above figure the conducting element PQ moves 

 to pq in time St, the total number of tubes of force cut by it 

 in this time is measured by the flux across the area PQ qp ; 

 and this, divided by St, is generally taken to be the measure 

 of E.M.F. across the moving element PQ; differing from the 



-=-, as above defined, by the differences of integrals of Yds 



along Qq and Pp, i. e. by 



dx \ dt dt dt J ' 



There is no more reason for assuming the magnetic E.M.F. 

 to be measured by the total number of tubes of force thus 

 cut, than by the differences of line-integral of the vector- 

 potential ; but it would seem better to assume in both cases 

 the same means of estimating the E.M.F., and to keep the 

 same meaning of yjr. 



Thus, if ty be regarded as the potential of free electricity 

 in the one case, it should be so also in the other. It would, I 

 think, prevent some confusion in the mind of the student. 

 For instance, with a substance at rest the equations are 



T>-- — -^t 

 dt dx 



ri __d&_d± 

 ^~ dt dy ' 

 dH. d\jr 

 K ~ dt dz ; 



