1899] ANIMAL SYMMETRY 53 



as the sphere and the circle are usually treated geometrically as 

 a polyhedron and a polygon respectively, but with an infinite number 

 of bounding sides. Other differences will be noticed by a detailed 

 comparison. 



In comparing the various meanings attached to the term "symmetry" 

 the only really consistent definition must be somewhat as follows : — 

 Symmetry of an organism is the system of arrangement of its constituent 

 parts in relation to each other and to a certain geometrical centre, which 

 may he called the centre or nucleus of symmetry. 



Animal symmetry is therefore merely a particular character of 

 form, and as such it must be in the same direct relation to environ- 

 ment as any other morphological character. In order to illustrate this 

 relation to its greatest extent one must adopt a classification of symmetry 

 which will bear direct comparison with the different grades of environ- 

 ment. Only in so far as it enables us to correlate form and environment 

 can a classification be regarded as " natural," just as a classification of 

 species can be regarded as " natural " only when it expresses the true 

 history of the changes of correlated form and environment, or the course 

 of evolution, in the genus or family. 



Our conceptions of space being based upon the three dimensions, we 

 naturally turn to the geometrical conceptions and their classification in 

 order to find a " natural" classification. In the inter-relation of 

 organism and environment and its determining influence, we find 

 that the three dimensional axes correspond to the lines of develop- 

 ment, and hence they are never inclined to each other. In other 

 words, we find no true " clinometric " forms, and we have only to 

 deal with the " orthometric." The stereometrical representatives of 

 the types will, therefore, all belong to the "right" series, and to this 

 extent there is a marked difference from the types of crystallography. 



Scattered throughout modern zoological literature we may find 

 statements that " radial " symmetry is correlated with or induced by 

 a sedentary or pelagic habitat, and others to the contrary, the latter 

 mainly relying upon the fact that there are, at the present state 

 of evolution, some sedentary or drifting organisms which show 

 little if any " radial " symmetry. It should not be necessary to 

 furnish proof that the symmetry of an organism tends to conform 

 to the symmetry of environment. Assuming this statement, it is 

 necessary to seek for a classification of environmental as a preliminary 

 to that of organismal symmetry. 



The widest division of symmetry of environment must depend upon 

 the three dimensions, and this consideration leads us to the following 

 divisions of animal form : — 



1. Centro-symmctry. — This consists essentially of repetition of parts 

 in three dimensions, hence the centre of symmetry is a point, the point 

 of intersection of the three dimensional axes (Fig. 1). The minimum 

 number of secondary centres of symmetry will be four, and the 



