174 Mr. O. Heaviside on the 



ment in the electrical sense in similar parts), joined in parallel, 

 having the A ends connected, and also the C ends, and we join 

 A to by an external independent conductor in which is an 

 impressed force e, the two lines must, from their similarity, 

 be equally influenced by it, so that similar parts, as B x in 

 one line and B 2 in the other, must be in the same state at the 

 same moment. In particular, their potentials must always be 

 equal, so that, if the points B x and B 2 be joined by another 

 conductor, there will be no current in it at any moment, so far 

 as the above-mentioned impressed force is concerned, however 

 it vary. The same applies when it is not mere variation of 

 the impressed force e, but of the resistance of the branch in 

 which it is placed. And, more generally, Bi and B 2 will be 

 always at the same potential as regards disturbances origina- 

 ting in the independent electrical arrangement joining A to C 

 externally, however complex it may be. 



There is, however, this point to be attended to, that might 

 be overlooked at first. Connecting the bridge-conductor from 

 B x to B 2 must not produce current in it from other causes 

 than difference of potential ; for instance, there should be, at 

 least in general, no induction between the bridge-wire and the 

 lines, or some special relation will be required to keep a balance. 

 This case might perhaps be virtually included under similarity 

 of environment. 



If we had sufficiently sensitive methods of observation, the 

 statement that one line must be an exact copy of the other 

 would sometimes have to be taken literally. But the word 

 copy may practically be often used to mean copy only as 

 regards certain properties, either owing to the balance being 

 independent of other properties, or owing to our inability to 

 recognize the effects of differences in other properties. Thus, 

 in the steady resistance-balance, we only require AB 2 and AB 2 

 to have equal total resistances, and likewise B X C and B 2 C ; 

 resistances in sequence being additive. But evidently, if the 

 balance is to be kept whilst Bj and B 2 are shifted together 

 from end to end of the two lines, the resistance must be 

 similarly distributed along them. 



If, now, condensers be attached to the lines, imitating a sub- 

 marine cable, though of discontinuous capacity, we require 

 that the resistance of corresponding sections shall be equal, as 

 well as the capacities of corresponding condensers, in order 

 that we shall have balance in the variable period as w T ell as in 

 the steady state ; and the two properties, resistance and ca- 

 pacity, are the elements involved in making one line a copy 

 of the other. 



In case of electromagnetic induction, again, if ABjC and 



