( 715 ) 



Api>lyiiig' tills correction, and cair) ing the longitudes forward to 

 J 900 Jan. 0.0, (Ireenwich M. T., we tind the values II below. 



Mean, loiuiitudes for 1900 Jan. 0.0. 

 1 {modern) II (Damoiseau) 



/^ = 142°.604 d= 0^010 J42°.645 ± °.004 

 4 = 99 .534 ± .007 99 .569 ± .00(3 



4 = 167 .999 ± .007 168 .028 =b .008 

 / = 234 .372 =t .002^ 234 .360 ± .010. 



4 



The estimated probable errors for Damoiseau do not contain the 

 p. e. of the mean motions used for carrying the longitudes forward 

 from 1750 to 1900. The uncertainty of Damauseau's mean motions 

 has been estimated by the late Prof. Oudemans in these Proceedings 

 (October 1906). He finds for the fonr mean motions, in units of the 

 eighth decimal place : 



±73 ±55 ±37 ±24 



Comparing the values I and II we find the following corrections 

 to Damoiseau's mean motions : 



dn, = — 0^0000 0075 ± °.0000 0020 

 on, — — .0000 0064 ± 16^ 



én, = — .0000 0053 ± 20 



on., = + .0000 0022 ± 18 



It is noticeable that these corrections are very nearly of the 

 magnitude of the uncei-tainties estimated by Oudemans. If these 

 corrections are applied, the resulting values do not satisfy the 

 condition 



n^ — 3^^^ -|" ^/ij = 0. 

 If, however, we apply the further corrections 



cfyij = - - 2 (hi^ =z: -|- 3 ön^ = — 3 



to the eighth decimal place, then the condition is rigorously satisfied. 



The mean motions thus derived are those finally adopted. They are 

 n, = 203^4889 9261 n, = 50°.3176 4587 

 n, = 101 .3747 6145 n, = 21 .5711 0965 

 These are the mean motions relatively to the point Aries. If the 



sidereal mean motions are required, they must be diminished by 



0^0000 3822. 



VI. The mass of the system. 



The determination of the mass of the system of Jupiter by Newcomb '), 



^) Astronomical papers of the American Ephemeris, Vol. 5, Part. 5. 



