pocket-watch), the only chronometer by which we can check the earth is one which goes much worse -the moon. The marvellous skill and vast labour devoted to the lunar theory by the great physical astronomers Adams and Delaunay, seem to have settled that the earth has really lost in a century about ten seconds of time on the moon corrected for all the perturbations which they had taken into account. M. Delaunay has suggested that the true cause may be tidal friction, which he has proved to be probably sufficient by some such estimate as the preceding.1 But the many disturbing influences to which the earth is exposed render it a very untrustworthy time-keeper. For instance, let us suppose ice to melt from the polar regions (20° round each pole, we may say) to the extent of something more than a foot thick, enough to give I'I foot of water over those areas, or 066 of a foot of water if spread over the whole globe, which would in reality raise the sea-level by only some such almost undiscoverable difference as 4 of an inch, or an inch. This, or the reverse, which

3

1 It seems hopeless, without waiting for some centuries, to arrive at any approach to an exact determination of the amount of the actual retardation of the earth's rotation by tidal friction, except by extensive and accurate observation of the amounts and times of the tides on the shores of continents and islands in all seas, and much assistance from truc dynamical theory to estimate these elements all over the sea. But supposing them known for every part of the sea, the retardation of the earth's rotation could be calculated by quadratures.

we may believe might happen any year, and could certainly not be detected without far more accurate observations and calculations for the mean sealevel than any hitherto made, would slacken or quicken the earth's rate as a time-keeper by onetenth of a second per year.1

Again an excellent suggestion, supported by calculations which show it to be not improbable, has been made to the French Academy by M. Dufour, that the retardation of the earth's rotation indicated by M. Delaunay, or some considerable part of it, may be due to an increase of its moment of inertia by the incorporation of meteors falling on its surface. If we suppose the previous average moment of momentum of the meteors round the earth's axis to be zero, their influence

1 The calculation is simply this. Let E be the earth's whole mass, a its radius, k its radius of gyration before, and k' after the supposed melting of the ice, and W the mass of ice melted. Then, since a2 is the square of the radius of gyration of the thin shell of water supposed spread uniformly over the whole surface, and that of either ice-cap is very approximately §a2 (sin 20°)2, we have

Ek Ek2+Wa' [3 - (sin 20°)'].

And by the principle of the conservation of moments of momentum, the rotatory velocity of the earth will vary inversely as the square of its radius of gyration. To put this into numbers, we take, as above, k' }a2 and a=21× 106. And as the mean density of the earth is about 5 times that of water, and the bulk of a globe is the area of its surface into of its radius,

will be calculated just as I have calculated that of the supposed melting of ice. Thus meteors

falling on the earth in fine powder (as is in all probability the lot of the greater number that enter the earth's atmosphere and do not escape into external space again) enough to form a layer about of a foot thick in 100 years, if of 24 times the density of water, would produce the supposed retardation of 10 on the time shown by the earth's rotation. But this would also accelerate the moon's mean motion by the same proportional amount; and therefore a layer of meteor-dust accumulating at the rate of of a foot per century, or I foot in 4,000 years, would suffice to explain Adams and Delaunay's result. I see no other way of directly testing the probable truth of M. Dufour's very interesting hypothesis than to chemically analyze quantities of natural dust taken from any suitable localities (such dust, for instance, as has accumulated in two or three thousand years to depths of many feet over Egyptian, Greek, and Roman monuments). Should a considerable amount of iron with a large proportion of nickel be found or not found, strong evidence for or against the meteoric origin of a sensible part of the dust would be afforded.

Another source of error in the earth as a timekeeper, which has often been discussed, is its shrinking by cooling. But I find by the estimates.

I have given elsewhere of the present state of deep underground temperatures, and by taking 100000 as the vertical contraction per degree centigrade of cooling in the earth's crust, that the gain of time on this account by the earth, regarded as a clock, must be extremely small, and may even not amount to more in a century than of a second or of the amount estimated above as

conceivably due to tidal friction.

1 66

Secular Cooling of the Earth,” Transactions of the Royal Society of Edinburgh, 1862; and Philosophical Magazine, January, 1863.

OF GEOLOGICAL DYNAMICS

[Address to the Geological Society of Glasgow,
April 5, 1869.]

PART I.-Reply to Professor Huxley's Address to the Geological Society of London, of February 19,

1869.

PART II.—Origin and Total Amount of Plutonic Energy. PART III.—Note on the Meteoric Theory of the Sun's Heat.

PART I.

I. IN a recent address (February 19th, 1869) to the Geological Society of London, from the Presidential Chair, Professor Huxley directs attention to the two following sentences, which he quotes from my lecture on "Geological Time," delivered to this Society on the 27th February, 1868:—

"A great reform in geological speculation seems It is quite

now to have become necessary.