160 THE QUANTITATIVE METHOD IN BIOLOGY 



into an urn. One case being extracted, the probability (fre- 

 quency) of each sort of prisms is given by {a + by° — viz. 



Height 



20 cm. 



21 „ 



22 „ 



23 ., 



24 „ 



25 .. 



26 „ 



27 ., 



28 „ 



29 „ 



30 „ 



Frequency 



1,000 : 1,024 



10,000 : 



45,000 : 

 120,000 : 

 210,000 : 

 252,000 : 

 210,000 : 

 120,000 : 



45,000 : 



10,000 : 

 1,000 : 



000= i: 1024= 0-098% 



= 10 : „ = 0-98 „ 



= 45: » = 4-39 .. 



= 120: „ =117 „ 



= 210: „ =20-51 „ 



= 252: „ =24-6 „ 



= 210: ,, =20-51 „ 



= 120: „ =11-7 „ 



= 45: .. = 4-39 » 



= 10 : „ = o-gS ,, 



= I : ,, = 0-098 „ 



When a large number of prisms, for instance, 102,400, are 

 extracted one by one, we may expect approximately the 

 following result : — 



Height of the 



prisms . 20 21 22 23 24 25 



Number of 



prisms . 100 

 Height of the 



prisms . 26 



Number of 



prisms 



1000 4500 12,000 

 27 28 29 



21,000 12,000 4500 1000 



21,000 25,200 

 30 

 100 



The eleven sorts of prisms are, as it were, specimens of a 

 certain species, a variable property of which (height) has been 

 measured. The above figures represent the variation curve, 

 which is governed by chance (Fig. 24.) 



§ 116.— SEVENTEENTH EXAMPLE (continued) .—Let us 

 now suppose that we find in the state of nature an unlimited 

 number of specimens of a given species varying with regard to 

 the property stature (height), the extremes being 20 and 30 cm. 

 A large number of specimens taken at random being measured, 

 a variation curve is obtained. It happens often (not always), 

 especially in the animal kingdom, that the successive values 

 are distributed approximately according to the rules of chance 

 (expressed by (i + i)"; see note, p. 147), just as in the above 

 variation curve of the species -prism. The latter (in which n = 10) 

 being taken as example and plotted out in the form of a diagram, 

 the obtained figure (Fig. 24) is the same as the curve of errors 

 mentioned in § 108. (See Fig. 18, p. 146, density of a solid 



