172 



SCIENCE. 



[N. S. Vol. XXIII. No. 579. 



For the vapors silicon tetrachloride, 

 titanium tetrachloride, and tin tetrachlo- 

 ride, we make the same assumptions as in 

 the last case about the freedom of the 

 chlorine atoms, and get 6 = 22. 



There is a difficulty which I can not solve 

 about the methane derivatives. Their spe- 

 cific heats have been determined only in 

 two cases, but we have two sets of values 

 of y, one obtained by Miiller, the other by 

 Capstick. Miiller 's values conform fairly 

 well to the hypothesis that the hydrogen 

 atoms of the methane (CH^) molecule are 

 fixed, and that each chlorine atom substi- 

 tuted for a hydrogen atom introduces 2 

 interior coordinates. 



CHj.... 

 CHjCl. 



CH2CI2. 



CHCL. 



(,» + S 



1.333 

 1.200 

 1.142 

 1.111 



1.32 

 1.20 

 1.12 

 1.11 



The agreement is very good. On the 

 other hand, Capstick 's numbers for y are 

 different, and generally larger than Miil- 

 ler 's. They do not fit easilj^ into any sim- 

 ilar scheme. 



The constant k = 0.9886 may be used to 

 calculate the atomic heats of the solid ele- 

 ments. To do this we make the hypothesis 

 that the aggregation in these solids is 

 atomic rather than molecular, and that 

 each atom vibrates in simple harmonic 

 motion about a position of equilibriiun. 

 On this assumption each atom will re- 



ceive, when heated, twice the energy that 

 is taken up by its three translational de- 

 grees of freedom. On the principle of 

 equipartition, the energy taken up by one 

 such degree of freedom is the same as that 

 taken up by one translational degree of 

 freedom of the hydrogen molecule, or is 

 equal to the constant k. The atomic heat 

 should therefore equal 6A;, or 5.93. A com- 

 parison of this with the observed values of 

 the atomic heats, which range from 5.5 to 

 6.3, indicates that the hypothesis upon 

 which the result is obtained is in the main 

 correct. It is useless to speculate on the 

 reasons for the different values of the 

 atomic heats of the different elements. We 

 can account for them without denying the 

 doctrine of equipartition by supposing that 

 the vibrations of the atoms are not strictly 

 simple harmonic. 



Hitherto we have followed Staigmiiller. 

 It seems to me clear, after studying his 

 results, that it is possible to account for 

 the specific heats of gases by supposing the 

 energy distributed equally over certain de- 

 grees of freedom ; and it seems to me, fur- 

 ther, that the explanations which Staig- 

 miiller has given of his choices of the 

 number of degrees of freedom which he 

 selects for each type of molecule are at 

 least plausible. The most striking featiire 

 of these choices is the small number of 

 internal degrees of freedom assigned to the 

 atoms. It seems as if the atoms were— 

 at least with respect to certain directions 

 of displacement — rigidly bound together. 

 Lord Rayleigh has remarked that, on the 

 ordinary theory of equipartition, no matter 

 how small the play of an atom may be in 

 the sense of a coordinate, the degree of 

 freedom thus indicated must have its full 

 share of energy; so that nothing short of a 

 truly rigid connection in one direction will 

 allow us to neglect the degree of freedom 

 in that direction. From this difficulty we 

 may escape by the use of the distinction 



