the effects of parallax, &c. of certain fixed stars. 329 
thirteen stars. These results contain the mean polar distance 
of each star reduced to January 1, 1819, the constant of 
aberration for each star, and the semi-parallax. 
In deducing the quantity of parallax, the results must be 
affected by any uncertainty in the constant of aberration, 
since the times of the observations must necessarily be ex- 
tended, so that the effects of aberration become sensible ; 
and in like manner, in investigating the constant of aberra- 
tion from observations of a given star, the parallax, if any, 
will be involved. Hence I adopted the following process in 
reducing the observations. The observed zenith distances of 
a given star were reduced to Jan. 1, 1819, by the common 
equations, taking the constant of aberration = 20", 25. The 
mean of these were taken. The correct mean zenith distance 
was supposed equal to this mean — e, the constant of aber- 
ration = 20,25 + x, and the semi-parallax =p . The equa- 
tions of condition resulting from the respective observations 
thus contained three unknown quantities. These equations 
were reduced to three, by the method of making the sum of 
the squares of the errors a minimum. The solutions of these 
three equations give the values of e, x and p, and thence the 
values of the mean polar distance, constant of aberration, and 
semi-parallax, as stated in Table 1. 
In regard to the selection of these stars, some were select- 
ed with a reference to my former results as to parallax; 
others, as being convenient for the investigation of the con- 
stant of aberration. 
The parallax resulting for «. Lyras does not materially differ 
from my first determination. That of a Aquilas is less than 
