NOTES 103 



exact equation given by the author in Phil. Trans., 

 loc. cit., when corrected according to the note at the end 

 of that paper. 



Mr. E. B. Wilson has investigated " The Revolution 

 of a Dark Particle about a Luminous Centre " (Annals 

 of Mathematics, Second Series, vol. viii, No. 3, April 

 1907) taking into account the three effects discussed in 

 the text and integrating the equations of motion. 



He finds that the fall inwards during the first revolu- 

 tion for a particle of density 5-5 and radius o'oi cm. will 

 be about 80 kilometres, agreeing with the value found 

 above. Its change of eccentricity will be about i in a 

 million, and it will in all probability make less than io 7 

 revolutions. 



