THE SUN'S DISTANCE FROM THE EARTH. [POPULAR DISCUSSION OF A MATERIAL ERROR, BY J. R. HIND, OF BISHOP'S OBSERVATORY, TWICKENHAM, ENGLAND.] Ir may occasion surprise to many who are accustomed to read of the precision now attained in the science and practice of astronomy, when it is stated that there are strong grounds for supposing the generally received value of that great unit of celestial measures-the mean distance of the earth from the sun-to be materially in error, and that, in fact, we are nearer to the central luminary by some 4,000,000 miles than for many years past has been commonly believed. The results of various researches during the last ten years appear, however, to point to the same conclusion, and, under the impression that the subject may be deemed one of more than scientific interest, Mr. Hind has drawn up the following popular outline of the actual state of our knowledge respecting it. The measure of the sun's distance which has been generally accepted by astronomers depends upon an elaborate discussion of the observations of the transits of the planet Venus over the sun's disk in the years 1761 and 1769, published by Professor Encke, of Berlin. The great importance of these rare phenomena in the solution of what has been justly termed "the noblest problem in astronomy," was first pointed out by our countryman Halley, towards the close of the seventeenth century. The principle involved is the determination of the amount of displacement of Venus upon the solar disk, as viewed from distant stations on the earth's surface, whereby the parallax of the planet is found, and hence from the known proportion of her distance to that of the sun the distance of the latter body can be inferred. In practice this principle resolves itself into one of two methods. The first, and by far the best, consists in the comparison of the observed duration of the transit at places favorably situated for shortening and lengthening it, either by difference of latitude alone, or in certain cases with the additional effect of the earth's rotation on her axis, which will diminish or increase the interval of transit, according as the observer is carried to meet the motion of Venus or the contrary. This method is independent of the longitudes of the stations, which are often very imperfectly known, but unfortunately it cannot be applied advantageously in every transit, and is liable to fail entirely if atmospherical circumstances interrupt the observations either at ingress or egress (or of the first and last contacts of the planet with the sun's disk). The second method is by comparison of observations of the absolute times of ingress only, or of egress only, at stations widely differing in latitude; here the longitude enters as an indispensable element, and it must be pretty exactly known to allow of a trustworthy result. At no period, probably, has an astronomical phenomenon excited a more wide-spread interest than previous to the year 1761, as the first of the transits of Venus drew nigh. The Royal Society, at that time under the presidency of the Earl of Macclesfield (a nobleman distinguished for his great attainments and zeal in the encouragement of this particular science), took action in 1760, and procured the fitting-out of two Government expeditions to points which had been judged favorable for the purpose in view. Mason and Dixon, originally destined for Bencoolen, were, fortunately as it happened, delayed on their passage, and stationed themselves at the Cape of Good Hope, while Maskelyne proceeded to St. Helena. The scientific academies of Paris, St. Petersburg, and Stockholm, aided by their respective Governments, despatched observers to the island of Rodrigues, in the Indian Ocean, and various parts of the extreme north of Europe, Siberia, and Tartary; indeed, from Lisbon to Pekin, and from Tornea, on the Gulf of Bothnia, to the Cape of Good Hope, preparations were made for observations which it was hoped would lead to a more precise knowledge of that unit of measures upon which all distances and dimensions beyond the moon depend. The result, however, disappointed expectation; the values of the solar parallax obtained by different calculators exhibited discordances which tended to throw doubt upon the whole, and hence it cannot be said that the transit of 1761 was of material service in the solution of the problem. Encke's researches assign 8".49 as the most probable parallax from this transit, but some of the cotemporary computers arrived at much larger numbers. The cause of this unsatisfactory conclusion is sufficiently evident. In 1761 it was impossible to fix upon stations so situated as to give the first method described above a chance of success, and hence the value of the observations depended upon an exact acquaintance with the