300 Dr. H. H. Poole on Vector Methods for 



Comparison of a Mutual Inductance with a Capacity 

 [ Carey Foster s Method'] . 



Fig. 6. 



Circuit Diagram 



c, r, 

 Vector Diagram 



Here, since A : and A 2 are at the same potential, the 

 triangle OPA evidently represents the P.D. vectors for the 

 arms OAx and OA 2 . The fall in potential due to the im- 

 pedance of the aim A 2 BA l5 through which the current c 2 

 passes, must be balanced by the E.M.F. induced in it by the 

 mutual inductance M. Now, the current in the primary of 

 the latter is the vector sum of c x and c 2 , therefore this E.M.F. 

 must be the vector sum of ci^lco and 6' 2 M&>, each vector being 



7T . 



-p in advance of the corresponding current vector. [The 



primary of M must obviously be so connected that the 

 E.M.F. is in the desired direction.] Hence, the figure 

 AQST represents this part of the circuit, the lengths of the 

 vectors being as shown. The triangles OPA and SQA are 

 evidently similar, so 



. , c 2 C 2 ~R 



sin <p = 



K< 



rj CiMa>' 

 M = KriR: 



and 



M)© 



c 2 r 2 c 2 (L 



COS <2> = = ^tif- 



c i^i c'iMffl 



M~ J ' n 



We must remember in using this method for measuring 

 a capacity by means of a variable mutual inductance, that if 

 we make r 2 infinite, c 2 becomes zero, and we obtain a perfect 

 balance with M = 0. If we start with a very large value 



