( 654 ) 



observed only iioar elongation. The series of observations niarle by Gill 

 at the Cape in 1891, arid the series of' photographs taken in the same 

 year by Donner (on the suggestion of Backlund) and continned by him 

 and by Kostinsky to 1898, are the first series of observations of the 

 satellites in every \mu{ of their orbits. The discussion of the Cape 

 observations of 1891 by me then suggested the desirability of further 

 observations, which were executed b}' Cookson with the Cape helio- 

 meter in 190J and 1902, while photographic observations were made 

 at the Cape in 1902, 1903 and 1904. 



It will be conducive to a good understanding of what follows if I 

 collect here at once all the notatif>ns used. 



The theory, which was compared with the observations, is 

 Souillart's ^). This theory gives the longitudes and latitudes of the 

 satellites, referred to the plane of Jupiter's orbit of 18500. As I 

 have explained in Cape XII. 3 ') |)age 96, the orbit of 1900-0 has 

 been used in its place. 



The radii-vectores and the longitudes of the satellites in their 

 orbits are given by the formulas : 



^'i = li -f i>i + inequalities 

 h =-- ni « + e, . 

 We have the rigorous equations: 



.,-3 ., + 2 f3=zzl80° 

 «J — 3 'i^ -\- 2 )i. = 0. 



1) Theorie analytique des mourements des satellites de Jupiter, par M. Souillart, 

 Memoirs R. A. S. XLV, 1880. 



Theorie analytique des mourements des satellites de Jupiter, seconde partie, 

 par M. Souillart, Mémoires des savants étrangers, XXX, 1887. 



2; Annals of the Royal Observatory at the Cape of Good Hope, under the 

 direction of Sir David Gill, K. G. B. Volume XII: 



Part I. (Not published). 



Fart II. Determination of the mass of Jupiter and orbits of the satellites, 

 by Bryan Gookson M. A. (190Ö). 



Part III. A determination of the inclinations and nodes of the orbits of 

 Jupiter's satellites, by Dr. W. de Sitter. (1906). 



Part IV. Determination of the elements of the orbits of Jupiter's satellites, 

 by Bryan Gookson. (1907). 



The titles of these papers, which I sliall often have to quote, are referred to 

 by the abbreviations used in the text above. I shall also often quote : 



Publications of the Astronomical Laboratory at Groningen, N'. 17. On the 

 Libration of the three inner satellites of Jupiter, by W. de Sitter, So. D. (1907), 

 which is referred to as: Gron. Publ. 17. 



