EMBRYONIC GROWTH 139 



Hammond's sheep (p. 88) : here, before birth, the normal 

 effect must have been proceeding ; but after birth the distal 

 regions increase least, the proximal regions most, with a graded 

 effect in between. 



Thus in the vertebrate body again, we would appear to 

 be dealing with a primary gradient effect, doubtless correlated 

 with Child's physiological or axial gradients, which auto- 

 matically has an effect upon growth, and secondary modi- 

 fications of this, imposed to effect growth in biologically 

 advantageous ways. (See also Bray's work, p. 259.) 



§ 7. The Mathematical Formulation of Relative 

 Growth in Embryonic Life 



Organs developing according to the law of antero-posterior 

 development are special cases of the more general rule that 

 during early development different organs do not originate 

 at the same time. They constitute the most abundant of 

 such cases, and have particular interest, e.g. in relation to 

 gradient theories. But from the point of view of formulating 

 qualitative rules of relative growth, they remain special cases 

 of the more comprehensive rule. 



This problem has only been adequately attacked by Schmal- 

 hausen (1927A, 1927B, 1930), and in what follows I can do little 

 save summarize his views and to comment briefly upon them. 



It is an obvious fact of observation that organs or parts 

 of the body in general grow more rapidly when first formed, 

 and that their absolute growth-rate (when external factors 

 such as temperature are kept constant) diminishes progress- 

 ively with time. Our previous method of establishing the 

 coefficient of relative growth for an organ by comparing its 

 size with that of some standard representing the measure of 

 the rest of the body at different absolute sizes, is completely 

 valid only on the assumption that the organ and the standard 

 part begin their careers simultaneously, so that the decrease 

 of absolute growth-intensity proceeds pari passu in both, 

 and time can therefore be neglected. Even when the origins 

 are not simultaneous, it will, however, usually provide 

 a close approximation when we are dealing with the later 

 stages of growth, for then the difference in time of origin 

 between organ and standard will be negligible in comparison 

 with the time that has since elapsed. This point is brought 

 out by Schmalhausen himself, who gives some theoretical 

 calculations on the subject (1927B, p. 41, etc.). 



