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 >y 



24 „ 



25 >> 



26 „ 



27 >. 



28 „ 



29 „ 



30 » 



Frequency 



1,000 : 



10,000 : 



45,000 : 



120,000 : 



210,000 : 



252,000 : 



210,000 : 



120,000 : 



45,000 : 



10,000 : 



1,000 : 



1,024,000= I : 

 = 10 : 



= 45: 

 = 120 : 

 = 210 : 

 = 252: 

 = 210 : 

 = 120 : 



= 45: 

 = 10 : 

 = I : 



1024 = 0-098 % 

 = 0-98 



= 4-39 

 = 117 

 = 20-51 

 = 24-6 

 = 20-51 

 = 11-7 



= 4-39 

 = 0-98 



= 0-098 



24 



25 



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 



Number of 



prisms . 100 1000 4500 12,000 

 Height of the 



prisms . 26 27 28 29 



Number of 



prisms . 21,000 12,000 4500 1000 100 



21,000 25,200 



30 



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 {\ + \Y\ 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 



