SECT. 2] AND WEIGHT 397 



averages for the early embryos reveal the difference by bending away 

 from the lines drawn on the basis of incubation or conception age. 



Schmalhausen, continuing earlier work on the growth of bacilli and 

 protozoa, has also put forward empirical formulae for the embryonic 

 growth of the chick, but his equation 



\^W= T, 



while fundamentally the same as that of Murray, has no velocity 

 constant. Fig. 42, taken from Schmalhausen's paper, shows that 

 the cube root of the weight plotted against the age only gives an 

 approximately straight line. Schmalhausen has included in the same 

 figure the curves obtained by other methods; thus curve P' is the 

 Minot (percentage growth-rate) curve for the wet weight, and Ps' 

 for dry weight, while the curve marked log o- ip is the log. weight 

 plotted against the age. As we have already seen, in the case of 

 McDowell's figures for the mouse, and Murray's figures for the chick, 

 this value always gives a curve rising concave to the abscissa. The 

 curves P and Ps in Fig. 42 represent the absolute wet and dry weights 

 respectively. 



Other empirical formulae have been proposed for growth-pro- 

 cesses from time to time. 



Embryonic growth can be expressed roughly by exponential curves ; 

 thus: 



W = wp\ 



where W is the mass of the embryo at time t, w the original mass, 

 and p a constant. Thus the equation of an exponential curve is one 

 in which the power is always changing. Janisch has given a dis- 

 cussion of the use of the exponential curve in all departments of 

 biology, and in it he shows how important this relation is in growth 

 phenomena. 



The "law of compound interest "however, put forward byBlackman 

 in 1919 for the growth of plants, and which has been shown by 

 Luyet to be a special form of the exponential relation 



W= w {i + ry, 



has not so far been of any assistance in describing embryonic growth. 

 Another form of the exponential curve, the arithmetical progression 

 method, which gives the equation 



log W - At, 



