~J 



512 M. E. Jochmann on the Electric Currents induced 



remain, as is well known, everywhere continuous and finite when 

 extended to all points of the conductor. 



The reduction of the integrals in the above expression may be 

 effected on observing that 



M*' -*) 2 ^(j _z) +v\y'-y) + w\z'-z)}(h' dy' dz' 



' ttV-aQg ^ v'ix'-x) 2 ^(a/-^)S 



-£-+-£-+-w-F"* ! 



The second integral, on the right of the above equation -sign, 

 vanishes in virtue of (1) ; the first, by performing one integra- 

 tion in each term and employing a known reduction-formula, 

 becomes transformed into 



- — -~~ (u 1 cos X -f- v 1 cos fi 4- w' cos v)d», 



and therefore, in virtue of the equation (2), also vanishes. The 

 whole equation, therefore, assumes the form 



3 (Vq^l! tyg{j—k) + v'(y'-y)+w\z'-z)\dx ! dy'dz t 



= 2 CvW 



^da/dy'dz'=2^. 

 r 3 * da? 



On treating in a similar manner the other constituents of X, we 

 find 



i : ( V~ * 



W y) {u'ix'-x) +v f {y ! -y) +w'{z' ~z)\da/ dy' dz' 



by 'bx 

 * y*~*yF~^ -{u'ix'-^+vW-y) +w'(z'-z)}d,v'dy'dz' 

 _ba by m 



These values being substituted in the expression for X, and the 

 components Y and Z being subjected to a similar treatment, the 

 following results are obtained : — 



