86 THE QUANTITATIVE METHOD IN BIOLOGY 



§ 71.— RAMIFICATION OF THE UNIAXIAL SYSTEM. 

 FIRST EXAMPLE: PSEUDOCH^TE GRACILIS {con- 

 tinued). GRADATION. HAIRS. IMPORTANCE OF THE 

 AXES. — The five groups of primordia which I have distin- 

 guished in an adult Spirogyra (§§ 57 and 60) are found in 

 Pseudochcete gracilis. Here they are, of course, to be measured 

 separately in the creeping stems (units A) and in the erect 

 branches B. In this way, it is possible to bring the description 

 of a given specimen x into the form of about a dozen of notions 

 (primordia) expressed by measurement. 



In the erect branches B we observe a very simple example 

 of gradation. Each of these branches has the form of a cone 

 which is very narrow in proportion to its height (length). The 

 constituent cells are (as in Spirogyra) of two sorts (differentia- 

 tion) : the terminal cell is conical ; each of the other cells has 

 the form of a truncated cone. The diameter of the cells 

 (expressed, for instance, by the diameter y of their proximal 

 base c) decreases regularly from the base (proximal extremity) 

 to the summit (distal extremity) of the conic branch. 



I call GRADATION the variation of a given primordium 

 along a given axis. (See §38 and Part VIII.) Here the varying 

 property is the diameter y. In a given cell, the value y^ of the 

 diameter measured at its base c depends on the distance x^ 

 between c and the origin (base) of the axis (branch). In other 

 words, in general, y is a function oi x. In the given example the 

 relation between y and x is very simple (the gradation curve 

 being a straight line, oblique in respect of the axis). 



The axis of an erect branch of Pseiidochcete gracilis is : (i) an 

 axis of segmentation (§ 54) ; (2) an axis of differentiation 

 (§55) 'y (3) 3-n axis of gradation. This is applicable in general 

 on any axis whatever.^ 



The great importance of the axes is brought into prominence 

 by the fact that an axis is always a line of segmentation, differ- 

 entiation and gradation. All the segments (individuals, units) 

 of a living being are arranged according to the direction of its axes 

 and all its properties are arranged with reference to these axes. 

 Each property ought to be measured in the direction of an axis, 

 or in a direction which is definite with regard to an axis. 



In an erect branch of Ps. gracilis we may measure the degree 

 of gradation ; this may be roughly expressed by the ratio 

 between the diameter of the base of the basal cell and the length 

 of the branch. This ratio, being a quotient obtained by divid- 

 ing a primordium with a second one, is a compound property. 



1 In an egg of Spirogyra, for instance (§ 54), the longitudinal axis is the axis 

 of segmentation and differentiation of the adult specimen. Since the trans- 

 verse diameter of the egg is variable along the mentioned axis, the latter is 

 also an axis of gradation. 



