Part 4

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.[2]

(From _Chambers’s Journal_, October 12, 1867.)

_ENCKE THE ASTRONOMER._

The years which have passed since Encke died have witnessed notable changes in the aspect of the science he loved so well. But we must look back over more than half a century, 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 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 encouragement 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 newly-discovered 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 as an astronomer, but by the general reader. Encke the man is presented to our view, as well as Encke the astronomer. With loving pains the pupil of the great astronomer handles the theme he has selected. The boyhood of Encke, his studies, his soldier life in the great uprising against Napoleon in 1813, and his work at the Seeberge Observatory; his labours on comets and asteroids; his investigations of the transits of 1761 and 1769; his life as an academician, and as director of an important observatory; his orations at festival and funeral; and lastly, his illness and death, are described in these pages by one who held Encke in grateful remembrance as ‘teacher and master,’ and as a ‘fatherly friend.’

Not the least interesting feature of the work is the correspondence introduced into its pages. We find Encke in communication with Humboldt, with Bessel and Struve, with Hansen, Olbers, and Argelander; with a host, in fine, of living as well as of departed men of science.

(From _Nature_, March 10, 1870.)

FOOTNOTES:

[1] Other green lines have since been discovered in the auroral spectrum; and occasionally a red line is seen.

[2] 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 skilfully-written paper on the same subject, from the pen of Mr. J. M. Wilson, of Rugby, had 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 a while 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 exactly the same events, and deal with exactly 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 fellow-collegian was disposed at the time to regard as either a wrong or a slight. Nothing was further from my intention than either.

_VENUS ON THE SUN’S FACE._

More than a century ago scientific men were looking forward with eager interest to the passage of the planet Venus across the sun’s face in 1769. The Royal Society judged the approaching event to be of such extreme importance to the science of astronomy that they presented a memorial to King George III., requesting that a vessel might be fitted out, at Government expense, to convey skilful observers to one of the stations which had been judged suitable for observing the phenomenon. The petition was complied with, and after some difficulty as to the choice of a leader, the good ship ‘Endeavour,’ of 370 tons, was placed under the command of Captain Cook. The astronomical work entrusted to the expedition was completely successful; and thus it was held that England had satisfactorily discharged her part of the work of utilising the rare phenomenon known as a transit of Venus.

A century passed, and science was again awaiting with interest the approach of one of these transits. But now her demands were enlarged. It was not one ship that was asked for, but the full cost and charge of several expeditions. And this time, also, science had been more careful in taking time by the forelock. The first hints of her requirements were heard some fourteen years ago, when the Astronomer-Royal began that process of laborious inquiry which a question of this sort necessarily demands. Gradually, her hints became more and more plain-spoken; insomuch that Airy—her mouthpiece in this case—stated definitely in 1868 what he thought science had a right to claim from England in this matter. When the claim came before our Government, it was met with a liberality which was a pleasing surprise after some former placid references of scientific people to their own devices. The sum of ten thousand five hundred pounds was granted to meet the cost of several important and well-appointed expeditions; and further material aid was derived from the various Government observatories.

And now let us inquire why so much interest is attached to a phenomenon which appears, at first sight, to be so insignificant. Transits, eclipses, and other phenomena of that nature are continually occurring, without any particular interest being attached to them. The telescopist may see half-a-dozen such phenomena in the course of a night or two, by simply watching the satellites of Jupiter, or the passage of our moon over the stars. Even the great eclipse of 1868 did not attract so much interest as the transit of Venus; yet that eclipse had not been equalled in importance by any which has occurred in historic times, and hundreds of years must pass before such another happens, whereas transits of Venus are far from being so uncommon.

The fact is, that Venus gives us the best means we have of mastering a problem which is one of the most important within the whole range of the science of astronomy. I use the term important, of course, with reference to the scientific significance and interest of the problem. Practically, it matters little to us whether the sun is a million of miles or a thousand millions of miles from us. The subject must in any case be looked upon as an extra-parochial one. But science does occasionally attach immense interest to extra-parochial subjects. And this is neither unwise nor unreasonable, since we find implanted in our very nature—and not merely in the nature of scientific men—a quality which causes us to take interest in a variety of matters that do not in the least concern our personal interests. Nor is this quality, rightly considered, one of the least noble characteristics of the human race.

