Write 

 and 



therefore 

 We have 

 and 



Laivs of Irreversible Phenomena 

 2d'Q=+dQ -rfiQ, . 

 + d«Q=+dQ -d'Q; 



-4Q=-d«>Q+d'Q;. 



387 

 (1) 

 (2) 

 (3) 

 (4) 

 (5) 



thus d°Q is the reversible, and d'Q the irreversible part of 

 the heat absorbed. Now, if we assume that these quantities 

 are of the form 



we may consider the new quantities 



SoQ = 2RJ^; 8'QrrSR^, 



(6) 



(7) 



5°Q + 8 / Q gives again £Q. Let us generally define SQ, 5°Q, 

 S'Q to represent the expressions which result if in the ex- 

 pressions of the quantities c/Q, d Q, and d ! Q (which we sup- 

 pose to be empirically known *), variations Sq { are substituted 

 in place of the corresponding differentials dq v 



§ 2. Statement of the Principle. — Let us consider a given 

 period of time, from t = t to t = t 1 . Let Sq., £*., BT, 8U, 

 SP^S^, as usual, represent variations which, between the 

 limits t = t and t~t 1} are functions of the time susceptible of 

 being differentiated, and which vanish at these limits them- 

 selves ; finally, let 8Q, 8°Q, B'Q be the corresponding in- 

 finitesimal expressions calculated as above stated. The 

 following principle seems then to hold in physical phenomena: 

 between t = t and t = t ± events which occur in the system 

 must be such that the equation 



JU 



dt{BT-bJJ + tFfiq i + BQ t }=0 



(10 



is satisfied. For brevity, this, when necessary, will be re- 

 ferred to as the Thermokinetic Principle. 



* To write down the expressions of dQ and d'Q, a much greater 

 number of variables would evidently be required in most cases than to 

 write d°Q j thus in most cases many of the coefficients R° will be equal 

 to zero. A similar remark applies to the coefficients P { , dT/dfy dT/d.^, 

 and $Ufdq t . 



2 E 2 



