liest authentic record (721 B. C.), as well as the hours of those of ancient intermediate date, did not agree with the hours at which they must have taken place in accordance with the present average motion of our satellite; but that they so differed as to point to the fact, that the moon's mean motion is somewhat quicker now than in ancient time. Astronomers failed to explain the cause of this, until, in 1787, it was accounted for by La Place, from a study of the effect which certain disturbances of Jupiter's orbit, has produced on those of his satellites (see L, on p. 251).

We have learned (T, on p. 257,) that the excentricities of the orbits of the planets are affected by their mutual disturbances; and above (p. 307), that the excentricity of the earth's orbit affects the motion of the moon, by causing her to be taken nearer to the sun at one time of our year, than at another. Now the action of all the rest of the planets upon the earth has thus been, as it were, reflected to the moon; for the earth's excentricity has been diminishing for many ages, and there has been, in consequence, a continual lessening of that portion of the sun's interference with the size of the moon's orbit, which results at and near our perihelion.

"The size of the moon's orbit has gradually (but insensibly) diminished; but the moon's place in its orbit has sensibly altered, and the moon's angular motion has appeared to be perpetually quickened. This phenomenon was known to astronomers by the name of the acceleration of the moon's mean motion, before it was theoretically explained by La Place. On taking it into account, the oldest and the newest observations are equally well represented by theory."-Airy's Gravitation, p. 109.

THE MOON'S REAL PATH.

F The attractions of the sun and earth, alternately united and opposed, render the moon's path about us, comparatively, one of complex irregularity. But such is the sun's mass that, even at his great distance, the moon's gravity towards him is greater than her gravity towards the earth, and keeps her in an orbit every where concave towards

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him; although, from the proximity of the earth, the attraction of its inferior mass compels her meanwhile to "do service" as a satellite, by producing, alternately, an acceleration and retardation of her motion about the sun.

It will be interesting to perceive the beauty of that adjustment, by which the Hand that lighted up the sun, and projected the moon as the lesser light to rule the night," has brought her, in effect, to circle around our earth, by appearing first on one side and then on the other, whilst moving in an orbit about the sun himself, generally speaking, of the same form as our own.

Let the darker, continuous, line represent nearly 1-13th of the earth's orbitual path around the sun; let m, the moon, be represented by the smaller of the two dots, and e, the earth, be represented by the greater: (the sun being at least two feet distant in the direction given by the little index.) Then, of the five relative positions of the earth and moon, No. 1 will represent their positions at the new moon, or the beginning of the lunar month: No. 2, their positions at the quadrature or first quarter: No. 3, at full moon: No. 4, at the second quadrature or third quarter; and No. 5, at the next new moon.

It may be seen, that in pursuing her course along the dotted line from m of 1 to m of 2, she is moving less rapidly than the earth; but that, in moving during the second week, or from 2 to 3, she goes over a longer space than the earth does during that period. This is also the case in moving from 3 to 4; but she is again retarded in passing from 4 to 5 to be again a new moon, or have that hemisphere which is turned towards us in darkness, or enlightened only by reflection from the earth.

It will be perceived that, whilst thus compelled to accompany the earth by the force of its attraction, the moon is, all the while, yielding obedience to the sun in performing a curve around him; but that the parts of this curve which are gone over by the moon in equal times, are alternately less and greater, as she is alternately under the influence of the sum of the attractions of the sun and earth, (as at m 3), and the difference of their attractions (as at m 1, or m 5).

PROBLEM C.

CELESTIAL GLOBE.

To find, nearly, the stars over which the moon will pass during several lunations; and to exhibit the effect of various positions of her node upon her altitude.

Read pages 304-306.

RULE (1). Fasten a silken or cotton cord, of little thickness, around the globe; and make it, throughout, coincide with the ecliptic. (It will be found convenient for this purpose, to elevate the North Pole 2340, and to bring the first point of Cancer to the meridian).

2. Find the moon's ascending node, as given below, or in the ephemeris for every sixth day. Place a finger of the left hand upon the cord, exactly at the node's place; and push northward, with a finger of the right hand, that portion of the cord which is exactly three signs, or 90°, in advance of the node, until it is 54° to the north* of the ecliptic.

3. At six signs,† or 180°, from the ascending node, is the place of the descending node :-let the finger be placed upon this, so as to secure the cord at this point also, whilst at the 90th degree beyond, it is, in like manner, pushed 540 to the south.

