Chapter 3

FOOTNOTES:[3]Two observations of Uranus, by Bradley, were discovered by the late Mr. Breen, and published in No. 1463 of theAstronomische Nachrichten.[4]Let the student make the following construction if he entertains any doubt as to the statements made above. Having traced the orbits of the earth and Uranus from my chart illustrating the article 'Astronomy' in theEncyc. Brit., let him describe a circle nearly twice as large to represent the orbit of Neptune as Bode's law would give it. Let him first suppose Neptune in conjunction with Uranus in 1820, mark the place of the earth on any given day in 1842, and the place of the fictitious Neptune; a line joining these points will indicate the direction of Neptune on the assumptions made. Let him next make a similar construction on the assumption that conjunction took place in 1825. (From the way in which the perturbation of Uranus reached a maximum between 1820 and 1825, it was practically certain that the disturber was in conjunction with Uranus between those years.) These two constructions will give limiting directions for Neptune as viewed from the earth, on the assumption that his orbit has the dimensions named. He will find that the lines include an angle of a few degrees only, and that the direction line of the true Neptune is included between them.[5]The problem is in reality, at least in the form in which Lescarbault attacked it, an exceedingly simple one. A solution of the general problem is given at p. 181 of my treatise on theGeometry of Cycloids. It is, in fact, almost identical with the problem of determining the distance of a planet from observations made during a single night.[6]It may be necessary, perhaps, to explain to some why the western side is on the right in the little maps illustrating this paper, and not, as usual with maps, on the left. We are supposed to look down towards the earth in the case of a terrestrial map, and to look up from the earth in the case of a celestial map, and naturally right and left for the former attitude become respectively left and right for the latter.

FOOTNOTES:

[3]Two observations of Uranus, by Bradley, were discovered by the late Mr. Breen, and published in No. 1463 of theAstronomische Nachrichten.

[4]Let the student make the following construction if he entertains any doubt as to the statements made above. Having traced the orbits of the earth and Uranus from my chart illustrating the article 'Astronomy' in theEncyc. Brit., let him describe a circle nearly twice as large to represent the orbit of Neptune as Bode's law would give it. Let him first suppose Neptune in conjunction with Uranus in 1820, mark the place of the earth on any given day in 1842, and the place of the fictitious Neptune; a line joining these points will indicate the direction of Neptune on the assumptions made. Let him next make a similar construction on the assumption that conjunction took place in 1825. (From the way in which the perturbation of Uranus reached a maximum between 1820 and 1825, it was practically certain that the disturber was in conjunction with Uranus between those years.) These two constructions will give limiting directions for Neptune as viewed from the earth, on the assumption that his orbit has the dimensions named. He will find that the lines include an angle of a few degrees only, and that the direction line of the true Neptune is included between them.

[5]The problem is in reality, at least in the form in which Lescarbault attacked it, an exceedingly simple one. A solution of the general problem is given at p. 181 of my treatise on theGeometry of Cycloids. It is, in fact, almost identical with the problem of determining the distance of a planet from observations made during a single night.

[6]It may be necessary, perhaps, to explain to some why the western side is on the right in the little maps illustrating this paper, and not, as usual with maps, on the left. We are supposed to look down towards the earth in the case of a terrestrial map, and to look up from the earth in the case of a celestial map, and naturally right and left for the former attitude become respectively left and right for the latter.

RESULTS OF THE BRITISH TRANSIT EXPEDITIONS.

Another noteworthy attempt has been made to estimate the distance which separates our earth from the mighty central orb round which she travels with her fellow-worlds the planets. In other words, the solar system itself has been remeasured; for the measurement of any part of the system is in fact the measurement of the entire system, the proportions of which, as distinguished from its actual dimensions, have long been accurately known.

I propose briefly to describe the results which have been obtained (after some three years of careful examination) from the observations made by the British parties sent north, south, east, and west to observe the transit of Venus on December 9, 1874; and then to consider how these results compare with those which had before been obtained. First, however, it may be well to remind the reader of the unfavourable conditions under which the task of measuring our distance from the remote sun must of necessity be attacked.

