258 CARNEGIE INSTITUTION OF WASHINGTON. 



I have therefore begun a search for assumptions as to the thermo- 

 dynamic properties of lava, which would be consistent with the data 

 at hand relative to surface rock, and to follow out the plan carried 

 through by Ritter for gases and vapors, determining the " adi- 

 abatic condition line " and the law of contraction and radiation, 

 assuming the adiabatic state maintained by an appropriate law of 

 conduction. If the law of conduction so determined should prove 

 plausible, and the rate of surface loss agree fairly well with observa- 

 tion, this would furnish a complete solution of a case perhaps not 

 remote from the actual, and the direction of departure from it would 

 give at least qualitative information of value. This is the only avenue 

 of approach I see just now. It is impossible to satisfy the condi- 

 tions by assuming a coefficient of expansion so small that even for 

 the earth the cooling is practically independent of the contraction, 

 for the thermodynamic law of entropy shows that part of the energy 

 from the gravitational source must take the form of internal potential 

 energy, not temperature, and the smaller the coefficient of expan- 

 sion, the larger this portion is. For a fictitious substance with zero 

 coefficient of expansion, there would be no rise of temperature at all. 

 This striking result from the law of reciprocity only shows again 

 what a great difference there is between the small masses of the lab- 

 oratory and the cosmic masses. 



It is fair to say that these criticisms are not peculiar to our point 

 of view, but apply with equal force to everything which I have seen 

 on the secular cooling of the earth. 

 Very truly yours, 



Arthur C. Lunn. 



