404 



NOTES. 



variable plane which nearly maintains a parallel position with regard to 

 itself while revolving about the 'sun, as in fig. 20, where EQ represents 

 it. The two hemispheres balance one another on each side of this plane, 

 and would still do so if al! the particles of which they consist were mov- 

 able among themselves, provided the earth were not disturbed by the 

 action of the sun and moon, which alters the parallelism of the equator 

 by the small variation called nutation, to be explained hereafter. 



NOTE 81, p. 23. If each particle, <J-c. Let P, P', P", foe., fig. 21, be 

 planets moving in their orbits about the center of gravity of the system. 



Fig. 21. 



Let P S M, P' S M', &c. be portions of these orbits moved over by the radii 

 vectores, S P, S P', foe., in a given time, and let p S m, p' S m' &c. be their 

 shadows or projections on the invariable plane. Then, if the numbers 

 which represent the masses of the planets, P, P' &c. be respectively mul- 

 tiplied by the numbers representing the areas or spaces p S m, p' S ', &c. 

 the sum of the whole will be greater for the invariable plane than it 

 would be for any plane that could pass through S, the center of gravity 

 of the system. 



NOTE 82, p. 23. The center of gravity of the solar system lies within 

 the body of the sun, because his mass is much greater than the masses 

 of all the planets and satellites added together. 



NOTE 83, pp. 24, 35. Conjunction. A planet is said to be in conjunc- 

 tion when it has the same longitude with the sun, and in opposition 

 when its longitude differs from that of the sun by 180 degrees. Thus two 

 bodies are said to be in conjunction when they are seen exactly in the 

 same part of the heavens, nnd in opposition when diametrically opposite 

 to one another'. Mercury and Venus, which are nearer to the sun than 

 the earth, are called inferior planets, while all the others, being farther 

 from the sun than the earth, are said to be superior planets. Suppose 

 the earth to be atE, figure 24 ; then a superior planet will be in conjunc- 

 tion with the sun at C, and in opposition to him when at O. Again, 

 suppose the earth to be in O, then an inferior planet will be in conjunc- 

 tion when at E, and in opposition when at F. 



NOTE 84, p. 25. The periodic inequalities are computed for a given 

 time ; and consequently for a given form and position of the orbits of the 

 disturbed and disturbing bodies. Although the elements of the orbits 

 vary so slowly that no sensible effect is produced on inequalities of a 

 short period ; yet, in the course of time, the secular variations of the ele- 

 ments change the forms and relative positions of the orbits so much, that 

 Jupiter and Saturn, which would have come to the same relative positions 

 with regard to the sun and to one another after 850 years, do not arrive 

 at the same relative positions till after 918 years. 



