( 235 ) 



If we substitute this value of — iu v' — v we find for the maximum 

 b ' 



value of V — V 



h b 



{v' — t')max. 



4 6 32 T 

 —r — 1 1 



a' 27 T,, 



As a matter of course it is better to restrict ourselves to tempe- 

 ratures above the critical. Below this temperature v' — r is not 

 single-valued and the incpiiry after the value of v' — v for such 

 points on the theoretical isothermal as for which the pressure 

 would be negative, has no sense. If we take as utmost case T=r 7)-, 



27 

 the maximum value v' — v has risen to -— h. 



5 



For the value of the proportion of the maximum amount of »' — v 

 and tlie initial value, we find 



,B2r_ w27n_ . 

 V27 .7}, J\S T J 



27 

 T to be taken between — 7), and 7},. This proportion which at 



27 

 T= —- Ti- is equal to unity, reaches the value of 2.27 at T^ Tj;. 



Now we can imagine the course of v' — v at all temperatures 



above the critical. 



27 

 1°. for 7'> — Tj, the limiting value of v' — ?> is negative and equal 



o 



to b ( — -^ _ 1 ) so contained between — h and 0. For decreasing 



value of V, the quantity descends to the value — h at v:=b. There 



is neither maximum nor minimum. 



27 27 



2°. for T between — 7), and —-, 11 the limiting value is positive 

 8 10 



and keeps between and b. For decreasing value of v, v — c 



descends down to — b. So there must be a value of v, at which 



V — V changes its sign. This value of v has been calculated above, 



a' b 

 and has been found to amount to -; , for which we may write 



