(27) 

 (28) 



( 522 ) 



The conditicns that .'"i , //i , -^i and ■r.,i/.,,z., are conjugated i)oiiits 

 thus become: 



Ill coiiseqiiciice of tlie clioice of the }'-a\is we tind : 



If we put .r.^ = />-[- S2' ^^ that ^5, is a small (|iia)itity we have: 



-2 -- ^''il-/ + '\^2y-2 + <^\!/^' 4- 



We now write the equations (27) (28) and (29) in full; we then 

 directly leave out the terms which are certainly small with lespect to 

 those written down, settin«r aside of what order d\ y^ c.^ and //.^ will 

 |)ro\e to be with res])ect to each other. We then find: 



■2e,.v, + d,y,^ -}-....=. -20,^, ^c\y, + (27/ 



d,,v,' + 2d,x,y, + 4.3^,' + ... = c'J, + 2c\y, + . . . . (28)' 

 c,.v,'- + 2d,.v,y,'- + de,y,* + . . . = 2pc\^, + P^-\y, + • • • • (29)' 



If we solve out of (27)' and (28)' §j and //^ at first approximation 

 we find : 



t, z=z «.fj -j- 1?/;^^ and /y., = «'.Ci + ^'//i^ 

 where a, ^, a' and /?' have detinite values. 



From this ensues that ^^ and i/^ will be of the same order of 

 magnitude as ,i\ and t/^'-, when namely those two correspond in 

 order. If on the contrary ,i\ and y^" are of different order, then §2 

 and y^ must be of the lowest order as one of them (namely o^i or y^*). 



From (29)' however ensues that '2ijc\ B., -\- /)r\ y, and so also 

 2c\ §j -\- c'2 ^2 ^i'6 of higher order than a.\ or y/-' or both ; hence out 

 of (27)' may be concluded at first approximation: 



2c,x,i-d,y,^ = (30) 



The equation of the l)ranch bOJj' of the binodal line (tig. 13) is 

 therefore represented at tirst approximation by (30;. This equation (30;, 

 however, corresponds entirely to (lOj representing a curve of contact 

 which touches the binodal line aO^a' (fig. 13) in the plaitpoint. 



In an entirely similar way as in IIa-x we can now deduce: 



"an accidental branch of a binodal line passing through a plaiti)oint 

 is in this point always curved in the same direction as the binodal 

 line to which the plaitpoint belongs." 



