( 45 ) 



fictitious system, all these p(>ints of' ^■oloeit_v coido l)ack in I\P^\ 



Itecaiiso di'ihiih' |)laii('s of collision A hclonu' l<> <'\<'i'_\ pair of 



[)oints of velocity UxUi • ■ ■ • 'i''*^' liclilioiis syslcin. tlicrclorc. is siil)- 

 jected lo llie coii(litio)i, that molecules with <k'liuile poijils of \clocii v 

 do uot collide accordiuu' to arbitrarily chosen planes or to planes 

 wliose direction is determined l)v cliance, hut accordinij,- lo |)lanes 

 wliicli are entirely (li'ti'niilnctl l)y tlie position of these points of xdo- 

 ci(y. This condition may he called an ordeuinii- jf the motions. 



We must, however, add another remark. In the natural system 

 we had not oidy points of \elocity in I\l\\ hnt also at the ends 

 of the other diameters of the sphere I\l\!, /VV ■ • • • ^^'le. and these 

 loo can reach the same jioinls <2i^2i' '^^ l\l\^ '•' only the j)lanes of 

 collision have every lime the required direction dillerent from .1. 

 Of all the points of velocity and planes of collision we ha\e just 

 now chosen and considered separately all those w Inch in the iiatin-al 

 system lie before, in the lictitious system after the collisions in 7^, /y. 

 We miglil, however, just as well have chosen ajid cojisidered sei)arately 

 those which in the natural system lie after, in the fictitious system 

 before the collision in Q^(}^\ in tiiis case we miuht have beeji inclined, 

 to call the lictitious system unordened. and the natural system ordened. 

 The ditfereiu'e l>etween the two would of course become clear, when 

 "we pai<l attention to the iinnihcr of collisions which cause the points 

 of velocity to pass from /\/\' to Q^Q^ , It^U^ etc. oi* \ice versa. 

 In reality the collisions in the natural system have a scattering' effect, 

 through which the distribntion of the points of \-elocity over the sphere 

 is more regular aiul arbitrary after impact than before. In this resjK>ct 

 there is a real dilference between the natui-al and (he lictitious .system, 

 that in the former the distribution before the collision is mor(^ irre- 

 gular, less accidental. The dilference between being ordened and 

 unordened in the molecular motions in the two systems ai)[)ears here 

 as a difference in the degree of the ordening. 



It seems to me that lliongh we cannot bi-iiiu forward conclusive 

 objections against the denomination nsed by IJoi/rz.MANN. yet further 

 considerations which throw some light on these phenomena, might 

 be of some value. 



3. The ordeiung of the motiojis, in which the difference between 

 the natni'al and tlu^ fictitions system consists, can oidy be clear, 

 when, as in (he kiiuMic theory of ga.ses, we examine larger masses 

 and mean \abu>s, in which the coordinates and \ clocities are c(»nsidered 

 as fluently varying (pian(i(ies. When \\(' lake the parlich's separately, 

 in which (he cooi'dinales and \elocilies are [>ertec(ly defined, (he 



