XVII] THE COMPARISON OF RELATED FORMS 721 



the description and classification of crystals, his methods were 

 immediately adopted and a new science came into being. 



A large part of the neglect and suspicion of mathematical 

 methods in organic morphology is due (as we have partly seen in 

 our opening chapter) to an ingrained and deep-seated belief that 

 even when we seem to discern a regular mathematical figure in 

 an organism, the sphere, the hexagon, or the spiral which we so 

 recognise merely resembles, but is never entirely explained by, 

 its mathematical analogue ; in short, that the details in which the. 

 figure differs from its mathematical prototype are rhore important 

 and more interesting than the features in which it agrees, and 

 even that the peculiar aesthetic pleasure with which we regard 

 a living thing is somehow bound up with the departure from 

 mathematical regularity which it manifests as a peculiar attribute 

 of life. This view seems to me to involve a misapprehension. 

 There is no such essential difference between these phenomena of 

 organic form and those which are manifested in portions of 

 inanimate matter*. No chain hangs in a perfect catenary and no 

 raindrop is a perfect sphere : and this for the simple reason that 

 forces and resistances other than the main one are inevitably at 

 work. The same is true of organic form, but it is for the mathe- 

 matician to unravel the conflicting forces which are at work 

 together. And this process of investigation may lead us on step 

 by step to new phenomena, as it has done in physics, where 

 sometimes a knowledge of form leads us to the interpretation of 

 forces, and at other times a knowledge of the forces at work 

 guides us towards a better insight into form. I would illustrate 

 this by the case of the earth itself. After the fundamental advance 

 had been made which taught us that the world was round, Newton 

 showed that the forces at work upon it must lead to its being 

 imperfectly spherical, and in the course of time its oblate spheroidal 

 shape was actually verified. But now, in turn, it has been shown 

 that its form is still more complicated, and the next step will be 

 to seek for the forces that have deformed the oblate spheroid. 



* M. Bergson repudiates, with peculiar confidence, the application of mathe- 

 matics to biology. Cf. Creative Evolution, p. 21, "Calculation touches, at most, 

 certain phenomena of organic destructioii. Organic creation, on the contrary, 

 the evolutionary phenomena which properly constitute life, we cannot in any way 

 subject to a mathematical treatment." 



T. G. 46 



