MOON 



297 



manner in which the moon moves over the surface 

 of the sky, changing place like a driving cloud, 

 though not with the same rapidity. 



We can reduce all such motions to movements 

 in the two easily-noted directions, first, north and 

 south ; secondly, east and west. And it is most con- 

 venient to take the sun as our point of reference. 

 Sometimes the moon is north of the sun, and some- 

 times south, sometimes east of it, and sometimes 

 west. It moves, then, in both of our two directions. 

 But when we compare the east and west motion 

 with the north and south we soon note an important 

 difference. The east and west motion is continu- 

 ously and steadilv /rom tcest to east, carrying the 

 moon right round the heavens ; starting at new 

 moon near the sun, and progressing until at full 

 moon nearly the whole breadth of the skv separates 

 them ; then still progressing, until the sun is 

 approached again from the np|>osit side. In fact, 

 it the sun stood still at its setting for a lunar 

 month, we should see the moon soar steadily 

 upwards in the western skv, cross the whole ex- 

 panse of heaven, and pass wrm helow the eastern 

 liorixon. Then it would continue its course, re- 

 turning to the sun, beneath our feet, and reach 

 nearly its original position. To perform this 

 cycle the moon takes 2!f53 days, which is called 

 its ty>uM/if<i/ /M-riod. If we took a bright star as 

 the starting-point and goal of the moon's circle, 

 instead of the sun, we should find the moon only 

 take 27 "32 days to return to the star. This is 

 called the moon's sidereal period. The cause of the 

 difference is that the star is steady in its position, 

 while the sun slowly moves in his annual course 

 in the same direction as the moon, which therefore 

 has to overtake the sun when returning to him. 

 Thus the motion from west to east is always in the 

 same direction ; but this is not the case with the 

 north and south motion. While performing its 

 cycle from west to east, say in the month of March, 

 the moon lx>gins by travelling northward at first, 

 but latterly swings as far southward. In autumn 

 the reverse is the case (see below). In Decem- 

 ber full moon occurs at the most northern point 

 of it< course, and in June at the southernmost. 

 In winter, therefore, we have at night most light 

 from the full moon, and in summer least. In 

 March the (/,/,';//< have least moonlight, and in 

 September they have most. Attentively consider- 

 ing all these movements, we soon see that the 

 moon travels round the earth in a curve not differ- 

 ing very much from a circle, for as it always appears 

 nearly of the same size, it must remain constantly 

 at nearly the same distance from the earth. 



We have now almost insensibly passed from the 

 observation of apparent motions to the idea of an 

 orbit or path, which the moon traverses. And this 

 leads at once to the consideration of the nature of 

 this orbit, or the moon's real motions. Accurate 

 olwervation reveals that the moon's distance from 

 the centre of the earth is not the same in different 

 parts of its orbit. It varies in apparent diameter 

 from a maximum of 33' 31" to a minimum of 

 29' 21". As this variation forbids the idea that the 

 orliit is a circle concentric with the earth, so it 

 also forbids the idea that it is a circle eccentrically 

 placed in regard to the earth. The true form is 

 found to be that of an ellipse having an eccentricity 

 of -05491, with the earth in one of the foci. This 

 ellipse is, however, continually distorted by various 

 inetjualities t<> lie noticed hereafter, chiefly due to 

 the sun's attractive energy, which continually con- 

 tends with that of the earth for the mastery over 

 it* satellite. 



The lunar orbit is inclined to the ecliptic (or 

 earth's orbit) at an angle of 5" 8' 40". The points 

 where the two intersect are called the Nodei (q.v. ), 

 and the line joining them the line of nodes. The 



point of her orbit nearest the earth is the perigee, 

 that most distant is the apogee, and the line joining 

 them is called the line of apsides. Both the line of 

 nodes and line of apsides change their place, the 

 former turning completely round in 6793-391 davs 

 = 18 '6 years, the latter in 3232 - 57 days = nearly 

 9 years. These motions take place, however, in 

 opposite directions : the line of apsides revolves 

 with the moon's orbital motion, the line of nodes 

 against it. These motions are due to the sun's 

 disturbing influence ( see PERTURBATIONS ). Each 

 day, on an average, the moon describes 13 10' 35" 

 of the circle of her path. To do this requires, at 

 its distance, an actual velocity of 2273 miles 

 per hour. This velocity is found to be exactly 

 what is required to balance the moon's weight, 

 supposing that to l>e reduced in proportion to the 

 square of its distance from the earth. Thus Newton 

 concluded that the force retaining the moon in its 

 orbit is simply its weight, or the mutual gravitation 

 between it and the earth. This conclusion is 

 verified by the elliptic form of the orbit, and the 

 place of the earth in one focus. For an orbit of 

 this form is produced by a force varying inversely 

 as the square of the distance. Both the form 

 of the orbit, then, and the varying nature of the 

 force governing it, as well as the powerful disturbing 

 influence of the sun, cause variations in the moon's 

 velocity. I'sually these are allowed for by taking 

 as a foundation the menu or average angular 

 velocity given above, and considering its variations 

 under the title of inequalities, which must all 

 be allowed for if the moon's place in the sky is to 

 be predicted with accuracy at any time. 



first in order is the elliptic inequality discovered 

 by Hipparchus. It is caused by the quicker or 

 slower motion of the moon as it passes over the 

 nearer or more distant parts of its elliptic orbit. 

 Its value is 6 18' nearly. Secondly, there is the 

 minimi n/uiitinii (discovered by Tycho Brahe), a 

 yetirli/ effect, arising from the increase and diminu- 

 tion of the sun's disturbing force, as the earth 

 approaches or leaves the sun in its annual course. 

 This amounts to 11' 10", and, as our earth is nearer 

 the sun in winter and farther off in Rummer, :t 

 causes the moon to be behind its mean place in 

 the first part of the year and l>efore it in the later 

 months. Thirdly, there is the variation (discovered 

 by Alml-Wefa). This arises from the changes in 

 direction and amount of the sun's disturbing force, 

 which are caused by the moon's motion in its own 

 orbit. Its effect on the moon's longitude may 

 amount to 39 31". Fourthly, there is the evcction, 

 deiiending on the position of the axis of the moon's 

 orbit, and the line of nodes, with regard to the 

 sun. Its effects are complicated, but mav amount 

 to P 16' 27" on the moon s longitude, and 8' 57" on 

 its latitude. 



Besides these, the parallactic inequality is inter- 

 esting, as giving a means of calculating the sun's 

 distance from our earth. The sun's disturbing 

 action varies in amount as the moon in its orbit 

 is nearest or farthest away from the sun. This 

 variation depends on the ratio of the moon's 

 distance to that of the sun ; so that, knowing the 

 amount of the inequality and the distance of the 

 moon, a value may ! found for the sun's distance. 

 Hansen showed by this means that the value long 

 received for the sun's distance required to be 

 diminished. See PARALLAX, SUN. 



The secular acceleration of the moon was dis- 

 covered by Halley in 1693 from a comparison of the 

 times of Eclipses (q.v.) many centuries apart. 

 This inequality is an increase of the moon's mean 

 motion by about 12" per century. It is partly due 

 to a slow change in the form of the earth's orbit, 

 by which the sun's disturbing force is slightly 

 lessened, which is equivalent to an increase of the 



