294 Br. Norman Campbell : Experiments on 



determined experimentally by the method described in the 

 note on p. 301 of this Journal. The experimental values 

 are very much less than those calculated; at the maximum 

 of the curve they are only about one third of those predicted 

 by the theory. Moreover, in the experimental results there 

 is no certain indication of the " arches " of the theoretical 

 curve ; but since, when the coupling is so large, the arches 

 are not very prominent, it is possible (though by no means 

 probable) that their absence is due to insufficient accuracy 

 of the measurements. 



The Damping. 



7. We must now inquire whether the discrepancy between 

 theory and experiment can be removed by taking the damping 

 of the oscillations into account. 



In fig. 5 the lines marked Xt (calc.) and \V (calc.) show 

 the relations between the logarithmic decrement of the oscil- 

 lations and their period, for the slower and more rapid com- 

 ponents respectively, calculated from (3) and (4); in this 

 calculation the values of Rj and R 2 are those determined 

 with steady currents, namely 1^ = 0623 ohm, R 2 = 2160 ohms. 

 The lines marked p (obs.) and p (obs.) give the values of 

 the decrements observed experimentally. 



It is evident at once that, at any rate for the slower com- 

 ponent of the oscillation, there is no agreement whatever 

 between the observed and the calculated values. The wide 

 difference shows that by far the greater part of the energy 

 loss represented by the damping occurs in the iron core, and 

 is not due to the cause contemplated by the theory, namely 

 the ohmic resistance of the windings. Moreover, since the 

 observed decrements decrease as the period increases, while 

 the calculated decrements increase, it is not even legitimate 

 to regard the loss in the core as adding to the effective 

 resistance of the circuits. It should perhaps be pointed out 

 that the excess of the damping observed over that calculated 

 cannot be due to an increase of resistance of the windings 

 at high frequencies owing to " skin effect," for the terms in 

 R x and R 2 in (3) are of the same order ; R : may increase 

 somewhat with the frequency, but R 2 , being the resistance 

 ot wire of very small cross-section, can hardly change 

 appreciably. 



Even more noteworthy than the great difference between 

 observed and calculated values for the slower component is 

 the difference between the values for the slower and the more 

 rapid component. According to (3) and (4) the damping of 

 the more rapid component should be greater than that of the 



