Is there any mode of motion in the region of the minute which, giving three-dimensional movements for its effect, still in itself escapes the grasp of our mechanical theories? I would point to electricity. Through the labours of Faraday and Maxwell we are convinced that the phenomena of electricity are of the nature of the stress and strain of a medium; but there is still a gap to be bridged over in their explanation—the laws of elasticity, which Maxwell assumes, are not those of ordinary matter. And, to take another instance: a magnetic pole in the neighbourhood of a current tends to move. Maxwell has shown that the pressures on it are analogous to the velocities in a liquid which would exist if a vortex took the place of the electric current: but we cannot point out the definite mechanical explanation of these pressures. There must be some mode of motion of a body or of the medium in virtue of which a body is said to be electrified. Take the ions which convey charges of electricity 500 times greater in proportion to their mass than are carried by the molecules of hydrogen in electrolysis. In respect of what motion can these ions be said to be electrified? It can be shown that the energy they possess is not energy of rotation. Think of a short rod rotating. If it is turned over it is found to be rotating in the opposite direction. Now, if rotation in one direction corresponds to positive electricity, rotation in the opposite direction corresponds to negative electricity, and the smallest electrified particles would have their charges reversed by being turned over—an absurd supposition. If we fix on a mode of motion as a definition of electricity, we must have two varieties of it, one for positive and one for negative; and a body possessing the one kind must not become possessed of the other by any change in its position. All three-dimensional motions are compounded of rotations and translations, and none of them satisfy this first condition for serving as a definition of electricity. But consider the double rotation of the A and B kinds. A body rotating with the A motion cannot have its motion transformed into the B kind by being turned over in any way. Suppose a body has the rotation _x_ to _y_ and _z_ to _w_. Turning it about the _xy_ plane, we reverse the direction of the motion _x_ to _y_. But we also reverse the _z_ to _w_ motion, for the point at the extremity of the positive _z_ axis is now at the extremity of the negative _z_ axis, and since we have not interfered with its motion it goes in the direction of position _w_. Hence we have _y_ to _x_ and _w_ to _z_, which is the same as _x_ to _y_ and _z_ to _w_. Thus both components are reversed, and there is the A motion over again. The B kind is the semi-negative, with only one component reversed.