VOL. LXXX.] PHILOSOPHICAL TRANSACTIONS. 731 



observations were continued near 2 months afterwards, and as he had from them 

 corrected the epochae of the old satellites, and improved the tables of the new 

 ones, he found that, besides many of these bright points which were completely 

 accounted for by the calculated places of the satellites, there were also many 

 more mentioned in his journal that would not accord with the situation of any 

 of them. 



The question then presented itself very naturally, what to make of these pro- 

 tuberant points? To admit 2 or 3 more satellites by way of solving such phe- 

 nomena appeared too hazardous an hypothesis; especially as these lucid points, 

 though some of them had a motion, did not seem willing to conform to the cri- 

 terion he had before used of coming off the ring, and showing themselves as 

 satellites. And yet a suspicion of at least one more satellite would often return ; 

 it was even considerably strengthened when he discovered, by means of re-calcu- 

 lating with great precision the whole series of observations, that in the beginning 

 of the season there had been some few mistakes in the names of the satellites, 

 when the observations of them were entered in the journal. In setting them 

 right, which threw a great light on the revolution of the 6th, and more espe- 

 cially on that of the 7 th, he found also, that some of the observations which 

 were entered by the name of the 7th satellite could not belong to that, nor to 

 any other known one. It remained therefore to be examined whether there 

 might not be sufficient ground to suspect the existence of an 8th satellite. 



In this situation of things, he thought it most advisable to draw out the whole 

 series of observations in a paper, beginning at the 5th satellite, and thus gra- 

 dually through the 4th, 3d, 2d, 1st, 6th, and 7th, to approach towards the 

 centre of Saturn ; that it might appear at last what observations were left unac- 

 counted for. By this means also it may be seen clearly with how scrupulous an 

 attention the identity of every satellite has been ascertained; and with a view to 

 give the strongest satisfaction in this respect, at least one observation of each has 

 been calculated for each night ; and the place thus computed is set down in the 

 notes, that it may be compared with the observed one. To facilitate this com- 

 parison, he delineated a scheme, in which the orbits of the satellites are drawn 

 in their due proportion. A few words will explain the construction and use of 

 this figure, which, notwithstanding its simplicity, is yet amply sufficient to as- 

 certain the accuracy of every observation. 



In each of the orbits, described round the centre of Saturn, at their propor- 

 tional distances, by way of marking them, is placed the satellite to which it 

 belongs, as it appeared to be situated the 18th of October, 1/89; also a gradua- 

 ted circle, the use of which is to find, by means of the tables, the apparent 

 place of a satellite for any given time; or, the apparent situation of the same 

 satellite being given, its real Saturnicentric place may be deduced from it. In 



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