138 PROBLEMS OF RELATIVE GROWTH 



evolutionary changes in proportion of parts which are difficult 

 to account for solely on variations in the time-relations of early 

 development. (E.g. increase in relative length of arm without 

 a corresponding change for the leg : the fact that the ratio 

 of radius/humerus increases during ontogeny, and increases 

 most in those animals in which it is highest in adult life, which 

 are, further, those with the greatest relative length of the 

 arm). Further, the work of Hammond on sheep previously 

 cited (p. 88) is conclusive proof that growth-gradients as defined 

 by me do exist in vertebrates and may even change their 

 sign, late in development, long after the embryonic period 

 is over ; while the disturbances of proportions which occur 

 in conditions due to glandular abnormality (e.g. acromegaly) 

 cannot originate in the embryonic period when there are no 

 functional ductless glands, but must be due to changes in 

 growth-intensity of parts during foetal and post-natal life. 



And the analysis of Lapicque (1907) and Dubois (1922) shows 

 that the growth of some organs at least, such as the brain, 

 do not take place according to a linear but to an exponential 

 function of body-size. My tentative conclusion would there- 

 fore be that in man as in other forms, the law of developmental 

 direction is of great importance, exerting effects on propor- 

 tionate size of parts long after it has actually ceased to be 

 at work in the early embryonic period, but that heterogony 

 of parts associated with gradients in actual growth-intensity 

 also operate during the whole of the later period of auxano- 

 differentiation. It must suffice here to point out the simi- 

 larity between these and the results obtained by Abeloos (1. c.) on 

 Planaria. The existence of an identical type of growth-gradient 

 in two such remote types as a flatworm and a mammal is striking. 



It should also be pointed out that the gradients revealed 

 by Scammon's figures are capable of modification and even 

 reversal. In the limbs of man, the gradient in male and 

 female must clearly be quantitatively different, in order to 

 produce the relatively smaller hands and feet of the female. 

 In women, further, the main body-gradient is clearly altered 

 by the accentuation of growth in the pelvic region, apparently 

 associated with diminished growth in the region of the shoul- 

 ders ; and the partition of growth-potential between trunk 

 and extremities appears to be shifted slightly in favour of 

 the trunk in the male as in Crustacea, e.g. Eupagurus (Bush, 1. c.) 

 and Gammarus (Kunkel and Robertson, I.e.). A case of 

 reversal of the limb-gradient has already been referred to in 



