( 659 ) 



mination of these ratios from tlie observations. This one unknown 

 — the scale- value of the system — from wliich the mass of the 

 planet is derived, can naturally only be determined from extra-eclipse- 

 observations. It has already been remarked that all series of such 

 observations made before 189J, were made with a view to this 

 determination. 



The number of nidcnowns of the [)roblem is thus 32, viz : 

 .4. the "own" inclinations and nodes y; ,6i... 8 unknowns 



the position of the equator co , ^ . . . 2 ,, 



the dynamical compression JIf ... 1 ,, 



B. mean longitudes with one rigorous condition « ; . . . 3 ,, 



,, motions ,, ,, ,, ,, ni ... 3 ,, 



the amplitude and phase of the libration k ,t^ . . . 2 ,, 



the own excentricities and perijoves et , coi . . . 8 ,, 



the mass of each satellite mi. . . 4 ,, 



C. the reciprocal of the mass of the system ^i . . . 1 ,, 



32 



The obserN'ations which have been used in the derivation of the 

 results to be communicated below are the following : 



1. Heliometer-observations made in 1891 at the Royal Observatory, 

 Cape of Good Hope, by Gii-l and E'inlay. These have been reduced 

 by me and were pnblished in my inaugural dissertation ^). After 

 'the pnblication some mistakes and errors of computation have been 

 found, which have been already coi-rected in the results used here. 

 The corrected results will soon be pnblished in Cape Annals, Vol 

 XIT, Part. I. 



The high order of accuracy of this series is due to the principle, 

 introduced by Gill, to measure only distances and position-angles 

 of the satellites relativelj^ to each other, and not relatively to the 

 planet "). Thus large systematic errors are avoided. 



2. Heliometer-observations made in 1901 and 1902 at the Cape 

 Observatory by Bryan Cookson, M. A., reduced by himself, and published 

 in Cape XII. 2. Corrections to the values of the unknowns as published 

 there were afterwards given in Cape XII.4, Appendix. In these series 



1) Reduction of Heliometer-observations of Jupiter's satellites, made by Sir 

 David Gill, K. C. B. and W. H. Finlay, M. A., by W. de Sitter. Groningen, 

 J. B. WOLTERS 1901. 



3) Hermann Struve had previously used the same method in his observations 

 of the satellites of Saturn. 



45* 



