The distance between the true and imaginary equinoxial points is called the EQUATION OF THE EQUINOXES.

The mean place of the equinox for any proposed time is given by tables; and the equation of the equinoxes for the proposed time gives the quantity to be added to, or subtracted from, the mean place, to find the true place.

186. Proportion of the mean precession due to the disturbing forces of the moon and sun.- If the entire amount of the mean precession in a given time be expressed by 7, the part due to the moon will be 5, and that due to the sun will be 2.

187. Like effects produced in the case of other planets.These disturbing effects produced upon the plane of the planet's equator, are not confined to the case of the earth. All the planets which have the spheroidal form, are subject to similar effects from the sun's attraction on their equatorial protuberance, the magnitude of these effects being, however, less as the distance from the sun is increased. In the case of the major planets, the sun's disturbing action on the planet's equator, proceeding from this cause, will be altogether insensible.

The disturbing forces of the satellites exerted upon the plane of the equator, in the cases of the major planets, however, must be considerable in magnitude, especially so far as relates to the inner satellites, and very complicated in its character, the precession and nutation of each of the satellites separately being combined in affecting the actual position of the pole of the planet.

Since, however, these phenomena are necessarily local, and manifested only to observers on the planet, they offer merely speculative interest to the terrestrial astronomer.

188.

CHAPTER X.

THE MOON.

The moon an object of popular interest.—Although it be in mere magnitude, and physically considered, one of the most insignificant bodies of the solar system, yet for various reasons, the MOON has always been regarded by mankind with feelings of profound interest, and has been invested by the popular mind with various influences, affecting not only the physical condition of the globe, but also the phenomena of the organised world. It has been as much an object of popular superstition as of scientific observation. These circumstances, doubtless, are in some degree owing to

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its striking appearance in the firmament, to the various changes of form to which it is subject, and above all to its proximity to the earth, and the close alliance between it and our planet.

189. Its distance.-The distance of the moon from the earth is assumed to be about thirty times the earth's diameter, or in round numbers 238,800 miles.

190. Linear value of 1" on it.-The linear value which corresponds to the visual angle of one second of space on the surface of the moon is 1158 mile. Any space, therefore, upon the moon, measured by its visual angle, can be reduced to its actual linear value, provided its direction be at right angles to the visual ray, which it will be if it be at the centre of the lunar disk. If it be between the centre and the edges it will be foreshortened by the obliquity of the moon's surface to the line of vision, and, consequently, the linear value thus computed will be the real linear value diminished by projection, which, however, can be easily allowed for, so that the true linear value can be obtained for every part of the lunar disk.

191. Its apparent and real diameter.-The apparent diameter of the moon is subject to a slight variation, owing to a corresponding variation due to the small ellipticity of its orbit. Its mean value is found to be 31' 9" 58, or, from the most exact methods, 2164 miles.

Since the superficial magnitude of spheres is as the squares, aud their volume or solid bulk as the cubes, of their diameters, it follows, that the superficial extent of the moon is about the fourteenth part of the surface, and its volume about the forty-ninth part of the bulk, of our globe.

192. Apparent and real motion. The moon, like the sun, appears to move upon the celestial sphere in a direction contrary to that of the diurnal motion. Its apparent path is a great circle of the sphere, inclined to the ecliptic at an angle of about 5° 8′ 48′′. It completes its revolution of the heavens in 274 7" 43".

This apparent motion is explained by a real motion of the moon round the earth at the mean distance above mentioned, and in the time in which the apparent revolution is completed.

193. Hourly motion, apparent and real. Since the time taken by the moon to make a complete revolution, or 360° of the heavens, is 274 7h 43m, or 655h.72, it follows, that her mean apparent motion per day is 13° 10′ 35′′, and per hour is 32′ 56′′, which is a little more than her mean apparent diameter. The rate of the moon's apparent motion on the firmament may therefore be remembered by the fact, that she moves over the length of her own apparent diameter in an hour.

For the method of determining the linear value of an arc of 1°, 1', or 1" at a distant object, see Chapter XXIII

Since the linear value of 1" at the moon's distance is 1158 mile, the linear value of 1' is 69 miles, and, consequently, the real motion of the moon per hour in her orbit, is 2289 miles. Her orbital motion is therefore at the rate of 383 miles per minute.

194. Orbit elliptical. Although in its general form and character the path of the moon round the earth is, like the orbits of the planets and satellites, circular, yet when submitted to accurate observation, we find that it is strictly an ellipse or oval, the centre of the earth occupying one of its foci. This fact can be ascertained by inmediate observation upon the apparent magnitude of the moon. It will be easily comprehended that any change which the apparent magnitude, as seen from the earth, undergoes. must arise from corresponding changes in the moon's distance from us. Thus, if at one time the disk of the moon appears larger than at another time, as it cannot be supposed that the actual size of the moon itself could be changed, we can only ascribe the increase of the apparent magnitude to the diminution of its distance. Now we find by observation that such apparent changes are actually observed in its monthly course around the earth. The moon is subject to a small though perceptible variation of apparent size. We find that it diminishes until it reaches a minimum, and then gradually increases until it reaches a maximum.

