CHAPTER IX. TRANSITS OF VENUS AND MERCURY. HOW SUN'S HORIZONTAL (112.) WE have thus far been very patient in our inves- CHAP. LX. tigations groping along-finding the form of the planetary Attempts to orbits, and their relative magnitudes; but, as yet, we know find the sun's nothing of the distance to the sun; save the indefinite fact, parallax. that it must be very great, and its magnitude great; but how great we can never know, without the sun's parallax. Hence, to obtain this element, has always been an interesting problem to astronomers. ancient The ancient astronomers had no instruments sufficiently' Difficulties refined to determine this parallax by direct observation, in the of manner of finding that of the moon (Art. 60), and hence the astronomers. ingenuity of men was called into exercise to find some artifice to obtain the desired result. After Kepler's laws were established, and the relative distances of the planets made known, it was apparent that their real distance could be deduced, provided the distance between the earth and any planet could be made known. Parallax of (113.) The relative distances of the earth and Mars, from the sun (as determined by Kepler's law) are as 1 to 1.5237; Mars. and hence it follows that Mars, in its oppositions to the sun, is but about one half as far from the earth as the sun is; and therefore its parallax (Art. 60) must be about double that of the sun; and several partially successful attempts were made to obtain it by observation. Maraldi obtains an the On the 15th of August, 1719, Mars being very near its opposition to the sun, and very near a star of the 5th mag- approxima. nitude, its parallax became sensible; and Mr. Maraldi, an tion to Italian astronomer, pronounced it to be 27". The relative parallax of distance of Mars, at that time, was 1.37, as determined from its position and the eccentricity of its orbit. But horizontal parallax is the angle under which the earth appears; and, at a greater distance, it will appear under a Mars. CHAP. IX. less angle. The distance of Mars from the earth, at that Observa time, was .37, and the distance of the sun was 1; therefore, : On the 6th of October, 1751, Mars was attentively obtions by War. served by Wargentin and Lacaille (it being near its opposi gentin Lacaille tion. and Dr. Hal tion to the sun), and they found its parallax to be 24′′.6. (114.) Not being satisfied with these results, Dr. Halley,. ley's sugges- an English astronomer, very happily conceived the idea of finding the sun's parallax by the comparisons of observations made from different parts of the earth, on a transit of Venus over the sun's disc. If the plane of the orbit of Venus. coincided with the orbit of the earth, then Venus would come between the earth and sun, at every inferior-conjunction, at intervals of 584.04 days. But the orbit of Venus is inclined to the orbit of the earth by an angle of 3° 23′ 28′′; and, in the year 1800, the planet crossed the ecliptic from south to north, in longitude 74° 54′ 12′′, and from north to south, in longitude 254° 54′ 12′′: the first mentioned point is called The nodes the ascending node; the last, the descending node. The nodes retrograde 31' 10" in a century. of Venus. What times transits may take place. (115.) The mean synodical revolution of 584 days correin the year sponds with no aliquot part of a year; and therefore, in the course of time, these conjunctions will happen at different points along the ecliptic. The sun is in that part of the ecliptic near the nodes of Venus, June 5th and December 6th or 7th; and the two last transits happened in 1761 and in 1769; and from these periods we date our knowledge of the solar parallax. (116.) The periodical revolution of the earth is 365.256383 days, and that of Venus is 224.700787; and as numbers they are nearly in proportion of 13 to 8. tions pared, Revolu com From this it follows, that eight revolutions of the earth 1 ་ require nearly the same time as 13 revolutions of Venus; CHAP. IX and, of course, whenever a conjunction takes place, eight years afterward another conjunction will take place very near the same point in the ecliptic.* The ratio of the times of these revolutions is directly compared, as terms of a fraction, thus, Compara. tive motions the earth. 365.256381; and it is of Venus and manifest that 365.256383 days, multiplied by the number 224700787, will give the same product as 224.700787 days multiplied by the number 365256383; that is, after an elapse of 224700787 years, the conjunction will take place at the same point in the heavens; and all intermediate conjunctions will be but approximations to the same point: and to obtain these approximate intervals, we reduce the above fraction to its approximating fractions, by the principle of continued fractions. (See Robinson's Arithmetic. ) The approximating fractions are To say nothing of the first two terms, these fractions show that two revolutions of the earth are near, in length of time, to three revolutions of Venus; three revolutions of the earth a nearer value to five revolutions of Venus; and eight revolutions of the earth a still nearer value to 13 revolutions of Venus; and 235 revolutions of