1874.] llO [Chase. 



_6 



^^ = Neptune's mean heliocentric distance, in units of Earth's mean 

 distance. 



jj = Saturn's mean distance. 



'■^^ = Asteroidal mean distance, or twice the mean distance of Mars. 



^j = Earth's secular mean perihelion distance. 



^V = Mercury's " " " 



J J = Major axis of Sun's orbit about centre of gravity of binary Star. 



j^ = Heliocentric distance of linear centre of oscillation of secular mean 

 perihelion centre of gravity of the binary Star. 

 The ritio of Y' to V" was determined by supposing Sun's radius to 



vary from r to n'^r. In such case, V oc j^] Y" cc ~ 2. 

 In the following table, A represents the theoretical values of T" and 



V" = -^-^^- \ ; C, 



the observed values. For T", C is the mean of the six several estimates 

 by Bianchi and Laugier, Lelambre, Petersen, Sporer, Carrington, and 

 Faye. The Sun's annual motion is given in units of Earth's radius 

 vector, C being Struve's estimate. For V, A, B, C, are respectively 

 deduced from g at Sun, Earth, Jupiter. 



A B. C 



T" 2203645 sec. 2163907 sec. 2162802 sec. 



y 265.66 mi. . 261.79 mi. 261.56 mi. 



4V"X 1 yr 1.678 r.v. 1.754 r.v. 1.623 r.v. 



The slight discrepancies in these values seem to be attributable to the 

 mean orbital eccentricity of the binary Star, but they are all within the 

 limits of uncertainty of observation. The heliocentric distance of the 

 mean perihelion centre of gravity of the binary Star, is 1.0188 X solar 

 radius ; Jupiter's mean orbital eccentricity is .04316. 



The correspendence betweea the theoretical and observed values of the 



~ series is given below, in units of Sun's radius. It is specially notice- 

 able that the series groups the principal planets into pairs. The values 

 of the secular mean apsides are taken from Stockwell's " Memoir on the 

 secular variations of the orbits of the eight principal planets." 



Theoretical. Observed. 



Neptune, mean 6450.776 6453.731 



Saturn " 2053.346 2049.514 



Asteroid " 653.600 654.760 



Earth, perihelion 208.048 207.583 



Mercury, " 66.224 68.483 



Sun, major axis 2.136 * 2.132 



Primary centre oscillation .679 .679 



A. p. S. — VOL. XIV. o 



