Part 5

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 minutes 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.

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 transit[3] 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 preliminary 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 Antarctic 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 would 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 processes 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 in 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 not 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 quite 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 to make use of those observations were misled. _Hinc illæ lacrymæ._ 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.

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 methods 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.)

FOOTNOTES:

[3] The reader will remember the time at which the essay appeared. For several reasons it seems well to leave the essay unaltered. In the second series of Light Science a later stage is presented, and the account is carried up to the present date in my work on _The Transits of Venus_.

[4] It is held to be of the utmost importance that all the observing parties should use similar telescopes.

_BRITAIN’S COAL CELLARS._

It would have been deemed a strange thought in the days of the Tudors to suggest that England’s greatness would one day depend,—or seem to depend,—on her stores of coal, a mineral then regarded as only an unpleasant rival of the wood-log for household fires. When Shakespeare put into the mouth of Faulconbridge the words—

This England never did, nor never shall, Lie at the proud foot of a conqueror, But when it first did help to wound itself,

he would have thought it a singular proviso that England should be watchful of her coal stores if she would preserve her position among the nations. And yet there is a closer connection between the present greatness of Britain and the mighty coal cellars underlying certain British counties than we are commonly prepared to acknowledge. Saxon steadiness and Norman energy have doubtless played their part in placing Britain in the position she now holds; but whatever may have been the case in past ages of our history, it is certain that at present there is much truth in Liebig’s assertion that England’s power is in her coal. The time may come again, as the time has been, when we shall be less dependent on our coal stores,—when bituminous bankruptcy will not be equivalent to national bankruptcy; but if all our coal mines were at this moment rendered unworkable, the power of England would receive a shock from which it would be ages in recovering.

I have quoted an assertion made many years since by Baron Liebig. The assertion was accompanied by another not less striking. ‘Civilisation,’ he said, ‘is the economy of power; and English power is coal.’ It is on this text that I propose now to comment. There has recently been issued a Blue Book, bearing in the most important manner on the subject of England’s coal-supply. For five years fifteen eminent Commissioners have been engaged in examining the available evidence respecting the stores of coal contained in the various coal-fields of Great Britain. Their inquiries were commenced soon after the time when the fears of the country on this subject were first seriously awakened; and were directed specially to ascertain how far those fears were justified by the real circumstances of the case. It will be well to compare the various opinions which were expressed before the inquiries were commenced, with the results which have now been obtained.

In the first place it should be noticed that the subject had attracted the attention of men of science many years ago. Some forty years[5] have passed since Dr. Buckland, in one of the Bridgewater Treatises, pointed to the necessity for a careful examination of our coal stores, lest England should drift unawares into what he called ‘bituminous bankruptcy.’ At that time the quantity of coal raised annually in England amounted to but about forty millions of tons. Ten years later the annual yield had risen to about fifty millions of tons; and then another warning voice was raised by Dr. Arnold. Ten more years passed, and the annual yield had increased to 83,635,214 tons, when Mr. Hull made the startling announcement that our coal stores would last us but about two centuries, unless some means were adopted to check the lavish expenditure of our black diamonds.

But it was undoubtedly the address of Sir W. Armstrong to the British Association, in 1863, which first roused the attention of the country to the importance of the subject. ‘The greatness of England,’ he said, ‘depends much upon the superiority of her coal, in cheapness and quality, over that of other nations. But we have already drawn from our choicest mines a far larger quantity of coal than has been raised in all other parts of the world put together; and the time is not remote when we shall have to encounter the disadvantages of increased cost of working and diminished value of produce.’ Then he summed up the state of the case as he viewed it. ‘The entire quantity of available coal existing in these islands has been calculated to amount to 80,000 millions of tons, which, at the present rate of consumption, would be exhausted in 930 years; but with a continued yearly increase of 2¾ millions of tons would only last 212 years.’

Other statements were not wanting, however, which presented matters in a more favourable light. Mr. Hussey Vivian, M.P., expressed the opinion that South Wales alone could supply all England with coals for 500 years. Mr. R. C. Taylor, of the Geological Society, said that our coal stores would suffice for 1,700 years. And there were some who adopted a yet more sanguine view of our position.