TRANSACTIONS OF SECTION D. 897 



repeat. If there be any here who hold such an opinion, I would ask them to read 

 Mr. Francis Galton's Essays on Heredity ; where a simple and quite unexpected 

 relation between parents and offspring is shown to be a direct consequence of the 

 fact that tliey vary by chance. This is the first and the most striking deduction 

 from the mathematical theory of organic variation, but it is not the only one. It 

 is enough, however, to show that the new method is not only a simple means of 

 describing the facts of variation, which facts very few people knew before, but it 

 is a powerful instrument of research, which ought to be quickly and generally 

 adopted by those who care for the problems of animal evolution. 



I think I have said enough to convince you how entirely Professor Pearson's 

 method promises to confirm the assertion that organic variation obeys the law of 

 chance. 



The other objections to Darwin's theory are not so easily answered. It is said 

 that small variations cannot be supposed to affect an animal's chance of life or 

 death ; but few persons have taken any pains to find out in any given case whether 

 the death-rate is in fact affected by small variations or not. It is said that the 

 process of Natural Selection is so slow that the age of the earth does not give time 

 for it to operate, but I know of few cases in which any attempt has been made to 

 find out by actual observation how fast a species is really changing. 



I can only attempt to discuss the importance of small variations, and the rate 

 of organic change, in the one case which I happen to know. The particular case' 

 I have myself studied is the variation in the frontal breadth of Carcinus tmenas} 



During the last six years my friend, Mr. Herbert Thompson, and I have studied 

 in some detail the state of this character in the small shore-crabs which swarm on 

 the beach below the laboratory of the Marine Biological Association at Plymouth. 



I will show you that in those crabs small changes in the size of the frontal 

 breadth do, under certain circumstances, affect the death-rate, and that the mean 

 frontal breadth among this race of crabs is, in fact, changing at a rate sufficiently 

 rapid for all the requirements of a theory of evolution. 



In Table IV. you see three determinations of the mean frontal breadth of these 

 crabs, expressed in terms of the carapace-length taken as 1000. You see that the 

 mean breadth varies very rapidly with the length of the crab, so that it was neces- 

 sary to determine it separately in small groups of crabs, such that the length of 

 no two crabs in a group differed by more than a fifth of a millimetre. The first 

 column of the table shows you the mean frontal breadth of twenty-five such groups, 

 between 10 and 15 millimetres long, collected in 1893. These crabs were measured 

 by Mr. Thompson. The second column shows you the mean frontal breadth in 

 twenty-five similar groups of crabs, collected in 1895, and also measured by Mr. 

 Thompson. You see that in every case the mean breadth in a group of crabs 

 collected in 1895 is less than it was in crabs of the same size collected in 1893. The 

 third column contains the result, so far as it is yet obtained, of my own measure- 

 ment of crabs collected this year. It is very incomplete, because the 1895 crabs 

 were collected in August and September, and I was anxious to compare them with 

 crabs collected this year at the same season, so that there has not yet been time 

 to measure the whole series. The measurements are suificient, however, to show 

 that the same kind of change has taken place during the last three years as that 

 observed by Mr. Thompson in the interval between 1893 and 1895. Making every 

 allowance for the smallness of the numbers so far measured this year, there is no 

 doubt whatever that the mean frontal breadth of crabs from this piece of shore is 

 considerably less now than it was in 1895 amo-.ig crabs of the same size.^ 



' In 1894 I gave an account of the variation of this dimension in female speci- 

 mens of various sizes {Roy. Soo. Proc, vol. Ivii.), and I put forward au hypothesis 

 of the amount of selective destruction due to variation in this character. That 

 hypothesis neglected several important facts which I now know, and was open 

 to other objections. I desire to replace it b}^ the results of the observations here 

 recorded. 



^ I shall of course consider it my duty to justify this statement by more extensive 

 measurement as soon as possible. In the meantime, I may say that I have measured 



^L other small groups of crabs, male and female, from the same place, at different 



^L seasons of the years 1896-1898, and the results agree with those recorded in the 



^ft table. 



■ 1898. 3 M 



