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 of50 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 sum51 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 unwise52 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, or53 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 easily54 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 use55 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 would56 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 vast57 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. Thus58 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 versa—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 noticed59 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 astro60nomer may inquire how much earlier it begins or ends in some places than in others.

Here is another artifice, extremely simple in principle, though not altogether so simple in its application. My readers must bear with me while I briefly describe the qualities of this second method, because in reality the whole question of the transit, and all the points which have to be attended to in the equipment and placing of the various observing parties, depend on these preliminary matters. Without attending to them—or at least to such primary points as I shall select—it would be impossible to form a clear conception of the circumstances with which astronomers have to deal. There is, however, no real difficulty about this part of the subject, and I shall only ask of the reader to give his attention to it for a very brief space of time.

Suppose the whole of that hemisphere of the earth on which the sun is shining when the transit is about to begin were covered with observers waiting for the event. As Venus sweeps rapidly onwards to the critical part of her path, it is clear that some of these observers will get an earlier view of the commencement of the transit than others will; just as at a boat-race, persons variously placed round a projecting corner of the course see the leading boat come into view at different times. Some one observer on the outer rim of the hemisphere would be absolutely the first to see the transit begin. Then rapidly other observers would see the phenomenon; and in the course of a few minutes61 some one observer on the outer rim of the hemisphere—almost exactly opposite the first—would be absolutely the last to see the transit begin. From that time the transit would be seen by all for several hours—I neglect the earth’s rotation, for the moment—but the end of the transit, like the beginning, would not be seen simultaneously by the observers. First one would see it, then in succession the rest, and last of all an observer almost exactly opposite the first.

Now, here we have had to consider four observers who occupy exceptional positions. There is (1) the observer who sees the transit begin earliest, (2) the one who sees it begin latest, (3) the one who sees it end earliest, and (4) the one who sees it end latest. Let us consider the first two only. Suppose these two observers afterwards compared notes, and found out what was the exact difference of time between their respective observations. Is it not clear that the result would at once afford the means of determining the sun’s distance? It would be the simplest of all possible astronomical problems to determine over what proportion of her orbit Venus passed in the interval of time which elapsed between these observations; and the observers would now have learned that that portion of Venus’s orbit is so many miles long, for they know what distance separated them, and it would be easy to calculate how much less that portion of Venus’s orbit is. Thus they would learn what the length of her whole orbit is, thence her distance from the sun, and thence the sun’s distance from us.

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The two observers who saw the transit end earliest and latest could do the like.

Speaking generally, and neglecting all the complexities which delight the soul of the astronomer, this is Delisle’s method of utilising a transit. It has obviously one serious disadvantage as compared with the other. An observer at one side of the earth has to bring his observations into comparison with those made by an observer at the other side of the earth. Each uses the local time of the place at which he observes, and it has been calculated that for the result to be of value there must not be an error of a single second in their estimates of local time. Now, does the reader appreciate the full force of this proviso? Each observer must know so certainly in what exact longitude he is, that his estimate of the time when true noon occurs shall not be one second wrong! This is all satisfactory enough in places where there are regular observatories. But matters are changed when we are dealing with such places as Woahoo, Kerguelen Land, Chatham Island, and the wilds of Siberia.

In the transit3 of 1874 there are many such difficulties to be encountered. In fact, it is almost impossible to conceive a transit the circumstances of which are more inconvenient. On the other hand, however, the transit is of such a nature that if once the pre63liminary difficulties are overcome, we can hope more from its indications than from those of any other transit which will happen in the course of the next few centuries.

The transit will begin earliest for observers in the neighbourhood of the Sandwich Islands, latest for observers near Crozet Island, far to the south-east of the Cape of Good Hope. It ends earliest for observers far to the south-west of Cape Horn, latest for observers in the north-eastern part of European Russia. Thus we see that, so far as the application of our second method is concerned, the suitable spots are not situated in the most inviting regions of the earth’s surface. As the transit happens on December 8, 1874, the principal northern stations will be very bleak abodes for the observers. The southern stations are in yet more dreary regions,—notwithstanding the fact that the transit occurs during the summer of the southern hemisphere.

For the application of Halley’s method we require stations where the whole transit will be visible; and as the days are very short at the northern stations in December, it is as respects these that we encounter most difficulty. However, it has been found that many places in Northern China, Japan, Eastern Siberia, and Manchouria are suitable for the purpose. The best southern stations for this method lie unfortunately on the unexplored Antarctic continent and the islands adjacent to it; but Crozet Island, Kerguelen Land, and some other places more easy of access than the Antarctic64 continent, will serve very well. Indeed, England has so many stations to occupy elsewhere that it is doubtful whether she will care to undertake the dangerous and difficult task of exploring the Antarctic wastes to secure the best southern stations. The work may fairly be left to other nations, and doubtless will be efficiently carried out.

