72 BELL SYSTEM TECHNICAL JOURNAL 



data are available^ for all of the noble gases from helium through xenon; 

 and I quote the values which they furnish for this "remainder": 



He 1.59 ± 0.01; Ne (two experiments) 1.56 ± 0.04, 1.59 ± 0.01 



Ar (two experiments) 1.61 and 1.61 ± 0.04; 



Kr 1.59 ± 0.02; Xe 1.588 

 The agreements are remarkably good, and when one remembers the contrast 

 and the subtlety of the two theories which they ratify conjointly, one deems 

 them among the most impressive in the whole of physics or of chemistry 

 either. The result for He implies that So = for liquid helium. 



There are data available also for the vapors of several metals, though for 

 these the experimentalist's task is much harder. It will be seen that in 

 most of the cases we may again rejoice in agreements, though within a 

 broader range of experimental unsureness; in a few there is disagreement, 

 and one can only wonder whether the measurer of vapor-pressure underesti- 

 mated his possible error. 



Na (two experiments) 1.57 ± 0.1 and 1.41 ± 0.03; 

 K 1.47 ± 0.04; Mg. 1.61 ± 0.2; Zn 1.51 ± 0.15; 

 Cd (two experiments) 1.63 ± 0.1, 1.51 db 0.1; Hg 1.62 ± 0.03; 

 Tl 1.40 ± 0.3; Pb (two experiments) 1.7 ± 0.2, 1.21 ± 0.26. 

 So the situation with respect to monatomic gases is satisfactory on the 

 whole and almost unblemished.^ But monatomic gases are but a small 

 proportion of all vapors: has not the theory something to say as regards 

 those which are diatomic — such as oxygen, hydrogen, nitrogen, carbon 

 monoxide — and even those which are polyatomic? 



The theory does indeed cover these; and the needed enlargement is simple 

 to write down, if not always easy to compute. Thus far the partition- 

 function has contained only the terms supplied by the translatory motions 

 of the molecules in the container — terms which depend on no other quality 

 of the molecules than their masses, and for a given mass are the same whether 

 the molecule is composed of a single atom or of two or of many. Now to 

 the partition-function so composed are to be added the terms deriving from 

 the rotation and from the vibrations of the molecules. Each new term is 

 of the familiar form exp{—Ei/kT), where now Ei is to stand for some 

 permitted energy-value of rotation or of vibration, and the summation is 



5 Data from the collation of Ditchburn and Gilmour {Rev. Mod. Phys. 13, 310, 1941), 

 except the value for xenon which is from Clusius. 



^ Here I must say, even if only in a footnote, that for atoms which ha ve angular momentum 

 there is still one more term in the additive constant occurring in the right-hand member of 

 (30). This term may be loosely described as referring to the "disorder" arising from the 

 fact that there are two or more different orientations of the angular momentum, between 

 which the atoms may choose. Its exact value (zero for the inert gases, riRlnl for the 

 alkali metals) is derived from the spectrum of the atom. Allowance is made for this 

 term in the computation leading to the value of the "remainder", and the agreements 

 here tabulated for Na and K sustain the allowance. A bad disagreement for tungsten 

 emerges from an early (1924) research by Lange. 



