1897] THE SCIENTIFIC MEASURE OF VARIABILITY 111 



What is it then that I have asserted ? Simply this, that if it 

 be necessary to compare the variability of the same organ in two 

 sexes which have on the average different sizes, it is absurd to use 

 absolute variations. This conclusion is nothing new ; it has long- 

 been familiar to craniologists and anthropologists. They have, for 

 instance, compared brain-weight relative to body-weight or to 

 stature. I contend that the proper measure is the percentage 

 variation on the mean. My words are, " I hold that the only 

 useful sense in which we can study relative variability is by 

 endeavouring to answer the problem. Is one sex closer to its 

 mean, more conservative to its type than the other? and that 

 the only scientific answer to this lies in the magnitudes of the 

 percentage variations of the two sexes for corresponding organs." 

 It will be seen at once that this is not, as Professor Weldon appears 

 to misinterpret it, an assertion of a single scientific measure of 

 variability but a statement of opinion as to the only useful way 

 in which we can compare in the two sexes the relative variability 

 in the same organ. Professor "Weldon, indeed, seems to confuse 

 two things, the scientific measure of variability and the effectiveness 

 of this variability for different organs in the struggle for existence. 

 Because the variability of one organ is said to be twice that of 

 another organ, it does not follow that the functional importance is 

 doubled. The scientific measure of variability is one thing, the 

 effectiveness of this amount of variability in the struggle for exist- 

 ence is another and different thing. But even here I am prepared 

 to assert, although I have not done so in my paper, that the co- 

 efficient of variation, without being proportional to the " effective- 

 ness," is far more reasonable as a measure of effectiveness, when we 

 are dealing with the same organ in different sexes, or in individuals 

 of the same sex at different ages, than absolute variation. It seems to 

 me that the non-regard of this point has led to the nugatory character 

 — not of the splendid system of measurements on crabs made by Pro- 

 fessor Weldon — but of several of the conclusions he has endeavoured 

 to base upon those measurements. I cannot get over the fact that 

 the variation of an inch in the leg of a pony is not the same thing 

 as a variation of an inch in the leg of a horse. Out of the 155 

 cases dealt with in my paper, woman is in 62 or 63, I think, 

 absolutely more variable than man, and man absolutely more 

 variable in some 85 ; in the remainder the sexes are sensibly equal. 

 But since woman is smaller than man in the weight and size of nearly 

 all organs, absolute variability can only be adopted with the same 

 justification as we should say that an inch is the same variation in 

 the leg of a pony or a horse, -or a cubic centimeter the same varia- 

 tion in the capacity of the brain of a man or a new-born infant. 



If Professor Weldon asserts that taking the co-efficient of variation 



