55 



After substitution of llie values of s from (5), pt from (4) and 

 vk : bk = r, this becomes : 



r 27 1 27 1 



■ f = s -~r'k, or ~l + —--{l-tk), . . (6a) 



r — 1 r' /j r' /^ 



8 A, r , 



in which also — can be written lor s according to (5). 



r — 1 /j r — 1 



r 8 A 



As with 8 = 2,11, ?'^2,1 the value of .9 or — -7^ amounts 



r — 1 r — 1 /j 



27 I 

 already to 7, and also 1 -\ — ~ -- --=1 — it follows necessarily that 



the value of x'k must either be^(almost") 31= or exceedingly small ^). 



In consequence of this the oi formulae (6), (7), and (8) can also 

 be kept unchanged. 



Let us now calculate the value of the characteristic function rp, 



/dfp\ 

 or rather of the quantity X = — v" • 



\dmjk 



Now we proved in a preceding Paper (see v. L. B, p. J104- 



1105), that when only a is a function of T, the coefficients of a* 



and ^ in the expression (da) for X both become = 0, and that 



therefore only : 



-." 



is left. 



In this experimentally the value — 40,8 is found for g"<2 ^), so 



^) We will just remind here of the fact, that some thirty years ago, when r 



27 

 was still =3, the value — 1 had to be assumed from /"= 1 + -r- (1 — t''') = 



T 



1 -f 3C1 — t'*) for f'jc to make /"= 7. Clausius' function t = 1 ; m satisfied this 



condition, but also the better function t = e^-"* of van der Waals. 



/er 8 

 2) The mere fact that so high a (negative) value is found for e"ii , i.e. 



dm^Jk 

 for V constant, is a proof that a (or h) must be a temperature-function. If 



one 



substitutes in the above given expression for F'j^, viz. F'k=[ ——^~ ] = 



\^ dm J 



= e"p - (a2— ^) a"^^^ — V6«2e'"^2_^, for F'k , f",.,< ^"^ ^'"v'^t I'^sp- the values 39,6, 



— 11,4 and 29,6 experimentally found (loc. cit. p. 1101 — 1103), one finds 



namely with «2 = 15, (3 = 0,9 for e'\, the value 39,6+14,1 .(—ll,4)+2,5 . 29,6 = 



= 39,6 — 160,7 + 74,0 = — 47. If the values —11,4 and 29,6 are raised resp. to 



— 12 and 36 for the reasons given on p. 1103 — 1105, one finds for e",2 the above 



given value — 40,8. At any rate this value differs much from 0, and a (or b) is 



therefore certainly a temperature-function. 



