Ill APPENDIX 



which, without them, would be simply a ponderous mass of use- 

 less material. 



I have selected from his observations as printed, all cases 

 wliere he has seen an object interior to Titania sufficiently well 

 to allow him to give an estimate of its position, excluding, of 

 course, all cases where he has subsequently proved that such 

 object was certainly a star. 



The cases for examination are — 



1. 1787, Feb. 10 Position of interior satellite 135= 



2. 1790, Jan. 18 " " " "following" 



3. 1790, Jan. 20 " " " 315° 



4. 1793, Feb. 5 " " " 250= 57 



5. 1793, Mar. 9 " " " 205° 



6. 1794, Feb. 28 " " " 66° 



7. 1794, Mar. 27 " " " 



8. 1798, Feb. 15 " " " 5° 11' 



9. 1801, Apr. 17 " " " 189° distance 18'' 



The elements which I have used are provisional ones derived 

 by Prof. Newcomb from Lassell's Malta observations. They are 

 amply adequate to the present inquiry. 



From these elements 1 have computed the angle of position 

 and distance of Umbriel and Ariel in each of the cases above 

 set down, and compared these with Herschel's observations, as 

 follows : — 



1. "1787, Feb. 10, 8^^ 57™. The first satellite is about 53° 

 n. p.; 8''33™ * * * * a supposed third is about 45' s. f. 

 In a little more than four hours I saw the satellites go on with 

 the planet, and also in their orbits. * * * * No subsequent 

 observation of the third was made." 



On this date Umbriel was in P = 82° distant 16" and Ariel 

 was n. p. Hence Herschel's " supposed third" was neither of 

 the inner satellites. 



2. " 1790, Jan. 18, 9^ 32™. There is a supposed third satel- 

 lite about two diameters of the planet following, extremely faint 

 and only seen by glimpses ; 1"^ 6™ after I could not perceive it ; 

 a fourth is about 70° n. p." 



" Two diameters" of the planet was about 8", and as Herschel 

 usually counted his distances from the limb of the planet in his 

 estimations, the distance from the centre would be about 10". 

 Umbriel was in P = 124° 23', and distant 13". 9. Ariel was in 

 P = 317° 10', distant 10".96. " 1" 6™ after" Umbriel w^as in 

 P = 118° 48', and distant 13".54 ; i. e., nearer to Uranus by 

 0".4. So far as the evidence goes we may reasonably infer that 

 Herschel had a glimpse of Umbriel. In the Phil. Ti'ciis., 1798, 

 p. 271, Herschel, in referring to this observation, speaks of it as 

 very certain, and supposes that the satellite might have been "11 

 or 12 degrees" from the parallel. The above identification, it is 



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