longitudes of the observers, which are open to considerable uncertainty in several of the most important cases. The transits of Venus generally happen in pairs, an interval of eight years elapsing between the two, while from the last of one pair to the first of the next either 105 or 122 years will intervene. The second transit is always more favorable for ascertaining the sun's distance than the first, which circumstance, added to the contradictory nature of the results derived in 1761, gave occasion to preparations in 1769 on even a greater scale than in the former year. The British Government again, at the instance of the Royal Society, equipped several expeditions to distant stations. Captain (then Lieutenant) Cook proceeded to the Pacific, and with Mr. Green, one of the assistants at the Royal Observatory, had a favorable view of the transit in the island of Tahiti, from a position still known as Point Venus; observers were also despatched to Hudson's Bay and to Madras. The Danish Government sent to Wardhus (an island in the Arctic Ocean, at the northeast extremity of Norway) a Vienna ecclesiastic, Father Hell, who had witnessed the previous transit at the observatory of that city, and who succeeded in establishing a most unenviable notoriety in connection with the second. The entrance of the planet upon the sun's disk was seen at nearly all the European observatories, and its departure therefrom at several points in Eastern Asia, at Manilla, Batavia, &c.; while the entire duration was watched at Wardhus, at different places in Lapland, at Tahiti, St. Joseph in California, and elsewhere. If the weather had been propitious at all the northern stations, the combination of the data thus obtained, with the observations of Captain Cook and Mr. Green in the Pacific, would, in all probability, have led to a very reliable de termination of the sun's distance: indeed, Pro fessor Encke, at the conclusion of his treatise on the subject, has a remark which virtually implies that complete observations at the eight northern stations, and a similar number in the Friendly Islands, would have given this distance more exactly than the whole 250 observations taken at both transits elsewhere. Unfortunately, clouds interfered at most of the selected stations, except Wardhus, and it consequently happens that the times noted by Hell and his assistants exercise a great influence on the final result. This would have been comparatively unimportant if the Viennese astronomer had not tampered with his observations to such an extent as to induce some of his cotemporaries (Lalande among the number) to regard them as forgeries. He delayed their publication for nine months, and repeatedly prevaricated respecting them; even when given to the world they were found to exhibit serious discordances from those of other observers; but, although the suspicions of his dishonesty were pretty general at the time, it was not until 1834 that positive proof was forthcoming. In that year Professor Littrow, of the Vienna Observatory, discovered among Hell's manuscripts a note-book which there is every reason to suppose was the identical one used at Wardhus. It then became apparent that the principal figures had been erased so as to be for the most part illegible; but from a careful examination of such as remained it was thought that one observation of the ingress and one of the egress might be depended upon; this was Littrow's opinion, and Encke, accepting his reasons, discussed the whole anew, and found the solar parallax to be 8".57, or, for the earth's distance from the sun, 95,365,000 miles. Although, for the reason stated, some suspicion has attached to the value of the solar parallax obtained from the transit of 1769, the first serious doubts as to its accuracy may perhaps be dated from the publication of Professor Hansen's elements of the moon's orbit in 1854. Several years previous Mr. Airy had brought to a conclusion one of the most valuable and laborious works ever undertaken in astronomy, the reduction on a uniform system and comparison with theory of the immense mass of lunar meridional observations taken at the Royal Observatory, Greenwich, between the years 1750 and 1830, the results of which were printed in 1847. These calculations furnished the means of improving the tables of the moon so far as depends upon observations in the meridian; but such observations are impracticable when she is near to the sun, and consequently several of the inequalities of her motion are not completely exhibited by them. It was for this reason, and to secure a hold upon her entire orbit, or very nearly so, that the Astronomer Royal some years since devised and erected at Greenwich an instrument specially intended for determining the place of the moon in any part of her diurnal path. The