That the determination of the sun’s distance is important, in an astronomical sense, will be seen at once when it is remembered that the ideas we form of the dimensions of the solar system are wholly dependent on our estimate of the sun’s distance. Nor can we gauge the celestial depths with any feeling of assurance, unless we know the true length of that which is our sole measuring-rod. It is, in fact, our basis of measurement for the whole visible universe. In some respects, even if we knew the sun’s distance exactly, it would still be an unsatisfactory gauge for the stellar depths. But that is the misfortune, not the fault, of the astronomer, who must be content to use the measuring-rod which nature gives him. All he can do is to find out as nearly as possible its true length.

When we come to consider how the astronomer is to determine this very element—the sun’s distance—we find that he is hampered with a difficulty of precisely the same character.

The sun being an inaccessible object, the astronomer can apply no other methods to determine its distance—directly—than those which a surveyor would use in determining the distance of an inaccessible castle, or rock, or tree, or the like. We shall see presently that the ingenuity of astronomers has, in fact, suggested some other indirect methods. But clearly the most satisfactory estimate we can have of the sun’s distance is one founded on such simple notions and involving in the main such processes of calculation as we have to deal with in ordinary surveying.

There is, in this respect, no mystery about the solution of the famous problem. Unfortunately, there is enormous difficulty.

When a surveyor has to determine the distance of an inaccessible object, he proceeds in the following manner. He first very carefully measures a base-line of convenient length. Then from either end of the base-line he takes the bearing of the inaccessible object—that is, he observes the direction in which it lies. It is clear that, if he were now to draw a figure on paper, laying down the base-line to some convenient scale, and drawing lines from its ends in directions corresponding to the bearings of the observed object, these lines would indicate, by their intersection, the true relative position of the object. In practice, the mathematician does not trust to so rough a method as construction, but applies processes of calculation.

Now, it is clear that in this plan everything depends on the base-line. It must not be too short in comparison with the distance of the inaccessible object; for then, if we make the least error in observing the bearings of the object, we get an important error in the resulting determination of the distances. The reader can easily convince himself of this by drawing an illustrative case or two on paper.

The astronomer has to take his base-line for determining the sun’s distance, upon our earth, which is quite a tiny speck in comparison with the vast distance which separates us from the sun. It had been found difficult enough to determine the moon’s distance with such a short base-line to work from. But the moon is only about a quarter of a million of miles from us, while the sun is more than ninety millions of miles off. Thus the problem was made several hundred times more difficult—or, to speak more correctly, it was rendered simply insoluble unless the astronomer could devise some mode of observing which should vastly enhance the power of his instruments.

For let us consider an illustrative case. Suppose there was a steeple five miles off, and we had a base-line only two feet long. That would correspond as nearly as possible to the case the astronomer has to deal with. Now, what change of direction could be observed in the steeple by merely shifting the eye along a line of two feet? There is a ready way of answering. Invert the matter. Consider what a line of two feet long would look like if viewed from a distance of five miles. Would its length be appreciable, to say nothing of its being measurable? Yet it is just such a problem as the measurement of that line which the astronomer would have to solve.

But even this is not all. In our illustration only one observer is concerned, and he would be able to use one set of instruments. Suppose, however, that from one end of the two-feet line an observer using one set of instruments took the bearings of the steeple; and that, half a year after, another observer brought another set of instruments and took the bearing of the steeple from the other end of the two-feet line, is it not obvious how enormously the uncertainty of the result would be increased by such an arrangement as this? One observer would have his own peculiar powers of observation, his own peculiar weaknesses: the other would have different peculiarities. One set of instruments would be characterised by its own faults or merits, so would the other. One series of observations would be made in summer, with all the disturbing effects due to heat; the other would be made in winter, with all the disturbing effects due to cold.

The observation of the sun is characterised by all these difficulties. Limited to the base-lines he can measure on earth, the astronomer must set one observer in one hemisphere, another in the other. Each observer must have his own set of instruments; and every observation which one has made in summer will have to be compared with an observation which the other has made in winter.

Thus we can understand that astronomers should have failed totally when they attempted to determine the sun’s distance without aid from the other celestial bodies.

It may seem at first sight as though nothing the other celestial bodies could tell the astronomer would be of the least use to him, since these bodies are for the most part farther off than the sun, and even those which, approach nearest to us are still far beyond the limits of distance within which the simple plan followed by surveyors could be of any service. And besides, it might be supposed that information about the distance of one celestial body could be of no particular service towards the determination of the distance of another.

