110 THE QUANTITATIVE METHOD IN BIOLOGY 



are possible and are really observed. In each system the 

 primordia themselves are combined (coexist) in a certain way, 

 which varies from one case to another, and the value of each 

 primordium is variable according to the species investigated. 

 Therefore the diversity of the chess-board system is practically 

 unlimited, although the fundamental plan of structure is always 

 the same. 



By the application of the principles expounded in §§ 77-86 it 

 is possible, I think, to disentangle even very complicated cases, 

 to bring innumerable facts, which seem to be accidental and 

 capricious, under general rules, and to establish comparable 

 figures for long series of specific forms. 



The investigation of a certain number of examples is indis- 

 pensable for the further development of the quantitative 

 method. It is advisable to begin this work with examples 

 which are not too complicated and to have recourse again and 

 again to the comparative method. Investigation of a certain 

 number of primordia in a series of well-known species of the 

 same genus (or allied genera) is, I think, the most profitable 

 way. 



§ 88. — SECOND SECONDARY SEGMENTATION 

 (SECOND CLEAVAGE) IN THE BIAXIAL SYSTEM. 

 RECTANGULAR TRIAXIAL SYSTEM. (See § 69, p. 83, 

 and § 77, p. 93) . — A rectangular biaxial system is produced by 

 primary segmentation NS and first secondary segmentation 

 or first cleavage EW. In such a system each segment may 

 be divided in its turn into individuals (segments) by a second 

 secondary segmentation or second cleavage according to an axis 

 ZN. Since this axis is perpendicular to the plane of the axes 

 NS and EW, I call it the axis Zenith-Nadir [ZN). It is the 

 second secondary axis or axis of the second cleavage. 



In this way a rectangular triaxial system is produced. In 

 a biaxial system the segments are united into one layer. A 

 triaxial system consists of two or several superposed layers of 

 segments, each layer being a biaxial system.^ 



In the simplest case a triaxial system has the form of a 

 rectangular, straight prism, consisting of several superposed 

 chess-board systems. This form is observed, for instance, in 

 Sarcina, in certain specimens of which it is remarkably regular. 



In a triaxial system three planes may be distinguished (just 

 as in a triaxial crystal) — viz. 



(i) The plane NS-EW, the position of which is determined 

 by the axes NS and EW (horizontal plane). 



(2) The plane NS-ZN, determined by the axes NS and ZN 

 (longitudinal plane). 



^ The choice of the axes NS; EW and ZN is arbitrary. See § 79, p. 95. 



