258 PROBLEMS OF RELATIVE GROWTH 



testis and pituitary. The identical growth-coefficient of the 

 pituitary in both races indicates that body-size here must 

 primarily depend upon other factors than relative pituitary size. 



Robb concludes with an interesting theoretical discussion, 

 which cannot be summarized here. One point deserves 

 mention : if an organ has a certain fraction in active hetero- 

 genic relation with the body, but also an inert fraction which 

 is isogonic, then the formula for its growth will be y = bx -+- c. 

 In some cases apparently irregular heterogony curves could 

 be made to conform to the simple heterogony formula by 

 correcting for such an inert fraction ; but this for the moment 

 remains speculative. 



Werner (1927) gives an elaborate discussion of form-changes 

 in the Cladoceran Macrothrix rosea. Certain parts appear to 

 show positive, others negative heterogony. But the growth- 

 changes are often complex, and would appear to indicate the 

 existence of elaborate gradient-fields controlling growth. 



Anderson (193 1) finds that the simple heterogony formula 

 applies to the growth of various parts in the Cladoceran 

 Daphnia magna. Interestingly enough, while carapace length 

 is positively heterogonic (relative to total length) until the 

 time of maturity, after which it becomes isogonic or slightly 

 negatively heterogonic, carapace height shows positive heter- 

 ogony throughout life, although its growth-coefficient is lower 

 after maturity. 



Adolph (1930) has an interesting note on the interrelated 

 effects of size and age upon metamorphosis in unoperated 

 frog larvae. He finds that for a given brood, (W — d) (A — e) 

 is a constant, where W is body- weight at completion of meta- 

 morphosis, A the age in days at which forelimbs appeared, 

 and d and e are constants. Thus no increase of size would 

 permit metamorphosis to occur before e days, but meta- 

 morphosis would never occur if the animal never attained to 

 body-weight d. We may conclude that the growth of the 

 thyroid (or of the thyroid-controlling agency of the pituitary) 

 normally shows a heterogonic relation to absolute size ; but 

 that time also, within limits, promotes its growth (see p. 39, n.). 



Further evidence of change of proportions with change of 

 size in termites (see p. 65) is afforded by the work of Light 

 (1927). In this paper he confined himself to the soldier caste 

 of Coprotermes. Thirteen species of different absolute size 

 were measured. There was no correlation between absolute 

 size and certain characters such as the length-width ratio of 

 the head. But there was for other characters, e.g. the ratio 



