VI 



that the radiating power of black bodies in various media was pro- 

 portional to the square of the refractive index of the medium, which 

 involves a corresponding law of radiation of electromagnetic 

 energy. 



In all these applications his attention was constantly directed to 

 the underlying molecular motions which explained the phenomena on 

 dynamical principles. It was in this connexion that he investigated 

 the dynamical foundations of the Second Law of Thermodynamics and 

 the molecular theory of gases and of electrolysis. 



In quite an early investigation he had been dominated by the con- 

 ception that heat in a body can be considered as separated into two 

 parts, one the kinetic energy of atoms, and the other the potential 

 energy of forces between atoms. His later investigations were 

 elaborations of these conceptions by the application of statistical 

 methods, and by mathematical analysis of the highest order. He 

 showed that the heat in a body could be expressed as the product of 

 two factors, one proportional to the mean kinetic energy of the atoms, 

 and the other depending on the mass, velocity, and period of their 

 motions. These factors may be identified with temperature and 

 entropy, and so furnish a dynamical basis for the theory of heat. 

 Involved in these investigations was the Theorem of the Virial, which 

 is so important in the dynamics of stationary motion. His theory is 

 in accordance with much that we know, though it neglects radiation, 

 and forces between molecules depending on their motions and posi- 

 tions, which may be systematically different before and after collision. 

 With the ether among the molecules it is almost impossible but that 

 some such forces exist, while the success of dynamical theories 

 that neglect them seems to show that their effect cannot be very 

 great. 



While Clausius was elaboi'ating these general results, he attacked 

 the simpler case of the molecular theory of gases. That the pro- 

 perties of gases were in some way due to the motions of their mole- 

 cules was a hypothesis as old at least as Bernoulli, but it was 

 Clausius who raised it to the rank of a theory, and he has been 

 described by Clerk Maxwell as the principal founder of the science. He 

 showed how Boyle's and Dal ton's laws followed from the theory, and 

 how they were approximate ; he proved the existence of intra- 

 molecular energy, and the necessity for Avcgadro's law, and for the 

 equality of mean energy of translation ; and, insisting on the necessity 

 for two atoms in a molecule, hastened the advent of the change in 

 atomic weights which chemists were adopting ; he investigated the 

 length of the mean free path of a molecule, and the rates of diffusion 

 and conductivity of heat in gases. 



In connexion with the molecular theory of matter, Clausius had 

 as early as 1851 investigated some of the laws of evaporation, and 