Not unfrequently we hear the measurement of the sun's distance, and the various errors which astronomers have had to correct during the progress of their efforts to deal with the problem, referred to in terms which would imply that astronomy had some reason to be ashamed of labours which are in reality among the most noteworthy achievements of their science. Because, some twenty years ago, the estimate of 95 million miles, which had for half a century held itsground in our books of astronomy as the true distance of the sun, was replaced for a while by an estimate of about 91½ million miles, which has in turn been displaced for an estimate of about 92-1/3 million miles, it has been said that astronomy has very little claim to be called the exact science. It is even supposed by some that astronomy is altogether at sea respecting the sun's distance—which, if the estimates of astronomers thus vary in the course of three-quarters of a century, may in reality, it is thought, be very different from any of the values hitherto assigned. Others suppose that possibly the sun's distance may vary, and that the diminution of three or four million miles in the estimates adopted by astronomers may correspond to an approach of the earth towards the sun by that amount, an approach which, if continued at the same rate, would, before many centuries, bring the earth upon the surface of the sun, to be consumed as fuel perhaps for the warming of the outer planets, Mars, Jupiter, and the rest.

All these imaginings are mistaken, however. The exactness of astronomy, as a science, does not depend on the measurement of the sun's distance or size, any more than the accuracy of a clock as a timekeeper depends on the exactness with which the hands of the clock are limited to certain definite lengths. The skill with which astronomy has dealt with this particular problem of celestial surveying has been great indeed; and the results, when considered with due reference to the conditions of the problem, are excellent: but in reality, if astronomers had failed utterly to form any ideas whatever as to the sun's distance, if for aught they knew the sun might be less than one million, or more than a million millions of miles from us, the exactness of astronomy as a science would be no whit impaired. And, in the second place, no doubts whatever need be entertained as to the general inference from astronomical observations that the sun's distance is between 92 and 93 millions of miles. All the measurements made during the last quarter of a century lie between 90 and 95 millions of miles, and by far thegreater number of those made by the best methods, and under the most favourable conditions, lie between 91 and 94 millions of miles. All the very best cluster closely around a distance of 92-1/3 millions of miles. We are not for the moment, however, concerned with the question of the exact distance, but with the question whether astronomy has obtained satisfactory evidence that the sun's distance lies in the neighbourhood of the distances deduced by the various methods lately employed. Putting the matter as one of probabilities, as all scientific statements must be, it may be said as confidently that the sun's distance lies between 85 millions and 100 millions of miles as that the sun will rise to-morrow; and the probability that the sun's distance is less than 90 millions, or greater than 95 millions of miles, is so small that it may in effect be counted almost as nothing. Thirdly, the possibility that the earth may be drawing nearer to the sun by three or four millions of miles in a century may be dismissed entirely from consideration. For, one of the inevitable consequences of such a change of distance would be a change in the length of the year by about three weeks; and so far from the year diminishing by twenty days or so in length during a century, it has not diminished ten seconds in length during the last two thousand years. If there has been any change year by year in the earth's distance from the sun, it is one to be measured by yards rather than by miles. Astronomers would be well content if their 'probable error' in estimating the sun's distance could be measured by thousands of miles; so that any possible approach of the earth towards the sun would go but a very little way towards accounting for the discrepancies between the different estimates of the distance, even if these estimates grew always smaller as time passed, which is assuredly not the case.

