SECT. 2] AND WEIGHT 417 



Crozier would only be true if the chick embryo, for instance, began 

 as a kind of watery ghost of dimensions equivalent to those it normally 

 has at hatching, and if development consisted in the gradual accu- 

 mulation of solid substances within it. This singular kind of pre- 

 formation certainly does not exist in reality. Snell developed another 

 equation, ^ 



(where A is the initial amount of substrate, x the amount of end- 

 product at time /, ex the corresponding concentration at time t, 

 Vq the volume of the organism at the beginning of the growth- 

 cycle, and iTi and K^ the velocity constants as before), which 

 he regards as the correct form for the representation of an auto- 

 catalysed monomolecular reaction in which the conditions are 

 similar to those in a growing animal, or in other words, where the 

 volume occupied by the reagents increases in proportion as the 

 end-product increases. Snell then showed that the curves obtained 

 by this equation did not resemble any of the empirical growth- 

 curves in the literature, and therefore concluded that there is no sound 

 basis for assuming that the master reaction is either monomolecular 

 or autocatalytic. Thus in the case of embryonic growth, where 



X 



— is almost constant, the curve approximates to that of a non- 



autocatalysed monomolecular reaction, and again to nothing that 

 is given by any actual embryo. 



In any case the only instance where a sigmoid curve has been shown 

 to fit the growth of an individual foetal organ is in the work of Faure- 

 Fremiet & Dragoiu on the lung of the embryo sheep. 



Robertson's point of view was adopted in the earlier work of Brody 

 and his collaborators, who, however, introduced new viewpoints 

 into it. Instead of plotting the absolute weights of the embryo 

 against time, they plotted the increments per time-unit, thus ob- 

 taining curves similar to those in Fig. 34 above. Obviously, in 

 a case where the absolute growth-curve was S-shaped, these incre- 

 ment curves would be doubly S-shaped, rising to a maximum at 

 half-time and thereafter falling away. Or, put mathematically, 

 from the differential equation 



I =Kx{A- x) 



NEI 27 



