Brightness of the Satellites of Jupiter. 345 
investigation ; or it may denote, in case geometrical researches 
should not countenance 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 spe- 
culation, as well as observation, is opened to our view ; and 
almost every attempt to enter upon the work must seem pre- 
mature, for want of more extended observations. However, from 
those that have been given, such as they are, I will shew how 
far we may be authorized to say, that the satellites revolve on 
their axes in the same time that they perform a periodical 
revolution 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 calculated from my own tables of 
the mean motion in degrees, and according to epochs conti- 
nually 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 cal- 
culation is not required. 
The observations extend from July 19, 1794, to November 3, 
1796 ; and therefore include a period which takes in 470 rota- 
tions of the 1st satellite; 234 of the 2d; 116 of the 3d; and 
5° of the 4th : that is, provided we admit that these rotations 
