LUNAR EVECTION, ETC.] 



ASTRONOMY. 



937 



These are the three greatest periodical fluctuations of the 

 moon in longitude. The efi'ect of the evectiou can be 

 explained by a diminution of the equation of the centre, 

 when the moon is at opposition and conjunction, and by 

 an increase in its value when at quadratures ; the amount 

 of the correction in the latter case not, however, being 

 BO considerable as in the former. If we suppose the Hue 

 of apsides to be in syzigy that is, new or full moon 

 the observed longitude will be found to be 80' greater 

 than the calculation ; and if the apsides are in quad- 

 ratures, or first and last quarters, the observed will be 

 found to be smaller by the same amount. The evectiou 

 depends on the double of the elongation of the moon 

 from the sun, the mean anomaly being subtracted from 

 the product, and the coefficient of this quantity, amount- 

 ing to 1 2CC 30". Hence, when the apsides are in 

 syziu'ies, at which period the eccentricity is greatest, the 

 greatest equation of the centre is 7 3iX ; and when in 

 quadrature, at which it is smallest, it is only 4 58'. At 

 the latter position of the apsides, the gravitation is 

 greatest at apogee, and least at perigee ; and in the 

 former case, the gravitation is greatest at perigee, 

 and- least at apogee ; and, consequently, the eccen- 

 tricity of the orbit is increased. The discovery of 

 the equation of the centre and evection is due to 

 Hipj.archus and Ptolemy. The more accurate obser- 

 vations of Tycho proved the existence of a second irre- 

 gularity, which is termed the variation. The observed 

 planes disagreeing with the computed act of syzigies and 

 quadratures, sometimes as much as 37' when the line of 

 apsides was in the octants, Tycho found that it depended 

 on the elongation of the moon from the sun. The cause 

 of this is the position and distance of the sun and the 

 earth ; for when the sun's disturbing force is at right 

 angles with the radius vector, the moon's motion is ' 

 accelerated from the quadratures to syzigies, and retarded 

 in the contrary direction. The coefficient is 35' 42", 

 and the increase is double the elongation of the moon 

 and sun. The annual equation follows nearly the same 

 law as the equation of the centre of the earth's orbit, 

 only with opposite signs. This is greatest in the months 

 of March and September, but almost vanishes in June 

 and December. From this it du rives its name the 



fig. 48, 



its nodes being subtracted, the coefficient is 8' 48*. In 

 addition to this, there is another remarkable inequality, 

 depending principally on the compression of the earth at 

 the poles, and which may be termed the spheroidal in- 

 equality. The theory of universal gravitation has come 

 to the aid of observation in detecting numerous inequa- 

 lities, which observation alone would scarcely ever be 

 able to discover, and has explained all those which were 

 previously known to exist. 



MOTION OF THE Moox IN SPACE. The" curve which 

 the moon describes in space may be laid down in the 

 following simple manner : Let the earth, T (Fig. 48), 

 pass round the sun, S' in the orbit T, T, T", <tc. An 

 observer on the earth will see the moon in various 

 positions in respect to the sun. When the earth is at T, 

 the moon will be at L, or in conjunction ; when at T', 

 the moon will be at L', or at its first quarter ; at L" at 

 full ; at L'" at last quarter ; and as the earth describes 

 its path around the sun, it follows that the curve described 

 by the moon in space will pass through the points L, L', 

 L", L'", <tc. This line is represented in the diagram as 

 considerably more curved than it really is, the distance 

 T L being onlyj^jth of the distance T S. 



ON THE HARVEST MOON. The phenomenon of the 

 harvest moon, when for some nights together, at that 

 period of the year, the moon rises nearly at the same 

 time, depends on the inclination of the ecliptic with the 

 horizon. That part of the ecliptic in which this inclina- 

 tion makes the least possible angle lies in the constella- 

 tion Aries (in north latitude) ; and when the sun is in 

 Libra, as at the time of the autumnal equinox, the 

 moon, when at full, will be near the first point of Aries, 

 and but little distant from the ecliptic. It is clear that, 

 when at this part of its orbit, as it travels from west to 

 east, the times of successive rising must be within a short 

 period of each other ; and if the ecliptic were wholly 

 parallel to the horizon, then it would rise exactly at the 

 same time on each night. As the moon, however, is 

 a little inclined to the ecliptic at some periods, this will 

 make the difference even less. In the latitude of Lon- 

 don, the least possible difference between the times of 

 successive rising of the moon, has been calculated at 

 seventeen minutes. When the constellation Libra rises, 

 Fig. 49. 



period being an anomalistic solar year, and the coefficient 

 11' 13". The motion of the moon, in consequence, is 

 slowest in winter and quickest in summer. It is due to 

 the disturbing force of the sun in different parts of its orbit, 

 being greatest at its least distance, and least at aphelion. 



The greatest of the periodical disturbances of the moon 

 in latitude depends on twice the elongation of the moon 

 from the sun, from which the distance of the moon from 



VOL. j. 



the ecliptic makes the greatest possible angle with the 

 horizon, and the differences between the times of suc- 

 cessive risings of the moon is then greatest. This takes 



60 



