188 THE PHILOSOPHY OF BIOLOGY 



distributions." ^ The 'Value of the first character 

 changes b}^ unity in any distribution : obviously there 

 cannot be a fraction of a ridge ; and this kind of 

 variation is called " discontinuous." The value of 

 the second character may change imperceptibly, and 

 it is therefore called " continuous," a term which is 

 not strictly accurate, since in applying it we assume 

 that the numerical difference between two variates 

 may be less than any finite number, however smalL 

 In this assumption we postulate for biology the dis- 

 tinctive mathematical concept of infinite divisibility. 



The difference from the mode, or mean, with 

 respect to a definite character in a fully grown organism 

 may be due to the direct action of the environment, in 

 the sense in which we have regarded the environment 

 as influencing the organism ; or it may be due to the 

 changes in the organism resulting from the increased 

 or decreased use of some of its parts. The conditions 

 with regard to nutrition, for instance, will not be the 

 same for all the individuals composing a cluster of 

 mussels growing on the sea-bottom. Those in the 

 interior of the cluster do not receive so abundant a 

 supply of sea-water as those on the outside of the 

 cluster ; and since the amount of food received by 

 any individual depends on the quantity of water 

 streaming over it in unit time, we shall find that the 

 internally situated individuals will be stunted or 

 dwarfed, while those on the outside will be well grown. 

 Such variations are acquired ones, but even when we 

 allow for them, even if we take care that all the 

 organisms studied live under conditions which are as 

 nearly uniform as possible, there will still be some 

 degree of variability. We cannot be sure that this 

 absolute uniformity ever exists ; and the notion of 



1 See Appendix, p. 350. 



