428 



NATURE 



[Sept. 14, 1876 



tation of temperature downwards in the upper strata, gradually 

 increasing to the whole normal rate which would be sensibly 

 reached at a depth of 600 metres. 



By a simple effort of geological calculus it has been estimated 

 that 1° per 30 metres gives 1000° per 30,000 metres, and 3333" 

 per 100 kilometres. This arithmetical result is irrefragable, but 

 what of the physical conclusion drawn from it with marvellous 

 frequency and pertinacity that at depths of from 30 to lOO 

 kilometres the temperatures are so high as to melt all substances 

 composing the earth's upper crust ? It has been remarked, in- 

 deed, that if observation showed any diminution or augmentation 

 of the rate of increase of underground temperature in great depths, 

 it would not be right to reckon on the uniform rate of l° per 30 

 metres, or thereabouts, down to yj or 60 or 100 kilometres. 

 "But observation has shown nothing of the kind, and therefore 

 surely it is most consonant with inductive philosophy to admit 

 no great deviation in any part of the earth's solid crust from the 

 rate of increase proved by observation as far as the greatest 

 depths to which we have reached ! " Now I have to remark upon 

 this argument that the greatest depth to which we have reached 

 in observations of underground temperature is scarcely one kilo- 

 metre ; and that, if a 10 per cent, diminution of the rate of 

 augmentation of underground temperature downwards were 

 found at a depth of one kilometre, this would demonstrate ' 

 that within the last 100,000 years the upper surface of the earth 

 must have been at a higher temperature than that now found at 

 the depth of one kilometre. Such a result is no doubt to be 

 found by observation in places which have been overflown by 

 lava in the memory of man, or a few thousand years farther 

 back : but if, without going deeper than a kilometre, a 10 

 per cent, diminution of the rate of increase of temperature 

 downwards were found for the whole earth, it would limit 

 the whole of geological history to within 100,000 years, or, 

 at all events, would interpose an absolute barrier against the 

 continuous descent of life on the earth from earlier periods 

 than 100,000 years ago. Therefore, although search in particular 

 localities for a diminution of the rate of augmentation of under- 

 ground temperature in depths of less than a kilometre may be of 

 intense interest, as helping us to fix the dales ef extinct volcanic 

 actions which have taken place within 100,000 years or so, we know 

 enough from thoroughly sure geological evidence not to expect to 

 find it, except in particular localities, and to feel quite sure that 

 we shall not find it under any considerable portion of the earth's 

 surface. If we admit as possible any such discontinuity within 

 900,000 years, we might be prepared to find a sensible diminution 

 of the rate at three kilometres depth : but not at anything less 

 than 30 kilometres if geologists validly claim as much as 

 90,000,000 of years for the length of the time with which their 

 science is concerned. Now this implies a temperature of 1000° 

 C. at the depth of 30 kilometres, allows something less than 

 2000° for the temperature at 60 kilometres, and does not 

 require much more than 4,000° C. at any depth, however 

 great ; but does require at the great depths a temperature of at 

 all events not less than about 4000° C. It would not take 

 much "hurrying up " of the actions with which they are con- 

 cerned, to satisfy geologists with the more moderate estimate of 

 50,000,000 of years. This would imply at least about 3000° 

 C. for the limiting temperature at great depths. If the actual 

 substance of the earth, whatever it may be, rocky or metallic, 

 at depths of from 60 to too kilometres, under the pressure 

 actually there experienced by it can be solid at temperatures of 

 from 3000° to 4000°, then we may hold the former estimate 

 (90,000,000) to be as probable as the latter (50,000,000) so far 

 as evidence from underground temperature can guide us. If 

 4000° would melt the earth's substance at a depth of 100 

 kilometres, we must reject the former estimate, though we might 

 still admit the latter ; if 3000" would melt the substance at a 

 depth of 60 kilometres, we should be compelled to conclude 

 that 50,000,000 of years is an over-estimate. Whatever may be 

 its age, we may be quite sure the earth is solid in its interior : 

 not, I admit, throughout its whole volume, for there certainly 

 are spaces in volcanic regions occupied by liquid lava ; but what- 

 ever portion of the whole mass is liquid, whether the waters of 

 the ocean or melted matter in the interior, these portions are 

 small in comparison with the whole, and we must utterly reject 

 any geological hypothesis which, whether for explaining under- 



I For proof of this and following statements regarding Underground 

 Heat I refer to " Secular Cooling of the Earth" Traiisactions of the Royal 

 Society of Edinburgh, 1862, and Thomson and Tail's " Natural Philosophy," 

 Appendix D. 



ground heat or ancient upheavals and subsidences of the solid 

 crust, or earthquakes, or existing volcanoes, assumes the solid 

 earth to be a shell of 30, or 100, or 500, or 1,000 kilometres 

 thickness, resting on an interior liquid mass. 



