( ^01 ) 



of I lie i-eproseiitiiig' poijil, and we nuiy now examine wluit takes 

 place with this vector dnring the motion. It is now obvious that tlie 

 represent ing' point moves in a space inek)sed by surfaces and spaces 

 as .i\ = y, A\ = (( — r etc. witli which it coUides when one of the 

 molecules of the system strikes against a wall of the vessel. When 

 two molecules collide, the representing [)oint strikes against a surface, 

 the equation of which has the form : 



Now 1)0K1<;l shows that for this ini[)act the same rules hold as for 

 ordinary collisions, so that the lines alojig which the point moves 

 before and after im[)act, lie in the same plane as the normal, the 

 normal dividing the angle of the first two lines into two equal 

 parts. The velocity, too, remains the same According to the above 

 we must Jiow imagine a finite s[)ace tilled with such representing 

 points, an intinitcly small [)encil of vectors of velocity starling from 

 each point, mutually equal, ami also equal for all the points. Now 

 a number of these representing points strikes against one of the 

 above mentioned surfaces, e.g. with equation 



(''^ - •^)^ 4- (//i - !Ur + (~x - ~~J' = 4r^ ; 

 this implies then that for these systems the first and the second 

 molecule collide. This surface is that of a cylindre of revolution of 

 the o)i — o^'' degree, against the outside of which the points strike.^) 

 The base of the cylindre is a s|)here, the descriptive lines have here 

 become descriptive spaces, luimely plane spaces ot'Sii — 3 dimensions. 



In the collision referred to, the extension from which the points 

 come being large conqmred to the dimensions of the section of the 

 cylindre (or at least of the same order) the infinitesimal pencil will 

 extends in the directions of the |)er[)endicular section of the cylindre, 

 so here in 3 dimensions, to a pencil of finite widtii. If from this we 

 take again an infinitesimal part, it comes from a definite point of 

 each section of the s| there, and so from the points of a descriptive 

 space of the cylindre. ') Part of this strikes again against another 

 cylindre (which e.g. involves collision of the 1^^ and the 3''^i molecule), 

 and the intinitely narrow pencil extends again to finite width; etc. 



The representing points which have not taken part in these col- 

 lisions sti'ike again against another surface, and the [)encil extends every 

 time to one an inlinite number of times wider, but every time in other 



1) If llie new coordinates ^. i', y. •■-', 2" and ^' determined by ; = ■] (.Ci -.r^) I 2, 

 i'= i (•'';3 + .Vi) ' ^ etc. are inli'odiiced, tlie eiiiiation of the surface l)ecomes 



2) Properly speulcing a narrow region in the direction of this descriptive space. 



27* 



