2] ON THE PERTURBATIONS OF URANUS. 35 



Mean longitude of the Planet, October 6, 1846... 323 2 



Longitude of the Perihelion ........................... 299 11 



Eccentricity of the Orbit ................................. 0'120615 



Mass (that of the Sun being 1) ..................... 0'00015003. 



r f). Q. 



49. From the values of m', 0, J, and , , found above, the values 



III/ II V 



of the quantities h, k, p, and q, corresponding to each hypothesis, are im- 

 mediately determined. Thus we find, 



IST HYPOTHESIS. 2ND HYPOTHESIS. 



rt , = 0'5 -', = 0-515 



a' a' 



h,= 23"'98 &,= - 19"-07 /,= 23'l 9 ,= -21*69 



h.,= - 47-58 fc,= - 11-00 h,= - 57'30 ,= - 3'83 



h 3 = - 1-93 A- 3 = - 7'64 /i 3 = - 3-40 3 = - 576 



p,= 9-93 q,= - 8-31 pi= G ' 52 Si 35 - 7 ' 34 



^> s = - 8'54 /= - 55-36 p a = - 1 -1 ^'2 ry,= -54'39 



^ 3 = 224-90 7 3 =- 171-63 p 3 = 104'21 </ 3 =-82'39 



50. And by substituting these values in the equations (e), (), (x), 

 and (T/), we obtain 



IST HYPOTHESIS. 2ND HYPOTHESIS. 



"=0-5 -, = 0-515 



a a' 



Se = - 49 / 77 Su = - o''702 8e =-4,3-23 Sri = - o''5417 



&B,= -130-69 8y,= 222-38 8^= 177 8y,= 123-98 



Sic. 2 = 1-02 Sy,= 2-83 801,= 1'13 S.^= 0'91 



and the corresponding corrections of the elliptic elements will be 



CN 



= 0-00000999 - = 0-00000771 



a a 



8e= 20-83 

 8sr = 127-27 



52 



