an improved Reflecting Circle. 37 1 
comparison of these expressions, shews at once the relative 
advantages of the different instruments. 
My construction offers considerable advantages, in every 
manner of using the Circle. If, instead of the crossed observa- 
tions, it should be wanted to employ the usual practice of ren- 
dering. the glasses parallel, a multiple of the distance may still 
be obtained by my instrument, equal to that of the other me- 
thod. For this purpose, the parallelism of the glasses may be 
effected, by means of the images of the sun, or the horizon of 
the sea, moving the index F, while the o of the Nonius is adapted 
to 360° of the limb, and the two clamps A, B, are fastened. 
After this, an observation of the distance to the right may be 
made, with the clamp A fastened, while the clamp B is loose ; 
the clamp D being also fastened, and the clamp C loose ; and, at 
the end of this observation, the Flying Nonius will give an angle, 
which will be only the half of the distance in my divisions, but 
which would be equal to the whole distance, if the divisions were 
according to the Sextant. After that, and while the clamps B 
and C are fastened, and the clamps A and D loose, the paral- 
lelism of the glasses may be again effected ; and the Nonius will 
advance the same quantity over the limb. The same addition 
will take place, by inverting the use of the clamps, and making 
another observation of the distance. The like alternate process 
may be continued indefinitely; and the result given by the in- 
strument will, with only one observation more, be the same as 
that of Borda’s method, and double the arch which would be 
obtained by Mayer’s Circle. 
Mr. Borda’s Circle is liable to a very great inconvenience in 
practice. Each index advances successively over the limb ; and, 
3 B 2 
