20 STABILITY OF THE SYSTEM. SBCT. HI. 



planets revolving within the orbit of any one, such as 

 Mars, by adding to the interior mass, increase the at- 

 tracting force of the sun, which, therefore, must con- 

 tract the dimensions of the orbit of that planet, and di- 

 minish its periodic time ; while the planets exterior to 

 Mars' orbit must have the contrary effect. But the 

 mass of the whole of the planets and satellites taken to- 

 gether is so small, when compared with that of the sun, 

 that these effects are quite insensible, and could only 

 have been discovered by theory. And, as it is certain 

 that the length of the major axes and the mean motions 

 are not permanently changed by any other power what- 

 ever, it may be concluded that they are invariable. 



With the exception of these two elements, it appears 

 that all the bodies are in motion, and every orbit in a 

 state of perpetual change. Minute as these changes 

 are, they might be supposed to accumulate in the course 

 of ages, sufficiently to derange the whole order of na- 

 ture, to alter the relative positions of the planets, to put 

 an end to the vicissitudes of the seasons, and to bring 

 about collisions which would involve our whole system, 

 now so harmonious, in chaotic confusion. It is natural 

 to inquire, what proof exists that nature will be pre- 

 served from such a catastrophe ? Nothing can be known 

 from observation, since the existence of the human race 

 has occupied comparatively but a point in duration, 

 while these vicissitudes embrace myriads of ages. The 

 proof is simple and conclusive. All the variations of 

 the solar system, secular as well as periodic, are ex- 

 pressed analytically by the sines and cosines of circular 

 arcs (N. 76), which increase with the time ; and, as a 

 sine or cosine can never exceed the radius, but must 

 oscillate between zero and unity, however much the 

 time may increase, it follows that, when the variations 

 have accumulated to a maximum, by slow changes, in 

 however long a time, they decrease, by the same slow 

 degrees, till they arrive at their smallest value, again to 

 begin a new course ; thus forever oscillating about a 

 mean value. This circumstance, however, would be 

 insufficient, were it not for the small eccentricities of 

 the planetary orbits, their minute inclinations to the 

 plane of the ecliptic, and the revolutions of all the bodies, 



