THE EULER-LAPLACE THEOREM ON THE DECREASE 



OF THE ECCENTRICITY OF THE ORBITS OF THE 



HEAVENLY BODIES UNDER THE SECULAR 



ACTION OF A RESISTING MEDIUM. 



By T. J. J. SEE. 

 (Read April 24, 191 5.) 



In the " Mecanique Celeste," Liv. VII., Chap. VI., §§ 29-30, 

 and Liv. X., Chap. VII., § 18, Laplace has developed the mathe- 

 matical theory of the secular action of a resisting medium, and ap- 

 plied it to the motions of the moon and planets. The first dis- 

 cussion herein cited was published in Volume HI. of the " Mecanique 

 Celeste," 1802. It is on this discussion by Laplace that modern 

 investigators chiefly base their treatment of the problems of a 

 resisting medium. Laplace's development of the theory therefore 

 has been of great service to science for more than a century. 



Recently, while occupied with a careful review of the theories of 

 magnetism and of gravitation since the time of Newton, I had occa- 

 sion to examine Euler's " Dissertatio de Magnete," 1744, " Opus- 

 cula," 1746-51 ; and while looking into this work was surprised 

 to find that Euler had preceded Laplace in his development of the 

 chief effects of a resisting medium by more than half a century. 

 Euler's work on the resisting medium will be found in the volume 

 of " Opuscula," Berlin, 1746, in the paper " De Relaxatione Motus 

 Planetarum," pp. 245-276. 



Having shown that the aphelia are undisturbed by resistance, 

 Euler considers in section XVII. the equations for the mean mo- 

 tion, and the return to perihelion, after changes in the mean motion 

 by the increments representing a whole revolution : 



nt -\- 27:, nt -\-47r, nt-\-6Tr, nt-\-'&TT, etc. 



Euler puts for the planetary orbit about the sun, 



344 



