890 
a. At high temperatures where, in consequence of the equation 
l—o 
2f 
WV, p becomes small when u, becomes large (supposing 
U, m 
/—o always remains comparatively small, which is fulfilled here, 
because we always consider solid (at most liquid) systems), (c), (d) 
and (e) with log (p + Vp”) = log (p + 1) =g pass into: 
lake 
2d | | 
uz ee a ye ise ire eet | 4 t, En ir J high (c ) 
en | ea ae a Tee oa =a en 
14 hart wl Lo 6& t, p e temp.) 
p é 
so that in the case of weak collisions (in which «, the constant of 
the repulsive force, is not very much greater than f, the constant 
of the attractive forces), in consequence of ~ in the denominators 
of the second terms in numerator and denominator of the above 
fraction for w,?, these latter terms will prevail; hence w,? will approach 
to */, u,’ (cy = 6). Whereas in case of strong collisions, when € is 
supposed very large with respect to /, or when p gradually increases 
somewhat on decrease of temperature, the first terms prevail, so that 
then uw? will more and more approach to w,*? (c, = 9). 
The ratios (a—s’): (/—o) and ¢,:¢, will be great for p small and 
j:€ not very much smaller than 1; smaller on the other hand for 
somewhat larger p, and e much greater than f. 
With regard to /—o and o—s’ themselves, it may be observed 
that according to the supposition /—-o always remains finite, so that 
m ; 
o—s' =U, Y= can become large at increasing temperature and 
€ 
finite «. But this increase’ is restricted first of all by this, 
that wz, can never become too great, because then our suppositions 
(solid state with small values of /— 6) would not be fulfilled ; and 
secondly by this that with comparatively large values of w,, in 
consequence of which 6—s’ would become too large, e will gradual- 
ly greatly increase, so that the molecules can never approach each 
other more closely than to a certain minimum distance. Only in case 
of very strong collisions (¢ very large with respect to f) 6—-s’ can 
approach to O at not too large values of u, 
mts 
It holds for ¢, and ¢, themselves, that ¢,=@ ye will always 
ati 
. m 
approach O at high temperature, while /, = 4 |e remains 
€ 
finite — unless e is very large, in which case ¢, can even become 
much smaller than ¢,. 
