Ixiv Proceedings of tlie South African Pliilosopliical Society. 



A series of observations was made with the hehometer in August 

 to December, 1891, in order to determine the mass of Jupiter and 

 correct the elements of the motions of his satelhtes. Ever since 

 telescopes were invented the phenomena of these satellites have been 

 regularly observed, especially the eclipses, and as the latter phenomena 

 are capable of fairly accurate observation they serve as a means of 

 determining terrestrial longitudes ; and, indeed, have well served that 

 purpose in recent Arctic expeditions. Laplace (in his Meclianique 

 Celeste) has developed the theory of the mutual perturbations of the 

 satellites; Bouvard, Delambre, and Damoiseau have successively 

 laboured to produce tables which should accurately represent the 

 observed phenomena, but from various causes Damoiseau's tables, 

 which in 1836, when they were published, very fairly represented the 

 observations, now show considerable discrepancies. 



The real obstacle to the construction of satisfactory tables w^as the 

 want of the best data. The only accurate observations available were 

 those of eclipses — they admirably determine the Jovicentric longitude 

 but leave the latitude determinable only by the duration of the 

 eclipse — and this duration is of course involved with many other 

 unknowns as well as uncertainties — personal, instrumental, and so 

 forth. What really was wanted was some independent determination 

 of the Jovicentric latitude of each satellite in many different parts of 

 its orbit. 



All observers of Jupiter's satellites employing methods other than 

 eclipses had measured the positions of the satellites relative to the 

 planet. In the new observations I observed the relative positions of 

 the satellites to each other, because it is obvious that the relative 

 co-ordinates of two sfiarply- defined small discs can be more accurately 

 measured than can the relative co-ordinates of the estimated centre 

 of a large disc like that of Jupiter and a small disc like that of a 

 satellite. The disadvantage of the method which I had adopted was, 

 of course, that the whole of the elements of all the satellites had to 

 be simultaneously regarded as unknown quantities, instead of 

 discussing those of each satellite independently. But de Sitter's 

 reduction of the observations, involving as it did the formation of 

 over 500 equations of condition and their simultaneous solution for 

 27 unknown quantities, showed that the result well repaid the labour 

 — as the probable error of the single observation came out only 

 + 0"-083. 



The resulting mass of Jupiter agreed exactly with that which 

 Newcomb had derived in an entirely different way, viz., by the 

 perturbations of Jupiter on the motions of comets and minor planets ; 

 important corrections of the elements of the satellites, especially of 



