804 



Dr. H. H. Poole on Vector Methods for 



Hence, as 8 (tan a)= ^ ' SR ] being a decrement in R, 



£p/_f]7i£R _ Vr^R. 

 Pi Pi 



If there are errors 3L 2 and 6^ in L x and R x respectively, 

 the resultant P.D. across the terminals of the telephone is 

 evidently 



a'SLf + SRf. 



Pi 



In order to measure a given inductance as accuratelv as 

 possible, we must arrange that a given error SLj in it shall 

 produce the maximum value of SEi. 



Rx should evidently be as small as possible since 

 (r x + R x ) 2 + Li 2 © 2 occurs in the denominator. Unless our 

 standard inductance L 2 is variable, it will probably be neces- 

 sary to introduce a non-inductive resistance in series with 

 the coil Lj in order to effect a balance, but this should be as 

 small as possible. 



8~F 

 It is obvious that -~ vanishes if r x is either zero or 



infinity, so there must be some value of it for which this 

 quantity is a maximum. 

 Since 



SJ&i V©?^ _ Ycor 1 



8L { Pl 2 (n + R^ + IV© 8 ' 



^©-^tC^iiO^L^-.^-.RO]; 



£F 



so for a maximum value of -^ we must make 



r 1 2 = R 1 2 + L l 2 o> 2 =I 



i i 



where Ix is the impedance of the arm AjB. This implies 

 that on the vector diagram (fig. 1) OA = AB. The same 



£F" 

 condition evidently ensures a maximum value of ^- . 



