30 
MR, DARWIN ON THE BODILY TIDES OF VISCOUS AND SEMI-ELASTIC 
potential has the form appropriate to the tidal problem. The laws of reduction of 
bodily tide, of its lagging, of the reduction of ocean tide, and of its acceleration, are 
somewhat more complex than in the case of pure viscosity ; and the reader is referred 
to § 8 for the statement of those laws. It is also shown that by appropriate choice of 
the values of the two constants, the solutions may be either made to give the results 
of the problem for a purely viscous sphere, or for a purely elastic one. 
The tables give the results, for the semidiurnal and fortnightly tides, of tins theory 
for spheroids which have the rigidity of glass or of iron—the two cases considered by 
Sir W. Thomson. As it is only possible to judge of the amount of bodily tide by the 
reduction of the ocean tide, I have not given the heights and retardations of the 
bodily tide. 
It appears that if the time of relaxation of rigidity is about one quarter of the tidal 
period, then the reduction of ocean tide does not differ much from what it would be if 
the spheroid were perfectly elastic. The amount of tidal acceleration still, however, 
remains considerable. A like observation may be made with respect to the accelera¬ 
tion of tide in the case of pure viscosity approaching rigidity: and this leads me to 
think that one of the most promising ways of detecting such tides in the earth would 
be by the determination of the periods of maximum and minimum in a tide of long 
period, such as the fortnightly in a high latitude. 
In § 10 it is shown that the effects of inertia, which had been neglected in finding 
the laws of the tidal movements, cannot be such as to materially affect the accuracy of 
the results. 
[" The hypothesis of a viscous or imperfectly elastic nature for the matter of the 
earth would be rendered extremely improbable, if the ellipticity of an equatorial 
section of the earth were not very small. An ellipsoidal figure with three unequal 
axes, even if theoretically one of equilibrium, could not continue to subsist very long, 
because it is a form of greater potential energy than the oblate spheroidal form, which 
is also a figure of equilibrium. 
Now, according to the results of geodesy, which until very recently have been 
generally accepted as the most accurate-—namely, those of Colonel A. It. Clarke t — 
there is a difference of 6,378 feet between the major and minor equatorial radii, and 
the meridian of the major axis is 15° 34' E. of Greenwich. 
The heterogeneity of the earth would have to be very great to permit so large a 
deviation from the oblate spheroidal shape to be either permanent, or to subside with 
extreme slowness. But since this paper was read, Colonel Clarke has published a 
revision of his results, founded on new data;J and he now finds the difference between 
the equatorial radii to be only 1,524 feet, whilst the meridian of the greatest axis is 
8° 15' west. This exhibits a change of meridian of 24°, and a reduction of equatorial 
* The part wit hin brackets [ ] was added in November, 1878, in consequence of a conversation with 
Sir W. Thomson. 
t Quoted in Thomson and Tait, Nat. Phil., sec. 797. t Phil. Mag., August, 1878. 
