January 4, 19 12] 



NATURE 



ment consists in accepting the antiquity of the earth, as 

 found by Prof. Strutt using a radio-active method, and then 

 examining the heat of the earth in the light of that result. 

 Every estimate as to the age of the earth assumes to some 

 degree a uniformity of present phenomena throughout the 

 whole life of tie earth ; this uniformity is assumed by Sir 

 Archibald Geikie in the rate of deposition of sediments," 

 by Prof. Joly for the addition of sodium to the sea,' by 

 Lord Kelvin for the conduction of heat by rocks, and, 

 finally, by Prof. Strutt for the rate of accumulation of 

 helium in minerals or rocks.* Now of all these processes 

 the last is the only one which is not altered by tempera- 

 ture, pressure, or other physical conditions. 



Prof. Strutt has concluded from a very refined deter- 

 mination of (i) the present rate of production of helium, 

 .-•nd (2) the total accumulated helium in thorianite that it 

 has taken 280 million years for the helium to accumulate. 

 As the earth is presumably older than the mineral, this is 

 a minimum age for the earth. 



The Heat of the Earth. 



The question at once arises how is it that the tempera- 

 ture gradient of the crust is not less than it actually is, 

 for, according to Lord Kelvin, after only forty million 

 years the gradient would have fallen to the present value. 

 During the remaining 240 million years it would have gone 

 on decreasing at a rate proportional to the square root of 

 the time. It becomes evident, then, that there is actually 

 a need for the heat supplied by the radio-activity of the 

 crust if all these deductions are to be reconciled. 



The Heat Stream from the Interior. 



The heat stream from the interior is that flowing through 

 the earth's surface layers. This is 



H = 4-rrr^ K (fd/dr 



= 5-1 X 10^" X 0*004 X 1/^200 

 = 6'4 X lo''^ calories ptr sec, 



where r is the earth's radius, dd/dr the temperature 

 gradient of the crust at the earth's surface, and K its 

 thermal conductivity. We must attempt to substitute such 

 numerical values for the temperature gradient and the con- 

 ductivity as will give a correct result for the earth's whole 

 surface. The nature of the data is indicated by the follow- 

 ing ' estimates : — 



Land Surface ; Average Temperature Gradient 



Prestwich 



Kelsiii ... 

 Schnidt 



1' C. per J430 cm. 



2750 i> 

 ,, 3200 ., 



Geikie 

 Brit. Assn. 

 C. King 



1° C. ptr 3100 cm. 

 >> 3240 ,, 

 » 3?9=> -> 



The value used above is i° per 3200 cm. 

 Land Surface 



Conductivity at ordinary temperature in calorie 

 degree"! cm.-l sec."i 



i Sedimentary rocks 

 ■' Igneous rock« 



0*0055 to o'co2i ; mean o"oo4i 

 o'oo53 to o"ooi7 ; mean o'oo42 



Mere if more uncertainty in the value of K than in that 



dOldr. .\ more accurate estimate of the heat loss of 



earth is desirable. Convection currents make the con- 



rtion method ordinarily inapplicable to the sea or lakes ; 



1 under special conditions, such as fresh water between 



and 4° C., might not the method be applicable to a 



lake? 



//(V(/ fro)ti h'adiiiiii and Thi)riiim in Hocks. 



Lord Kelvin supposed that this heat stream, which we see 



amounts to 6X10'" calories per sec, came from the sensible 



li' at of the earth's interior as it cooled by loss to the 



surface. That the heat of disintegration of radium might 



"' ly an important part in cosmical physics was pointed out 



Rutherford and Soddy.' The accurate determination of 



Geikie, Brit. Ass. Rep., 1899. ■> Joly, IJrit. A».s. Rep. 



' I'l'-'^".'.'''''^- ^°y- ^°'^- • J°'y> " Radioactivity and GeoloRy." 



4 Phil. Mag., May, 1903 ; Proc. Roy. Soc 



NO. 2201, VOL. 88] 



radium and thorium in rocks has shown that there is an 

 embarrassingly large supply of heat being continuously 

 emitted by these substances. Determinations of radium in 

 rocks have been made by Strutt and Joly and others, but 

 there is need for a systematic survey. 



Radium in Igneous Rocks. 



There is rather a wide difference between the mean of 

 Joly's large number of determinations and the mean of 

 other observations. There is clearly a discrepancy, which 

 would probably be most quickly elucidated by the chief 

 observers determining the radium in specimens of the 

 same rock. If we give equal weight to the mean of Joly's 

 observations 7x10-'^, and to 1-3x10-'^ the mean of other 

 observers, the final average is 4-1 x 10-" gm. Now the 

 heat given out by radium ' in complete radio-active equi- 

 librium (uranium to radium F) '' is o-o6 calorie per sec. 

 per gm., so that each gm. of the earth's crust, on account 

 of the radium it contains, is the source of 4-ixio-'*X 

 o-o6 = 2-5 x lo-'^ calorie per sec, a source of heat un- 

 affected, so far as experiment has shown, by temperature 

 or pressure. 



Thorium in the Earth's Crust. 



But the uranium-radium series are not the only source 

 of such heat ; thorium is also widely distributed. Fewer 

 rocks have been examined for it than for radium, but the 

 following results have been recorded : — 



Thorium in Igneous Rocks. 



The heat emitted by thorium in radio-active equilibrium 

 is 5x10-" calories per sec. per gm.,' and that by the 

 average ainount of thorium in rocks ()-5Xio-" cai. mi-.- 

 gm.-'. 



Heat due to Radium and Thorium in Rocks. 

 Thus the heat emitted by the uranium, radium, and 

 thorium found in surface rocks is (24-6-|-6-5)io-'* = 

 3x10-"' cal. per sec. per gm. Blanc,'" having found 

 nearly four times as much thorium as our mean value, con- 

 cluded that thorium contributed as much heat as uranium 

 and radiuin. 



Distribution of A'adio-.i. ln'r KliDuiits. 

 If the whole ma>> of the eartii (i)xii>-' gm.) weie the 

 source of as much radio-active heat ns the surface rocks, 

 the heat emitted would be i-8xio'* calorics per sec, or 

 about 300 times the heat flowing from the interior as 

 deduced from the conductivity and tetiiperature gradient of 

 the surface rocks. But if the interior of the earth gains 

 more heat than it loses, then its temperature is rising ; nor 

 is the geological and other evidence that the earth was once 



7 Von Schwcidler and He»», " Ls R»diuin," February. 1)09. 



» Holtwood, Amer.Joum. Set., 1908. 



» Pegram and W ebb, /'/ij'. K*v., 1908. 



1" Science Abs., No. 1057, 1909. 



