722 PATTERNS AND PROBLEMS OF DEVELOPMENT 



differ in certain organs of the two sexes, male and female chelae of cer- 

 tain decapods, for example, or even on the two sides of the individual 

 body, in decapods with unequal chelae. Although the growth gradients 

 of later stages may differ widely from the gradient patterns of early de- 

 velopment, it appears, beyond question, that they are in some way re- 

 lated to, and developmental consequences of, the earlier pattern and the 

 specific constitution of the protoplasm in which it appears. 



SOME OTHER ASPECTS OF GROWTH PROBLEMS 



Certain inorganic systems which show a sort of growth and develop- 

 ment have often been compared with growth and form in organisms. 

 The analogy of crystal growth and reconstitution of form to organismic 

 growth has been pointed out repeatedly, and a crystalline structural pat- 

 tern has been postulated by some biologists as the basis of developmental 

 pattern."^ Various physicochemical experiments have been devised in 

 which diffusion and precipitation of inorganic substances in a colloid 

 substrate result in growth, often definitely directed, of a precipitate and 

 development of form. Inorganic "cells" have been made, and various 

 simulations or models of cell form have been produced, with inorganic 

 substances. The Liesegang rings, patterns resulting from diffusion and 

 precipitation of inorganic salts in a gel substrate under certain conditions, 

 have been regarded by some as highly significant in relation to organismic 

 form. Under certain conditions surface tension may be a factor in pro- 

 ducing definite form. Tension and pressure influence growth and are es- 

 sential factors in determining form of various parts of organisms. The 

 book Growth and Form by D'Arcy Thompson (191 7) presents a most in- 

 teresting and valuable discussion of these data and of the physical char- 

 acteristics and problems of growth.^ 



Mathematical analyses of various aspects of growth and form in organ- 

 isms have produced many interesting results which cannot be discussed 

 here. Certain of them, particularly those having to do with organismic 

 form, are presented in Thompson's book. A recent analysis of differential 

 or relative growth, that is, of gjowth rates of parts or organs in relation 

 to rate of the whole organism, formulates a law of constant differential 



7 See pp. 5, 296, 394, 629, 694. 



8 See also Liesegang, 1907, and other papers for periodic patterns resulting from diffusion 

 of salts in a colloid substrate, and the summary by Zeiger, 1939, of papers concerned with pat- 

 terns of this type. Various inorganic growth patterns and sunulations of organismic growth 

 and form are described by Leduc (1910). 



