314 Sir William Herschei/s observations and experiments 
of the first magnitude, I expected to find among those of the 
second. 
The first I tried was jQ (Fl. 33) Pegasi, but I found it not 
quite bright enough. 
The light of a Andromedag, which next I tried, was nearly 
equalised to that of Arcturus ; and the observation being 
repeated on a different night gave it equal. 
Now as in these experiments the standard star is supposed 
to be one of the first order of distances, it follows that, if 
Arcturus were put at twice its distance from us, it would then 
appear like a Andromedag, as a star of the 2d magnitude, and 
would also at the same time be really a star of the 2d order 
of distances. 
In order to obtain some other stars whose light might be 
equalised by one quarter the light of Arcturus, I tried many 
different ones, and found among them a Polaris, 7 Ursag, and 
$ Cassiopeag. These stars therefore may also be put into the 
class of those whose light is equal to the stars of the second 
order of the distance of Arcturus. 
For the purpose of ascertaining the extent of natural vision, 
it will not be necessary here to give the equalisation of stars 
of the 3d, 5th, 6th, or 7th order of distances; but taking now 
the light of one of the stars of the 2d order of distances for 
a standard, I tried many that might be expected to have the re- 
quired light, and found that when a Andromedag, with its light 
reduced to one quarter, was in the standard telescope, the 
equalising one gave p, (Fl. 48.) Pegasi for a star of the 4th 
order of distances. That is to say, the equalisation proved 
that, if Arcturus were placed at four times its distance from 
