Fig. 7.—When the spokes move slightly more (AC) or slightly less (AD) than half the angle (AB) between them, during the eclipse of the lens, the curious illusion of seeing twice the number of spokes in the wheel is produced.
In the course of elucidating this problem Monsieur Bull discovered another curious optical illusion produced by the moving wheel. Still taking the four-spoke wheel as an illustration, we will suppose that between each exposure the spokes are displaced a little more or a little less than half the angle between them. As the spokes are set 90 degrees apart, the half-way point will be 45 degrees. When a succession of such pictures is thrown upon the screen, it is not four spokes which are seen, but eight ([Fig. 7]). Monsieur Bull is engaged upon a series of experiments to ascertain why this peculiar optical illusion should prevail, and the explanation will prove interesting.
Another interesting and more conclusive illustration of the optically illusory properties of the cinematograph was demonstrated to me by Monsieur Bull. In order to be absolutely positive that an apparatus which he uses in certain cinematographic investigations should maintain the speed he desires, he has contrived a tuning-fork control for his electric motor. This tuning-fork resembles a large trembler blade, such as is used in the high-tension accumulator and coil ignition system upon motor cars. This particular instrument is timed to make, say, 40 vibrations per second, and at this speed, of course, it emits a distinctive musical note. This tuning-fork controls the electric motor driving the apparatus. For the purpose of illustration we will suppose it to be necessary that the speed of the motor shall not exceed 40 revolutions per second. In the earliest experiments he depended upon his ear to detect whether the motor and tuning-fork were in synchrony. He varied the speed of the motor until its hum was dead in tune with that of the tuning-fork.
But, as he thought that his ear might not be infallible, he devised an ingenious synchronising apparatus based upon the cinematographic principle. A small disk of cardboard provided with two holes near its edge, at opposite points of the circumference, is mounted upon the spindle of the tiny motor. Behind this disk is placed a small adjustable mirror. A pencil of electric light is projected horizontally in such a manner that it strikes the cardboard disk at right angles, and, when a hole on the disk is brought into line with it, it passes through and falls upon the mirror. The mirror is then set so as to reflect and focus the pencil of light in a small circle upon the free vibrating extremity of the tuning-fork. Naturally a strong shadow is thrown by the latter upon the white wall behind.
In the daylight the vibration of this fork is distinctly visible, and although it is slight and rapid it can be followed without any effort. But when the room is darkened, the ray of light is thrown upon the tuning-fork from the mirror. When the motor bearing the cardboard disk is set in motion a very curious effect is produced. The pencil of light reflected against the tuning-fork becomes interrupted twice in every revolution of the disk, that is 80 times per second, so that, looking at the background upon which the tuning-fork is silhouetted, the effect produced is precisely similar to that observable upon the cinematograph screen, where the passage of the light from the lantern is interrupted by the rotary action of the shutter. If the revolving speed of the motor, that is the number of revolutions per second, is the same as the number of vibrations per second of the tuning-fork, viz. 40, the end of the fork, as one looks at the illuminated circle on the wall against which the shadow is thrown, appears to be at rest. One only needs to touch the end of the fork, however, to be certain that it is vibrating.
Now if the motor be thrown out of synchrony with the tuning-fork, even if it makes only 39 or 41 instead of 40 revolutions per second, the disturbance is shown instantly, because looking at the illuminated tuning-fork one observes it jumping spasmodically. This movement becomes more pronounced as the harmony between the revolutions of the motor and the fork is disturbed, the jumps of the blade at times being apparently of a very severe character. Moreover, curiously enough, under the illumination of the ray of light the erratic movements of the blade appear to be three or four times more severe than they really are. But as the motor revolutions and the tuning-fork vibrations are brought into synchrony, the movements grow quieter, until at last the tuning-fork once more appears to be quiescent.
The explanation of this quasi-cinematographic illusion, which is as interesting and as puzzling as that of the wheel, is very simple, for it is based indeed upon the same phenomena. As the cardboard disk is provided with two small holes spaced 180 degrees apart, the passage of the ray of light is intercepted by the opaque section of the disk 80 times per second when the motor revolutions and the tuning-fork vibrations are in absolute synchrony. The result is that at this speed the light strikes the tuning-fork each time at the instant it is at the half-way point in its oscillating travel. One hole in the disk comes before the light when the blade has completed half its movement in one direction, while the second hole comes into line with the light when the blade is at the same point on its return journey. Consequently the light falls upon the blade at the same spot every time, causing the eye to imagine that it sees the blade always in the one position as if under a steady ray of continuous light. Hence comes its apparent quiescence. But directly the speed of the motor is altered in relation to the vibration of the tuning-fork, the rays of light catch the blade at varying points in its travel, and these changes, coming in quick succession, convey the visual idea of movement. Acceleration of the motor so that its revolving speed per second exceeds the number of the tuning-fork vibrations, causes the perceptible movements to be made more quickly, while on the other hand deceleration slows them down. In reality the eye imagines that it sees more than what actually takes place; it imagines that the blade of the fork is kicking spasmodically and viciously, whereas in fact the extent of the movement to and fro is constant and never changes.
While the experiment is peculiarly fascinating, its application is extremely useful to the worker. It offers a means of being absolutely certain about the speed at which the instrument utilised in a particular investigation is running, so that the resulting calculations may be completed without the slightest error.