This conclusion was first arrived at by Hopkins, who may 

 therefore properly be called the discoverer of the earth's solidity. 

 He was led to it by a consideration of the phenomena of pre- 

 cession and nutation, and gave it as shown to be highly probable, 

 if not absolutely demonstrated, by his confessedly imperfect and 

 tentative investigation. But d rigorous application 01 the perfect 

 hydrodynamical equations leads still more decidedly to the same 

 conclusion. 



I am able to say this to you now in consequence of the con- 

 versation with Professor Newcomb to which I have already 

 alluded. Admitting fully my evidence for the rigidity of the 

 earth from the tides, he doubted the argument from precession 

 and nutation. Trjing to recollect what I had written on it 

 fourteen years ago in a paper on the Rigidity of the Earth, 

 published in the Transactions of the Royal Society, my con- 

 science smote me, and I could only stammer out that I had 

 convinced myself that so and so, and so and so, at which I had 

 arrived by a non-mathematical short cut, were true. He hinted 

 that viscosity might suffice to render precession and nutation 

 the same as if the earth were rigid, and so vitiate the argument 

 for rigidity. This I could not for a moment admit any more 

 than when it was first put forward by Delaunay. But doubt 

 entered my mind regarding the so and so, and so and so ; and I 

 had not completed the night journey to Philadelphia which 

 hurried me away from our unfinished discussion before I had 

 convinced myself that they were grievously wrong. So now I 

 must request as a favour that each one of you on going home 

 will instantly turn up his or her copies of the Transactions of 

 the Royal Society for 1862, and of Thomson and Tait's " Natural 

 Philosophy," vol. i., and draw the pen through §§ 23-31 of my 

 paper on the " Rigidity of the Earth " in the former, and through 

 everything in §§ 847-849 of the latter, which refers to the effect 

 on precession and nutation of an elastic yielding of the earth's 

 surface. 



When those passages were written I knew little or nothing of 

 vortex motion ; and until my attention was recalled to them by 

 Prof. Newcomb, I had never once thought of their subject in 

 the light thrown upon it by the theory of the quasi-rigidity 

 induced in a liquid by vortex motion which has of late occupied 

 me so much. With this fresh light a little consideration sufficed 

 to show me that (although the old obvious conclusion is of course 

 true, that if the inner boundary of the imagined rigid shell of 

 the earth were rigorously spherical, the interior liquid could 

 experience no precessional or nutational influence from the 

 pressure on its boundmg surface, and therefore if homogeneous 

 could have no precession or nutation at all, or if heterogeneous 

 only as much precession and nutation as would be produced by 

 attraction from without in virtue of non-sphericity of its surfaces 

 of equal density, and therefore the shell would have enormously 

 more rapid precession and nutation than it actually has — forty 

 times as much, for instance, if the thickness of the shell is sixty 

 kilometres) a very slight deviation of the inner surface of the 

 shell from perfect sphericity would suffice, in virtue of the quasi- 

 rigidity due to vortex motion, to hold back the shell from taking 

 sensibly more precession than it would give to the liquid, and 

 to cause the liquid (homogeneous or heterogeneous) and the 

 shell to have sensibly the same precessional motion as if the 

 whole constituted one rigid body. But it is only because of the 

 very long period (26,000 years) of precession, in comparison with 

 the period of rotation (one day), that a very slight deviation fiom 

 sphericity would suffice to cause the whole to move as if it were 

 a rigid body. A little further consideration showed me — 



(i) That an ellipticity of inner surface equal to 



^ ^ 26000 X 365 



would be too small, but that an ellipticity of one or two hundred 

 times this amount would not be too small, to compel approximate 

 equality of precession throughout liquid and shell. 



(2) That with an ellipticity of interior surface equal to -^^ if 

 the precessional motive were 26,000 times as great as it is, the 

 motion of the liquid would be very different from that of a rigid 

 mass rigidly connected with the shell : 



(3) That with the actual forces and the supposed interior 

 ellipticity of -^^ the lunar nineteen-yearly nutation might be 

 affected to about five per cent, of its amount by interior 

 liquidity. 



(4) Lastly, that the lunar semi-annual nutation must be largely, 



