Laics of Irreversible Phenomena, 389 



dynamics with what, from Helmholtz, received that designa- 

 tion. Equation (I.) accordingly becomes 



£*{«t-s||'8 ?4 +spa«-(|?-4)»+8'Q J =°- ( 2 ) 



Now let us further assume that the following equations are 

 true : — 



H=°< g" ds (3) 



they are found to hold good in all cases of which we have 

 precise knowledge ; lastly, let us suppose that there is no 

 term containing 8§ in the expression for 8'Q. (With respect 

 to this point compare § 12.) Equation (2) may now be 

 divided into 



^-r;=o, w 



and 



d* 



j"*«ft { ST-S gs^ + SP^+S'Q J =0. . (III.) 



This equation expresses the principle in a form similar to 

 that of equation (I.). It is a useful equation, owing to the 

 readiness with which it admits of application in various cases, 

 but its abstract generality is of course much more restricted 

 than that of the fundamental equation. 



§ 6. Reversible Dynamics. — In Dynamics properly so-called, 

 i. e. in Reversible Dynamics, ideal phenomena of motion are 

 dealt with, and the notion of temperature is not taken into 

 account. Therefore, in Reversible Dynamics a function Y can 

 be considered, depending on the remaining variables q. only, 

 which does not differ, except by a constant, from the " poten- 

 tial energy " U ; this is a remark already made by M. Duhem. 

 Of course it must be restricted to the Dynamics of points and 

 of rigid bodies, since, for instance, in Hydrodynamics and 

 Aerodynamics the difference between the quantities V and U 

 is variable and depends on the compressibility of the fluid. 



From (III.) we obtain, leaving out the irreversible term 

 5'Q, the fundamental principle of Reversible Dynamics. 



§ 7. Electromagnetic irreversible phenomena. — Energy stored 

 in the aether can be transferred to matter and converted into 

 heat ; this phenomenon, when it occurs, is a thoroughly ir- 

 reversible one. 



