FORMS OF LIFE 



mathematical formulce, is called crystallography. There 

 is a parallel branch of the science of biological forms, 

 promorphology, which has been greatly neglected. 

 These two branches of investigation have the common 

 aim of detecting an ideal law of symmetry in the bodies 

 they deal with and expressing this in a definite mathe- 

 matical formula. 



The number of ideal fundamental forms, to which we 

 may reduce the symmetries of the innumerable living 

 organisms, is comparatively small. Formerly it was 

 thought sufficient to distinguish two or three chief 

 groups: (i) radial (or actinonaorphic) types, (2) bilateral 

 (or zygomorphic) types, and (3) irregular (or amorphic) 

 types. But when we study the distinctive marks and 

 differences of these types more closely, and take due 

 account of the relations of the ideal axes and their poles, 

 we are led to distinguish the nine groups or types which 

 are found in the sixth table. In this promorphological 

 system the determining factor is the disposition of the 

 parts to the natural middle of the body. On this basis 

 we make a first distinction into four classes or types: 

 (i) the centrostigma have a point as the natural middle 

 of the body; (2) the centraxonia a straight line (axis); 

 (3) the centroplana a plane (median plane) ; and (4) the 

 centraporia (acentra or anaxonia), the wholly irregular 

 forms, have no distinguishable middle or symmetry. 



I. Ckntrostigmatic Types. — The natural middle of the 

 body is a mathematical point. Properly speaking, only one 

 form is of this type, and that is the most regular of all, 

 the sphere or ball. We may, however, distinguish two sub- 

 classes, the smooth sphere and the flattened sphere. The 

 smooth sphere Qiolosphcera) is a mathematically pure sphere, 

 in which all points at the surface are equally distant from the 

 centre, and all axes drawn through the centre are of equal 

 length. We find this realized in its purity in the ovtun of 

 many animals (for instance, that of man and the mammals) 

 and the pollen cells of many plants; also cells that develop freely 



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