374 Lord Kelvin [April 27, 



kinetic energy of one component of the motion of the inertial centre, 

 where P denotes the ratio of the mean potential energy of the relative 

 displacements of the parts to the mean kinetic energy of the whole 

 system. Now, according to Clausius' splendid and easily proved 

 theorem regarding the partition of energy in the kinetic theory of 

 gases, the ratio of the difference of the two thermal capacities to the 

 constant-volume theimal capacity is equal to the ratio of twice a single 

 component of the translational energy to the total energy. Hence, if 

 according to our usual notation we denote the ratio of the thermal 

 capacity pressure-constant to the thermal capacity volume-constant by 

 k, we have, 



k _ 1 = 2_ 



3*(1+P/ 



§ 24. Example 1. — For first and simplest example, consider a 

 monatomic gas. We have i = 1, and according to our supposition 

 (the supposition generally, perhaps universally, made) regarding 

 atoms, we have P = 0. Hence, k — 1 = § . 



This is merely a fundameutal theorem in the kinetic theory of 

 gases for the case of no rotational or vibrational energy of the mole- 

 cule ; in which there is no scope either for Clausius' theorem or for 

 the Boltzmaun-Maxwell doctrine. It is beautifully illustrated by 

 mercury vapour, a monatomic gas according to chemists, for which 

 many years ago Kundt, in an admirably designed experiment, found 

 k — 1 to be very approximately § ; and by the newly discovered gases 

 argon, helium, and krypton, for which also k — 1 has been found to 

 have approximately the same value, by Rayleigh and liamsay. But 

 each of these four gases has a large number of spectrum lines, and 

 therefore a large number of vibrational freedoms, and therefore, if 

 the Boltzmann-Maxwell doctrine were true, k — 1 would have some 

 exceedingly small value, such as that shown in the ideal example of 

 § '26 below. On the other hand, Clausius' theorem presents no difficulty ; 

 it merely asserts that k — 1 is necessarily less than | in each of these 

 four cases, as in every case in which there is any rotational or vibra- 

 tional energy whatever ; and proves, from the values found experi- 

 mentally for k — 1 in the four gases, that in each case the total of 

 rotational and vibrational energy is exceedingly small in comparison 

 with the translational energy. It justifies admirably the chemical 

 doctrine that mercury vapour is practically a monatomic gas, and it 

 proves that argon, helium, and krypton, are also practically monatomic, 

 though none of these gases has hitherto shown any chemical affinity or 

 action of any kind from which chemists could draw any such conclusion. 



But Clausius' theorem, taken in connection with Stokes' and 

 Kirchoff's dynamics of spectrum analysis, throws a new light on what 

 we are now calling a " practically monatomic gas." It shows that, 

 unless we admit that the atoms can be set into rotation or vibration 

 by mutual collisions (a most unacceptable hypothesis), it must have 

 satellites connected with it (or ether condensed into it or around it) 



