( 306 ) 



To facilitate these observations I tliought it desirable to calculate 

 in advance the conjunctions of any two satellites for the most favourable 

 part of 1908. 



We have to consider that while formerly the orbits of the 

 satellites were determined by repeatedly measuring the distances 

 and their angles of position relatively to the planet, this method is 

 now replaced by the measurement of the distances and the angles 

 of position of the satellites relative to each other (especially with 

 the heliometer) (6). For observations during a moderate interval the 

 periodic times of the satellites may be assumed to be accurately 

 known. Admitting this, if. leaving out of consideration Kepplers 

 third law, we introduce the major axis of each satellite as an unknown 

 quantity, the total number of such unknowns will be six for each 

 orbit at a determined time. If, as was done by Bessel at Koningsberg 

 in 1834—39, and by Schur at Göttingen in 1874— 1880, the distance 

 and the angle of position between the planet and the satellite are 

 measured, we get two equations with six unknown quantities. If 

 however we measure the distance and the angle of position of 

 two satellites relative to each other, the number of unknown 

 quantities in these equations is doubled and thus becomes 12. If 

 finally all the combinations two by two, are observed, as was done 

 by Gill and Finlay at the Observatory of the Cape, we get a great 

 number of equations with a total of 24 unknown quantities. These 

 equations must then be solved by the method of least squares. 

 This number becomes 29 if we add the masses of the satellites, (only 

 to be found by the perturbations caused by one satellite in the 

 motion of the others,) and the compression of Jupiter (7), given by 

 the retrogradation of the lines of the Nodes on the fixed planes. 



Now the observation of an occultation, even of a conjunction with- 

 out an occultation, can be made by everybody possessing a telescope 

 of sufficient power. Such an observation also furnishes two equations 

 between the unknown quantities, at least if, for a non central occul- 

 tation or a simple conjunction, the ditference in latitude is measured 

 at the filar micrometer. This consideration engaged me to compute 

 in advance the time of these conjunctions for the most favourable 

 part of 1908. If by experience we find that this preliminary work 

 leads to valuable results, it might be worth while to continue it for 

 some future period, for instance for 1914. 



For the moment at which the mean fixed plane passes through 

 the centre of the Earth, I find, 1908 July 8, I9^',6 Mean Time at 

 Greenwich, (5). 



This date, it is to be regretted, is very unfavourable. For on that 



