164 PROBLEMS OF RELATIVE GROWTH 



depends upon the numerical values of the one, two or three 

 main growth-ratios concerned in the production of conical, 

 true logarithmic-spiral, or sheared (turbinate) logarithmic- 

 spiral form respectively. 



Thus the essential growth-mechanism underlying the auxo- 

 differentiation stage of development of a single appendage 

 (chela, vertebrate limb), a series of appendages (hermit-crab, 

 stag-beetle), a region of the body (brachyuran abdomen), a 

 rhinoceros horn, a vertebrate tooth, or a molluscan shell, are 

 all of the same fundamental nature. In every case we find 

 constant differential growth-ratios, and these are arranged in 

 growth-gradients culminating in growth-centres. If we wish 

 to think analytically about organic form and proportions, we 

 must think in terms of constant differential growth-ratios organ- 

 ized in the form of growth-gradients. And if we are ever to 

 solve the problem of growth physiologically, we should do well 

 to concentrate on discovering the biochemical basis for growth- 

 centres and the physiological reasons for the graded distribution 

 of growth-potential on either side of these centres. 



