78 Dr. McLachlan on Effective Inductance, Effective 



Substituting in (19) for L, C. a> , co h we find L e = 2'34 

 x 10 ~ 3 henry. Substituting- in (14) for R e we obtain 

 R e =76 ohms. Thus it is quite evident that the effective 

 resistance cannot be disregarded. If is taken as 0*1 micro- 

 farad. L e still has the same value but R e is now 240 ohms. 

 The variation in R e is a result of the assumption regarding 

 the value of C, or of the fact that the correct value of co is 

 not known. If the value used in the experiments were 

 known, we should be able to find the correct value of R e . 



From the preceding analysis we can immediately suggest 

 a method of obtaining R e and L e experimentally. The 

 method is to find co or f using the primary winding, 

 preferably with the secondary removed, and a condenser. 

 The latter can be varied to vary /. / is then found when 

 an air-cored coil, of such a value that the former is not 

 increased more than about 10 per cent., is put in series. 

 L e and R e are obtained by substitution in the formulae 

 given above. In order to secure accuracy the measurement 

 of/ requires careful attention*. The above rests on the 

 assumption that the oscillations are damped sine waves, and 

 that there is no variation of L e and R e due to the slight 

 change in frequency. If we assume R e oca) and L e ocl/G>, 

 we can obtain formula? for L e and R e of the same nature as 

 those already given. This refinement is hardly justifiable. 



It is possible to examine these experiments from another 

 point of view. We have 



2 _ _!_ Bl 

 w ~L e C 4L» 



or 4w 2 CL f <2 -4L e -f CR/ = 0. . . . (20) 



Assuming that R and L are constant, we have 



4a> o 2 O L e 2 -4L e + C R e 2 = 0, 



4a) 1 2 C 1 L/-4L e + C 1 R e 2 = 0, 



where C and C ± are two values of the primary capacity as 

 used in experiments in the above paper (loc. cit.). 

 Solving these equations we obtain 



L ' = ri(c u /T„ 2l -C 1 °/T 1 1 ) (21) 



* See Taylor-Jones and Campbell (locc. citt.). 



