( 318 ) 



ScHUR improved in different respects the reduction of the observations 

 of the measures made by Bessel. In consequence, the mean errors 

 of the single determinations of Bessel were considerably lessened. 

 The numbers quoted just now, became : 



for I ± 0"-21, 



„ II d= 10, 



„ III ± -26, 



„ IV db -30, 



Mean: ± 0"-24. 



As has been mentioned already. Gill and Finlay, acting on a 

 suggestion formerly made by Otto Struve^), did not measure the 

 distances and the angles of position of tiie satellites relative to the 

 centre of the planet, but relative to each other. (The instrument 

 at their disposal, a heliometer of Repsold, aperture 7^ inch = 19-05 

 cm., focal distance somewhat over 2 Meter, far surpassed in 

 perfection all the instruments used up to that time). These observations 

 can be made with much more precision. The drawback is that the 

 formation of the equations of condition and their solution become 

 more complex and absorb much more time. Both the gentlemen 

 named and Mr. de Sitter have not been deterred by this conside- 

 ration. They found ± 0"-087, a number considerably less than that 

 of Bessel, for the probable error of the measurement of a single 

 distance. Mr. de Sitter even finds that the probable error of the 

 mean distances (the real unknown quantities) does not exceed 

 ± 0"020 or d= 0"021. 



(7) It may be remarked that Mr. de Sitter found it expedient 

 to alter the choice of the unknown quantities. He retained for 

 each satellite : the longitude in the orbit, the inclination and the 

 ascending node relative to an adopted position of the fixed plane, 

 but not the eccentricity nor the position of the perijovium and 

 the mass. There thus remained as unknown quantities only three 

 elements of each satellite. On the other hand he introduced corrections 

 of the coefficients of the perturbations or rather of the periodic 

 terms, which afterwards must lead to the knowledge of the mass 

 of the satellites, to that of the eccentricities and of the position of the 



1) Vide the first report of Hermann Struve, in the first supplementary vol. of 

 the Pulkowa observations, 1st page at the bottom. 



