48 THE QUANTITATIVE METHOD IN BIOLOGY 



sideration among all the indigenous and cultivated plants of 

 Central Europe.^ 



In a similar way, limiting ourselves to the British flora, the 

 combination leaves angulmerve, perianth of 5 segments, 6-8 

 stamens, i ovary, 3 styles is found only in the genus Polygonum. 



Holcus lanatus is characterized among all the British grasses 

 by the following combination : — 

 Property a : each spikelet two-flowered. 



„ b : glume of the upper flower of each spikelet awned. 

 „ c : glume of the lowest flower of each spikelet awnless. 

 „ d : axis of the spikelet glabrous. 

 „ e \ sheath of the upper leaf of the fertile stem downy. 



Holcus mollis is characterized by the following combination : — 

 a, b, c, d and 

 Property/ : sheath of the upper leaf of the fertile stem glabrous. 



The combinations abode and abcdf represent respectively 

 H. lanatus and H. mollis as exactly as the combinations KNOOO 

 and NaNOGG represent respectively potash-salpetre and soda- 

 salpetre. 



It is ordinarily impossible to find the characteristic combina- 

 tion of a species without investigating a sufficient number of 

 primordia in all the species of the genus, the family, etc., to 

 which it belongs, plasticity, gradation and even (in certain 

 cases) the succession in the course of the individual develop- 

 ment being taken into account. 



In the floras and the faunas a mere enumeration of properties 

 of each species is given. The reader, in other words, the un- 

 fortunate biologist, who wants to identify a plant or an animal 

 is requested to discover by himself the characteristic combina- 

 tions. 



§ 40.— PHYLLGTAXIS. (See §30 (4)).— This part of botany, 

 which is the study of the relative position of the cauloms and 

 the phylloms, is entirely based upon quantitative data. It 

 might be called geometrical botany. It includes, among other 

 things, the knowledge of the floral diagrams, which is of high 

 importance for descriptive botany. The fundamental principles 

 of phyllotaxis are expounded in the classic text-books ; therefore 

 I content myself with this short reference to it. 



§41.— THE QUANTITATIVE METHOD APPLIED TO 

 PHYSIOLOGICAL FUNCTIONS AND PROPERTIES. (See 

 § 30 (5)). — In the physiology of animals and also, to a certain 

 degree, in the physiology of plants much progress has been 

 made by the use of the quantitative method. By the measure- 



1 A combination of properties is comparable to a word, which represents 

 an exact notion, although each isolated letter is deprived of any significance. 



