130 THE QUANTITATIVE METHOD IN BIOLOGY 



EXAMPLE (C) : I suppose two dice the six faces of which axe 

 coloured with six pure spectral colours — viz. 



red =r = T orange = = 2 yellow = y = 3 

 green = g' = 4 blue =6 = 5 violet =v = 6 

 The dice being cast, the thirty-six possible events (combina- 

 tions of colours) may be found by means of the expression 

 {r + o-{-y-\-g + b + v)^ (compare Table P, p. 127) — ^viz. : 



Table € 



B 



D 



When both terms of each pair are added (in one or another 

 way) the following colours are perceived : — 



(i) The pairs in which both terms are alike give a pure 

 spectral colour (see the diagonal row AD) ; this occurs six times. 



(2) The pairs which consist of two complementary colours 

 (red + green, yellow + blue, orange + violet) give white ; this 

 occurs six times (rg, ov, yb, gr, vo, by). 



(3) The pairs which consist of different (not complementary) 

 colours give a mixed colour ; this occurs twenty-four times. 



The respective frequencies are thus : 



mixed : white : pure = 24 16:6 = 4:1:1 



(See experimental verification in § 103.) 



EXAMPLE (D) : I suppose that the figures on the faces of the 

 first die represent a corresponding number of cubic centimetres 

 of an acid liquid and that the figures of the second die represent 

 in the same way an alkaline liquid, both liquids being prepared 

 in such a way that i cubic centimetre of the first neutralizes 

 exactly i cubic centimetre of the second. The two dice being 

 cast, the thirty-six possible events are given in Table P (p. 127). 

 If thirty-six mixtures are made in the proportions (volumes) 

 indicated by the figures of each pair, it is seen that : 



(i) The pairs in which the first fi^re is predominant give an 

 acid mixture ; this occurs fifteen times. 



(2) The pairs in which the second figure is predominant give 

 an alkaline mixture ; this happens also fifteen times. 



(3) The pairs in which both figures are equal give a neutral 

 mixture ; this occurs six times. 



The respective frequencies are thus : 



acid : alkaline : neutral = 15 : 15 : 6 = 5 : 5 : 2 

 (See experimental verification in § 103.) 



