Vibrations elucidated by Simple Experiments. 251 



(4) This mass representing M should have to be greater for 



closer coupling and less for looser coupling, 



(5) That its presence should not disturb the value of the 



other masses previously used in the separate systems, 

 and 



(6) That all relations should be quantitatively accurate ? 



If we demand from a model these six points we may 

 perhaps look in vain for satisfaction not only in the past but 

 in the near future also. But can any model proposed as 

 analogous be deemed exact and complete if it lack any one 

 of these points ? 



Consider now a few typical analogies that have been pub- 

 lished. As models for the phenomena of induced currents 

 there is the set of toothed wheels and rack by Sir Oliver 

 Lodge (' Modern Views of Electricity ') and the three con- 

 nected masses sliding on parallel bars by Sir Joseph J. 

 Thomson (' Electricity and Magnetism,' art. 231, Cambridge, 

 1909) . The former appears to be qualitative. The latter is 

 quantitative, indeed its author shows that each of the two 

 connected masses together with a quarter of the connecting- 

 mass function as the two self-inductions, and a quarter of 

 the connecting mass as the mutual induction ; while the 

 remaining quarter of that mass is left unappropriated. 



We may next notice the model due to W. S. Franklin 

 (see fig. 5, p. 558 of " Some Mechanical Analogies in Elec- 

 tricity and Magnetism," Electrician, pp. 556-559, July 28, 

 1916). This may be regarded as a development of that due 

 to Sir J. J. Thomson, by the simple addition of springs to the 

 extreme masses. The model thus imitates electrical circuits 

 having capacities and hence characteristic periods. 



A very different model has been proposed and realised by 

 Prof. Thomas R. Lyle (see " On an Exact Mechanical Analogy 

 to the Coupled Circuits used in Wireless Telegraphy, and 

 on &c," Phil. Mag. [6] xxv. pp. 567-592, April 1913). In 

 this device two simple pendulums of lengths l x and l 2 with 

 bobs of masses mi and m 3 hang from a freely-moving carriage 

 of mass M. The electrical potential differences at the con- 

 densers here correspond to the angular displacements l and 

 # 2 of the pendulums. It is then shown (p. 575) that the 

 quantities respectively analogous to the self and mutual 

 inductions are : 



M + m 2 M4ffli "] 



m l Ql^m 1 +m f ) S ^ m 2 (M +m, + wj 2 )/ I 



and — n r— „. 



(M + mi+m^ 2 J 



