VOL. LXXXVII.] 



PHILOSOPHICAL TRANSACTIONS. 



1Q3 



investigation ; or it may denote, in case geometrical researches should not counte- 

 nance a sufficient deviation from the spherical form, that some part of the discs of 

 these satellites reflects hardly any light, and therefore in certain situations of the 

 satellite makes it appear of a smaller magnitude than in others. Here then we see 

 evidently that a considerable field for speculation, as well as observation, is opened 

 to our view ; and almost every attempt to enter on the work must seem premature, 

 for want of more extended observations. However, from those that have been 

 given, such as they are, I will show how far we may be authorised to say, that the 

 satellites revolve on their axes in the same time that they perform a periodical revo- 

 lution about the planet. 



I shall take the usual method of throwing the observations of each satellite into 

 a graduated circle. The zero of the degrees into which I suppose it divided, is in 

 all observations assumed to be in the place of the geocentric opposition. In order 

 to bring these observations to the circle, the places of the satellites have been cal- 

 culated from my own tables of the mean motion in degrees, and according to 

 epochs continually assumed from the geocentric conjunctions pointed out in the 

 configurations of the Nautical Almanac; and the nearest of these conjunctions 

 have been always used. This method is fully sufficient for the purpose, as greater 

 precision in the calculation is not required. The observations extend from July ] 9, 

 1794, to November 3, 1796; and therefore include a period which takes in 470 

 rotations of the 1st satellite; 234 of the 2d; 1 1 6 of the 3d; and 50 of the 4th; 

 that is, provided we admit that these rotations are performed in the same time as 

 the satellites revolve in their orbits. In the following table are the calculated places 

 of the satellites; the correct sidereal times, given with the observations, having 

 been turned into mean time. 



Positions of the 4 Satellites of Jupiter at the Time of the Observations. 

 Time of observation. 



1794. 



9 h 



8 



8 



10 



July 19 

 July 21 

 July 26 

 July 28 

 July 30 



July 31 8 



Aug. 1 .... 8 



Aug. 9 8 



1795. 



Sept. 30 7 



Oct. 2 7 



21 r 

 57 

 56 

 59 

 27 

 40 

 56 

 42 



37 



32 



It will be necessary now to explain in what manner, with the assistance of this 

 table, the observations of the brightness and magnitudes of the satellites have been 

 reduced to the expressions they bear in the 4 circles of the figures 1 , 2, 3, 4, pi. 4. 

 By way of uniformity I judged it would be best to reduce the estimations of mag- 

 nitude to those of brightness ; as it may be justly supposed that when a satellite is 



vol. xviii. C c 



