moon at its greatest declination, and, of course, without the CHAP. VII. plane of the ring. Let P be the polar star. The attraction of m on the ring inclines it to the moon, and causes it to have a slight motion on its center; but the motion of this ring is the motion of the whole earth, which must cause the earth's axis to change its position in relation to the star P, and in relation to all the stars. When the moon is on the other side of the ring, that is, opposite in declination, the effect is to incline the equator to the opposite direction, which must be, and is, indicated by an apparent motion of all the stars. A slight alternate motion of all the stars in declination, corresponding to the declinations of the sun and moon, was carefully noted by Dr. Bradley, and since his time has been fully verified and definitely settled: this vibratory motion is known by the name of nutation, and it is fully and satisfactorily explained on the principles of universal gravity; and conversely, these minute and delicate facts, so accurately and completely conforming to the theory of gravity, served as one of the many strong points of evidence to establish the truth of that theory. ral effect of nutation il. (206.) By inspecting Fig. 46, it will be perceived that The gene. when the sun and moon have their greatest northern declinations, all the stars north of the equator and in the same hemi- lustrated by sphere as these bodies, will incline toward the equator; or all Fig. 46. the stars in that hemisphere will incline southward, and those in the opposite hemisphere will incline northward; the amount of vibration of the axis of the earth is only 9′′.6 (as is shown by the motion of the stars), and its period is 18.6, or about nineteen years, the time corresponding to the revolution of the moon's node. When the moon is in the plane of the equator, its attraction can have no influence in changing the position of that plane; and it is evident that the greatest effect must be when the declination is greatest. Where the node must be to the moon's The moon's declination is greatest when the longitude of to correspond the moon's ascending node is 0, or at the first point of Aries. The greatest declination is then 28° on each side of the clination. greatest de. CHAP. VII. equator; but when the descending node is in the same point, the moon's greatest declination is only 18°. Hence there will be times, a succession of years, when the moon's action on the protuberant matter about the equator must be greater than in an opposite succession of years, when the node is in an opposite position. Hence, the amount of lunar nutation depends on the position of the moon's nodes. Monthly nu. tation, effect small. The mean moon on the It is very natural to suppose that the period of lunar nutation would be simply the time of the revolution of the moon; and so, in fact, it is; but the corresponding amount is very small, only about one-tenth of a second. This is because half a lunar revolution, about 13 days, while the moon is on one side of the equator, is not a sufficient length of time for the moon to effect much more than to overcome the inertia of the earth; but, in the space of nine years, effecting a little more than a mean result at every revolution, the amount can rise to 9".6, a perceptible and measurable quantity. (207.) The mean course of the moon is along the ecliptic: effect of the its variation from that line is only about five degrees on each mass of mat- side; hence, the medium effect of the moon on the protuberant around mass of matter at the equator is the same as though the ter the equator. Solar nu tation. moon was all the while in the ecliptic. But, in that case, its effect would be the same at every revolution of the moon; and the earth's equator and axis would then have an equilibrium of position, and there would be no nutation, save the slight monthly nutation just mentioned, which is too small to be sensible to observation; and the nutation that we observe, is only an inequality of the moon's attraction on the protuberant equatorial ring; and, however great that attraction might be, it would cause no vibration in the position of the earth, if it were constantly the same. We have, thus far, made particular mention of the moon, but there is also a solar nutation; its period is, of course, a year; and it is very trifling in amount, because the sun attracts all parts of the earth nearly alike; and the short period of one year, or half a year (which is the time that the unequal attraction tends to change the plane of the ring in one direction), is too short a time to have any great effect, on CHAP. VII. the inertia of the earth. The solar nutation, in respect to declination, is only one second. (208.) Hitherto we have considered only one effect of nutation that which changes the