THE VALUE OF SCIENCE 555 



three points M M' to be in a straight line. This condition that the 

 two objects form their image on is therefore necessary, but not suffi- 

 cient 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 a, it is because M and P coincide; if B touches my finger 

 at the instant /?, it is because M' and P coincide. Therefore M and 

 M' coincide. Thus this condition that if A touches my finger at the 

 instant a, B touches it at the instant /?, is at once necessary and suffi- 

 cient for M and M' 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 de- 

 termine 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 A. I make a series of 

 movements, corresponding to a series 8 of muscular sensations. After 

 these movements, at the instant a, my second finger receives a tactile 

 impression that I attribute likewise to A. 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 B ; I then make a series of move- 

 ments, corresponding to a series S' of muscular sensations. I know 

 that this series S f is the inverse of the series S and corresponds to con- 

 trary movements. I know this because many previous experiences 

 have shown me that if I made successively the two series of move- 

 ments 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 /?', when the second 

 series of movements is ended, my first finger would feel a tactile im- 

 pression 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, 



