l appear fully equal to that of circles of the larger
dimension. The comparison with the two stations, at which a more than
usual attention was bestowed, is the more appropriate, because it was
essential to the purposes for which the latitudes of the French stations
were required, that the observations should always be conducted with the
utmost possible regard to accuracy.

"It would appear, therefore, that in a repeating circle of six inches,
the disadvantages of a smaller image enabling a less precise contact
or bisection, and of an arch of less radius admitting of a less minute
subdivision, may be compensated by the principle of repetition."

Captain Sabine has pointed out Maranham and Spitzbergen as places most
favourable to the comparison. Let us take the former of these places,
and compare the observations made there with the small repeating
instrument of six inches diameter, with those made by the French
astronomers at Formentera, with a repeating circle of forty-one
centi-metres, or about sixteen inches in diameter, made by Fortin. It
is singular that this instrument was directed, by the French Board
of Longitude, to be made expressly for this survey, and the French
astronomers paid particular attention to it, from the circumstance
of some doubts having been entertained respecting the value of the
principle of repetition.

The following series of observations were made with the two instruments.
[I have chosen the inferior meridian altitude of Polaris, merely because
the number of sets of observations are rather fewer. The difference
between the extremes of the altitude of Polaris, deduced from sets taken
above the pole by the same observers, amounts to seven seconds and a
half.]

Latitude deduced from Polaris, with a repeating circle, 16 inches
diameter.--BASE DU SYSTEME METRIQUE, tom. iv. p. 376. 1807.

Number of Latitude Names of Observers.
Observations. of Formentera.

deg. min. sec.
64 38 39 55.3 Biot
100 54.7 Arago
10 56.2 Biot
88 56.9 Biot
120 56.7 Arago
84 54.9 Biot
100 56.5 Arago
102 57.1 Arago
80 54.5