19".] INCREASE OF THE SUN'S MASS. 273 



it correspondingly in going from the aphelion to the perihelion ; so 

 that only periodic changes of the elements c and tt occur. 



Accordingly it foUows that the only possible cause which could 

 have diminished and practically obliterated the eccentricities of the 

 orbits of the planets and satellites is the secular action of a resisting 

 medium, as fully set forth in Volume II. of my " Researches on the 

 Evolution of the Stellar Systems," 1910. Increasing the central 

 mass accelerates the mean motions, and thus hecomes very sensible 

 in the theory of the motions of the planets; but it has no eftect on 

 the shape of their orbits. The almost circular form of the planetary 

 orbits, therefore, may be referred to the secular action of a resisting 

 medium and to no other cause whatsoever. 



This result is of no ordinary interest, since it refers the round- 

 ness of the planetary orbits to but a single physical cause, and gives 

 us what mathematicians call a unique solution of the leading problem 

 of cosmogony. For Babinet's criterion shows beyond doubt that 

 the "planets never were detached from the central bodies which now 

 govern their motions ; and the argument given in A'olume II. of my 

 " Researches " proves that all these bodies were formed in the 

 distance and afterwards neared the central masses about which they 

 now revolve. The demonstration of the true mode of formation of 

 our solar system is therefore supported by the necessary and suffi- 

 cient conditions usually required in mathematical reasoning; and we 

 may say that the laws of the formation of the solar system have been 

 confirmed by mathematical criteria having all the rigor required in 

 the science of geometry. This generalization will, I think, add not 

 a little to our interest in the geometry of the heavens; and it is 

 equally worthy of the attention of the astronomer, the geometer and 

 the natural philosopher, who so long struggled to unfold the wonder- 

 ful process involved in the formation of the planetary system. 



U. S. Naval Observatory, 

 Mare Island, California, 

 March 20. 191 1. 



