TRANSACTIONS OF SECTION A. 517 



moon's distance augmented from n,, to n earth's radii, the energy which has been 

 converted into heat in the process is 



iji) — 1 — 8-84 ^_- — --j times the earth's kinetic energy of rotation. 



From these data it results that the heat generated in the lengthening of the 

 day from twenty-three to twenty-four hours is equal to the amount of heat lost by 

 the earth, at its present rate of loss, in 23,000,000 years. 



Now if this amount of heat, or any sensible fraction of it, was actually 

 generated within a few hundred miles of the earth's surface, the temperature 

 gradient in the earth must be largely due to it, instead of to the primitive heat of 

 the mass. 



Such an hypothesis precludes the assumption that the earth is simply a cooling 

 mass, and would greatly prolong the possible extension of geological time. It 

 must be observed that this view is not acceptable unless we admit that the earth 

 ■can adjust itself to the equilibrium figure adapted to its rotation.' 



It seems also worthy of suggestion that our data for the average gradient of 

 temperature may be somewhat fallacious. Kecent observations^ show that the 

 lower stratum of the ocean is occupied by water at near the freezing temperature, 

 whilst the mean annual temperature of the earth's surface, where the borings have 

 "been made, must be at least 30° higher. It does not then seem impossible that 

 the mean temperature gradient for the whole earth should differ sensibly from the 

 mean gradient in the borings already made. 



The foregoing remarks have not been made with a view of showing Sir William 

 Thomson's argument from the cooling of the earth to be erroneous, but rather to 

 maintain the scientific justice of assigning hmits of uncertainty at the very least 

 as wide as those given by him. Professor Tait =" cuts the limit down to 10,000,000 

 years ; he may be right, but the uncertainties of the case are far too great to 

 justify us in accepting such a narrowing of the conclusion. 



The third line of argument by which a superior limit is sought for the age 

 of the solar system appears by far the strongest. This argument depends on the 

 amoimt of radiant energy which can have been given out by the sun. 



The amount of work done in the concentration of the sun from a condition of 

 infinite dispersion may be computed with some accuracy, and we have at least a 

 rough idea of the rate of the sun's radiation. From these data Sir William 

 Thomson concludes : — ■* 



' It seems, therefore, on the whole most probable that the sun has not illu- 

 minated the earth for 100,000,000 years, and almost certain that he has not done 

 so for 500,000,000 years. As for the future, we may say, with equal certainty, 

 that inhabitants of the earth cannot continue to enjoy the light and heat essential 

 to their life for many million years longer unless sources now unknown to us are 

 prepared in the great storehouse of creation.' 



This result is based on the value assigned by Pouillet and Herschel to the 

 sun's radiation. Langley has recently made a fresh determination, which exceeds 

 Pouillet's in the proportion of eight to five.^ With Langley's value Thomson's 

 estimate of time would have to be reduced by the factor five-eighths. 



In considering these three arguments I have adduced some reasons against 



' Since the meeting of the Association Sir William Thomson has expressed to me 

 his absolute conviction that, with any reasonable hypothesis as to the degree of 

 viscosity of the more superficial layers, and as to the activity of tidal friction, the 

 disturbance of temperature gradient through internal generation of heat must be 

 ■quite infinitesimal. 



' ' Challenger ' Expedition. 



» Recent Advances in Physical Science (1885). 



* Thomson and Tait, Nat. Phil. Appendix E. 



" Langley {Ann. Rep. R. A. S. 1885) estimates that 3 calories per minute are 

 received by a square centimetre at distance unity. This gives for the total annual 

 radiation of the sun 4-38 x 10^^ calories. Thomson gives as Pouillet's estimate 

 ■6 X lO*" times the heat required to raise 1 lb. of water 1° Cels., or 272 x 10" calories. 



