Ill] OF CURVES IN GENERAL 141 



an "elastic curve" (though it is not mathematically identical with it) 

 that it may be roughly simulated by a watchspring, lying between 

 two parallel straight lines and touching both of them. It has its 

 kinetic analogue in the motion of a pendulum, which starts from 

 rest and comes to rest again, after passing midway through its 

 maximal velocity. It indicates a balance between production and 

 waste, between growth and decay: an approach on either side to 

 a state of rest and equilibrium. It shows the speed of a train 

 between two stations ; it illustrates the growth of a simple organism, 

 or even of a population of men. A certain simple and symmetrical 

 case is called the Verhulst- Pearl curve, or the logistic curve. 



(4) Lastly, in order to leave a certain minimum, or zero-hne, and 

 return to it again, the simplest way will be by a curve asymptotic 

 to the base-line at both ends — or rather in both directions; it will 

 be a bell-shaped curve, having a maximum midway, and of necessity 

 a point of inflection on either side ; it is akin to, and under certain 

 precise conditions it becomes, the curve of error or Gaussian curve. 



Besides the ordinary curve of growth, which is a summation- 

 curve, and the curve of growth-rates, which is its derivative, there 

 are yet others which we may employ. One of these was introduced 

 by Minot*, from 'a feeling that the rate of growth, or the amount 

 of increment, ought in some way to be equated with the growing 

 structure. Minot's method is to deal, not with the actual increments 

 added in successive periods, but with these successive increments 

 represented as percentages of the amount already reached. For 

 instance, taking Quetelet's values for the height (in centimetres) of 

 a male infant, we have as follows: 



But Minot would state the percentage-growth in each of these 

 four annual periods at 39-6, 13-3, 9-2 and 7-3 per cent, respectively: 



Years 1 2 3 4 



Height (cm.) 50-0 69-8 79-1 86-4 92-7 



Increments (cm.) — 19-8 9-3 7-3 6-3 



(per cent.) ~ 39-6 13-3 9-2 7-3 



* C. S. Minot, On certain phenomena of growing old, Proc. Amer. Assoc, xxxix, 

 1890, 21 pp.; Senescence and rejuvenation, Journ. Physiol, xii, pp. 97-153, 

 1891; etc. Criticised by S. Brody and J. Needham, ojp, cit. pp. 401 seq. 



