( 778 ) 



. J^ 

 From the values of x we liud the tuUowiiig values oi —- 



at 



'— ^ — 0°.13664 - 0M3932 — ÜM4105 



(It 



— — .032105 — .032633 — .032974 



dt 



1_J^ _ .006814 — 0. 006916 — .006983 



dt 



-^ — .001839 — .001854 — .001863 



dt 



From the values of u\ and y„ we lind for the inclination and node 

 of the equator on Leverrier's orbit of .Jupiter of 19()0-() : 



w 3°.1107 ± °-0043 3°-1169 ± °.0022 3°. 0680 



d 315.727 ± -042 315.735 ± -041 315.410 



With the exception of y. all uidoinwns in the two solutions agree 

 Avithin the sum of their pi'obal)le errors, and with only one excep- 

 tion (y,) all the corrections to the adopted values are nianj- times 

 larger than their probable errors. 



The residuals of the two solutions VI and Vll are given in the 

 following table together with those of S(j1. I. The probable errors, 

 which have been added for comparison are somewhat larger than 

 those of the observed L p and A q, because by the transformation 

 from tip and A (^ to A ,t' and Ay, the p.e. must be somewhat 

 increased, even if we consider the coefficients Oy as absolutely exact. 



The p.e. of weight unity, which was ± Ü°.0086 for Sol. I, is 



± 0°.0065 for Sol. VI antl ± ()°.()064 for Sol. Vil. But it is chietly 



in their consistency with the theoretical conditions, that both solutions 



are incomparably better than Sol. I. The inclinations are now constant 



within the probable errors. The residuals of the nodes only show a 



systematic tendency for Satellite I (in Sol. VII, where the motions 



of the nodes were not derived from the observations, also for Sat. II). 



Still the agreement with the theoretical motions is much improved. 



dT 

 The value of — ^ derived from Sol. VI irrespective of the theoretical 

 dt 



conditions would be 0°.125O, while the value corresponding to the 



value of sc in this solution is 0°.1366. This is a great improvement 



compared with Sol. I (0°.0121). 



The results for Sat. Ill in JilOl an<l 1902, which in all solutions 



gave large residuals, have in the sulutions \\ and VII been rejected. 



This rejection has no appreciable intluence on the values of the 



unknowns, niir on the other residuals, but it reduces the p. e. of 



