340 Rev. 0. Fisher, On the hypothesis of a [May 30, 



internal friction. One part of this energy turns into potential 

 energy of the moon's position relatively to the earth, and the 

 rest develops heat in the interior of the earth." It is evident 

 therefore that, knowing the initial and present circumstances, 

 it is possible to estimate the total amount of energy converted 

 into heat without knowing the lapse of time in which it has 

 occurred. Darwin finds the common period of rotation, when 

 the moon separated from the earth, to have been 5 h. 36 m., 

 taking the viscosity at that time as small, the earth being sup- 

 posed to have been " a cooling body gradually freezing as it cools." 

 The present rate of rotation relative to the moon (the lunar day) 

 is 23 h. 56 m. The total heat generated in the earth in the 

 course of this lengthening of the day if applied all at once would 

 he says* be sufficient to heat the whole mass of the earth about 

 3000° Fah. supposing it to have the specific heat of iron. In 

 Table iv. of the former paper -f- he had given 1760° Fah. as the 

 temperature corresponding to a period of rotation of 6 h. 45 m., 

 so that it appears that the additional 1240° must be due to 

 the loss on the difference between 6 h. 45 m. and 5 h. 36 m., 

 or 1 h. 9 m., and he remarks that, "The whole heat generated 

 from first to last gives a supply of heat at the present rate of 

 loss for 3560 million years. This amount of heat is certainly 

 prodigious, and " he adds, " I found it hard to believe that it 

 should not largely affect the underground temperature"^; but a 

 further calculation led him to believe that it need not do so, 

 for he found that 0"32 of the whole heat would be generated 

 within the central eighth of the volume of the earth, and only 

 one-tenth within 500 miles of the surface. The heat generated 

 at the centre is 3 T 7 ¥ times the average, that at the pole 1/2^ 

 of the average, and at the equator 1/12| of the average; and it 

 turned out that the heat, being so centrically produced, would, on 

 account of the slowness of conduction, not have had time to reach 

 the surface in the 57 million years postulated. This conclusion 

 depending on conduction would of course be true only in the case 

 of a solid earth, the interior of which had the particular viscosity 

 which has been assumed, on which the 57 million years depend. 



In connection with this point a serious difficulty seems to 

 arise. Lord Kelvin, in his well-known paper "On the secular cooling 

 of the Earth §," held that, when according to his view it solidified 

 in a comparatively short period of time, the interior was at the 

 temperature of solidification suited to the pressure at every depth, 

 and, because the cooling would not even yet have penetrated to 



* "Problems connected with the tides of a viscous spheroid," p. 592. 



t "On the precession of a viscous spheroid," p. 494. 



X p. 561. 



§ Trans. Boy. Soc. Edin. vol. xxm. pt. i., p. 157, and Nat. Phil., App. D. 



