4 ART. VII. 1. United States Astronomical Expedition to the Southern Hemisphere during the Years 1849, 50, 51, 52. Vol. III. The Solar Parallax. By LIEUT. J. M. GILLISS, LL. D., Superintendent Pub. Doc. Washington: 1856. 2. Astronomical and Meteorological Observations made at the United States Naval Observatory during the Year 1863. By CAPTAIN J. M. GILLISS, U. S. N., Superintendent Pub. Doc. Washington: 1865. NEXT to the earth the sun is to us the most important body in the universe. A body on which so much of our physical happiness depends must, at an early age, have stimulated mankind to make exertions to ascertain its distance. At first appearance it might have seemed imposssible to measure the distance of a body to which it is impossible for us to go. But the ingenuity of man seems to know no bounds; and when he has once determined to solve a question, the means of doing it are certain to be discovered. "The measure of the sun's distance," says the English Astronomer Royal, Airy, " has always been considered the noblest problem in astronomy." To this Dr. Gould adds: "This distance, known or unknown, is, and must ever be, the standard length in which every linear measure of a celestial object beyond the moon is directly or indirectly expressed; whether it be the distance of a satellite, a comet, or a fixed star; the dimensions of a planet, or the gauge of a nebula. It is the astronomical unit, and every stellar distance is only known as a proportional one until this unit is established. It is, therefore, manifestly the duty of astronomers to flinch from no labor which gives a remote prospect of increasing the precision of our measurement of this fundamental quantity." Let us now sketch the history of the many attempts that have been made by astronomers in all ages of the world, from the most ancient of which we have any account down to the most recent, to determine the sun's distance. We shall thus learn how one difficulty after another has been overcome in approximating to the solution of this important but difficult problem. Those who have no knowledge of the fundamental principles on which the solution of this problem is based can have but a faint conception of the reliance to be placed on the astronomer's determination of this very important astronomical unit. In order to find the distance of the sun from the earth, we must, in general, know the numerical value of his parallax. Parallax may be defined to be the apparent change of place of an object in consequence of being viewed from different points not in the same straight line with that object. These are the methods of finding the distance of the sun from the earth without finding the parallax directly; we shall mention each in its proper place. Cleomedes offered the following argument to prove that the sun is larger than it appears to be, and, consequently, that his distance must be considerable. He said that when the sun is rising behind a mountain the edges of his disc are often, at the same time, seen on the opposite sides of the mountain; and he inferred that the sun, which appears no more than a foot in diameter, must in reality be larger than the mountain. Aristarchus, who flourished about 230 years B. C., proposed a method for determining the distance of the sun by comparing his distance with that of the moon, and, consequently, finding it without knowing the solar parallax. If we could tell exactly when the moon's disc is dichotomized, or half enlightened, we should then know that the triangle formed by lines connecting the centres of the earth, sun, and moon, would be right-angled at the moon; and as the sun and moon are then frequently both above the horizon, the angular distance between them can be measured, and thus the three angles of the triangle will become known and the relation of the sides will be known, and hence the ratio of the sun's distance to that of the moon will also be known. As the distance of the moon is pretty accurately known, the distance of the sun can be found. This is the first method of finding the sun's distance without a knowledge of his parallax. Aristarchus attempted to put it into practice. found the angular distance between the sun and the moon equal to 879, or the angle at the centre of the sun equal to 30. This makes the distance of the sun nineteen times as great as that of the moon.* This we now know to be far from correct, but it must have assisted materially in enabling the ancients to form a conception of the approximate magnitude of the universe. The great difficulty with the method of Aristarchus consisted in determining exactly when the moon's disc was dichotomized, and in He • The Origin and Progress of Astronomy, by John Narrien, F. R. A. S., pp. 206-207. measuring the angular distance between the sun and moon with such instruments as he possessed. Instead of the angle at the sun being 39, as found by Aristarchus, we now know it to be no more than S' or 9'. Although the modern astronomer could approximate much more nearly to the relative distances of the sun and moon by this method, yet he would meet with too many obstacles in the way of bringing it practically into use to make it valuable in these days of exact determination. In consequence of the roughness of the lunar surface, which is brought out as soon as it is examined with a telescope of moderate power, the line which divides the dark from the illuminated part becomes so broken that it would be with no little difficulty that the time could be determined when it exactly bisects the lunar disc. Again, the unequal refraction to which the sun and moon are subject when they are both above the horizon renders the exact determination of the angular distance of the sun from the moon a matter of considerable difficulty. Succeeding philosophers, by employing the method of Aristarchus and making more exact measurements, arrived at much more approximate results. Pliny informs us that Posidonius found the distance of the sun and moon from the earth to be respectively 500,000,000 and 2,000,000 stadia, which determination makes the distance of the sun 250 times that of the moon a result far from the truth, but a great step towards an exact determination. It is thought, however, that this result was brought out only by a fortunate compensation of errors. The Arabian astronomers have given numbers expressing the distance of the sun from the earth, but these seem to be derived from theory rather than from direct measurement. Alfraganus makes the distance of the sun equal to 610 diameters of the earth; and Ibu Junis increased it to 883 diameters.