moon, and that when this error was corrected the acceleration could not be entirely accounted for by the theory of gravitation. It was presently shown by the eminent astronomer Delaunay (not to be confounded for a moment with the Delaunay who has recently insisted on the inferiority of the weaker sex) that this unexplained part of the acceleration of the moon may be explained on the assumption that it is not the moon which is gaining, but the earth which is losing time; in other words, that the great terrestrial clock, the rotating earth, by which we measure time, is not going at a uniform rate, but is gradually losing its rotation spin. Laplace's assertion that the earth's rate of rotation, so far as astronomy can measure, is appreciably constant, was based on his investigation of the moon's so-called acceleration. Supposing that no part of this change remained unexplained, when solar and planetary perturbations of the moon were taken into account, he naturally inferred that the great terrestrial timepiece is keeping most perfect time. Finding, on the contrary, that a part of the acceleration does remain unexplained, we are justified in assuming, as at least a possible interpretation of the excess of acceleration, that our chief timepiece is losing time. Delaunay pointed to the tides as a probable and sufficient cause of this change-the great tidal wave carried, not bodily, but still swayingly, against the direction of rotation, checking the earth's rotation spin slowly but 'exceeding surely.'

Next, it was shown that, accompanying this change, there must be a gradual loss of lunar motion, accompanied by a gradual recession of the moon.1

In the essay which follows, on The Birth of the Moon, I describe more at length these two processes of change.

This may seem inconsistent with what we said above about the lunar acceleration which astronomers have endeavoured to explain. But this acceleration is one of the temporary changes which the moon's motion undergoes. It alternates with a similarly temporary retardation, in periods of great length indeed, but not to be compared with the enormous time-intervals which we are considering.

Here, for the present, let it suffice to note that astronomy recognises them as taking place, and that they therefore are among the processes which we may carry back in imagination to a very remote past, in order that we may recognise what probably was the initial condition-at any rate, a very early condition-of the orbs in which they are taking place.

Of course it is an obvious thought that if the moon is thus receding now, and has been receding in the past, she will one day part company with the earth altogether, and that she was at one time quite close to the earth, and even a part of the earth's mass. Considering, also, the change in the earth's rotation period, and carrying our thoughts as far back into the vistas of the past for this change as for the other, we see a time when the earth was rotating so fast that its equatorial parts were barely restrained by gravity from yielding to the tremendous resulting centrifugal tendency. A simple calculation shows that if the earth rotated once in about one hour and a third, retaining its shape unchanged (which last it could not do unless very much more rigid than it is), a body at the equator would be absolutely weightless. But a much slower rate of rotation than this would suffice to break off the equatorial regions. If the earth rotated once in about three hours, the equator would increase its distance from the polar axis, the centrifugal tendency (the rate of rotation continuing) would be greater and the surface gravity less, and the material of the equatorial surface parts would be separated from the rest of the earth's substance.

Dr. Ball follows Mr. Darwin in taking about this rotation rate-one spin in three hours-as that existing when the moon's mass separated from the earth. If we assume the earth at that stage of her existence to have been, apart from centrifugal effect, of the same volume and mass as at present, her substance possibly liquid, but not in great part vaporous, this estimate would be justified. But it appears to me we must not overlook the probability that the separation of the moon from the earth took place when a large

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part of the earth's mass continued vaporous through intensity of heat. If that were so, the earth's volume would then have been much greater than at present, even though her mass may have been, as it probably was, much smaller. What we see now in the giant planets, long after the moongenerating part of their career, seems to confirm this view, which à priori reasoning renders probable. We have also to take into account the smaller mass of the earth at that remote period, before those many millions of years throughout which the earth has been gathering year by year hundreds of millions of meteoric masses.

Now, with a larger and less dense orb, a slower rotation rate-probably a rotation rate very much slower-would have sufficed to cause the earth to part with matter from its equatorial regions, where, of course, the centrifugal tendencies resulting from over-rapid rotation would be most pronounced.