the earth a very near value to 382 revolutions of Venus. The period of eight years, under favorable circumstances, will bring a second transit at the same node; but if not in eight years, it will be 235 years, or 235+8=243 years. For a transit at the other node, we must take a period of 235-8 years, divided by 2, or 113 years; and sometimes the period will be eight years less than this, or 105 years. The first transit known to have been observed was in 1639, December 4th; to this add 235 years, and we have the time of the next transit, at the same node, 1874, December 8th; and eight years after that will be another, 1882, December 6th. The first transit observed at the ascending node, was K at the same CHAP. IX. If the proportion had been exactly as 13 to 8, then the Periods of conjunctions would always take place exactly at the same conjunctions point; but, as it is, the points of conjunction in the heavens time of the are east and west of a given point, and approximate nearer and nearer to that point as the periods are greater and greater. year. Only two transits can happen at in years. To be more practical, however, the intervals between conjunctions are such, combined with a slight motion of the nodes, tervals of 8 that the geocentric latitude of Venus, at inferior conjunctions near the ascending node, changes about 19' 30" to the north, in the period of about eight years. At the descending node, it changes about the same quantity to the southward, in the same period; and as the disc of the sun is but little over 32', it is impossible that a third transit should happen 16 years after the first; hence only two transits can happen, at the same node, separated by the short interval of eight years. Periods be tween the transits Venus. puted. of (117.) If at any transit we suppose Venus to pass directly over the center of the sun, as seen from the center of the earth—that is, pass conjunction and node at the same time — at the end of another period of about eight years, Venus would be 19' 30" north or south of the sun's center; but as the semidiameter of the sun is but about 16', no transit could happen in such a case; and there would be but one transit at that node until after the expiration of a long period of 235 or 243 years. After passing the period of eight years, we take a lapse of 105 or 113 years, or thereabouts, to look for a transit at the other node. Transits (118.) Knowing the relative distances of Venus, and the can be com- earth, from the sun— the positions and eccentricities of both Dr. Halley orbits—also their angular motions and periodical revolutions— to find the every circumstance attending a transit, as seen from the sun's paral- earth's center, can be calculated; and Dr. Halley, in 1677, read a paper before the London Astronomical Society, in shows how lax. continued. Text note in 1761, June 5th; eight years after, 1769, June 3d, there was another; and the next that will occur, at that node, will be in 2004, June 7th, 235 years after 1769. which he explained the manner of deducing the parallax of CHAP. IX. the sun, from observations taken on a transit of Venus or Mercury across the sun's disc, compared with computations made for the earth's center, or by comparing observations made on the earth at great distances from each other. Why the transits of the solar pa The transits of Venus are much better, for this purpose, than those of Mercury; as Venus is larger, and nearer the Venus are earth, and its parallax at such times much greater than that better adaptof Mercury; and so important did it appear, to the learned ed to give world, to have correct observations on the last transit of rallax than Venus, in 1769, at remote stations, that the British, French, those of Merand Russian governments were induced to send out expeditions to various parts of the globe, to observe it. "The famous expedition of Captain Cook, to Otaheite, was one of them." (119.) The mean result of all the observations made on that memorable occasion, gave the sun's parallax, on the day of the transit (3d of June), 8".5776. The horizontal parallax, at mean distance, may be taken at 8".6; which places the sun, at its mean distance, no less than 23984 times the length of the earth's semidiameter, or about 95 millions of miles. cury. The result problem. This problem of the sun's horizontal parallax, as deduced The imporfrom observations on a transit of Venus, we regard as the tance of this most important, for a student to understand, of any in astronomy; for without it, the dimensions of the solar system, and the magnitudes of the heavenly bodies, must be taken wholly on trust; and we have often protested against mere facts being taken for knowledge. A general (120.) We shall now attempt to explain this whole matter on general principles, avoiding all the little minutia which explanation render the subject intricate and tedious; for our only object is to give a clear idea of the nature and philosophy of the problem. Let S (Fig. 26) represent the sun, and mn and PQ small portions of the orbits of Venus and the earth. As these two bodies move the same way, and nearly in the same plane, we may suppose the earth stationary, and Venus |