( 298 ) 
Ú 
d 
dp dvd dvy dp ) ee dv 
= ik er SSS ee 1 er | — 
Crake. oat Hea (aT aT ) EL STEN a 
or Vy 
Vd 
Da 
Vy 
dp Ne. d 
and in words: (=) is the mean value of (=) between the volumes 
dT COËT or v 
v, and vg. At the critical temperature the mean value is the 
pressure-variation co-efficiént itself or 
lee 
2. By integrating the isentropic relation 
7 \ _ (op 
& = (Ge), 
d 
and by putting (vd — vo) (=) instead of n2— 1» and proceeding as in 1°. 
coer 
3. By using the po7-surface. 
At the critical point a tangent to this surface may be drawn 
parallel to the v-axis. The tangent-plane at the critical point is thus 
at right angles to the pZ-plane, and its section is a straight line. 
Each curve on the pv7-surface which passes through the critical point 
and whose osculating plane at the critical point, while cutting the 
tangent plane to the peT-surface at an angle, is not perpendicular to 
the pT-plane as is the case with the tangent plane to the pvT-surface, is 
projected on the p7-plane as a curve touching the above named section. 
Hence 1. the border curve, of which the osculating plane co-in- 
cides with the tangent plane to the pvZ-surface at the critical point, 
9 the section of the peZ-surface by a plane at right angles to the 
v-axis, 3. the isentropic line for the critical point, etc. All these 
lines have projections on the pT-plane, touching each other in the 
d ee 
projection of the critical point and hence give Ee values with dif- 
ferent indices v‚.n, coéx., ete. which are equal to one another at the 
eritieal point. 
dns dd te tn 