When the apparent magnitude is least, it is at its greatest distance, and when greatest, at its least distance. The positions in which these distances lie are directly opposite. Between these two positions the apparent size of the moon undergoes a regular and gradual change, increasing continually from its minimum to its maximum, and consequently between these positions its distance must gradually diminish from its maximum to its minimum. If we lay down on a chart or plan a delineation of the course or path thus determined, we shall find that it will represent an oval, which differs however very little from a circle; the place of the earth being nearer to one end of the oval than the other.

195. Moon's apsides—apogee and perigee—progression of the apsides.-The point of the moon's path in the heavens at which its magnitude appears the greatest, and when, therefore, it is nearest the earth, is called its PERIGEE; and the point where its apparent size is least, and where, therefore, its distance from the earth is greatest, is called its APOGEE. These two points are called the MOON'S APSIDES.

If the positions of these points in the heavens be observed accurately for a length of time, it will be found that they are subject to a regular change; that is to say, the place where the moor appears smallest will every month shift its position; and a corresponding

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change will take place in the point where it appears largest. movement of these points in the heavens is found to be in the same direction as the general movement of the planets; that is, from west to east, or progressive. This phenomenon is called the PRO

GRESSION OF THE MOON'S APSIDES.

The rate of this progression of the moon's apsides makes a complete revolution in a similar direction as the motion of the moon, in 3232.5753 mean solar days, or nearly nine years.

196. Moon's nodes-ascending and descending node their retrogression. If the position of the moon's centre in the heavens be observed from day to day, it will be found that its apparent path is a great circle, making an angle of about 5° with the ecliptic. This path consequently crosses the ecliptic at two points in opposite quarters of the heavens. These points are called the MOON'S NODES. Their positions are ascertained by observing from time to time the distance of the moon's centre from the ecliptic, which is the moon's latitude; by watching its gradual diminution, and finding the point at which it becomes nothing; the moon's centre is then in the ecliptic, and its position is the NODE. The node at which the moon passes from the south to the north of the ecliptic is called the ASCENDING NODE, and that at which it passes from the north to the south is called the DESCENDING NODE.

These points, like the apsides, are subject to a small change of position, but in a retrograde direction. They make a complete revolution of the ecliptic in a direction contrary to the motion of the sun in 186 years, being at the rate of 3′ 10′′6 per day.

197. Rotation on its axis.-While the moon moves round the earth thus in its monthly course, we find, by observations of its appearance, made even without the aid of telescopes, that the same hemisphere is always turned towards us. We recognise this fact by observing that the same marks are always seen in the same positions upon it. Now in order that a globe which revolves in a circle around a centre should turn continually the same hemisphere towards that centre, it is necessary that it should make one revolution upon its axis in the time it takes so to revolve. For let us suppose that the globe, in any one position, has the centre round which it revolves north of it, the hemisphere turned toward the centre is turned toward the north. After it makes à quarter of a revolution, the centre is to the east of it, and the hemisphere which was previously turned to the north must now be turned to the east. After it has made another quarter of a revolution the centre will be south of it, and it must be now turned to the south. In the same manner, after another quarter of a revolution, it must be turned to the west. As the same hemisphere is successively turned to all the points of the compass in one revolution, it

is evident that the globe itself must make a single revolution on its axis in that time.

It appears, then, that the rotation of the moon upon its axis, being equal to that of its revolution in its orbit, is 27d 7h 43m, or 655 43. The intervals of light and darkness to the inhabitants of the moon, if there were any, would then be altogether different from those provided in the planets; there would be about 327h 52m of continued light alternately with 327h 52m of continued darkness; the analogy, then, which, as will hereafter appear, prevails among the planets with regard to days and nights, and which forms a main argument in favour of the conclusion that they are inhabited globes like the earth, does not hold good in the case of the moon.

198. Inclination of axis of rotation.—Although as a general proposition it be true that the same hemisphere of the moon is always turned toward the earth, yet there are s. all variations at the edge called librations, which it is necessary to notice. The axis of the moon is not exactly perpendicular to its orbit, being inclined to the ecliptic at the small angle of 1° 30' 10"8. By reason of this inclination, the northern and southern poles of the moon lean alternately in a slight degree to and from the earth.

199. Libration in latitude. When the north pole leans towards the earth, we see a little more of that region, and a little less when it leans the contrary way. This variation in the northern and southern regions of the moon visible to us, is called the LIBRATION IN LATITUDE.

200. Libration in longitude. In order that in a strict sense the same hemisphere should be continually turned toward the earth, the time of rotation upon its axis must not only be equal to the time of rotation in its orbit, which in fact it is, but its angular velocity on its axis in every part of its course, must be exactly equal to its angular velocity in its orbit. Now it happens that while its angular velocity on its axis is rigorously uniform throughout the month, its angular velocity in its orbit is subject to a slight variation; the consequence of this is that a little more of its eastern or western edge is seen at one time than at another. This is called the LIBRA

TION IN LONGITUDE.

201. Diurnal libration.—By the diurnal motion of the earth, we are carried with it round its axis; the stations from which we view the moon in the morning and evening, or rather when it rises and when it sets, are then different according to the latitude of the earth in which we are placed. By thus viewing it from different places, we see it under slightly different aspects. This is another cause of a variation, which we see in its eastern and western edges: this is called the DIURNAL LIBRATION.

202. Phases of the moon. While the moon revolves round