we soon reach through mathôÙeôÙmatôÙiôÙcal analysis to mathôÙeôÙmatôÙiôÙcal synthesis; we discover homologies or identities which were not obvious before, and which our descriptions obscured rather than revealed: as for instance, when we learn that, however we hold our chain, or however we fire our bullet, the contour of the one or the path of the other is always mathôÙeôÙmatôÙiôÙcally homologous. Lastly, and this is the greatest gain of all, we pass quickly and easily from the mathôÙeôÙmatôÙiôÙcal conception of form in its statical aspect to form in its dynamical relations: we pass from the conception of form to an understanding of the forces which gave rise to it; and in the representation of form and in the comparison of kindred forms, we see in the one case a diagram of forces in equiôÙlibôÙrium, and in the other case we discern the magnitude and the direction of the forces which have sufficed to convert the one form into the other. Here, since a change of material form is only effected by the movement of matter, we have once again the support of the schoolmanãs and the philosopherãs axiom, ãIgnorato motu, ignoratur Natura.ã
In the morphology of living things the use of mathôÙeôÙmatôÙiôÙcal methods and symbols has made slow progress; and there are various reasons for this failure to employ a method whose advantages are so obvious in the inôÙvesôÙtiôÙgaôÙtion of other physical forms. To begin with, there would seem to be a psychological reason lying in the fact that the student of living things is by nature and training an observer of concrete objects and phenomena, and the habit of mind which he possesses and cultivates is alien to that of the theoretical mathematician. But this is by no means the only reason; for in the kindred subject of mineralogy, for instance, crystals were still treated in the days of Linnaeus as wholly within the province of the naturalist, and were described by him after the simple methods in use