However it may be with this hypothesis and although I am led to prefer to it others considerably more complicated, it is certain that we are told in some way that there is something in common between these sensations a + a´ and b +b´, without which we should have no means of recognizing that the object B has taken the place of the object A.
Therefore I do not further insist and I recall the hypothesis I have just made: I suppose that I have ascertained that the impressions which I attribute to B are transmitted to me at the instant β by the same fibers, optic as well as tactile, which, at the instant α, had transmitted to me the impressions that I attributed to A. If it is so, we shall not hesitate to declare that the point occupied by B at the instant β is identical with the point occupied by A at the instant α.
I have just enunciated two conditions for these points being identical; one is relative to sight, the other to touch. Let us consider them separately. The first is necessary, but is not sufficient. The second is at once necessary and sufficient. A person knowing geometry could easily explain this in the following manner: Let O be the point of the retina where is formed at the instant α the image of the body A; let M be the point of space occupied at the instant α by this body A; let M´ be the point of space occupied at the instant β by the body B. For this body B to form its image in O, it is not necessary that the points M and M´ coincide; since vision acts at a distance, it suffices for the three points O M M´ to be in a straight line. This condition that the two objects form their image on O is therefore necessary, but not sufficient for the points M and M´ to coincide. Let now P be the point occupied by my finger and where it remains, since it does not budge. As touch does not act at a distance, if the body A touches my finger at the instant α, it is because M and P coincide; if B touches my finger at the instant β, it is because M´ and P coincide. Therefore M and M´ coincide. Thus this condition that if A touches my finger at