I have been in the habit, during the last ten years, of pointing out when lecturing on the moon that she probably had her origin as part of the vaporous or partly vaporous mass whence the earth also was formed, and that to this origin she owed the peculiar rotational motion which keeps the same face ever directed towards the earth. I can see nothing in Mr. Darwin's researches which should lead us to forsake this, the most natural interpretation of the moon's origin; on the contrary, the vast duration of the past periods necessary for the increase of the moon's distance from actual contact with the earth to her present orbit, and for the increase of the terrestrial day from three hours to twenty-four, suffices of itself to assure us that the earth at that remote

time must have been in great part vaporous. The giant planets also, as I have already hinted, tell the same story; for though they have thrown off their moons-Saturn, perhaps, has not quite finished the work-they are still, as we can see from their small density and their aspect, in great part vaporous. When they were beginning the work of moon-formation, many tens of millions of years ago, they

were, we may be sure, still hotter, and therefore a much larger portion of their mass was vaporous.

But it is the manner of the moon's birth, as suggested by Mr. Darwin (Dr. Ball accepting the suggestion as probably sound), which seems to me least likely to accord with the probable manner of the moon's generation, and also to correspond least with à posteriori evidence.

Mr. Darwin pictures the earth rotating once in three hours, with a double tidal wave (a wave affecting the fluid substance of her entire mass), raised by solar action. Such a wave, synchronising with what may be called the pulsation period of the earth (with the dimensions she then had), would get higher and higher, just as a pendulum receiving a succession of minute but well-timed impulses swings farther and farther, until at length cohesion would no longer be possible, and the mass out of which the moon was one day to be formed was thrown off. The considerations I have indicated above would not affect this reasoning; they would only modify our views as to the size and condition of the earth when the moon's mass was thus liberated, and therefore as to the rate of the earth's rotation spin at the time, and the period of the moon's first free revolution. But there is a more important consideration, now to be taken into account, which forbids us, I think, to believe that the moon's mass was thus thrown off, as it were, by a single effort. The monstrous tidal pulsation which would undoubtedly take place under the conditions described, would inevitably lead to the throwing off of a small mass long before it had attained swing enough, so to speak, to throw off such a mass as the moon's-one eighty-first part of the entire mass of the earth. Most probably, too, the crests of each tidal wave would throw off a mass of matter at about the same time, forming, for the time, two small moons instead of one large one. Still more probably, in my opinion, the crest of each wave would scatter cosmic spray rather than a single great globular mass. After each wave had thus swollen and eventually burst into spray, it would

gradually subside for a while, the solar tidal impulses no longer quite synchronising with the earth's tidal pulsation; but presently the waves would begin to grow again, would flow larger and larger, until again a flight of small masses would be flung from the summit of each. Again and again the process would be repeated, until at length the earth's constantly changing rotation rate would cause the sun's tidal action no longer to synchronise with the earth's pulsation period. Then, and only then, the earth would cease to throw off cosmical spray.

Now what would be the condition of the matter thus thrown off, and what its subsequent behaviour? Each particle, each globule of molten matter, would behave just as the moon, according to the theory we are considering, has actually behaved. It would begin from the first moment of its separate existence to retreat slowly from the earth. Long before the tidal wave had again grown sufficiently high to throw off spray, the spray last thrown off would have passed beyond its reach. Again, each of the tiny globules thus thrown off from the earth would at first travel nearly in the plane of the earth's equator (later influences would modify this relation considerably). Thrown off with slightly varying directions and degrees of velocity, the bodies expelled on opposite sides at one of these earth-spasms, would before long have spread themselves all around the earth, some gaining on the main body, others losing. Probably before the next flights of cosmical spray left the earth, the bodies last thrown off would form a tolerably uniform very narrow ring around the earth.

This process would have continued between certain definite epochs-the first being the time when the earth's rotation began to approach to synchronism with her pulsation period,' the last being the time when there began to be no

That is the period of vibration of her mass after any impulse (affecting the whole earth) had been received from without. The earth would as certainly have had such a pulsation period as the vibrating substance of a bell has.