of the Georgian planet. 299 
constantly used in my sweeps of the heavens, and was found 
to be very effective for the discovery of faint nebulae and mi- 
nute clusters of stars, is hardly sufficient to show the satellites 
steadily; for, unless every thing is favourable, their faint 
scintillation will only be perceived by interrupted glimpses. 
The magnifiers 300, 460, 600 and 800, it will appear by 
the following observations, have gradually been found to be 
more effective on the objects on which they were used ; ac- 
cording to the clearness of the air, the altitude of the planet, 
the absence of the moon, the high polish of the mirror, and 
other circumstances : on particular occasions, when doubt- 
ful points were to be resolved, even 1200 has been most 
effective. The higher magnifiers 2400, 3600 and 7200 have 
also been used to scrutinize the closest neighbourhood of the 
planet, in order to discover additional satellites; but, from 
the appearance of the known ones, which began to be nebu- 
lous, I concluded that these powers W’ere not distinct enough 
to be used on this occasion. 
As the following observations are given for the purpose of 
enabling astronomers to calculate the elements of the orbits 
and motions of the satellites with mathematical precision, I 
have endeavoured to save them some labour by giving a 
clear statement of the general outlines of them; and that 
some judgment may be formed of their accuracy, which I 
hope will be found considerable, a short detail of the method 
I have pursued will be necessary. 
For ascertaining the position of the satellites from which 
their periodical revolutions were determined, three different 
methods have been used. 
Coarse estimations were made when they seemed to be 
Q q 2 
