Part 7

So far the illustration corresponds well with what had been done during a quarter of a century or so before the last transit of Venus. Several different methods of determining the sun's distance had been applied to correct a value which for many reasons had come to be looked upon with suspicion. This value--95,365,000 miles--was known to be certainly too large. The methods used to test it gave results varying between about 90 million miles and about 96 million miles. But all the methods worthy of any real reliance gave results lying between 91 million miles and 94 million miles. Not to enter more fully into details than would here be suitable, we may pass on at once to say that those most experienced in the matter recognised seven methods of determining the distance, on which chief reliance must be placed. Of these seven methods, six--each applied, of course, by many different observers--were dealt with exhaustively by Professor Newcomb, of the Washington Observatory, a mathematician who has undoubtedly given closer attention to the general problem of determining the sun's distance than any living astronomer. The six methods give six several results ranging from about 92,250,000 miles to about 92,850,000 miles; but when due weight is given to those of the six methods which are undoubtedly the best, the most probable mean value is found to be about 92,350,000 miles. The seventh method, conceived by Leverrier, the astronomer to whom, with our own Adams, the discovery of Neptune was due, and applied by him as he only could have applied it (he alone possessing at once the necessary material and the necessary skill), gives the value, 92,250,000 miles. From this it may fairly be concluded that Newcomb's mean value, which has in fact been accented by all American and Continental astronomers, is certainly within 600,000 miles, and most probably within 300,000 miles of the true mean distance of the sun.

But now, to revert to our illustrative case, let us suppose that after passing the windows of six or seven horologists, from whose clocks we have obtained such satisfactory evidence as to the probable hour, we bethought ourselves of a place where, from what we had heard, a still more exact determination of the hour might be obtained. While still on the way, however, we learn from a friend certain circumstances suggesting the possibility that the clocks at the place in question may not be so correct as we had supposed. Persisting, however, in our purpose, we arrive at the place, and carefully compare the indications of the various clocks there with the time indicated by our watch, corrected (be it supposed) in accordance with the results of our former observations. Suppose now that the hour indicated by the various clocks at this place, instead of agreeing closely with that which we had thus inferred, differs from it by fully half a minute. Is it not clear that instead of being led by this result to correct our former estimate of the probable hour, we should at once infer that the doubts which had been suggested as to the correctness of the various clocks at this place were fully justified? The evidence of the other sets of clocks would certainly not be invalidated by the evidence given by the set last visited, even if the accuracy of these had not been called in question. But if, as supposed, some good reason had been given for doubt on this point,--as for instance, that of late the supervision of the clocks had been interrupted,--we should not hesitate for a moment to reject the evidence given by these clocks, or at least to regard it as only tending to demonstrate what before we had been led to surmise, namely, that these clocks could not be relied upon to show true time. If however, furthermore, we found, not only that the mean of the various times indicated by the clocks at this last-visited place differed thus widely from the time which we had every reason to consider very nearly exact, but that the different clocks here differed as widely from each other, it would be absurd to rely upon their evidence. The circumstance that there was a range of difference of fully half a minute in their indications would of itself suffice to show how untrustworthy they were, at least for the use of any one who wished to obtain the time with great accuracy. Combined with the observed difference between their mean time and that before obtained, this circumstance would prove the inaccuracy of the clocks beyond all possibility of doubt or question.

Now the case here imagined corresponds very closely with the circumstances of the recent attempt to correct our estimate of the sun's distance by Delisle's method. Our Government astronomers bethought themselves of this method as likely to give the best possible means for correcting, by observations of Venus in transit, the estimate of the sun's distance which had been deduced by Newcomb, and confirmed by Leverrier. While as yet their plans were not finally decided upon, reasons for questioning this conclusion were indicated to those officials by unofficial astronomers entertaining very friendly feelings towards them. Retaining, however, their reliance on the method thus called in question, they carried out their purpose, though fortunately making provision, very nearly sufficient, for the use of another method. Now, instead of the estimate of the sun's distance obtained from the observations by Delisle's method agreeing closely with Newcomb's mean value,--about 92,350,000 miles,--it exceeds this value by about a million miles. (See, however, note on the last page of this article.) According to various ways of considering the results sent in by his observers, the chief official astronomer obtains a mean value ranging from about 93,300,000 miles to about 93,375,000 miles. The last named estimate seems preferred on the whole; but if we take 93,350,000 miles, we shall probably give about the fairest final mean value. We have seen, however, that the results of observations by seven distinct methods give values ranging only between 92,250,000 miles and 92,850,000 miles,--the six best methods giving values ranging only between 92,250,000 miles and about 92,480,000 miles. The new value thus lies 500,000 miles above the largest and admittedly the least trustworthy of the seven results, 870,000 miles above the next largest, a million miles above the mean value, and 1,100,000 miles above the least value. It certainly ranges 500,000 miles above the largest admissible value from those seven trusted methods, dealt with most skilfully, cautiously, and laboriously, by such mathematicians as Newcomb and Leverrier.

