94 Potts — Rowland's New Method. 



Making these substitutions and dividing (1) by (2), we have 



O^-m H.K,-R,R,-^L- 6 1) R , 



C, E,(R,+K,)+r(K,+ B.)+<W(B,+R 4 ) W 



Now taking only the real part of the above quantities we have 



Q 



~ COS <f> = 



(R 1 R 4 -R 1 RJ{B 4 (B 1 +RJ+r(^+B 4 )} + (i--W^R 1 (R,+RJ 

 I R 4 (R,+ H 3 )+r(R 3 +Rlr+W(R7FR 4 )^ ~J*) 



If = 90°, cos (f> = or 



(R,R 4 -R 1 R 1 ){R 4 (R 1 +R 1 )+r(R 1 +R 4 )} + 



^-&Yl)r 3 (R 3 +R 4 )=0 



or R - R ' R * I l l h*g\ R 3+R 4 (5) 



° r 1_ R 3 + \c ^ L JR 4 (R 2 +R 3 )+r(R s +R 4 ) 



This then is the condition satisfied when there is no deflec- 

 tion of the electro-dynamometer. 



The first term of the above is the same as the expression for 

 R l5 when the adjustment is conditioned b} r no deflection of a 

 galvanometer in the cross-connection, and a direct current is 

 used. The second is a correction term, always very small, at 

 most one per cent and often entirely negligible. In a circuit 

 carrying an alternating current the effective values of R 1? etc., 

 are not usually the same as their actual ohmic values, but 

 are larger. They include that part of the impedance against 

 which work must be done to maintain the current. Let R 2 , 

 R 3 and R 4 be as nearly as possible pure ohmic resistances, i. e. 

 let their actual values be equal to their effective ones. And let 

 the arm 1 contain iron, a condenser possessing electric absorp- 

 tion, or any piece of apparatus using energy which is not 

 expended in heating the conductors of that arm. The value 

 of R 1 calculated by the above formula will, be the effective 

 resistance, and this, less the actual value as measured by a direct 

 current, will be the increased resistance due to the hysteresis of 

 the iron, the energy-loss by electric absorption, etc. 



In the measurement of certain quantities (e. g. hysteresis 

 loss in iron) by this method, it is necessary to insert in arm 1 

 of the bridge a large coil. Such a coil acts not as a pure self- 

 induction, but on account of the numerous turns of the wire 

 so close to one another as a self-induction in multiple with a 



