26o Annual Report of the Council. 



should of itself pass from a colder to a hotter body. 

 This essential idea he further developed in his memoirs 

 of 1854, 1862, and 1865, basing on it a great mechanical 

 principle, as Thomson had on Joule's Law, and enun- 

 ciating them together at the end of the last named 

 paper ; — The energy of the universe is constant, the entropy 

 of the universe tends to a maximum : principles now usually 

 called the Conservation and Dissipation of Energy. During 

 this stage of his activity, two Englishmen, Thomson and 

 Rankine, were working in the same direction ; it is no 

 part of our purpose to raise small questions of priority^ 

 the work of each was original and distinctive, and 

 the new science of thermo-dynamics had need of all. 

 The fundamental ideas of the mechanical theory of heat 

 called not only Joule and Kronig, but also Clausius back to 

 Daniel Bernoulli's kinetic theory of gases. In a paper on 

 the Form of Motion which we call heat (1857) he deduced 

 Boyle's law with less special assumption than Joule had 

 employed, arrived at the conditions under which Charles' 

 law holds good, and established the law of Avogadro. 

 In a paper (1858) on the mean free path of a gas molecule, 

 he developed the statistical method of investigation which 

 the character of the problem makes necessary, and opened 

 the way to his successors. From this point Maxwell and 

 Boltzmann have carried the method to its fullest extent. 

 In this short notice we can only allude to Clausius' service 

 to Abstract Dynamics by his introduction of the Virial, to 

 his modification and development of W. Weber's electro- 

 dynamic theory, and to the papers on the theory of dynamo- 

 electric machines, which occupied the last years of his life. 

 Clausius' papers form a very long list, and are characterised 

 by an originality, thoroughness, and breadth of view which 

 are excelled by few. He was active in the discharge of his 

 duties as a professor, and that he performed his duties to 

 the State may be inferred from the fact that during the war 



