Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/868

798 M:, having completed her course from the sun to the sun again, she disappears, and we say it is new moon. The moon s absolute distance from the earth is obtained by means of her parallax, which on account of her proximity is very considerable. On comparing her parallaxes ob served at different times, they are found to differ con siderably in value. These differences in the value of the parallax arise from the variations of the moon s dis tance from tlie earth. But it is also observed to differ sensibly at different points of the earth s surface, even at the same instant of time, on account of the spheroidal figure of the earth. Hence it is necessary, in speaking of the horizontal parallax, to specify the place of the observation.

 

  HERE INTERVENES A SPACE EQUAL To -&amp;gt; ABOUT -190 TIMES THE DISTANCE: M, M 5 FIG. 34. Diagram illustrating the Phases of the Moon. FIG. 35. Diagram illustrating the Phases of the Moon.

 

  Since the parallax of the moon is subject to incessant variation, it is necessary to assume a certain mean value, about which the true and apparent values may be con ceived to oscillate. This is called the constant of paral lax. If we abstract all the inequalities of the lunar orbit, and suppose the moon to be at her mean distance and mean place, the constant of parallax will be the angle under which a given semidiameter of the earth is seen by a spectator at the moon in such circumstances. But, for convenience, the constant of parallax is understood to be&#61;earth. e i uat - j ad. which, see Chapter IV., is in reality moon ft mean diBt. 7 &#61;sine of the mean horizontal parallax. The best modern observations assign 57 2&quot;7 as the value of the lunar mean equatorial horizontal parallax, corre sponding to a distance of 238,818 miles. The mean equa torial parallax being 57 2&quot; 7, its double is 1 54 5&quot; 4, which expresses the angle subtended by the diameter of the earth at the distance of the moon. The angle subtended by the moon at the same distance is 31 5&quot; l ; whence the diameter of the moon i is to that of the earth as 31 5&quot; l is to 1 54 5&quot; 4, or as 3 to 11 nearly. The accurate expression of the above ratio is 1 : 0*27251 ; hence the true diameter of the moon is 2725 diameters of the terrestrial equator. The surface of the moon is consequently (0 02725) 2&#61;0742&#61;-J^.^J-TT of that of the earth, and its volume (0-2725) 3&#61;0-0202&#61;T^^TT OT, in round numbers, -^ths of the volume of the earth. For other elements, see table of Lunar Elements, p. 782. The Ascending Node of the lunar orbit is that point of the ecliptic through which the moon passes when she rises above the ecliptic towards the north pole ; it is distin guished by the character a. The Descending Node, y, is the opposite point of the ecliptic, through which she passes when she descends below that plane towards the south. The position of the nodes is not fixed in the heavens. They move in a retrograde direction, or contrary to the order of the signs; and their motion is so rapid that its effects become very apparent after one or two revolutions. The mean retrograde motion of the nodes is found, by the comparison of observations made at distant epochs, to amount to 19 21 18&quot; 3 in a mean solar year, and the time in which they make a tropical revolution is con sequently 6793-391 mean solar days. The inclination of the lunar orbit is observed to vary between 5 3 and 5 13. The mean inclination may be taken at 5 8.

The inclination of the lunar orbit to the plane of the terrestrial equator occasions considerable differences in the intervals between the moon s rising or setting on successive days, and gives rise to the phenomenon of the Harvest Moon. As the daily motion of the moon is about 1 3 from west to east, it follows that if she moved in a plane parallel to the equator, she would rise 50 minutes later every successive evening. For the sake of explanation, we may here suppose the moon to move in the plane of the ecliptic. Now, the time in which a given arc of the ecliptic rises above the horizon depends on its inclination to the horizon. In our latitudes the inclination of the ecliptic at different points to the horizon varies so much, that at the first point of Aries an arc of 1 3 becomes visible in the short space of 17 minutes, while at the 23d of Leo the same arc will only rise above the horizon in 1 hour and 17 minutes. Hence, when the moon is near the first point of Aries, the difference of the times of her rising on two successive evenings will be only about 17 minutes; and as this happens in the course of every revolution, she will rise for two or three nights every month at nearly the same hour. But the rising of the moon is a phenomenon which attracts no attention, excepting about the time when she is full, that is, when she rises at sunset. In this case she is in opposition to the sun, and consequently, if she is in Aries, the sun must be in Libra, which happens during the autumnal months. At this season of the year, therefore, the moon, when near the full, rises for some evenings at nearly the same hour. This circumstance affords important advantages to the husbandman, on which account the phenomenon attracts particular attention. It is obvious that, as this phenomenon is occasioned by the oblique position of the lunar orbit with regard to the equator, the effect will be greater than what has just been described if the plane of that orbit makes a greater angle with the equator than the plane of the ecliptic does. But we have seen that the plane of the moon s orbit is inclined to the ecliptic in an angle exceeding 5; consequently, 