171 PHILOSOPHICAL TRANSACTIONS. [ANNO 1798. 



the clearness of the air, during a time of l h 5', which elapsed between the first 

 and second observation, might render an object invisible, which, as the first ob- 

 servation says, was " excessively faint, and could only be seen by glimpses." 



From the observed distance, which is put at " 2 diameters of the planet," we 

 may conclude what would be the distance of its greatest elongation. For, 2 diame- 

 ters from the disc of the planet give 1\ from the centre. Now, the distance of 

 the apogee at this time, by my tables, was .64, supposing that of the greatest 



2 5 x 4" 1 2 



elongation 1; therefore we have the radius of its orbit — '■ ^ — : — = lO^.l. 



This calculation is not intended to determine precisely the distance of the satel- 

 lite, but only to show that its orbit is more contracted than that of the 1st, and 

 that consequently it is an interior satellite. 



If any doubt should be entertained about the validity of this observation, we 

 have a second, and very striking one, of March 5, 179 4 ; where an interior satel- 

 lite was suspected south following the planet, at one-third of the distance of the 

 1st. March 4, when a description was made of the stars, as in figure 4, this 

 satellite was not in the place where it was observed the 5th. And, by an exami- 

 nation of the same stars March 7, it appears, that even the smallest stars n m o, 

 of the 5th, were seen in their former places, but not the satellite. The observa- 

 tion therefore must be looked upon as decisive with regard to its existence. If any 

 doubt should arise, on account of the suspicion not being verified with 480, I 

 must remark, that being used to such imperfect glimpses, it has generally turned 

 out, even when I have given up as improbable the existence of a supposed satel- 

 lite seen in that manner, that it has afterwards nevertheless been discovered that a 

 small star remained in the place where the satellite had been suspected to be situa- 

 ted. From the assigned place of this satellite, at •£- of the distance of that of the 

 first, it appears that this observation belongs to the interior satellite of Jan. 18, 

 179O, which has already been examined. The 1st satellite was this evening at its 

 greatest elongation, 4- of which is about ll". The apogee distance of a satellite 

 whose greatest distance is lO^.l would have been fy'.l on the day of our observa- 

 tion; but not being come to the apogee, by many degrees, it could not be so 

 near the planet. 



For the sake of greater precision, let us admit that the satellite was exactly 

 south following ; that is 45° from the parallel, and 45 from the meridian ; then, 

 by calculation, a satellite whose orbit is at l6".l from the planet, would, in the 

 situation now admitted, have been 7".l from its centre, which might coarsely be 

 rated at -J- of the distance of the first. But the estimation of 1 1" is probably more 

 accurate than that in the 1st observation, where 2 diameters are given. And, by 

 calculating from this quantity, we find that the greatest elongation distance of the 

 satellite is lb" .b : now putting 2-l diameters in the first observation, instead of 2, 

 the distance deduced from it will come out 19".3 ; which is certainly an agreement 

 sufficiently near to admit both observations to belong to the same satellite. 



March 27, 1794, was a 3d observation, which will assist in supporting the 2 



