Formulas used in Inductance Measurements. 807 



The resistance of A 2 BO and A 2 BC is r 3 + 2 * , but since 



?'2 + ^4 



L 

 „__ K „«j ? V*4 ri>\ 



and 



7\ + R 



T. 



this reduces to 



3 7\ + R r 2 +r 4 rj + R' 



L 



The reactance of A 2 is 



K(n + R)' 



where /? is the impedance of the branch OAxC. 



So p'=^, and if a. is the angle of lead of the joint 



current tan«=- p-, so a is equal to the angle POC 



(fig. 5). 



p" is most easily obtained from the admittance vector 

 diagram for the arms OA x and CA : in parallel. 



Here I is the impedance of A X (J and 6 its angle of lag. 

 We have 



• o" = — 



JL i l I j. 2cos(9 - _P" 



p "2- ri 2 + I 2+ fiI - ri2I 2; 



also sin/3= 'Vsin 0= -sin ; 



J P 



so /3, the angle of lag of the total current in these arms, is 



