398 NOTES. 



circle, or two right angles. The points E and e are the solstices, 

 where the sun is at his greatest distance from the equinoctial. 

 The equinoctial is everywhere ninety degrees distant from its poles 

 N and S, which are two points diametrically opposite to one another, 

 where the axis of the earth's rotation, if prolonged, would meet the 

 heavens. The northern celestial pole N is within 1 24' of the pole 

 star. As the latitude of any place on the surface of the earth is equal to 

 the height of the pole above the horizon, it is easily determined by 

 observation. The ecliptic E T e ^ is also everywhere ninety degrees 

 distant from its poles P and p. The angle P C N, between the poles P 

 and N of the equinectial and ecliptic, is equal to the angle e C Q., called 

 the obliquity of the ecliptic. 



NOTE 47, p. $. Longitude. The vernal equinox, T, 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 

 direction in which they all revolve. The vernal equinox is generally 

 called the first point of Aries, though these two points have not coin- 

 cided 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 T, 

 fig. 10, be the line of the equinoxes, and T the vernal equinox, the true 

 longitude of a planet p is the angle T Sp, and its mean longitude is the 

 angle T C m, the sun being in S. Celestial longitude is the angular 

 distance of a heavenly body from the vernal equinox ; whereas terres- 

 trial 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, 57. Equation of the center. The difference between 

 T Cm and T Sp, 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 PDA the true place is before the mean place. At 

 its maximum, the equation of the center measures C S, the eccentricity 

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

 an ellipse and in a circle whose diameter AP 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 

 perihelion, 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. Q. 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 mCn; 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 

 mCn, there will be ten degrees in the arc mn. It is evident that there 

 are 90 in a right angle, mC d, or quadrant, since it is the fourth part 

 of 3600. 



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 dSdand DSd, which measure her apparent distance from the 

 sun, are right angles. 



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

 6, C S is the eccentricity of the orbit, P Q A D. Thf less C 8, the m<re 



