28 THE QUANTITATIVE METHOD IN BIOLOGY 



species is variable in respect of almost aU its properties : we 

 realize this better when we have recourse to measurement than 

 when we content ourselves with mere observation.^ 



EXAMPLES OF QUANTITATIVE VARIATION IN 

 PLANTS : In Mnium serratum (an acrocarpic moss) I have 

 measured the length of the leaves of a number of fertile stems. 

 In one stem this length varied between i-02 and 471 mm. In 

 the same species the number of cells of the leaves of the fertile 

 stem (counted in the transversal direction, at the place of the 

 greatest breadth of the leaf, excluding the differentiated border 

 and the nerve) varied between 20 and 57. 



In an allied species {Mn. suhglobosum) the limits were : 

 length of the leaves, 1-02 to 734 mm. ; number of cells, 23 

 to 106. 



EXAMPLES OF QUANTITATIVE VARIATION IN 

 ANIMALS : In twenty-eight specimens of Sciurus caroUnensis 

 four properties were measured by J. A. ALLEN. ^ The 

 extreme values were : length of the body, 8-25 to 10 -20 inches ; 

 length of the tail, 675 to 875 inches. In the fore-foot the 

 range of variation was less and in the head smaller still. 



In Pseudoclytia pentata (a hydromedusa) the radial canals 

 were counted by A. G. MAYER ^ : the extreme values were 

 2 and 8. (See also Fig. i.) 



Whatever may be the measured property, the figures seem 

 at first sight to be capricious and independent of any rule 

 whatever. The majority of biologists have been discouraged by 

 the disconcerting variation which is almost always observed, 

 and look therefore upon dimensions and numbers as being of 

 accessory importance. 



More than seventy years ago QUETELET * initiated a new 

 method for the quantitative study of variable properties. 

 According to this method a given property is measured in a 

 large number of specimens of the same species (one of the 

 examples studied by QUETELET was the height of soldiers). 

 The distance between the Hmits (extreme values) is divided 

 into a certain number of equal intervals ; the specimens are 

 distributed among the intervals according to their value 

 (individual figure). In this way a variation curve of the 



^ Properties whicli are really invariable are exceedingly rare. For instance, 

 the number of fingers in man seems to be invariable. Examples of (hereditary) 

 Polydactyly are, however, not so rare as one is tempted to believe. Even 

 examples of cyclopism (one eye on the median line) have been observed. 



^ Bull. Mus. Comp. Zoology, Harvard, 1871. Quoted according to 

 H. M. VERNON, Variation in Animals and Plants (Intemat. Scient. Series, 

 London, 1903), p. 4. 



' Science Bull. Brooklyn Museum, vol. i. Quoted according to VERNON, 

 loc. cit., p. 90. 



' QUETELET, Lettres sur la TMorie des Probabilitis, Brussels, 1846. An- 

 thropometrie, 1870. QUETELET was bom at Ghent in 1805. 



