NOTES. 399 



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

 CS is zero, the ellipse becomes a circle. 



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

 of the sun. P N A it, the orbit jv_. jg 



of a planet moving from west 

 to east in the direction N p. 

 Let E N m e n be the shadow 

 or projection of the orbit on 

 "the plane of the ecliptic, then 3? 

 N S w is the intersection of 

 these two planes, for theorbif 

 rises above the plane of the 

 ecliptic toward Np, and sinks 

 below it at N P. The angle 

 p N m, which these two planes 

 make with one another, is the N 



inclination of the orbit P N p A to the plane of the ecliptic. 



NOTE 54, p. 9. Latitude of a planet. The angle p S m. fig. 12, or the 

 height of the planet p above the ecliptic E N m. In this case the latitude 

 is north. Thus, celestial latitude is the angular distance of a celestial 

 body frour the plane of the ecliptic, whereas terrestrial latitude is the 

 angular distance of a place on the surface of the earth from the equator. 



NOTE 55, p. lO.J\Todes. The two points N and a, fig. 12, in which 

 the orbit N A n P of a planet or comet intersects the plane of the 

 ecliptic eNEw. The part N An of the orbit lies above the plane of 

 the ecliptic, and the part nPN below it. The ascending node N is the 

 point through which the body passes in rising above the plane of. the 

 ecliptic, and the descending node n is the point in which the body sinks 

 below it. The nodes of a satellite's orbit are the points in which it 

 intersects the plane of the orbit of the planet. 



NOTE 56, p. 10. Distance from the sun. S p in fig. 12. If T be the 

 vernal equinox, then T Sp is the longitude of the planet p, mSp is its 

 latitude, and Sp its distance from the sun. When these three quantities 

 are known, the place of the planet p is determined in space. 



NOTE 57, pp. 10, 58. Elements of an orbit. Of these there are seven. 

 Let P N A n, fig. 12, be the elliptical orbit of a planet, C its center, S the 

 sun in one of the foci, T the point of Aries, and E N e n the plane of the 

 ecliptic. The elements are, the major axis A P ; the eccentricity C S ; 

 the periodic time, that is, the time of a complete revolution of the body 

 in its orbit; and the fourth is the longitude of the body at any given in- 

 stant: for example, that at which it passes through the perihelion. P, the 

 point of its orbit nearest to the sun. That instant is assumed as the origin 

 of time, whence all preceding and succeeding periods are estimated. 

 These four quantities are sufficient to determine the form of the orbit and 

 the motion of the body in it. Three other elements are requisite for 

 determining the position of the orbit in space. These are, the angle 

 T S P, the longitude of the perihelion : the angle A N e, which is the 

 inclination of the orbit to the plane of the ecliptic ; and lastly, the angle 

 T S N, the longitude of N the ascending node. 



NOTE 58, p. 10. Whose planes, <$-c. The planes of the orbits, as 

 P N A n, fig. 12, in which the planets move, are inclined or make small 

 angles e N A with the plane of the ecliptic E N e n, and cut it in straight 

 lines, N S n passing through S the center of the sun. 



NOTE 59, p. 12. Momentum. Force measured by the weight of a 

 body and its speed, or simple velocity, conjointly. The primitive momen- 

 tum of the planets is, therefore, the quantity of motion which was im- 

 pressed upon them when they were first thrown into space. 



NOTK 60, p. 12. UnftfMf pfjiiV&rivm. A body is paid to be in pqnili- 



