-sect, iv.] INTRODUCTION. 19 



or Heterogeneity is found in the bodies of all organisms, even 

 in the simplest. 



Now in a wide survey of the forms of living things there is 

 a fact with regard to the presence of this Heterogeneity which bo 

 the purpose of our present consideration is of the highest con- 

 sequence. This may perhaps be best expressed by the state- 

 ment that in the bodies of living things Heterogeneity is generally 

 orderly and formal ; it is cosmic, not chaotic. Not only are the 

 bodies of all organisms heterogeneous, but in the great majority 

 the Heterogeneity occurs in a particular way and according to 

 geometrical rule. This character is not peculiar to a few 

 organisms, but is common to nearly all. We will now examine 

 this phenomenon of geometrical order in Heterogeneity and try 

 to see some of the elements of which it is made up. 



Order of form will first be found to appear in the fact that in 

 any living body the Heterogeneity is in some degree symmetri- 

 cally distributed around one or more centres. In the great 

 majority of instances these centres of symmetry are themselves 

 distributed about other centres, so that in one or more planes the 

 whole body is symmetrical. 



The idea of Symmetry which is here introduced is so familiar 

 that it is scarcely necessary to define it, but as all that follows 

 depends entirely on the proper apprehension of what is meant by 

 Symmetry it may be well to call attention to some of the phenomena 

 which the term denotes. 



In its simplest form the Symmetry of a figure depends on the 

 fact that from some point within it at least two lines may be 

 taken in such a way that each passes through parts which are 

 similar and similarly disposed. The point from which the lines 

 are taken may be called a centre of Symmetry and the lines may 

 be called lines of Symmetrical Repetition. 



Commonly the parts thus symmetrically disposed are related 

 to each other as optical images [in a plane mirror passing through 

 the centre of Symmetry and standing in a plane bisecting the 

 angle which the lines of Symmetrical Repetition make with each 

 other]. For a figure to be symmetrical, in the ordinary sense of 

 the term, it is not necessary that the relation of optical images 

 should strictly exist, and several figures, such as spirals, &c., 

 are accordingly described as symmetrical. But since the relation 

 of images exists in all cases of bilateral and radial symmetry, which 

 are the forms most generally assumed in the symmetry of organ- 

 isms, it is of importance to refer particularly to this as one of 

 the phenomena often associated with Symmetry. 



In the simplest possible case of Symmetry there is a series 

 of parts in one direction corresponding to a series of parts in 

 another direction. Perhaps there is no organism in which such an 

 arrangement does not at some time and in some degree exist. 

 For even in an unsegmented ovum or a resting Amoeba there is 



