NOTES. 



443 



supposed to be sufficient alone, but M. Poisson has shown that to be a 

 mistake ; that these three conditions are requisite for the necessary con- 

 vergence of the series, and that therefore the stability of the system 

 depends on them conjointly with the periodicity of the sines and cosines of 

 each term. The author is aware that this note can only be intelligible to 

 the analyst, but she is desirous of correcting an error, and the more so as 

 the conditions of stability afford one of the most striking instances of 

 design in the original construction of our system, and of the foresight and 

 supreme wisdom of the Divine Architect. 



NOTE 78, p. 22. Resisting medium. A fluid which resists the motions 

 of bodies, such as atmospheric air, or the highly elastic fluid called ether, 

 with which space is filled. 



NOTE 79, p. 23. Obliquity of the ecliptic. The angle e op q, fig. 11, 

 between the plane of the terrestrial equator q op Q, and the plane of the 

 ecliptic E cyo e. The obliquity is variable. 



NOTE 80, p. 23. Invariable plane. In the earth the equator is the 

 invariable plane which nearly maintains a parallel position with regard to 

 itself while revolving about the sun, as in fig. 20, where E Q represents 

 it. The two hemi- 

 spheres balance one 

 another on each side 

 of this plane, and 

 would still do so if 

 all the particles of 

 which they consist 

 were moveable 

 among themselves, 

 provided the earth 

 were not disturbed 

 by the action of the 

 sun and moon, which 

 alters the parallel- 

 ism of the equator 

 by the small varia- 

 tion called nutation, 

 to be explained hereafter. 



NOTE 81, p. 24. If each particle, 

 be planets moving in 

 their orbits about the 

 centre of gravity of the 

 system. Let P S M, 

 P 7 S M 7 , &c., be portions 

 of these orbits moved 

 over by the radii vec- 

 tores S P, S P 7 , &c., in 

 a given time, and let 

 p S m, p' S m', &c., be 

 their shadows or pro- 

 jections on the invari- 

 able plane. Then, if the 

 numbers whichrepresent 



Let P, P', P", &c., fig. 21, 

 Fig. 21. 



M 



