1892.] liquid condition of the Earth's interior. 847 



100 million years, may be put at about 209° Fab. This calculation 

 involves the assumption that the ratio of the rate of thickening to 

 the rate of retardation (or remelting) is constant, or, what is equi- 

 valent to this, that the thickness of the crust varies as the square 

 root of the time since it began to be formed. It was there shown* 

 that the assumption of constancy of the above ratio of the rates of 

 thickening and retardation of thickening is probable, because, if 

 their ratio varied as any power of the time, it would lead to 

 unnatural consequences. I now find that the assumption that the 

 store of heat was initial is not necessary, because the same formula 

 can be obtained without that assumption, so long as we adhere to 

 the other assumption that the thickness of the crust varies as the 

 square root of the time, or to its equivalent. Such a calculation 

 is sufficient to show that the amount of heat, carried off by con- 

 duction through the crust in an interval even so long as 100 million 

 years, must have been quite inconsiderable compared to the whole 

 amount generated in the interior. 



As the most extreme case possible of volcanic action we can 

 estimate approximately the fall of temperature of the earth sup- 

 posing the whole of the water of the ocean to have been originally 

 in solution with the magma of the interior, and to have carried off 

 a corresponding amount of heat. Professors Riicker and Roberts- 

 Austen have determined the temperature of melting basalt to be 

 about 920° C. f Now the total heat of steam at t degrees C. given 

 off in condensing into water at 0° C. is given by the formula 



605-5 +0-305*+; 



whence it appears that unit of vapour at 920° C. will have parted 

 with 886 units of heat in condensing to water at 0° C. Hence every 

 unit mass of the ocean on the hypothesis now made represents 886 

 units of heat removed from the interior of the globe ; for remem- 

 bering that the main body of water in the great oceans is at very 

 low temperatures, and that a large volume of water at the poles is 

 frozen, it is not a violent supposition to assume 0° C. as the mean 

 temperature. 



Now even supposing the ocean to cover the globe and to be four 

 miles deep, its volume will be about 0'003 of the whole globe. The 

 density of the globe is 5*5 that of water. Hence the mass of the 

 ocean is 0003/55 times the mass of the globe. Then, taking as 

 Darwin has done the specific heat of the globe to be that of iron, viz. 

 1/9, we get the mean temperature of the interior reduced by this 

 means by 4°"53 C. or 8° F., an inappreciable amount compared with 

 the 3000° F. attributed to tidal action, by which the earth is 

 estimated to have been heated. 



* Appendix to Physics of the Earth's Crust, p. 21. 



t " Nature," vol. xliv., p. 456. Also Phil. Mag., Oct. 1891. 



% Tait's Heat, § 166. 



VOL. VII. PT. VI. 27 



