( 105 ) 



of t lie centre derived from the observations — which moreover are 

 only little larger than their probable errors — do not represent a 

 true excentricity. It is not impossible that they are produced by the 

 existence of surface markings on the disc of the satellite, causing the 

 centre of light, which is observed by the heliometer, to bedisplaced 

 relatively to the centre of gravity, the displacement being different 

 at different epochs. Any attempt to explain the observed A, and / 

 on this hypothesis would, however, necessarily involve so many 

 undeterminate quantities, that ils success would lie no proof of its 

 representing a true fact of nature. 



3. Determination of the libration from tin' observations. 



In a communication made by me in 1905 to the "Nederlandsen 

 Natuur- en Geneeskundig Congres", l ) I have shown : 



that the libration probably has an appreciable coefficient, 



that the determination from the observations, nol only of die 

 phase and amplitude, but also of die period of die libration, is oi 

 the highest importance for the derivation of the masses, especially 

 of the mass of Satellite I, 



that this determination is possible from the observations made al 

 the observatories at the Cape, Helsingfors and Pulkowa, 



that most probably the period differs considerably from the value 

 adopted by Laplace and Souillart, and 



that this determination is intricately connected with an investigation 

 of the long-periodic inequalities in the longitudes of the satellites, 

 and that consequently die whole problem can only be solved by 

 successive approximations. 



In number 17 of the Publications of the Astronomical Laboratory 

 at Groningen, which will soon be published, all these conclusions 

 are confirmed and the successive approximations are carried out. In 

 this communication I cannot dwell upon the details of this investiga- 

 tion, nor upon the difficulties which were encountered. I must confine 

 myself to a brief statement of the results. 



The observations used are the heliometer-observations of the Cape 

 Observatory already quoted above, and further photographic plates 

 taken at Helsingfors in the years 1892—93, 1893—94, 1894—95, 

 1895—96 and 1897, at Pulkowa in 1895—96, 1897 and 1898, and 

 at the Cape in 1904. I thus had at my disposition ten oppositions 



l ) '■'Over de libratie der drie binnenste groote satellieten van Jupiter en eene 

 nieuwe methode ter bepaling van de mas*a ran Satelliet I." Handelingen van 

 het 10de Congres, pages 125—1:28. 



