58 Mr. J. P. Dalton on the 



respectively. This equation is equivalent to 



1 1 (t>-Ht)£fo = 2(T-U), .... (5) 



or IP = 2(T-U), (6) 



where U and T are the energies in the steady state, electric 

 and magnetic respectively, and P is the total impulse, or 

 generalized momentum generated in the circuit in the steady 

 state. This result is here obtained for a specific circuit, but 

 is much more generally applicable. 

 Putting v = const. = E, we obtain 





E(i-I)<ft=2([J-T), (7) 



a theorem, enunciated and proved by Heaviside * in most 

 general terms, connecting the amounts o£ work performed by 

 a cell of constant e.m.f. in establishing a given final distri- 

 bution of current with, or without, the storing of energy in 

 the field. 



§ 3. Now arrange a balance containing in each arm a coil 

 in part shunting a condenser. Since no current traverses the 

 galvanometer in the state of balance, its resistance may be 

 taken to be zero without any loss of generality. The 

 extra current in one direction through the galvanometer is 



■ •p 1 , JS , while that in the opposite direction is ^J * , where 

 -tli -r 1*2 A r ±i s + ±t 4 



e is the impulsive e.m.f. generated in an arm; for the parts 

 of the balance separated by the galvanometer are, in effect, 

 independent of each other as far as internal actions are 

 concerned. For balance these extra currents must be equal, 

 or, on integration, the condition for zero integral extra- 

 current becomes 



E x + R 2 K 3 + E 4 



whence, in conjunction with (6), 



Tj-Ui _ T 2 -U 2 = T 8 -U ? _ T 4 -U 4 

 P 2 -Ri E 4 K 3 



This energy equation also follows at once on applying 

 equation (5) to each arm of the bridge in succession subject 



* O. Heaviside, ' Electrical Papers,' i. p. 4G4 ; ii. p. 361. 



i$) 



(9) 



