( ::•' ) 



Let .r„ )/„„ lio apprnxiniato values of .»•„ and ,v„, Ihiis .'■„ = ,?•„„ -f rf.v 

 ttnd //, = //„„ + (^.'/o- We have tlieii : 



■I'i — Hi' di.„ = ,/■(■„ -j- L.fi -\- (ti' .i-„„ 



.'// — It' rf.'/„ = ,'/(■„ + ^!ti + f'' .'/o« 

 If we suppose tliat the approximation .r„„ _?/„„ is aireadv so ^ood 

 that ff.c„ and rf?/^ can lie neglected, then these equations become: 



71 Wl Fi ^= .(•,•„ -|- i^.r,- -f- fi;' ,r 



(9) 



(10) 

 y,- im Fi = yi„ -\- Ly , + f*/ ,'/„„ 



Next 1 compute the quantities ƒ/,• and (t; from the equations : 



9i «"' ^; = ■'■/o + ^ •'•<• + M.' •'•00 I 



ƒ/,■ co« Gi — y,„ + A yi 4- ft/ y„„ ) 



The other unknowns are then determined from the equations : 



y: = üi 1 



/^o + ^(^-0=gJ (12) 



fit I 



dr- 



If these equations give constant values for y, and values of — ^ 



(It 



which can by an acceptable value of y. be made consistent wilh 



the theory, then the appromation is sulïicient, if not, then a new 



approximation must be made. As a first approximation I have assumed: 



•'•„„ = .'/,,„ = 0- 



The e([uations (12) were then formed and sohed. In this solution 



I have determined the values of — -- for the four satellites separately 



without iutnuiucing the theoretical ratios ab initio. The equations (12) 

 then consist of two sets for each satellite and each of these 8 sets 

 is independent of all others. The residuals which remain after tlie 

 substitution of the resulting values of the unknowns will be given 

 below together with those from the other solutions. The probable 

 error of unit weight was ± ()°.008G. 



The motions of the noiles in this solution are (Sol. I); 



dr. „ dr. 



— 1 = 0^01213 — ■' = 0°.005S7 



dt dt 



dr, dr. 



— •* = 0°.030266 — ■* = 0°.00189. 



dt dt 



If these tire compared with the theoretical values, it appears at 

 Once that their ratios are very different. Tlie node of satellite I, 

 which according to the theory has a yearly motion of about 50°, in 

 this solution shows a motion of about 5^ The ratios of the three 



54 



Proceedings Royal Acad. Amsterdam. Vol, Vlll. 



