TRANSACTIONS OF THE SECTIONS. 5 



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 precession aiid nutation, and gave it as shown to be highly 

 probable, if not absolutely demonstrated, by his confessedly imperfect and tentative 

 investigation. But a rigorous application of the perfect hydrodynamical equations 

 leads still more decidedly to the same conclusion. 



I am able to say this to vou now in consequence of the conversation with Pro- 

 fessor Newcomb, to which 1 have already alluded. Admitting fully my evidence 

 for the rigidity of the earth from the tides, he doubted the argument from preces- 

 sion and nutation. Trying 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 conscience 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- 

 niathematieal 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 Phila- 

 delphia which hurried me away from our unfinished discussion before I had con- 

 vinced 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 di-aw the pen through §§ 2.5-31 of my paper on the 

 " Rigidity of the Earth " in the former, and through every thing in §§ 847, 848, 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 Professor Newcomb I had never once 

 thought of this subject in the light thro\vn upon it by the theor}^ 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 

 bounding surface, and therefore if homogeneous could have no precession or nuta- 

 tion at all, or if heterogeneous only as much precession and nutation as woidd be 

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

 equal density, and therefore the shell woidd have enormously more rapid precession 

 and nutation than it actually has — forty times as much, for instance, if the thickness 

 of the shell is 60 Irilometres) 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 

 g-ive 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 pre- 

 cession, in comparison with the period of rotation (one day), that a very slight 

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

 rigid body. A little further consideration showed me : — 



(1) That an elHpticity of inner surface equal to — — 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 y^Q, if the precessional 

 motion 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 uineteen-yearly nutation might be affected to about five per cent, of its 

 amount by interior liquidity. 



