( -«> ) 



other motions also dilTer considerably from their theoretical values^ 

 Moreover the inclinations are far from constant, as Avill be seen at 

 once from an. inspection of the residuals Ay. 



- . . , dr 



It must be mentioned that the value of -- agrees ap[)ro.\ima1eIy 



«ith the value derived by Cookson from the observations of 1891, 

 1901 and 1902. This could have been expected since Cookson in 

 this determination also neglected the corrections to the position of 



the equator. The ditference between Cookson's value of — and the 

 ' dt 



value of Sol. I is not due to a bad agreement of the observations of 

 1903 and 1904 with those of 1901 and 1902 (which on the contrary 

 agree extremely well), but to the fact that in Sol. I the corrections 

 to the elements of the other satellites were eliminated by means of 

 the transformation from Ap and hq to L,n and Ay, while Cookson 

 did not eliminate these corrections but neglected them. 



I have now made a number of further solutions, in \vhich I started 

 with approximate values .(•„„ and //„„, and introduced the unknowns 



7i ri^ (f.v^ (fi/^ X, 



thus rigorously subjecting the motions of the nodes to the theoretical 

 condition. The unknowns rf y„ and x are badly separated. The 

 weight of the determination of x is considerably diminished by the 

 introduction as unknowns of the corrections to the position of the 

 ecpiator. That this must of necessity be so, is easily seen. If we had 

 observations of only one satellite at two epochs, it Avould be /H;j>(W.s77>/é' 

 to determiue both the motion of the node and the equator. We 

 would in that case liave only four data (the values of p and r/ at 

 each of the epochs) for the determination of the five unknowns 



dr 



y, r, — , .(•„, and //„. Now x is practically determined from satellite 



II alone. The motions of the nodes of III and IV are too slow^, 

 and the inclination of I is too small, to allow a determination of 

 the motions of the nodes of these satellites to be made, the accuracy 

 of which would he even remotely comparable to that of sat. II. 

 The motions of the nodes of I, III and IV are derived theoretically 

 from that of II. If therefore the latter is known, each of the three 

 others provides a determination of the equator. Then the determina- 

 tion of X from II must be repeated with this new position of the 

 equator, and so on nntil a satisfactory agreement is reached. ') 



') Cookson has in his discussion of thu observations of 1891, 1901 and 1902, 

 used this method, but he rested content with the first approximation. His corrections 

 to the equator derived from satellites III and IV are in the same ctirection as the 

 values found 1)y lae. 



