science is itself a powerful instrument of precision, which, if applied in the right way to data of the right sort, may yield important results. Biologists like Loeb, Francis Galton, Karl Pearson, Driesch, physiologists like Helmholtz and Chauveau, psychologists like Wundt and Fechner, the leading physical chemists, van't Hoff, Arrhenius, Roozeboom, Ostwald, van der Waals, van Laar, Nernst, Le Chatellier, Bancroft, have all employed mathematics as a necessary part of their equipment, and more especially has knowledge been advanced by physicists like Maxwell, Lord Kelvin, Helmholtz, Hertz, the Curies, Stokes, J. J. Thomson and Gibbs, who have got at the more imperceptible aspects of nature by deductive methods "interlaced with physical induction and experience." In the discovery of radium by the Curies all the processes up to the use of pitchblende were inductive; after that every step taken was pure deduction, based upon the a priori assumption of an unknown substance. Maxwell could predict the existence of electromagnetic waves from his equations[1] at least twenty-five years before their actual demonstration by Hertz[2] and Gibbs's algebraic statement of the theorems of chemical statics was far in advance of their laboratory verification.
Ostwald, in his interesting "Biologic des Naturforschers,"[3] has divided men of science into two classes: The classicists (Klassiker), men like Newton, Lagrange, Gauss, Harvey, who, dealing with a limited number of ideas in their work, seek formal perfection and attain it, leaving no school of followers behind them, but only the effect of the work itself; and the romanticists (Romantiker) who, like Liebig, Faraday, Darwin, Maxwell, are bold explorers in unknown fields, men fertile in ideas, leaving many followers and many loose ends of unfinished work which others complete. In the logical perfection of his work and in his unusual talent for developing a theme in the most comprehensive and exhaustive manner, Gibbs was emphatically the Klassiker. But in the scientific achievement of his early manhood he showed something of the spirit of the Romantiker also. His mathematical theory of chemical equilibrium was, as we have seen, far in advance of any experimental procedure known or contemplated at the time of its publication, and, although some of his predecessors, like James Thomson, Massieu, Horstmann, had come within sight of the new land and even skirted its shores, Gibbs, with the adventurous spirit of the true pioneer, not only conquered and explored it, but systematically surveyed it, living to see part of his territory occupied by a thriving band of workers, the physical chemists. Cayley, in his report on theoretical dynamics in 1857,[4] expressed his conviction that the science of statics "does not