Can we hesitate as to the inference we should deduce from this result? We need not for a moment call in question the skill or care with which the British observing parties carried out their operations. Nor need we doubt that the results obtained have been most skilfully and cautiously investigated by those to whom the work of supervision and of reduction has been entrusted. We need not even question the policy of devoting so large a share of labour and expense to the employment of a method held in little favour by most experienced Continental and American astronomers, and objected to by many in England, including some even among official astronomers. It was perhaps well that the method should have one fair and full trial. And it is certain that all who have taken part in the work have done their duty zealously and skilfully. Captain Tupman, to whom Sir George Airy, our chief official astronomer, entrusted the management of the calculations, has received, and justly, from his official superior, the highest commendation for his energy and discrimination. But beyond all manner of doubt the method employed has failed under the test thus applied to it. I do not say that hereafter the method may not succeed. Some of the conditions which at present render it untrustworthy are such as may be expected to be modified with the progress of improvement in the construction of scientific instruments. But as yet the method is certainly not trustworthy.

This might be safely concluded from the wide discrepancy between the new result and the mean of those before obtained. Yet if all the various observations made by the British observing parties agreed closely together, the circumstance, though it could hardly shake our inference on this point, would yet cause some degree of perplexity, since, of itself, it would seem to imply that the method was trustworthy. Fortunately we are not thus troubled by conflicting evidence. The indications of the untrustworthy nature of the method, derived from the discordance between the results obtained by it and those before inferred, are not a whit clearer, clear and convincing though they are, than are the indications afforded by their discordance _inter se_. The distance derived from northern and southern observations of the beginning of transit ought of course to be the same as that derived from northern and southern observations of the end of transit. If both sets of observations were exactly correct, the agreement between the results would be exact. The discordance between them could only be wide as a consequence of some serious imperfection in this method of observing a transit. But the discordance is _very_ wide. The observations of the beginning of transit by the British parties give a distance of the sun exceeding by rather more than a million miles that deduced from the observations of the end of transit.

I am well assured that neither Continental nor American astronomers will accept the new estimate of the sun's distance, unless--which I venture to predict will not be the case--the entire series of transit observations should seem to point to the same value as the most probable mean. Even then most astronomers will, I believe, think rather that transits of Venus do not afford such satisfactory means of determining the sun's distance as had been supposed. This opinion, it is well known, was held by Leverrier, insomuch that he declined to support with the weight of his influence the proposals for heavy expenditure by France upon expeditions for observing the recent transit and the approaching transit of the year 1882.

I doubt whether many, even among British astronomers, will accept the new value. Already the Superintendent of the _Nautical Almanac_ has given his opinion upon it in terms which cannot be regarded as favourable. 'It is well known,' he says (I quote at least from an article which has been attributed to him without contradiction on his part), 'that some astronomers have not expected our knowledge of the sun's distance to be greatly improved from the observations of the transit of Venus. Many, we can imagine, will regard with some suspicion' so great a value as 93,300,000 miles (I substitute these words for technical expressions identical in real meaning). 'Nevertheless, whatever degree of doubt might be entertained by competent authorities, it appears to have been felt by those immediately responsible for action, in different civilised nations where science is encouraged, that so rare a phenomenon as a transit of Venus could not be allowed to pass without every exertion being made to utilise it.'

Sir George Airy, very naturally, attaches more value to the result of the British expeditions, or at least of that part of the operations for which he was responsible, than others are disposed to do. In an address to the Astronomical Society, he expressed the opinion that 'the results now presented are well worthy of very great confidence.... Considering that the number of observers was eighteen, and that they made fifty-four observations, and considering also the degree of training they had, and their zeal, and the extreme care that was taken in the choice of stations, I think,' he said, 'that there will not be anything to compete with the value which has been deduced.' This is, as I have said, very naturally his opinion; and although ordinarily it is rather for the employers than for the employed to estimate the value of the results sent in, yet at least we cannot object to his just and generous praise of those who have worked under his orders.

