314 THE BORDERLAND OF SCIENCE. 



ing that the rate of increase here contemplated cannot 

 possibly continue during many years, and that even 

 the assumption of an arithmetical rate of increase at 

 the present mean rate over-estimates the annual con- 

 sumption for any time far removed from the present. 



In all such progressions, statistics indicate a wavelike 

 alteration. Just as in the shape of a wave's front, we 

 see a gentle slope, then a more rapid slope, and then, 

 up to the wave's summit, a gradually diminishing 

 slope, so, in statistical progressions, we recognise a 

 gradual increase at first, then a more rapid increase, 

 then a diminishing increase, until the absolute maxi- 

 mum is reached, after which comes a gradual decrease. 

 But the rear of such a statistical wave may be alto- 

 gether unlike the front in other words, the rate and 

 manner and variations of decrease may be quite unlike 

 the rate and manner and variations of increase. It is 

 so with the progress of epidemics, with changes of 

 population in the complete history of a nation from its 

 rise to its decadence, with the growth of a trade, with 

 every known subject to which statistical research has 

 been applied. There may be alternate wavelike rise 

 and fall, there may be so slow a rate of increase or 

 decrease that the crest or valley of the wave seems long 

 in passing, and the decrease after increase, or vice 

 versa, may so far differ from the preceding phase as to 

 be almost imperceptible ; but in every case there is to 

 be recognised, either once or more than once, the wave- 

 form of rise or of fall.* 



* Let any one try such an experiment as the following, and ho will 



