Fig. 4.—During the eclipse of the lens the spokes have moved a distance equal to the angle between them, causing the spokes apparently to stand still while the wheel is moving.
To reduce the explanation to its simplest form we will suppose that a wheel has four spokes spaced equidistantly, that is, 90 degrees apart, and that the wheel is moving from right to left. As a matter of fact such an example is not the best for the purpose, but it shall be taken merely because it is the simplest to understand. An exposure is made, the wheel being photographed in the position shown in [Fig. 3]. The lens is eclipsed by the shutter, and the film is jerked downwards into position in the gate so as to bring a fresh unexposed surface before the lens. While this operation is taking place, we will suppose that the wheel, continuing its forward movement, completes one quarter of a revolution. Consequently when the second exposure is made spoke 1 has moved 90 degrees, which is the angle between each spoke. Accordingly it now occupies exactly the same position as that of spoke 2 at the time of the first exposure. Spoke 2 has moved to the position formerly occupied by spoke 3. Spoke 3 has travelled sufficiently to take the place of spoke 4, while 4 has gone to that of 1 ([Fig. 4]). If four exposures are made, and the spokes move 90 degrees each time the lens is closed, when the four pictures are thrown successively upon the screen they will look exactly alike. The spokes will appear to be quite stationary, although the rim of the wheel will have moved a distance equal to its circumference across the screen. Consequently, if a dozen, a hundred, or a thousand exposures are made under these conditions, the spokes moving 90 degrees between each exposure, a quaint skidding effect will be produced. All the spokes being alike the eye is unable to detect that any displacement has taken place between one exposure and another. This impression of the spokes standing still while the wheel is moving, must arise in every case in which the wheel moves sufficiently to cause the spokes to cover a distance equal to the angle between them during the interval while the lens is eclipsed by the shutter. It will happen equally whether the wheel has four, sixteen, or more spokes.
Fig. 5.—During the eclipse of the lens the spokes move less than the angle (AB) between them, producing apparent backward motion of the spokes while the wheel is running forwards.
Fig. 6.—During the eclipse of the lens the spokes move more than the angle (AB) between them, and accordingly the wheel is seen to be moving naturally.
Now we will suppose that the revolving speed of the wheel is retarded, causing less than a quarter of a revolution to be completed between each exposure. The spokes, let us say, move through an angle of 85 degrees instead of 90 degrees while the lens is eclipsed. The eye at first receives the impression shown in [Fig. 3]. As the wheel only covers 85 degrees during the eclipse, in the second picture the eye observes that movement has occurred. Spoke 1 is now behind the point formerly occupied by spoke 2 (shown by the dotted line in [Fig. 5]) in the first exposure. The lens is eclipsed once more, and the spoke moves another 85 degrees. When the next picture is seen spoke 1 has fallen still farther behind the 90 degrees mark, and this indication of less movement than the right angle becomes accentuated with each succeeding exposure. Accordingly, the spokes in the successive pictures appear to be moving at a less speed than the rim of the wheel, and forthwith the eye imagines that the spokes are travelling backwards, although meantime the wheel rim is seen to be advancing across the screen. This remarkable effect is produced whenever the advance of the wheel is such as to cause the spokes to move less than the angle between them, no matter what the size of the angle may be.
We will now suppose that the revolving speed of the wheel is accelerated so as to cause more than a quarter of a revolution to be made while the lens is eclipsed—that the spokes move forward 95 degrees between each exposure. In this case, while the first picture will show the position indicated in [Fig. 3], the next exposure will show spoke 1 in the position shown in [Fig. 6], that is, in advance of the angle of 90 degrees and in advance of the position occupied by spoke 2—(see the dotted line)—in the first exposure. In the third picture the spoke will be shown still farther in advance of the right angle mark, and the effect will be produced of the spokes apparently gaining upon one another. When a series of pictures taken under such conditions is thrown upon the screen in rapid succession, the spokes and rim will be seen to be moving harmoniously in the forward and correct direction. Accordingly natural movement of the wheel only can be shown when the spokes of the wheel, irrespective of their number, move a distance equal to more than the angle between them.