position of the plane of the equator—or, what is the same thing, that which changes the position of the earth's axis; but there is another effect, of greater magnitude, earlier discovered, and better known, resulting from the same physical cause, we mean the PRECESSION OF THE EQUINOXES. First prin examined. We again return to first principles, and consider the mutual attraction between a ring of matter and a body situated ciples again out of the plane of the ring; the effect, as we have several times shown, is to incline the ring to the body, or (which is the same in respect to relative positions), the body inclines to run to the plane of the ring. plane of the The mean attractions of the sun and one plane, the ecliptic. The mean attraction of the moon is in the ecliptic. The sun is all the while in the ecliptic. mean attraction of both sun and moon is in one plane, the moon are in ecliptic; but the equator, considered as a ring of matter surrounding a sphere, is inclined to the plane of the ecliptic by an angle of 231 degrees, and hence the sun and moon have a constant tendency to draw the equator to the ecliptic, and actually do draw it to that plane; and the visible effect is, to make both sun and moon, in revolutions, cross the equator sooner than they otherwise would, and thus the equinox falls back on the ecliptic, called the precession of the equinoxes. sion of the equinoxes. The annual mean precession of the equinoxes is 50".1 of The precesarc, as is shown by the sun coming into the equinox, or crossing the equator at a point 50".1 before it makes a revolution in respect to the stars. Perhaps it is clearer to the mind to say, that the sun is drawn to the equator by the protuberant mass of matter around the earth, and, in consequence, arrives at the equator, in its apparent revolutions, sooner than it otherwise would. But the truth is, that the ecliptic is stationary in position, s* Natural mode of ex pression. CHAP. VII. and the equator, by a slight motion, meets the ecliptie; which motion is caused by the attractions of the sun and moon, as has been several times explained. the equinox. es. The true If the moon were all the while in the ecliptic, the precesphysical cause of the sion of the equinoxes would then be a constantly flowing quanprecession of tity, equal to 50".1 for each year; but, for a succession of about nine years, the moon runs out to a greater declination than the ecliptic, and, during that time, its action on the equatorial matter is greater than the mean action, and then comes a succession of about nine years, when its action is less than its mean; hence, for nine years, the precession of the equinoxes will be more than 50".1 per year, and, for the nine years following, the precession will be less than 50".1 for each year; and the whole amount of variation, for this inequality, in respect to longitude, is 17".3, and its period is half a revolution of the moon's nodes. This inequality is called the equation of the equinoxes, and varies as the sine of the longitude of the moon's nodes. Equation The equation of the equinoxes, of course, affects the length of the equi- of the tropical year, and slightly, very slightly, affects side noxes. Mean and time. real time. There is a true equinox and a mean equinox; and, as sidetrue sidereal real time is measured from the meridian transit of the equinox, there must be a true sidereal and a mean sidereal time; but the difference is never more than 1.1 s. in time, and, generally, it is much less. Explanation of Fig. 47. (209.) In the hope of being more clear than some authors have been, in explaining the results of precession, we present Fig. 47. E represents the pole of the ecliptic, and the great circle around it is the ecliptic itself. P is the pole of the earth, 23° 27′ from the pole E, and around P, as a center, we have attempted to represent the equator, but this, of course, is a little distorted; and are the two opposite points where the ecliptic and equator intersect; E is the first meridian of longitude; P is the first meridian of right ascension. The angle EP is 23° 27', and EP, produced, is the meridian passing through the solstitial points. To obtain a clear conception of the precession of the equinoxes, the stars the ecliptic, and its pole E, must be considered as FIXED, CHAP. VII as having a slow motion of 50".1 per an and the line From the num, on the ecliptic, in a retrograde direction; and this must fixed posi carry the pole P, around the point E, as a center, carrying tion of the ecliptic, and also the solstitial points backward on the ecliptic. of the stars have proper motions; but, putting that stance out of the question, the stars are fixed, and the eclip Some also of the circum- stars, the stars never change lati tic is fixed; therefore, the stars never change latitude, but tude. |