Multiplication of Extremes 767 



After this hasty survey of the more reliable 

 facts of the practice of an asexual multiplica- 

 tion of the extremes of fluctuating variability, 

 we may now return to the previously mentioned 

 theoretical considerations. These are con- 

 cerned with an estimation of the chances of the 

 occurrence of deviations, large enough to ex- 

 hibit commercial value. This chance may be 

 calculated on the basis of Quetelet's law, 

 whenever the agreement of the fluctuation of the 

 qualit}^ under consideration has been empiric- 

 ally determined. In the discussion of the meth- 

 ods of comparing two curves, we have pointed 

 to the quartiles as the decisive points, and to 

 the necessity of drawing the curves so that these 

 points are made to overlie one another, on 

 each side of the average. If now we calculate 

 the binomium of Newton for different values of 

 the exponent, the sum of the coefficients is 

 doubled for each higher unit of the exponent, 

 and at the same time the extreme limit of the 

 curve is extended one step farther. Hence it is 

 possible to calculate a relation between the 

 value of the extreme and the number of cases 

 required. It would take us too long to give this 

 calculation in detail, but it is easily seen that 

 for each succeeding step the number of individ- 

 uals must be doubled, though the length of the 

 steps, or the amount of increase of the quality 



