GRADATION 199 



and following each other in the direction of the axis a, and if we 

 measure in those sections any physical property (dilatability, 

 conductibility, compressibility, refraction, specific gravity, etc.) 

 we obtain the same value for each and all. The same con- 

 stancy is observed along the axes h (slices parallel to the plane 

 ac) and c (slices parallel to the plane ah) . 

 All the crystals are governed by the same law. 



§ 138.— THE AXES OF THE LIVING BEINGS ARE 

 ALSO LINES OF STABILITY.— I consider now a living 

 being, limiting myself to the pluricellular animals and plants. 

 Here we also distinguish axes which are hnes of stability.^ 

 Each pluricellular specimen is a society consisting of a certain 

 number of individuals (segments or biological units; cells, etc. 

 See § 54) associated into a certain state of equilibrium and 

 ordered according to the axes. 



When the axes of the living beings are looked upon as being 

 lines of stability and ordonnance, they are no longer arbitrary 

 or abstract conceptions. They acquire the same mechanical 

 significance as the axes of a crystal, and a comparison between 

 both is founded upon real analogy. 



§ 139.— DIFFERENCE BETWEEN THE AXES OF THE 

 LIVING BEINGS AND THOSE OF THE CRYSTALS. 

 GRADATION. — A fundamental difference between the axes 

 of the living beings and those of the crystals depends on Grada- 

 tion. In a plant or an animal the value of a given property, 

 measured successively at different places along a given axis, is 

 variable instead of being constant as in the crystals. Its varia- 

 tion is regular ; that is to say, ruled by a geometrical law, which is 

 to be discovered by measurement in each peculiar case and may 

 be represented by a gradation curve} 



§ 140.— EXAMPLES OF GRADATION. FIRST EX- 

 AMPLE : THE FERTILE STEM OF POA TRIVIALIS (A 

 GRASS). — I call this stem a specimen or individual of the first 

 order ; it is a uniaxial system. It consists of two segments 

 (individuals or units) of the second order — viz. : (i) the basal 

 (proximal) segment or stem properly so called ; (2) the terminal 

 (distal) segment or inflorescence (panicle, the lateral branches 

 of which are neglected here). Both segments are distinctly 

 different by a number of properties (differentiation). 



» See on the different systems of axes which are observed in the living beings 

 (uni-, bi-, triaxial systems, etc.), §§ 54, 77, 88. 



See on the axes of unicellular beings, § 60 (egg of Spirogyra). See on curved 

 axes, which consist of a succession of straight simple axes, § 84. 



2 In the crystals, the gradation curve of any property is always a straight 

 line parallel to the axis. Therefore we may say that gradation does not exist. 



