286 • Mr. J. J. Thomson on ' 



w= -£ + -j 

 a£ p 



a£ p 

 <ZA , R 

 at p 



where p is the resistance of the medium. 

 We shall suppose p to be infinite, so that 



df da dh 



u= dt' v= di> w= di- 



Differentiating (5) with respect to y, (6) with respect to z, 

 and subtracting, we get, remembering 



dx dy dz ' 



K \dx 2 dy 2 + dz 2 ) 



_f A +6—+ -V— --^U ^_7>^ 

 \ d# dy dz)\dy dy) dy dz 



,(dq __dr\/de db\ fdr dq\/dc __ d&\ 

 \dy dz)\dy dz) \dy dz)\dz dy) 



dp dc dr da da dq dp db ._. 



dy 6?a? c&e dy dz doc dz dx* ^ ' 



with corresponding equations for g and A. 



Again, differentiating (8) with respect to y, (9) with respect 

 to x, subtracting, and remembering 



we get 

 but 



da db dc _~ 



dx dy dz "" ' 



. ( du 



^ V \ ' d 2 c d 2 c d 2 c 

 dxf~^*dy* + di? ; 



df da 



. d C df dg 1 _ d 2 c d 2 c a?c 

 ^^Jt\a\^dxj^dx~ 2 + dy' 2 + d? J 



