408 Dr. Rankine on Thermodynamic and Metamorphic 



relating, not to the two fundamental laws of thermodynamics, 

 but to some of their applications. (See in particular the papers 

 of Professor Clausius in PoggendorfFs Armalen, vol. xcvi. p. 73, 

 in the ' Proceedings ' of the Swiss " Naturforschender Gesell- 

 schaft" for 1863 and 1865, and in the Bibliotheque Universelle 

 (Geneva) for October 1865.) 



2. According to the Second Law of Thermodynamics, the 

 quantity of heat which a body receives or gives out during any 

 given indefinitely small change of figure and dimensions is 

 expressed in every case as follows, 



rdcp, 



in which t is the absolute temperature and <p the " Thermodyna- 

 mic Function." <, ■■ 



The thermodynamic function is made up of two parts, as fol- 

 lows, 



<£ = khyp.logT + F; 

 so that 



t# = ^t+t^F (1) 



In these expressions fe is the real specific heat of the substance, 

 being the part of the specific heat due to the energy of molecular 

 motions alone ; and F is what 1 have proposed to call the " me- 

 tamorphic function;" so that rd¥ is the quantity of heat which 

 is transformed into mechanical work, whether external or inter- 

 nal, during any indefinitely small change in the condition of the 

 body. In all those expressions quantities of heat are supposed 

 to be expressed in units of mechanical work. 



3. Let x, y } z, &c. denote changes of different kinds in the 

 dimensions and figure of a substance, and X, Y, Z, &c. the 

 forces of the nature of elastic stress by which such changes are 

 promoted; so that Xdx + Ydy-\-Zdz + &c. is the external work 

 performed during a given indefinitely small change of figure and 

 dimensions. Then the metamorphic function F is the integral 

 of the following set of differential equations*: — 



dT_d%. ^_^Z. ^F_^Z. 

 dx~ dr ' dy dr ' dz ~ dr' 



When, as is the case in the most frequent class of questions 

 in thermodynamics, the change under consideration is simply a 

 change of volume, the preceding set of differential equations are 

 reduced to the following single equation, 



dv~ dr' • ■ ■ ■ ■ ■ ■ W 



* See Proceedings of the Philosophical Society of Glasgow for 1853; 

 Edinburgh Philosophical Journal for 1855. 



