Jan. 1 8, 1872] 



NA TURE 



12- 



cocks began to crow, the shadow now was inverted, and by 

 degrees got smaller, until at nine o'clocl< the ec'ipse was over. 

 I cannot but suppose that the scientific men must liave had grand 

 opportunities of observation, and that to-day's pencil will carry 

 home many a description- Anything more beautiful, more sub- 

 lime, or more perfect, it would be impossible to conceive. 

 Upway Ho'Jse, Mercara, Coorg, R. N. Taylor 



Ooly, Dec. 12, 1871 



The Rigidity of the Earth 



I HAVE been ur^ed from several quarters to defend my argu- 

 ment for the rigidity of the earth against attacks which are sup- 

 posed (0 have been mrde upon it. It has, in fact, never been 

 attacked to my knowle<lge, and I feel under no obligation to 

 defend it. There is, I believe, a general impression that grave 

 objections to it have been raised by M Delaunay, and it seems 

 that even in this country some geological writers and teachers, 

 in their reluctance to abandon the hypothesis of a thin solid 

 crust, enclosing a wholly liquid ''mass, hastily concluded that all 

 dynamical arguments against it had been utterly overthrown by 

 Delaunay. 



In point of fact Delaunay made no reference at all to the tidal 

 argument, and clearly was unaware that I had brought it for- 

 ward when he made his communication on the " Hypothesis of 

 the interior fluidity of the terrestrial globe,"* to the French 

 Academy, three years and a half ago, objecting to Hopkins's 

 argument fourided on precession and nutation, and merely quotmg 

 me as having expressed acquie.-cence. On this subject I say 

 nothing at present, except that ten years ago, before I expressed 

 (in my first communication of the tidal argument to the Royal 

 Society) my assent to Hopkins's argument from precession and 

 nutation, I had thought of the objection to this argument since 

 brought forward by Delaunay, and had convinced myself of its 

 invalidity. But I hope to be able on some future occasion to re- 

 turn to the subject, and to prove that any degree of viscosity, 

 acting in the manner and to the effect de-cribed by Delaunay, 

 must in an extremely short time abolish the distinction between 

 summer and winter. My reason for wri'ing to you at present is 

 that I see in Mr. Scrope's beautiful book on Volcanoes (lust 

 published as a second ediiion) a sentence (" Prefatory Remarks," 

 page 24), written on the supposiiion that the tidal argument had 

 been brought forward for ttie first time at the recent meeting of 

 the liritish Association in Edinburgh. I therefore take the liberty 

 of suggesting to you that a reprint of the short abstract of my 

 tidal argument, which appeared in the Proceedings of the 

 Royal Society, for May i6, 1S62, might not be inappropriate to 

 your columns. I ooght, however, to inform you that the tidal 

 argument was carefully re-stated in the first volume of the treatise 

 on Natural Philosophy, by Prof. Tait and myself, published in 

 1S67, bat as the volume is at present out of print, you may not 

 consider this objection fatal to my proposal, 



Glasgow University, Jan. 9 William Tho.mson 



Absti-ad of Paper on the liighiity of the Earth, by Prof. Sir 

 William Thomson, F.R.S., recdvcd April 14, 1862 



The author proves that unless the solid substance of the 

 earth be on tlie whole of extremely rigid material, more rigid for 

 ins'ance than steel, it must yield under the tide-generating influ- 

 ence of sun an I moon to such an extent as to very sensibly dim.i- 

 nish the actual phenomena of the tides, and of precession and 

 nutation. Results of a mathematical theory of the deformation 

 of elastic spheroids, to be communicated to the Royal Society t 

 on an early occasion, are used to illustrate this suljject. For in- 

 stance, it is shown that a homogeneous incompressible elastic 

 spheroid of the same mass and volume as the earth, would, if of 

 the same rigidity as glass, yield about \, or if of the same rigidity 

 as steel about | of the extent that a perfectly fluid globe of the 

 same density would yield to the lunar and solar tide-generating in- 

 fluence. Theactuilphenomenaoftides(ttiat is, the relative motions 

 of a comparatively light liquid flowing over the outer surface of the 

 solid substance of the earth), and the amounts of precession and 

 nutation, would in one case be only 'I and in the other 5 of the 

 amounts which a perfectly rigid spheroid of the same dimensions, 

 of the same figure, the same homogeneous den^^ity, would exhibit 

 in the same circumstances. The close agreement with the re- 

 sults of observation presented by the theory of precession and 

 nutation, always hitherto worked out on the supposition that 



* CompUs Rcndusior lvL\y 13. 1868. 



f Communicated August 22, 1862, and read November 27, of same year 

 " Dynamical Problems regarding Elaslic Splieroidal Shells and Spheroids, 

 of incompressible Liquids." 



