I GROWTH OF THE GERM-CELLS 17 



It has however been proposed by Robertson that the average 



Ax 



increment for a short interval of time, namely, the ratio - -> 



At 



would be the more proper measure of the rate, the velocity of 

 a chemical or physical reaction being indeed expressed in 

 this way. 



Now if the graph of the rate as so measured be constructed 

 it will evidently be of a totally different character, rising from 

 a minimum to a maximum, and then descending to a minimum 

 again. In the human being, as a matter of fact, there are 

 four periods in each of which a maximum rate is thus 

 attained : the first before birth, the second at the time of 

 birth, the third about the sixth year, and the fourth about 

 the sixteenth. 



Now such a graph resembles that constructed for the rate of 

 an autocatalytic unimolecular chemical reaction, as Robertson 

 has pointed out. Robertson, indeed, following Loeb, suggests 

 that the growth of the body depends on the synthesis of 

 nucleins, and that this involves reactions of this kind. But 

 however that may be, it is not difficult to put to the test the 

 supposed resemblance of the change in the animal growth- 

 rate to the change in the rate of the kind of chemical reaction 



o 



alluded to. The velocity of such a reaction at any moment is 

 given by the equation 



where x is the amount of change that has been accomplished 

 at that moment (t), A the final amount to be accomplished, 

 and A x consequently the amount that still remains to be 



accomplished at the moment in question. 



^ 

 It follows from this that where x= '-> that is, when the 



<w 



reaction is half over, the velocity attains a maximum, since 



, dx 



dx 



which is equal to zero when x = - , and since 



1963 C 



