( 490 ) 



— IP' rcos(n, r)<}o — ^ PT (J5) 



ƒ 



Here r represents tlie radius veelor drawn Iroiii llic oriuiii of llie 

 system ot' coordinates to a point of I he snrlaee, do repivsents an 

 element of that snrfaee, (■(>s{i),r) the cosine o(" the anule \vhich tlie 

 radius rector forms with the norinal to the surface. /*' is the force 

 per unit of surface which |)revents tlie niolecuk^s to leave the space and 

 com|)els them to return towards the iusidc of il. We may disliugiiish 



in it the molecular pi'essurc and the [)ressui-e p exercised i)\ the 

 wall. 



Foi" the case of ;ni iuiauiuar\ separatiuii' surface, m. — is the 



' ' <lf (It 



numienlum iu the direction of the positive ./-axis con\-eyed through 



the surface to the insich' of il. Momentum couveyed to the outside 



has lo he taken into account witli the ucLiatixc sig'ii. hi this case 



also the ri.^hthand memiu>r may he re|)i"esciiled hy ('(piatioii (/>*) 



though here the .syml)ol /*' docs nol any lousier re[>rescnl a force 



which really acts on the molecules. 



In the case that the xoliimc really occiipicfl ity the molecules 



is not so small that we may neglect it, also ihe xiri.il of the 



forces eventuating in the mnliial collisions of the molecules imisi he 



taken into account. If \ve denote this \iiial by / then we niny 



write e(piation (.1) in ihe following- foi-m; 



^m.s' = — 7 — (Pr co.< {n. r) ,h — — I -|- :) PV. 



2^ius^ and / heing independeiil of ihe properlies of ihe bordering 

 surface, /' cannot depend n|K)n lliem (mIIici-. /' appears t(t he greater 

 than /" : for a wall this is because the uumbtM- of collisions is 

 augmenteil in consequence of the abbreviation of the mean length 

 of path which a molecule describes between two successive collisions; 

 for an imaginary separating surface this is because the conveyance 

 of momentum through that sni-face has augmented in conse<(uence 

 of the fact that in collisions between two molecules whose centers 

 lie at opposite sides of the separating surfa<'e, the momentum is 

 transplaced instanlaueously from the center of one molecule to that 

 of the otiiei-: so the momentum has been transported Avith intinife 

 velocity. 



But the way in xvhicii we have derived the ((uanlily /' >vhich 

 may be estimated to rei»resent the pressure i»re\'ailing iji the gaseous 

 or in the liipiid phase, warrants in any case that this ([iiantity is 



