by 03 1=90°, sin 0^ = 1. This is namely the lowest teinperaluie at 

 which a vahie for 0^ is still possible. F'rom (6) follows namely 



sm'' = — {1 -\- q>), so that — (1 -j- (f) can never become greater than 



a'' a" 



1, hence (f never greater than (a" — s'): ■s*'' = 1 : /;^ 



When we represent this limiting valne of ff =z ]\J : hfrn^^ by (p^, 

 we get therefore 



1 1 — ?2* 



^- = P^^n^' ...... (9) 



when we put the ratio x : a = ?i. Accordingly, as long as y remains 

 <^7^, (T^ To), the quantity 1 — ^V/^ also remains ^0 in the above 

 integral. 



Og is = 90° in the limiting case q^ :^ (f^; then all the entering 

 molecules collide, also those that strike at an angle <9 = 90°, which 

 iust reach the rim of the sphere r =: s, and will yield there a 

 minimum value for r for the last time. 



But as soon as the temperature becomes still lower, and tp 

 becomes > (fo, all the entering molecules collide without previous 

 minimum, i.e. they all strike at angles <^ 90° with the normal. For 

 these values of ff we siiall therefore have to execute a .separate 

 integration later on, i. e. for all the values from ff ^ff\ toy = oo (T=0). 



Now the integration with respect to r yields: 



J r \/p^r^—a^ {f — cos'' 6) a Vp"— cos^ 6» V >^ a^ (/>» 



-a^p^-cos'6) 



cos' 6) 

 when we put 1 — k*(p = p^. As s hi^O^ = — (1 -\-(f),cos^Ogis theveïove 



s' a'—sW s' \ a'—s' 



= 1 (1 + u) = i- 1 -, , f = — ^ P'- Hence the quan- 



a' 



tity />' is also = cos'^d^, so that />" — cos'^6 always remains 



positive. For cos'^d is at most =cos''0^ in /j. 



At the limit ?•,/» 'he quantity under the rootsign, viz. p^r' —a' 

 {p^—cos'^8) is always ^0, because then dr:clt = (compare (3")). 

 Hence we have after introduction of the limits: 



90 To 



1 r sindfiS cos 6 IT dx x 



/i = — I — ^==^= Bg tq — = — I rir=z Bq tg — , 



% 



when we write — dcosd for sin'UlO, and x for cosO, so that cusV^^ 

 is represented by x^. Now ilBgtg ^ dx-M p^ — .z'% so that we find: 



.1* 



