J 200 



succeeded as jet. For v = oo, however, t^ is always =1, and b 

 becomes bg, wliile for v = b, where t, =: oo, J is = y = y,. Hence 

 the fictitious quantity b will lie between bg and r,, i.e. between 



6 



(bg)^ y f{b) = lY X 4 m X ƒ (^) for v = oo, and about N X - rn 



(with cubic distribution) for v = v„. Only at high temperature 

 f{b)= 1 may be put, and the upper limit becomes =N X^in. 

 (m = volume of one molecule). ') 



That Xs becomes infinitely great for v = v^, is clear when we 

 consider that then the molecules (cubically distributed) get to lie 

 close against each other, so that every time a fiiiite number of 

 molecule centres will lie inside an infinitely thin spherical shell, 

 which causes the number of molecules per volume unity not to 

 iiave the ordinary middle value n at those places, but to be 

 = ?i X T.^ = 00. Then the middle value n is formed by the alternate 

 values (between two centres) and oo (at the place of the centres). 



XII. Another Derivation of the Virial Collision. 



When objections should be raised against the way in which the 

 distribution factor e-^^r is introduced also for the virial of collision, 

 in view of the circumstance that it may be expected that the density 

 of the molecules will not be modified any further aftei- passage 

 through the sphere of attraction, so that the assumption of 7^r = + a 

 for the collision (which would render the said factor = 0) seems 

 unjustifiable {P,- can, indeed, never become oo, because just so much 

 work is performed by the quasi-elastic forces till the normal (relative) 

 velocity of the colliding molecule is exhausted) — we can also arrive 

 at the result of (5) and (6) in the following way, which is not open 

 to (he same objection. 



In the foregoing paper we found for the virial of collision the 

 following expression : 



727'' ih \ 

 n = ^^ [1 -« \/r 4- |(« l/T')' - |(« i/T')»], 



V 



in which « represents a coefficient which is in connection with the 

 atomic forces within the molecule, and determines the degree of 



1) We draw attention here to this, that whereas from t? = oo to v = t'o the 

 real quantity hg = {hg)^ X A^^) X '^s increases from hg to oo (in consequence 

 of Ts), the fictitious quantity b in v — b will decrease from bq to ftp — about 



