( -'^y ) 



error of projection, etc. are avoidcil. Tlie >traiglitiicss of tlio cvliiider 

 was repeatedly tested by comparison witli a stretched s[)iderline. 

 Its errors are certainly smaller than 0.2 micron. The position-angles 

 were read off by two microscopes, and the orientation of the plate 

 was determined from a pair of standard stars, which were for this 

 purpose photographed on each plate, and from trails of the satellites. 

 Tiie errors of observation of tiie measnres of the satellites are satis- 

 factory, distortion of the photographic film cannot be detected, and 

 the discnssion of a dozen plates, which were specially taken for this 

 purpose, shows that the determination of the orientation from the 

 trails is always practically free from systematic errors, while the 

 same can be said of the determination from the standard stars under 

 certain conditions, which are however not always fuliilled. The 

 accidental errors of both determinations are very small. 



The image of the planet has not been measured. The observed 

 co-ordinates contain therefore an unknown additive constant (different 

 for each separate plate), which was eliminated by using in the 

 subsecpient reductions the co-ordinates referred to the mean of all 

 the satellites occurring on the plate as origin. The equations of con- 

 dition and normal equations for these relati\e co-ordinates are very 

 simi)le and symmetrical. The limited space at my disposal prevents 

 me however from entering into more details regarding the measures 

 and reductions. I will at once state the results. 



The unknowns which were determined from each opi)osili()ii were 

 the corrections to the adopted values of the elements ji and <j of 

 the four satellites which are defined by the formulas : 

 p = i sin (— ^) 

 7 =:icos{— Sh) 

 Avhere / and ^ are the inclination and ascending node of the orbital 

 plane of the satellite referred to the fundamental plane. Tlie longitude 

 of the node is counted from the ascending node of the plane of 

 Jupiter's orbit on the fundamental plane. The quantities referring to 

 the four satellites arc distinguished by the suffixed luimerals 1 to 4. 



The following table contains the results of tlie different series of 

 observations with their probable errors. 



The values for 1891 {Heliometer) are those derived in my disser- 

 tation with a few unsignificant corrections in the last decimal places. 

 The results from the heliometer and those from the plates ha\e been 

 combined with the relative weights 2 and 1. 



The results for 1901 and 1902 are quoted from the communication 

 by Mr. Cooksqn in the Monthly Notices. 



I hflvc howevQr been vompellocl to rcJQCt ^;'< ftiul Lq^ for 190i 



