536 TRANS. ST. LOUIS ACAD. SCIENCE. 



as to preserve the potential ( V) constant. In this case a current 

 of constant intensity would flow through the wire, and as V= — 

 it is clear that r must change at a uniform rate, or 



--^'■'^^'-^ - - - (3) 



where i' — / is the duration of the operation. Further, 



r r 



and i>= ^ ■ 



hence dE=dFdr=2- p^ ds dr = ^ drdu , 



«'* E-E'=^//drdo> = ^(r-r') - - (4) 



This is the stored energy during the operation. But the energy 

 of the electrification at first was h rV^, and at the end is i r'V^, 

 so that there has nevertheless been a diminution of energy of 



B-E' ==-^-(r-r') - - - (5) 



It appears that, under conditions of our experiment, the sphere 

 has less energy at the close of the experiment than at the begin- 

 ning by a quantity — (r — r'), while the equal energy repre- 

 sented by the potential of the electrification on itself was added. 

 The total energy lost by the shell was, therefore, 



£ = V^{r—r') - - - (6) 

 The current in the wire was, by Ohm's law, 



^~ df— R ' 

 hence . >^ ^, f^ , x 



and hence the energy of the current during the operation was 



or by (3), £_r;i;rr: ... (7) 



The expressions (6) and (7) must be equal to each other, and 

 hence Rv = i , or i? = — , 



where v is the constant velocity of each point in the surface of the 

 shell during the operation. 