But in truth, if we consider the nature of the task undertaken by astronomers in this case, we can only too readily understand that their measurements should differ somewhat widely from each other. Let us picture to ourselves for amoment the central sun, the earth, and the earth's path, not as they really are, for the mind refuses altogether to picture the dimensions even of the earth, which is but an atom compared with the sun, whose own proportions, in turn, mighty though they are, sink into utter insignificance compared with the enormous scale of the orbit in which the earth travels around him. Let us reduce the scale of the entire system to one 500-millionth part of its real value: even then we have a tolerably large orbit to imagine. We must picture to ourselves a fiery globe 3 yards in diameter to represent the sun, and the earth as a one-inch ball circling round that globe at a distance of about 325 yards, or about 350 paces. The diameter of the earth's orbit would on this scale, therefore, be somewhat more than a third of a mile. If we imagine the one-inch ball moving round the fiery globe once in a year, while turning on its axis once in a day, we find ourselves under a difficulty arising from the slowness of the resulting motions. We should have found ourselves under a difficulty arising from the rapidity of the actual motions if we had considered them instead. The only resource is to reduce our time-scale, in the same way that we have reduced our space-scale: but not in the same degree; for if we did we should have the one-inch ball circling round its orbit, a third of a mile in diameter, sixteen times in a second, and turning on its axis five thousand times in a second. Say, instead, that for convenience we suppose days reduced to seconds. Then we have to picture a one-inch globe circling once in rather more than six minutes about a globe of fire 3 yards in diameter, one-sixth of a mile from it, and turning on its axis once in a second. We must further picture the one-inch globe as inhabited by some 1,500 millions of creatures far too small to be seen with the most powerful microscope—in fact, so small that the tallest would be in height but about the seven-millionth of an inch—and we must imagine that a few of these creatures undertake the task of determining from their tiny home swiftly rotating as it rushes in its orbit around a large globe of fire, 325 yards from them—the number of yards really intervening between that globe and their home. If we rightly picture these conditions, which fairly represent those under which the astronomer has to determine the distance of the sun from the earth, we shall perceive that the wonder rather is that any idea of the sun's distance should be obtained at all, than that the estimates obtained should differ from each other, and that the best of them should err in measurable degree from the true distance.

Anything like a full explanation of the way in which transits of Venus across the sun's face are utilised in the solution of the problem of determining the sun's distance would be out of place in these pages. But perhaps the following illustration may serve sufficiently, yet simply, to indicate the qualities of the two leading methods of using a transit. Imagine a bird flying in a circle round a distant globe in such a way that, as seen from a certain window (a circular window suppose), the bird will seem to cross the face of the globe once in each circuit. Suppose that though the distance of the globe is not known, the window is known to be exactly half as far again from the globe as the bird's path is, and that the window is exactly a yard in diameter. Now in the first place, suppose two observers watch the bird, one (A) from the extreme right side, and the other (B) from the extreme left side of the window, the bird flying across from right to left. A sees the bird begin to cross the face of the globe before B does,—say they find that A sees this exactly one second before B does. But A's eye and B's being 3 feet apart, and the bird two-thirds as far from the globe as the window is, the line traversed by the bird in this interval is of course only 2 feet in length. The bird then flies 2 feet in a second (this is rather slow for a bird, but the principle of the explanation is not affected on that account). Say it is further observed that he completes a circuit in exactly ten minutes or six hundred seconds. Thus the entire length of a circuit is 1,200 feet,—whence by the well-known relation between the circumference and the diameter of acircle, it follows that the diameter of the bird's path is about 382 feet, and his distance from the centre of the globe 191 feet. So that the distance of the globe from the window, known to be half as great again, is about 286½ feet.

If we regard the globe as representing the sun; the window of known size as representing our earth of known dimensions; the bird travelling round in a known period and at a distance whose proportion to the window's distance is known, as representing Venus travelling in a known period round the sun and at a distance bearing a known proportion to the earth's; this way of determining the distance of a remote globe illustrates what is called Delisle's method of determining the sun's distance. It requires that the two observers, A and B, should each make exact note of the moment when the bird seemed to begin to cross the disc of the remote globe; and in like manner Delisle's method requires that two observers, widely separated on the earth in a direction nearly parallel to that in which Venus is travelling, should make the most exact note of the moment when Venus begins to cross the sun's face. Also, as all I have said about the bird's beginning to cross the face of the distant globe would apply equally well if said about the end of his seeming passage across that disc, so two observers, widely separated on the earth, can determine the sun's distance by noting the end of her transit instead of the beginning, if they are suitably placed for the purpose. The window of our illustration remains unchanged during the bird's imagined flight, but as the face of the earth turned sunwards (which corresponds to that window) is all the time changing with the earth's rotation, a different pair of stations would have to be selected for observing the end of transit, than would be suitable for observing the beginning.

