472 TEE POPULAR SCIENCE MONTHLY 



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, physiolo- 

 gists like Helmholtz and Chauveau, psychologists like Wundt and 

 Fechner, the leading physical chemists, van't Hoff, Arrhenius, Eooze- 

 boom, Ostwald, van der Waals, van Laar, Nernst, Le Chatellier, Ban- 

 croft, have all employed mathematics as a necessary part of their equip- 

 ment, 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 unknovm substance. Maxwell could predict the existence of electro- 

 magnetic waves from his equations^ at least twenty-five years before 

 their actual demonstration by Hertz^" and Gibbs's algebraic statement 

 of the theorems of chemical statics was far in advance of their labora- 

 tory verification. 



Ostwald, in his interesting " Biologic des Naturforschers,"^^ 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 {Eomantiker) who, like Liebig, Fara- 

 day, 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 Eomantiker also. His mathematical theory of 

 chemical equilibrium was, as we have seen, far in advance of any experi- 

 mental 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," expressed his conviction that the science of statics " does not 



Thil. Tr., 1865., CLV., 497-501. 



^""Tagebl. d. Versamml. d. deutsch. Naturf. u. Aerzte 1889," Heidelberg, 

 1890, 144-9. 



"^ Deutsche Rev., 1907, XXXII., Pt. I., 16. 



^ " Report British Association for the Advancement of Science," 1857. 