results given by this instrument, which is known as the altazimuth, have proved of great value in affording a check upon the amount of several irregularities indicated by theory, and particularly upon one technically called the parallactic equation, which is directly connected with the solar parallax, or, in other words, with the earth's distance from the sun. If the amount of this inequality, as given by observation, does not agree with that computed with an assumed value for the sun's distance, we know that the latter requires correction, and it is easy to ascertain to what amount. Professor Hansen found that the Greenwich meridian observations required a mate rial diminution in the sun's distance, and were confirmed by a long series taken at Dorpat, in Russia; while the same conclusion was drawn by Mr. Airy from the observations with the altazimuth instrument in other parts of the moon's orbit. The solar parallax finally given by Hansen is 8".97, about four-tenths of a second greater than was inferred from the transits of Venus, and corresponding to a diminution of more than 4,000,000 miles in the earth's distance from the sun. Within the last few years M. Le Verrier has completed a most rigorous application of the theory of attraction to the motions of the earth, Venus, and Mars, as defined by a long course of observation at Greenwich and other astronomical establishments. Nothing can excel in completeness the three investigations of this eminent mathematician. The theory of the earth was published in 1858, in the Annales of the Observatory of Paris, and contains one striking result bearing upon the subject of my communication. The inequality technically called the lunar equation was found to require an increase of one-twelfth part, which would render necessary an augmentation of Encke's solar parallax of nearly four-tenths of a second, and therefore a diminution of the assumed distance of the earth from the sun very nearly to the same amount assigned by Hansen's researches connected with the moon. M. Le Verrier adopts 8".95 for the parallax in his solar tables, but does not, in this place, insist upon its substitution for the number given by the transits of Venus. The earth's mass as referred to the sun's would, from the same cause, require increasing to the extent of nearly a tenth part of the whole. In the theory of the planet Venus it is found impossible to account for the motion of the line of nodes (the points where her orbit intersects the ecliptic) with the received values of the planetary masses; but, if a correction be applied to the mass of the earth of about the same magnitude as indicated by M. Le Verrier's previous researches, the calculated motion of the nodes would agree with that resulting from observations as far back as they can be depended upon. In this case, however, it would be necessary to diminish the adopted measure of the earth's distance from the sun by a thirtieth part,-affording another and quite independent corroboration of the error with which it is affected. In 1861 the investigation of the orbit of Mars was completed, and forms, with the tables of the planet, a part of the last volume of the Paris Annales. M. Le Verrier announces, as the fait capital to which his discussion had led him, the absolute impossibility of representing the observations without a motion of the perihelion (or nearest point of the orbit to the sun) greater than is consistent with the planetary masses employed, and the equal impossibility of providing for the increase of disturbing force, except by the addition of at least a tenth part to the assumed mass of the earth, with the corresponding diminution in her distance from the sun. Notwithstanding these very remarkable and confirmatory results, M. Le Verrier appears to have been at this time very strongly impressed with the exactness of Encke's parallax, and terms the unavoidable increase of the received value "a grave objection" to the augmented mass of the earth derived from his theories. He had previously detected a motion of the perihelion of the planet Mercury, due to some unknown cause, and proposed to account for this and the other anomalous motions I have alluded to, by the following assumptions: 1. There exists, besides the planets Mercury, Venus, the Earth, and Mars, a ring of asteroids between the Sun and Mercury, the aggregate mass of which is comparable to that of Mercury. 2. At the distance of the earth from the sun there is a second ring of asteroids, the mass of which is at most equal to a tenth of the earth's. 3. The total mass of the asteroids between Mars and Jupiter is at most equal to one-third of the mass of the earth. 