Sir W illi am Herschel’s astronomical observations , &c. 303 
orbits of the planets and of their satellites; the diameters 
of the sun, the moon, and the rest of the bodies belonging 
to the solar system, as well as the distances of comets, 
have all been successfully ascertained. The parallax of 
the fixed stars has also been an object of attention; and 
although we have hitherto had no satisfactory result from 
the investigation, the attempt has at least so far succeeded 
as to give us a most magnificent idea of the vast expan- 
sion of the sidereal heavens, by showing that probably the 
whole diameter of the earth's orbit, at the distance of a star 
of the first magnitude, does not subtend an angle of more 
than a single second of a degree, if indeed it should amount 
to so much ; with regard to more remote objects, however, 
such as the stars of smaller size, highly compressed clusters 
of stars and nebulas, the parallactic method can give us no 
assistance. 
I. Of the local situation of the stars of the heavens. 
The superficial situation of the stars having already been 
carefully assigned in the catalogues of astronomers, it will be 
proper to examine how far the arrangement of the stars into 
a certain order of magnitudes can assist us to determine their 
local situation. 
When we look at the heavens in a clear night, and ob- 
serve the different lustre of the stars, we are impressed with 
a certain idea of their different magnitudes ; and when our 
estimation is confined to their appearance only, we shall be 
justified in saying, for instance, that Arcturus is larger than 
Aldebaran; the principle on which the stars are classed is, 
therefore, entirely founded on their apparent magnitude, or 
mdcccxvii. R r 
