222 THE QUANTITATIVE METHOD IN BIOLOGY 



The above deduction is verified. The Grass z is, indeed, 

 a specimen (taken at random) of Dactylis glomerata. This 

 example gives us an idea of the way in which it may be dis- 

 covered whether a given species is new for the flora of a certain 

 area or even new for science, if we have tables of constants at 

 our disposal. 



The SECOND METHOD is applicable as often as it is possible 

 to measure the same primordia in two or several specimens 

 which belong with certainty to the same species (in the case of 

 the Grasses two or several stems of one plant or one patch). 

 Example : I take (at random) three fertile stems of one patch 

 of Alopecurus pratensis and measure the length of the blade of 

 the upper leaf. The figures are 153, 132 and 47 mm. Taking 

 Table I., the values 153 and 132 do not give us any information, 

 but by means of the figure 47 Bromus asper is excluded. Etc. 

 See my paper on Mnium. 



The THIRD METHOD is applicable if one specimen (in the 

 case of the Grasses one inflorescence) affords opportunity of 

 measuring certain primordia two or several times. Example : 

 I measure in one inflorescence, u, the length of the awn of the 

 first flowering glume of several spikelets. Among the examples 

 which I have collected I choose one in which the figures were 

 57, 6'2 and 8"2 mm. Taking Table IV., the figures 57 and 62 

 do not give decisive information, but from the value 8 '2 it may 

 be deduced that u is Alopecurus pratensis. 



In the above examples it has been possible to identify a speci- 

 men by means of a few figures. This happens more frequently 

 than one would think. It is, of course, often necessary to 

 measure a rather large number of primordia, especially when 

 we want to make a choice between numerous species. (An ex- 

 ample is given in my paper on Mnium, Table XXXIX.) 



DESCRIPTION OF ONE SPECIMEN. BERTILLONAGE. 

 — One figure, representing the value of one primordium of one 

 specimen, has rarely any value as long as it is taken isolatedly. 

 When a sufficient number of primordia of one specimen are 

 measured, the combination of figures obtained is a bertillonage : 

 it is a quantitative diagnosis of the specimen (compare § 140). 

 A bertillonage has been hitherto looked upon as being useful 

 only for the identification of an individual among all the speci- 

 naens of the same species, A bertillonage has, however, a much 

 higher significance. The species itseK is included in the com- 

 bination of figures. (See the combinations of x, y and z, pp. 

 220-221.) I have tried a very large number of examples taken 

 at random among species of Carabus, Mnium and Graminece. 

 I never found an exception. 



See my paper on Mnium, § 18 : the value of bertillonage 

 for descriptive botany and zoology. 