* These numbers, although far from being correct, served to convey more accurate ideas of the magnitude of the physical universe. Copernicus adopted a value of the sun's distance corresponding to 571 diameters of the earth. A distance nearly the same was adopted by other astronomers that lived about his time or a little later. Tycho Brahé, the great Danish astronomer, by his accurate observations, laid the foundation for more exact knowledge respecting the sun's distance. *Narrien's Origin and Progress of Astronomy, p. 307. While Kepler was engaged in his celebrated researches on the planet Mars, and by means of which he discovered two of the well-known laws of physical astronomy, which bear his name, he took the opportunity to institute a searching scrutiny into the value of the solar parallax by reducing in the most careful way the numerous observations of Tycho Brahé. The conclusion to which he finally arrived was that the solar parallax did not exceed one minute of arc. This value of the sun's parallax makes his distance only the one-seventh of what it is now known to be. In 1609, in his "New Astronomy, or Commentaries on the Motions of Mars," he regarded it difficult to assigu limits to the solar parallax nearer than 0° 4′ 55′′ and 0° 1′45′′, corresponding to a distance of 350 and 1,000 diameters of the earth. "In his Ephemerides for 1617 and 1617, he supposed the parallax to be 2' 29", according to Tycho Brahé, who deduced it from observations of the moon. Peter Crüger, Kepler's intimate friend, upbraided him for removing the sun to such a huge distance,' which would destroy the value of all Tycho's tables, after he had himself adopted the Tychonian value in the Ephemeris a few years before; but Kepler replied that he had studied the subject with care, and did not hesitate to reduce Tycho's parallax by 1' 40", or two-thirds of its whole amount."* Kepler finally adopted a value of the sun's distance equal to 1,800 diameters of the earth, corresponding to a parallax of 49". This parallax is still five-and-ahalf times too great. In 1647 Godfrey Wendelin, a Belgian astronomer, deduced a parallax from morning and evening observations of the moon equal to 15" at the outside. This corresponds to a distance of 6,870 diameters of the earth. He fixed, as the most probable number, 7,328 diameters. In 1665 Ricciolus thought the above value of the sun's distance too great, and fixed upon a value of the solar parallax between 28" and 30", and concluded that neither of these values could be more than a few seconds of arc from the truth. The next attempt to determine the solar parallax was made by Cassini and Richer. The former resolved to attack the problem indirectly by finding the parallax of the planet Mars. When Mars is in opposition he Gould's Treatise on the Solar Parallax, U. S. Naval Ast. Expedition, p. lxi ; and Grant's Hist. Phys Ast., p. 211. is much nearer the earth than the sun; and by finding the parallax, and thence the distance of Mars, we can arrive at the distance of the sun from the earth by means of Kepler's third law. In consequence of the great eccentricity of the orbit of Mars, his distance from the earth at different oppositions is very various, as may be seen by the following table. If the earth's distance from the sun be called unity, the distance of Mars from the earth will be at the opposition in February 13... . We thus see that the distance of Mars at one opposition may be little more than half of what it is at another.* The French Academy sent M. Richer, in 1672, to Cayenne, in South America, to make observations on Mars, then in opposition, while Cassini, Picard, and Roemer made observations upon the planet at Paris and Brion. "The planet had been compared, both at Cayenne and Paris, with Aquarius, but Cassini did not succeed in obtaining any good value, farther than deducing an upper limit of 9′′, if the observations were to be trusted. In 1684, however, Cassini published a memoir revising his computations from the materials, and from correspondent observations, in 1672, September 5th, 9th, and 24th, deduced as the equatorial horizontal parallax of Mars, 25", = 3," corresponding to a solar parallax of 9′′. 5 = 1," or a distance from the earth of 21,600 terrestrial semi-diameters, and with a possible error of 2,000 or 3,000 semi-diameters. From these values he inferred the true diameter of the sun to be just one hundred times that of the earth.t We have now given an account of the first set of observations that gave the observers a value of the parallax which we may call approximate, since we know it to be embraced within the limits of the probable error of the result. If the planet Mars or any other celestial body be viewed when it rises, and also when it sets, it will not be seen in the same direction, even if the body and the earth See Smithsonian Report for 1859, p. 295. † Gould, U. S. N. Ast. Ex., p. lxiii. |