WITH THE TIDES OF A VISCOUS SPHEROID. 
591 
que l’on est convenu d’appeler la croute terrestre, et presque sur toute la croute ter- 
restre. La croute glisse sur linterieur plastique. Elle parvient a entrainer l’interieur, 
car, sinon, l’axe cle la rotation du globe demeurerait parallele a lui-meme dans l’espace, 
ou neprouverait que des variations insigniliantes, et le phenomene de la precession cles 
equinoxes n’existerait pas. Ainsi la croute et 1’interieur se meuvent de quantites 
inegales, d’ou le deplacement geographique du pole sur la sphere. 
“Cette idee a ete emise, je crois, pour la premiere fois, par M. Evans ; depuis par 
M. J. Peroche.” 
Now with respect to this view, it appears to me to be sufficient to remark that, as 
the axes of the precessional and nutational couples are fixed relatively to the moon, 
whilst the earth rotates, therefore the tendency of any particular part of the crust to 
slide over the interior is reversed in direction every twelve lunar hours, and therefore 
the result is not a secular displacement of the crust, but a small tidal distortion. 
As, however, it was just possible that this general method of regarding the subject 
overlooked some residual tendency to secular distortion, I have given the subject a 
more careful consideration. From this it appears that there is no other tendency to 
distortion besides that arising out of tidal friction, which has just been discussed. It 
is also found that the secondary tides must be very small compared with the primary 
ones ; with the present angular velocity of diurnal rotation, probably not so much in 
height as one-hundredth of the primary lunar semi-diurnal bodily tide. 
It seems out of the question that any heterogeneity of viscosity could alter this 
result, and therefore it may, I think, be safely asserted that any sliding of the crust 
over the interior is impossible—at least as arising from this set of causes. 
The second part of the paper is an investigation of the amount of work done in the 
interior of the viscous sphere by the bodily tidal distortion. 
According to the principles of energy, the work done on any element makes itself 
manifest in the form of heat. The whole work which is done on the system in a given 
time is equal to the whole energy lost to the system in the same time. From this 
consideration an estimate was given, in the paper on “ Precession,” of the whole amount 
of heat generated in the earth in a given time. In the present paper the case is 
taken of a moon moving round the earth in the plane of the equator, and the work 
done on each element of the interior is found. The work done on the whole earth is 
found by summing up the work on each element, and it appears that the work per 
unit time is equal to the tidal frictional couple multiplied by the relative angular 
velocity of the two bodies. This remarkably simple law results from a complex law of 
internal distribution of work, and its identity with the law found in “Precession,” 
from simple considerations of energy, affords a valuable confirmation of the complete 
consistency of the theory of tides with itself. 
Fig. 2 gives a graphical illustration of the distribution in the interior of the work 
done, or of the heat generated, which amounts to the same thing. The reader is 
referred to Part II. for an explanation of the figure. Mere inspection of the figure 
MDCCCLXXIX. 4 G 
