an error of a technical kind in Laplace's process— the omitting to take into account in the tangential component of the sun's disturbing force on the moon, the disturbing influence of the variation of the eccentricity of the earth's orbit, and he worked out the theory with this correction.

17. The result, roughly stated, was to halve the amount of acceleration calculated by Laplace and to leave half of Dunthorne's observed relative acceleration of the moon to be accounted for otherwise. In 1853, Adams communicated to Delaunay, one of the great French mathematicians, his final result, that at the end of a century the moon is 57 seconds of angle in advance of the position she had when relatively to the meridian of the earth, according to the angular velocity of the moon's motion at the beginning of the century, and the acceleration of the moon's motion truly calculated from the various disturbing causes then recognised. This, then, shows an unaccounted for gain per century of 11"4 per century of angular velocity of the moon's motion, on the hypothesis that the earth's angular velocity is uniform.

Delaunay soon after verified this result, and about the beginning of 1866 suggested that the true explanation may be the retardation of the earth's rotation by tidal friction. Using the hypothesis that the cause of the discrepancy is retardation by tidal friction, and allowing for the consequent retardation of the moon's mean motion, Adams, in an estimate which he has recently worked out in conjunction with Professor Tait and myself, found, on a certain assumption as to the proportion of retardations due to the moon and the sunthat 22 seconds of time is the error by which the earth would in a century get behind a thoroughly perfect clock rated at the beginning of the century.

18. Thus the most probable result that physical astronomy gives us up to the present time is that the earth is not an accurate chronometer, but, on the contrary, is getting slower and slower, if tested by a truly perfect clock-a clock as good as an astronomical clock ought just now to be, and that is at least 200 times as good as astronomical clocks are because astronomical clocks

are just as great a disgrace to the mechanical genius of Europe and America as chronometer watches are a credit. Astronomical clocks go only about two or three times as well as pocket chronometer watches; although the latter, from the continual agitations to which they are exposed, are in very disadvantageous circumstances. When they shall be made two or three hundred times as good as they are, we shall have an instrument which, for use during a few centuries, will be a superior time-keeper to the earth; and it will not then be necessary to set the clock by the stars, but we shall test the earth's motion by the clock. However, that is only in anticipation. Perhaps we may not live to see that use of the clock. In the meantime we are obliged to put up with the earth and stars as a means for regulating our clocks. Failing a good clock to check the earth by, we have to take the best we can find and apply corrections to it. The moon is a very unequal time-keeper, but by prodigious labour, carried out by Newton, Clairaut, Laplace, Plana, Hansen, Adams, and Delaunay, the errors

in the moon's motion are very accurately known. The moon's rotation round the earth is as it were a clock hand going round in about 29 days, and the earth is as it were the hand of another clock going round in 24 hours. The only timekeeper by which we can at present test the accuracy of the earth's motion is the moon. Imperfect as the moon is, an error has, you see, been discovered in the earth as a time-keeper, on reference to the Consider that fact, and see whether it justifies the statement I have referred to by Playfair in his Illustrations of Hutton's theory, that there is nothing in the motions of the heavenly bodies that tends to their own dissolution or to a permanent alteration of the existing state of things. For instance, no resistance tending to stop the progress of the earth!

moon.

19. Now, if the earth is losing angular velocity at that great rate, at what rate might it have been rotating a thousand million years ago? It must have been rotating faster by one-seventh part than at present, and the centrifugal force must have been greater in the ratio of the square

of 8 to the square of 7, that is, in the ratio of 64 to 49. There must have then been more centrifugal force at the equator due to rotation than now in the proportion of 64 to 49. What does the theory of geologists say to that? There is just now at the equator one two-hundred-and-eighty-ninth part of the force of gravity relieved by centrifugal force. If the earth rotated seventeen times faster bodies would fly off at the equator. The present figure of the earth agrees closely with the supposition of its having been all fluid not many million years ago.

20. The centrifugal force a hundred million years ago would be greater by about 3 per cent. than it is now, according to the preceding estimate of tidal retardation; and nothing we know regarding the figure of the earth, and the disposition of land and water, would justify us in saying that a body consolidated when there was more centrifugal force by 3 per cent. than now might not now be in all respects like the earth, so far as we know it at present. But if you go back to ten thousand million years ago-which does