an improved Reflecting Circle. g6y 
The same process may be repeated, by fixing alternately one 
of the indexes, and moving the other, and continuing successive 
sets of observations ; each set of two crossed observations, one 
to the right and another to the left. The angle given by the 
instrument, will be equal to double the angular distance multi- 
plied by the number of sets observed, or, in other terms, to 
the angular distance multiplied by the number of observations, 
which are always supposed to be made by pairs ; an odd obser- 
vation being of no value in this manner of using the Circle. 
I have expressed myself as if the observations could always 
be made by looking alternately at each object through the tele- 
scope, in order to bring into contact the doubly reflected image 
of the other object. This is not the case in the observations of 
the distances from the moon to the sun, or a star; it being then 
indispensable to compare, by reflection, the brightest of the two 
heavenly bodies ; but there is a very easy method of obviating 
that inconvenience. After the contact of the images of S and L 
is observed, with the telescope, directed to L, the position of the 
plane of the instrument may be inverted, turning it round the 
axis of vision O B L ; the incident ray will then answer to the 
point S', equally distant from L as S, and the crossed observa- 
tions will still give SS', or double the distance. 
Whether a Circle is used simply, as Mayer proposed it, or 
according to Borda’s method, its peculiar advantages chiefly 
depend on the multiplication of the distance required. I have 
therefore turned my attention to the improvement of this prin- 
ciple; and, with that view, I have contrived the construction 
which I am going to describe. 
In the crossed observations made with Borda’s Circle, the in- 
dexes move alternately through an arch which, in the divisions. 