the solid parts of the earth are perfectly rigid, renders it scarcely 

 possible to admit that there can be any such discrepancy between 

 them as 3 to 5, and therefore almost necessary to conclude that 

 the e.irth is on the whole much more rigid than steel. But to 

 make an accurate comparison between theory and observation, 

 as to precession, it is necessary to know the absolute amount of 

 the moment of inertia about some diameter ; and from this we 

 are prevented by the ignorance in which we must always be as 

 to the actual law of density in the interior. Hence the author 

 anticipates that the actual deformation of the solid eirth by the 

 lunar and solar influence may be more decisively tested by ob- 

 serving the lunar fortnightly and the so'.ar half-yearly tides.* 

 These tides, it may be supposed, wdl follow very closely the 

 " equilibrium theory " of Daniel Bernouilli for all oceanic sta- 

 tions, and the author suggests Iceland and Teneriffe as two sta- 

 tions well adapted for the differential observations that would be 

 required. 



The earth's upper crust is possibly on the whole as rigid as 

 glass, more probably less than more. But even the imperfect 

 data forjudging referred to above render it certain that the(V?;Y/j 

 dsa lohole must be far more rigid than glass, and probablyeven more 

 rigid titan steeh Hence the interior must be on the whole more 

 rigid, probably many times more rigid, than the upper crujt. 

 This is just what, if the whole interior of the earth is solid, 

 might be expected when the enormous pressure in the interior is 

 considered, but it is utterly inconsistent with the hypothesis held 

 by so many geologists that the earth is a mass of melted matter 

 enclosed in a solid shell of only from 30 to 100 miles' thick- 

 ness. Hence the investigations now brought forward confirm 

 the conclusions arrived at by Mr. Hopkins, that the solid crust 

 of the earth cannot be less than Soo miles thick. The author 

 indeed believes it to be extremely improbable that any crust 

 thinner than 2,000 or 2,500 could maintain its figure with suffi- 

 cient rigidity against the tide-generating forces of the sun and 

 moon, to allow the phenomena of the ocean tides and of preces- 

 sion and nutation to be as they are. 



Exlraet from Thomson and Tail's " A'alural Philosophy." 



"§832 All dynamical investigations (whether 



" static or kinetic) of tidal phenomena, and of precession and 

 " nutation, hitherto published, with the exception referred to 

 " below, have assumed that the outer surface of the solid earth 

 " is absolutely unyielding. A few years ago, for the first time, 

 " the question was raised : Does the earth retain its figure with 

 " practically perfect rigidity, or does it yield sensibly to the de- 

 " forming tendency of the moon's and sun's attractions on its 

 " upper strata and interior mass ? It must yield to some extent, 

 " as no substance is infinit<-ly rigid. But whether these solid 

 " tides are sufficient to be discoverable by any kind of observa- 

 " tion, direct or indirect, has not yet been ascertained. The 

 " negative result of attempts to trace their influence on ocean 

 " and lake tides, as hitherto observed, and on precession and 

 " nutation, suffices, as we shall see, to disprove the hypothesis 

 " hitherto so prevalent, that we live on a mere thin shell of solid 

 " substance enclosing a fluid mass of melted rocks or metals. 

 " and proves, on the contrary, that the earth is much more rigid 

 " than .any of the rocks that constitute its upper crust." 



"§833 The character of the deforming influence will be 

 " understood readily by considering that if the whole earth were 

 " perfectly fluid, its bounding surface would coincide with an 

 " equipotential surface relatively to the attraction of its own 

 " mass, the centrifugal force of its rotation and the tide generat- 

 " ing resultant of the moon's and sun's forces, and their kinetic 

 "reactions. Thus there would be the full equilibrium lunar and 

 " solar tides ; of 2I times the amount of the disturbing deviation 

 " of level if the fluid were homogeneous, or of nearly twice 

 " this amount if it were heterogeneous with Laplace's hypotheti- 

 " cal law of increasing density. If now a very thin laycr'of 

 " lighter Hquid were added, this layer would rest covering the 

 " previous bounding surface to very nearly equal depth all round, 

 " and would simply rise and fall with that surface, showing only 

 " infinitesimal variations in its own depth, under tidal influences. 

 " Hence had the solid part of the earth so little rigidity as to 

 "allow it to yield in its own figure very nearly as much as if it were 

 " fluid, there would be very neatly nothing of what we call tides 

 " — that is to say, rise and fall of the sea relat.vely to the land • 

 " but sea and land together would rise and fall a fevt feet every 



• High tide, as far as the influence of either body is concerned, is pro- 

 duced at the poles, and lowaverage water at the equator, when its decima- 

 tion, whether north or south, is greatest, and low water at the poles and high 

 water at the equator, when the disturbing body crosses the plane of the 

 equator. 



