CHAPTER IX.

OBLIQUITY OF THE ECLIPTIC.

"The obliquity of the ecliptic to the equator," says Dr. Brewster," was long considered as a constant quantity.Even so late as the end of the 17th century, the difference between the obliquity, as determined by ancient and modern astronomers, was generally attributed to inaccuracy of observation, and a want of knowledge of the parallaxes and refraction of the heavenly bodies. It appears, however, from the most accurate modern observations, at great intervals, that the obliquity of the ecliptic is diminishing.

By comparing about 160 observations of the ecliptic, made by ancient and modern observers, 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, 1825, to 23° 27′ 41′′.

Professor Vince, after stating 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, extracted from Rees' Cyclopædia, will give an idea of the diminution of the obliquity.

The part of the table on the left, taken from actual observations, ancient and modern, will be found nearly to coincide with that on the right, formed, by calculation from the most accurate modern observations.

The attraction of the moon, on the spheroidical figure of the earth, affords so natural an explanation of the cause of diminution, in the obliquity of the ecliptic, that it is wonderful any other should have been sought.

Let T, (Plate VIII. Fig. 5.) be the earth, M the moon, NS the earth's axis, E Q the equator; the line T Ma radius of the moon's orbit at a node, or where it coincides with, the plane of the ecliptic; A B the diameter of the earth, as cut by the plane of the ecliptic. In the triangle A MQ, the line, M Q may represent the force of the moon's attraction on the accumulated inatter of the earth, at the equator, on the side next to the moon. This force by the principles of motion, may be resolved into two other forces,* represented by the lines A M and AQ; the former of which being in the plane of the ecliptic, cannot affect the inclination; but the latter operates to diminish the obliquity.— This force must act in every part of the moon's orbit, except at the beginning of Aries and Libra.

* Enfield, Mechanics, Book II, Chapter III, Prop. XVI.

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OBLIQUITY OF THE ECLIPTIC.

and least on

The action of the moon on the opposite side of the earth, must be counter to that we have considered. But, from the well known principle, that the force of gravity diminishes as the squares of the distances increase, the effect on dif ferent sides of the earth must be unequal, that side, which is opposite to the moon. But if the force of the moon's attraction on the different sides of the earth were equal, the counter action on the opposite side must be less than the diminishing action on the side of the earth next to the moon; for the line B E is equal to A Q; but the line BM is longer than A M. If therefore B E and B M represent a force equal to A Q and A M, as in the hypothesis, B E must be less in proportion to the whole than A Q; BE being less in proportion to B M than AQ is to AM. Unequals being taken from equals, the remainders are unequal.

The inclination of the moon's orbit to the plane of the ecliptic must cause her action to be greater at some times than at others; but cannot prevent her operating in every revolution to diminish the obliquity.

The attraction of the sun on the matter accumulated at the earth's equator must produce an effect similar in kind to that of the moon. But the distance of the sun from the earth is so great, that the line A Q bears a very small proportion to the line Q M or AM. The attraction of the sun also, in different parts of the earth, becomes almost equal, as in the case of the tides. The effect of the other planets on the obliquity must be extremely small.

If the explanation here given of the cause of the diminution in the obliquity be just, it can neither become stationary nor increase without power extrinsic to the solar system; but must continually decrease, and in time become extinct.Should the earth continue to such an event, the variety of seasons must cease. But to produce such an event, at the present ratio of decrease, would require about 165,000 years from the present time; a period too immense for our comprehension. He, who formed the earth by a word, can destroy

it at pleasure, or renovate it, so as to produce "seed time and harvest, and summer and winter."

CHAPTER X.

SECTION I.-PARALLAX.

Parallax, as before defined, is the difference between the true and apparent place of a heavenly body. The true place of a body is where it would appear if seen from the centre of the earth; apparent, where seen from its surface. Parallax is largest at the horizon and decreases to the zenith, where it is nothing.

Let A B D (Plate VII. Fig. 10,) be the earth, Cits centre; M N OP, the moon in different altitudes. When the moon is at M, she would be seen from the earth's centre among the stars at E; but as seen from A, the surface, 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 is lessened, as from the different stations, she would be seen at I and K. At P, having no parallax, she appears at the same place, being seen at Z, both from C and A.

This parallax decreases with the distance (Plate VII. Fig. 10,) of the body from the earth, being inversely as the distance.* It is often called diurnal parallax.

Annual parallax is the difference in the apparent place of a heavenly body, as seen from opposite points in the earth's orbit. This orbit is about 190 millions of miles in diameter.

*This is manifest from a view of the figure. It is however capable of demonstration; for the angle A M C is equal to the angle M C V+M V C, as in Plate VII, Fig. 6. But the sum of these angles is greater than the angle MV C, the whole being greater than a part; the angie A M C is therefore greater than the angle MV C.

Hence an object, unless immensely distant, as seen from one part, must appear in a very different place in the heavens, from the same object as seen from the opposite part.

SECTION II.

PARALLAX OF THE MOON.

The diurnal parallax of the moon has been long known. It may be obtained from one observation, when she passes the meridian of a place, if the latitude of the place and the moon's declination be accurately ascertained. The latitude of many places is well known; of any, may be known. The declination of the moon may be calculated for any time. It may be obtained with accuracy in an eclipse, central, or nearly central, at the meridian over which the moon passes at the middle of such eclipse.

Let A B D be a meridian of the earth (Plate VII, Fig. 11.) C, its centre; M, the moon. The angle at C may be found by adding the declination of the moon to the latitude of the place, or subtracting it from that latitude, as the case may require; the angle CA M is obtained by subtracting the zenith distance of the moon, found by observation, from 180°. Then these two angles CA M+A C M taken from 180° leave the angle A M C, the moon's parallax. To find the side CM, the distance of the moon, the side A C is given, being the semi-diameter of the earth, and all the angles.By trigonometry, as the sine of the angle A M C is to the side A C; so is the sine of the angle CA M, to the side C M.

In taking the altitude or zenith distance of a heavenly body, allowance must be made for refraction. Parallax depresses; refraction elevates the body. See Refraction. For other allowances, see Latitude.

Astronomers recommend, as the best method to find this parallax, two observations taken on the same meridian, one