606 JOHN JOHNSTON AND PAUL NIGGLI 
By comparison of the above results with those of Table I we 
see how much greater the effect of unequal pressure may be. For 
example, take the case of lead, the melting-point of which is changed 
+o°oo08 by 1 atm. uniform pressure, but —o?24, or 30 times as 
much, by 1 atm. excess pressure on the solid phase. 
The sequence of the metals when arranged in the order of their 
@ values (as computed from equation VII) is identical with that 
obtained when they are arranged in the order of their flow pressures 
or of any of their elastic properties (e.g., tensile strength, hardness). 
This parallelism is a striking corroboration of the effectiveness of 
unequal pressure in correlating phenomena attending the deforma- 
tion of crystalline solids." 
It is of interest to inquire if there is any relation between the 
hardness of minerals and any of their other properties. There is 
a parallelism between the hardness of the metals (as ordinarily 
measured) and the calculated ¢ values, which depend upon the 
density, heat of melting, and temperature of melting. Of these 
three factors the first lies within comparatively narrow limits for 
a series of minerals; the second is not known, but probably lies 
also between comparatively narrow limits im general;? the limits 
within which the melting-point lies are comparatively much wider 
apart. Consequently, we should expect that there is a rough 
parallelism between the hardness of minerals and their melting- 
point. 
That this expectation is justified is shown by Fig. 4, in which 
the melting-point of those minerals which give congruent melting- 
points is plotted against the hardness; this has been done for all 
minerals for which the necessary data could be found in Landolt- 
Bornstein Tabellen. All of the points lie within a zone the breadth 
of which is no greater than one might expect from the very uncertain 
nature of the measurements of hardness, and in view of the circum- 
stance that the latent heat has not been taken into account. When 
the latent heat is taken into account (which is possible only for a 
few of the metals) and the ¢ values plotted against hardness the 
* For a discussion of this question see Johnston, Jour. Am. Chem. Soc., XXXIV 
(1912), 788; Z. anorg. Chem., LXXVI (1912), 361. 
* The exceptional cases would be those in which the heat of melting is very small. 
