by a Magnet in a Rotating Conductor. 511 



the conditions to which u', v 1 , w' are subject in the case of a con- 

 stant electro-dynamic condition. For every point within the 

 conductor we then have 



g + * + £-* >> 



and for every point of the surface of the conductor 



u' cos \ + v' cos fi-i-iv 1 cos v=0, . . (2) 



where \ f fi, v denote the angles between the positive directions 

 of the coordinate axes and the normal to the surface of the con- 

 ductor drawn inwards from the point x' } y' y z' on the same. The 

 last equation expresses, of course, the condition under which the 

 component of the current, perpendicular to the surface of the 

 conductor, will vanish at every point of the same; whilst the 

 expression on the left of the first equation represents the incre- 

 ment of negative electricity in the conductor-element dec', dy', dz' t 

 which increment must likewise vanish on the hypothesis of a 

 constant current-system. By introducing the values 



(3) 



— dx 1 dy 1 dz 1 , 

 /3=£ydx'dy'dz', 



the expression for X assumes the form 



+ 3*[u r^^ 2 \u'(x'-x)+v'(y'-y) + w' (z f - z)\ dx 1 dy' dz' 



+ b( ^~^¥~ y) -{u'(x'-x) + J(y'-y)+w\z'-z)\dx'dy'dz' 



+ fo fy-gK**--*) J^-a.) + v'(y'-y) + w\z' -z) } dx' dy' dz^ . 



These integrals, it may be observed, have finite and determinate 



values, since the factors 5 — > o > 5 



r z r f 



are severally less than unity, and moreover all integrals of the 



form 



M Ob •"" X 



\u' . . dx 1 dy' dz' 



