Mr. de Mendoza Rios on 
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the centre, with an additional index, which I shall call the horizon 
index , in order to distinguish it from the centre index , to which 
the centre glass is attached. This instrument is represented in 
Plate XXIX. Fig. 1 ; and the manner of using it is as follows. 
After the index A is set at o, (the beginning of the divisions,) 
the two glasses are rendered parallel , as is usually practised 
with Hadley's Quadrant, by moving the horizon index B,. 
till the horizon of the sea, (or the sun, or any other object,) 
or its direct image, and the doubly reflected image of the same, 
seen through the telescope, coincide. After fixing the horizon 
index in that position, the centre index A is to be moved, in 
order to measure the distance of the two objects S and L, 
(which I shall suppose the sun and moon,) by bringing into 
contact the doubly reflected image of the sun with the direct 
image of the moon, seen through the telescope. The centre 
index will then be at M, and the arch o M might give, as in 
the Sextant, the angular distance required ; but the construction 
of the Circle renders it easy, in this position, to effect again the 
parallelism of the glasses, and to make another observation 
of the contact, in the like manner as from o ; which operation 
will bring the centre index to N. The index will then give 
oN, or double the distance ; and, as it must be divided by 2, in 
order to have the angle required, the errors of division and 
eccentricity, which, together, I shall call the error of the instru- 
ment , will be likewise reduced to one half. It is obvious, that 
by successive repetitions of the same process, triple, quadruple, 
&c. the distance may be obtained, and the said error further 
reduced, in the inverse ratio of the multiplication of the distance, 
to any degree of approximation required. 
The method of rendering the glasses parallel, by means of the 
