NOTES. 467 



N A n P of a planet or comet intersects the plane of the ecliptic e N E . The 

 part N A n of the orbit lies above the plane of the ecliptic, and the part n P N 

 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. 12. Distance from the sun, S p in fig. 12. If <Y> be the vernal 

 equinox, then <Y> S p is the longitude of the planet p, m S p is its latitude, and 

 S p its distance from the sun. When these three quantities are known, the 

 place of the planet p is determined in space. 



NOTE 57, pp. 12, 67- 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 centre, S the sun in one 

 of the foci, <y> the point of Aries, and E N en the plane of the ecliptic. The 

 elements are the major axis A P ; the excentricity 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 instant: 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 <Y> S P, the longitude of the perihelion; the angle ANe, which is the 

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

 <Y* S N, the longitude of N the ascending node. 



NOTE 58, p. 12. Whose planes, $c. The planes of the orbits, as P N A w, 

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

 with the plane of the ecliptic EN en, and cut it in straight lines, N S n passing 

 through S, the centre of the sun. 



NOTE 59, p. 14. Momentum. Force measured by the weight of a body and 

 its speed, or simple velocity, conjointly. The primitive momentum of the 

 planets is, therefore, the quantity of motion which was impressed upon them 

 when they were first thrown into space. 



NOTE 60, p. 14. Unstable equilibrium. A body is said to be in equilibrium 

 when it is so balanced as to remain at rest. But there are two kinds of equili- 

 brium, stable and unstable. If a body balanced in stable equilibrium be slightly 

 disturbed, it will endeavour to return to rest by a number of movements to and 

 fro, which will continually decrease till they cease altogether, and then the body 

 will be restored to its original state of repose. But, if the equilibrium be un- 

 stable, these movements to and fro, or oscillations, will become greater and 

 greater till the equilibrium is destroyed. 



NOTE 61, p. 16. Retrograde. Going backwards, as from east to west, con- 

 trary to the motion of the planets. 



- 



NOTE 62, p. 16. Parallel directions. Such as never meet, though prolonged 

 ever so far. 



H H 2 



