1()4 PHILOSOPHICAL TRANSACTIONS. [ANNO 1797. 



at any given time larger in proportion to another than it was at another time, it 

 will also be brighter than it was at that other time, due regard being had tQ the light 

 of the satellite to which its magnitude has been compared. To manage the space 

 allotted to the figure advantageously, I have used the abbreviations formerly em- 

 ployed in my catalogue of nebulae, vb, cb, b, pB, pF, f, cf, vf, for all the gra- 

 dations of light that are necessary to express the brightness of the satellites at the 

 time of observation. It will be easily remembered that b and f mean bright and 

 faint; and p, c, v, stand for pretty, considerably, and very. 



Now, when the observation mentions the brightness of the satellite, I place it 

 in the figure as it is given. In that of the first, for instance, July 19, 1794, we 

 find the satellite called very bright; I therefore set down in fig. 1, at 127°, vb. 

 But where the brightness is not expressed, I have recourse to the comparative 

 magnitude, if that can be had. By fig. 3, it appears that the 2d satellite is less 

 subject to a change of brightness than either the 1st or 4th: it becomes, for that 

 reason, a pretty good standard for the light of these other satellites. Therefore, in 

 the observation of October 2, 1795, for instance, where the 1st satellite is de- 

 scribed as undoubtedly less than the 2d, I set down very faint, or vf, at 341° of 

 the circle of fig. 1 ; for in the observation of July 19, before-mentioned, when the 

 satellite was called very bright, it was at the same time described as undoubtedly 

 larger than the 2d. In this case, as regard must be had to the relative state of the 

 satellite we refer to, the 4 figures will assist us in determining the condition of 

 the light of the satellite we wish to admit as a standard. 



In reducing the 2d satellite to the circle, I have generally used a reference to the 

 magnitude of the 1st, where marks of brightness were wanting; and sometimes 

 also to the magnitude of the 4th, and even of the 3d. The 3d satellite can hardly 

 be ever compared to any but the 2d in magnitude; and this only in its degree of 

 excess. The magnitude of the 4th satellite has been generally compared with that 

 of the 1st; and also sometimes with that of the 2d. To make an application of 

 the contents of the figures, will now require little more than a bare inspection 

 of them. 



The 1st satellite appears evidently to have a rotation on its axis that agrees with 

 its revolution in its orbit. It cannot be supposed that, in the course of 470 revo- 

 lutions, all the bright observations could have ranged themselves in one half of the 

 orbit, while the faint ones were withdrawn to the other. The satellite appears in 

 the middle of the duration of its brightness, when it is nearly half way between its 

 greatest eastern elongation, in the nearest part of its orbit; or when advancing 

 towards its conjunction. I have pointed out this circumstance by a division with 

 dotted lines, and the words bright and faint, inserted within the circle, fig. 1 1 

 This satellite therefore revolves on its axis in l d 18 h 26 m .6. 



The 2d satellite, though much less subject to change, on account, as we may 

 suppose, of having only a small region on its body which reflects less light than the 

 rest; has nevertheless its rotation directed by the same law with the 1st. It will 



