March 7, 1S95] 



NATURE 



439 



on the thermal conductivities \k) and specific heats (c) of 

 five rocks. 



Density 

 Basalt 30144 ... ^-O'i763 + ooo0296/ [be- 



tween 0° and 60 ] 

 r = oT946-i-0'ooo575(/ - 

 60) [between 60' and 

 no ] 

 /■ = 0'oo3i7;i +000001/; 

 Marble ... 27036 ... £- = o'20279 + o'oci0466./ 



/■ = o 00540 1 1 - o ■000005. ') 

 Rock salt ... 2-i6r ... c = o'2i46-rOOooi7/ 



k = oo\n\\ - -0044/1 

 Anhydrite of Jura ... a'Sga ... c = o'i8o2 + o'ooo3./ 



/t — 0'OI23|l -O"0O24./i 



iTuartz ... 2-638 ... £- = o-i754 + oooo4./ 



i=o-oi576|i -0-0019./; 



These results show practically no change of thermal 

 conductivity with temperature for Basalt and Marble. 

 For Rock .Salt, .Anhydrite of Jura, and Ouartz, they show 

 diminutions of thermal conductivity amounting per 100' 

 C. to 44 per cent., 24 per cent., and 19 per cent, respec- 

 tively. They contrast curiously with the 75 per cent. 

 augmentalion of thermal conductivity per 100 C. 

 (Naturk, January 3, p. 226), used by Prof. Perry in 

 his estimate of the age of the earth, and they form 

 a practical comment on his statement (N.\ture, January 

 3, p. 226) :— "From the analogies with electric conduc- 

 " tion, one would say, without any experimenting, that as 

 "a metal diminishes in conductivity with increase of 

 "temperature, so a salt, a mixture of salts, a rock, may 

 "be expected to increase in conducti\ ity with increase of 

 " temperature." 



Since the beginning of January I have myself been 

 endeavouring to find by experiment the proportionate 

 differences of thermal conductivity of rocks at different 

 temperatures : and before the end of January I had 

 made some preliminary experiments on slate and sand- 

 stone, from which 1 was able to tell Prof. Perry that the 

 thermal conductivity of each of these two rocks is 

 probably less at higher temperatures than at lower. 

 .Since that time I ha\e been arranging for experiments 

 on granite, in which as rapid progress as I would ha\e 

 liked has been impossible for many reasons, including 

 the necessity of standardising a Kew certificated thermo- 

 meter of 1886, now for the first time being compared 

 with an air thermometer in my laboratory. Unless its 

 differences from the air thermometer are much larger 

 than can be expected from what we know of the behaviour 

 of mercury-in-glass thermometers generally, it is already 

 almost proved that the thermal conductivity of granite 

 is less between 150'' C. and 250' than between 50' and 

 150^ 



.^.s to specific heats there can be little doubt but that 

 they increase with temperature up to the melting point 

 of rock, but the rate of augmentation assumed by Prof. 

 Perry is about five times as much as that determined 

 up to I2CO by the experiments of Rue ker and Roberts- 

 Austen {Phil. Mag., 1S91, second half-year, p. 3531 for 

 Basalt, and of Carl ISarus (/'/;/'/. Mag., 1S93, first half- 

 year, pp. 301-303) for Diabase ; these being apparently 

 the orily experiments hitherto made on specific heats of 

 rock at temperatures beyond the range of the mercury- 

 in-glass thermometer. 



Taking the primitive temperature as 4000' C. and the 

 thermal conductivity and the specific heat at this tem- 

 perature respectively 30 times and 14). times their values 

 at the surface, and throwing in a factor 3 for three-fold 

 density at the greater depths (though the average density 

 of the ivhole earth is scarcely double that of the upper 

 rust) Perry takes the product of three factors 

 30Xi4lX3and so finds in round numbers 1300 times 

 my estimate as his corrected estimate of the age of the 

 earth ! ! (Nature, January 3, p. 227.) 



