( 28 ) 



iPT _i\ O rw 



'd^~'W^ (1 - ,^\N ~ 



as we have also found Iiefore (see p. 481 of my first coininiinication). 

 Whereas for « = a point of inflection at x z= (N = 1) was 

 determined with the aid of the simple equation 2 0=zl, or 0=72, 

 this condition becomes, in the case we are treating now, somewhat 

 more intricate. If we equate namely the second number of equation 

 (3) lo zero, and further j)ut .i'=0, iV=l, then we find : 



0(2 6—1) + 2«=0, 



so 



We find therefore that a point of infiection occurs beyond x^O, 

 always when 



^' — è ^ + » > (4) 



In the case of tin-nicrciiri/ (see the second communication) we had 

 ^'=0,396, and «=0,0453; therefore: 



0,1568 - 0,1980 4- 0,0453 = 0,0041. 

 This value being positive, a point of infiection was to be expected 

 between ,*'=:0 and ,i==l. In fact a point of infiection was found at 

 .^,'=0,75. 



The equation (4) may also be derived in the following way with- 

 out making use of equation (3). If we resolve equation (1) into a 

 series according to ,r, we get for small \^alues of x: 

 T = T, (1 — Ox -f (^^ — i ^ 4- «) x\ . .). 



The melting-point curve turns therefore at ,r=:0 the concave side 

 towards the ordinate .ri=0 in the case that 0' — ^ ^ + « <[ ; and 

 as the curve approaches the ordinate x=A asymptotically, a point 

 of inflection cannot occur. If on the other hand 0^ — \6 -]- a'^0, 

 then liie coiircv side is turned towards the ordinate t6' = and there- 

 fore a point of infiection mud necessarily occur between x=0 

 and .i'=l. 



As can be -\-co at the utmost, there must exist a value, which the 

 abscissa of the point of infiection cannot exceed. This maximum value 

 is found l)y equating the second member of equation (3) to zero, 

 and 6^ to 00 [lY being equal to — log (l-ev)], so we find: 



1 i^ ^ _iYi+,_^Vi^^^*i^'! + 



-2«%(l-.^^)(l-2r.^0 ^^ 

 (1+r..)^ 

 Only if «=0, this may simply be written: 



