178 PROBLEMS OF RELATIVE GROWTH 



comb's regression-curve is parabolic, being represented by 

 the formula 



L=1 + |C(0+O 2 



where L is the length of the comb after the lapse of time t 

 from the onset of regression, I the final length at the end of 

 regression, 6 the total time taken for regression, and C a 

 constant (varying from individual to individual). This is of 

 some interest, as body-size does not enter into the formula 

 at all. The converse curve, of comb-growth produced by 

 injection of male sex-hormones in capons has been recently 

 determined by Blyth, Dodds and Gallimore (1931). The 

 authors do not discuss this aspect of their work, but plotting 

 their data shows that the curves for re-growth are quite 

 different from Pezard's curves for regression. They show a 

 well-marked point of inflexion and are often very regular. 

 They could be represented by an expression of the form 

 x = A + B# 2 — Cx 3 , which is equivalent to saying that 

 Robertson's autocatalytic growth-formula would apply to 

 them. It is interesting to find this difference between the 

 positive and negative aspects of the same growth-process. 



Grafts of female comb or wattles on to male hosts become 

 larger than similar grafts on hosts of their own sex (Kozelka, 

 1930). The response of the comb to the sex-hormone is 

 brought about by a specific mucoid layer in the dermis 

 (Hardesty, 1931) : i.e. this is the true heterogonic tissue. 



A great deal has been written as to the ' all-or-none ' law 

 of the action of the sex-hormones on comb-growth, some 

 writers, like Pezard, maintaining that it holds, others, like 

 Benoit, opposing the idea. It would appear that Benoit is 

 correct, but that the range over which the action of the sex- 

 hormones is proportional to its amount is very limited. Above 

 this point, the maximum reactivity of the comb has been 

 reached, and increase of testis-size is not followed by further 

 increase of comb-size. 



That the matter need not be so simple as this, however, 

 is shown by experiments on mammals. Collip (1930), by in- 

 jecting a particular fraction of placenta-extract into rats, has 

 produced in both sexes accessory sexual organs (seminal 

 vesicles, vagina, etc.) far exceeding in absolute and relative 

 size anything normally found in the species ; on the other 

 hand, injection of anterior pituitary (in females) causes an 

 acceleration of maturity but without disproportionate size of 



