554 PROCEEDINGS OF THE AMERICAN ACADEMY. 



melting curve to be a parabola, but this extrapolation is open to very 

 great question. He himself remarks that at high pressures the equi- 

 librium curves tend to show less curvature than one would expect from 

 their behavior at low pressures. 



The idea of a maximum seems opposed to our common-sense feeling 

 of what to expect. If there is a maximum, it is possible by taking the 



substance through an isothermal cycle 

 from the domain of the liquid into 

 that of the solid and back into that of 

 the liquid again to find a necessary 

 connection between the compressibility 

 of liquid and solid over a wide pressure 

 range. This is unexpected in view of 

 our present experience that there is no 

 necessary connection between the prop- 

 erties of liquid and of solid. It is to 



iij 



0. 



PRESSURE be noticed that the nearest approach 



Figure 43. Tammami's com- *« ^ maximum found here, on the 

 plete equilibrium curve between H-L curve, was neatly avoided by the 

 liquid and crystal. The crystal appearance of another form of ice. 

 is stable only within the closed Proceeding from the probable exist- 

 region. ^^^g ^^ ^ maximum, Tammann has 



developed his well-known theory of the 

 nature of the complete equilibrium curve between liquid and solid. 

 The ideal curve (Figure 43) according to this theory is a closed curve, 

 the crystalline solid having existence only in the interior of the curve. 

 The complete curve may not be realizable for all substances, since part 

 of the curve may fall at negative pressures or at temperatures below 

 the absolute zero. As a matter of fact, only the two upper quadrants 

 have been realized for known substances, and even then, no substance 

 has been found in both the two upper quadrants. The upper left-hand 

 quadrant is that for normal substances, while the upper right-hand 

 quadrant shows the behavior of water and ice I. 



We turn now to the evidence on these points afforded by the present 

 work on water. First for the equilibrium curves alone. These all 

 show curvature in the direction demanded by Tammann's complete 

 diagram, on the I-L curve the fall of temperature becoming more rapid 

 at higher pressures, and on the other curves the rise of temperature 

 becoming less rapid with rising pressure. Except on the I-L curve, 

 this behavior is just exactly what one would expect on nearly any con- 

 ceivable theory, the effect of temperature becoming less at higher 

 pressures. This is the behavior also on the liquid-vapor curve, which 



