250 Prof. Barton and Miss Browning on Coupled 



III. Previous Mechanical Analogies. 



A number of mechanical models have already been devised 

 capable of motions analogous to electrical vibrations or 

 induced currents, and probably all have considerable value, 

 but, perhaps, none has an action that is exactly and com- 

 pletely analogous to the electrical phenomena in the fullest 

 sense of the words. If any proposed model were at once 

 exactly analogous, quite simple, and capable of easy adjust- 

 ments so as to exhibit all the features of the electrical case, 

 it might put an end to further work in this direction, though 

 other models might still present a purely mechanical interest. 

 But, so far as is known to the present writers, it appears 

 that no such simple, exact and complete analogy has hitherto 

 been put forward. 



In order to submit to critical examination a few typical 

 models which have been advanced, let us review the chief 

 features of the electrical case. Each electrical circuit has 

 its own capacity and inductance, the latter (L and N) being 

 usually held to function as inertias, while the former (R and S) 

 are likened to the reciprocals of spring factors. Hence each 

 circuit has its definite period. Two such circuits are then 

 brought near enough to involve appreciable electromagnetic 

 induction. They are then said to be coupled. In this state 

 the phenomena in each circuit depend partly upon those in 

 the other. The single factor that expresses this dependence 

 or cross-connexion between the variables is M, the coefficient 

 of mutual induction. It is of the same physical nature as 

 the two inductances of the separate circuits, thus it also 

 functions as an inertia. This is all on the assumption that 

 the currents i and j in the circuits are analogous to velocities 

 in the mechanical case, since the kinetic energy T in the 

 coupled circuits is known to be given by 



T^iLP + MzZ + iN/ 2 (22) 



Hence, in a model completely analogous to the electrical 

 case, we might naturally look for : 



(1) Masses in each system to represent the inductances L 



and N, 



(2) Spring factors to represent the reciprocals of the 



capacities R and S, and also 



(3) Some third mass to represent M, the mutual induction of 



the circuits as coupled. 



Further, might we not legitimately ask that in an 

 exact analogy, 



