no PROBLEMS OF RELATIVE GROWTH 



has a straighter skull, with higher nasal region, than demanded 

 by theory : and he therefore suggests that this form is not on 

 the direct line of equine descent. The genus Parahippus is 

 generally recognized as ancestral to Equus (see Matthew, 1926), 

 but it contains a number of ' widely varying distinct species ' 

 (Matthew, 1. c, p. 160). We may therefore agree with Thomp- 

 son that the particular species he has figured is an aberrant 

 type. This is a remarkable achievement, and clearly provides 

 a new method in detailed paleontological research, which is 

 clearly of real value. 



If, however, a way could be found of taking account of the 

 changes in absolute size which so frequently accompany direct- 

 ive evolution, and automatically induce changes in proportions 

 of limbs, etc., a further analysis might be possible, which would 

 enable us to distinguish what we might call the consequential 

 changes in form from the strictly adaptive, meaning by the 

 former those changes in proportions which, unless counter- 

 acting growth-mechanisms are evolved, automatically accom- 

 pany change of size, and by the latter such changes as are 

 specifically related to mode of life, and presumably are brought 

 about by natural selection (which, of course, in such case must 

 act via the genes which control the growth-gradients). But 

 of these and other evolutionary bearings of the existence of 

 growth-centres and growth-gradients I shall deal more fully 

 in a later chapter. 



The graphic method of D'Arcy Thompson enables us to 

 postulate that orderly growth-gradients must exist in the 

 body as a whole, though from his figures it is further clear 

 that the main system of gradients need by no means be so 

 simple as in the case of Orthagoriscus, but that a number of 

 gradients may be combined even along a single axis of the 

 body ; further, that minor gradients may be locally super- 

 posed upon major ones ; and that the various components of 

 the system as a whole appear to interact with and modify 

 each other. 



§ 2. General Growth-gradients : Quantitative Analysis 



Our further task is to try to find out whether these growth- 

 gradients can be expressed, even approximately, in quanti- 

 tative terms, and whether we can discover any empirical 

 rules concerning the nature of the influence exerted by one 

 gradient upon another. To do this is no easy task, for it 

 demands quantitative measurements, either of mass or linear 



