VOL. LXXX.] PHILOSOPHICAL TRANSACTIONS. 735 



the moon nearly at the full, should so often escape our notice in its frequent re- 

 volutions, unless it varied much in its apparent brightness. 



To this we must add another argument drawn from the number of lucid spots, 

 which will not agree with the motion of one satellite only; whereas, by admitting 

 a revolution of the ring itself, in lO"^ 32™ 15\4; and supposing all the spots to 

 adhere to the ring, and to share in the same periodical return, provided they last 

 long enough to be seen many times, we shall be able to give an easy solution to 

 all the remaining observations. 



For instance, let «, (3, y, ^, i, represent five spots on the ring of Saturn, situated 

 as in fig. 5, pi. 8; where the ring is supposed to be divided into36o degrees, and 

 the spot a placed at 27l°.5; (3 at 70°.2; y at 183°.0; ^ at 142°.5; and i at 358°.6. 

 Then will the ring, with the spots thus placed, serve as an epocha for the year 

 1789; by which, with the assistance of a table constructed on the before men- 

 tioned period of the rotation of the ring, we may calculate their situation for 

 any required time; and to render this calculation perfectly convenient, a table is 

 given, ready prepared for the purpose, at the end of the other tables. Dr. H. 

 then gives another set of observations, which had all been previously calculated 

 by the tables of such of the 7 satellites as were not already in view, and had 

 been found to belong to neither of them ; but in the notes that are given with 

 them they have been again calculated by the table of the rotation of the ring 

 for every time they were observed, on a supposition of their being spots ad- 

 hering to it. He then adds; 



The great accordance between the observed places of these spots and the cal- 

 culated ones, seems to establish the rotation of the ring of Saturn on an axis, 

 so as hardly to leave any doubt on the subject. The time of it, we have al- 

 ready seen, is 10^ 32™ 15^4. It may be objected, that many of the observations 

 are such as would also agree with other assignable periods, especially when the 

 number of spots is so considerable as 5 ; but the most material observations, 

 which are those on the spot a, setting aside all the rest, seem alone to amount to 

 a proof not only of a rotation of the ring, but of the time in which it is per- 

 formed. 



It may be expected, that having now sufficiently examined the whole series of 

 observations of the last new satellites, we can give their periodical times and dis- 

 tances more accurately than before. The times indeed are full as well ascer- 

 tained as we can expect to have them : for on calculating 6 satellites by his tables 

 back to Aug. 19*^ 12*^ 19™ 56% 1787, we find their places 341°.l the 5th; 

 10°.6the4th; 2n°.l the 3d; 158°.9 the 2d; 80°.2 the 1st; and 288°.8 the 

 6th. And Dr. H's journal contains the fullest assurance that they were thus 

 situated at the time for which this calculation is made. We may therefore fix 

 the period of the 6th at l'^ S'^ 53™ 8^9. The 7th satellite can only be traced 

 back, as far as the 8th of Sept. 1789; so that its revolution will require at least 



