460 BUDOLP JULIUS EMANUEL CLAUSIUS. 



The constructive power thus exhibited, this ability to bring order 

 out of confusion, this breadth of view which could apprehend one 

 truth without losing sight of another, this nice discrimination to sep- 

 arate truth from error, — these are qualities which place the possessor 

 in the first rank of scientific men. 



In the development of the various consequences of the funda- 

 mental propositions of thermodynamics, as applied to all kinds of 

 physical phenomena, Clausius was rivalled, perhaps surpassed, in 

 activity and versatility by Sir William Thomson. His attention, 

 indeed, seems to have been less directed toward the development of 

 the subject in extension, than toward the nature of the molecular 

 phenomena of which the laws of thermodynamics are the sensible* 

 expression. He seems to have very early felt the conviction, that 

 behind the second law of thermodynamics, which relates to the heat 

 absorbed or given out by a body, and therefore capable of direct 

 measurement, there was another law of similar form, but relating to 

 the quantities of heat (i. e. molecular vis viva) absorbed in the per- 

 formance of work, external or internal. 



This may be made more definite, if we express the second law in 

 a mathematical form, as may be done by saying that in any reversible 

 cyclic process which a body may undergo 



(UQ 



/ 



t »' 



where dQ h an elementary portion of the heat imparted to the body, 

 and t the absolute temperature of the body, or the portion of it which 

 receives the heat. Or, without limitation to cyclic processes, we 

 may say that for any reversible infinitesimal change, 



dQ = tdS, 



where S denotes a certain function of the state of the body, called by 



Clausius the entropy. The element of heat may evidently be divided 



into two parts, of which one represents the increase of molecular 



vis viva in the body, and the other the work done against forces, 



either external or internal. If we call these parts d II and dQ^, we 



have 



dQ^dff+dQ^. 



Now the proposition of which Clausius felt so strong a conviction 

 was that for reversible cyclic processes 



rdQ. 



/ 



^t ="■ 



