Mr. de Mendoza Rios on 
370 
Adapt the o of the Flying Nonius to 360° of the limb ; and 
then fasten the two clamps A, B, of the centre index* EE, 
by which the divisions will be kept in the same relative situa- 
tion. Then, turn round the horizon index FF, and make an 
observation of the distance to the right. The contact must be 
adjusted by the screw G, the clamp C being fastened. Leave 
this clamp fastened, and loosen the clamp A ; thus turn the in- 
strument, and make a crossed observation to the left, adjusting 
by means of the screw H, after having fastened the clamp D. At 
the end of this observation, the Flying Nonius will give the 
distance. Fasten now the clamp A, and loosen the clamps B 
and C, leaving the clamp D fastened ; then turn the instrument 
again, and make a crossed observation to the right. At the end 
of this observation, the Flying Nonius will give double the dis- 
tance. By successively inverting the use of the clamps, this al- 
ternate process may be continued ad libitum ; and each crossed 
observation will increase the reading, by an arch equal to the 
distance. 
Let the number of observations be n, and the angular distance 
D. The arch given by my improved circle will be = D (n — 1 ). 
In Borda’s Circle, (reducing the divisions of the Sextant to those 
of the Theodolite I use,) the arch is = D x \ n ; and, either n 
must be an even number, or the odd observation must be lost. 
In Mayer’s Circle, the arch is = ■§■ D and the number n, 
which comprehends the observations for the parallelism of the 
glasses and those for the distance, must likewise be even. The 
* Properly speaking, neither the centre nor the horizon indexes act, in this instru- 
ment, as such, both of them being deprived of the Nonius, which is transferred to the 
flying circle ; but, for the sake of perspicuity, I continue the use of those expressions, 
in order to distinguish the plates or rules which carry the centre and the horizon 
