three points 0 to be in a straight line. This condition that the two objects form their image on is therefore necessary, but not sufficient for the points and to coincide. Let now 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 touches my finger at the instant , it is because and coincide; if touches my finger at the instant , it is because and coincide. Therefore and coincide. Thus this condition that if A touches my finger at the instant , touches it at the instant , is at once necessary and sufficient for and to coincide.
But we who, as yet, do not know geometry can not reason thus; all that we can do is to ascertain experimentally that the first condition relative to sight may be fulfilled without the second, which is relative to touch, but that the second can not be fulfilled without the first.
Suppose experience had taught us the contrary, as might well be; this hypothesis contains nothing absurd. Suppose, therefore, that we had ascertained experimentally that the condition relative to touch may be fulfilled without that 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 a a tactile impression which I attribute to the object . I make a series of movements, corresponding to a series of muscular sensations. After these movements, at the instant , my finger receives a tactile impression that I attribute likewise to . Afterwards, at the instant , 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 I then make a series of movements, corresponding to a series of muscular sensations. I know that this series is the inverse of the series 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 and to , the primitive impressions would be reestablished, in other words, that the two series mutually compensate. That settled, should I expect that at the instant , when the second series of movements is ended, my first finger would feel a tactile impression attributable to the object ?
To answer this question, those already knowing geometry would reason as follows: There are chances that the object has not budged,
