instrument of precision, our mathematical methods are but an approximation to the subtler aspects of nature, and it is only by eternal vigilance in regard to sources of human error that workers in physical science have put aside personal equation and infallibility and thus avoided what Rowland calls the "discontinuity" of the ordinary legal or cultivated mind.[1] "Gibbs has: not sought to give a mechanical explanation of heat," says Professor Bumstead, "but has limited his task to demonstrating that such an explanation is possible. And this achievement forms a fitting culmination of his life's work."[2]
The naturalist Haeckel has explicitly denied the doctrine of universal increase of entropy[3] because, pointing as it does to the ultimate thermal death of different worlds, it conflicts with his monistic conception of the universe as a perpetuum mobile, consisting of infinite substance in eternal motion, without beginning and without end. Yet the cosmogony of Kant and Laplace, which Haeckel accepts, points to the same conclusion as well as to formative periods in the history of the solar and sidereal systems, in which entropy decreases, and energy, instead of dissipating; tends, after a maximum of degradation, to concentrate. Even possibilities of this kind put the second law on a lower plane of probability than the first as far as man is concerned, unless it be that the irreversible processes of nature are in reality cyclic, in which case we should have Nietzsche's "eternal return" of all things. But as Bumstead has so admirably said, "It is nearer the truth to base the doctrine of entropy upon the finite character of our perceptions than upon infinity of time."
In connection with the validity of the second law arises the important question of the extent of its application to animate nature and whether it is capable of reversal in vital processes. "The first law (conservation of energy) has been proven," says Ostwald, "with an exactness of 1: 1,000 even for physiological combustion (including mechanical and psychical work performed)." The second law, whether in the Clausius form of increase of entropy, the Kelvin form of dissi-
- ↑ H. A. Rowland, Am. J. Sc., 1899, 4. s. . VIII., 409.
- ↑ Bumstead, Am. J. Sc., 1903, 4. s M XLI., 199.
- ↑ Haeckel, "The Riddle of The Universe," New York, 1900, 246-248.
We have formulas and tables; we make use of thermodynamics and the differential calculus; but this is for the most part a vain show. Long before we reach the point where the formula is to be tested experimentally we slip in a simplifying assumption: that the concentration of one component may be considered as a constant; that the heat of dilution is zero; that the solute may be treated in all cases as though it. were an indifferent gas; that the concentration of the dissociated portion of a salt may be substituted for the total concentration; etc., etc. The result is that our calculations apply at best only to limiting or ideal cases, where an error in deducing the formula may be masked by errors in observation. Helmholtz did not do this, but Helmholtz is considered old-fashioned." W. D. Bancroft, J. Phys. Chem., 1899, III., 604.
