Ill] OF STATISTICAL CURVES 139 



The curves we mostly use, other than the Gaussian curve, are 

 time-diagrams. Each has a beginning and an end; and one and 

 the same curve may illustrate the life of a man, the economic history 

 of a kingdom, the schedule of a train between one st^^tion and 

 another. What it then shews is a velocity, an acceleration, and 

 a subsequent negative acceleration or retardation. It depicts a 

 "mechanism" at work, and helps us to see analogous ' mechanisms 

 in different fields; for Nature rings her many changes on a few 

 simple themes. The same expressions serve for different orders of 

 phenomena. The swing of a pendulum, the flow of a current, the 

 attraction of a magnet, the shock of a blow, have their analogues in 

 a fluctuation of trade, a wave of prosperity, a blow to credit, a tide 

 in the affairs of men. 



The same exponential curve may illustrate a rate of cooHng, a loss 

 of electric charge, the chemical action of a ferment or a catalyst. 

 The S-shaped population-curve or "logistic curve" of Verhulst (to 

 which we are soon coming) is the hysteresis-curve by which Ewing 

 represented self-induction in a magnetic field ; it is akin to the path 

 of a falhng body under the influence of friction; and Lotka has 

 drawn a curve of the growing mileage of American railways, and 

 found it to be a typical logistic curve. A few bars of music plotted 

 in wave-lengths of the notes might be mistaken for a tidal record. 

 The periodicity of a wave, the acceleration of gravity, retardation 

 by friction, the role of inertia, the explosive action of a spark or 

 an electric contact — these are some of the modes of action or "forms 

 of mechanism" which recur in Hmited number, but in endless shapes 

 and circumstances*. The way in which one curve fits many 

 phenomena is characteristic of mathematics itself, which does not deal 

 with the specific or individual case, but generalises all the while, and 

 is fond (as Henri Poincare said) of giving the same name to different 

 things. 



Our curves, as we have said, are mostly time-diagrams, and 

 represent a change in time from one magnitude to another; they are 

 diagrams of displacement, in Maxwell's phrase. We may consider 

 four different cases, not equally simple mathematically, but all 



* See an admirable little book by Michael Petrovich, Les micanismes communs 

 aux phenomenes disparates, Paris, 1921. 



