20 INTRODUCTORY I 



which it had passed from the nucleus, as ' yolk-nucleus', during 

 the growth of the oocyte ; in the latter it lies in the nuclei, 

 which apparently have taken it up. Still, there may be 

 synthesis of nucleins in later stages, and the idea may be 

 substantially correct. 



Again, the internal factor A, which gives the definite limit 

 to which the growth can proceed, might possibly be looked for 

 in the capacity of the fertilized ovum to divide a given number 

 of times and no more. If this were so, then the rate of cell- 

 division in the Metazoa would not be governed by the same law 

 as in the Protozoa, if in the latter the rate of division is given by 

 km (n m), where m is the number of divisions that have taken 

 place at any moment, n the total number that can take place, 

 while in the former the rate of growth is given by y 2 m ( 2 n 2 m ), 

 where y is the initial size of the plasma of the ovum. 



More probably it will be necessary to look for a wider for- 

 mula, which will include both these, as for instance that the 

 processes of cell-division, of synthesis of nucleins, and of syn- 

 thesis of all those cytoplasmic substances and secretions on 

 which growth depends, are all conditioned by the presence of 

 certain extra-cellular ferments of a certain intensity, whose 

 activities become progressively diminished by the combination 

 of the ferments with the products of the reaction, the reversi- 

 bility of the reaction, and other causes. 



Before bringing this part of the subject to a conclusion it 

 may be pointed out that Minot's expression for the growth- 

 rate (the percentage increment) states the facts in another way, 

 though it fails in not calling attention to both the factors in- 



volved. The equation -- = kx (A x) 



may be approximately written 



Ax Ax 1 , , . x 



= kx(A x) or x - - = k (Ax). 



At At x 



The expression on the left is proportional to Minot's percent- 

 age increment, that on the right the velocity of a unimolecular 

 reaction, the graph for which (logarithmic) resembles the 

 graph of rates constructed by Minot's method. 



The next feature of interest presented by growth is the 



