Formula' used in Inductance Measurements, 805 



We see that for a given value of co it is best to make 

 r l = I l , so that 



SE _V»Ii 



81* Pi 2 ' 



but p 1 a =r 1 2 + Ii 2 + 2r 1 I 1 co&6 (see fig. 1), 



= 2I 1 2 (l + cos(9) when ri=Ii, 



and Ixsin # = 1^0) ; 



j>E_ V sin V 



•'• SL, " 2L(1 + cos 6) " 2L 2 * 



Hence we should use the highest available frequency in 

 order to make 6 us large as possible. 



In the case considered above the available voltage V is 

 assumed to be fixed and the telephone impedance infinitely 

 high. In this case it is evident that the points 0, A 2 , and B 

 on the vector diagram being fixed independent of L 1? the 

 sensitivity is independent of the magnitudes of r 2 , R 2 , and L 2 , 

 and all we need do is to make the ratios of these quantities 

 correct. 



In practice, a current flows through the telephone and 

 reduces the P.D. SE, the amount of this reduction depending 

 on the resistances and reactances of the bridge-arms as com- 

 pared with the telephone. It is not necessary to consider 

 the question very exactly, as it is obvious thsit the smaller 

 r 2 , R 2 , and L 2 are, the lower will be the impedance to this 

 transverse current and the smaller the reduction in SE. We 

 do not, however, gain much by making r 2 , E 2 , and L 2 

 much smaller than r l5 E x , and L : respectively. The latter 

 quantities may be regarded as already fixed, since it 

 has been shown above that r x should be approximately 

 equal to Ij. 



On the other hand, it is evident that the smaller r 2 , R 2 , 

 and L 2 are, the larger will be the current c 2 , and, if the 

 generator resistance is appreciable, the smaller the available 

 voltage V. There is not much use, however, in attempting 

 to reduce the total generator current by making the impe- 

 dance p 2 very much greater than the parallel impedance p x . 



Hence we see, in a general way, that it is best to have 

 /■.,. K 2 , and L 2 of about the same size as r l5 R 1? and Lj 

 respective!}'. 



