Carbon and arsenic are the only two elements that have a melting-point above the boiling-point; and among compounds carbonic acid and fluoride of silicium are the only other bodies with similar properties. Now the melting-point of arsenic is about 1·2 times its absolute boiling-point. With carbonic acid and fluoride of silicium the melting-points are about 1·1 times their boiling-points. Applying these ratios to carbon, we find that its melting-point would be about 4400°. Therefore, assuming the following data: Boiling-point 3870° Ab. Melting-point 4400° Critical temperature 5800° Critical pressure 2320 Ats. the Rankine or Van der Waals formula, calculated from the boiling-point and critical data, would be as follows: log. P = 10·11 - 39120/T, and this gives for a temperature of 4400° Ab. a pressure of 16·6 Ats. as the melting-point pressure. The results of the formula are given in the form of a table: Temperature Pressure Ab. Ats. 3870° 1·00 Boiling-point. 4000° 2·14 4200° 6·25 4400° 16·6 Melting-point. 4600° 40·4 4800° 91·2 5000° 193 5200° 386 5400° 735 5600° 1330 5800° 2320 Critical point (15 tons per square inch). [Illustration: FIG. 19. CURVE OF VAPOUR PRESSURE OF CARBON] If, then, we may reason from these rough estimates, above a temperature of 5800° Ab. no amount of pressure will cause carbon vapour to assume liquid form, whilst at 4400° Ab. a pressure of above 17 atmospheres would suffice to liquefy some of it. Between these extremes the curve of vapour pressure is assumed to be logarithmic, as represented in the accompanying diagram. The constant 39120 which occurs in the logarithmic formula enables us to calculate the latent heat of evaporation. If we assume the vapour density to be normal, or the molecule in vapour as C_{2}, then the heat of volatilisation of 12 grms. of carbon would be 90,000 calories; or, if the vapour is a condensed molecule like C_{6}, then the 12 grms. would need 30,000 calories. In the latter case the evaporation of 1 grm. of carbon would require 2500 calories, whereas a substance like zinc needs only about 400 calories. CHAPTER IX GENESIS OF THE DIAMOND Speculations as to the probable origin of the diamond have been greatly forwarded by patient research, and particularly by improved means of obtaining high temperatures, an advance we owe principally to the researches of the late Professor Moissan.