124: BRUSH— DISCUSSION OF [April 24, 



Let us consider the effect of .r on a planetary orbit: If the orbit 

 is circular, .r = o because there is no change of velocity; but if the 

 orbit is excentric, s obviously grows in value and importance with 

 the excentricity, though always equaling zero at aphelion and peri- 

 helion. Fig. 4 illustrates the sun and a planet at aphelion in an ex- 



p,-vvgnrrierited 



aggeratedly excentric orbit. As the planet moves from aphelion 

 to perihelion, normal attraction between the sun and planet is aug- 

 mented by the positive acceleration of both as before explained; and 

 while the planet moves from perihelion to aphelion normal attraction 

 is diminished by negative acceleration. 



If I am not mistaken in my mechanics, the gravitational disturb- 

 ance above described will slightly change the shape of the orbit, and 

 cause a continual advance in the position of perihelion by advancing 

 the line of apsides. Probably the effect is too small to be detected 

 in the case of any of the planets of the solar system except perhaps 

 IMercur}^, because of the small excentricity of their orbits; but the 

 high excentricity of Mercury's orbit possibly may reveal it, and I 

 hope it may be found adequate to account for some of the anoma- 

 lious secular advance of the perihelion of Mercury's orbit. I shall be 

 glad to have my astronomical friends investigate this. 



The orbit of the moon is not very excentric, but she moves 

 toward and away from the sun almost the full diameter of her orbit 



