1879.] ^l [Chase. 



radius, and also inversely as the disturbing mass, the first group leads to 

 the equation 



Earth X 1 year X (Neptune's r. vec.) 2 



Sun X 1 day X (Earth's r. vec. f 

 This equation gives 



= 1 (It) 



Sun's mass = 330, 375. ^ 



" parallax =8. "816 [■ (12) 



" distance = 92,717,000 miles. ) 



In considering this'and other relations of mass to aethereal disturbance, it 

 is well to remember that the simple disturbance varies as the mass ; the 

 vis viva, or radius of consequent oscillation, as the square of the mass ; and 

 the consequent orbital period, as the cube of the mass. 



By introducing the vector-radii also into the cubical factor of (10) and 

 designating secular perihelion, mean perihelion, mean aphelion, secular 

 aphelion, respectively, by subscript 1, 2, 3, 4, 5, we find 



Sat.., x Sat. 4 "] 



J up. 2 x Ura. 3 = 1 | 



(18) 



Sat 3 x Sat, 4 . _ 1 



Jup. s x Ura. 2 



The greatest deviatiou from exactness, in the first of these equations, is 

 less than \ of one per cent.; in the second, less than Jg- of one per cent. 

 The mean deviation, in the square root of the product of the two equa- 

 tions, is only g 1 ^ of one per cent. 



We see by (5) and (13), as well as by ordinary astronomical investiga- 

 tions, that questions of relative mass are intimately connected with those 

 of orbital eccentricity. One of the most interesting evidences of such 

 connection, in this special line of investigation, is to be found in the posi- 

 tion of the mean fulcrum of the system, or centre of gravity of Sun and 

 Jupiter, together with the significance which it lends to equations (5), (6), 

 (8), (13), as well as to the fundamental increment which is the ground of 

 equation (3). The orbital vis viva has lengthened the radius-vector of 

 simple equilibrium by T \ of its value. For 5.2028 X 214.524 = 1116.125 ; 

 if of 1116.125 = 1050.471. The limit of synchronous radial and circular 

 oscillations is at 2 r. Deducting 2 from 1050.471 we find 

 Sun's mass 



"Jupiter's mass" = 1048 - 471 < 14 > 



Equations 7, 8 and 9 give the following theoretical values, for Uranus 

 and Neptune, which I compare with Ncwcomb's : 



Sun -=- Theoretical. Newcomb. 



Uranus 22116 22600 ± 100 



Neptune 19352 19380 to 19700 



Newcomb gives two estimates for Neptune, one (19380 ± 70) from satel- 

 lite, the other (19700) from perturbations of Uranus. The latter agrees 



