CONSTITUTED OF SPHERICALLY SYMMETRICAL MOLECULES. 



465 



of f is theoretically unsound, and (ii) that the internal energy does not travel at the 

 same rate as the translational energy. Hence the agreement of MEYER'S theory with 

 experiment must be accidental. 



I'.oi.T/M \\v, who opposed Mi.\ i:i;'> \ie\v, developed a theory of conduction* on the 

 basis of M \.\\\ KI.I.'S hypothesis, taking into account the internal energy. Heobtained 

 the foll<>\\ ing relation between / and y, the ratio of the specific heats, 



This reduces to MAXWELL'S law when y = $, but the formula, as we shall see, is 

 not borne out by the experimental data. 



I have not attempted to work oxit a theory of conduction in polyatomic gases, and 

 shall t)e content with pointing out how (in a general way, and with some marked 

 exceptions, which may, however, be due to faulty data) / tends to be larger or 

 smaller (while always less than 2) according as a gas has less or more internal energy. 

 The table below gives the values of & for all the gases for which determinations 

 are available, together with y, C r , //, and the values of / calculated from them, and 

 also f as calculated from BOLTZMANN'S formula. The gases are arranged in increasing 

 order of y, i.e., in diminishing order of /3, the ratio of internal energy to total energy. 



* TOGO. Ann.,' 157, 1876, pp. 457-469. The theory is partly empirical, being an adaptation of 

 MAXWELL'S formula in which / = . BOLTZMANX states (p. 468) that the numerical coefficients would 

 have to be altered if any other molecular hypothesis were adopted. Our theorem shows that this is not 

 true, at any rate when y 



- 

 



t These values of y are taken from JEANS' "Dynamical Theory of Gases " (pp. 220, 221), except where 

 the contrary is indicated. 



1 LANDOLT and BORNSTEIN'S tables ; observed by MULLER. 



2 'Smithsonian Physical Tables,' 1910; observed by MULLER. 

 8 Ibid. ; by WULLNER. 



J These values of C are taken from JEANS' treatise (p. 218), except where the contrary is indicated. 

 They are due to WIEDEMANN and WULLNER. 



VOL. CCXI. A. 3 O 



