APPLICATION OF THE QUANTITATIVE METHOD 217 



be exactly determined and measured, gradation being taken into account. 

 Seedlings and cuttings should be compared and cultivated under various con- 

 ditions of existence, and we should have recourse as often as possible to 

 hybridization. ^, . < 



In this way, it may be hoped that light will be thrown upon that foggy 

 department of systematic science. 



Whatever the theory may be, it is a matter of fact that critical 

 species are a small minority and that the independence of species 

 is the ordinary rule among living organisms. One may ask 

 whether the belief that the notion of species is artificial has not 

 its origin rather in the vagueness of the existing descriptions than 

 in the living objects. 



The quantitative method is independent of any theory : it 

 may be appUed immediately to the description of the very 

 numerous species of animals and plants which are, in fact, 

 independent, whatever the explanation of that independence 

 may be. And, moreover, the constants of those complex 

 species which include critical subspecies may be established, 

 each species being taken as a whole. The constants of the sub- 

 species may be eventually determined later on. Since they 

 are, of course, included within the limits of the species, their 

 determination does not affect the latter. ^ 



§ 150.— EXAMPLE OF APPLICATION : THE QUANTI- 

 TATIVE DESCRIPTION AND IDENTIFICATION OF 

 GRAMINEiE. — In my memoir on Mnium I have given a first 

 example of application of the method to systematics. Here I 

 give a second example. 



I have applied the method to the Graminece of the Manchester 

 district. Since the number of primordia (characters) is practic- 

 ally unhmited in those plants, a choice must be made. I have 

 measured about 25 primordia of the fertile stem (including 

 inflorescence, spikelets and flowers). For each primordium in 

 each species I have determined the limits of variation — that is 

 to say, the lowest and the highest value, which are specific 

 constants. 



In order that we might find the Umits without being com- 

 pelled to measure an excessive number of specimens, the 

 MATERIAL IS COLLECTED in the following way :— I try to 

 find specimens of a given species under conditions of existence 

 as various as possible : on dry and wet, sunny and shady spots, 

 on rich and poor soil, on walls and rocks and on the banks of 

 rivers and streams, in forests and gardens and on cultivated 



1 In the memoir on GraminetB which I intend to publish later on, I hope to 

 discuss the notion of species (and subspecies) in relation with specific con- 

 stants, and also to suggest an explanation of the so-called adaptation of the 

 RACE to the conditions of existence, independent of the direct influence of the 

 surroundings and without the intervention of natural selection. 



