1214 
0Z OZ ? 
«e— +y——Z4+4Z,=0 
Oa " Oy 
a D (1) 
dz OZ 
(v7—a) + (y—@)—--272+6=0 
Ow Oy 
If we develop these with regard to «, y, P and 7’ and call 
“ee and y= we find, if we keep to the same notation as in 
communication (LI): 
ade + bdy + tcda? -+ ddady + hedy* -+.... 
SOP ee DATE Wide tae sae eee ee 
irda® 4 sdady + Stdy” SE a ASP Bar She En (5) 
In equation (3) are wanting the terms dr dP, dy dP, de dT and 
dydT. A, B,C. and D have herein the same significance as in 
communication II; therein, however we must now call «=a, y=, 
2, = randy =O: 
We now allow the liquid, saturated with # and in equilibrium 
with vapour, to proceed along the line Z/°Z, in fig. 1 (IV). For 
this we call dy =tgg .dx; from (2) and (3) now follows: 
(a + btgg) de + He + 2dtg p + ety’ gp)de + . 
EE APE DaT Ae eh ee | oo 
Mr Qsta gg + tlg op) dae 4+... == AdP BHT Fres > 
We now allow the straight line ZZ, in fig. 1 (IV) to coincide 
with the line X/Y of this figure. As X/Y is the tangent in the 
point # at the liquidum line of the heterogeneous region passing 
through /, this is determined by : 
(ar + fis)dx + (as + By)dy = ada 4- bdy = 0. 
Hence, if in fig. 1 (IV) the line ZFZ, coincides with the line 
NEN, a+b p=; 
If we substitute this value of fy g in (4) and (5) we get: 
gp Oder tem CIP + DAT +... 
Ee — AdP— BAT + (7) 
A ent He a MA a U Ee ( TORO . . . . 
ee a | 
In this Q and S have the same value as in communication (LD, 
namely: 
Q = 2abd—a*e-—b*e 
Sat + b?’r—2abs = (rt—s”) (a’r + Zas + B°4) 
At first, we may limit ourselves to terms recorded in (6) and 
(7); from this we find: 
