244 THE POPULAR SCIENCE MONTHLY. 



orbits of the planets are to some extent affected. The mutual actions 

 of the planets present many problems of the highest interest, and, it 

 should be added, of the greatest difficulty. Many of these difficulties 

 have been overcome. It is the great glory of the French mathema- 

 ticians to have invented the methods by which the nature of the solar 

 system could be studied. The results at which they arrived are not a 

 little remarkable. They have computed how much the planets act and 

 react upon each other, and they have shown that in consequence of 

 these actions the orbit of each planet gradually changes its shape and 

 its position. But the crowning feature of these discoveries is the 

 demonstration that these changes in the orbits of the planets are all 

 periodic. The orbits may fluctuate, but those fluctuations are confined 

 within very narrow limits. In the course of ages the system gradually 

 becomes deformed, but it will gradually return again to its original po- 

 sition, and again depart therefrom. These changes are comparatively 

 so small that our system may be regarded as substantially the same 

 even when its fluctuations have attained their greatest amplitude. 

 These splendid discoveries are founded upon the actual circumstances 

 of the system, as we see that system to be constituted. Take, for in- 

 stance, the eccentricities of the orbits of the planets around the sun. 

 Those eccentricities can never change much ; they are now small quan- 

 tities, and small quantities those eccentricities must forever remain. 

 The proof of this remarkable theorem partly depends upon the fact 

 that the planets are all revolving around the sun in the same direction. 

 If one of the planets we have named were revolving in an opposite 

 direction to the rest, the mathematical theory would break down. We 

 would have no guarantee that the eccentricities would forever remain 

 small as they are at present. In a similar manner, the planets all move 

 in orbits whose planes are inclined to each other at very small angles. 

 The positions of those planes fluctuate, but these fluctuations are con- 

 fined within very narrow limits. The proof of this theorem, like the 

 proof of the corresponding theorem about the eccentricities, depends 

 upon the actual conditions of the planetary system as we find it. If 

 one of the planets were to be stopped, turned round, and started off 

 again in the opposite direction, our guarantee for the preservation of 

 the planes would be gone. It therefore follows that, if the system is 

 to be permanently maintained, all the planets must revolve in the same 

 direction. 



In this connection it is impossible not to notice the peculiar cir- 

 cumstances presented by the comets. By a sort of convention, the 

 planets have adopted, or, at all events, they possess, movements which 

 fulfill the conditions necessary if the planets are to live and let live ; 

 but the comets do not obey any of the conditions which are imposed 

 by the planetary convention. The orbits of the comets are not nearly 

 circles. They are sometimes ellipses with a very high degree of ec- 

 centricity ; they are often so very eccentric that we are unable to dis- 



