XOVEMBEB 20, 1903.] 



SCIENCE. 



645 



I contrasted the purely sensible basis and 

 the abstract but inevitable mathematical 

 structure of thermodynamics, on the one 

 hand, with the mathematical theory of 

 electricity and magnetism as it stands in 

 Maxwell's 'Treatise,' on the other hand. 

 Maxwell's theory is, of course, largely 

 based on sensible things, but sensible things 

 which are more or less inadequate to de- 

 termine the essential elements of the theory, 

 so that conception enters as an important 

 and vital part of the theory. I stated that 

 perhaps we are to have in thermodynamics 

 a branch of physics which is to remain 

 independent of conceptions, to remain, in 

 other words, a purely algebraic structure 

 resting upon an adequate foundation of 

 axiomatic evidence which may be directly 

 perceived. I do not now think that this 

 is to be the case, but I think that the ideas 

 of the kinetic theory, or, as Gibbs puts it, 

 the ideas of statistical mechanics, are des- 

 tined to become vital in the subject of 

 thermodj'namics ; and I think that it is 

 of the greatest importance in the treatment 

 of thermodynamics, to reach conceptions 

 of every fundamental notion with the help 

 of the kinetic theory (statistical mechan- 

 ics). 



In view of my opinion as to the vital 

 importance of .statistical mechanics in 

 thermodynamics, I shall suggest, whenever 

 I can do so brieflj', the molecular concep- 

 tions of the various notions of thermo- 

 dynamics. 



The Molecular Conception of Thermal 

 Equilibriutn.— The molecular motion at a 

 given point in a gas (and no doubt in any 

 substance) in thermal equilibrium is en- 

 tirely erratic; an irregular and extremely 

 rapid succession of fits and starts occurs 

 as the molecules collide against each other, 

 and the character of the molecular motion 

 at the point is still further complicated by 

 the fact that different molecules are con- 

 tinually passing the given point from 



every direction and with every variety of 

 speed and oscillatoiy motion. Because of 

 the enormous number of molecules in any 

 perceptible volume of a substance it is the 

 average character of the molecular motion, 

 only, which has to do with temperature 

 and pressure and in general with all 

 thermal properties of substances; and, 

 because of the enormous number of mole- 

 cules, this average character of molecular 

 motion is constant and uniform throughout 

 a substance when the substance is in ther- 

 mal equilibrium. 



2. REVERSIBLE PROCESSES. 



A substance in thermal equilibriiim is 

 generally under the influence of external 

 agencies. Thus, surrounding substances 

 confine the given sub.stance to a certain 

 region of space and they exert upon the 

 given substance a constant pressure; sur- 

 rounding substances are at the same tem- 

 perature as the given substance and the 

 molecules of the given substance rebound 

 from surrounding substances with their 

 motion, on the average, unchanged; sur- 

 rounding substances may exert constant 

 magnetic or electric influences upon the 

 given substance, and so on. However, a 

 substance can not be in thermal equilibrium 

 when work is continually done upon or 

 done by it, or when heat is continually 

 given to or taken from it. 



If the external influences which act upon 

 a fluid in thermal equilibrium are made 

 to change very slowly, causing the pressure 

 and volume of the fluid to pass very slowly 

 through a continuous series of values and 

 in general involving the doing of work 

 upon or by the fluid and the giving of heat 

 to or taking of heat from the fluid, the 

 fluid will pass slowly through a process 

 C07isistmg of a co7itinuous series of states 

 of thermal equilibrium. Such a process 

 is called a reversible process, for the reason 

 that the fluid will pass through the same 



