THE COEFFICIENT OF GROWTH-PARTITION 53 



carapace length, mm 

 13 16 20 



a characteristic eye-size towards the attainment of which the 

 rate of eye-growth is regulated. 1 



In general, as is well known, 

 the rate of regeneration is higher 

 the more material is removed. 

 This fits in with the ideas here 

 presented and with the concep- 

 tions of Przibram (1. c), but it 

 throws into relief the very real 

 difference between the idea of 

 a constant differential growth- 

 ratio and a constant coefficient 

 of growth-limitation. Let us 

 consider a Planarian worm, in 

 which according to Abeloos (I.e.) 

 the trunk grows heterogonically 

 with reference to the head. 

 During normal growth the rela- 

 tion is one of a constant differ- 

 ential growth-ratio. But dur- 

 ing regeneration, the more is 

 cut off, the more rapidly regen- 

 eration takes place : i.e. the 

 smaller the fraction of the body 

 left, the more rapid is the 

 growth-ratio of the regenerate. 

 What is constant is the final 

 partition-coefficient between 

 head-material and trunk- 

 material ; the normal constant 

 differential growth-ratio is the 

 special case of growth during 

 which the partition-coefficient 

 is always of this limiting value. 



Finally, the case of Inachus, 

 investigated by G. Smith (1906A) 

 whose data have been further 

 analysed by me (unpublished) 

 also supports this view-point. At Naples, /. mauritanicus , the 

 species of Inachus studied by Smith, shows three forms — ' low ' 



1 Further details as to the specific growth-intensities of eyes and 

 other organs when heteroplastically transplanted are recorded in 

 Chapter VI. 



Fig. 32.- — Chela breadth against 

 carapace length in the male of the 

 spider-crab, Inachus mauritanicus ; 

 logarithmic plotting. (See Table 

 IIIa.) 



The ' low ' males (below about 14 mm. cara- 

 pace length) and the ' high ' males (above about 

 20 mm.) fall on a single curve with diminishing 

 growth-coefficient (mean value of k over 2-3 ; 

 for ' low ' males, about 2-6; for 'high' males, 

 about 1-4). Between these sizes the chela 

 regresses to a narrow female type, then enlarg- 

 ing again with a very high growth-coefficient. 



(Constructed from the data of G. W. Smith, 1906A.) 



