omer of Samos, flourished about the middle of the third century before Christ. He proposed to find this parallax by observing the instant, when exactly one half of the moon's disk is illuminated.) This happens a little before the first, and a little after the last quarter. The moon, as seen from the sun, is then at her greatest elongation. In the triangle formed by the earth, the sun, and the moon, the angle at the moon is a right angle; and the angle formed at the earth, by the moon's distance from the sun, is taken by observation. If then the distance of the moon from the earth be known, the distance of the sun may be found by an easy process in rectangular trigonometry. Hipparchus proposed to obtain a triangle for finding the sun's parallax, by observing the exact time the moon is in passing the earth's shadow, in a lunar eclipse. But all attempts to ascertain this parallax prior to the seventeenth century, can scarcely be called approximations to the truth.

The present manner of finding the sun's parallax by the transit of Venus over the disk of the sun, is considered the greatest improvement in modern astronomy, as it furnishes a means of ascertaining with sufficient accuracy, the magnitude of the planets, and their distance from the sun. The important use to be made of this transit, was first suggested by Dr. Halley. Kepler first predicted the passing of planets over the sun's disk, foretelling the transit of Mercury in 1631, and the transits of Venus in 1631, and in 1761; but it seems not to have occurred to him, that these transits might be used in finding the distances of the planets. Dr. Halley early in life formed an idea, that such transits might be used for finding the parallax of the sun. The thought occurred to him, when he was at the island of St. Helena, viewing the stars round the south pole; and when he had an accurate view of Mercury passing over the sun's disk. But Mercury being too near the sun to be conveniently used for the intended purpose, it is necessary to have recourse to Venus.

The transit of Venus happens but seldom. Horrox, a young English astronomer, and his friend, Mr. Crabtree, appear to have been the first, who had a view of this singular and pleasing phenomenon. On the 24th of November, O. S. 1639, they saw Venus passing over the sun's disk. But their observations were imperfect, the sun going down in England during the transit. From this time no other transit of Venus occurred, till the 6th of June, 1761. Dr. Halley in a paper communicated to the Royal Society, in the year 1691, gave particular directions for taking this, and the following transit in 1769, though he knew they must happen some time after his decease.

For the manner of taking the transit, and constructing the mathematical figures for obtaining the parallax, the student is referred to the author's larger work, Ferguson, and Prior, on the same subject.

The sun's horizontal parallax is equal to the angle under which the semi-diameter of the earth would be seen at the sun as before stated. This angle being obtained, and the semi-diameter of the earth known, the distance of the earth from the sun may be easily found, by those who are tolerably versed in trigonometry. When this distance is known, the distances of the other planets from the sun, may be easily ascertained; for the great law of Kepler applies; as the square of the earth's periodical time, a sidereal year, is to the cube of its distance; so is the square of any other planet's periodical time, to the cube of its distance from the sun. A concise method of determining the distances of the other planets from the sun by the distance of the earth, may be to assume a proportional distance for the earth, and say,-as the proportional distance of the earth from the sun is to its real distance; so is the proportional distance of any other planet from the sun to its real distance. The proportional distances of the planets was not difficult to obtain; and has been long known.

If the distance of the earth from the sun be assumed at 100,000, the distances of the other principal planets

would be,

It is amusing and gratifying to know what vast interest was felt in the transit of 1761, and what vast pains were taken to observe it with accuracy. Persons were sent into various parts of the world, to make observations on this important phenomenon.

Mr. Short, of London, made his observations at the Saville house in London, in the presence of several of the royal family. The transit was observed at the royal observatory at Greenwich and other places in England; at Paris, by De la Lande; at Stockholm observatory, latitude 590 201 N. longitude, 18° east from Greenwich, the whole transit being visible, was observed by Wargentin. It was also observed at Hernosand in Sweden; at Torneo in Lapland ; at Tobolsk in Siberia; at Madras, at Calcutta, and at the Cape of Good Hope. Dr. Maskelyne's observations at St. Helena, interrupted by the cloudy state of the weather, were not completely successful, The same happened in part at London, and at the royal observatory in Greenwich. Early in the morning,' June 6th, 'when every astronomer was prepared for observing the transit, it unluckily happened, that both at London and the royal observatory at Greenwich, the sky was so overcast with clouds, as to render it doubtful whether any part of the transit should be seen; and it was 38 minutes, 21 seconds past seven o'clock, apparent time, at Greenwich, when the Rev. Mr. Bliss, astronomer royal, first saw Venus on the sun.'

Mr. Short took great pains in computing the sun's

parallax from the best observations, both in England and in other countries on this transit of 1761, and found it to have been 8."52, on the day of the transit, when the earth was very near its aphelion, or the sun near its greatest distance from the earth; consequently 8."65, when the sun is at its mean distance. Prior in his lectures considers this mean parallax 8."73, which does not materially differ from the above statement. In the projection of eclipses, the parallax of the sun is usually considered 9".

The observations on the transit of 1769 did materially differ in their result from those of 1761. They rather confirmed the parallax deduced from the prior observations.

What is parallax? To what is it equal? What is the difference between diurnal and annual parallax? Does diurnal parallax increase or decrease with the nearness of the heavenly body? Does parallax make a body appear above or below its true place? In what is the horizontal parallax of the moon of great importance? How did Aristarchus propose to find the sun's horizontal parallax? How did Hipparchus propose to obtain a triangle for finding the sun's parallax? Who first suggested the use to be made of the transit of Venus over the sun's disk? What did Kepler predict? How was Dr. Halley engaged when the thought occurred to him that transits might be used for finding the sun's parallax? Who first viewed Venus passing over the sun's disk? When was the first transit of Venus observed? Who gave directions for taking the transits of 1761 and 1769? If the distance of the earth from the sun be known, how can the distance of the other planets be ascertained? Was there much interest felt in the transit of 1761? Where was it observed? What prevented the transit from being fully observed in some places? From the various observations on the parallax, what did Mr. Short make the parallax? From this what would be the mean paraliax? What effect had the observations on the transit of 1769 on the result of the preceding observations?

CHAPTER XII.

The Fixed Stars.

THE fixed stars are so denominated from their always retaining the same situation in relation to each other. We have seen, that the earth is at one season of the year 190,000,000 miles distant from its situation at the opposite season; yet these stars have no sensible parallax. The star, which is north at one time, is north at any other time. Most of the stars indeed appear to have a diurnal revolution round the earth; but this arises from the rotation of the earth on its axis, and is no more than is caused by that rotation.

That the stars always retain the same apparent situation must be owing to their iminense and inconceivable distance. Let two persons be placed one rod distant from each other, east and west. An object, which is due north from one, will easily be perceived not to be north of the other. But let the object be ten miles distant from these observers, and if it be north of one, it will scarcely be perceived not to be north of the other; the angle can be ascertained only by nice observation. Let this principle be applied to the fixed stars, and the student will be sensible, that their distance is truly immense. We form very inadequate ideas of the earth's distance from the sun; of course of twice that distance. See the time it would require a courier to pass from the earth to the sun; section upon the earth. But this immense distance, 190,000,000 miles, makes no perceptible difference in the situation of the fixed stars, even when viewed with the nicest instruments. From what we know,' says Mr. Ferguson, of the immense distance of the stars, the nearest may be coinputed at 32,000,000,000,000 of miles from us, which is farther than a cannon ball would fly in 7,000,000 of years."