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



Summarizing these points, we see that in measuring a 

 given inductance L x by comparison with a standard L 2 we 

 should endeavour to satisfy the following conditions : — 



(1) The frequency used should be as high as possible. 



(2) The resistances R x and R 3 should be as small as 



possible compared with the reactances L^o) and L 2 o>. 



(3) The resistances r t and r 2 should be about equal to 



the impedances of the corresponding inductive 

 arms. 



(4) The inductances L^ and L 2 (and hence the corre- 



sponding resistances) should not differ greatly in 

 magnitude. 



The first three conditions may be further summarized by 

 the statement that the triangle OAB should be approxi- 

 mately isosceles and as nearly as possible right angled, 



Comparison of a Self-Inductance with a Capacity. 



Suppose we are measuring a given self-inductance by 

 comparison with a standard condenser, it is evident that if 

 we neglect the current through the telephone and assume 

 V constant, the points 0, A 2 , B, and (fig. 5) are unaffected 

 by the changes of L and R, while A 1 moves exactly as in the 

 last case, and we arrive at the same conclusions. 



As before, the current that actually flows through the 

 telephone renders it expedient to make the transverse im- 

 pedance as low as possible. In this case it is perhaps worth 

 while considering the magnitude of this impedance more 

 fully. Strictly speaking, we should also consider the angle 

 between this impedance vector and that for the telephone, 

 but this would involve a knowledge of the angle of lag of the 

 telephone. As, however, this angle of lag seems unlikely to 

 be very large, and hence the angle between the two impe- 

 dance vectors will probably be small compared with a right 

 angle, it will suffice to make the network impedance as low 

 as possible and disregard its phase-angle. 



Let us neglect the generator impedance, so that as far as 

 the small transverse current, which may be regarded as super- 

 imposed on the main currents, is concerned, we may treat 

 the network as two impedances p' and p" in series, p' being 

 the impedance of the branches A 2 B0 and A 2 B0 and 

 the arm A 2 in parallel, and p" that of 0A X and 0A X in 

 parallel. 



