THE SCIENCE OF ASTRONOMY. 295 



This has given rise to many beautiful mathematical investigations, and 

 developments into series. But the modern researches have shown that 

 we are not sure of our theoretical results obtained in this way, and we 

 are thrown back on empirical methods. Perhaps the theories may be 

 improved. It is to be hoped that the treatment of the differential 

 equations may be made more general and complete. Efforts have been 

 made in this direction by Newcomb and others, and especially by 

 Glyden, but so far without much practical result. 



The problem of three bodies was encountered by the mathematicians 

 who followed Newton, and many efforts were made to solve it. These 

 efforts continue, although the complete investigations of Lagrange 

 appear to put the matter at rest. The only solutions found are of very 

 special character. Laplace used one of these solutions to ridicule the 

 doctrine of final causes. It was the custom to teach that the moon was 

 made to give us light at night. Laplace showed by one of the special 

 solutions that the actual conditions might be improved, and that we 

 might have a full moon all the time. But his argument failed, since 

 such a system is unstable and cannot exist in nature. But some of the 

 efforts to obtain partial solutions have been more fruitful, and G. W. 

 Hill has obtained elegant and useful results. These methods depend 

 on assumed conditions that do not exist in nature, but are approxi- 

 mately true. The problem of two bodies is a case of this kind, and the 

 partial solutions may illustrate, but will not overcome, the fundamental 

 difficulty. 



The arrangement of our solar system is such that the distances of 

 the planets from one another are very great with respect to their 

 dimensions, and this facilitates very much the determination of their 

 motions. Should two bodies approach very near each other the dis- 

 turbing force might become great, even in the case of small masses. In 

 the case of comets this condition happens in nature, and the comet may 

 become a satellite of a planet, and the sun a disturbing body. In this 

 way it is probable that comets and meteoric streams have been intro- 

 duced into our solar system. We have here an interesting set of prob- 

 lems. This question is sometimes treated as one of statics, but since the 

 bodies are in motion it belongs to dynamics. Further study may throw 

 light on some relations between the asteroids and the periodical comets. 



The great question of astronomy is the complete and rigorous test 

 of the Newtonian law of gravitation. This law has represented observa- 

 tions so well during a century and a half that it is a general belief that 

 the law will prove true for all time, and that it will be found to govern 

 the motions of the stars as well as those of our solar system. The proof 

 is cumulative and strong for this generality. It will be a wonderful 

 result if this law is found rigorously true for all time and throughout 

 the universe. Time is sure to bring severe tests to all theories. We 



