derived from an Analysis of our ideas of Direction and Position. 461 



geometrical figure is, I believe, the fact that the knowledge of 

 position and figure is acquired by the exercise of distinct facul- 

 ties — sight and touch ; and thus, while we are seeking the ulti- 

 mate analysis of the conceptions in question, our attention is 

 distracted by the two classes of phsenomena. Now it is well 

 known that the born-blind are as capable of geometrical reason- 

 ing as those in full possession of their faculties. It is plain, 

 then, that all that is necessary for the groundwork of demon- 

 stration must be given independent of sight ; and it will tend to 

 simplify the inquiry into the real foundations of the science, if we 

 place ourselves in the mental condition of the blind, and consider 

 all knowledge of position for which the student must have credit 

 in the course of demonstration, to have been acquired by actual 

 motion through the several points of the system to which the 

 reasoning relates. 



The positions ascertained by such a course of experience will 

 of course have reference, in the first instance, to the station of 

 the observer at the commencement of the experiment ; and in 

 order to provide him with a definite point of departure, we shall 

 suppose him to make some one point in his own body coincide 

 with a certain point A in the external system. The structure of 

 his bodily frame will then supply him with three standard direc- 

 tions transverse to each other, up and down, right and left, fore and 

 aft, diverging from the point A in the external system, and by 

 reference to these he will distinguish any intermediate direction. 

 Now let the observer begin to move in any direction, in the 

 direction due forwards for example, and by such a motion let 

 him arrive at a second point B. He will carry with him the 

 consciousness of the same standard directions, up and down, 

 right and left, fore and aft, which will now be recognized as di- 

 verging from the point B instead of A. But as these directions 

 have reference only to the structure of the observer's own body, 

 it is necessary, in order to preserve any correspondence between 

 the analogous directions in the external system at B and at A 

 (between right and left at B, and right and left at A, for instance), 

 that the observer should avoid all rotation of his own body in 

 the external system during the passage from A to B. To that 

 efifect we shall introduce the condition, that while he is moving 

 from one point to another in the external system, no change 

 shall be made in the direction of the point towards which he is 

 moving, as measured on the scale of his bodily structure ; that 

 is to say, that if B be directly in front of the observer when he 

 begins to move from A, his motion shall be such as to keep that 

 point directly in front as long as he is moving towards it. With 

 this condition as to the mode in which the observer is supposed 

 to make himself acquainted with the system submitted to his 



