RELATIONS OF ANIMAL MORPHOLOGY 255 



The fact that few morphologists have a taste for mathematics 

 cannot stay the inevitable trend of the science toward greater pre- 

 cision of expression and toward mathematical analysis. Until recent 

 years characteristics have been described only in the crude language 

 of adjectives and adverbs where greater precision is necessary, 

 quantitative expression is inevitable. So we have seen during the 

 past ten years the rise of biometry and its application to many mor- 

 phological problems. Biometry had its beginning in the suggestive 

 investigation of Galton; its great development in the last ten years 

 has been due, above all, to the tremendous activity of Karl Pearson 

 and the workers he has gathered about him. By the aid of efficient 

 methods of analysis we are able to state quantitatively not only the 

 mean value of any measurable characteristic, but also the degree 

 of its variability and the closeness of associated variability of two 

 interdependent organs. Moreover, it is possible to study the nature 

 of the variability exhibited by any characteristic in any homogeneous 

 lot of individuals and to draw an inference from the nature of this 

 variability as exhibited in the variation polygon concerning the 

 condition of the characteristic in question in the given race. A person 

 of experience can tell from a glance at the variation polygon whether 

 the race is in a condition of equilibrium so far as this characteristic 

 goes, or whether it is breaking up into several forms, or is, perhaps, 

 evolving into some other condition. The quantitative expression 

 gives a means of measuring change of the mode from epoch to epoch 

 which Weldon used in studying the crabs at Plymouth, and which 

 enabled him to demonstrate a progressive change in form. It gives 

 also a means of measuring the alteration of an organ in different en- 

 vironments, and so of estimating the effects of changed external con- 

 ditions. Thus it has been shown that the modal number of ray flowers 

 in the ox-eye daisy depends upon the conditions of nutrition in the 

 soil; the chela of the male crab, Eupagurus, is relatively smaller in 

 deep Avater; the mud-snails, Nassa, of brackish water are depauperate. 



Again, mathematical methods have given us a measure of the corre- 

 lation between organs, so that, the exact relation between human 

 stature and the length of a long bone being known, the stature of ex- 

 tinct races may be calculated from a collection of disinterred femurs. 

 Pearson has been able to show that there is no correlation between 

 shape or size of the head and intelligence, and to demonstrate the 

 efficiency of vaccination and the non-inheritableness of cancer. The 

 opinion that various bodily characteristics are bound together has 

 been substantiated by studies in the correlation of all sorts of organs 

 in plants and animals and the degree of this correlation measured. This 



There is also one journal devoted exclusively to biometry, Biometrika, published 

 in London and edited by Pearson, Weldon, and Davenport, with the advice of 

 Francis Galton. 