What England will actually undertake has not yet been fully decided upon. We may be quite certain that she will send out a party to Woahoo or Hawaii to observe the accelerated commencement of the transit. She will also send observers to watch the retarded commencement, but whether to Crozet Island, Kerguelen Land, Mauritius, or Rodriguez is uncertain. Possibly two parties will be sent out for this purpose, and most likely Rodriguez and Mauritius will be the places selected. It had been thought until lately that the sun would be too low at some of the places when the transit begins, but a more exact calculation of the circumstances of the transit has shown this to be a mistake. Both Crozet Island and Kerguelen Land are very likely to be enveloped in heavy mists when the transit begins—that is, soon after sunrise—hence the choice of Mauritius and Rodriguez as the most suitable station.

England will also be called on to take an important part in observing the accelerated end of the transit. A party will probably be sent to Chatham Island or Campbell Island, not far from New Zealand. It had been thought that at the former island the sun would65 be too low; but here, again, a more exact consideration of the circumstances of the transit has led astronomers to the conclusion that the sun will be quite high enough at this station.

The Russian observers are principally concerned with the observation of the retarded end of the transit, nearly all the best stations lying in Siberia. But there are several stations in British India where this phase can be very usefully observed; and doubtless the skilful astronomers and mathematicians who are taking part in the survey of India will be invited—as at the time of the great eclipse—to give their services in the cause of science. Alexandria, also, though inferior to several of the Indian stations, will probably be visited by an observing party from England.

It will be seen that England will thus be called on to supply about half-a-dozen expeditions to view the transit. All of these will be sent out in pursuance of Delisle’s mode of utilising a transit, so that, for reasons already referred to, it will be necessary that they should be provided with instruments of the utmost delicacy, and very carefully constructed.4 They will have to remain at their several stations for a long time before the transit takes place—several months, at least—so that they may accurately determine the latitude of the temporary observatories they will erect. This is a work requiring skilled observers and recondite processes66 of calculation. Hence it is that the cost of sending out these observing parties is so considerable.

The only English party which will apply Halley’s method of observation is the one which will be stationed at Mauritius, under Lord Lindsay. This part of their work will be comparatively easy, the method only requiring that the duration of the transit should be carefully timed. In fact, one of the great advantages of Halley’s method is the smallness of the expense it involves. A party might land the day before the transit, and sail away the day after, with results at least as trustworthy as those which a party applying Delisle’s method could obtain after several months of hard work. It is to this, rather than any other cause, that the small expense of the observations made in 1769 is to be referred. And doubtless had it been decided by our astronomical authorities to apply Halley’s method solely or principally, the expense of the transit-observations would have been materially lessened. There would, however, have been a risk of failure through the occurrence of bad weather at the critical stations; whereas now—as other nations will doubtless avail themselves of Halley’s method—the chance that the transit-observations will fail through meteorological causes is very largely diminished. Science will owe much to the generosity of England in this respect.

It is, indeed, only recently that the possibility of applying Halley’s method has been recognised. It had been thought that the method must fail totally in67 1874. But on a more careful examination of the circumstances of the transit, a French astronomer, M. Puiseux, was enabled to announce that this is not the case. Almost simultaneously I published calculations pointing to a similar result; but having carried the processes a few steps further than M. Puiseux, I was able to show that Halley’s method is not only available in 1874, but is the more powerful method of the two.

Unfortunately, there is an element of doubt in the inquiry, of which no amount of care on the part of our observers and mathematicians will enable them to get rid. I refer to the behaviour of Venus herself. It is to the peculiarity we are now to consider that the quasi-failure of the observations made in 1769 must be attributed. It is true that Mr. Stone, the first-assistant at the Greenwich Observatory, has managed to remove the greater part of the doubts which clouded the results of those observations. But not even his skill and patience can serve to remove the blot which a century of doubt has seemed to throw upon the most exact of the sciences. We shall now show how much of the blame of that unfortunate century of doubt is to be ascribed to Venus.

At a transit, astronomers confine their attention to one particular phase—the moment, namely, when Venus just seems to lie wholly within the outline of the sun’s disc. This at least was what Halley and Delisle both suggested as desirable. Unfortunately, Venus had not68 been consulted, and when the time of the transit came she declined to enter upon or leave the sun’s face in the manner suggested by the astronomers. Consider, for example, her conduct when entering on the sun’s face:—

At first, as the black disc of the planet gradually notched the edge of the sun’s disc, all seemed going on well. But when somewhat more than half of the planet was on the sun’s face, it began to be noticed that Venus was losing her rotundity of figure. She became gradually more and more pear-shaped, until at last she looked very much like a peg-top touching with its point the edge of the sun’s disc. Then suddenly—‘as by a lightning flash,’ said one observer—the top lost its peg, and then gradually Venus recovered her figure, and the transit proceeded without further change on her part until the time came for her to leave the sun’s face, when similar peculiarities took place in a reversed order.

