c 4a > 



PoiNTARÉ says aluml lliis iii liis ■''rii(MiinHlyiianii(|iH'"', thai il ciiliivlv 

 exfliules llie |K)syil»ilily of a iiiccliaiiical e\|»laiiali(>ii of Ihc iiiii\erse. 



Tlio jnolions of wliicli inccliaiücs treat, are all rcNcrsihlc ; llifpc 

 occur only forces \\ liicli depond on place, so relations Itctwccji llie 

 O''' an<l the 2'"^ derixative accordinu' to time ; if llw siun (tf / is i-cnersed, 

 these equations retain Iheir \ali<lity. It is tiiie thai in mechanics 

 also cases are treated in which the llrsl deri\ati\(' accoi-<lin,u to / 

 occurs in the ecpiations (friction^: we are, h()\V(»\-er. justified in cailinü' 

 tliese cases not i)urely nu'chanic, Itecause in them heal is jtroduced, 

 so that in a complete explanation we must introduce considerations 

 (theniiodynamic ones), which we are just tryinu' t»» soi\e in pni-el\ 

 mechanic ones. It is therefore desirable to call oidv those cases 

 purt'/i/ mechanic which are twri'i-sihli'; these oidy are cons(M-\alive. 

 In the above-mentioned ]iol |>urely mechanic cases there is dissipation 

 of energy, so that, the law for the conserxation of oierux beinu- a 

 general law of nature, a mechanical description of them is not com- 

 })lete. The kinetic theory of gases shows us tJhat this desci-i|)tion onlv 

 mentions the visible motions in the system, iuit not the molecular 

 motion, which is required to make the desci-iption conqdele. The 

 word mechanic, occurring in the (piestion raised in the begimu'nu- 

 must therefore be interpreted in such a way that we consider oul\ 

 cases of conservative systems as purely mechanic. 



The question Avhether the irreversibility of the nalinal phen(Mneua 

 decmrely e.i'cludes a mechanical explanation, must be answered in the 

 negatixe, when we succeed in giving a mechamcal descri[>tion of one 

 ty[>ical and sinqile irreversible process, or iji oIIum- words, if we can 

 iKtint out in a certain case that a |)rocess consisting of |MU-elv 

 mechanic, so i-eversible motions, is irrevei-sible. We musi then at the 

 same time get an insight into the question, how it is in general 

 possible, that a process in its general character can be so diHereut 

 from that of the |>artial jirocesses of which it consists. 



2. HoLTZMANN has shown that we nuN't with such a case, though 

 an abstract one, when we have a perfect ua->. consisting ofperfeclh 

 elastic spheres, between which m» oihei' forces act than those e\'en- 

 tuating in collisions Iu-Iwi'mi two particles, lie proxcd that the func- 

 tion H = // hij t il i'i. ill which /'/cj is the niMuber of the nu»lecules 

 w'iiose points of velocity lie in the v(»lume element f/u> of the velocitx' 

 diagram'), can oidy be made smaller, never greatei- by the collision^. 



') The "velocity tliagi-ani" is ül)taiii('(l i)y r<'|»icsciiliii^- Iht- vciocily of i-vrry 

 molecule by a vector di'awn from a tixed point. This vector ends in the "point of 

 velocity" of this molecule. 



