CONCLUSION 243 



§ 8. Conclusion 



We have now completed our brief survey. Starting from 

 the fact of obviously ' dysharmonic ' or heterogenic growth, 

 we have discovered our first new empirical law — the law of 

 constant differential growth-ratio. We have then recognized 

 that it is only a special case of the law of differential growth- 

 partition, which is the prime quantitative basis of relative 

 growth. Passing on from that, we have found a further and 

 quite unexpected empirical law — that the existence of a 

 differential growth-ratio in an organ or region seems always 

 to be associated with a growth-gradient culminating in a 

 growth-centre ; or in other words, that the distribution of 

 growth-potential is not marked by discontinuities or by 

 frequent oscillations, but occurs in an orderly and continuously 

 graded way. And we then showed that these localized growth- 

 gradients were but special cases of growth-gradients permeating 

 the whole body. These laws, however, only appear to apply 

 to the stages of growth occurring after histological differentia- 

 tion has been completed. Very rapid growth, obeying quite 

 other laws, occurs during the earlier period. For these two 

 phases of development, the terms histo-differentiation and 

 auxano-differentiation are proposed. 



After demonstrating that these growth-gradients were opera- 

 tive both in multiplicative and accretionary growth, giving 

 rise to structures as dissimilar as a crustacean chela or a 

 fowl's comb on the one hand, and a Nautilus shell or a rhino- 

 ceros horn on the other, we made it probable that the growth- 

 gradients were either directly or indirectly correlated with 

 the morphogenetic gradients or fields of Child, Weiss and others, 

 and in general with the various polarized and field effects in 

 the animal body. 



In a discussion of the obscure subject of the physiological 

 basis of growth-gradients, we discovered that the existence 

 of a single appendage with high growth-ratio is associated 

 with a slight increase of growth in the regions immediately 

 posterior to it, but a slight decrease in those immediately 

 anterior. The meaning of this remains quite unknown, but 

 it has certain parallels in the field of regeneration and of 

 experimental embryology. Further, the study of relative 

 growth confirms that of regeneration in making us believe 

 that the relative growth-rate (differential growth-ratio) of a 

 part is determined in some way as an equilibrium between 



