644 



SCIENCE. 



[X. S. Vol. XVIII. Xo. 4(i4. 



any of the generalizations of systematic 

 physics. I shall consider later the rela- 

 tions of biology and statistical physics, not, 

 of course, from the point of view of the 

 biologist, for this would be to discuss the 

 relation of organism to environment, but 

 in the light of some of the ideas of ther- 

 modynamics. 



The biologist and the engineer need to 

 have precise knowledge of thermodynamics, 

 inasmuch as it is thermodynamics chiefly 

 which determines the limits of correct ap- 

 plication of the ideas and methods of sys- 

 tematic physics to natural phenomena. 



This subject of thermodynamics is so 

 little understood that I am not willing to 

 proceed to a precise discussion of the qiies- 

 tions set forth in a general way above, 

 without first giving an outline of the 

 fundamental ideas of thermodynamics, 

 which I shall give as concisely and con- 

 cretely as possible. I feel justified in 

 taking yoi;r time in this way for the reason 

 that here and there throughout my presen- 

 tation you will find that the ideas are new, 

 and, furthermore, I wish this paper to be 

 readable by biologists and engineers. 



In some instances I shall insist upon 

 what may seem to be unnecessarily fine 

 distinctions; but Whewell says very aptly 

 that 'In order to acquire any exact solid 

 knowledge the student must possess with 

 perfect precision the ideas appropriate 

 to that part of knowledge.' If there is 

 any branch of physics where perfect pre- 

 cision of ideas is demanded it is, I think, 

 in the subject of thermodynamics, espe- 

 cially if the boundaries between the legit- 

 imate realm of thermodynamics and the 

 almost untouched realm of statistical 

 physics are to be sharply defined. 



Pei-fect precision of ideas is tested, as 

 Whewell says, by the extent to which one 

 perceives axiomatic evidence in a subject, 

 and I give this sketch of thermodynamics 



exactly with the view of setting forth 

 axiomatic evidences. 



1. THERMAL EQUILIBRIUM. 



When a substance is shielded from out- 

 side disturbance it settles to a state in 

 which there is no tendency to further 

 change of any kind. Such a state is called 

 a state of therynal equilibrium. 



When a substance has settled to thermal 

 equilibrium it is said to have a definite 

 temperature. The notion of temperature, 

 that is the precise idea of temperature, as 

 a physical fact is derived from the notion 

 of thermal equilibrium. Also the idea of 

 differences of temperature as physical facts 

 (not as quantities) is derived from com- 

 parisons of states of thermal equilibrium. 



The idea of thermal eciuilibrium applies 

 to a limit which is never realized. It is 

 impracticable to shield a substance com- 

 pletel.y. Failure of two kinds occurs, 

 namely, failure to prevent exchange of en- 

 ergy between one system and another, 

 either in the form of mechanical work or 

 in the form of heat, and failure to prevent 

 exchange of matter between one system 

 and another. This second failure is very 

 marked in the case of radioactive sub- 

 stances. Furthermore, our accepted no- 

 tions as to the quickness with which a gas, 

 for instance, settles to thermal equilibrium 

 may be altogether wrong, for Boltzmann 

 has pointed out that even a small mass of 

 gas shielded completely in a vessel may, for 

 all we know, require months to settle to 

 anything approaching complete thermal 

 equilibrium. 



Before proceeding with this outline of 

 thermodynamics I wish to state what is my 

 opinion as to the influence which the kinetic 

 theory (of gases) is destined to have upon 

 the subject of thermodynamics. Several 

 years ago, in writing a review of Duhem's 

 elaborate mathematical development of 

 thermodynamics, 'Mechanique Chemique, ' 



