226 



NA TURE 



[January 3, 1895 



If we take k as 195 times that of the surface-rock, and 

 k'c as 35 times that of the surface-rock, and if the shell 

 has a depth of 3272 x lo' centimetres (about 20 miles), 

 the time of cooling until the temperature-gradient is 

 I Cent, degree in 2743 centim. is wo/-^ than 127 X 10* 

 years." ' 



I kept no copy of the letter which 1 sent to Prof. Tail 

 with the foregoing document. In it I e.\plained my diffi- 

 culty in getting Lord Kelvin to re-consider the internal 

 heat question, and I asked for his advice. 



Extract from Letter of Prof . Tail, November 22, 1894. 

 . . . my entire failure to catch the object of your paper. For 

 I seem to gather that you don't object to Lord Kelvin's mathe- 

 matics. Why, then, drag in mathematics at all, since it is 

 absolulely obviou.'; that the better conductor the interior in com- 

 parison with the skin, the longer ago must it have been when 

 the whole was at 7000° F. : the state of the skin being as at 

 present ? 



I don't suppose Lord Kelvin would care to be troubled with 

 a demonstration <il that. 



As to the validity, crmore properly \.he fluusibilily of his or 

 your assumptions, I don't suppose anyone will ever be in a 

 position to judge. He took the simple and apparently possible 

 case of uniform conductivity all through — having no data what- 

 ever. What if he had assumed, as he was quite entitled to do, that 

 the conductivity diminishes very fast with rise of temperature? 



But I need not say any more, as I seem to have entirely 

 missed your point. 



Letter to Prof. Tail, Novemlie:- 26, 1S94. 



Dear Prof. Tait,— I should have been on the whole better 

 satisfied if you had opposed my conclusions. Vou say I am 

 right, and you ask my object. Surely Lord Kelvin's case is 

 lost, as soon as one shows that there are possible conditions as 

 to the internal slate of the earth which will give many times the 

 age which is your and his limit. . . . What troubles me is that 

 I cannot see one bit that you have reason on your side, and yet 

 I have been 50 accustomed to look up to you and Lord Kelvin, 

 that I think I must be more or less of an idiot to doubt when 

 you and he were so " cocksure." The argument from the sun's 

 heat seems to me quite weak. Even a geologist without mathe- 

 matics can see that the time given by Lord Kelvin will be in- 

 creased if we assume that in past limes the sun radiated energy 

 at a smaller rale than at present, much of its mass being possibly 

 cold atd in the meteor form, and the rate m-iy have greatly 

 varied from lime lo lime. This is not only possible but 

 probable, and it is for you and Lord Kelvin to prove a negative. 



Then the Tidal Relarda' ion argument I Even if your rate of 

 retardation is correct, the real basis of your calculation is your 

 asiumption that a solid earlh cannot alter its shape (diminishing 

 its equatorial radius by a few miles) even in 1000 million years, 1 

 under the action of forces constantly tending to alter its shape, 

 and yet wc see the gradual closing up of passages in a mine, and 



^ion for any case is ttii> ; — A sphere of radius R of 

 M:ity per unit volume iticin surrountjed by a shell of 

 V, and capacity for heat per unit volume c ; take 

 ■: temperature at the surface, cqu.-ii to /■,'t74y': 



we know that wrinkling and faults and other changes of shape 

 are always going on in the solid earth under the action of long- 

 continued forces. I know that solid rock is not like cobbler's 

 wax, but 10' years is a very long lime, and the forces are great ! 



I had thought these two arguments to be mere supporters of 

 ihe internal heat one which I took to be Ihe only important 

 one, like a diamond whose pure sparkle was brought into relief 

 by two rubies. 



If I were alone in my opinion, I should still have the courage, 

 I think, to write as I do ; but as I have already told you, I did 

 not venture to write and speak to Lord Kelvin, or write to you 

 until I found that so many of my friends .igreed with me — 

 Fitzgerald, O. Reynolds, I.armor, Henrici, Lodge, Ileaviside, 

 and many others. Fitzgerald is the only man to whom I have 

 mentioned my notion about the sun's heat, but he quite agrees 

 with me. I have not put before him my notion about the Tidal 

 Retardation argument. . . . 



