Resistance of Compound Conductors. 471 



and I gave the following formulae* as applicable to the case 

 in which the only sensible induction among the sides of the 

 quadrilateral is the self-induction L of the conductor P : — 



QR-SP=/ML, . . . (1) 



M(P + Q + R + S) = SL (2) 



The electrical vibrations are here supposed to follow the har- 

 monic law, with frequency p/2tt. " It will be seen that the 

 ordinary resistance balance (SP=QR) is departed from. The 

 change here considered is peculiar to the apparatus, and, so 

 far as its influence is concerned, it does not indicate a rea 

 alteration of resistance in the wire. Moreover, since p is 

 involved, the disturbance depends upon the rapidity of vibra- 

 tion, so that in the case of ordinary mixed sounds silence can 

 be attained only approximately. Again, from the second 

 equation we see that M is not in general a correct measure of 

 the value of L. If, however, P be very small, the desired 

 condition of things is approached ; since, by the construction 

 of the apparatus, Q + R + S is constant (say W), and if P be 

 small enough S does not differ much from W, i. e. most of 

 the wire forming the three sides of the combination is devoted 

 to the member opposite to P." 



The formulae are easily proved. Since there is no current 

 through the bridge, there must be the same current (x) in P 

 and one of the adjacent sides (say) R, and for a like reason 

 the same current y in the sides Q and 8. The difference of 

 potentials at time t between the junction of P and R and the 

 junction of Q and S may be expressed by each of the three 

 following equated quantities : — 



from which the required results are obtained by elimination 

 of the ratio x : z/, and introduction of the supposition that all 

 the quantities vary harmonically with frequency jpj^Tr. 



The inadequacy of Prof. Hughes's original interpretation 

 has been remarked upon also by Prof. Weberj and by Mr. 0. 

 Heavisideif, who have obtained the corrected formulae. I 

 give them here because I agree with Prof. Weber that this 

 form of apparatus possesses distinct advantages. As he points 

 out, if P be known, the application of (2) really presents no 

 difficulty, and allows of L being readily found in terms of M. 



* Journ. Tel. Eng. vol. xv. p. 54. 

 t El. Rev., April 9, 1886; July 9, 1886. 

 t Phil. Mag. August 1886. 

 2 K2 



