82 THE QUANTITATIVE METHOD IN BIOLOGY 



carried out in a satisfactory way, the term convergent adaptation is a delusive 

 screen behind which we conceal the problems which ought to be solved. And 

 moreover, even if convergent adaptation were proved to be a reality, it would 

 give us merely a physiological explanation, the morphological aspect of each 

 example being simply overlooked. 



I think it is preferable to adopt the method of the mineralogists. We 

 know many examples of substances, completely different by their chemical 

 constitution, which occy^in the same crystalline form. The mineralogists, 

 looking upon each cvysfJi as being a system of molecules which are in equili- 

 brium, have built up a morphology of the crystals which is an exact science 

 quite independent of any theory about the origin and the transformations of 

 the crystallized substances. This has been rendered possible by discerning 

 and measuring the simple properties of the crystals. 



Two different substances, both of which crystallize in the form of a regular 

 octahedral or a pentagonal dodecahedral are in the same state of equilibrium. 

 In a similar way, a ripe fruit of a given Myoxmycet and a ripe fruit of a Ly co- 

 per don are in a comparable state of equilibrium : they are, as it were, 

 crystallized in the same system. ^ I express this by saying that mechanical 

 concordance exists between them. Similarly, an adult Pediastrum, an adult 

 Spirogyra, the fore-legs of Gryllotalpa and Talpa, etc., are systems of material 

 parts which are in equilibrium, for a very simple reason : if they were not in 

 equilibrium they would be modified (further developed) till a state of equili- 

 brium is reached. (See §45.) 



We are tempted to consider that the above-mentioned objects are known 

 when they have been described in a few lines by means of vague terms (long, 

 short, broad, narrow, convex, oboval, etc.). In reality, such descriptions, 

 piled up in thousands of volumes, are incomplete. In a similar way, the term 

 octahedral gives incomplete information about a crystal, because a number of 

 different octahedrals exist which can only be distinguished by the measurement 

 of their angles and internal properties. The quantitative investigation of the 

 primordia of animals and plants would not only enable us to describe and to 

 identify them more exactly than by the ordinary method : we may expect 

 to find in the collected data (figures ! ) material for a morphology of the states 

 of equilibrium — which might be, in a certain sense, a crystallography of the 

 organisms, quite independent of any theory about their origin and genealogy. 



Between the suggested line of investigation and classic morphology there 

 is neither discordance nor contradiction. Following the method based upon 

 the measurement of the primordia, we want to avail ourselves of the information 

 already collected by systematic natural history, embryology, classic morphology 

 and also physiology ^ — trying to complete and to perfect this information by 

 investigating the facts from a different standpoint. 



See on PARALLEL VARIATION, § 135. 



§66.— SPECIAL SYSTEMS OF SEGMENTATION. HI. 

 PEDIASTRUM AND EUASTROPSIS {continued). SENSI- 

 TIVE PERIOD. — Two specimens of Pediastrum which differ 

 by the number of cells may be looked upon as being of different 

 age with reference to the primordium number. In the course 

 of the development of each specimen this number passes 

 through the values (compare § 59) : i, 2, 4, 8 . . . 2**, which 

 coincide with o, i, 2, 3 . . . n cell-divisions. 



In a specimen h consisting, for instance, of 2^ = 32 cells, each 

 cell considered separately has been after the fifth division in a 



1 At least with reference to a part of their properties. 



2 I am using here the term physiology in its broadest sense, including biology 

 properly so-called (pollination of flowers, dissemination of seeds, symbiosis, 

 etc.), heredity (Mendelism, etc.), etc. 