4. The masses of the last two groups are complementary to each other: ten times the mass of the group at the earth's distance, plus three times the mass of the group situate between Mars and Jupiter, gives a sum equal to the mass of the earth. "This last conclusion," adds M. Le Verrier, "depends on the measure of the distance of the earth from the sun by the transits of Venus, which astronomers agree in considering as very precise." Now, it is to be remarked that the first of these assumptions may be admitted in explanation of the motion of the perihelion of Mercury, without affecting the question of the earth's distance: indeed, it acquires additional probability from the fact that dark spots have from time to time been observed to traverse the sun's disk, and from their rapid motion and well-defined appearance have been considered bodies of a planetary nature revolving within the orbit of Mercury. The existence of a ring of asteroids in the vicinity of the earth's path, and with an aggregate mass sufficient to explain the observed motion of the node of Venus and the perihelion of Mars, is perhaps a more disputable point. I shall not, however, stop to inquire how far it may be favored or otherwise by our present knowledge of meteoric astronomy, but proceed to mention the further evidence which has been forthcoming since the publication of M. Le Verrier's investigations, and would rather induce us to adopt a diminished measure of the earth's distance from the sun, as the most probable solution of the difficulty. M. Léon Foucault, of Paris, has succeeded in measuring the absolute velocity of light by means of the "turning mirror,"-an experimental determination of no little interest and significance. He concludes that it cannot differ much from two hundred and ninety-eight millions of French metres per second, or 185,170 English miles, which is a notable diminution upon the velocity previously derived from astronomical data alone. The time which light requires to travel from the sun to the earth is known with great precision; at the mean distance of the latter it is rather less than 8 minutes 18 seconds, and if this number be combined with M. Foucault's measure of the velocity it will be evident that the received distance is too great by about one-thirtieth part, that light, in fact, has not so far to travel before it reaches the earth as generally supposed. The corresponding solar parallax is 8".86, which approaches much nearer to M. Le Verrier's theoretical value than to the one depending on the transits of 1761 and 1769. So curious a corroboration of the former deserves especial remark. The very rare occurrence of the transits of Venus has naturally induced astronomers to consider other practical methods of approximating to the sun's distance, admitting of more frequent repetition, though not possessing in a single ap plication the same amount of accuracy. Among these the observation of the planet Mars at stations widely differing in latitude has received much attention. The orbit of this planet is so excentrical as to cause a material variation in its distance from the earth when in opposition, and consequently most favorably placed for observation. In some years it will not approach within twothirds of the distance of the earth from the sun, while in others it will be separated from us by little more than one-third of the same, and in such cases we have opportunities of ascertaining the sun's parallax from that of the planet, either by a system of observations at different points of the earth's surface, or even by measuring its distance from neighboring stars, at a single station. The nearer we are to Mars, the greater the probability, cæteris paribus, of an exact result. Suppose we have a number of determinations of the planet's distance from the celestial equator at an observatory in north latitude (as Greenwich or Poulkova), and others on corresponding dates at an observatory in the opposite hemisphere (as the Cape or Melbourne), and that from the known rate of the apparent motion of Mars we reduce them to the same instant, care being taken to eliminate the effect of refraction, the declinations will still exhibit a discordance, which, neglecting error of observation, will be due to the sum of the parallaxes of Mars at the two observatories. From this quantity the sun's parallax can be inferred, since we know the exact proportion which the distance of the planet bears to that of the sun. In 1857 Mr. Airy drew attention to two oppositions of Mars, 1860 and 1862, peculiarly favorable for such observations, and strongly recommending that an attempt should be made to correct the received distance of the sun by means of them. In 1860 the observations wholly failed through an unusual prevalence of clouded skies at the best stations; but, in 1862, numerous comparisons of the planet with stars in his vicinity were procured at Greenwich, Poulkova, the Cape of Good Hope, and