114 Randomness and its scientific treatment. [CHAP. v. 



trust our own unaided efforts to do this, that we rely upon 

 the help of such a table of figures to do it for us, and then 

 examine with what sort of efficiency they can perform the 

 task. The problem of drawing straight lines at random, 

 under various limitations of direction or intersection, is 

 familiar enough, but I do not know that any one has sug 

 gested the drawing of a line whose shape as well as position 

 shall be of a purely random character. For simplicity we 

 suppose the line to be confined to a plane. 



The definition of such a line does not seem to involve 

 any particular difficulty. Phrased in accordance with the 

 ordinary language we should describe it as the path (i.e. any 

 path) traced out by a point which at every moment is as 

 likely to move in any one direction as in any other. That 

 we could not ourselves draw such a line, and that we could 

 not get it traced by any physical agency, is certain. The 

 mere inertia of any moving body will always give it a 

 tendency, however slight, to go on in a straight line at each 

 moment, instead of being instantly responsive to instanta 

 neously varying dictates as to its direction of motion. Nor can 

 we conceive or picture such a line in its ultimate or ideal con 

 dition. But it is easy to give a graphical approximation to it, 

 and it is easy also to show how this approximation may be 

 carried on as far as we please towards the ideal in question. 



We may proceed as follows. Take a sheet of the ordinary 

 ruled paper prepared for the graphical exposition of curves. 

 Select as our starting point the intersection of two of these 

 lines, and consider the eight points of the compass in 

 dicated by these lines and the bisections of the contained 

 right angles \ For suggesting the random selection amongst 



1 It would of course be more com- digits ; but this is much more trou- 

 plete to take ten alternatives of direc- blesome in practice than to confine 

 tion, and thus to omit none of the ourselves to eight. 



