NOTES. 437 



NOTE 47, p. 9. Longitude. The vernal equinox, cyo, fig. 11, is the 

 zero point in the heavens whence celestial longitudes, or the angular 

 motions of the celestial bodies, are estimated from west to east, the direc- 

 tion in which they all revolve. The vernal equinox is generally called the 

 first point of Aries, though these two points have not coincided since the 

 early ages of astronomy, about 2233 years ago, on account of a motion in 

 the equinoctial points, to be explained hereafter. If S cyo, fig. 10, be the 

 line of the equinoxes, and cyo the vernal equinox, the true longitude of a 

 planet p is the angle cyo S p, and its mean longitude is the angle oo C m, 

 the sun being in S. Celestial longitude is the angular distance of a 

 heavenly body from the vernal equinox ; whereas terrestrial longitude is 

 the angular distance of a place on the surface of the earth from a meridian 

 arbitrarily chosen, as that of Greenwich. 



NOTE 48, pp. 9, 58. Equation of the centre. The difference between 

 cyo C m and r *j S p, fig. 10 ; that is, the difference between the true and 

 mean longitudes of a planet or satellite. The true and mean places only 

 coincide in the points P and A ; in every other point of the orbit, the true 

 place is either before or behind the mean place. In moving from A 

 through the arc A Q P, the true place p is behind the mean place m ; and 

 through the arc P D A the true place is before the mean place. At its 

 maximum, the equation of the centre measures C S, the excentricity of the 

 orbit, since it is the difference between the motion of a body in an ellipse 

 and in a circle whose diameter A P is the major axis of the ellipse. 



NOTE 49, p. 9. Apsides. The points P and A, fig. 10, at the ex- 

 tremities of the major axis of an orbit. P is commonly called the perihe- 

 lion, a Greek term signifying round the sun ; and the point A is called the 

 aphelion, a Greek term signifying at a distance from the sun. 



NOTE 50, p. 9. Ninety degrees. A circle is divided into 360 equal 

 parts, or degrees ; each degree into 60 equal parts, called minutes ; and 

 each minute into 60 equal parts, called seconds. It is usual to write these 

 quantities thus, 15 16' 10", which means fifteen degrees, sixteen minutes, 

 and ten seconds. It is clear that an arc m n, fig. 4, measures the angle m 

 C n ; hence we may say, an arc of so many degrees, or an angle of so 

 many degrees ; for, if there be ten degrees in the angle m C n, there will 

 be ten degrees in the arc m n. It is evident that there are 90 in a right 

 angle, m C d, or quadrant, since it is the fourth part of 360. 



NOTE 51, p. 9. Quadratures." A celestial body is said to be in quad- 

 rature when it is 90 degrees distant from the sun. For example, in fig. 

 14, if d be the sun, S the earth, and p the moon, then the moon is said to 

 be in quadrature when she is in either of the points Q or D, because the 

 angles Q S d and D S d, which measure herv apparent distance from the 

 sun, are right angles. 



NOTE 52, p. 9. Excentricity. Deviation from circular form. In fig. 

 6, C S is the excentricity of the orbit P Q A D. The less C S, the more 

 nearly does the orbit or ellipse approach the circular form ; and, when C S 

 is zero, the ellipse becomes a circle. 



NOTE 53, p. 9. Inclination of an orbit. Let S, fig. 12, be the centre 

 of the sun, P N A n the orbit of a planet moving from west to east in the 



