324 Models of the Aether. 



objection.* Before proceeding to consider models which are not 

 constituted by a continuous medium, mention must be made of 

 a suggestion offered by Biemann in his lecturesf of 1861. Rie- 

 mann remarked that the scalar-potential and vector-potential 

 a, corresponding to his own law of force between electrons, 

 satisfy the equation 



+ div a = ; 



an equation which, as we have seen, is satisfied also by the 

 potentials of L. Lorenz.j This appeared to Riemann to indicate 

 that <j> might represent the density of an aether, of which a 

 represents the velocity. It will be observed that on this 

 hypothesis the electric and magnetic forces correspond to second 

 derivates of the displacement a circumstance which makes it 

 somewhat difficult to assimilate the energy possessed by the 

 electromagnetic field to the energy of the model. 



We must now proceed to consider those models in which 

 the aether is represented as composed of more than one kind of 

 constituent : of these Maxwell's model of 1861-2, formed of 

 vortices and rolling particles, may be taken as the type. Another 

 device of the same class was described in 1885 by Fitz Gerald ; 

 this was constituted of a number of wheels, free to rotate on 

 axes fixed perpendicularly in a plane board ; the axes were fixed 

 at the intersections of two systems of perpendicular lines ; and 

 each wheel was geared to each of its four neighbours by an 

 indiarubber band. Thus all the wheels could rotate without 

 any straining of the system, provided they all had the same 

 angular velocity; but if some of the wheels were revolving 

 faster than others, the indiarubber bands would become strained. 

 It is evident that the wheels in this model play the same part 

 as the vortices in Maxwell's model of 1861-2 : their rotation is 



* Cf. H. "Witte, Ueber den gegenwdrtigen Stand der Frage nach einer mecha- 

 nischen Erkldrung der elektrischen Erscheinungen ; Berlin, 1906. 



t Edited after his death by K. Hattendorff, under the title Schwere, Elektricitiit, 

 und Magnetismus, 1875, p. 330. 



I Cf. p. 299. 



Scient. Proc. Koy. Dublin Soc., 1885; Phil. Mag. June, 1885; Fitz Gerald's 

 Seient. Writings, pp. 142, 157. 



