349 
of the Georgian planet. 
In the same manner, nine single periods of the second satel- 
lite have been calculated by combining the observation of the 
16th of February 1787, with one or more of the succeeding, 
as far as 1797 : the observations of 1798 being too close to 
the node to give a result that might be depended upon. 
It will be proper to give the particulars of one of the single 
periods, to show what degree of accuracy has been used in 
the calculation. 
By observation, the position of the second satellite, February 
1 6, 9 11 38' 1787, was 3 0 sf. The situation of the parallel of 
declination, by analogy (1) was such that the point F, upon 
the outer circle of Fig. 1. was opposite to 26 1° 14' of the 
inner circle; 3 0 sf therefore, was at 238° 14/ of the inner 
circle. By analogy ( 2 ) , we then find the inclination of the 
plane of the orbit to the plane of projection, which enables 
us, by the argument of the satellites being 78° 14/ from the 
greatest southern elongation, to reduce the apparent place in 
the circle to the real one, in the orbit elliptically projected. 
The correction for this reduction will be + 2° 27' ; which 
being applied, gives 260° 41/. But this being the situation 
which is numbered from the moveable zero, marked 360, it 
must be brought to its fixed distance from the ascending node 
by analogy (3) ; which gives the distance of the zero from 
that node for this day 104° 25'; and this being added to the 
former quantity, gives the real place of the satellite in its orbit 
from the ascending node 5 0 6'. 
To combine this with the observation of March 28, 10^36' 
1 797) when the same satellite was 8o° 44/ nf ; we find that 
F, in the parallel should now point to 281° 4' of the inner 
circle ; and that consequently 8o° 44' on the outer circle, will 