Nevertheless, it must not be forgotten that on a former occasion when equal satisfaction was expressed with the result of a rather less costly but still a laborious and difficult experiment, the scientific world did not accept (and has since definitely rejected) the conclusion thus confidently advanced. I refer to the famous Harton Colliery experiment for determining the mass of the earth. The case is so closely analogous to that we are dealing with, that it will be instructive briefly to describe its leading features. Maskelyne, formerly the chief Government astronomer of this country, from observations of the effect of the mass of Mount Schehallien in deflecting a plumb-line, had inferred that the density of the earth is five times that of water. Bouguer from observations in Chimborazo, and Colonel James from observations on Arthur's Seat, had deduced very similar results. From pendulum observations on high mountains, Carlini and Plana made the earth's density very nearly the same. Cavendish, Reich, and our own Francis Baily, weighed the earth against two great globes of lead, by a method commonly known as the Cavendish experiment, but really invented by Michell. These experiments agreed closely together, making the earth's density about 5-1/2 times that of water, or giving to the earth a mass equivalent to that which would be contained in 6,000 millions of millions of millions of tons. Now, from the Harton Colliery experiments, in 1854, in which the earth's weight was estimated by comparing the vibrations of a pendulum at the mouth of the mine with those of a similar pendulum at a depth of about 1,260 feet, it appeared that the earth's density is rather more than 6-1/2 times that of water, corresponding to an increase in our estimate of the earth's mass by nearly 1,100 millions of millions of millions of tons, or by more than a sixth of the entire mass resulting from the most trustworthy former measurements. Sir G. Airy considered that 'this result will compete on at least equal terms with those obtained by other methods;' but nearly a quarter of a century has passed during which no competent astronomer has adopted this opinion, or even suggested any modification of the former mean estimate of the earth's mass on account of the unexpectedly large value deduced from the Harton experiment.

It appears to me probable that a similar fortune will attend the latest measurement of the sun's distance. But fortunately the matter will not rest merely on measurements already made. Many fresh measurements will be made during the next few years by methods already tried and _not_ (like Delisle's transit method) found wanting. The recent close approach of the planet Mars was not allowed to pass without a series of observations specially directed to the determination of the sun's distance; and we know that observations of Mars are among the most advantageous means available for the solution of this difficult problem. It was indeed from such observations that the first really trustworthy measures of the sun's distance were obtained two centuries ago. The small planets which travel in hundreds between the paths of Mars and Jupiter have also been pressed into the service. And now so many of these are known that scarcely a month passes without one or other of them being favourably placed for the purpose of distance measurements. For this too their star-like discs make these bodies specially suitable.

The most probable inference respecting the results obtained by the British expedition is that their chief value resides in the evidence which they afford respecting the Delislean method of observation. They seem to demonstrate what had before been only surmised (though with considerable confidence by some astronomers), that this method cannot be relied upon to correct our estimate of the sun's distance. In the transit of 1882, which by the way will be visible in this country, we may be certain that other and more satisfactory methods of observation will be employed.

