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XVII. On an improved Reflecting Circle. By Joseph de 
Mendoza Rios, Esq. F. R. S. 
Read June 4, 1801. 
In Practical Astronomy large instruments are useful, not only 
to enable the observer to read the angles to a small fraction of 
a degree, but likewise to diminish, in the construction, the in- 
accuracies which proceed both from the errors of the divisions 
and the eccentricity of the index. Frames of considerable di- 
mensions admit also the application of telescopes with great 
magnifying powers, which is a circumstance of the utmost im- 
portance in celestial observations. As the reflecting instruments 
employed at sea are supported by the hand, their weight and 
scale are limited within a narrow compass ; and it seemed very 
difficult to obviate, by any expedient, the inconveniences arising 
from the smallness of their size, while it was impossible to in- 
crease it. The celebrated Tobias Mayer contrived, however, a 
method to determine, at one reading, instead of the simple angle 
observed, a multiple of the same angle; and, by this means, 
the instrument became, in practice, capable of any degree of 
accuracy, as far as regards the above mentioned errors. His 
invention is essentially different from the mere repetition of 
the observations ; and my object requires that I should explain 
the principle upon which it is founded. 
Mr. Mayer proposed to complete the limb of the Sextant, 
making a whole Circle, with the horizon glass moveable round 
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