348 Dr. Herschei/s observations of the satellites 
The periodical revolutions of the satellites determined. 
In the natural order of investigating the motions of the 
satellites, the first consideration ought to be to identify the 
observations, lest a star should have been mistaken for a 
satellite, or one satellite for another ; but as the calculations 
required for this purpose cannot be made without proper 
tables of their periodical revolutions, I have proceeded in the 
following manner. 
The earliest angles of the positions of the satellites which 
appeared to be sufficiently accurate for the purpose of settling 
their motions were taken 1787, February 16, 9 h 38' mean 
time. With a wire for the parallel in the focus of the eye- 
glass, and a magnifying power of 300, the position of the 
first satellite was five degrees north following ; and that of 
the second was three degrees south following : the motion of 
the satellites being so near the parallel, there can be no mate- 
rial error in the estimation of the angles ; and to prevent the 
influence of a diversity of errors, I have fixed upon the 
above-mentioned time as a general epoch to which every 
calculation of the motion of the satellites has been referred, 
not only in the determination of the periods, but also in every 
identification. 
With the assistance of the analogies that have been given, 
seven single periods of the revolution of the first satellite were 
calculated, from the union of which a general compound 
period has been deduced. The single periods were calculated 
from a combination of the observation of the 16th of February 
1787, with one of the same year, and with six more of the 
years 1790, 91, 92, 93, 94 and 96. 
