SECT. 2] AND WEIGHT 405 



value is a true measure of the former, "There are other and perhaps 

 more significant phenomena", said Murray, "than the growth rate, 

 which change with age." 



Murray himself proposed the use of a variant of the usual Minot 

 curve by differentiating twice instead of once so as to get the ac- 

 celeration and not the velocity. Thus, after having found the per- 

 centage growth-rate by the equation 



dt[_w\ t' 



where K ^ 3-6, he went on to find the negative acceleration for each 

 day during embryonic growth : 



dw 



d 

 dt 



dt 



= - Kt^. 



This value, so obtained, is, as it were, the negative increment of 

 the percentage growth-rate, and shows a regularly declining curve 

 (for the chick) as in Fig. 44. Such a curve must obviously suffer 

 from the same disadvantages as the curve from which it is derived, 

 and does not escape from Brody's criticism that the arbitrarily 

 chosen time-units are incommensurable at different developmental 

 stages. 



In 1922 Przibram observed that in many cases of post-embryonic 

 growth the curve obtained by calculating according to Minot's 

 method was extremely like a regular hyperbola, but he did not find 

 that this was true for any example of embryonic growth. We shall 

 see later what further use of this idea has been made, 



2-6. Yolk Absorption-rate 



Another way of regarding embryonic growth (of a lecithic Ggg) 

 is to concentrate attention on the whole system, instead of upon 

 the growth of the embryo alone. It was in this way that Gray 

 treated the development of the trout embryo in the paper already 

 mentioned (p. 369 and Appendix i). He assumed that the rate of 

 growth of the embryo was proportional to the dry weight of the 

 embryo and to the dry weight of the remaining yolk. This idea had 

 already been introduced for the trout by Kronfeld & Scheminzki 

 (see p. 369 and Fig. 41) but Gray's figures were much more complete, 

 and showed very clearly a falling off of growth towards the end of 



