726 Fluctuations 



be demonstrated the most readily by placing a 

 sufficient number of adult men in a row, arrang- 

 ing them according to their size. The line pass- 

 ing over their heads proves to be identical with 

 that given by the law of probability. Quite 

 in the same way, stems and branches, leaves and 

 petals and even fruits can be arranged, and 

 they will in the main exhibit the same line of 

 variability. Such groups are very striking, and 

 at the first glance show that the large majority 

 of the specimens deviate from the mean only to 

 a very small extent. Wider deviations are far 

 more rare, and their number lessens, the greater 

 the deviation, as is shown by the curvature 

 of the line. It is almost straight and horizontal 

 in the middle portion, while at the ends it 

 rapidly declines, going sharply downward at 

 one extreme and upward at the other. 



It is obvious however, that in these groups 

 the leaves and other organs could conveniently 

 be replaced by-simple lines, indicating their size. 

 The result would be quite the same, and the lines 

 could be placed at arbitrary, but equal dis- 

 tances. Or the sizes could be expressed by fig- 

 ures, the compliance of which with the general 

 law could be demonstrated by simple methods 

 of calculation. In this manner the variability 

 of different organs can easily be compared. 



Another method of demonstration consists in 



