MEASUREMENT OF VARIABLE PROPERTIES 129 



Between the limits i and 36 several irregular gaps exist ; 

 the distribution of the frequencies is also very irregular. It 

 seems as if the above figures were accidental, independent of 

 any rule whatever. They are, however, governed by definite 

 rules, which are rules of chance. I have verified the above 

 calculated figures by experiment. (See § 103.) 



EXAMPLE (B) : Let us suppose that the figures of each pair 

 in Table /3 (p. 127) express the length and the breadth of thirty- 

 six leaves of a certain species, and let us calculate the ratio 

 breadth : length of each of them (in each pair of figures in Table /5 

 the first figure expresses the breadth). The following result is 

 obtained : — 



Table S (Compare Table P, p. 127) 



B 



D 



If the thirty-six figures in Table S had been obtained from 

 the measurement of thirty-six leaves, we might be tempted to 

 bring them into the form of a variation curve (see p. 29 and 

 § 108) — viz. 



Ratio breadth : length : 0-0 -99 = 15 leaves 



I - I -99 = 12 „ 

 „ ,, „ 2 - 2 • 99 = 4 



»» n y, 3 - 3 • 99 = 2 



»y y> >, 4-4-99 = 1 



>y >y ,, 5 - 5 • 99 = 1 „ 



Jf >> y> O - . . . = I „ 



A certain regularity is observed in this curve : it recalls 

 certain unilateral curves which have been actually obtained 

 and described. (See experimental verification in § 103.) 



Remark about the preceding examples {dice ) : Starting from the thirty-six pairs 

 of figures in Table ^ (p. 127), and taking successively the sum (Table 7, p. 127) 

 the product (p. 128) and the quotient (Table 5, p. 129) of the figures of each 

 pair, we have obtained three different results : in two cases (sum and quotient) 

 the distribution of the frequencies is regular or fairly regular ; in one case 

 (product) it seems to be capricious. In the three cases, the cause of the 

 observed facts is chance (combined cause). In each cast chance brings about 

 certain reactions which are going on till a certain state of eciuilibrium exists 

 and the corresponding values of the dice (dots) become visible. The two 



lues (one of each die) which become visible at the same time are the ex- 



sion of forces which may work together in various ways. In other words, 



' M cs which depend on the specific energy of the dice are brought as it were 



into action by chance. The system of two dice is a sort of machmcry, through 



^ ich chance is acting. In the three given examples the effects depend on 



machinery, the cause CHANCE being exactly the same in each. 



