1903.] Thermal Relations of Energy of Magnetisation. 233 



force its way, to be expelled again by the elasticity of its walls when 

 the stream begins to set in the reverse direction. This increase of 

 kinetic pressure on the turbine roughly represents the electromotive 

 pressure on a motor due to the increased magnetic flux, and the 

 energy spent in expanding the reservoir as it fills up represents the 

 energy of magnetisation of the iron. If things were perfectly reversi- 

 ble in the reservoir, that is if the iron were perfectly soft, the latter 

 energy would rise and fall concomitantly with the alternations of 

 pressure on the motor, but of course if its temperature remained con- 

 stant it would contribute nothing to the energy driving the motor, 

 which must be introduced into the system from an extraneous source. 

 But if there are frictional resistances involved in filling the reservoir, 

 the operations will not be perfectly reversible, and mechanical energy 

 will be lost in it by conversion into heat ; and moreover on account 

 of the phase of its changes getting out of step — still more by perma- 

 nent delays such as are classed under hysteresis — it will operate less 

 efficiently in directing the stream of energy towards the turbine. 

 Both these statements have analogical application to the iron in a 

 magnetic circuit. 



An example is provided by the ring-coil aforesaid. Suppose that 

 when the current has ceased in the coil the core retains permanent 

 magnetism, its energy being the latter term in the formula above. 

 This corresponds to the reservoir becoming temporarily choked, so 

 that it retains its contents after the pressure that drove the liquid 

 into it has been removed. The question arises whether this retained 

 energy is available for mechanical work. The present aspect of the 

 matter appears to lead to the conclusion (Lord Kayleigh's) that it will • 

 not be available to any considerable extent unless its pressure in the 

 reservoir is considerable, that is, in the magnetic case, unless the iron 

 is not very receptive of magnetisation. 



The paradox that energy of residual magnetism, which is outside the 

 electrokinetic system, can on running down affect that system, shows 

 that the circumstances are more general than an analogy of a pure 

 dynamical system of finite number of degrees of freedom can illustrate. 

 In fact the equations of dynamics imply permanent structure of the 

 system; whereas in Professor E wing's illustrative model of para- 

 magnetisation, when the displacement is great enough the structure 

 changes by the component magnets toppling over,* and after the 

 general disturbance thus set up has subsided with irrecoverable loss of 

 energy into heat, there remains a new structure to deal with. The 

 only way to estimate the available part that may be latent in the great 

 store of energy of residual magnetism of an iron core is thus by the 

 empirical process of detailed experiment. Lord Rayleigh has inferred 



* The effective susceptibility dljdH. becoming enormous in the steep part of the 

 characteristic curve. 



