84 PHYSICS OF MATTER 



years, a period in close agreement with that found by Helmholtz 

 and Kelvin from the radiation of the sun. 



It should be remarked, however, that in discussing the state of 

 things in the earth's interior, where the pressures so far transcend 

 anything that can be approached in the laboratory, such constants 

 as melting-points should be looked on with great suspicion. 



Assuming Laplace's law of distribution of density in the earth, the 

 pressure at a depth of one two-hundredth of the earth's radius is 

 8600 atmospheres, while at the centre of the earth it becomes more 

 than three million atmospheres. Now the largest pressures that have 

 been used in high temperature experiments are less than three thou- 

 sand atmospheres. It is evident, then, that any conclusion as to 

 melting-points from laboratory data must be violent exterpolations, 

 if deduced for the enormous pressures at depths greater than one 

 one-hundredth of a radius within the earth, where the pressure will 

 be over 17,000 atmospheres. 



But not only is there necessarily great uncertainty as to the 

 fusing-points at these great pressures, but it seems probable that such 

 a process as fusion marked by sudden increase in liquidity can hardly 

 take place at all. In the phenomenon of fusion, the equilibrium of 

 a substance may be regarded as conditioned by the external 

 pressure, the cohesive pressure, and the internal pressure due to 

 the translatory kinetic energy of the molecules, which may be 

 called the kinetic pressure. In a state of equilibrium, the external 

 pressure plus the cohesive pressure must equal the kinetic pressure, 

 the last tending to produce expansion, while the two former act to 

 cause contraction. At ordinary atmospheric pressures in the liquid 

 and solid state, the cohesive pressure is enormously greater than the 

 external pressure. In water at ordinary temperatures it is estimated 

 about 6500 atmospheres, while in a solid such as steel it may have 

 a value of perhaps 18,000 atmospheres. And not only is this cohesive 

 force great relatively to the external pressure, but it decreases w r ith 

 great rapidity as the substance expands. Under these conditions 

 it is easy to see that a slight rise in temperature with consequent 

 expansion and weakening of the cohesive pressure while the kinetic 

 pressure is increased may bring the substance to a point of trans- 

 ition, a melting-point or boiling-point where great changes occur 

 within narrow limits of temperature. 



But if we conceive the external pressure to be so great that the 

 cohesive pressure is relatively insignificant, then we should not expect 

 to find any sharply marked changes of state for small changes of 

 temperature or pressure. 



To make the case definite assume a temperature of 1000 degrees 

 absolute scale, and a pressure of 1,000,000 atmospheres, and suppose 

 the cohesive pressure is 10,000 atmospheres. Under these circum- 



