128 THE QUANTITATIVE METHOD IN BIOLOGY 



of six events (second die). In each of the thirty-six possible 

 combinations one event of the first series coexists with one event 

 of the second series. The two figures (facial values) of each 

 combination may be looked upon as being two causes or forces, 

 which may work together in order to produce a certain effect. 

 This is easily realized if we suppose that each cast with two dice 

 indicates, by the sum of both figures (facial value of the com- 

 pound event), for instance, a number of kilograms which 

 ought to be raised, of kilometres which ought to be travelled 

 over, of shillings which ought to be paid, etc. 



In the simplest case the effect (resultant) of the two co- 

 existing causes is expressed by the sum of their facial values 

 and may be calculated by means of a simple addition : in this 

 way the thirty-six possible compound events are reduced to 

 eleven (§ loi), the frequencies of which are given in Table 7 

 (p. 127). Two coexisting causes (forces), however, may be 

 associated into one resultant in an unlimited number of ways ; 

 the effect may depend not only on their sum, but, for instance, 

 on their difference, their product, their quotient; on the 

 diagonal of a rectangle the length and the breadth of which 

 are indicated by the two coexisting figures ; on the volume of a 

 cone determined by these figures, etc. 



Whatever may be the way in which two simple causes (the 

 coexistence of which depends on chance) work together, aU the 

 possible effects and the frequency of each of them may be 

 calculated a priori. 



Starting from one cast with two dice (Table p, p. 127), I 

 take the following four examples : — 



EXAMPLE (A) : By means of the thirty-six pairs of figures 

 in Table ^3 we may construct thirty-six rectangles, the surface 

 of each being the product of the figures of the corresponding 

 pair. With reference to the resulting products, the thirty-six 

 possibilities are reduced to eighteen, because a number of those 

 products are reaHzed in more than one way — viz. 

 Surface i reahzed in i way Surface 15 reahzed in 2 ways 



16 



17 

 18 



19 



20 



21-23 



24 



25 

 2^29 



30 



31-35 



36 



I 

 

 2 

 O 

 2 

 O 

 2 

 I 

 O 

 2 

 O 

 I 



