( 46 ) 



difference between a natnral and a fictitious system does not appear, 

 and I lie |)rocess can only ho laken as perfectly revei-sihle. 



The resnlt of each of the steps of which the whole process is 

 huilt up (free path -|- collision), is determined 1**^ hy the coordinates 

 aud Aclocities, 2"^^ hy the direction of the normal to the collision 

 plane. In the statistical method of treatment of the kinetic theory 

 of gases the latter is considei'e«l as an independent datum, which 

 therefore is thoufiht to he delined hy chance; we may then <;i\e it 

 diiferent \alues. which are <listi-il)nted accordin^ï to chance, i. e. 

 regularly, and iji this way the scattering-, regulating effect of the 

 collisions appears, which is the cause of the irrexersihility of the 

 process. In the [)urely mechainc conception, in which we must take 

 the condition of every se|)arate |>article as rigorously delined, the 

 direction of \\\v normal is no independent datum; in reality this 

 direction is accui-alely detined \)\ the coordinates and the velocities 

 of the collidiug |)articles. Here the result is therefore deternnnecl 

 hy the coordinates and the velocities oidy and according to this way 

 of considering the question, the process nnist he considered to he 

 reversible. 



The ({uestioJi how it is j)ossible that a process may be considered 

 in two ways, so totally different c(nnes therefore to the same as the 

 (|uestion, how (|uaiitities which in reality are rigoi'ously determined 

 hy other (piantities, may yet he considei-e<l to he independent aud 

 determined by chance. 



We shall find the answer to this (|uesti(tn in the fact, that vei-y 

 small xariations in the coordinates and velocities bring about consider- 

 able vai-iations in the direction of tlic noi-uial. If we determine the 

 directions by means of the |>oinIs in which they cut a sj^Iierical 

 surface described with a radius e(|iial to the mean free path, the 

 velocities being measured by the path covered in the mean time 

 interval between two collisions, and if we call the ratio between the 

 i-adius of a molecule and the mean free path a small (piantity of 

 the first ordei-, then we may formulate this pj-oposition more pre- 

 cisely as follows: variations of a given order of smallness in the 

 coordinates and the velocities hring about variations in the direction of 

 the normal which are of one order lower: variations in the direction 

 of the normal give rise to variations of the same order in the coor- 

 dinates and the velocities after impact. 



If we ascribe to the coordinates and the velocities of two colliding 

 molecules values .r^ i/^ :^ ,r.^ //., .., h^ i\ /i\ //, r.^ n\, which are rigorously 

 determined, then the direction of the normal X (i v is also rigorously 

 determined. If however \ve mean h\ these 12 data that these quantities 



