112 THE QUANTITATIVE METHOD IN BIOLOGY 



mechanical concordance and social equivalence have been often 

 lost out of sight, and even physiological analogy has been rather 

 neglected, especially by the zoologists. In spite of all this, the 

 knowledge already gathered affords a guide for the quantitative 

 investigation of the primordia in the triaxial systems. 



§ 89.— RECTANGULAR TRIAXIAL SYSTEM {continued). 

 EXAMPLES. — According to the general scientific method, 

 which consists in proceeding from the simple to the intricate, 

 we ought to begin the quantitative investigation of the triaxial 

 system with the study of simple examples, limiting ourselves 

 to some easily measurable primordia. I give here four 

 examples : 



FIRST EXAMPLE : The root of many Phanerogams before 

 the secondary growth is initiated. This organ may be regarded 

 as a triaxial system, the axes being longitudinal {NS), peri- 

 clinal (tangential, EW) and anticlinal (radial, ZN).^ On a 

 transverse section of the root (plane EW-ZN) the following 

 ten primordia may be measured (the list is incomplete) : — 



(i) The number of cells of the cortex in the radial (anticlinal, 

 ZN) direction. In each root these cells ought to be counted 

 according to three or four or even more radii, the mean value 

 being taken as the figure of the root. 



(2-4) The number of ceUs of the endodermis and their radial 

 and tangential dimensions. 



(5) The number of radial rays of the xylem. 



(6) The mean number (or, in each root, the minimal and 

 maximal number) of ligneous vessels in one ray. 



(7-10) In the phloem bundles the number and the dimensions 

 of the cells in the radial and the tangential direction (investigat- 

 ing three or four bundles and taking the mean values ^ as the 

 figures of the root). 



It would be very interesting to study in this way the root of 

 a series of species of one genus (for instance, of Allium, Iris, 

 Narcissus, Poa, etc.). Of course roots of several specimens of 

 each species ought to be studied, terminal branches of the root 

 system (social equivalence, see §§ 74-75) being taken and the 

 sections being made at a given distance from the summit in 

 each and all. 



A monograph of a genus being obtained, it would be interesting 

 to cultivate certain species under different conditions (in sand, 

 clay, peat; moist and dry, etc.), and to study quantitatively 

 the plasticity of the primordia above mentioned. By means of 



1 Considering any cell whatever, its simple axes are NS, EW and ZN. 

 Its simple axis NS belongs to the longitudinal axis which passes through its 

 centre. Similarly its simple axis ZN is a part of a radial axis and its simple 

 axis EW is a part of a curved (circular) periclin axis. (See, on the curved 

 axes, § 84.) 



2 Or the minimal and the maximal values. 



