71] 



CYCLIC SYSTEMS. 



139 



Dicydic Systems. The preceding example will suffice as a 

 mechanical model to illustrate the phenomenon of self-induction 

 of an electric current (Chapter XII). To illustrate mutual in- 

 duction we must have at least two cyclic coordinates. Such 

 models have been proposed by Maxwell, Lord 

 Rayleigh*, Boltzmann, J. J. Thomson f, and the 

 author J. In the model of J. J. Thomson, there 

 are two carriages of mass m^ and w 2 sliding on 

 parallel rails, Fig. 29, their distances from a 

 fixed line perpendicular to the rails being x 

 and a? 2 . Sliding in swivels on the carriages is 

 a bar, on which is a third mass ra 3 . We shall suppose that this 

 mass is movable along the bar, and is at a distance y from the 

 line midway between the rails, y being positive when ra 3 is nearer 

 w 2 . Then, if d is the distance between the rails, 



and the kinetic energy is, if we may neglect y in comparison 

 with #/, a? a ', 



T = 



4- 



The system is cyclic, y being the positional, x^ and # 2 the 

 cyclic coordinates. The positional force 



y i \ i r y 

 d 2+ 2d)~ X * Xz d 2 



vanishes if #/ = x*. The cyclic forces are 



/I y 



S (4 + S 



* PMi. Mag., July 1890, p. 30. 



t Elements of Mathematical Theory of Electricity and Magnetism, p. 385. 



I Science, Dec. 13, 1895. 