So much for the method called Delisle's. The other is in principle equally simple. In the imaginary experiment just described we supposed the two observers at the right and left sides of the circular window. Imagine them now to watch the bird from the top and bottom of the window, 3feet apart. Suppose they note that the two tracks along which, as seen from these two points, the bird seems to cross the face of the distant globe, lie at a distance from each other equal to one-third of the globe's apparent diameter. Now, the bird being twice as far from the globe as from the window, the two tracks on the globe necessarily lie twice as far apart as the two points from which they are seen—or they lie 6 feet apart. The globe's diameter therefore is 18 feet. Knowing thus how large it is, and knowing also how large it looks, the observers know how far from them it lies. So, in the Halleyan method of determining the sun's distance by observing Venus in transit, astronomers are stationed far north and far south on the sunlit half of the earth, corresponding to the window of the imaginary experiment. Venus corresponds to the bird. The observers note along what track she travels across the sun's face. (That they partially determine this by noting how long she is in crossing, in no sense affects the principle of the method.) They thus learn that such and such a portion of the sun's diameter equals the distance separating them,—some six or seven thousand miles perhaps,—whence the sun's diameter is known. And as we know how large he looks, his distance from the earth is determined.

A peculiarity distinguishing this method from the former is that the observers must have a station whence the whole transit can be seen; for practically the place of Venus's track can only be ascertained satisfactorily by timing her passage across the sun's disc, so that the beginning and end must be observed and very carefully timed. This is to some degree a disadvantage; for during a transit lasting several hours the earth turns considerably on her axis, and the face turned sunwards at the beginning is thus very different from the face turned sunwards at the end of transit. It is often exceedingly difficult to find suitable northern and southern stations belonging to both these faces of the earth. On the other hand, the other method has its peculiar disadvantage. To apply it effectively, the observer must knowthe exact Greenwich time (or any other selected standard time) at his station,—or in other words he must know exactly how far east or west his station is from Greenwich (or some other standard observatory). For all the observations made by this method must be compared together by some absolute time standard. In the Halleyan method the duration of transit only is wanted, and this can be as readily determined by a clock showing local time (or indeed by a clock set going a few minutes before transit began and showing wrong time altogether, so only that it goes at the right rate) as by a clock showing Greenwich, Paris, or Washington time. The clock must not gain or lose in the interval. But a clock which would gain or lose appreciably in four or five hours, would be worthless to the astronomer; and any clock employed for scientific observation might safely be trusted for an interval of that length; whereas a clock which could be trusted to retain true time for several days, is not so readily to be obtained.

We need not consider here the origin of the misapprehension (under which our principal Government astronomer lay for some time), that the Delislean method was alone available during the transit of 1874, the Halleyan method, to use his words, 'failing totally.' The British stations were selected while this misapprehension remained as yet uncorrected. Fortunately the southern stations were suitable for both methods. The northern were not: for this reason, simply, that one set were so situated that night began soon after the beginning of transit, which alone could be observed; while the other set were so situated that night only came to an end a short time before the transit ended, so that the end of transit only could be observed. No doubt when the mistake just mentioned had been clearly recognised,—as it was early in 1873,—measures would have been taken to rectify its effect by occupying some suitable northern stations for observing the whole transit, if Great Britain had been the only nation taking part in the work. Fortunately, however, other nations might be trusted to occupy the northern region, which hadso long been overlooked. England simply strengthened the southern observing corps: this could be done without any change by which the Government astronomers would have seemed to admit that 'some one had blundered.' Thus the matter was arranged—America, Russia, and Germany occupying a large number of stations admirably suited for applying the method which had been supposed to 'fail totally.' The British Official astronomers, on whom of course responsibility for adequately observing the transit (or at least for properly applying money granted by the nation for the purpose) alone rested, did in reality all, or nearly all, that was necessary in doubling some of the southern observing parties, and strengthening all of them; for unquestionably other nations occupied suitable northern stations in sufficiently strong force.

It is to be remembered, however, in estimating the probable value of the result which has been deduced from the British observations, that as yet only a portion of these observations has been effectively dealt with. The British observations of the beginning of transit at northern and southern stations give, when combined together, a value of the sun's distance. The British observations of the end of transit at other northern and southern stations give also, when combined together, a value of the sun's distance. And both sets combined give of course a mean value of the sun's distance, more likely on the whole to be correct than either value taken separately. But the British observations of the duration of transit as observed from southern stations do not of themselves give any means of determining the sun's distance. They must be combined with observations of the duration of transit as observed from northern stations; and no British party was stationed where such observations could be obtained. The value, then, of these particular British southern observations can only be educed when comparison is made between them and the northern observations by American, German, and Russian astronomers.

