of sight being fulfilled and that, on the contrary, that of sight can not be fulfilled without that of touch being also. It is clear that if this were so we should conclude that it is touch which may be exercised at a distance, and that sight does not operate at a distance.
But this is not all; up to this time I have supposed that to determine the place of an object I have made use only of my eye and a single finger; but I could just as well have employed other means, for example, all my other fingers.
I suppose that my first finger receives at the instant α a tactile impression which I attribute to the object A. I make a series of movements, corresponding to a series S of muscular sensations. After these movements, at the instant α', my second finger receives a tactile impression that I attribute likewise to A. Afterward, at the instant β, without my having budged, as my muscular sense tells me, this same second finger transmits to me anew a tactile impression which I attribute this time to the object B; I then make a series of movements, corresponding to a series S´ of muscular sensations. I know that this series S´ is the inverse of the series S and corresponds to contrary movements. I know this because many previous experiences have shown me that if I made successively the two series of movements corresponding to S and to S´, the primitive impressions would be reestablished, in other words, that the two series mutually compensate. That settled, should I expect that at the instant β', when the second series of movements is ended, my first finger would feel a tactile impression attributable to the object B?
To answer this question, those already knowing geometry would reason as follows: There are chances that the object A has not budged, between the instants α and α', nor the object B between the instants β and β'; assume this. At the instant α, the object A occupied a certain point M of space. Now at this instant it touched my first finger, and as touch does not operate at a distance, my first finger was likewise at the point M. I afterward made the series S of movements and at the end of this series, at the instant α', I ascertained that the object A touched my second finger. I thence conclude that this second finger was then at M, that is, that the movements S had the result of bringing the second finger to the place of the first. At the instant β the object B has come in contact with my second finger: as I have not budged, this second finger has remained at M; therefore the object B has come to M; by hypothesis it does not budge up to the instant β'. But between the instants β and β' I have made the movements S´; as these movements are the inverse of the movements S, they must have for effect bringing the first finger in the place of the second. At the instant β´ this first finger will, therefore, be at M; and as the object B is likewise at M, this object B will touch my first finger. To the question put, the answer should therefore be yes.
We who do not yet know geometry can not reason thus; but we ascertain that this anticipation is ordinarily realized; and we can always explain the exceptions by saying that the object A has moved between the instants α and α', or the object B between the instants β and β'.
But could not experience have given a contrary result? Would this contrary result have been