( 118 ) 



is an asymptote of the cuIhc ciirxe. I( lias two brandies, of which 

 the one {dGEd') situated above tiie asymptote, is given by vahies 

 of z, which are larger llian :,, the other {d"OHFd"'), below the 

 asymptote for 5<C-,. 



a becomes equal to zero not only for :: = 0, but also for two 

 other real values of z, of which the one is positive, the other negative; 

 I shall call the positive root z^, the negative one z^. In the same manner 

 /? vanishes for ^ == and also for two other real valnes of c, of which 

 again one {z^ is positive, the other (^.) negative. We can prove 

 that always z^'^z^; for z.^ and z^, three cases are possible: both 

 are larger than z■^, and then z^^z^, or both are equal to z^, or 

 both are smaller than "i and then z^ <[ j,. With the values of the 

 derivatives, to be introduced presentl3% the order of the roots is : 



and hence follows the form of the cubic curve as it is drawn in the 

 figure ^). 



One can easily see that i\cf,i^ Vh above the branch z'^ z^, and 

 within the branch c<^c,, while Vj:^i<^v/c in the area which lies 

 partl}'^ between those two l)ranches and which extends further to the 

 right of both. 



Retrof/rade vimdensation is of the tirst kind when VTpi<CvTr, ii»d 

 of the second when VT,,i^vrr- According to form. (41) and (2G) 

 VTfd^ i^Tr when />?„, and in^„^ -\- RTj^m^^ have the same sign; 

 m*^^ ~\- RTtrn^^ is positive outside the parabola bAOb' and negative 

 inside, while /»„i is positive above the straight line Oa and negative 

 below it. Hence we have VTpi^i^Tr and retrograde condensation 

 of the second kind: 1"' . inside the parabola J)AOh' and below the 

 straight line Oa, 2'"'. outside the parabola and above the straight line; 

 at all other points rj;,/ < ''7V and the retrograde condensation is of 

 the first kind. 



Here follow the physical characteristics of the fields into which the 

 figure is diA'ided l)y the boundaries under consideration : 

 Field 1 : 7'.,/,/ > T,, , />,^,/ > pj, , iV/>/ > ^k , vT,d ^ ^Tr , r. c. H 



2 : T,^/ > Tk , Pj.^,1 > pi: , v.,;>l < vk , vTf^i > vTr, r. c. H 



3 : Trfji > Ti, , p,-^l > Pt , vj-^u < vie , vTpl < vTr , r. c. I 



4 : Tri,i > Tfc , p,.^,i > p/, , v,-!,! > n , vTpl < VTr , r. c. I 



5 : T,;,/ > T^- , P.c.1 < Pk , ^V' > ''/' ' '"^'/'^ < ''^'- ' ^' ^- ^ 



6 : 7V/./ < ï'a- . Pxrl < Pk , v,:,,i > vt , VT,d > ^Tr , r. c. H 



7 : 7V.^/ < Tfc , 7^,^/ < 77t , i'x,l > ^^• , VT,1 < ^r. , r. c. I 



8 : T,.^./ < 7')^ , Px,l < P/. , 'Vy,/ < t'/L- , «r/./ < VTr. r. c. I 



9 : 7^.vW < ^Y- , P.r,d > ?'i- , rx,,i < r^- , r7>/ < vTr • r. c. I. 



1) It will be seen that this form agrees entifely willi that derived by Ivohteweg 

 in the x, y-diagram from a special equation of stale. 



