M 



ASTRONOMY. 



[LUNAR PARALLAX, BTC. 



enable* ui to perceive a small portion of the disc, other- 

 wise invisible. The fi rut, or the libration in kngttvd*, 

 aris from the two motion* of rotation and translation 

 not being exactly equal, and thai the appearance of the 

 moon'* borders will likewise partake of this inequality. 

 The second arises from the circumstance that the axis of 

 rotation is not exactly perpendicular to the plane of its 

 orbit, but is inclined to it by an angle of 37'. This is 

 called the libratio* in latitude. Thus, when the moon is 

 at L (Fig. 44), we see without difficulty the pole q, but 

 Pi.44. 



applying the corroctioM for parallax and semi-diameter 

 before mentioned. We thus determine its angular dis- 

 placement* with respect to the equator, and find that it 

 describes a revolution in a period of about 27 days, re- 

 turning nearly to the point of departure ; but if, during 

 several lunations, its progress be watched, we shall find 

 that its inclination to the equator differs by an angle 

 varying from 18 to 20. Instead, however, of referring 



to the equator, if we 

 use the ecliptic, we 

 shall find that it con- 

 stantly preserves the 

 same relation viz., 

 an inclination of about 



Kl 46. 



cannot perceive the opposite pole p. But when the moon 

 is at L' the pole p becomes visible, while the pole q 

 vanishes from our view. The position of a spot near the 

 moon's equator at a, would, therefore, to a spectator on 

 the earth, appear in different positions ; this libration is 

 directed perpendicularly to the plane of its. orbit, or 

 nearly to the plane of the ecliptic. 



Finally, there is a tliird libration, called the diurnal 

 libration, which depends on the positions of the moon to 

 an observer on the earth's surface, in the interval from 

 rising to setting. In consequence of the proximity of 

 the moon, the spots will not retain the same positions at 

 rising and passage across the meridian ; but the effect at 

 its maximum is only 32", and is scarcely worth attention, 

 PARALLAX OF THB MOON. Before attempting to deduce 

 the orbit that the moon describes around the earth, we 

 ahall find it imperatively necessary to correct the results 

 of observation for "Parallax." Parallax is the angle 

 which the radius of the earth subtends at the moon. It 

 is seen entirely in a vertical direction on the meridian, 

 and can be determined in the following manner : 



If the zenith distance of the moon's centre be observed 

 by two astronomers at two stations, differing considerably 

 in latitude north and south, as Greenwich and the Cape 

 of Good Hope, as (B and C) in Fig. 45, we shall have 



the angles Z B L and 

 B' C L. The latitudes 

 of the two stations, 

 B E and C O E, are 

 well-known, and their 

 difference of longitude is 

 also accurately known. 

 The motion of the moon 

 in zenith distance is 

 known to a great cer- 

 tainty, and thus the 

 data are perfectly comparable. If the moon were as dis- 

 tant as the fixed stars, the sum of the zenith distances 

 thus found would be precisely equal to the sum of the 

 latitudes, north and south, of the two observatories, 

 when proper allowance has been made for refraction. 

 But the effect of parallax will be in both cases to 

 increase the apparent zenith distances, and the observed 

 sum will be greater than the sum of the latitudes by the 

 whole amount of the two parallaxes. In this manner, 

 by corresponding observations of the moon at her meri- 

 dian passage, the constant of the horizontal parallax has 

 been determined. (See Note at page 92C). 



In its practical application to the results of observa- 

 tion, it is customary to correct the zenith distances for 

 the angle made by the direction of the plumb-line at each 

 station, and a line drawn to the centre of the earth. 

 This is termed the angle of the vertical ; and its value, 

 a* well as the radiiix of the earth at the two stations, are 

 known from the "figure of the earth." The point of 

 reference to which horizontal parallaxes are referred, in 

 the case of the moon, is the radius of the equator ; and, 

 in this manner, the individual result* of observation 

 corrected for the effect of parallax in altitude, which 

 varies as the line of the zenith distance. 



Ta Mix>s'i PATU i* TUB HEAVENS. By the transit 

 instrument and mural circle, we are now able to trace 

 Uio path of the moon in the heavens, after properly 



The figure (Fig. 40) 

 will show the orbit of 

 the moon in its pro- 

 gress through two 

 lunations. EE repre- 

 sents the earth's equa- 

 tor, A B C D the eclip- 

 tic, and near A BCD 

 the orbit of the moon is seen inclined to the ecliptic by 

 an angle of 5 9'. The intersections of the orbit N N' 

 are termed the nodes. Supposing N to represent the 

 node at one lunation, at the next it will be found to 

 have retrograded to N', and at each succeeding lunation 

 in the same manner, always preserving the same incli- 

 nation to the ecliptic, till, at the end of about 19 years, 

 it returns to the position N. This will naturally cause 

 a variation in its inclination with regard to the equator, 

 which is chown by the figure (Fig. 47). 



Let A B C D be the ecliptic, E E the equator, N 

 L N' the orbit of the pj g . 47. 



moon, O P the axis of 

 the earth, O K the axis 

 of the ecliptic, and O R 

 the axis of the moon's 

 orbit. In the motion 

 of the axis of the moon's 

 orbit around the pole 

 of the ecliptic, it will E 

 describe a small circle, 

 R R' R", round the 

 point K. The axis O 

 R describes a cone of 

 revolution, of which the 

 axis of the figure is the 

 line O K. In this mo- 

 tion the angle of O R with O K is always equal to the 

 inclination of the moon's orbit, or 6 9'. The inclination 

 that the equator will make with the moon's orbit will be 

 successively the angles P O R', P O R, and P Q R"; 

 and as the angle P O K is the obliquity of the ecliptic, 

 or 23 28', the angles P O R' and P R" will he the 

 minima and maxima inclinations, being 18 19' ;md 28" 

 37' respectively. (See also Fig. 31). 



MOTION OF THE APSIDES. The line of the apsides of 

 the moon has been found to have a very rapid, though 

 not uniform motion, amounting to 6' 41 daily, which is 

 direct, or according to the order of the signs, and the 

 major axis of the ellipse thus makes a complete revo- 

 lution in 3,232i days. In one hundred Julian years, or 

 3(1,525 days, the line of the apsides makes eleven com- 

 plete revolutions -f 109 2' 4<>"-6; and at the present 

 time this motion decreases 50" '4203 in one hundred 

 years. The longitude of the perigee may be calculated 

 for any period that in 1801, January 1 (Paris time), 

 being 266 Iff 7" '5. The true longitude of the moon, 

 supposing it to move in an elliptic orbit, whose eccen- 

 tricity is 0-0548442 in parts of the semi-major axis, or 

 the greatest equation of the centre is 6 17' l'.'"7, 

 might thus be calculated for any period in the ordinary 

 manner ; but a great number of minute correct 

 must be applied to it before the tabular plane, thus 

 obtained, would be found to agree with the observed 

 plane of the moon. 

 EVKC-TIO.N, VARIATION, AND ANNUAL EQUATION. 



