1918] on Vibrations: JVIechanicai, Musical, and Electrical 247 



But let two electrical vibration circuits of comparable inductances 

 and periods be placed together and started, then there is not only 

 the action of the driver but also a distinct reaction of the driven 

 on the driver. Hence, as the vibrations of one circuit start those 

 of the other, the latter by their growth check the forruer, causing 

 them to die away. Thus there may be an interchange of energy 

 between them. This, as we have seen with pendulums, corresponds 

 to the superposition of vibrations of slightly differing periods, pro- 

 vided the action and reaction are small and the interchange slow. 

 Further, it is known that if two such circuits are closely coupled 

 those two periods differ more widely. Hence a third circuit (say a 

 cymometer) responding to either of them may detect these separate 

 periods by giving a resonance curve with two humps instead of one. 



IV.— Traces fro:^ Coupled Pexdulums. 



It has been seen that there is a certain general analogy between 

 mechanical and electrical vibrations, whether free, forced or coupled. 

 The question now arises as to whether this analogy may reach or 

 approach a quantitative exactness in all or any respect, and whether 

 it can be utilised in any way. 



Various mechanical vibrating systems differ widely. Some re- 

 semble the electrical case very closely, but none appears to be 

 completely and exactly analogous to them in every detail. Indeed 

 the electrical case seems to be slightly simpler than any mechanical 

 analogy yet put forward. But the differences are small, and the 

 mechanical analogy may be highly useful as affording visible and 

 tangible illustrations of those subtle electrical vibrations which can 

 be neither seen nor handled. Especially is this the case if the model 

 is readily adjustable to represent the various relations of the con- 

 stants concerned and can be used for any initial conditions. Thus 

 from such analogies some benefit may accrue to the non-mathematical 

 student. But perhaps the highest advantage is realised only by 

 those who combine the mathematical with the experimental study 

 and grope after the ideal model which shall represent exactly the 

 electrical or other phenomena in question. But whatever the uses 

 of such models, certain it is that their design and study have 

 exercised a fascination on many eminent scientists. In this con- 

 nection, it may suffice to mention Faraday, Maxwell, Lord Kelvin, 

 Lord Rayleigh, Sir Oliver Lodge, Sir Joseph Thomson, Professors 

 J. A. Fleming, T. R. Lyle, and ^X. S. Franklin. ^ 



For either quantitative work or mere illustration the usefulness of 

 such a model is much enhanced if its vibrations leave traces. This 

 is easily arranged by letting the bobs carry funnels of sand under 

 which a blackboard moves imif ormly at right angles to the direction 

 of vibration. In the portable apparatus shown in Fig. 1 the 



S 2 



