SECT. 2.] Randomness and its scientific treatment. 97 



draws a bow at a venture , or at random , we mean only 

 to point out the aimless character of the performance; 

 we are contrasting it with the definite intention to hit a 

 certain mark. But it is none the less true, as already 

 pointed out, that we can only apply processes of inference to 

 such performances as these when we regard them as being 

 capable of frequent, or rather of indefinitely extended repeti 

 tion. 



Begin with an illustration. Perhaps the best typical 

 example that we can give of the scientific meaning of 

 random distribution is afforded by the arrangement of the 

 drops of rain in a shower. No one can give a guess where 

 abouts at any instant a drop will fall, but we know that if 

 we put out a sheet of paper it will gradually become uni 

 formly spotted over; and that if we were to mark out any 

 two equal areas on the paper these would gradually tend 

 to be struck equally often. 



2. I. Any attempt to draw inferences from the as 

 sumption of random arrangement must postulate the oc 

 currence of this particular state of things at some stage or 

 other. But there is often considerable difficulty, leading oc 

 casionally to some arbitrariness, in deciding the particular 

 stage at which it ought to be introduced. 



(1) Thus, in many of the problems discussed by mathe 

 maticians, we look as entirely to the results obtained, and 

 think as little of the actual process by which they are obtained, 

 as when we are regarding the arrangement of the drops of 

 rain. A simple example of this kind would be the following. 

 A pawn, diameter of base one inch, is placed at random on 

 a chess-board, the diameter of the squares of which is one inch 

 and a quarter: find the chance that its base shall lie across 

 one of the intersecting lines. Here we may imagine the 

 pawns to be so to say rained down vertically upon the board, 

 v. 7 



