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d<a; 

 t (1 — J, the other ratios r y -, and the motions — depending on the 



masses. Thus if certain values of the masses arc adopted, the ratios 

 Ty are thereby determined. It' then //; and I; of the four satellites 

 are known from the observations, then from the eight linear equations 

 [13] (consisting of two sets of four each, with the same coefficients) 

 we can determine the eight unknowns </, sin oj, and r, cos to,-, and 

 from these again <■; and to,-. The method is exactly the same as the 

 one used by me for the determination of the inclinations and nudes 

 (see these Proceedings, 1906 March, pages 767 — 780). The values of 

 hi and hi have been determined from the heliometer-observations 

 made at the Cape Observatory, in 1<S91 by Sir David Gill, and in 

 1901 and 1902 by Mr. Bryan Cookson. The results from these 

 observations have been treated by the method just delineated, in two 

 different suppositions regarding the masses, i.e. regarding the ratios 



