196 THE POPULAR SCIENCE MONTHLY 



instrument of precision, our mathematical methods are but an approxi- 

 mation to the subtler aspects of nature, and it is only by eternal vigi- 

 lance in regard to sources of human error that workers in physical sci- 

 ence have put aside personal equation and infallibility and thus avoided 

 what Eowland calls the " discontinuity " of the ordinary legal or culti- 

 vated mind. 140 " Gibbs'has not sought to give a mechanical explana- 

 tion of heat," says Professor Bumstead, "but has limited his task to 

 demonstrating that such an explanation is possible. And this achieve- 

 ment forms a fitting culmination of his life's work." 141 



The naturalist Haeckel has explicitly denied the doctrine of uni- 

 versal increase of entropy 142 because, pointing as it does to the ultimate 

 thermal death of different worlds, it conflicts with his monistic con- 

 ception, 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 con- 

 centrate. 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 impor- 

 tant 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- 



We have formulas and tables; we make use of thermodynamics and the differ- 

 ential 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. 



140 H. A. Rowland, Am. J. 8c, 1899, 4. s., VIII., 409. 



141 Bumstead, Am. J. 8c, 1903, 4. s., XLL, 199. 



142 Haeckel, " The Riddle of The Universe," New York, 1900, 246-248. 



