14 POPULAR LECTURES AND ADDRESSES. 



of the heavenly bodies cannot become infinite, but 

 must oscillate within certain limits. 



l-'or instance, during a period very many 

 thousands of years say the eccentricity of the 

 earth's orbit round the sun may go on increasing. 

 It might be supposed that that eccentricity 

 could go on increasing so much, that at last the 

 earth's path might cross that of one of the other 

 planets. Serious disturbances in the motions of 

 the two bodies might result, or even a fatal 

 collision. But the theorem of the French mathe- 

 maticians asserts, that while the eccentricity 

 might go on increasing for a certain time, it has 

 its limits ; thus declaring that there arc oscilla- 

 tions and variations, but no continued variation in 

 OIK- direction. And this is a very important 

 theorem undoubtedly. On details of the formula 

 expressing it are founded all the calculations of 

 modern physical astronomers regarding what are 

 called the secular variations of the elements of 

 the planetary orbits. lUit the I'Ycnch mathema- 

 tns were quite aware that, in making this state- 

 ment, they neglected resistance. Those who 