Williamstown, Victoria. If those at Greenwich and Williamstown are combined, the sun's parallax is found to be 8".93, while Poulkova and the Cape give 8".97, numbers in close accordance with the theoretical values already mentioned. There is but little probability that any further light will be thrown on the question of parallax from observations of Mars during the next ten years, the planet's distance from the earth in opposition being always too great to afford that method a fair chance of suc cess. To recapitulate briefly: a diminution in the measure of the sun's distance now adopted is implied by-1st, the theory of the moon, as regards the parallactic equation, agreeably to the researches of Professor Hansen and the Astronomer Royal; 2d, the lunar equation in the theory of the earth, newly investigated by M. Le Verrier; 3d, the excess in the motion of the node of the orbit of Venus beyond what can be due to the received values of the planetary masses; 4th, the similar excess in the motion of the perihelion of Mars, also detected within the past few years by the same mathematician; 5th, the experiments of M. Foucault on the velocity of light; and 6th, the results of observations of Mars when near the earth about the opposition of 1862. I subjoin a few of the numerical changes which will follow upon the substitution of M. Le Verrier's solar parallax (8".95) for that of Professor's Encke, on which reliance has so long been placed. The earth's mean distance from the sun becomes 91,328,600 miles, being a reduction of 4,036,000. The circumference of her orbit, 599,194,000 miles, being a diminution of 25,360,000. Her mean hourly velocity 65,460 miles. The diameter of the sun 850,100 miles, which is smaller by nearly 38,000. The distances, velocities, and dimensions of all the members of the planetary system of course require similar corrections if we wish to express them in miles; in the case of Neptune, the mean distance is diminished by thirty times the amount of correction to that of the earth, or about 122,000,000 miles. The velocity of light is decreased by nearly 8000 miles per second, and becomes 183,470 if based upon astrononomical data alone. These numbers will illustrate the great importance that attaches to a precise knowledge of the sun's parallax, in our appreciation of the various distances and dimensions in the solar system. The first of the ensuing pair of transits of Venus will take place on the 9th of December (civil reckoning), 1874, and the second on the 6th of December, 1882. I have calculated the circumstances of both phenomena from M. Le Verrier's new tables of the sun and planet, the full details of which may be found in the Comptes Rendus of the Paris Academy of Sciences for July 22, 1861. For the transit of 1874, December 9, I find "The conjunction in right ascension at 4h. 59m. 13s. A.M., mean time at Greenwich, Venus north of sun's centre by 14m. 15s. External contact at ingress, 1h. 46m. 56s. A.M.; internal ditto, 2h. 15m. 578. A.M.; internal contact at egress, 5h. 57m. 5s. A.M.; external ditto, 6h. 26m. 5s. A.M. "The first contact at ingress will take place in the zenith in longitude 151 degrees 22 minutes east, and latitude 22 degrees 57 minutes south, and the last contact at egress in longitude 81 degrees 36 minutes east, and latitude 22 degrees 58 minutes south. As viewed in an inverting telescope, the planet will enter upon the sun's disk at a point about 131 degrees from north towards the west, and will leave it about 160 degrees from north towards the east." Turkey, &c. The entire duration may be observed in Australia, New Zealand, British India, China, Tartary, and the islands of the Indian Ocean, including Madagascar. The astronomical conditions, however, will not be very favorable for the investigation of parallax, either by the first or second method to which allusion has been made. Thus, for observations of the difference of duration of transit, we must rely upon stations selected so as to offer the greatest difference of latitude, without the possibility of introducing the additional effect of the earth's rotation. The Russian authorities, always energetic in matters of science, may provide for the observation of the phenomenon in Eastern Siberia, and observers might be located in various parts of Central Asia. For southern stations we have Australia, New Zealand, and several islands in the Indian Ocean, including Kerguelan's Land, but, as remarked by the Astronomer Royal (whose lucid address on this subject, published in the Monthly Notices of the Royal Astronomical Society for May, 1857, I am here chiefly following), "the observable difference of durations will probably not be half of that in 1882.” The successful application of the second method, viz., the comparison of differences of absolute times of ingress