106 Randomness and its scientific treatment. [CHAP. V, 



much larger than m as we please : i. e. the chance may be 

 made to approach as near to unity as we please. 



I cannot but think that there is a similar fallacy in De 

 Morgan s admirably suggestive paper on Infinity (Camb. 

 Phil. Trans. Vol. 11.) when he is discussing the &quot;three-point 

 problem&quot;: i.e. given three points taken at random find the 

 chance that they shall form an acute-angled triangle. All 

 that he shows is, that if we start with one side as given and 

 consider the subsequent possible positions of the opposite 

 vertex, there are infinitely as many such positions which 

 would form an acute-angled triangle as an obtuse : but, as- 

 before, this is solving a different problem. 



9. The nearest approach I can make towards true indefi 

 nite randomness, or random selection from true iridefiniteness,. 

 is as follows. Suppose a circle with a tangent line extended 

 indefinitely in each direction. Now from the centre draw 

 radii at random ; in other words, let the semicircumference 

 which lies towards the tangent be ultimately uniformly in 

 tersected by the radii. Let these radii be then produced se 

 as to intersect the tangent line, and consider the distribution 

 of these points of intersection. We shall obtain in the result 

 one characteristic of our random distribution; i.e. no portion 

 of this tangent, however small or however remote, but will 

 find itself in the position ultimately of any small portion of 

 the pavement in our supposed continual rainfall. That is, 

 any such elementary patch will become more and more closely 

 dotted over with the points of intersection. But the other 

 essential characteristic, viz. that of ultimately uniform dis 

 tribution, will be missing. There will be a special form of 

 distribution, what in fact will have to be discussed in a 

 future chapter under the designation of a law of error , by 

 virtue of which the concentration will tend to be greatest at 

 a certain point (that of contact with the circle), and will thin 



