WITH THE TIDES OF A VISCOUS SPHEROID. 
589 
earth’s mass varies inversely as the sixth power of the moon’s distance, multiplied by 
the angular velocity of the earth relatively to the moon. And according to that 
theory, in very early times the moon was very near the earth, whilst the relative 
angular velocity was comparatively great. Hence the screwing action may have been 
once sensible.'"' 
Now this sort of motion, acting on a mass which is not perfectly homogeneous, 
would raise wrinkles on the surface which would run in directions perpendicular to the 
axis of greatest pressure. 
In the case of the earth the wrinkles would run north and south at the equator, and 
would bear away to the, eastward in northerly and southerly latitudes; so that at the 
north pole the trend would be north-east, and at the south pole north-west. Also the 
intensity of the wrinkling force varies as the square of the cosine of the latitude, and 
is thus greatest at the equator, and zero at the poles. Any wrinkle when once formed 
would have a tendency to turn slightly, so as to become more nearly east and west, 
than it was when first made. 
The general configuration of the continents (the large wrinkles) on the earth’s sur¬ 
face appears to me remarkable when viewed in connexion with these results. 
There can be little doubt that, on the whole, the highest mountains are equatorial, 
and that the general trend of the great continents is north and south in those regions. 
The theoretical directions of coast line are not so well marked in parts removed from 
the equator. 
* This result is not strictly applicable to the case of infinitely small viscosity, because it gives a finite 
tbougb very small circulation, if tbe coefficient of viscosity be put equal to zero. 
By putting e=0 in (17'), Part I., we find a superior limit to the rate of distortion. With tbe present' 
angular velocities of tbe earth and moon, - - must be less than 5 x 10 -9 cos 2 0 in degrees per annum. 
clt 
d L 
It is easy to find whfen — would be a maximum in the course of development considered in “ Preces- 
at 
sion;” for, neglecting the solar effects, it will be greatest when i°(n —O) is greatest. 
Now-r 2 (n— Q) varies as [l+/( — /<£ —-l -3 ]^ 12 ) and this function is a maximum when 
- 1 f (i+;0—r 1 +=o. 
15 
15 O n 
Taking p=4‘0074, and A-=27‘32, we have 109‘45| :-1 + 80‘293=0. 
Q 0 
The solution of this is f= - 2218. 
With this solution will be found to be 56 million times as great as at present, being equal to 
dt 
18' cos 2 0 per annum. With this value of £, the length of the day is 5 hours 50 minutes, and of the 
month 7 hours 10 minutes. 
This gives a superior limit to the greatest rate of distortion which can ever have occurred. 
By (19'), however, we see that the rate of distortion per unit increment of the moon’s distance may be 
made as large as we please by taking the coefficient of viscosity small enough. 
These considerations seem to show that there is no reason why this screwing action of the earth should 
not once have had considerable effects. (Added October 15, 1879.) 
