1902.] The Dissipation of Energy by Electric Currents. 371 

 "When m = 1, this is equal to 



P 



When m is small, the expression tends to 



P 



4. When the currents are assumed to flow in cylindrical shells 

 similar to the original, let 2z cm. be the length. The radius of the 

 shell = z/m cm. 



The thickness of the plane end is 8z, and of the curved surface - 8z. 



m 



Denoting by <f> the angle xOQ, fig. (i), the E.M.F. round the ele- 

 mentary circuit 



= 2tt/B10- s . 4 * sin <£. 



m 



The resistance of the circuit 



= / 4 ' 3m2 + 4m 3 sin <f> ^ = 4(m 2 +l) 

 \38<f>8z ms8<f)8z sin / ^ 8<f>8z ^ 



The dissipation of energy in watts per cubic centimetre is 



W ma 



m d (m? + l)a 3 p J 



1(3 



When //i = 1, this is equal to 



2tt 2 o / 2 B 2 10- 16 



— -«-^ , 



5 p 



or 3-95fl 2/ 13 1U — . 



P 



When //J is very small the value is approximately 

 7'9m 2 a 2J - 



7° 



5. When the current in any section is assumed to be of uniform 

 density throughout, the rectangular circuit must be such that QL 

 being this circuit QP = LR, fig. (ii). 



The area enclosed by the circuit is 



±z ( </(a 2 - x 2 ) -ma + z) (a), or 4y (ma - J (a 2 - o: 2 ) + y) 2 (/3), 

 and the length 



4 (2.2 + v/(a 2 - x 2 ) - ma) (a), or 4 (2y + ma - ^(a 2 - x 2 ) ) (f3), 



