132 
Proceedings of the Royal Society of Edinburgh. [Sess. 
amount of kinetic energy. The success or failure of the model must be 
judged by its ability to act in this way. 
Suppose that a bar magnet, of length a and magnetic moment nxa, is 
pivoted at the origin (which is one of its magnetic poles) so that the bar 
is free to rotate in a plane, say the plane of yz. Let i/j be the angle which 
the bar makes at time t with the axis of y, so that the co-ordinates of the 
extremity (the other pole) at time t are 
(0, acosij/, asiiuf/). 
Suppose, moreover, that an electron of charge e is free to move along 
the axis of x, its co-ordinates at time t being (x, 0, 0). When the electron 
is in motion, it creates a magnetic field, the magnetic force at the movable 
SCtSC 
pole of the magnet due to this cause being of magnitude where r 
denotes the distance from the electron to the movable pole of the magnet, 
and being directed at right angles to the magnet in the plane yOz ; so 
that it tends to set the bar magnet in rotation about the origin in the 
plane yOz, just as if instead of the moving electron we had an electric 
current along the axis of x. Thus if the moment of inertia of the bar 
magnet about the origin is denoted by a, its equation of motion is 
fxea^x ^ 
( 1 ) 
Moreover, when the bar magnet is rotating, it sets up an electric field, 
the electric force at the electron along the axis of x due to this cause being 
: so that if the electron has a mass m, its equation of motion is 
mx -f 
jjiea^xj/ 
(2) 
We can further suppose that there are several such bar magnets 
rigidly connected like the spokes of a wheel, so that they rotate together 
in the plane of yz, each magnet having one of its poles at the origin of 
co-ordinates and having its direction at every instant radial from the 
origin. We thus obtain a structure essentially similar to one of those 
which have been proposed by Sir Alfred Ewing * for the purpose of 
explaining induced magnetisation. Denoting by M the sum of the 
values of /x corresponding to the different bar magnets in the structure, 
* “On Models of Ferromagnetic Induction,” Proc. R.S.E., 1922. The structure in 
question is described in § 30 of his paper, and is depicted in plate ii, fig. 22. It was while 
I was listening to Sir Alfred Ewing’s exposition of his model before the Koyal Society of 
Edinburgh that the ideas which have led to the present paper originated. 
