150 Royal Society : — 



and moon to such an extent as to very sensibly diminish 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 on an early occasion, are used 

 to illustrate this subject. For instance, it is shown that a homoge- 

 neous incompressible elastic spheroid of the same mass and volume 

 as the earth, would, if of the same rigidity as glass, yield about -J, 

 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 influence. The actual phenomena 

 of tides (that 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 the one case be 

 only J, and in the other |- of the amounts which a perfectly rigid 

 spheroid of the same dimensions, the same figure, the same homoge- 

 neous density, wduld exhibit in the same circumstances. The close 

 agreement with the results of observation presented by the theory of 

 precession and nutation, always hitherto worked out on the suppo- 

 sition that the solid parts of the earth are perfectly rigid, renders it 

 scarcely possible to admit that there can be any such discrepance 

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

 that the earth 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 pre- 

 vented 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 earth by the lunar and solar influence 

 may be more decisively tested by observing the lunar fortnightly and 

 the solar half-yearly tides*. These tides, it may be supposed, will 

 follow very closely the "equilibrium theory" of Daniel Bernouilli 

 for all oceanic stations, and the author suggests Iceland and Tene- 

 riffe as two stations 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 for 

 judging referred to above, render it certain that the earth as a whole 

 must be fa?' more rigid than glass, and probably even more rigid than 

 steel. Hence the interior must be on the whole more rigid, probablv 

 many times more rigid, than the upper crust. 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 onlv 

 from 30 to 100 miles thickness. Hence the investigations now- 

 brought forward confirm the conclusions arrived at by Mr. Hopkins, 



* High tide, as far as the influence of either body is concerned, is produced at 

 the poles, and low (average) water at the equator, when its declination, whether 

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

 equator, when the disturbing body crosses the plane of the equator. 



