PART VIII 

 GRADATION 



§ 136.— COMPARISON BETWEEN LIVING BEINGS 

 AND CRYSTALS.— Attempts to establish a comparison 

 between living beings and crystals have been made repeatedly 

 and often discussed in biological literature. The remarkable 

 regularity of a number of forms of life ^ has probably been the 

 origin of such attempts. Along this line, however, no results 

 of any real value have been hitherto attained, because the 

 attempted comparisons have been merely based upon simili- 

 tudes of the exterior forms. The real nature of the crystals, 

 which depends on their internal constitution rather than on 

 their external aspect, has been overlooked, and this has 

 rendered fruitless the attempts under consideration. More- 

 over, the universal occurrence in the living beings of curved 

 lines which are never observed in crystals seemed until now to 

 be an insuperable obstacle, and no attention has been paid to 

 gradation, which is the key to the whole subject (§ 139). 



In the comparison which I advance in the following para- 

 graphs, there is no question of external similitudes. 



§ 137.— THE AXES OF THE CRYSTALS ARE LINES 

 OF STABILITY. — A crystal is a system of material parts 

 which are in a certain state of stability. In each crystal we 

 discern a certain number of imaginary straight Unes or axes 

 (ordinarily three, sometimes four) which may be caUed lines of 

 stabihty or equilibrium. The constitutive parts or units 

 (molecules, particles) of a given crystal are all alike and arranged 

 in a certain way according to the axes. AU the successive 

 points of a given axis are identical. The value of any property 

 whatever of a crystal is invariable along each of its axes. 



I take, for instance, an orthorectangular prism ^ : in such a 

 crystal we discern three axes, a, b and c, each of which is per- 

 pendicular to the plane of the two others. The crystal may 

 be compared to a society of individuals (units) associated into 

 a rectangular triaxial system. (See § 88.) If we divide the 

 crystal into successive slices (sections) parallel to the plane be 



^ Diatoms, polyhedric cells in many animals and plants, tetrads, prismatic 

 stems ; Echinids, etc. 



^ A straight prism, the base of which is a rectangle. 



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