(44) 



As this I'liiiclioii taken with the roversed simi, expresses at (lie same 

 lime llie logarithm of' the "|>i(il»;il)ility" of a certain (listi-il)iitioii of 

 tiie velocities, Boltzmann e.\[»resses his result also under the follo^villg• 

 form: the effect of the collisiojis is that a gas always gets from a 

 more impi-ohahle to a more pi-oltahh' condition. 



Here we have thei-eture a ])i'ocess, consisting of i)ui-ely mechanic 

 partial processes, \\hich shows change in one direction oidy. That 

 however Bottzmanns considerations have not yet led to a })erfectly 

 satisfactory insight, and tiiat this contrast is felt as a contradiction, 

 is proved by the objections and douhls, Avliich ha\e been addnced 

 against these consi(UM-ations \\ithont i-efnting them. Let ns assnme 

 a fictitious system in which at the moment t^ all the |>laces are tiie same, 

 bnt all the Aclocilies exactly the op})osite of tliose of the real system. 

 The two systems can represent a gas in exactly the same way, there 

 being ]io possibility of seeiiiii' w liich is the real and which the ficti- 

 tions one. Yet the fictitious one will snccessively |)ass throngh all 

 the conditions throngh which the natnral one has jjassed before the 

 lime /„, in re\erse order; all the collisioJis take j)lace in ojtposile 

 direction, and the system gets from a "more probable" to a "more 

 im))robable" condition. 



Boltzmann denies that this inxoh'es a coiitradiclion. foi- the ticlilious 

 svstem is '^ nioh'ciihi i'-(ii'(>rilin'f\ That this i-einark does iiol sol\'e the 

 difficully f l>Kii,T,oriN, ainoiiu others, expressed doubts as to this in a 

 note in the French translation of Boltzmanns \'orlesiingen) mnst 

 be ascribetl to the fact, that the ideas "ordened" and "nnordened" 

 for molecniar moiious are difficult to define sharply. Sometimes ordened 

 is intei-preled a^ if il meant that in the lictitious system to every 

 molecule its futnre course is accurately prescril)ed. This however is 

 not satisfactory. B' we know at the moment ^„ the places and velo- 

 cities of the natural system, we are enabled to determine beforehand, 

 so to prescribe, the future course for the natural and lor the fictitious 

 system and for both in exactly the same way. 



The fact that the motions in the fictitious system are ordened 

 can be better [lointed out by means of the following consideration. 

 \ï we take two grouj>s of molecules with the points of velocity /"'i and 

 7V, which come into collision, then after the collision the |»oints of 

 velocity Q^ and Q^, R^ and /t/ etc., will all lie on a s[)here of 

 which the line P^P^ is a diameter. The places of Q, li, .... on the 

 sphere de[)en(l on the dii-ection of the j)lanes of collision .1, 7>, .... ; 

 to e\'ery plane of collision belongs a definite place of the })oints of 

 velocity and the latter are scattered all over the sphei-e, because the 

 former have all kinds of directions. B' we now take the reversed. 