But two things aid the astronomer at this point. First of all, he has discovered the law which associates together the distances of all the planets from the sun; so that if he can determine the distance of any one planet, he learns immediately the distances of all. Secondly, the planets in their motion travel occasionally into such positions that they become mighty indices, tracing out on a natural dial-plate the significant lesson from which the astronomer hopes to learn so much. To take an instance from the motions of another planet than the one we are dealing with. Mars comes sometimes so near the earth that the distance separating us from him is little more than one-third of that which separates us from the sun. Suppose that, at such a time, he is seen quite close to a fixed star. That star gives the astronomer powerful aid in determining the planet’s distance. For, to observers in some parts of the earth, the planet will seem nearer to the star than he will to observers elsewhere. A careful comparison of the effects thus exhibited will give significant evidence respecting the distance of Mars. And we see that the star has served as a fixed mark upon the vast natural dial of the heavens, just as the division-marks on a clock-face serve to indicate the position of the hands.

Now we can at once see why Venus holds so important a position in this sort of inquiry. Venus is our nearest neighbour among the planets. She comes several millions of miles nearer to us than Mars, our next neighbour on the other side. That is the primary reason of her being so much considered by astronomers. But there is another of equal importance. Venus travels nearer than our earth to the sun. And thus there are occasions when she gets directly between the earth and the sun. At those times she is seen upon his face, and his face serves as a dial-plate by which to measure her movements. When an observer at one part of the earth sees her on one part of the sun’s face, another observer at some other part of the earth will see her on another, and the difference of position, if accurately measured, would at once indicate the sun’s distance. As a matter of fact, other modes of reading off the indications of the great dial-plate have to be adopted. Before proceeding to consider those modes, however, we must deal with one or two facts about Venus’s movements which largely affect the question at issue.

Let us first see what we gain by considering the distance of Venus rather than that of the sun.

At the time of a transit Venus is of course on a line between the earth and the sun, and she is at somewhat less than a third of the sun’s distance from us. Thus whatever effect an observer’s change of place would produce upon the sun would be more than trebled in the case of Venus. But it must not be forgotten that we are to judge the motions of Venus by means of the dial-plate formed by the solar disc, and that dial-plate is itself shifted as the observer shifts his place. Venus is shifted three times as much, it is true; but it is only the balance of change that our astronomer can recognise. That balance is, of course, rather more than twice as great as the sun’s change of place.

So far, then, we have not gained much, since it has been already mentioned that the sun’s change of place is not measurable by any process of observation astronomers can apply.

It is to the fact that we have the sun’s disc, whereby to measure the change, that we chiefly trust; and even that would be insufficient were it not for the fact that Venus is not at rest, but travels athwart the great solar dial-plate. We are thus enabled to make a time measurement take the place of a measurement of space. If an observer in one place sees Venus cross the sun’s face at a certain distance from the centre, while an observer at another place sees her follow a path slightly farther from the centre, the transit clearly seems longer to the former observer than to the latter.

This artifice of exchanging a measurement of time for one of space—or _vice versâ_—is a very common one among astronomers. It was Edmund Halley, the friend and pupil of Sir Isaac Newton, who suggested its application in the way above described. It will be noticed that what is required for the successful application of the method is that one set of observers should be as far to the north as possible, another as far to the south, so that the path of Venus may be shifted as much as possible. Clearly the northern observers will see her path shifted as much to the south as it can possibly be, while the southern observers will see the path shifted as far as possible towards the north.

One thing, however, is to be remembered. A transit lasts several hours, and our observers must be so placed that the sun will not set during these hours. This consideration sometimes involves a difficulty. For our earth does not supply observing room all over her surface, and the region where observation would be most serviceable may be covered by a widely-extended ocean. Then again, the observing parties are being rapidly swayed round by the rotating earth and it is often difficult to fix on a spot which may not, through this cause, be shifted from a favourable position at the beginning of the transit to an unfavourable one at the end.

Without entering on all the points of difficulty involved by such considerations as these, I may simply indicate the fact that the astronomer has a problem of considerable complexity to solve in applying Halley’s method of observation to a transit of Venus.

It was long since pointed out by the French astronomer Delisle that the subject may be attacked another way—that, in fact, instead of noticing how much longer the transit lasts in some places than in others, the astronomer may inquire how much earlier it begins or ends in some places than in others.