Physics. — ''On the Cour.'^e of the Values of a and h f or Hydrogen 

 at Dijf'erent Temperatures and Volumes". IV. (Continued). 

 By Dr. J. J. van IjAar. (Communicated by Prof. H. A. Lorentz). 



(Communicated in the meeting of March 23, 1918). 



§ XX. The value of a below the limiting temperature. 



In this case the integrations need no longer take place in difTerent 

 stages, since a minimnm distance r,a, which is dependent on 6, need 

 no longer he reckoned with, so that tii-st the integi-ation with i-espect 

 to S can he carried out, and then with respect tor. All the entering 

 molecules, from 0=^0 to Ü z=. 90°, will now come in collision ; for 

 the limiting temperature 1\ the molecules that sti'ike under an 

 angle <^ ^ 90° will jnst i)ass the rim of the molecule that is 

 supposed not to move. We have, therefore, now to integrate 

 (see § XVI): 



2a' r r dr X sin 6 dS 



s {a^—s^)J J r V^a' cos' d \ {ar—r') (P 7» - 1 ) 



in which /^/- is now always ^ 1, and in the limiting case rp = ^0 = 1 : /,' 

 assnmes the value 1. When we pnt {a"" — f'){k^cp — 1) = g-', we get 

 therefore: 







a = V. X 



2a" rdr r d {a COS 8) 



'la'' rdr r d{acc 



(Mx« X -r^ ^ — 77=. 



■ =^ s («*—«') J r J V',f^a 



e 



in which we may w^rite for the second integral: 



log {a cos 6 + V q^ -r «" «os* 6) _ = log 

 so that we have still to integrate: 



a+\/q' + a' 



2a' rdr /a , /- a^\ 



s 



If in the first place (f is near (p^, then q approaches 0, and the 

 integral approaches to 