4. The position of the cord now marks out the moon's path for the current month; and, since the places of the nodes for any two consecutive months differ only about 110, the moon's path for the last month and the succeeding one, as well as that for the present month, is thus nearly represented.

5. The pole being elevated for the latitude given, the points of greatest north and south declination of the cord

* The degrees of celestial latitude in the Zodiac are, generally, all marked out on the Celestial Globe.

+ If the ascending node be brought to one side of the horizon, the descending node will be found cut by the other side, whatever be the elevation of the pole, since there is always an exact half of the ecliptic above the horizon.

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when brought to the meridian, will enable us to find the greatest and least meridian altitudes possible, for the month, by counting upward from the south point of the horizon.

Example 1. What stars will lie in, or very near to, the moon's path when her ascending node (8) is 20 ; and what are the greatest and least meridian altitudes she can possibly have during such a lunation in latitude 51 North?

Here, having placed the cord so as, throughout, to coincide with the ecliptic, I arrange it as directed, by securing it at 20 and 20 my, whilst it is made to range to the 5th degree north of 20 II, and the 5th degree south of 20 : and thus placed, it shews that the moon's path (as seen from the earth's centre) will be over * of Capricornus, * of Pisces, the Pleiades and 8 in the Bull's horn, south of Pollux, (8 of Gemini,) just north of Regulus, (a of Leo,) just south of Spica, (a of Virgo,) and Antares, (a of Scorpio,) &c. By bringing the cord where its north and south declinations are greatest to the brazen meridian, and elevating the North Pole 51°, I find that it reaches an elevation above the south point of the horizon of 66 in one case, and of only about 91o in the other.

2. The moon's ascending node was 1° :-How did her path then lie with respect to Pollux-Presepe (in Cancer), Regulus, Spica, Antares, a and 8 of Capricornus, a and of Aries, the Pleiades, and Aldebaran (Hyades)?

B

Answer, 5° S. of Pollux, 6° N. of Spica, &c., &c.

3. About nine years and a half after the time of the position of the moon's node last given, her ascending node is 1° v :-How does her path now lie with respect to the above-mentioned stars?

4. D's & 1° Ŏ:-Note the distance of her geocentric path during that lunation, from the Pleiades-8 of Taurus (Bull's horn), Pollux, the Presepe (Cancer), Regulus, Spica, y of Libra, Antares, a and 8 of Capricornus ?

5. D's 8, 27 V
6. D's 8, 3

Note, in each of these two cases, the moon's positions with regard to the following stars, and her greatest and least meridian altitudes for those two months, in latitude 51° N. :Mesartim, of Aries, the Pleiades, the Presepe, Regulus, Spica, Antares, 8 of Capricornus.

* See question 11, p. 162.

7. What are the greatest and least altitudes of the moon possible at her southing in lat. 51 N., if her ascending node be 1° :-is not the position of her node given in question 6, nearly the least favourable for her altitude, and which position is least of all so ?

8. Refer to the fifth column at the head of page 51: and find by the globe, from the place of the moon's ascending node for the 1st of June, given there, what stars she occulted or made a very near approach to during that month, as well as during the May and July of that year?

9. D's 8, 17° m :-Where exactly, did the moon's geocentric path lie :-note it particularly with reference to B of Scorpio, Antares, a and B (head of Capricornus), of Taurus, and Spica (a of Virgo); and find the greatest and least meridian altitudes possible, under these circumstances, in the latitude of Petersburgh?

PROBLEM D.

CELESTIAL GLOBE.

To find the time of the moon's "transit" or coming to the meridian, her longitude at noon being given.

RULE 1. If the moon be past "full," find her longitude for the noon of the preceding day;-if she be not yet full, find her longitude for the present (given) day.

2. Place the extreme corner of a very small patch of moistened paper, (or a small dot of ink,) on the ecliptic in the longitude thus found.

3. Bring the sun's place to the brazen meridian, and set the hour circle to 12. Turn the globe westward until the mark of the moon's longitude for the last noon come to the meridian, and count the time elapsed :—this would shew the time of her southing, if she had been fixed since the last noon.

4. Now shift (eastward) the mark of her longitude one quarter of a degree for every half-hour elapsed; and this

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