CHAPTER III 



GROWTH-CENTRES AND GROWTH- 

 GRADIENTS 



§ i. Growth-gradients within Single Organs 



SO far we have only dealt with the question of relative 

 growth in whole organs or regions of the body ; and in 

 our first chapter we have found an approximation to a 

 simple mathematical formulation of relative growth, which 

 we have called the law of constant differential growth-ratio. 

 This, as we have further seen, is what we should have expected 

 if we had worked on the problem a priori. It teaches us the 

 striking fact that relative growth-rates of different parts of 

 the body may stay constant over long periods of growth, 

 which clearly is important as a contribution to the problem 

 of form co-ordination and the orderliness of form-change, but 

 it sheds little light upon any aspect of the growth-process 

 itself. 



In this chapter, however, we shall deal with certain further 

 empirical laws or rules which will, I think, have to be taken 

 into careful consideration in any future investigation of the 

 biology and physiology of growth. It is of some interest that 

 these rules, which to my mind constitute the most important 

 part of any contribution made by me to the study of relative 

 growth, emerged quite incidentally out of the investigations 

 on differential growth-rates. In studying these latter, I had 

 a perfectly clear-cut aim — to see whether change of propor- 

 tions could be envisaged as the result of any simple laws of 

 relative growth. But of the growth-gradients to be discussed 

 in this chapter, I had no suspicion : their existence thrust 

 itself upon me as a new empirical fact, any explanation of 

 which is for the moment entirely problematical. I say a new 

 empirical fact, for although D'Arcy Thompson (1. c.) had 

 already adumbrated a similar view, for one thing he had not 

 fully generalized it or pursued its consequences to their limit, 

 and for another, it was new to me, as I had not at first grasped 



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