108 Proceedings of the Royal Society of Edinburgh. [Sess. 
Returning now to the normal action of a diatomic gas such as N 2 , 0 2 , 
CO, or NO, in which the observed specific heat at ordinary temperatures is 
completely accounted for by molecular movements of translation and 
rotation, it is clear that any increase of specific heat when the tempera- 
ture is raised implies that additional energy is then taken up in 
establishing vibration, and that the principle of equipartition thereby fails. 
At ordinary temperatures the terms E' and E" make up substantially all 
the energy ; the vibration term E y// , representing to-and-fro movements of 
the pair of atoms, is generally insignificant. At high temperatures E"' 
becomes relatively larger, with the effect that the specific heat C v increases 
above |R, and y is reduced below 1*4. In the molecules of these gases, 
energy of vibration, in any amount that is sufficient to affect measurably 
the specific heat, is produced only by comparatively violent encounters. 
But in some diatomic gases, notably the vapours of the halogen elements, 
it is observed that at ordinary or moderate temperatures C v exceeds fR 
and y is less than 1*4. There the atoms are heavy and presumably 
the bonds between the pair are relatively weak, so that vibrations which 
contribute a substantial part of the whole energy are set up by low- 
temperature encounters, vibrations of relatively long period being excited 
at relative low temperature. 
In a triatomic gas the atoms presumably group themselves with the 
massive particles at the corners of a triangle, and in a polyatomic gas at 
the corners of a polyhedron. In either case there are clearly three effective 
freedoms of rotation, and the principle of equipartition applied to them 
makes E" equal to fRT. Hence, in such gases, so long as the vibratory 
energy is negligible we should have C v = 3R and y = 1^. The fact that, 
when the specific heat of such gases is measured in the normal state, C v is 
found to be greater than 3R, and y always less than 1J, means that there 
is an appreciable amount of energy of vibration, even at ordinary tempera- 
tures. This is especially noticeable in polyatomic gases, where the possible 
modes of to-and-fro vibration of atoms are more numerous. In C0 2 there 
are, as we saw, three characteristic modes ; * one at least of these modes is 
excited by low-temperature encounters sufficiently to contribute an amount 
of energy which reduces y from 1*333 to about 1*30. In polyatomic gases 
values of y as low as 1*13 or lower are found at ordinary temperatures.f 
The increase in specific heat which is produced by heating shows that the 
* An interesting paper by Bjerrum ( Vorhandl . d. deutsch. Phys. Gesellschaft , 1914, p. 737) 
suggests various configurations of a C0 2 molecule to give the three observed periods of 
vibration. 
f Capstick, Phil. Trans., A, 1895, vol. 186, p. 588. 
