I dt_ 



\ w 



=-k 



424 ON INCREASE IN SIZE AND WEIGHT [pt. iii 



the mathematical expression for it must take account of its smooth 

 nature. Brody found the relationship between the relative rates of 

 growth k ^j^ 



W 



to be k = log [R + i), 



where R is Minot's percentage growth-rate. The latter can, therefore, 

 only be used when it does not exceed 10 per cent, for the period 

 under consideration, i.e. never in embryological work. 



Brody also criticised the methods of Pearl, whose equation 



dW _ k 

 dt t- a 



does not take account of the fact that part of growth is self-accele- 

 rating, and also Pearl & Reed's modification of the original Robertson 

 equation. He maintained that the best way was to plot the log. 

 weight against the age, when, if the result is a straight line, the rate 

 of instantaneous growth, A;, must be a constant. This will not of 

 course be confused with the 

 fractional persistency con- 

 stant referred to above, for 

 the latter only refers to the 

 autostatic or self-inhibitory 

 phase. The autokinetic or 

 self-acceleratory phase is ^ 

 clearly the more important ^ 

 and interesting for em- 

 bryologists. 



Figs. 52 a, b, taken from 

 Brody's paper, show the 

 data of various workers for 

 the wet weight of chick 

 embryos treated in the way 

 described, namely, the log. 

 weight plotted against the 

 age. It will be noted that a series of straight lines result, forming a 

 system concave to the abscissa and rising rapidly but more quickly 

 at first than later. The curve is thus the exact opposite of the Minot 



Cms 



,.:? 



*«jy 



6 10 12 14 16 Ifl 20 

 Incubation Age 



Fig. 52 a. 



