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



and inquire what would generally happen in practice, sup 

 posing him blindfolded, there cannot be much doubt that 

 the volumes would not be selected equally often. On the 

 contrary, it is likely that there would be a tendency to in 

 creased frequency about a centre indicated by the height 

 of his shoulder, and (unless he be left-handed) a trifle to the 

 right of the point exactly opposite his starting point. 



If the question were one which it were really worth 

 while to work out on these lines we should be led a long 

 way back. Just as we imagined our rifleman s position (on 

 the second supposition) to be determined by two inde 

 pendent coordinates of assumed continuous and equal facility, 

 so we might conceive our making the attempt to analyse the 

 man s movements into a certain number of independent 

 constituents. We might suppose all the various directions 

 from his starting point, along the ground, to be equally 

 likely; and that when he reaches the shelves the random 

 motion of his hand is to be regulated after the fashion of a 

 shot discharged at random. 



The above would be one way of setting about the state 

 ment of the problem. But the reader will understand that 

 all which I am here proposing to maintain is that in these, 

 as in every similar case, we always encounter, under this 

 conception of randomness , at some stage or other, this 

 postulate of ultimate uniformity of distribution over some 

 assigned magnitude: either time ; or space, linear, superficial, 

 or solid. But the selection of the stage at which this is to 

 be applied may give rise to considerable difficulty, and even 

 arbitrariness of choice. 



5. Some years ago there was a very interesting discus 

 sion upon this subject carried on in the mathematical part of 

 the Educational Times (see, especially, Vol. VII.). As not 

 unfrequently happens in mathematics there was an almost 



