THE SECULAR EFFECTS OF THE IXXREASE OF THE 



SUN'S MASS UPON THE MEAN MOTIONS, MAJOR 



AXES AND ECCENTRICITIES OF THE 



ORBITS OF THE PLANETS. 



Bv T. J. J. SEE. 

 {Read April _'/, 1911.) 



In the days of Newton, Lagrange and Laplace, it was assumed 

 that the formation of the planetary system was essentially complete, 

 and the sun's attraction rigorously constant from age to age ; and it 

 was scarcely deemed necessary to consider the secular efit'ects of 

 slight modifying causes such as the downfall of cosmical dust upon 

 the bodies composing the solar system. But the progress of the past 

 century has shown that the Newtonian hypothesis of a constant 

 mass and a central attraction depending wholly on the distance, but 

 not on the time, is at best a very rough approximation to the truth; 

 for in addition to the downfall of cosmical dust upon all the bodies 

 of our system, it has been shown by the researches of Arrhenius, 

 Schwartzchild and others, that the sun especially is losing finely 

 divided matter under the action of repulsive forces such as we see 

 illustrated in the streamers of the corona and the tails of comets. 

 In our modern studies of the orbital motions of the heavenly bodies, 

 therefore, we have to take the central mass as variable with the 

 time, and consider the small secular changes which will follow from 

 a variation of the central attraction incident to a gradual change of 

 mass. 



These questions have been treated in some form by many of the 

 successors of Newton ; and even this great philosopher himself in 

 one case supposed that the central mass might be varied by a comet 

 falling into the sun.^ Laplace devotes considerable attention to the 

 secular equations for determining the eltects of the decrease of the 

 sun's mass due to loss of light, then supposed to be of corpuscular 



* " Principia." Lib. III., last proposition. 



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