of Edinburgh, Session 1883 - 84 . 935 
saying that lines so meeting are different adiahatics, — not branches 
of the same one. 
As Mr Riicker (Proc. Roy. Soc., vol. xxii.) has pointed out, it 
is possible that there may be a point of maximum temperature on 
the adiabatics within the region where ^ is negative, for the sub- 
dt° 
stance is rising in temperature, while doing work by its expansion. 
This must be determined by experiment. 
In the surface referred to above, there are three cylindrical regions, 
the projections of which on the plane (p, t) give the three curves 
already mentioned as separating the regions which represent the three 
different states. The triple point line is the line of intersection of 
these surfaces, Mr Rucker shows that, along the triple point line, 
and along all other isothermals in these cylindrical regions, the 
adiabatics coincide for some distance with the isothermals. He 
gives formulae for determining the distances for which they coin- 
cide. Consider portions of the substance in the three different 
conditions, such that the state of the mixture is represented by a 
point on the triple-point line. If there is enough steam to just 
melt all the ice, the adiabatic and isothermal will coincide all along 
the triple-point line in the direction of lessening volume. If not, 
then the adiabatic will enter the liquid-solid surface. If more than 
enough, then it will enter the liquid-gaseous surface. On expan- 
sion, the lines will only coincide until all the water disappears, 
when the adiabatic will enter the solid-gaseous surface. 
If with Professor J. Thomson we consider that portion of an 
isothermal where change of state occurs to be curved in the 
plane {p, v), so as to have parts corresponding to unstable condi- 
tions, there must always be more unstable conditions along an 
isothermal in the region separating the liquid and gaseous states 
than in the other two similar regions ; or else there are more such 
unstable conditions in that region near the triple point line than at 
a distance from it. 
3 R 
VOL. XII. 
