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XXI. On the Self-induction of Wires. — Part VI. 

 By Olivee Heaviside*. 



THE most important as well as most frequent application 

 of Mr. S. H. Christie's differential arrangement, known 

 at various times under the names of Wheatstone's parallelo- 

 gram, lozenge, balance, bridge, quadrangle, and quadrilateral, 

 is to balance the resistances of four conductors, when sup- 

 porting steady currents due to an impressed force in a fifth, 

 and is done by observing the absence of steady current in a 

 sixth. But its use in other ways and for other purposes has 

 not been neglected. Thus, Maxwell described three ways of 

 usiug the Bridge to obtain exact balances with transient cur- 

 rents (these will be mentioned later in connection with other 

 methods); Sir W. Thomson has used it for balancing the 

 capacities of condensers f; and it has been used for other 

 purposes. But the most extensive additional use has been 

 probably in connection with duplex telegraphy ; and here, 

 along with the Bridge, we may include the analogous differ- 

 ential-coil system of balancing, which is in many respects a 

 simplified form of the Bridge. 



On the revival of duplex telegraphy some fifteen years ago, 

 it was soon recognized that " the line" required to be balanced 

 by a similar line, or artificial line, not merely as regards its 

 resistance, but also as regards its electrostatic capacity — ap- 

 proximately by a single condenser ; better by a series of smaller 

 condensers separated by resistances ; and, best of all, by a more 

 continuous distribution of electrostatic capacity along the 

 artificial line. The effect of the unbalanced self-induction 

 was also observed. This general principle also became clearly 

 recognized, at least by some, — that no matter how complex a 

 line may be, considered as an electrostatic and electromag- 

 netic arrangement, it could be perfectly balanced by means 

 of a precisely similar independent arrangement ; that, in fact, 

 the complex condition of a perfect balance is identity of the 

 two fines throughout. The great comprehensiveness of this 

 principle, together with its extreme simplicity, furnish a strong 

 reason why it does not require formal demonstration. It is 

 sufficient to merely state the nature of the case to see, from 

 the absence of all reason to the contrary, that the principle is 

 correct. 



Thus, if AB X C and AB 2 C be two identically similar inde- 

 pendent lines (which of course includes similarity of environ- 



* Communicated by the Author. 



t Journal S. T. E. and E. vol. i. p. 394. 



