496 JOHN JOHNSTON AND PAUL NIGGLI 
rule to which there are very many exceptions. From the above we 
see that the rule—in spite of its breadth—will not be generally 
applicable; for if it were, it would imply limitation of the type of 
possible configuration of the diagram of state, whereas there is no 
reason to believe that such limitations exist. 
From this point of view also we can see how the phenomena of 
monotropy and of allotropy are related. Whether one or the other 
of these phenomena occurs depends again on the position of the 
lines representing the internal equilibrium, especially in relation to 
the unmixing curves. 
The foregoing brief account of the theory of allotropy proposed 
by Smits has been given mainly for the purpose of bringing one 
point to the attention of geologists and mineralogists: namely, that 
it aids in familiarizing us with the idea that pure phases (even 
crystalline) are not necessarily made up of a single molecular 
species, an idea which is supported by a considerable array of 
facts and is in conflict with no direct experimental evidence. In 
addition, it indicates that even metastable states, the existence of 
which has often been looked upon as a proof of lack of com- 
plete validity of physico-chemical principles, may also be treated 
theoretically. 
Monotropic transformations—Monotropic changes are irrever- 
sible; they occur when a form which is metastable under the par- 
ticular conditions passes over into a form which is essentially stable 
under those conditions of temperature and pressure. Monotropic 
changes therefore occur whenever the rate of transformation 
becomes appreciable; moreover, since this rate is different under 
different conditions, the transition temperature is not a definite 
point but may lie within a very wide range. As an illustration 
consider the two principal forms assumed by calcium carbonate. 
All the evidence indicates that aragonite is metastable at tempera- 
tures above the ordinary; yet in the dry state it does not go over 
into calcite until about 400°. Yet the transition to calcite—which, 
being more stable, has at any definite temperature a lower vapor 
pressure and (in any single solvent) a smaller solubility than arago- 
nite—takes place very slowly at 100° in presence of water, and more 
rapidly and at a lower temperature in presence of water containing 
