servers, with the obliquity of 23° 28′ 16′′, as observed by Tobias Mayer, in 1756, we have found that the diminution of the obliquity of the ecliptic, during a century, is 51"; a result which accords wonderfully with the best observations." This would bring the obliquity at the present time, 1831, to 23° 27′ 38′′.

The above statement, though contrary to the opinion of some philosophers, is in accordance with the true principles of Newtonian philosophy, and is corroborated by the best modern astronomers. Professor Vince, having stated the observations of many authors, ancient and modern, concludes: "It is manifest, from these observations, that the obliquity of the ecliptic continually decreases; and the irregularity, which here appears in the diminution, we may ascribe to the inaccuracy of the observations; as we know that they are subject to greater errors than the irregularity of this variation."

The following table will give an idea of the diminution of the obliquity for many centuries. It was extracted from Rees's Cyclopædia.

A small difference will be seen between the statement of Dr. Rees and that of Professor Vince, respecting the obliquity, as observed by some of these authors. But as the general principle is not affected, it may be useless to attempt a reconciliation.

The part of the table on the left was taken from observation. It will be found very nearly to coincide with that on the right, formed by calculation from the observations of the most accurate modern astronomers.

The attraction of the Moon on the spheroidical figure of the Earth is, without doubt, the cause of the diminution above stated. [See a demonstration of this in the author's larger work on astronomy.] The action of the Sun upon the same figure must have an effect similar to that of the Moon; but far less in quantity, on account of his immense distance. The principle is nearly similar to that of the tides, as may be seen in the demonstration.

If such be the cause of diminution, the obliquity must continually decrease, and in time become extinct. But, at the present ratio of diminution, such an event cannot occur under about 160,000 years, a period stretching beyond the most distant wish of the present inhabitants respecting the concerns of this world.

The variety of seasons, it is true, must cease at such an event. But long ere that time the earth may be "dissolved;" or it may be renovated, so as to produce "seed time and harvest, and summer and winter."

Why does the obliquity of the equator to the plane of the ecliptic deserve a place in a compendium of astronomy? How was this obliquity long considered? To what was the difference between the obliquity, as determined by ancient and modern astronomers, long attributed? Does it appear now, that the obliquity is increasing or diminishing? What is the diminution in a century? What is the cause of the diminution? If the Moon's attraction on the spheroidical figure of the Earth be the cause of diminution in the obliquity, what must in time be the effect? According to the present diminution of the obliquity, how many years would be required to bring the equator to the ecliptic? Ought the present inhabitants to be anxious respecting such an event?

CHAPTER XI.

Parallax.

THE true place of a heavenly body is the situation in which it would appear, if seen from the centre of the earth; the apparent, where it is seen from the surface. The angular difference between these, the true and apparent place, is what is understood by parallax. It is equal to the angle under which the semi-diameter of the earth would appear at the Sun or a planet.

Paral

lax is greatest at the horizon, called horizontal parallax. Decreasing from this, it becomes nothing at the zenith. Plate v. Fig. 7 let A B D be the Earth; C its centre; M N O P the place of the Moon at different altitudes. When the Moon is at M, she would appear from the Earth's centre among the stars at E; but as seen from the surface at A, she appears at F. When at N, she would be seen from the centre at G; but from A she seems at H. At O, her parallax being lessened, she would be seen from the different stations at I and at K. Having no parallax at P, she appears at the same place from C and from A, being seen in the zenith as at Z.

This is called diurnal parallax. Annual parallax is the difference between the apparent place of a heavenly body, as seen from opposite points of the Earth's orbit. The diameter of this orbit is about 190 millions of miles. A spectator at one season of the year, as the 20th of June, must be the whole of this diameter distant from his place at the opposite season, the 20th of December. Hence an object, unless inconceivably distant, as seen from one part, must appear in a very different place, from the same object, as seen from the opposite part.

Diurnal parallax, usually denominated parallax, with

out epithet, increases with the nearness of the body to the Earth. The Moon, being the nearest heavenly body, has the largest parallax; while the fixed stars, being immensely distant, have no perceptible parallax, the semidiameter of the Earth appearing, at that distance, no more than a point.

Parallax always depresses a body, making it appear below its true place."

The horizontal parallax of the Moon has long been known. It is of great importance in the calculation and projection of eclipses.

The parallax of the Sun has been an object of attention from the greatest antiquity. Aristarchus, an astronomer 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 until 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 ascer