"The practical value of the six-inch repeating circle may be estimated, by comparing the differences of the partial results from the mean at each station, with the correspondence of any similar collection of observations made with a circle, on the original construction, and of large dimensions; such, for instance, as the latitudes of the stations of the French are, recorded in the Base du Systeme Metrique: when, if due allowance be made for the extensive experience and great skill of the distinguished persons who conducted the French observations, the comparison will scarcely appear to the disadvantage of the smaller circle, even if extended generally through all the stations of the present volume; but if it be particularly directed to Maranham and Spitzbergen,--at which stations the partial results were more numerous than elsewhere, and obtained with especial regard to every circumstance by which their accuracy might be affected, the performance of the six-inch circle will 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.