for animals and plants: but as soon as Haû¥y showed the application of mathematics to {721} the description and clasôÙsiôÙfiôÙcaôÙtion of crystals, his methods were immediately adopted and a new science came into being.
A large part of the neglect and suspicion of mathôÙeôÙmatôÙiôÙcal 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 mathôÙeôÙmatôÙiôÙcal figure in an organism, the sphere, the hexagon, or the spiral which we so recognise merely resembles, but is never entirely explained by, its mathôÙeôÙmatôÙiôÙcal analogue; in short, that the details in which the figure differs from its mathôÙeôÙmatôÙiôÙcal prototype are more 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 mathôÙeôÙmatôÙiôÙcal 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 matter1. 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 mathematician to unravel the conflicting forces which are at work together. And this process of inôÙvesôÙtiôÙgaôÙtion 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