310 Dr. Brinkley’s results of the application of 
when the mean index correction is used ; but still the final 
results are the same. 
The zenith distances determined in the two positions of the 
circle differ by the effect of the errors of division of the circle. 
These affect both the observations of the star and of the col- 
limator; and the quantity of error in the index correction 
arising from the errors of division, will always have a con- 
trary effect in the east and west positions. This will account 
for the apparent diversity in some of the means of the zenith 
distances determined in the two positions. The greatest dis- 
cordance is in the case of a Cygni. From thence it appears 
possible, that the error of a zenith distance determined by 
help of the collimator with the face of the circle in one posi- 
tion only may amount to i~, arising from the errors of divi- 
sion in the Dublin circle. It is not probable that a greater 
error would be found to exist in any part of the circle ; but 
the effect of errors of division in the index corrections, as 
determined by the collimator, necessarily disappears by 
taking the mean of the east and west results. Therefore the 
means of the two positions ought to exhibit the results the 
same as determined by the method of reversion. The com- 
parison given in Table I. (notwithstanding some of the stars 
have been only observed a few times), proves in a most satis- 
factory manner the exactness to be obtained by the use of 
the collimator. Of the 20 stars, only two differ by 1" 
from the former determination, and these do not differ by 
more than ii". 
In Table I./. w. signifies that the observations were made by 
the fine wire of the telescope, which is about of an inch 
in diameter, and was kindly furnished me by Dr. Wollaston : 
