CHAPTER VI 



HETEROGONY, GROWTH-GRADIENTS AND 



PHYSIOLOGY 



§ i. Normal Proportions as result of a 

 Partition-equilibrium 



THIS chapter cannot but be an unsatisfactory one, for 

 the simple reason that we know so extremely little 

 about the physiological or biochemical processes 

 underlying growth in general and growth-gradients in par- 

 ticular. All that can here be attempted is to bring together 

 some of the scattered facts and indications which are in any 

 way connected with the problem. 



In the first place, as we have seen in the first chapter, there 

 are strong grounds for believing that the normal growth-ratio 

 of a heterogonic organ is in some way determined as result 

 of a balance between its size and that of the body, equilibrium 

 being attained when the formula y = bx k is satisfied. When- 

 ever y < bx k , the growth-ratio of y (the heterogonic organ) 

 is accelerated (k^. ^>k), and becomes normal once more (= k) 

 when the organ reaches the size demanded by the original 

 formula. The organ can become smaller than its size for 

 growth-equilibrium in a number of ways. The most obvious 

 is by amputation of the organ, in types where regeneration 

 is possible. Its regenerative growth-ratio is then much more 

 rapid than its normal growth-ratio would have been, and 

 gradually slackens down until it becomes normal with the 

 attainment of proper relative size by the organ. This is only 

 a special case, for all organs, whether heterogonic or not, 

 appear to exhibit the same behaviour during regeneration. 

 Przibram (1917) has in mantids given a beautiful analysis of 

 the way in which the excess growth-ratio falls away to normal 

 as regeneration proceeds. The close approximation of his 

 results (p. 51) to the laws governing the flow of E.M.F. 

 between regions of differing electric potential is a further 



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