218 THE QUANTITATIVE METHOD IN BIOLOGY 



fields, on the heath, in waste places, in meadows, etc.^ From 

 each spot I collect the largest and the smallest specimens ^ and 

 measure them. In this way the work required for the discovery 

 of the limits is reduced to a minimum. ^ 



The description of a species consists of a table in which the 

 constants of each primordium are given. 



Remark : Those constants are something quite difierent from the limits 

 of variation represented by the extremities of a variation curve constructed 

 by the measurement of a series of specimens collected (according to the 

 ordinary biometrical method) at random on one spot or in one locality. See 

 pp. 182, 188. 



EXAMPLE (here I content myself with nine primordia) : 



Specific description of Alopecurus pratensis L. : 



1. Length of the upper internode of the fertile stem : 129-678 mm. 



2. Length of the blade of the upper leaf of the fertile stem : 12-253 mm. 



3. Length of the inflorescence : 24-183 mm. 



4. Length of the first empty glume : y&6-6-^2 mm. 



5. Breadth of the first empty glume : i-38-2'20 mm. 



6. Number of nerves of the first empty glume : 3-3. 



7. Number of nerves of the second empty glume : 3-3. 



8. Length of the (first) flowering glume : 3'44-5'97 mm. 



9. Length of the awn of the (first) flowering glume : 4'73-9'99 mm. 



The ratio (length first empty glume) : (length first flowering glume) varies 

 between 0-94 and 1-17. 



In the above table I give an example of a ratio, which is, of 

 course, not a primordium but an empirical value calculated 

 arbitrarily from two primordia. We might also take arbitrarily 

 the sum, the product, the square root of the product, etc. 

 (§ 102). Such empirical values may render in certain cases 

 good services, although their biological or mechanical signifi- 

 cance is very vague. The constants of the primordia are, on 

 the contrary, figures which have been obtained by direct 

 measurement without any calculation. They are the expres- 

 sion of observed facts. 



TABLES OF IDENTIFICATION are constructed in the 

 following way, limiting myself in one or another way. I take, 

 for instance, all the species of a genus, or the species of a family 

 which are indigenous in a given country or district, etc. For 

 each primordium a table is drawn up in which the minimal and 

 maximal values of each species are given. In the following 

 example I content myself with four primordia, one ratio and six 



iThe possible conditions of life are very varied for the majority of the 

 species, although many of them are ordinarily found under certain definite 

 conditions. In LEO GRINDON'S Flora of Manchester (1857) the ordinary 

 surroundings of each species are exactly indicated. 



2 And, as much as possible, those specimens which are conspicuous by one 

 or another peculiarity, for instance by very long or short leaves very large 

 or small spikelets, etc. 



^ And it may be added that many interesting observations are made in the 

 field. 



