an improved Reflecting Circle . 373 
opposite one another, might however be advantageous, in order 
to correct the errors of eccentricity; but, in my opinion, a 
greater number ought not, in any case, to be used. 
Before I conclude this Paper, I shall remark, that my im- 
provement may be partially applied to a Circle, where the 
telescope and the horizon glass are attached, or fixed, to the 
main frame of the instrument. The Flying Nonius, acting then 
with the single centre index, will only give the same result as 
Borda’s Circle ; but this construction seems to me greatly pre- 
ferable to all the other plans executed till now ; the whole ap- 
paratus being more solid and simple, and its use not liable to 
the errors which arise from the motion of the horizon index. 
With this construction, we may likewise employ a method 
of ascertaining the place where the parallelism of the glasses 
was observed to take place, and of setting the index afterwards 
in the same situation, as often as is necessary for the repetition 
of the observations. A piece may be used, so contrived as to be 
attached to, or detached from, one side of the index, by means 
of a screw ; and provided besides with other screws, to fasten it 
to any part of the limb. This rectification piece, being previ- 
ously attached to, and carried with, the index, must be fixed in 
the situation it occupied when the contact of the images was 
observed. The index will then be detached from it, in order to 
observe the distance, and afterwards must be brought back to 
the same position as before, contiguous to the rectification piece. 
The like alternate process may be repeated ; and the Flying 
Nonius, going with the index in the motions forwards, and 
standing still in the motions backwards, will give the multiple of 
the observed angle, without performing the observation for the 
parallelism more than once in the beginning. In Mayer’s Circle, 
