350 Dr. Herschel’s observations of the satellites 
be opposite to i° 48' of the inner circle ; and that to reduce it 
by the inclination of the orbit, a correction of + 15 0 41' must 
be applied, which gives its situation in the apparent elliptical 
orbit 17 0 41' from zero. And when the distance of this point 
from the ascending node, which now is ,91° 6', is added, we 
have the satellite’s real place in its orbit 108° 47'. Then as in 
1787. it was at 5 0 6', and is now at 108° 47', it must have 
moved over an arch of 103° 41' of its orbit, to which, if we 
add 274 revolutions, we find that the sum of its motion 
amounts to 98743,68 degrees. The interval of time, in which 
it has moved over this number of degrees, will be found to 
be 3693,040277 . . days ; from this we obtain the required 
periodical time, which is 13 d n h 8' 19". This single period 
differs only 40" from the compound mean period of the revo- 
lution of the second satellite. 
The seven detached periods of the first satellite, and the 
nine of the second have all been calculated in the same man- 
ner ; and in order to obtain a mean value of them, I judged 
it proper to allow to the duration of every interval of the 
time, for which they were calculated, its due weight in the 
scale, by compounding them together. This was done by 
adding together the single intervals of time in each period, 
and also adding together the number of degrees passed over 
in each single period, and computing then the compound 
period by these collected sums of times and motions, the 
result of which is, that the first satellite makes a synodical 
revolution about the planet in 8 d i6 h 56' 5" ,2, and the second 
in 13 d n h 8' 59". 
