500 Mr. A. Campbell on the Mea 



burcmen 



t 0] Mutual 



condenser and a variable self-inductance brought to resonance. 

 Another method which J. have found very convenient for the 

 same purpose is that of Hughes's In- 

 ductance Bridge * as developed by Lord 

 Rayleigh f, in which a mutual inductance 

 is compared against an independent self- 

 inductance. 



The connexions are shown in fig. 4, 

 where M is a variable mutual inductance; 

 L a self-inductance of resistance P ; Q, 

 R, and 8 non-inductive resistances ; E a 



source of alternating: 



or 



intermittent 



current of steady frequency, and G the 

 vibration galvanometer. 



R + S is kept constant, Z being a slider by which S, which 

 is entirely a slide-wire, can be gradually varied down to zero. 



As Lord Rayleigh has shown, the conditions for a balance 

 are 



QR-SP=/ML (4) 



and M(P + Q + R + S) = SL, ...... (5) 



where p~27rn, n being the frequency. 



Let Q as well as R -f S have a fixed value. For good 



sensitivity the resistance P usually will have a temperature 



coefficient not negligible, as the whole or part of the arm may 



be of copper- 

 Two cases arise according as we consider P (1) known and 



constant, or (2) only approximately known and variable. 

 Case 1.— Let P be constant, and hence 



P + Q + R + S = const. = a (say) ; 



also R-f-S = b. 



Let L also be constant and known, and let 

 obtained by varying M and the position of Z. 

 Then we have 



balance be 



(2 ^ = r = p(f-p) 





(6) 



Thus n is expressed in terms of the single variable S, and 

 the slide-wire may be marked directly with the values of the 

 frequency deduced from (6). 



If wide range of frequencies is to be dealt with, various 



* Prof. E. D. Hughes, Jour. Inst. Elect. Eng. xv. p. 6. Jan. 1886. 

 t Lord Rayleigh, Phil. Mag. Dec. 1886. 



