72 THE RATE OF GROWTH [ch. 



the duration, of growth. It is in the main true, as Minot has 

 said, that the rabbit is bigger than the guinea-pig because he 

 grows the faster ; but that man is bigger than the rabbit because 

 he goes on growing for a longer time. 



In ordinary physical investigations dealing with velocities, as 

 for instance with the course of a projectile, we pass at once from 

 the study of acceleration to that of momentum and so to that of 

 force; for change of momentum, which is proportional to force, 

 is the product of the mass of a body into its acceleration or change 

 of velocity. But we can take no such easy road of kinematical 

 investigation in this case. The "velocity" of growth is a very 

 different thing from the "velocity" of the projectile. The forces 

 at work in our case are not susceptible of direct and easy treatment ; 

 they are too varied in their nature and too indirect in their action 

 for us to be justified in equating them directly with the mass of 

 the growing structure. 



It was apparently from a feeling that the velocity of growth ought in some 

 way to be equated with the mass of the growing structure that Minot* intro- 

 duced a curious, and (as it seems to me) an unhappy method of representing 

 growth, in the form of what he called " percentage- curves " ; a method which has 

 been followed by a number of other writers and experimenters. Minot's method 

 was to deal, not with the actual increments added in successive periods, such 

 as years or days, but with these increments represented as percentages of the 

 amount which had been reached at the end of the former period. For instance, 

 taking Quetelet's values for the height in centimetres of a male infant from 

 birth to four years old, as follows: 



Jlinot would state the percentage growth in each of the four annual periods 

 at 39-6, 13-3, 9-6 and 7-3 per cent, respectively. 



Now when we plot actual length against time, we have a perfectly definite 

 thing. When we differentiate this LjT , we have dL/dT , which is (of course) 

 velocity; and from this, by a second differentiation, we obtain d^L/dT-, that 

 is to say, the acceleration. 



* Minot, C. S., Senescence and Rejuvenation, Journ. of Physiol, xn, pp. 97— 

 153, 1891; The Problem of Age, Growth and Death, Poj). Science Monthly 

 (June-Dec), 1907. 



