470 Proceedings of the Royal Society of Edinburgh. [Sess. 
of all nuclei. But then no physical distinction is left to account for the 
splitting of the isothermal. 
4. Physical, and even geometrical, continuity debars the adoption, above 
the triple-point, of a construction which is inapplicable below and at it. 
Therefore, if physical continuity of the three states of matter is to be 
regarded as a possibility, the following modification of Thomson’s suggestion 
seems to be necessary. 
Regard a complete isothermal as constituted of three portions A B, B C, 
C D, characteristic respectively of the liquid, solid, and vapour states. At 
the point B the liquid and solid states merge, without change of volume, 
but with change of molecular configuration. Similarly, merging of the 
solid and vapour states occurs at the point C. The diagram above refers to 
any substance such as water-substance below its triple-point ; the diagram 
below refers to a substance of that kind above the triple-point. Change of 
molecular configuration, such as is here supposed to take place at the 
points B and C, is analogous to the change (now well known through 
Kelvin’s discussion of Madan’s observations) which occurs in crystals of 
chlorate of potash at a high temperature. The normal isothermal proceeds 
by the path A a b c cl D, the positions of a b and c d being such that the 
areas a B b and cCd are equal. If, in the absence of nuclei for solidification, 
the pressure is reduced to a value less than that corresponding to the posi- 
tion a b, but greater than that corresponding to the position c d, the produc- 
tion or introduction of effective nuclei will give rise to explosive solidifica- 
tion. If, subsequently, the pressure on the ice is reduced to a value less 
than that corresponding to the position c d, the presence of effective nuclei 
would cause explosive evaporation. On the other hand, if, in the liquid, 
nuclei for evaporation are present while nuclei for solidification are absent 
or ineffective, the normal isothermal will be ApqrD, determined by the 
condition that the areas p B q and qCr are equal. 
At the triple-point b and c coincide, ice water and steam being in mutual 
equilibrium. Above the triple-point, normal solidification takes place at a 
less pressure than that of normal vaporisation. Consequently any solid 
produced in the manner indicated by, say, the course a b at once evaporates 
if vapour nuclei be present. That is to say, in the presence of effective 
nuclei for vaporisation, ice cannot exist above the triple-point. So, if ice 
always effectively provides nucleation for vaporisation, we have an explana- 
tion of the impossibility of superheating ice. It would be of interest to 
test the point farther by an attempt to superheat ice which has first, if 
possible, been super-pressed at a temperature immediately below the triple 
point. 
