166 Prof. A. S. Eddington on Astronomical 



formula ; the first was not given by him explicitly, but is 

 almost implied by his remarks on p. 88. 



Since we are taking de and edvr to be centennial changes, 

 must be taken as the angular motion of the planet in a 

 century. Hence the coefficient v6\2c 2 is proportional to the 

 linear velocity x angular velocity of the planet — i. e. to 

 the acceleration, or to the inverse square of the radius of 

 the orbit. If r is the radius of the orbit, K a constant for 

 all planets, we have 



de— ? . Y cos -57, 



edm = + -5- . V sin -sr. 



r 2 



Let (ds) 2 = (de) 2 -{■ (eder) 2 ; then ds measures the total dis- 

 tortion of the orbit, which may be due partly to de and partly 

 to edns. We see that 



ds= — — . 



The angle between the perihelion and the direction of Y does 

 not affect ds, but determines in what proportions ds is to be 

 resolved between de and ed-u?*. 



For the moment we shall suppose the orbits of the four 

 inner planets to be coplanar, so that Y is the same for all, 



and hence ds varies as -s. The values of r 2 for the four 



planets are in the ratios 1 : 3'5 : 6*7: 15*5. In order to 

 account for the motion of the perihelion of Mercury, we 

 must assume a value of Y such that ds for Mercury is 

 about 8". (According to the table at the beginning of the 

 paper the required value of ds is 8"*3; Lodge's value of 

 the solar motion on p. 91 would give ds somewhat larger.) 

 The corresponding values for the other planets are then: 



ds= >/\(de) 2 + (edvj) 2 }. 



Mercury 8 



Yenus.... ., 2*3 



Earth M9 



Mars 0-51 



* The following geometrical construction is useful. _ Represent the 

 eccentricity by a vector drawn in the direction of aphelion. Compound 

 with it the vector ds=KY/r 2 drawn in the direction of V. The resultant 

 represents the new eccentricity and direction of aphelion. 



