The moon's age is usually reckoned from the new moon, and the rules by which Easter Is found depend, or should depend, upon a correct knowledge of this age at the beginning of the year, called the Erect.
Hut all readers should remember that the sun and moon by which Easter is found are not the real bodies, but fictitious ones, moving not with the real but the overage motions, and therefore sometimes before And sometimes behind the real bodies. It should then be no matter of surprise if, as will happen, Easter Sunday should sometimes Ire seven days sooner or later than it would be if the real bodies were employed. [FASTER, MrTIIOD or 1''INDIX0.] We now 'some to the actual motion of the moon round the earth, which Is the most complicated quiation in astronomy. Iteughly speak ing. it may be said that the moon's 'notion is circular,which is sufficient for the explanation of the phases; it in somewhat, but very little, more correct to say it is elliptical. If the moon's orbit were actually exhibited in space, an ellipse might be found which would nearly fit one of its convolutions ; but the succeeding couvolutions would depart further and further from such an ellipse, and it would be nineteen years before a convolution would again occur which is situated in space near to the ellipse with which we started. And though astronomers have found a way of simplifying the question, by supposing the moon has had or «ill have in the course of the year. We may explain the apparent path in the heavens by the annexed figure, which represents a portion of the apparent heavens : T is the earth in the centre; .r.r.rx is the circle of the ecliptic ; yyyy and sztz are small circles parallel to the ecliptic, and each distant from it in the heavens by an angle of 5° 8' 47"'9. The moon may rise 8' 47'15 above xxx.r, or fall as much below ass:; but these two circles are chosen because they are means: that is to say, for every convolution which rises above xxxx there will be another, described at some other time, at which it falls short of xxxx; so that in a long series of years the sum of all the arcs by which convolutions rise above xxxx would be equal to the sten of those area by which other convolutions do not attain xxxx. The angle 5° 8' 47'.9 is, in the astronomer's elliptic fiction, the mean inclination of the orbit to the plane of the ecliptic. The dotted line is one complete convolution of the orbit and the greater part of another. We suppose the moon to set off from its highest point (high and low have reference to the ecliptic) A, at or very near yyyy: thence it falls to the descending node n, and continues to descend to its lowest point c, whence it rises to the ascending node n, and thence ascends to E, thence to the next descending node thence to o, 110 lowest point (at or near razz), and to tho next ascending node ti, &c. In this way
the whole of the lunar zodiac is interlaced with the convolutions of its orbit, which go on for ever ; nor have we any reason to suppose that the cycle of convolutions is over complete, so as to begin again.
The first thing we have to notice is what is called the regressive motion [Morton] of the nodes. The first node we meet with Is n, and the next, D, is not exactly opposite to a, but a little behind the opposite point ; the next, r, is still more behind R. The words before and behind have reference to the direction of the motion. This recension of the node amounts, one year of 365 days with another, to 19' 19' 42'316, and the node makes a complete retrograde revolution in 679313910S mean solar days, or IS'6 years nearly. The point in which the moon ascends through the ecdptic falls back more than twice the moon's diameter in each revolution. The amount, however, is subject to some variation ; that given above is its average.
Again, the apparent diameter of the moon is observed to vary, owing to an alteration of her distance from the earth- When least, it is 29' 2'91 ; when greatest, 33' 31".07. But it is observed OIL the least and greatest diameters of a single revolution are not exactly the A.111111 as those of another revolution ; and also that the place where the diameter is least is not exactly opposite to that in which it is greatest, but always in advance. Thus the diameter, being greatest at A, becomes least at r, in advance of the point opposite to A, greatest again at p (in advance of A), and least again at R. Now the Apparent diameter must be least when the distance is greatest, and rice vend ; the point of a convolution most distant from the earth is called the apo-gee, that nearest to the earth the peri-gee. There is, then, a progression of the apogee, and its average quantity is no less than 6' 41" for each solar day, or 40' 39' 45'36 in 365 days, which is equivalent to a complete revolution in 3232'575343 mean solar dale, or about nine years. The quantities above given are averages, for the actual progression is irregular.