588 
MR. G-. H. DARWIN ON PROBLEMS CONNECTED 
In the second paper the inertia was still neglected, but the effects of these tan¬ 
gential actions were considered, in as far as they modified the rotation of the spheroid 
as a whole. In that paper the sphere was treated as though it were rigid, but had 
rigidly attached to its surface certain inequalities, which varied in distribution from 
instant to instant according to the tidal theory. 
In order to justify this assumption, it is now necessary to examine whether the tidal 
protuberances may be regarded as instantaneously and rigidly connected with the 
rotating sphere. If there is a secular distortion of the spheroid in excess of the 
regular tidal flux and reflux, the assumption is not rigorously exact; but if the dis¬ 
tortion be very slow, the departure from exactness may be regarded as insensible. 
The first problem in the present paper is the investigation of the amount of secular 
distortion, and it is treated only in the simple case of a single disturbing body, or 
moon, moving in the equator of the tidally-distorted spheroid or earth. 
It is found, then, that the form of the lagging tide in the earth is not such that the 
pull, exercised by the moon on it, can retard the earth’s rotation exactly as though the 
earth were a rigid body. In other words, there is an unequal distribution of the tidal 
frictional couple in various latitudes. 
We may see in a general way that the tidal protuberance is principally equatorial, 
and that accordingly the moon tends to retard the diurnal rotation of the equatorial 
portions of the sphere more rapidly than that of the polar regions. Hence the polar 
regions tend to outstrip the equator, and there is a slow motion from west to east 
relatively to the equator. 
When, however, we come to examine numerically the amount of this screwing 
motion of the earth’s mass, it appears that the distortion is exceedingly slow, and 
accordingly the assumption of the instantaneous rigid connexion of the tidal protube¬ 
rance with the. mean sphere is sufficiently accurate to allow all the results of the paper 
on Precession ” to hold good. 
In the special case, which was the subject of numerical solution in that paper, we 
were dealing with a viscous mass which in ordinary parlance would be called a solid, 
and it was maintained that the results might possibly be applicable to the earth within 
the limits of geological history. 
Now the present investigation shows that if we look back 45,000,000 years from 
the present state of things, we might find a point in lat. 30° further west with reference 
to a point on the equator, by 4§' than at present, and a point in lat. 60° further west 
by lljk The amount of distortion of the surface strata is also shown to be exceedingly 
minute. 
From these results we may conclude that this cause has had little or nothing to do 
with the observed crumpling of strata, at least within recent geological times. 
If, however, the views maintained in the paper on “ Precession as to the remote 
history of the earth are correct, it would not follow, from what has been stated above, 
that this cause has never played an important part; for the rate of the screwing of the 
