Of the chemistry of his day and generation, Kant declared that it was ãa science, but not science,ãããeine Wissenschaft, aber nicht Wissenschaftã; for that the criterion of physical science lay in its relation to mathematics. And a hundred years later Du Bois Reymond, profound student of the many sciences on which physiology is based, recalled and reiterated the old saying, declaring that chemistry would only reach the rank of science, in the high and strict sense, when it should be found possible to explain chemical reactions in the light of their causal relation to the velocities, tensions and conditions of equiôÙlibôÙrium of the component molecules; that, in short, the chemistry of the future must deal with molecular mechanics, by the methods and in the strict language of mathematics, as the astronomy of Newton and Laplace dealt with the stars in their courses. We know how great a step has been made towards this distant and once hopeless goal, as Kant defined it, since vanãt Hoff laid the firm foundations of a mathôÙeôÙmatôÙiôÙcal chemistry, and earned his proud epitaph, Physicam chemiae adiunxitÿ£¢1.
We need not wait for the full realisation of Kantãs desire, in order to apply to the natural sciences the principle which he urged. Though chemistry fall short of its ultimate goal in mathôÙeôÙmatôÙiôÙcal mechanics, nevertheless physiology is vastly strengthened and enlarged by making use of the chemistry, as of the physics, of the age. Little by little it draws nearer to our conception of a true science, with each branch of physical science which it {2} brings into relation with itself: with every physical law and every mathôÙeôÙmatôÙiôÙcal theorem which it learns to take into its employ. Between the physiology of Haller, fine as it was, and that of Helmholtz, Ludwig, Claude Bernard, there was all the difference in the world.
As soon as we adventure on the paths of the physicist, we learn to weigh and to measure, to deal with time and space and mass and their related concepts, and to find more and more our knowledge expressed and our needs satisfied through the concept of number, as in the dreams and visions of Plato and Pythagoras; for modern chemistry would have gladdened the hearts of those great philosophic dreamers.
But the zoologist or morphologist has been slow, where the physiologist has long been eager, to invoke the aid of the physical or mathôÙeôÙmatôÙiôÙcal sciences; and the reasons for this difference lie deep, and in part are rooted in old traditions. The zoologist has scarce begun to dream of defining, in mathôÙeôÙmatôÙiôÙcal language, even the simpler organic forms. When he finds a simple geometrical construction, for instance in the honey-comb, he would fain refer it to psychical instinct or design rather than to the operation of physical forces; when he sees in snail, or nautilus, or tiny foraminiferal or radiolarian shell, a close approach to the perfect sphere or spiral, he is prone, of old habit, to believe that it is after all something more than a spiral or a sphere, and that in this ãsomething moreã there lies what neither physics nor mathematics can explain. In short he is deeply reluctant to compare the living with the dead, or to explain by geometry or by dynamics the things which have their part in the mystery of life. Moreover he is little inclined to feel the need of such explanations or of such extension of his field of thought. He is not without some justification if he feels that in admiration of natureãs handiwork he has an horizon open before his eyes as wide as any man requires. He has the help of many fascinating theories within the bounds of his own science, which, though a little lacking in precision, serve the purpose of ordering his thoughts and of suggesting new objects of enquiry. His art of clasôÙsiôÙfiôÙcaôÙtion becomes a ceaseless and an endless search after the blood-relationships of things living, and the pedigrees of things {3} dead and gone. The facts