18 INTRODUCTORY I 



die (A Vx] 7 , . . 



= 2/c, that is, is negative. 



Hence, if we suppose the growth-rate of the animal organism 

 to depend in the same way upon x, the amount of growth 

 already accomplished, and upon A x, the amount still to be 

 accomplished at any particular moment, then the theory may 

 readily be checked by ascertaining whether the rate is indeed 

 at a maximum when the growth is half done. 



Robertson, calculating from the data given for human and 

 other growth, has found that this is very approximately true. 

 One instance will suffice here, the growth of the human being 

 during the fourth period (second post-natal) from the ninth 

 to the thirtieth year. 



If a graph be constructed whose ordinates are the succes- 

 sive rates \-zi\ an d whose abscissae are the successive weights 



(x), it will be found that the maximum rate occurs when half 

 the increase of weight to be achieved during this period has 

 been attained. From the formula the theoretical rates for 

 the successive weights may be calculated, and their graph 

 compared with that of the observed rates. 



There are means by which the value of the hypothesis may 

 be tried. The value of the constant k for instance may be 

 found, the theoretical weights (x) then calculated and compared 

 with the actual ones. Robertson has found the agreement to 

 be very fairly good. 



A botanical instance may be quoted here. The measure- 

 ments made, many years ago, by Errera for the growth of the 

 sporangium-bearing hypha of the fungus Phycomyces show 

 very clearly that the rate ascends to a maximum when the 

 growth is half completed. 



The body of a Metazoon is often compared to the sum-total 

 of all the individuals produced by the repeated division of 

 a single Protozoon, and it might perhaps be thought that the 

 rate of growth of this total would alter, in the same way as 

 the growth-rate of a Metazoon. But this is apparently not 

 the case. We know indeed from the researches of Calkins, 

 Woodruff, and others that the rate of division of Protozoa 



