432 PRINCIPLES OF EMBRYOLOGY 



of the toes. The different toes do not react equally, and although they fall 

 roughly into order from more sensitive to less sensitive, the effects are 

 somewhat irregular as between different animals Tschumi foimd that if a 

 toe were reduced below a certain minimal size at the time of its first 

 appearance it did not persist in later development but eventually dis- 

 appeared, probably owiug to a process of the nature of competitive inter- 

 action, by which the other toes drew away from it all the available supplies 

 of essential metabolites (cf. Lehmann 1953). Thus four-toed or three-toed 

 conditions may arise secondarily, if there is a sufficient disparity in size 

 in the digits as they are originally formed. 



One cannot close even such a short discussion of animal pattern as this 

 without referring to the famous work of D'Arcy Thompson, On Growth 

 and Form (19 16). By showing that many animal forms share certain mathe- 

 matical properties with shapes that are known to arise in the inorganic 

 world, D'Arcy Thompson had a most important influence, both in per- 

 suading biologists that form offers a problem which should be analysed 

 in causal terms, and in making it seem not too impossibly difficult for 

 such an analysis to be carried out. These services were very great ones; 

 but nevertheless nearly all this task of understanding remains for the 

 future. A large part of D'Arcy Thompson's work dealt with one special 

 category of forms, namely those of simple cells and of small groups of 

 cells. Even if one accepted his discussion, which is framed in terms of the 

 surface tension of liquid films — and would nowadays be rejected by many 

 who feel that the cell membrane cannot be regarded as a liquid — still one 

 would be forced to admit that the principles he discussed throw little 

 light on the initiation of a pattern such as that of a pentadactyl limb. 

 Again, he discussed the forms that arise from particular types of differ- 

 ential growth, such as that which causes the shell of a gastropod or a 

 cephalopod to be twisted into a spiral; but interesting though that is, it 

 leaves unsolved the fundamental question of how the pattern of differ- 

 ential growth rates arises in the first place. The most essential problem of 

 form is one which cannot be approached by a mathematical analysis of 

 the ways in which animal shapes become transformed during develop- 

 ment. It is the question of how form originates from the formless, and 

 demands either an experimental attack or a mathematical analysis of a 

 different kind, perhaps similar to that begun by Turing. 



Perhaps the most cheering thing that can be said about the problem of 

 form is that it does not, perhaps, pose itself in its full intensity as often as 

 might appear at first sight. The majority of animal forms develop out of 

 something which already has some degree of pattern within it. For 

 instance, an egg, as we have frequently seen, is by no means the com- 



