80 APPLICATION OF TH.E PRECEDING RESULTS 



and consequently 



V+D V= ft (x cos OT + y sin tsr) -f hD<j) (y cos CT x sin OT) 

 = $B -jcos OT + -^ sin OT cos (< -or) D<j>[ 



-f /:ty 1 sin is - cos -cr cos ((/> TO-) Ztyh , 

 = fixcos jw - -5 cos (< - -BT) Ztyl 



H- /%/ sin JOT -~ cos (< -cr) Ztyj- . 



When therefore <f> is augmented by the infinitely small angle 

 D(j>, -cr receives the corresponding increment -5 cos (< w) Z>(/>, 



and the form of V remains unaltered ; the preceding reasoning 

 is consequently applicable to every instant, and the general re- 

 lation between < and OT expressed by 



= DOT + -5 cos (< - OT) D$ : 



a common differential equation, which by integration gives 

 77 



sn 



H being an arbitrary constant, and 7, as in the former part of 

 this article, the smallest root of 



Let OT O and < be the initial values of TO- and </> ; then the 

 total potential function at the next instant, if the electric fluid 

 remained fixed, would be 



V t = ft (x cos vTfi + y sin vr ) + (x sin </> 7 cos <f> ) bd<p, 



arid the whole force to move a particle p, whose co-ordinates 

 are x, y, z, 



