Maxwell. 277 



to them in the circumference of the adjacent vortex ; and it 

 seems, therefore, as if the motion would be discontinuous. 

 Maxwell escaped from this difficulty by imitating a well-known 

 mechanical arrangement. When it is desired that two wheels 

 should revolve in the same sense, an " idle " wheel is inserted 

 between them so as to be in gear with both. The model of the 

 electromagnetic field to which Maxwell arrived by the intro- 

 duction of this device greatly resembles that proposed by 

 Bernoulli in 1736.* He supposed a layer of particles, acting as 

 idle wheels, to be interposed between each vortex and the next, 

 and to roll without sliding on the vortices ; so that each vortex 

 tends to make the neighbouring vortices revolve in the same 

 direction as itself. The particles were supposed to be not other- 

 wise constrained, so that the velocity of the centre of any 

 particle would be the mean of the circumferential velocities of 

 the vortices between which it is placed. This condition yields 

 (in suitable units) the analytical equation 



47Ti = curl H, 



where the vector i denotes the flux of the particles, so that its 

 ^-component i x denotes the quantity of particles transferred 

 in unit time across unit area perpendicular to the ^-direction. 

 On comparing this equation with that which represents Oersted's 

 discovery, it is seen that the flux i of the movable particles 

 interposed between neighbouring vortices is the analogue of 

 the electric current. 



It will be noticed that in Maxwell's model the relation 

 between electric current and magnetic force is secured by a 

 connexion which is not of a dynamical, but of a purely kine- 

 matical character. The above equation simply expresses the 

 existence of certain non-holonomic constraints within the 

 system. 



If from any cause the rotatory velocity of some of the 

 cellular vortices is altered, the disturbance will be propagated 

 from that part of the model to all other parts, by the mutual 



* Cf. p. 100. 



