1897] KARL PEARSON ON EVOLUTION 53 



to answer the problem : Is one sex closer to its mean, more con- 

 servative to its type, than the other ? and that the only scientific 

 answer to this lies in the magnitude of the per centage variations of 

 the two sexes for corresponding organs." 



The meaning of this may be made clear by an example. Suppose 

 a number of sticks, about a yard long, to be chosen by some rough 

 process of measurement ; and suppose that more careful examination 

 showed the average length of these sticks to be 3 feet, while half 

 the sticks were between 2 feet 1 1 inches and 3 feet 1 inch in 

 length. Suppose, further, a second group of sticks, whose average 

 length is G feet, while half the sticks lie between 5 feet 10 inches 

 and 6 feet 2 inches. Now, since one inch is the same fraction of 

 three feet that two inches is of six feet, Professor Pearson asserts that 

 the only scientific view of the variability of the two sets of sticks is 

 that which treats the two bundles as equally variable ; and he 

 accordingly defines the " coefficient of variation," or measure of 

 variability, as the ratio of the " Standard Deviation " or " Error of 

 Mean Square " to the Mean. 



Now, it may at once be freely admitted that the coefficient of 

 variation, as above defined, is an exact measure, and probably the 

 best available measure, of the degree to which a group of animals is 

 " close to its type " ; that is to say, it is a measure of the extent 

 and frequency of the mistakes a man would make, if he should 

 simplify a discussion of these animals by using, instead of the 

 individual animals, a series of perfectly average " types." It is 

 precisely the measure of accuracy of the customary morphological 

 definition of a species or variety. But the student of evolution may 

 have to concern himself with another measure of variability, when 

 he asks not " how close is the race to its type," but " how much 

 material for Selection is afforded by the variability of the race ? " 



The functional importance of a variation of known magnitude, 

 and the effect of such a variation upon the selective death-rate, 

 seem legitimate, if difficult, subjects of scientific inquiry ; and if it 

 can be shown that an organ in one sex gives more scope for the 

 selective formation of varieties or races than does the corresponding 

 organ in the other sex, it is surely legitimate (neglecting the possible 

 complications due to peculiarities of heredity) to say that one sex 

 is more variable than the other. For example, it is certainly 

 possible, in the case of the common fowl, to produce races of cocks 

 which differ more from each other in the length of their tail- 

 feathers than do any hens yet produced ; and the statement, that 

 the tail of cocks in general is more variable than the tail of hens in 

 general seems thereby justified, whether the " coefficient of variation " 

 in the cocks of any one race be greater than that of the corre- 

 sponding hens or not. 



