Now when a complex displacement of this kind is put into a cord, its image at once springs up. The displacement represented by M N O at once calls up the displacement represented by O N′ M′, and this condition of displacement and image displacement continues repeating itself till the cord comes to rest.
If the diagram be closely looked at, it will be seen that it exhibits the image relationship twice over. For the movement of the particle P from P to M has its image in the motion of another particle from its place of repose to the position O. The disturbance itself, M N O, consists of displacements and image displacements; and this disturbance, with its image O N′ M′, makes the wave from crest to crest.
The “twist” which we consider in these pages is like the wave motion, but with a third component added, so that in the complete motion there is a displacement coming out from the plane of the paper, as well as the displacements in the plane of the paper itself.
And just as the wave displacement produces a real image of itself in a medium which it does not distort as a whole, so there is nothing arbitrary in our assuming that an electric twist calls up the real image of itself in an insulating medium—that is, a medium which it cannot twist as a whole.
If L M N O is a wave motion, then L′ M′ N′ O is its image, as produced by moving it round out of the plane of the paper—Diagram II. If the wave disturbance is moved round in the plane of the paper, the original wave L M N O becomes L′ M′ N′ O—Diagram III.—a shape which bears no resemblance to the transmitted wave.
Consider O N M L to be a bent piece of wire lying on the paper; if it is moved round O, keeping on the paper, it becomes O N′ M′ L′. To become like O N′ M′ L′ in Diagram II. it must move up from the paper and down again on the right.
Thus adopting this artificial aid to thought—that a displacement calls up an image displacement—we get the rule that this displacement, the image, can be got from the original displacement by moving the original displacement half-way round, using as the plane in which the turning is made that plane which is given us by taking these two directions—the direction in which the wave is moving, and a direction at right angles to the directions in which the displacements which form the wave take place.