FE. Nipher—Expression of Electrical Resistance. 467 
epcuwe ae 
. HOF =e J fir dao =>(r-1/) (4) 
This is the stored energy during the operation. But the en- 
ergy of the electrification at first was 4rV’, and at the end is 
$7’ V’, so that there has nevertheless been a diminution of energy 
of EE = (r—r’) (5) 
t appears that, under conditions of our experiment, the 
sphere has less energy at the close of the experiment than at 
the beginning by a quantity (r—7’), while the equal energy 
represented by the potential of the electrification on itself was 
added. The total energy lost by the shell was, therefore, 
EH= V"(r—r’) (6) 
The current in the wire was, by Ohm’s law, 
Ov fF. 
cde oe 
hence Q—-QV= re-%), 
and hence the energy of the current during the operation was 
vos 
=>, (¢ —t), 
Ver—r' 
et 7 
or by (3), = fie (7) 
The expressions (6) and (7) must be equal to each other, and 
1 
hence Be eA Or. mes 
where v is the constant velocity of each point in the surface 
of the shell during the operation. This problem 1s well known, 
and a solution of it is given in Mascart and Joubert’s treatise. 
The above solution is new to the writer, and embraces some 
features of interest. 
