relating to an Insulated Circuit. 325 



of the latter. Indeed this quantity is inappreciable, and vanishes 

 in the problem. 



A length of cable B M forty-three miles in length, of the same 

 pattern as the length A B, and having its end M insulated, was 

 attached to the circuit at B, thus representing the " body B, " of 

 Ohm's problem. This becomes charged, subtracting electricity 

 from the dynamic charge of the circuit; and by Ohm's formula 

 the line of tension H D should fall to a position G E such that 

 the quantity of electricity represented by the parallelogram 

 GHDE which the circuit has lost shall equal the charge which 

 the length B M has received, and which is represented by the 

 parallelogram B F M Z, whilst still preserving the necessary con- 

 dition that the tension throughout the length B M, represented 

 by B F, shall equal the tension B E, to which the tension at B 

 has fallen in the cable forming the principal part of the circuit. 



The tension at B was accordingly measured, before the length 

 B M was added, by placing it in contact with a condenser having 

 an inductive capacity equal to that of one mile of cable, and then 

 discharging the condenser through a galvanometer, the swing of 

 the needle reaching 7°. The quantity thus subtracted from the 

 circuit, though, strictly speaking, slightly altering the conditions, 

 is so small as to produce no sensible difference. The length B M 

 being now added, the condenser was again charged by contact 

 at B and discharged through the galvanometer, and gave a swing 

 of 4°-3. 



Now by Ohm's formula we have 



where 



u = 7, 



r=AB = 78, 



R = BM = 43; 



consequently u= ^ — ^ =4*5 instead of 4*3. 



The difference between the calculated and observed values of 

 u are, it may be fairly admitted, within the limits of error occa- 

 sioned by the difficulty of reading to the fraction of a degree. 



