220 THE QUANTITATIVE METHOD IN BIOLOGY 



Table V 

 Ratio (length ist empty glume) : (length ist flowering glume) 



Minimum Maximum 



Glyceria fluitans 0'39 Glyceria fluitans 0'55 



Festuca pratensis Huds. 0-39 Bromus asper 0'64 



Bromus asper 0'50 Festuca pratensis Huds. 0'65 



Melica uni flora 0"82 Alopecurus pratensis I'ly 



Alopecurus pratensis 0-94 Melica uni flora I '19 



Agrostis alba i'o8 Agrostis alba i"5i 



USE OF THE TABLES OF IDENTIFICATION : Suppose 

 that we want to identify a Grass ;*; with one or several fertile 

 stems, and that we have no other information than that it be- 

 longs to one of the species mentioned in the Tables I.-V. The 

 THREE METHODS of using the tables which I have given in 

 my paper on Mnium are also applicable to the Grasses. 



According to the FIRST METHOD I measure the primordia 

 of one stem and of one spikelet of its inflorescence. The figures 

 are (this example is taken at random) : 



Specimen x 



Length blade upper leaf .... 70 mm. 



first empty glume . . . . 4-9 „ 

 „ flowering glume ... 5-1 



awn first flowering glume . . 7 '5 „ 



Ratio length (ist empty) : (ist flowering) glume 0-97 „ 



I begin with Table I. : minimum, Bromus is excluded ; maxi- 

 mum, no species excluded. 



Table II. : minimum, no species excluded ; maximum, 

 Agrostis, Glyceria and probably Festuca excluded. (Since the 

 constants are not definitively established, the difference between 

 4'3 and 4*9 is rather too small to be decisive.) 



Table III. : minimum, exclusion of Bromus confirmed ; 

 maximum, exclusion of Agrostis confirmed, Melica probably 

 excluded. 



Table IV. gives a decisive answer : minimum, no species 

 excluded ; maximum, all the species excluded except 

 Alopecurus. Here, however, the exclusion of Bromus is only 

 probable (for the above given reason), but Bromus has already 

 been excluded. 



It may be concluded that x is Alopecurus pfatensis. 



I measure in a similar way the primordia of one stem and one 

 spikelet of a Grass y. The figures are : 



