Page:Encyclopædia Britannica, Ninth Edition, v. 2.djvu/841

about 27, and the point now directly opposite the sun has, of course, advanced by the same amount. The moon has, therefore, to travel further on before she is again exactly opposite the sun. It is found that this happens rather more than 2 days later ; or, in other words, that the in terval between successive full moons amounts to about 29| days. This interval is called a lunar month, or lunation; the period during which the moon completes the circuit of the heavens being called a sidereal month. The lunation

is also called a synodical month.

The path in which the moon travels is found to be inclined at an angle of about 5 9 to the ecliptic. But continued observation shows that the path, while retaining this inclination, shifts slowly in position the points where it intersects the ecliptic gradually retrograding (on the whole) until, in the course of about 18

It follows, from the varying position of the moon s apparent path with respect to the ecliptic, that her range north and south of the equator is variable. When she crosses the ecliptic, at or near the two points where the ecliptic crosses the equator, the inclination of her path to the ecliptic is either added to or subtracted from the in clination of the ecliptic to the equator, so that her range in declination is, in one case, 23 27 + 5 9 , or 28 36 ; and in the other, 23 27 - 5 9 , or 18 1 8 . When she crosses the ecliptic at or near the two points where the ecliptic is furthest from the equator, the inclination of her path to the equator is nearly the same as that of the ecliptic, the two paths the ecliptic, or sun s path, and the apparent lunar path crossing the equator at different points.

Thus far there is nothing in the observed celestial mo tions which opposes itself to the belief that the earth is a fixed centre around which the celestial bodies are carried the star-sphere by the diurnal rotation, the sun circling round the earth in his yearly course on the ecliptic, and the moon in her monthly (lunar) course on a variable path, and both these orbs partaking in the diurnal rotation of the star-sphere, just as bodies in a moving vehicle par take in the motion of the vehicle, even though they may also be in motion among themselves.

One circumstance in the moon s apparent motions serves, however, to show that the bodies thus far observed lie at different distances, and falls properly to be considered in this place, seeing that the attention of astronomers must first have been directed to it when they were engaged in determining the moon s motions.

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Fig. 15.—Diagram illustrating Lunar Parallax.

The earth being, as we have seen, a globe, and the sun and moon being apparently carried round this globe by the daily rotation, which is uniform, it would naturally occur to astronomers that, if these motions take place around the centre of the earth, they cannot appear altogether uniform as seen from the eccentric position of an observer placed anywhere on the surface. The stars, indeed, seem to be carried uniformly round, but that has been explained as due to their enormous distance. The sun moving mani festly within the stellar concave, and the moon travelling apparently within the sun s orbit (as may be inferred from j^ ph aaes ^ it m ight W ell be that their motions would be found affected by the eccentricity of the observer s position. Suppose, for example, that the centre of the earth is at P, fig. 15, and the observer is at E, and let EM H represent a line of sight from E to the moon s centre when she is in the horizon (refraction being neglected). Then a line PM H from the centre of the earth to the moon is inclined to the horizon line EM U ; and if we draw Pm h parallel to EM., so that either line represents the direction of the moon as observed from E, we see that, if she were observed from P, she would appear raised by the angle included be tween the lines PM H and Pm b . From E, then, she is seen lower down than her true geocentric position bv the angle M H P?n h ; and similarly it is seen that, if the moon be at M, the direction EM in which she is seen is lower down that *s, is less inclined to the horizon line Ew h by the angle EMP, or its equal, MPm ; if the moon were at M , the displacement would be equal to the angle EM P ; and only when she is at the zenith Z does her direction EZ agree with her geocentric direction PZ. Her observed path from horizon to horizon, when she rises high in the south, but does not reach the zenith, will be as the path m l m 3 m s (fig. 1G), where her geocentric path is as M E M.,M W . This will happen if she is near enough to the earth for the angle EM H P (fig. 15), to be appreciable; and all that has here been said of the moon is equally true of the sun, or any other celestial body. But in their case no appreci able displacement occurs (at least none which the earlier modes of observation could indicate). In the case of the moon the displacement is very marked, being found to amount nearly to a degree when the moon is on the horizon. Such displacement is called parallax. Thus, when any celestial body is at M (fig. 15), the angle EMP (or MP//&), between the geocentric direction PM, and the apparent direction EM, is called the parallax of the body. When the celestial body is at M^ so that its true direction is horizontal, the parallax EM B P, is manifestly greater than for any other position of the body at the same dis tance from P. This maximum parallax is called the horizontal parallax, and may be defined as the maximum angle subtended by the earth s radius, as supposed to be seen from the body.

Fig. 16.—Observed aud Geocentric Paths of the Moon.

It may be noticed, in passing, that if the geocentric distance of a celestial body=d, the earth s radius=r, and the horizontal parallax=p, then

This is manifest from fig. 15, where sm. PM H E=:r . Again, in the case of a body at M, using the same symbols, and calling the apparent altitude MEM K a, and the parallax p, we have

That is,

For every celestial body, except the moon, the parallax