AT HIGH PRESSURES BY OPTICAL METHODS. 
147 
that a relation of some kind exists between the physical constants of polymorphic 
modifications if these are formed from the same molecules of the liquid phase, and, as 
will be shown, the measurements given al)ove also indicate tlie existence of such a 
relationship. Conclusions may, to a certain extent, be drawn, even as to the nature 
of this relationship, but as this case is only a single one—tlie only one which until 
now has been investigated—the relationship observed might, of course, depend upon a 
singular coincidence, although this is not probable, and the discussion to follow is 
therefore given with all reserve. 
The two melting-point curves are perfectly straight lines within the limits as set 
by the accuracy of the measurements. The upper one has been followed over a 
pressure range of 1,060 kg./cm.^, the lower one over one of 1,330 kg./cm.^. If we 
continued these melting-point curves towards negative pressures in the diagram we 
should find that they would intersect at a pressure value of about —17,000 kg./cm.^, 
and at a temperature between —270° C. and —280° C., that is, at the ahsolute zero. 
The conclusion to be drawn therefrom is that the differeyice hetween the ahsolute 
melting- 2 iomts of the tiro modifications at any pressure is similar to the difference of 
the ahsolute melting-pyoints at ordinary pressure, the melting-point values thus 
converging towards unit value at the absolute zero. 
If we further inquire into tlie cause of this relation, we find that the direction of 
the melting-point curve is determined by the product of the absolute melting-point 
into the quotient given by the volume change at the melting-point divided by the 
latent heat of crystallization in the Clapeyron-formula for the change of the melting- 
point by pressure. If the ratio between the absolute ^melting-points of two crystalline 
forms remains constant at all temperatures and the melting-point values converge 
toward unit value at the absolute zero, as in tliis case, it is therefore necessary that 
the ratio between these quotients in the Clapeyron-formula should also remain 
constant at all temperatures, and that the absolute values of the quotients should 
themselves also converge towards unit value at the absolute zero. Nothing at present 
is known about the absolute values of the factors entering into this quotient in the 
Clapeyron-formula, and of the absolute change of these factors with changing 
temperature, but the fact that a volume factor, as well as a lieat factor, in the case of 
both modifications is affected by pressure in a similar way is of considerable interest. 
The changes of the latent heats of crystallization must depend on the changes of 
the specific heats of the liquid and of the crystals, and to these changes the changes 
of the latent heat of transition between the two modifications probably also 
corresponds. The volume changes again must depend upon the compressibility of the 
liquid and of the crystals. The intersection of the melting-point curves at the 
absolute zero thus points to the probability that the values of all these properties for 
both modifications converge toward unit value at the absolute zero. 
It may suffice here to point out briefly that in tlie case of the energy factors this is 
what is required by the heat theorem of Neenst, and that the other factors again 
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