CHAPTER XVII 



ON THE THEORY OF TRANSFORMATIONS, OR THE 

 COMPARISON OF RELATED FORMS 



In the foregoing chapters of this book we have attempted to study 



the inter-relations of growth and form, and the part which the 



physical forces play in this complex interaction; and, as part of 



the same enquiry, we have tried in comparatively simple cases 



to use mathematical methods and mathematical terminology to 



describe and define the forms of organisms. We have learned in so 



doing that our own study of organic form, which we call by Goethe's 



name of Morphology, is but a portion of that wider Science of Form 



wtjch deals with the forms assumed by matter under all aspects 



and conditions, and, in a still wider sense, with forms which are 



theoretically im^aginable. 



The study of form may be descriptive merely, or it may become 



analytical. We begin by describing the shape of an object in the 



simple words of common speech : we end by defining it in the precise 



language of mathematics; aild the one method tends to follow the 



other in strict scientific order and historical continuity. Thus, for 



instance, the form of the earth, of a raindrop or a rainbow, the 



shape of the hanging chain, or the path of a stone thrown up into 



the air, may all be described, however inadequately, in common 



words ; but when we have learned to comprehend and to define the 



sphere, the catenary, or the parabola, we have made a wonderful 



ai^d perhaps a manifold advance. The mathematical definition of 



a "form" has a quahty of precision which was^ quite lacking in our 



earlier stage of mere description; it is expressed in few words or 



in still briefer symbols, and these words or symbols are so pregnant 



with meaning that thought itself is economised; we are brought 



by means of it in touch with Galileo's aphorism (as old as Plato, as 



old as Pythagoras, as old perhaps as the wisdom of the Egyptians), 



that "the Book of Nature is written in characters of Geometry*." 



♦ Cf. Plutarch, Symp. viii, 2, on the meaning of Plato's aphorism ("if it actually 

 was Plato's"): ttwj HXdrufv iXeye t6v d^bv ad yeuifxeTpe'tv. 



