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 

 certain of 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 in order to describe and define the forms of organisms. 

 We have learned in so doing that our own study of organic form, 

 wliich we call by Goethe's name of Morphology, is but a portion 

 of that wider Science of Form which deals with the forms assumed 

 by matter under all aspects and conditions, and, in a still wider 

 sense, with forms which are theoretically imaginable. 



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 ; and 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 and perhaps a manifold advance. The mathe- 

 matical definition of a "form" has a quality 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 



* Reprinted, with some changes and additions, from a paper in the Trans. 

 Roy. Soc. Edin. L, pp. 857-95, 1915. 



