parallax of certain fixed stars. 279 
Let i = index error. 
d — mean polar distance of a star of the standard 
catalogue deduced from observation. 
c = mean polar distance of the same star in the cata- 
logue. 
Then 
i — d — c 
Let 0 = observed polar distance. 
r = refraction. 
p = parallax. 
a — aberration of light. 
n = nutation. 
s = semiannual equation. 
v = annual variation. 
Then z'=o + r-|-/> + a + ft-|-s + i> — c 
these quantities being applied with proper signs. 
Now i partakes of the error or uncertainty of each of these 
quantities. 
1 . Let us suppose that there is no error from the observa- 
tion or construction of the instrument ; that is, let us suppose 
0 exact. 
2. As to refraction. Any uncertainty in the quantity of 
refraction affects the index error, and therefore the required 
polar distance of a star, although that star should be in or 
near the zenith. Thus the determination of the polar distance 
of a star in the zenith, will partake of any uncertainty in the 
refraction of the lower stars used for the index error. 
Let us see to what this may amount as to the index error 
by a single star. 
Bradley’s refractions, by which the Greenwich observa- 
