Ill] OF CURVES OF GROWTH 95 



length or stature, and in short that infant, boy and man are not 

 similar figures*. The change of form seems sHght and gradual, but 

 behind it he other and more complex things. Th6 changing ratio 

 between height and weight imphes changes in the child's metabolism^ 

 in the income and expenditure of the body. The infant stores up 

 fat, and the active child "runs it off" again; at four years old or 

 five, bodily metaboUsm and increase of weight are at a minimum; 

 but a fresh start is made, a new "nutritional period" sets in, and the 

 small schoolboy grows stout and sJ3rong|. 



Our curve of growth shews at successive epochs of time the height 

 or weight which has been reached by then; it plots changing 

 magnitude (y) against advancing time (x). It is essentially a 

 cumulative or summation curve; it sums up or "integrates" all the 

 successive magnitudes which have been added in all the foregoing 

 intervals of time. Where the curve is steep it means that growth 

 was rapid, and when growth ceases the curve becomes a horizontal 

 line. It follows that, by measuring the slope or steepness of our 

 curve of growth at successive epochs, we shall obtain a picture of 

 the successive velocities or growth-rates. 



The steepness of a curve is measured by its "gradient J," or we 

 may roughly estimate it by taking for equal intervals of time 

 (strictly speaking, for each infinitesimal interval of time) the incre- 

 ment added during that interval; and this amounts in practice to 

 taking the differences between the values given for 'the successive 

 epochs, or ages, which we have begun by studying. Plotting these 

 successive differences against time, we obtain a curve each point on 

 which represents a certain rate at a certain time; and while the 

 former curve shewed a continuous succession of varying magnitudes, 

 this shews a succession of varying velocities. The mathematician 

 calls it a curve of first differences ; we may call it a curve of annual 

 (or other) increments ; but we shall not go wrong if we call it a curve 

 of the rate (or rates) of growth, or still more simply, a velocity-curve. 



* According to Quetelet's data, man's stature is multiplied by 3-4 and his weight 

 by 20-3, between birth and the age of twenty-one. But the cube of 3-4 is nearly 

 40; so the weight at birth should be multiplied forty times by the age of 

 twenty-one, if infant, boy and man were similar figures. 



t Cf. T. W. Adams and E. P. Poulton, Heat production in man, Ouy's Hospital 

 Reports (4), xvn, 1937, and works quoted therein. 



I That is, by its trigonometrical tangent, referred to the base-line. 



