INDUCTANCE AND CAPACITY 417 



In order that the detector current may be zero, 

 Z x m P = Z P m x . 



When the values of Z x and Z P have been substituted and the 

 quadrature components separated, the horizontal component 

 gives 



m- x T X 

 m P ~ r P 

 or 



m x = ^m x (49) 



and the vertical component gives 



= (50) 



m P L P 



As (50) must be satisfied and the self-inductances of the 

 secondaries of the mutual inductances cannot be varied at will, 

 it is necessary to include the variable self-inductance Z/. 



If the source of current and the detector are interchanged and 

 the secondaries of the mutual inductances are connected in 

 opposition, the arrangement will be balanced if the two sec- 

 ondary e.m.fs. are equal at every instant; that is, when 



- 1 ' r> 



, m x Z x f 



. . = -=- as before. 



A disadvantage of the method just given is that r x and r P 

 include the resistances of the copper secondaries of the mutual 

 inductances; they must be determined by a separate bridge 

 measurement. 



A. Campbell 24 has developed the method so that these re- 

 sistances are replaced in the formula for m x by those of care- 

 fully calibrated bridge coils. The connections are shown in 

 Fig. 243. Here m P is a variable standard of mutual inductance; 

 the inductance and the resistance of its primary circuit are 

 fixed. 



In carrying out the measurement the switches are first thrown 

 to position 1, the desired values of R M and R N unplugged and a 



27 