Before concluding, it may be well to make a few remarks upon some misapprehensions which seem to exist as to the propriety in the first place, and the desirability in the second, of comments upon the arrangements adopted by Government astronomers to utilize particular astronomical phenomena, and upon the value of the results which may be obtained by means of such arrangements. Many seem to suppose that astronomical matters are in some sense like military or naval (warlike) manoeuvres, to be discussed effectively only by those who 'are under authority, having (also) soldiers under them,' in other words by Government astronomers. It would be very unfortunate for science were this so, seeing that in that case those chiefly responsible for the selection of methods and the supervision of operations would be perfectly free from all possibility of criticism. No one under their authority would be very likely to speak unfavourably of their plans. And no one possessing higher general authority would be likely to have any adequate knowledge of astronomy to form an opinion, either as to the efficiency of the arrangements adopted in any case, or as to the significance of the results obtained. In warlike matters, to some degree, the wisdom of the strategy employed is tested by results which all can appreciate, seeing that they affect directly the well-being of the nation. Moreover, there are special reasons in these cases why in the first place there should be a complete system of subordination, and why in the second few should undertake the study of the science unless they proposed to take their part in its practical application and therefore to submit to its disciplinary system. But it is quite otherwise with the science of astronomy. The nation requires, chiefly for the regulation of its commerce, a certain number of trained astronomers, to carry out systematically observations of a certain class,--observations having in the main scarcely any closer relation to the real living science of astronomy than land surveying has to such geology as Lyell taught, or the bone-trade to the science of anatomy. The stars by their diurnal motion form the most perfect time-measurers, therefore they must be constantly timed by trained observers. The sun and moon are the most effective time-indicators for seamen, and therefore their movements must be most carefully noted. Our _Nautical Almanac_ in fact embodies the kind of astronomical materials which Government astronomers are employed to collect and arrange. Such work may rather be called celestial surveying than astronomy. But from the days of Flamsteed, the first of our Astronomers Royal (as the chief Government astronomer is technically called) whose contemporary, Newton, discovered the great law of the universe, to those of Maskelyne and Sir G. Airy, whose contemporaries, the elder and the younger Herschel, disclosed the structure of the universe, there have always been astronomers outside the ranks of official astronomy, in no way desirous of entering those ranks, and in fact so taking their course from the beginning of their study of the science as to preclude themselves from all possibility of undertaking any official duties in astronomy. 'Non sua se voluntas,' necessarily, 'sed suæ vitæ rationes, hoc aditu laudis, qui semper optimo cuique maxime patuit, prohibuerunt:' though, indeed, it may not untruly be said that to one who apprehends the true sublimity of astronomy as a science the routine of official astronomy is by no means inviting, and probably personal tastes have had very much to do with the choice, by such men, of the more attractive departments of astronomy. Be this as it may, it is certain that the astronomers who thus keep outside the official ranks are not only free, and may not only be fully competent, to express an opinion on the arrangements made by Government astronomers, or on the results obtained by them, but as the only members of the community who are at once free and able so to do, their right to speak may often involve, in some degree, the duty of speaking. If through some mistake wrong arrangements were proposed for instance,--and all men, even officials (Herbert Spencer says, _especially_ officials), are apt to make mistakes,--then, unless non-official astronomers, who had carefully examined the subject, expressed their doubts, it is certain that there would be no means whatever of correcting the error, or even of detecting its consequence, until many years had elapsed. The leading official astronomers would in such a case be apt, in fact they are apt enough as it is, to stand by each other,--a chief in one department commending the zeal and energy of the chief in another department, this chief in turn commending the industry and ability of the other, and so forth,--while subordinates of all ranks might be apt either to maintain a judicious silence, or else at least to avoid any utterance which would endanger their position. It may, on the one hand, be to some degree questioned whether it would be fitting that discipline should be so far neglected in such a case that a subordinate should have eyes to see, or ears to hear, or thoughts to note, any error on the part of his superior in office. And on the other hand, those who know little or nothing of astronomy can of course form no opinion on astronomical matters, however high they may be in authority outside matters scientific. To assert, then, that it is either improper or undesirable for unofficial astronomers to comment on the plans or results of astronomers employed and paid by the nation is practically equivalent to asserting that it is improper or undesirable for the work of these paid astronomers to be examined at all,--a conclusion manifestly absurd.[7]

FOOTNOTES:

[Footnote 7: The following lines are from a letter of mine, which appeared in the _Times_ of April 13, some time after the present article was written:--

'A few months ago I said in these columns that the determination of the sun's distance, then recently communicated to Parliament--namely, 93,375,000 miles--was probably some 800,000 miles too great; and I spoke of the method on which the determination was based as to some degree discredited by the wide range of difference both between that result and the mean of the best former measurements, and between the several results of which that one was itself the mean. Captain Tupman, as straightforward as he is skilful and zealous, announces as the result of a re-examination of the British observations a distance about 600,000 miles less than the above, or, more exactly, about 92,790,000 miles, as the sun's mean distance. But while he obtains from the ingress observations a mean distance of only 92,300,000 miles, he obtains from the egress observations a mean distance of about 93,040,000 miles; and the value, 92,790,000 miles, is only obtained as the mean of these two values duly weighted, the egress observations being more satisfactory than the ingress observations. 'It appears to me that the doubts which I formerly expressed as to the trustworthiness of the method employed, are to some degree justified.

'To the general public it will be more interesting to inquire what probably is the true mean distance of the sun. To this it may be replied that in all probability the sun's mean distance does not lie so much as 600,000 miles on either side of the value 92,300,000 miles' (it should be 92,400,000).]

_THE PAST HISTORY OF OUR MOON._