190 THE QUANTITATIVE METHOD IN BIOLOGY 



primordium indicates the existence of two specific forms. 

 Unfortunately, little attention, if any attention at all, has been 

 paid to the variation steps and the specific limits of variation 

 , (minimal and maximal values) . 



I think that the application of the followed method to the 

 difficult problems under consideration is fruitless or at least 

 premature. 



Scientific progress is obtained by proceeding from the simple 

 to the complicated. Very numerous specific forms of animals 

 and plants are easily recognizable : it is possible to investigate 

 them quantitatively, determining the constants (limits of 

 variation) and eventually the variation steps of numerous 

 properties for series of (not critical) allied forms ; for instance, 

 for series of species of one genus or allied genera. 



In the higher forms of life, numerous measurable properties exist which 

 have been hitherto completely or almost completely overlooked. Examples : 

 Dr FRIEDRICH HEINCKE i has examined a number of so-called local 

 races of the herring in respect of about 25 different characters, and some in 

 respect of over 50 characters. I have measured 38 properties (characters) 

 in 90 species of Carabus and Calosoma — a dozen of properties of the leaves 

 of the mosses of the genus Mnium (see Part IX.) — and more than 25 properties 

 of the fertile stem, the leaves and the flowers of more than 25 species of 

 GraminecB. (See Part IX.) 



A complete and exact description of the species which are 

 DISTINCTLY CHARACTERIZED is, in the present state of 

 science, an attainable object of the quantitative method. It 

 may be expected that the description of a few hundreds of 

 species by means of figures will be sufficient to demonstrate the 

 value of the quantitative method for descriptive science. The 

 collected data will afford a base of comparison for the investiga- 

 tion of the critical species, the local races, etc. We will be, 

 however, very often compelled to have recourse for critical 

 specific forms to the experimental method (see § 17), the results 

 of the experiments being expressed by measurement. 



§ 131.— RELATION BETWEEN THE VARIATION 

 STEPS AND CERTAIN QUESTIONS OF PHYLLOTAXIS. 

 PRIMULA OFFICINALIS, MYOSOTIS, GERANIUM, 

 ROSACE^.— In § 126 I have called attention to the fact that 

 the significance of a given value depends on the series of varia- 

 tion steps to which it belongs. In certain cases exact informa- 

 tion about the variation steps might perhaps throw any light 

 upon certain phyllotaxic and other morphological problems. 



In Primula and Myosotis the corolla consists of five petals 

 and is ordinarily looked upon as being cyclic (verticillate) . In 

 Geranium the gynaecium is also pentamerous and described 

 as cyclic. 



1 Quoted after VERNON, loc. cit., p. 322. 