But even if the ratios of thermal conductivities and of 



specific heats at the higher and lower temperatures were 

 as assumed. Prof. Perry's product of the two corres- 

 ponding factors vastly over-estimates the age. Of this 

 I thought I had given a sufficient warning when I wrote 

 to him (December 13;, "But your solution on the sup- 

 position of an upper stratum of constant thickness, 

 having smaller conductivity and smaller thermal capacity 

 than the strata below it, is very far from being applic- 

 able to the true case in which the qualities depend on the 

 temperature." (Nature, January 3, p. 227.) It is 

 obvious that the supposed higher thermal conductivity 

 and the higher specific heat, if beginning suddenly at a 

 short distance below the surface, and continuing con- 

 stant to the great depth, would greatly prolong the time 

 of cooling to the same surface-gradient, beyond what 

 it would be with these qualities increasing continuously 

 with temperature. For the simple case of conductivity 

 assumed to increase in the same proportion as specific 

 heat, Prof Perry has himself since given in a later 

 communication (Nature, February 7, pp. 341-342) the 

 necessary correction of his previous mathematics : and 

 in an example of his own choosing (50 per cent, aug- 

 mentation of each quality per loo' elevation of tempera- 

 ture), he now finds 121 times my estimate for the age of 

 the earth, instead of 441 times as by the formula which 

 he used in his first article. 



When the ratio of thermal conductivity to specific heat 

 per unit bulk varies with the temperature, the problem 

 of secular cooling presents mathematical difficulties 

 which, so far as 1 know, have not been hitherto attacked ; 

 but I find it quite amenable to analytical treatment, and 

 I hope before long to be able to offer a paper to the 

 Royal Society of Edinburgh on the subject, as an appendix 

 to my original paper " On the Secular Cooling of the 

 Earth," published in its Transactimis (1S62,. I have 

 already worked out numerically two cases, in one of 

 which both conductivity and specific heat increase with 

 temperature, and in the other the specific heat increases 

 with the temperature but the conductivity is constant. 

 The first of these is at present only interesting as a 

 mathematical exercise because, according to present 

 knowledge, it is moie probable that the thermal con- 

 ductivity decreases than increases with increasing 

 temperature. To the results of the second I shall refer 

 later as substantially helping us towards a revised 

 estimate of the time which has elapsed since the con- 

 solidation of the earth. 



Twelve years ago, in a laboratory established by Mr. 

 Clarence King in connection with the United States 

 Geological Survey, a very important series of experimental 

 researches on the physical properties of rocks at high 

 temperatures was commenced by Dr. Carl Barus for the 

 purpose of supplying trustworthy data for geological 

 theory. Mr. Clarence King, in an article " On the .\ge of 

 the Earth '' \>\x\>\\^\ie.A\n\.\\e. American Journal 0/ Science 

 (vol. xlv., Jan. 1893), used data thus supplied, to estimate 

 the age of the earth more definitely than was possible for 

 me in 1S62 with the very meagre information then 

 available as to specific heats, thermal conductivities, and 

 temperatures of fusion. I had taken 7000' F. (387 1' C.) 

 as a high estimate of the temperature of melting rock. 

 Even then I might have taken something between 

 looo' C. and 2000 C. as more probable, but I was most 

 anxious not to //«rtVr-estimate the age of the earth, and 

 so I founded my primary calculation on the 7000' F. for 

 the temperature of melting rock. Now we know from the 

 work of Carl Barus {Phil. Mag. 1S93, first half -year, pp. 

 1 86, 1 87, 301-305) that Diabase, a typical Basalt of very 

 primitive character, melts between iioo C. and 1170' 

 and is thoroughly liquid at I200^ The correction from 

 3871 C. to 1200' or I 322 of that value, for the 

 temperature of solidification, would, with no other change 

 of assumptions, reduce my estimate of 100 million 

 to I (3-22)- of its amount or a little less than ten million 



NO. 1323. VOL. 5 l] 



