888 REPORT— 1898. 



will become total at Greenwich at 10.57 p.m. ; and I imagine you will all feel sure, 

 on reading that statement, that when December 27 comes the eclipse will occur ; 

 and it will become total at 10.57 p.m. It will not become total at 10.50 p.m., and 

 it will not wait until 11.0 p.m. You will say, therefore, that eclipses of the moon 

 do not occur by chance. 



What is the difference between these two events, of which we say that one 

 happens by chance, and the other does not ? The difference is simply a difference of 

 degree in our knowledge of the conditions. The laws of motion are as true of moving 

 pence as they are of moving planets ; but it happens that we know so much about 

 the sun, and the earth, and the moon, that we know the circumstances which 

 'affect their relative positions very accurately indeed, so that we can predict within 

 less than a minute the time at which the shadow of the earth will next fall upon 

 the moon. 



But the result of tossing a penny depends upon a very large number of things 

 which we do not know. It depends on the shape and mass of the penny, its 

 velocity and direction when it leaves one's hand, its rate of rotation, the distance 

 of one's hand from the table, and so on. If we knew all these things before toss- 

 ing the penny, we should be able to predict in each case what the result would be, 

 and we should cease to regard pitch and toss as a game of chance. 



As it is, all we know about these complicated conditions is that if we toss a 

 penny for a number of times, the conditions which give ' heads ' will occur about 

 as often as the conditions which give ' tails.' 



If you examine any event which occurs by chance, you will find that the 

 fortuitous character of its occurrence always depends upon our ignorance concern- 

 ing it. 



If we know so little about a group of events that we cannot predict the result 

 of a single observation, although we can predict the result of a long series of ob- 

 servations, we say that these events occur by chance. And this statement seems 

 to me to contain the best definition of chance that can be offered. 



If we use the word chance in this sense, we see at once that our knowledge of 

 animal variations is precisely knowledge of the kind referred to in our definition 

 of chance. We know with some certainty the average characters of many species 

 of animals ; but we do not know exactly the character of the next individual of 

 these species we may happen to look at. So that in the present state of our know- 

 ledge it is a j)riori certain that the great majority of animal variations should 

 occur by chance, in the sense in which we have used the phrase ; and I will show 

 you in a moment illustrations of the fact that they do so occur. 



But before doing so, I would point out the difference between the sense in which 

 we have used the word chance, and the sense in which it is used by many objectors 

 to the theory of Natural Selection. Such epithets as blind, lawless, and the like, 

 are constantly applied to chance ; and a kind of antithesis is established between 

 events which happen by chance, and those which happen in obedience to natural 

 laws. In many German writings, especially, this antithesis between Zufdlligkeit 

 and Gesetzmdssigkeit is strongly insisted upon, whenever organic variation is dis- 

 cussed. 



This view of chance is not supported by experience ; and indeed, if it could be 

 shown that anything in human experience were absolutely lawless, if it could be 

 shown that in any department of Nature similar conditions did not produce similar 

 effects, the whole fabric of human knowledge would crumble into chaos, and all 

 intellectual effort would be a profitless waste of time. There is not the slightest 

 reason to believe that any such absolutely lawless phenomena do exist in Nature ; 

 so that we need pay no further attention to the writers who assume that chance 

 is a lawless thing. 



But if chance is a perfectly orderly and regular phenomenon, then the question, 

 whether animal variations occur by chance or not, can be settled by direct observa- 

 tion. I will now show you one or two examples of events which undoubtedly 

 occur by chance, and then compare these with one or two cases of organi 

 variation. 



As events which occur by chance, I have taken the results of tossing twelve 