We must not, then, be disheartened if the results of theBritish operationsaloneshould not seem to be altogether satisfactory. For it may still happen that that portion of the British operations which only has value when combined with the work of other countries may be found to possess extreme value. We had good reason for doubting beforehand whether results of any great value could be obtained by Delisle's method. It was only because Halley's was supposed to fail totally that the Government astronomers ever thought of employing that method, which the experience of former transits had taught us to regard as of very little value.

It may be asked, however, how we are to form an opinion from the result of calculations based on the Delislean operations during the last transit, whether the method in satisfactory or not. If as yet the sun's distance is not exactly determined, a result differing from former results may be better than any of them, many will think; and therefore the method employed to obtain it may be more satisfactory than others. If, they may reason, we place reliance on a certain method to measure for us a certain unknown distance, how can we possibly tell from the distance so determined whether the method is trustworthy or not?

Perhaps the readiest way of removing this difficulty, and also of illustrating generally the principles on which the determination of the most probable mean value of many different estimates depends, is by considering a familiar experience of many, a case in which the point to be determined is the most probable time of day. Suppose that we are walking along a route where there are several clocks, the time shown by our own watch being, for whatever reason, open to question. We find, say, that as compared with our watch time, one clock is two minutes fast, the next three minutes fast, the next one minute slow, and so on, two or three perhaps being as much as six or seven minutes fast, and two or three being as much as three or four minutes slow as compared with the watch. We note, however, that these wider ranges of difference occur only in the case of clocks presumably inferior—cheap clocks in smallshops, old clocks in buildings where manifestly the flight of time is not much noted, and so forth. Rejecting these from consideration, we find other clocks ranging from one minute or so before our watch time to four minutes or so after it. Before striking a rough average, however, we consider that some among these clocks are placed where it is on the whole better to be a minute or two before the time than a second late,—as, for instance, at banks, where there may be occasion to send out clerks so as to make sure of reaching certain places (Clearing-House, General Post-office, and so forth) within specified time limits. On the other hand, we note that others of these clocks are placed where it is better to be a minute or two after time than a second before it,—as at railway stations, post-offices, and so on, where it is essential that the public should be allowed time fully up to a specified hour, for some particular service. Taking fair account of such considerations, we might find that most probably the true time lay between half a minutebeforeand two minutes and a halfafterour watch time. And thus we might infer that in reality the true time was one minute or so later than that shown by our watch. But if we were well acquainted with the characteristics of different clocks along our route, we might infer the time (nay, we might to all intents and purposesknowthe time) far more accurately than this. We might, for instance, pass six or seven shop-windows where first-class specimens of horological work were shown,—in each window, perhaps, several excellent clocks, with compensated pendulums and other contrivances for securing perfect working. We might find at one of these shops all such clocks showing the same time within two or three seconds; at the next all such clocks also agreeinginter sewithin two or three seconds, but perhaps their mean differing from the mean at the last shop of the kind by seven or eight seconds; and all six or seven shops, while showing similar agreement as regards the clocks severally displayed at each, agreeing also with each other so closely that ten or twelve seconds would cover the entire rangebetween their several mean times. If this were observed, we should not hesitate to place entire reliance on these special sets of clocks; and we should feel certain that if we took the mean of all their means as the true time (perhaps slightly modifying this mean in order to give due weight to the known superiority of one or other of these clock-shops), we should not be in error by more than five or six seconds, while most probably we should have the time true within two or three seconds.

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, notonly 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 probablygive 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 ofscientific 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 discordanceinter 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 isverywide. 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 Franceupon 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 theNautical Almanachas 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 5½ 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 6½ 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 suggestedany 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 andnot(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 Governmentastronomers 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) manœuvres, 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. OurNautical Almanacin fact embodies thekind 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,especiallyofficials), 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, tostand 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]

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