an improved Reflecting Circle. 3 65 
horizon of the sea, is not accurate, on account of the indistinct- 
ness of the images ; and, when the sun is used for that purpose, 
the observation becomes fatiguing to the eye. The repetition of 
that operation, by one or the other method, remained therefore 
a considerable inconvenience attached' to Mr. Mayer's Circle. 
The author himself seems to have been of that opinion, as he 
proposed to provide the instrument -with a diagonal rule, fixed 
upon one of the indexes,, so that the other index should touch 
it when the glasses were parallel; but an adjustment of this 
nature must be subject to great errors, and was never adopted* 
in practice.. The Chevalier de Borda, wishing to remove that 
imperfection, had the happy idea of rendering the parallelism 
of the glasses unnecessary, by substituting the observation of 
the angular distance of the two objects, to that of the coincidence 
of the images of the same object. This constitutes the second 
great improvement of the Reflecting Circle, which it is necessary 
for me to explain, before I proceed to the account of my own. 
investigations. * 
In Borda's Circle, the telescope is fixed at some distance from 
the centre, and the horizon glass is carried near the border of the 
instrument, as in Plate XXIX. Fig. 2, By this arrangement, the. 
rays of light can arrive at the centre glass, both from the hea- 
venly bodies situated to the right of the horizon index, as S', and 
froni those situated to the- left, as S. Thus, if the glasses are pa- 
rallel to one another, when the centre index is at o, it is obvious 
that there are two ways of making, the observations. While the. 
* It does not belong to my present plan, to explain the effect of Borda’s improve- 
ment in correcting the errors which arise from the want of parallelism in the surfaces 
of the glasses. This will be fully considered in another Paper, where I intend to give 
an account of several investigations which I have made upon that particular subject. 
