43 2 Mr. Pond on the Declinations 
quantities is the greatest error of division, which has in this 
case influenced each result in an opposite direction. For 
instance, let us suppose the errors of division never to exceed 
2", but occasionally to amount to that quantity, on several 
parts of the circle ; it will then sometimes occur that each 
index will give 2" too much in one position of the instrument, 
and 2" too little in the other ; there will then appear a diffe- 
rence of 4" in the error of collimation ; but the observations 
in these extreme cases will not on that account be the less to 
be depended on ; on the contrary, the probability is in favour 
of their superior accuracy. 
Nor, on the other hand, will those observations which give 
the mean error of collimation deserve greater confidence 
than the rest, since it is evident that some of them may be, 
and most probably are, affected with the greatest possible 
error ; for we suppose the most erroneous observation to arise 
from the greatest error of division occurring on each of the 
four arcs in the same sense, that is all plus or all minus ; 
nevertheless, the observation thus erroneous, will give the 
mean error of collimation. 
By an attentive consideration of these circumstances, correc- 
tions might perhaps be obtained which would somewhat 
diminish the probability of error. But it is to the principle of 
the revolving microscopes, that in the future construction 
of instruments we should look for perfection. In the French 
circle of repetition, too great a sacrifice is made to the sup- 
posed advantage of reading off a great number of observations 
at once. Our best instruments are too well constructed to 
stand in need of this contrivance, as the divisions on a two- 
feet circle are read off with precision to a single second. 
