expended. The doing of work may show itself in a variety of ways-in the generation of heat, in the production of light, in the raising of weights, and so on; but in every case an equivalent force must be expended. If the brakes are applied to a train in motion, intense heat is generated in the substance of the brake; now, the force employed by the brakesman is not equivalent to the heat generated. Where, then, is the balance of force expended? We all know that the train's motion is retarded, and this loss of motion represents the requisite expenditure of force. Now, is there any process in nature resembling, in however remote a degree, the application of a brake to check the earth's rotation? There is. The tidal wave, which sweeps, twice a day, round the earth, travels in a direction contrary to the earth's motion of rotation. That this wave 'does work,' no one can doubt who has watched its effects. The mere rise and fall in open ocean may not be strikingly indicative of work done;' but when we see the behaviour of the tidal wave in narrow channels, when we see heavily-laden ships swept steadily up our tidal rivers, we cannot but recognise the expenditure of force. Now, where does this force come from? Motion being the great forcemeasurer,' what motion suffers that the tides may work? We may securely reply, that the only motion which can supply the requisite force is the earth's motion of rotation. Therefore, it is no idle dream, but a matter of absolute certainty, that, though slowly, still very surely, our terrestrial globe is losing its rotation-movement.

6

6

Considered as a time-piece, what are the earth's errors? Suppose, for a moment, that the earth was timed and rated two thousand years ago, how much has she lost, and what is her 'rate-error?' She has lost in that interval nearly one hour and a quarter, and she is losing now at the rate of one second in twelve weeks. In other words, the length of a day is now more by about one-eighty-fourth part of a second than it was two thousand years ago. At this rate of change, our day would merge into a lunar month in the course of thirty-six thousand millions of years. But after a while, the change will take place more slowly, and some trillion or so of years will elapse before the full change is effected.

Distant, however, as is the epoch at which the changes we have been considering will become effective, the subject appears to us to have an interest apart from the mere speculative consideration of the future physical condition of our globe. Instead of the recurrence of ever-varying, closely intermingled cycles of fluctuation, we see, now for the first time, the evidence of cosmical decay—a decay which, in its slow progress, may be but the preparation for renewed genesis-but still, a decay which, so far as the races at present subsisting upon the earth are concerned, must be looked upon as finally and completely destructive.*

(From Chambers's Journal, October 12, 1867.)

* In the Quarterly Journal of Science for October 1866, a more detailed but somewhat less popular account of the subject of the above paper is presented. A few months earlier, a charmingly-written paper on the same subject, from the pen of Mr. J. M. Wilson, of Rugby, had

53

ENCKE THE ASTRONOMER.

FOUR years have passed since Encke died. Even those four years have witnessed notable changes in the aspect of the science he loved so well. But we must look back over more than fifty years, if we would form an estimate of the position of astronomy when Encke's most notable work was achieved. At Seeberge, under Lindenau, Encke had been perfecting himself in the

appeared in the Eagle, a magazine written by and for members of St. John's College, Cambridge. Although my paper in the Quarterly Journal of Science was written quite independently of Mr. Wilson's (which, however, I had read), yet it chanced that in describing the same mathematical relations, and the same sequence of events, I here and there used language closely resembling his. I fear this led for awhile to some misconception; but I was fortunately able to show in Mr. De la Rue's address to the Astronomical Society, on the same subject, passages yet more strikingly resembling some in Mr. Wilson's paper (written subsequently and quite independently). The fact would seem to be that if two persons describe the same events, and deal with the same mathematical relations, it is almost certain that in more than one passage they will use somewhat similar expressions.

I was actually indebted to Mr. Wilson's paper for one illustration, however, that derived from the movements of a supposed artificial moon; and I think that had his paper appeared in a magazine printed for general circulation, I should have referred to it. As it was, this seemed useless so far as the readers of the Quarterly Journal of Science were concerned. The circumstances of the case were, indeed, far from calling for a reference; while I had in a sense made the illustration my own by detecting an important miscalculation in the original (the amount of advance being either doubled or halved-I forget which). Had I referred to Mr. Wilson's paper, I must needs have mentioned this mistake; and it would have appeared as though I had had no other purpose in making the reference.

I mention these matters to explain what I fear my esteemed fellowcollegian was disposed at the time to regard as either a wrong or a slight. Nothing was further from my intention than either.

higher branches of mathematical calculation. He took the difficult work of determining the orbital motions of newly-discovered comets under his special charge, and Dr. Bruhns tells us that every comet which was detected during Encke's stay at Seeberge was subjected to rigid scrutiny by the indefatigable mathematician. Before long a discovery of the utmost importance rewarded his persevering labours. Pons had detected on November 26, 1818, a comet of no very brilliant aspect, which was watched first at Marseilles, and then at Mannheim, until December 29. Encke next took up the work, and tracked the comet until January 12. Combining the observations made between December 22 and January 12, he assigned to the body a parabolic orbit. But he was not satisfied with the accordance between this path and the observed motions of the body. When he attempted to account for the motions of the comet by means of an orbit of comparatively short period, he was struck by the resemblance between the path thus deduced and that of Comet I, 1805. Gradually the idea dawned upon him that a new era was opening for science. Hitherto the only periodical comets which had been discovered except Lexell's-the 'lost comet '— had travelled in orbits extending far out into space beyond the paths of the most distant known planets. But now Encke saw reason to believe that he had to deal with a comet travelling within the orbit of Jupiter. On February 5, he wrote to the eminent mathematician Gauss, pointing out the results of his inquiries, and saying that he only waited for the en

couragement and authority of his former teacher to prosecute his researches to the end towards which they already seemed to point. Gauss, in reply, not only encouraged Encke to proceed, but counselled him as to the course he should pursue. The result we all know. Encke showed conclusively that the newlydiscovered comet travels in a path of short period, and that it had already made its appearance several times in our neighbourhood.

From the date of this discovery, Encke took high rank among the astronomers of Europe. His subsequent labours by no means fell short of the promise which this, his first notable achievement, had afforded. If he effected less as an astronomical observer than many of his contemporaries, he was surpassed by few as a manipulator of those abstruse formulæ by which the planetary perturbations are calculated. It was to the confidence engendered by this skill that we owe his celebrated discovery of the acceleration of the motion of the comet mentioned above. Assured that he had rightly estimated the disturbances to which the comet is subjected, he was able to pronounce confidently that some cause continually (though all but imperceptibly) impedes the passage of this body through space, and so-by one of those strange relations which the student of astronomy is familiar with the continually retarded comet travels ever more swiftly along a continually diminishing orbit.

Bruhns' Life of Encke is well worth reading, not only by those who are interested in Encke's fame and work