PREFACE. i x 



and are exact. This does not make them more difficult to 

 establish than the approximate laws for systems of a great 

 many degrees of freedom, or for limited classes of such 

 systems. The reverse is rather the case, for our attention is 

 not diverted from what is essential by the peculiarities of the 

 system considered, and we are not obliged to satisfy ourselves 

 that the effect of the quantities and circumstances neglected 

 will be negligible in the result. The laws of thermodynamics 

 may be easily obtained from the principles of statistical me- 

 chanics, of which they are the incomplete expression, but 

 they make a somewhat blind guide in our search for those 

 laws. This is perhaps the principal cause of the slow progress 

 of rational thermodynamics, as contrasted with the rapid de- 

 duction of the consequences of its laws as empirically estab- 

 lished. To this must be added that the rational foundation 

 of thermodynamics lay in a branch of mechanics of which 

 the fundamental notions and principles, and the characteristic 

 operations, were alike unfamiliar to students of mechanics. 



We may therefore confidently believe that nothing will 

 more conduce to the clear apprehension of the relation of 

 thermodynamics to rational mechanics, and to the interpreta- 

 tion of observed phenomena with reference to their evidence 

 respecting the molecular constitution of bodies, than the 

 study of the fundamental notions and principles of that de- 

 partment of mechanics to which thermodynamics is especially 

 related. 



Moreover, we avoid the gravest difficulties when, giving up 

 the attempt to frame hypotheses concerning the constitution 

 of material bodies, we pursue statistical inquiries as a branch 

 of rational mechanics. In the present state of science, it 

 seems hardly possible to frame a dynamic theory of molecular 

 action which shall embrace the phenomena of thermody- 

 namics, of radiation, and of the electrical manifestations 

 which accompany the union of atoms. Yet any theory is 

 obviously inadequate which does not take account of all 

 these phenomena. Even if we confine cur attention to the 



