﻿Manchester Memoirs, Vol. xlix. (1905), No. i\ 1 1 



or ' Mendclian ' first in the title of this paper, or to the 

 result of a very great number of tosses — an approximation 

 to 50 % heads and 50 % tails, which is close in proportion 

 as the number of trials is great. The first difference that 

 I mention between these two meanings of chance, as illus- 

 trative of the characters of the two classes into which we 

 have divided our aspect of things, is that, while in the 

 case of the first it is impossible to predict the result of a 

 single trial, there is nothing easier to foretell than the 

 result of a very large number ; nothing is more uncertain 

 than the former, nothing more certain than the latter. A 

 second difference between these two groups is that that 

 which is true of the mass is not necessarily true of all the 

 component individuals, though it may be of some : in the 

 case of coin-tossing, the statement that the result of an 

 infinitely large number of trials is an equal number of heads 

 and tails is contradicted at every single toss, though this 

 would not be the case if some of the coins we tossed had 

 half the head and half the tail on each side of the coin.* Is 

 it necessary to add that from the fact that what is true of 

 the mass is not true of the individual it does not follow 

 that assertions about the individual are antagonistic 

 to statements about the mass ? It is important to 

 realise this truth because it is seldom done and ap- 

 parently difficult, the difficulty resulting from the extreme 

 difference of the two points of view. A midge walking 

 across a picture of a meadow done by the three-colour 

 process would assert that it was traversing a white plain, 

 over which were distributed patches of different sizes and 

 three colours, red, blue, and yellow : a child would main- 



* I have found Galton's apparatus for illustrating the origin of the curve 

 of frequency {Natural Inheritance, p. 63. Fig, 7) very useful for explaining 

 the difference between these two classes. An example of the first is afforded 

 by allowing a single shot to run down the inclined board ; an example of 

 the second by displaying the result of a thousand such events. 



