112 MICHELSON— FORM ANALYSIS. 



[April 1 8 



This, however, may well be left open, so that specialists in the 

 various branches of science may elaborate details in such a way as to 

 best fit their respective needs. 



It will be noted that the proposed system extends the idea of 

 radial symmetry to include the vast array of natural forms which 

 radiate, though not necessarily from a center of figure and which 

 would otherwise be considered either unsymmetrical, or as having 

 merely axial or plane symmetry. 



Another point is the explicit recognition of '' odd " symmetry. 

 This kind of symmetry is admitted by the mathematician on the 

 same terms as " even " — though not so generally by the biologist 

 or the crystallographer. It is easy to show that the one is quite as 

 logical as the other. 



The definition of symmetry is necessarily arbitrary — as in fact is 

 well shown by the varied significance attached to the term by 

 biologists, crystallographers and mathematicians. The last are com- 

 ing to recognize any form as symmetrical when any admitted essen- 

 tial character is unaltered by any specified operation. So broad a 

 definition would scarcely emphasize what is generally understood by 

 the term; but if the ''operations" be restricted to (i) rotation 

 through two right angles, and (2) reflection in a plane, a symmetrical 

 form may be defined as one whose corresponding points are {a) 

 equidistant from a point, a line, or a plane; and {h) in which con- 

 gruence may be obtained by a single " operation." 



If condition a is fulfilled, but not h (as in the case of triclinic 

 crystals)", or if more than one operation is required for congruence, 

 the form may be said to have partial symmetry.^ 



II. Unsymmetrical Forms. 



Forms exist in endless variety which do not fall under any of 

 these divisions, whose beauty and interest may be fully as striking 

 as the symmetrical forms. 



These may be classified according to the following scheme, which 

 is only provisional. 



A. Rhythmic. 



^If it were not for condition a the helix would have to be considered a 

 symmetrical form; but h provides that it have partial symmetry. 