November 27. 

 Dear Prof. Perry. — 1 should like to have your answers to 

 t:^'0 questions : — 



(t) What grounds have you for supposing ihe inner materials 

 of the earlh to be belter conductors than the skin ? 



(2) Do you fancy that any of \\\e aJvaiice^i geologists would 

 thank you for 10'" years instead of 10' ? Their least demand is 

 for 10'- : — (or fart of the mere secondary period I 



Yours truly, 



P. G. Tait. 



' Th' ,-tn.:r.! . 

 cori'. 

 thiot 

 E . 



The:, 



e 

 Ian e 



R/bii. 



.2VR j5in£ 



All e 



* - 4 sin 2e 



a'743' 



enables / to be calculated. It would no doubt be possible, but il would 

 hardly }>e worth while, to find the %'alucs of m and 6 which would give a maxi- 

 mum vaUic for /. In one of the above ca»es I took r nearly it. and in the 

 other 7/3. 



lam quite unable to attack the problem of the cooling of a sphere from an 

 arbitrary initial condition, in which the dilTusivity for heat is an arbitrary 

 function of r. 



T • 'i'lnof ^L wfi, ..vc a greater age to the 



Ear' .•, a;;ain, it ■' o worth whito to spend 



mu' Mv 7"tri -n to fix a hijjhcr limit 



to thr a;;- .,t ir.r 1 t!,at such a higher limit 



must be greater f ^Ired inillion years. 



Sorr- of my *: f : not publishing the 



abf'-' .ind am still his 



aff' . '.tolcn from him, 



as I I , liecn uniformly 



kind 1'- tr:', . r, 1 tK'tr l,.nr !'• i t.ni-.«lir,, l„ ,i,,j,i |,jve fouud this 

 difficult. One thinK has not yet happened ; 1 have Dot yet receis'ed the 

 Ihirty pieces '>f silver. 



Noz'ei/iber 29, 1S94. 



Dear Prof. Tait,— It is for Lord Kelvin lo prove 

 that there is not greater conductivity inside. Nevertheless I 

 will slate my grounds : — 



I (o). In page 6 of the paper sent you I say " I am not in 

 a position to criticise the argument from tide phenomena 

 which Lord Kelvin or Mr. Darwin would now put forward on 

 the subject of much inleinal fluidity of the earlh. The argu- 

 ment from precession has been given up. Of course, much 

 internal fluidity would practically mean infinite conductivity for 

 our purpose. But there is no doubt of a cerlain amount of 

 fluidity inside, even now, and taking il that the inside of the 

 earth is a honeycomb mass of great rigidity, partly solid and 

 partly fluid, we have reason lo believe in very much greater 

 quasi conductivity inside than of true conductivity in the surface 

 rocks." 



1 ($). Even if we assume perfect solidity, and even neglect- 

 ing our knowledge of much iron — surely there can be no doubt 

 of the conductivity of rock iiiiieasing with the temperature. 

 From Ihe analogies with electric conduction, one would say, 

 without any experimenting, that as a metal diminishes in con- 

 ductivity with increase of temperature, so a salt, a mixture of 

 salts, a rock, may be expected to increase in conductivity with 

 increase of temperature. I presume that Evereit's book is 

 recognised now as giving the most exact information on these 

 subjects. He nowhere suggests that rock diminishes in con- 

 ductivity with temperature. Every case he gives shows an 

 increase. I have made out the following table from the only 

 quotations which Everett gives from Dr. Robert Wel)er ; only 

 five cases, but probably representative. 



Percentage increase for a rise of 100° Centigrade. 



.Mic.iceous gneiss 

 Mica schist 

 Eurile ,.. 



Gneiss 



Micaceous schist 



Average ... 



Average, leaving out 

 Eurite 



431 



75 



NO. 1.3 14, VOL. 51] 



Even if the conductivity and speciiic heal did not alter, 

 inasmuch as Ihe internal density is grcaler, the volumetric 

 capacity is greater ; and if it is three limes as great, we have 

 three limes Lord Kelvin's age. In fact, the rule given at page 

 4 of my paper is Ihc same as this : — If the conductivity inside is 



