Mr. de Mendoza Rios on 
S 68 
is equal to double the distance: for example, the centre index 
comes, in the first crossed observation, from m to m' ; in the third 
crossed observation, from m' to m”, &c. and the horizon index, in 
the second crossed observation, to h* ; in the fourth crossed ob- 
servation, to h ", &c. and, by each of the two indexes may be found 
the same multiple of the distance required. Let us now place 
the Nonius in a circle moving round the centre, over, or adja- 
cent to, the usual limb which contains the divisions : it will 
easily be conceived, that, by attaching that circle, which I shall 
■call the Flying Nonius, alternately to each of the indexes, it will 
■serve as Nonius for both ; and that, after any number of obser- 
-vations, it will give the compound motion of the two indexes. 
Thus, after the first-observation, the Flying Nonius will, at each 
crossed observation, advance double the distance over the divi- 
sions, while each separate Nonius, fixed on the indexes, requires 
a set of two observations, to produce the same effect in Borda’s 
'Circle. 
Plates XXX. XXXI. and XXXII. exhibit a perspective view, 
a plan, and a section, of the instrument, which, for the sake 
of. distinction, I shall call my Improved Reflecting Circle. The 
last -Plate is particularly intended to shew the compound handle, 
which I have adapted to the instrument, in order to hold it with 
convenience and ease in every position.* These three repre- 
• The use of Mayer’s Circle, or of Borda’s, as constructed till row, with only one 
handle attached to the centre, is extremely inconvenient in several positions, and par- 
ticularly when it must be kept inverted downwards during the observation. For this 
reason, I thought it of importance to contrive such a support as would enable the ©b. 
server to hold the instrument with the same ease in every direction. This is effected 
by means of the compound handle, attached to the horizon index, by the brace V and 
screw X, (Plates XXX. XXXI. and XXXII.) which index turns round the centre with 
the handle. When Mr. Troughton began to construct this sort of instruments, I 
