402 ON INCREASE IN SIZE [pt. iii 



embryonic development in man as 3650 per cent, and above. It 

 was not unnatural to enquire whether the Minot growth-rate of the 

 original dividing egg-cell was even finite. 



The dissatisfaction was voiced in 191 7 by d'Arcy Thompson, who 

 wrote as follows: "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 introduced a curious and (as it seems 

 to me) an unhappy method of representing growth in the form of 

 what he called 'percentage-curves'. Now when we plot actual length 

 against time we have a perfectly definite thing. When we differentiate 

 this LjT we have dLjdT which is of course velocity, and from this 

 by a second differentiation we obtain d^LjdT^, that is to say, the 

 acceleration. But when you take percentages of jv, you are deter- 

 mining dyly and when you plot this against dx you have —-^ or 



dx 



— ^ or - . ^ , that is to say, you are multiplying the thing you wish 

 y.dx y dx 



to represent by another quantity which is itself continually varying, 

 and the result is that you are dealing with something very much less 

 easily grasped by the mind than the original factors. Minot is of 

 course dealing with a perfectly legitimate function of x and y and 

 his method is practically tantamount to plotting logy against x^ 

 that is to say, the logarithm of the increment against the time. [Cf. 

 log. weight-age curves.] This could only be defended and justified if it 

 led to some simple result, lOr instance if it gave us a straight line, or 

 some other simpler curve than our usual curves of growth". This 

 criticism was justified, for the Minot curve is certainly no simpler 

 than the untouched growth curves ; it merely falls instead of rising. 



But d'Arcy Thompson did not point out the presence of a 

 definite fallacy in Minot's way of looking at growth, a physio- 

 logical rather than a mathematical one. This was grasped by Brody, 

 who has written as follows: "Minot's method for computing growth- 

 rates gives an exaggerated decline in the percentage rates of growth 

 with increasing age simply because an arbitrary unit of time, e.g. 

 a week, does not have the same significance at different ages. It is, 

 for example, entirely appropriate to express the gain in weight during 

 a week as a percentage of the weight at the beginning of the week 

 (Minot's method) for a 6-month old chicken, because the weights 

 (i.e. the number of cells or other reproducing units) at the beginning 



