582 PROCEEDINGS OF THE AMERICAN ACADEMY. 



imagined to be due to a restriction of thermal vibrations already almost 

 infinitesimal. 



These facts add strong support to the many-sided inference drawn from 

 other facts that some repulsive tendency other than heat-vibration must 

 be the cause of the permanent volume of solids and liquids — some tend- 

 ency which is an intrinsic property of the atoms themselves. If so, this 

 property must exist in the atoms of a gas as well as in those of a solid 

 and liquid, and must also in a gas prevent the actual collision of the 

 atomic centres, and thus take part in the "covolume " of the equation of 

 van der Waals. This conclusion is not in any way inconsistent with the 

 kinetic theory of gases, — in a gas the compressible molecules must still 

 be supposed to be separate and to produce j^ressure by the momentum of 

 their impact. In this connection it might be well to call attention to 

 other evidence to be drawn from the viscosity of gases, that the bulk of 

 polyatomic gas-molecules must be of the same order as that of monatomic 

 gas-molecules, j^oyes and Goodwin * found that the viscosity of mer- 

 cury vapor seems to show its molecule to be about the same bulk as the 

 molecule of carbon dioxide, and they sum up their investigation with 

 these words : "These results indicate that the atoms and molecules are 

 of the same order of magnitude, and that the spaces between the atoms 

 within the molecule, if any exist, are not large in comparison with those 

 occupied by the atoms themselves." 



In short, the " atomic environment " is really the volume which comes 

 into consideration in all cases where the atomic volume is to be considered 

 at all, and hence should be considered as the true volume of the atom. 

 The conception of a hard, central particle is unnecessary, and assumptions 

 concerning the supposed volume of the atomic centre must be of the 

 most vague and hypothetical character, since this supposed volume never 

 comes within the ran^e of direct relative measurement. Since the meas- 

 urable atomic volume is compressible, it is reasonable to assume that the 

 atom is compressible, and that this atomic elasticity affords the possibility 

 of heat vibration in solids and liquids composed of contiguous particles. 



Some of the many other arguments in favor of this point of view have 

 been already recounted in the three previous papers, and need not be 

 recapitulated here. The object of the present paper is to bring a greater 

 degree of numerical accuracy into the interpretation of the facts, and to 



* A. A. Noyes and Goodwin, These Proceedings, 32, 235 (1897). Professor 

 Noyes has kindly called my attention to this work. See also Lord Rayleigh, Phil. 

 Trans., 186 A, 187 (1895). Schultze Drude's Ann. (4) 5, 140 (1901). 



