( 495 ) 



§ '2. Ill order to iiilrodiici' ilic inlcnial \ irial / I slartod tVoiii iho 

 supposition that tlic distance spheres of the iiioleeides experience a 

 |»ressnre wliieh is on averaue ecpial to /'. As I never lonnd a dii'ect 

 pi'oof of ihis tiiesis I will ui\e it lieic. The prcssin-c /' nanielv niav 

 i. a. I)«' considered to I'cprescnt the pressure exercised auainst a solid 

 unniovinu' wall, disrejiartlin.ii' the molecular pressure. 'I'lie distance 

 splieres, however, are not to he regarded as a solid, iiinnoving- wall. 

 In consecpu'uce of their motion the luimher of collisions against a 

 surface element (/n of a dislaiu*e sphei-e is ur<\itei- than that (t)i an 

 ecpial elenu^nt of the wall: moreoxci- the force in each collision is 

 proportional to the relatixc xclocity of the molecules, which is ui-eajei- 

 than the velocity of each molecule separately. 



Ki-om these two circumstances we are apt to assume that the average 

 pressure on the distance s|)heres would he u'i'eater than /^ 



On th(^ other liand the iuipnlse of a molecule colliding,' with a 

 velocity .s- iKtrmally a.üainsl a solid, unmo\ ing- wall is 2 m s. If, 

 howe\er, the molecide colliders with the \elocity .v ceiilrally ajiiainst 

 another ujimoAinu' molecule with the same mass, then the lirsi molecule 

 will be stopped an<l the sec(»nd will ohtaiii the \-elocity s; so the 

 iu.'pidse is in this case only ins. 



In consetpience of this circumstance we should he inclined to expect 

 the pi'essure on a distaiu'e sphere to he suïaller than /'. 



The following: simple calculation n\ ill suHice to show that these 

 iidluences cancel each other and that th<' pi'essure exercised on tiie 

 distance spheres is really e(pial to /\ at least in tlie case that we 

 ma\ neglect the \-olume of the molecules w itli regard to the volume 

 ill which they are contained. 



Let us imagine two molecules I aiul II A\ith the same mass. The 

 same jii-oposition might he proved w ithoiil difliciilty also for mixtures, 

 so for molecules willi iinecpial masses, hut 1 will couline myself here 

 lo molecules with the same mass. The \"elocilies of the moleciih^s 

 will he denoted hy .v and .v, and the components of these velocities 

 hy n, i\ tr and //,, /•,, //',. The chance that molecules occur w ho.se 

 velocities lia\ e these comixments will he represented hy F{H,i\tr) 

 and F (if^, '\, ti\) and the relalixc xclocity ity ■<,.. Then we liaxc: 



V ^ ("-",)■-' + (';-'•,)' -f ("•-"•,)■■'• 



If wo lake the direction of s,. as the axis of a system ofs|>heiicaI 

 coordinates, and if wo call the latitude <f the longitude if', then a 

 surface element of the dislaiice s|»here of molecule I will he repre- 

 s<'iited hy /- s/'/i <f il(f(li\\ The iiiiuiher of collisions per unit of time 

 of molecules of group II against such a surface element is: 



F [u, r, iv) F (//,. i\. a\) till dc die dii^ di\ dii\ s,. r" sin <f cos if d*f di\\ 