only or of egress only, will render necessary a precise determination of many distant longitudes between the Mauritius, or the Isle of Bourbon, and the Sandwich Islands. In the transit of 1882, the first and preferable method may be advantageously used under certain conditions. The entire duration will be observable in the United States and in a part of British North America, and in this region will be shortened not only by northern position, but by the effect of the earth's rotation, which must carry the observer to meet the motion of the planet. On the contrary, the duration would be lengthened by the latter cause and by southern position in those parts where an Antarctic continent was laid down some years since by Admiral Wilkes. Assuming that land is really to be found in that region and may be approached in December, there can be no doubt, on merely scientific considerations, that observers would be very advantageously placed upon it in 1882. For the application of the second method, the island in the western part of Similarly, for the transit of 1882, December 6, the Indian Ocean will have the ingress accelerated, my computation gives, "The conjunction in right ascension at 4h. 20m. 14s. P.M., mean time at Greenwich; Venus south of sun's centre 11m. 6s. External contact at in gress, 1h. 55m. 388. P.M.; internal ditto, 2h. 15m. 568. P.M.; internal contact at egress, 7h. 52m. 27s. P.M.; external ditto, 8h. 12m. 478. P.M. The first contact at ingress will take place in the zenith in longitude 31 degrees 5 minutes west, and latitude 22 degrees 40 minutes south, and the last contact at egress in longitude 125 degrees 20 minutes west, and latitude 22 degrees 42 minutes south. viewed in an inverting telescope, the planet will enter upon the sun's disk at a point about 35 degrees from north towards the west, and will leave it about 66 degrees from north towards the east." As while the Atlantic seaboard of North America will have it retarded. The egress will be retarded in part of the Australian continent, including New South Wales and Victoria, in New Zealand, the New Hebrides and many islands of the Polynesian group, and will be accelerated in the United States, the West India Islands, and the northeastern part of South America. In this case, also, numerous longitudes would require determination with greater accuracy than they are probably as yet known. The ingress will be visible in England, the first external contact at Greenwich taking place at 1h. 59m. 57s. P.M. It is scarcely to be doubted that every possible use will be made of the transits of 1874 and 1882 to improve our knowledge of the great astronomical unit, the measure of the sun's distance, and From the preceding numbers it will appear that that all the resources of modern science and all no part of the transit of 1874 can be witnessed the facilities afforded by modern enterprise will in England. The egress only will be visible in be combined for that purpose. No other opporthe southeast of Europe near sunrise-in Italy,tunity of the kind will occur until the year 2004. INDEX. ABSTRACTS of U.S. Laws (Dec. 1, 1862, March 3, Adjutant-Generals (Assistant) of U.S. Volunteers, Adjutant-General's Department, U.S., officers, 126. African Slave-Trade, Arbitrators and Judges under Agricultural Colleges, U.S. grant of lands to, 254. AGRICULTURAL PRODUCTS in the loyal States, 1859, AGRICULTURAL PROGRESS of the loyal and disloyal Agriculture and Agricultural Returns: California, 434, 435. Colorado, 446. Iowa, 413. Kansas, 430. Maine, 273. Kentucky, 367. Ohio, 377. freesborough or Stone River-Shelbyville-Tul- Army of New Mexico, operations of, 467. Army of the South, operations of-Charleston- Army of the Tennessee, operations of Opening of Army of Virginia and North Carolina, operations Assay Office, New York, 215. See Mints. Astronomical Phenomena, 12-35. American vessels, exports of U.S. domestic pro- Astronomical Publications in 1863, 37. ducts, by (1862), 196. Andorra-government, &c., 554. Animals exported from U.S. (1858–1862), 193. Apportionment of Representatives in Congress, 71. situation, boundaries, 443. officers, courts, judiciary, &c.-mineral dis- ARKANSAS: Baden-ministry, finances, army, &c., 557. tabular exhibit of condition of all the banks, number of (National), 212-214. loyal State officers (1861), courts, judiciary, Belgium-ministry, finances, army, &c., 558, 559. &c., 362. Arkansas Post, capture of, 465, 473. Armies of the U.S., operations of (1863), 462-471. mortality and sickness in, 63. Volunteers of. See tables of Volunteers in Army of the Cumberland, operations of, 468; Mur- Big Black River Bridge, battle of, 466, 482. See each State. Boards of Education in the States. Bounties to volunteers. See Finances and Volun- Brazil-ministry, finances, army, navy, &c., 559, |