204 Lord Rayloigh. On the Bridge Metliod in its [Feb. 19, 



employed in ordinary testing. In the conjugate "battery" branch a 

 periodic electromotive force of given frequency is the origin of the 

 currents. 



Special attention will be given to the case where the branches are 

 equal in pairs, e.g., a = c, I = d (fig. 1). The advantages of this 

 arrangement are important even in ordinary resistance testing, and 

 in the generalised application are still more to be insisted upon. By 

 mere interchange of a and c and combination of results, the equality 

 of 6 and d can be verified independently of the exactitude of the 

 i-atio a : c. 



FIG. l. 



If any element in the combination, for example o, be a mere re- 

 sistance, the difference of potentials at its terminals (V) is connected 

 with the current, x, by the relation 



V = ax. 



We have, however, to suppose that a is not merely a resistance or 

 even combination of such. It may include an electromagnet,* and it 

 may be interrupted by a condenser. So long as the current is 

 strictly harmonic, proportional to ev', the most general possible 

 relation between V and x is expressed by 



V = (a!+ta,)a;, 



where ctj and toj are the real and imaginary parts of a complex co- 

 efficient a, and are functions of the frequency pfeir. In the particu- 

 lar case of a simple conductor, endowed with inductance L, ai repre- 

 sents the resistance, and a-, is equal to jpL. In general, a t is positive ; 

 but Oj may be either positive, as in the above example, or negative. 

 The latter case arises when a resistance, R, is interrupted by a con- 

 denser of capacity C. Here cti = R, a, = 1/pC. If there be also 

 inductance L, 



oj = R, o,=^)L 1/pC. 



* An electromagnet here denotes a conductor with sensible inductance. It 

 may be present if the range of magnetisation be small. ' Phil. Mag.,' March, It 



