142 THE RATE OF GROWTH [ch. 



Now, in our first curve of growth we plotted length against time, 

 a very simple thing to do. When we differentiate L with respect to T, 

 we have dL/dT, which is rate or velocity, again a very simple thing ; 

 and from this, by a second differentiation, we obtain, if necessary, 

 d^L/dT^, that is to say, the acceleration. 



But when you take percentages of y, you are determining dyjy, 

 and w^hen you plot this against dx, you have 



^, or -^, or -.^. 

 dx ' y.dx' y' dx' 



That is to say, you are multiplying the thing whose variations 

 you are studying by another quantity which is itself continually 

 varying; and are dealing with something more complex than the 

 original factors*. Minot's method deals with a perfectly legitimate 

 function of x and y, and is tantamount to plotting log y against x, 

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

 This would be all to the good if it led to some simple result, a straight 

 line for instance ; but it is seldom if ever, as it seems to me, that it 

 does anything of the kind. It has also been pointed out as a grave 

 fault in his method that, whereas growth is a continuous process, 

 Minot chooses an arbitrary time-interval as his basis of comparison, 

 and uses the same interval in all stages of development. There is 

 little use in comparing the percentage increase fer week of a week- 

 old chick, with that of the same bird at six months old or at six 

 years. 



The growth of a population 



After dealing with Man's growth and stature, Quetelet turned to 

 the analogous problem of the growth of a populatfon — all the more 

 analogous in our eyes since we know man himself to be a "statistical 

 unit," an assemblage of organs, a population of cells. He had read 



* Schmalhausen, among others, uses the same measure of rate of growth, in the 

 form 



log F-logF dvl^ 

 ^~ k{t-t) ~^ dt v' 



Arch. f. Entw. Mech. cxm, pp. 462-519, 1928. 



