INDUCTANCE AND CAPACITY 403 



The above results could have been obtained directly from equa- 

 tion (20), page 389. As no assumption was made in the deduction 

 of that equation as to the relation of i B to t, the bridge current 

 may be assumed as sinusoidal, 



IB = IB sin cot. 

 Substituting in (20) gives 



[L N L X - L M L P ] (- / B co 2 sin &>) + [- RpL M + R N L X + R X L N 



- R M L P ] (Isu cos + [R N R X - R M Rp] (I B sin orf) = 



which must be true for all values of I. 



Consequently the coefficients for both the cosine term and for 



the collected sine terms must be zero. 



/. - [L N L X - L M L P ] o> 2 + R N R X - R M R P = 

 and 



RpLn RN!JX RX!JN + RM!JP = 



The sine terms correspond to the horizontal component in the 

 previous demonstration while the cosine term corresponds to 

 the vertical component. 



The Anderson Bridge. The determination of an inductance in 

 terms of a capacity may conveniently be made by means of the 

 Anderson bridge. 21 This apparatus is a development of the 

 bridge arrangement given by Maxwell.* 



The connections are shown in Fig. 235. 



All the resistances except R x are supposed to be non-inductive. 

 The condenser is placed at C and r is an adjustable resistance. 



When variable currents are used, as was originally intended, 

 the bridge is first balanced for steady currents, the battery cir- 

 cuit being kept closed. After balance has been attained, the 

 capacity C and the resistance r are adjusted until there is no 

 deflection of the galvanometer when the battery circuit is made 

 and broken. It will be noted that the adjustment of C and r 

 does not disturb the steady current balance but does affect the 

 rate at which the potential of the junction e rises. As the 

 initial values of the potentials of b and e are the same and the 

 final values are the same, there will be no current in the de- 



* "Treatise on Electricity and Magnetism," third edition, Art. 778. 