Here was a serious difficulty indeed. For when was the moment of true contact? Was it when the peg-top figure seemed just to touch the edge of the sun? This seemed unlikely, because a moment after the planet was seen well removed from the sun’s edge. Was it when the rotund part of the planet belonged to a figure which would have touched the sun’s edge if the rotundity had been perfect elsewhere? This, again, seemed unlikely, because at this moment the black band connecting Venus and the sun was quite69 wide. And, besides, if this were the true moment of contact, what eye could be trusted to determine the occurrence of a relation so peculiar? Yet the interval between this phase and the final or peg-top phase lasted several seconds—as many as twenty-two in one instance in 1769—and the whole success of the observation depended on exactness within three or four seconds at the outside.

We know that Venus will act in precisely the same manner in 1874. If we had been induced to hope that improvements in our telescopes would diminish the peculiarity, the observations of the transit of Mercury, in November 1868, would have sufficed to destroy that hope, for even with the all but perfect instruments of the Greenwich Observatory, Mercury assumed the peg-top disguise in the most unpleasing manner.

It may be asked, then, What do astronomers propose to do in 1874 to prevent Venus from misleading them again as she did in 1769? Much has already been done towards this end. Mr. Stone undertook a series of careful researches to determine the law according to which Venus may be expected to behave, or to misbehave herself; and the result is, that he has been able to tell the observers exactly what they will have to look for, and exactly what it is most important that they should record. In 1769, observers recorded their observations in such doubtful terms, owing to their ignorance of the real significance of the peculiarities they witnessed, that the mathematicians who had to70 make use of those observations were misled. Hinc ill? lacrym?. Hence it is that an undeserved reproach has fallen upon the ‘exact science.’

The amount of the error resulting from the misinterpretation of the observations made in 1769 was, however, very small indeed, when its true character is considered. It is, indeed, easy to make the error seem enormous. The sun’s distance came out some four millions of miles too large, and that seems no trifling error. Then, again, the resulting estimate of the distance of Neptune came out more than a hundred million miles too great; while even this enormous error was as nothing when compared with that which resulted when the distances of the fixed stars were considered.

But this is an altogether erroneous mode of estimating the effect of the error. It would be as absurd to count up the number of hairs’ breadth by which the geographer’s estimates of the length and breadth of England may be in error. In all such matters it is relative and not absolute error we have to consider. A microscopist would have made a bad mistake who should over-estimate the length of a fly’s proboscis by a single hair’s breadth; but the astronomer had made a wonderfully successful measurement of the sun’s distance who deduced it within three or four millions of miles of the true value. For it is readily calculable that the error in the estimated relative bearing of the sun as seen from opposite sides of the earth corresponds to the angle which a hair’s breadth subtends when seen from a distance of 125 feet.

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The error was first detected when other modes of determining the sun’s distance were applied by the skilful astronomers and physicists of our own day. We have no space to describe as fully as they deserve the ingenious processes by which the great problem has been attacked without aid from Venus. Indeed, we can but barely mention the principles on which those methods depend. But to the reader who takes interest in astronomy, we can recommend no subject as better worth studying than the masterly researches of Foucault, Leverrier, and Hansen upon the problem of the sun’s distance.

The problem has been attacked in four several ways. First, the tremendous velocity of light has been measured by an ingenious arrangement of revolving mirrors; the result combined with the known time occupied by light in travelling across the earth’s orbit immediately gives the sun’s distance. Secondly, a certain irregularity in the moon’s motion, due to the fact that she is most disturbed by the sun when traversing that half of her path which is nearest to him, was pressed into the service with similar results. Thirdly, an irregularity in the earth’s motion, due to the fact that she circles around the common centre of gravity of her own mass and the moon’s, was made a means of attacking the problem. Lastly, Mars, a planet which, as we have already mentioned, approaches us almost as nearly as Venus, was found an efficient ally.

The result of calculations founded on these methods72 showed that the sun’s distance, instead of being about 95,000,000 miles, is little more than 91,500,000 miles. And recently a re-examination of the observations made upon Venus in 1769 led Mr. Stone to believe that they point to a similar result.

Doubtless, however, we must wait for the transit of Venus in 1874 before forming a final decision as to the estimate of the sun’s distance which is to take its place in popular works on astronomy during the next century or so. Nothing but an unlooked-for combination of unfavourable circumstances can cause the failure of our hopes. Certainly, if we should fail in obtaining satisfactory results in 1874, the world will not say that the generosity of the English Government has been in fault, since it would be difficult to find a parallel in the history of modern science to the munificence of the grant which has been made this year for expeditions to observe a phenomenon whose interest and importance are purely scientific.

(From St. Paul’s, October 1869.)