RELATIVE GROWTH AND RECAPITULATION 235 



latory phenomenon follows automatically. Similar reasoning 

 will apply to such cases as the negative heterogony of the tail 

 of fetal man or positive heterogony of the toes of the Jacana 

 after hatching (Beebe ; see p. 262). 



As regards vestigial organs, the arm-chair critic often 

 demands of the evolutionist how the last stages in their reduc- 

 tion could occur through selection, and why, if reduction has 

 gone as far as it has, it could not go on to total disappearance. 

 In the light of our knowledge of relative growth, we may 

 retort that we would expect the organ to be formed of normal 

 or only slightly reduced relative size at its first origin, but 

 then to be rendered vestigial in the adult by being endowed 

 with negative heterogony. If rate-genes are as common as 

 they appear to be, then what we have called the line of bio- 

 logical least resistance would be to produce adult vestigiality 

 of an organ by reducing its growth-coefficient. So long as it 

 is reduced to the requisite degree of insignificance at birth 

 (or at whatever period a larger bulk would be deleterious), 

 there is no need for reduction of its growth-rate to be pressed 

 further. But the negative heterogony with which it is endowed 

 will continue to operate, and it will therefore continue to 

 grow relatively smaller with increase of absolute size. This 

 last fact may account for the apparently useless degree of 

 reduction seen in some vestigial organs, e.g. that of the whale's 

 hind-limb. The degree of reduction may be useless considered 

 in relation to the adult, but the relative size in the adult may 

 be merely a secondary result of the degree of negative heter- 

 ogony needed to get the organ out of the way, so to speak, 

 before birth. In addition threshold mechanisms will possibly 

 be at work, so that the organ, after progressive reduction, 

 eventually disappears entirely. 



In such cases quite small differences in growth-ratio, if the 

 range of absolute size over which they operate is considerable, 

 will make quite large differences in final relative size, a fact 

 which indubitably will help to account for the high variability 

 of vestigial organs. Even when the organ itself never grows, 

 as in the imaginal structures of insects with a metamorphosis, 

 a similar degree of variability may be brought about by 

 relatively small variations in the rate-genes responsible. As 

 Goldschmidt has shown by his classical researches on sex 

 in Lymantria, the end-result in such cases depends on the 

 amount of some effective substance produced by the gene at 

 the critical period for differentiation of the organ affected. 



