83. This motion which we have supposed to be around a vertical axis, we may equally suppose to take place around a horizontal axis. We shall then see in succession the two opposite sides, and the bases of the parallelopipedon with different appearances, according to their various positions; or, in other words, according to the angle formed by the planes and the visual ray. These appearances will help more and more to form the idea of the third dimension, which is not to be found in the primitive plane, and consequently to supply what was wanted to constitute the idea of a solid.
84. Just as we have supposed the eye fixed and the object movable, we may suppose the eye in motion and the object immovable. The result is the same; for, it is evident that if the eye should move around the parallelopipedon, now vertically, and now horizontally, it would experience the same sensations as when it was quiet, and the parallelopipedon moved. Thus, although we suppose the subject wholly deprived of the sense of touch, so as to be unable to perceive its own motion, it can still form the idea of solid by the impressions of sight alone. True, it could distinguish which moved, the eye or the object, but this does not interfere with the formation of the idea composed of the three dimensions.
[CHAPTER XV.]
SIGHT AND MOTION.
85. I said that the observer could not distinguish between his own motion and that of the object; sight alone can not give us a true idea of motion. Thus in a boat, although we are certain that we are moving, the motion seems to us to be in the objects along the shore. Also if the motion of the object and that of the observer are simultaneous, in the same direction, and with the same velocity, all appearance of motion is lost. But if there are two objects, one of which moves in the same direction as ourselves, and the other in the opposite direction, we perceive only the latter. Thus in a canal boat, the horse which walks on the bank in the same direction which the boat follows, seems to move without advancing. Of the two motions of the horse, we perceive only the vertical, the horizontal escapes us.
The reason of this is clear, we can judge the object only by our impressions. When the impression varies, we have the idea of motion; but not otherwise. When the object or the eye is in motion, there is a succession of impressions on the retina, from which the idea of motion arises. But if the motion of the eye accompanies the motion of the object, one cancels the other, the impression on the retina is constant, and the object does not seem to move.
86. In the same manner if the motion of the object and that of the eye are simultaneous, but of unequal velocity, we perceive only the difference; that is to say, if the motion of the eye be represented by 3 and that of the object by 5, the motion of the object will appear as 2, or the difference between 5 and 3. If our motion is more rapid than the motion of the object, although in the same direction, the object will appear to move in the opposite direction, as when we sail down a river faster than the current, the water seems to flow backwards. An immovable object at the same time seems to move in a direction opposite to our own with greater velocity than the current; for, here also, of the two motions we perceive only the difference. The motion of the boat, which is equal to 5, seems transferred to the fixed object, which appears to move in the opposite direction with the velocity represented by 5; and if we suppose the velocity of the current to be equal to 3, it will have the appearance of moving backwards with a velocity of 5-3, or 2.
87. From these considerations it would seem to follow that although sight is sufficient to give us the idea of motion, it is not sufficient to enable us to distinguish our own motion from that of the object, but for this we have need of touch. But this is not so; for by sight alone, we can distinguish the motion of the eye from that of the object, and if in some cases this is impossible, the same is true of touch.
We must observe that in the above examples touch is of much less use than sight in order to preserve us from illusions. How by the aid of touch alone could we perceive the motion of a boat gliding smoothly down a river? Sometimes by the help of sight we observe this motion, especially if we regard the objects along the bank which we pass; but touch is essentially limited to what affects the body immediately, and therefore cannot discover motion when the body is not affected by it.