896 



REPORT — 1898. 



on one side of the mean than on the other ; and the selective destruction necessary 

 in order to raise the mean number of glands by one would be very different from 

 the amount of destruction necessary in order to lower the mean by one. Further, 

 the mean number of glands in these pigs is 3^ ; the number which occurs oftenest, 

 the 'modal ' number as Professor Pearson calls it,' is three. Now it is impossible to 

 lower this number till it is less than 0, so that it can only be diminished by three ; 

 but it is conceivable that it should be increased by more than three. So that the 

 amount of selective destruction required in order to change either the mean or the 

 modal character of these pigs in one direction would be greater than the amount 

 required in order to produce a change of equal magnitude in the opposite direction, 

 and the amount of possible change is greater in one direction than in the other. 



Now let us pass on to another example. 



Table III. shows the variation in the number of petals in a race of buttercups 

 studied by Professor de Vries. You see that the most frequent number of petals 

 is five, and that no buttercups whatever have less than five petals, though a con- 

 siderable number have more than five ; and here again you see the way in which 

 Profes.sor Pearson's formula fits the observations. 



Table III. — Professor Pearsons expression for the variation in the race of 

 Buttercups described by Professor de Vries. 



You see that if this table (which is based on very few specimens) really 

 represents the law of variability in these buttercups, no amount of natural or other 

 selection can produce a race with less than five petals out of them. While it is 

 conceivable that selection might quickly raise the normal number of petals, it 

 could not diminish it, unless the variability of the race should first change.- 



These examples, which are typical of others, must suffice to show the way in 

 which the theory of Chance, as developed by Professor Pearson, can express the 

 facts of organic variation. 



I think you will agree that they also show the importance of investigating 

 these facts. For of the four characters we have examined, we have seen that two — 

 namely, human stature and the antero-lateral carapace-length of Carcinus mosnas — 

 vary so as to afford nearly equal material for selective modification in either 

 direction ; one character, the number of Muller's glands in swine, offers distinctly 

 greater facility for selective modification in one direction than in the opposite 

 direction; and the last character, the number of petals in a race of buttercups, 

 appears to ofler scope for modification in one direction only, at least by selection in 

 one generation. 



Knowledge of this kind is of fundamental importance to the theory of Natural 

 Selection. You have seen that the new method given to us by Professor Pearson 

 afibrds a means of expressing such knowledge in a simple and intelligible form ; 

 and I, at least, feel very strongly that it is the duty of students of animal evolution 

 to use the new and powerful engine which Professor Pearson has provided, and to 

 accumulate this kind of knowledge in a large number of cases. 



1 know that there are people who regard the mode of treatment which I have 

 tried to describe as merely a way of saying, with a pompous parade of arithmetic, 

 something one knew before. This criticism of Professor Pearson's work was 

 actually made to me the other day by an eminent biologist, whose name I will not 



' All attempts to confine the word ' average ' to the most frequently occurring 

 magnitude, and the word ' mean ' to the arithmetic mean of the series, have failed to 

 secure support. Therefore Professor Pearson's proposal to call the value which 

 occurs ofteuest the ' mode ' is very useful. 



2 Of course we know that selection does change thv3 variability of a race. 



