412 ELECTRICAL MEASUREMENTS 



After this preliminary balance has been obtained, the unknown 

 inductance L' X) of resistance R' x , is introduced at n and the 

 balance again obtained by adjusting m and changing the variable 

 resistance from r to r'. Then, 



L x + L' x - L P = 2m 

 Rx + R'x - [Rp + 0' - r)] = 



.'.R'x = r' - r 

 L' x = 2m. 



Obviously inductances from zero up to a maximum of twice 

 the full value of the mutual inductance can be measured. 



In obtaining the inductance it is not necessary to know the 

 values of any of the resistances. The variable resistance r may 

 be made of two small and straight wires placed a few millimeters 

 apart and short-circuited by a bridge piece. The inductance 

 of such an arrangement may be calculated, if it is necessary 

 to allow for it. 



The apparatus should be so arranged that the equality of the 

 ratio arms may be tested and their adjustment to exact equality 

 facilitated by interchanging them. Any lack of equality affects 

 the value of R x much more than that of L x . 



Effect of Eddy Currents. The fundamental assumption on 

 which the theory of any mutual inductance bridge rests is that 

 the current flowing in the primary of the mutual inductance in- 

 duces an e.m.f. in the secondary which is in quadrature with the 

 primary current. This assumption will be rendered invalid and 

 absurd results will be obtained with the bridge if its construction 

 is such that eddy currents are set up in neighboring masses of 

 metal or in the wire of the coils themselves, if the wire be large. 

 The effect becomes more pronounced as the frequency is 

 increased. 



The primary current will induce an electromotive force in the 

 eddy current circuits which will be in quadrature with itself. 

 Assuming that the inductances of these circuits are negligible, 

 the eddy currents will, in turn, induce an electromotive force in 

 the secondary which will be in quadrature with themselves, and 

 therefore in opposition to the primary current. In addition, 

 there is the direct induction from the primary to the secondary, 



