20 PLANETARY INEQUALITIES PERIODICAL. 



By this principle philosophers have, so to speak, 

 decomposed the physical system of the world, reduced 

 it to its single element, and then re-composed it. 

 Viewed in this relation, physical astronomy is, unques- 

 tionably, of all the sciences, the most complete, the 

 most sublime, and that in which the human intellect is 

 most elevated. " But that which gives it, above all, 

 an inestimable value, is its perfect certainty."" Other 

 branches of science have changed incessantly, and 

 several must still undergo modifications, several perhaps 

 be abandoned : yet, whatever be the progress of know- 

 ledge, whatever the expansion of intellect, the principle 

 of universal gravitation is established irrefragably, and 

 the main deductions from it rest on an immovable foun- 

 dation. 



Before I quit this subject, I venture upon one more 

 observation. It has been demonstrated by Lagrange 

 and Laplace, having been on some points preceded by 

 T. Simpson, Clairaut, Frisi, and others, that all the 

 planetary inequalities are PERIODICAL, each returning 

 after a certain time, to go through the same series of 

 changes which it had formerly exhibited; the whole sys- 

 tem oscillating, as it were, between certain limits which 

 it can never pass. Now, this property, so essential to 

 the well-being of the inhabitants of the several planets, 

 requires the concurrence of these four, independent, 

 conditions : that the force shall be inversely as the 

 square of the distance, that the masses of the revolving 

 bodies be small, compared with that of the central body, 

 that the eccentricities of the orbits be inconsiderable, 

 and that the planes of those orbits be originally not 

 much inclined to each other. The irresistible conclu- 

 sion Thus furnished is, that all this is the work of intelli- 



