α α α B. M. As exclusively used for this purpose. Observations of the Pole-star are likewise Appendix. the easiest and surest, as, besides its brightness, it has the advantage, that its J. L. slow motion in altitude permits taking longer sets of repeated observations Tiarks, H. without any hurry; whereas, in other stars, the time in which they can be tronomer's observed with safety is so short, that some expedition is required in order to Report. obtain a set which will fully ensure the benefit of the principle of repetition, on which the chief excellency of Borda's circle depends. Mr. Pond has estimated, some years ago, the possible errors to which his determinations of ẞ Ursæ β Minor. and a Herculis, Procyon and a Serpentis, and a and 7 Pegasi and & Aquarii 3 Leonis and Regulus, are yet liable, at half a second; those of a Aquila and a Ophiuchi he then believed to be probably determined within a second of the truth. As it is not likely that the errors of several stars will all fall on one side, it may fairly be presumed, that by taking a mean of the latitudes derived from various stars, whose determinations are subject to so small errors only, the uncertainty still existing, respecting the single stars, will entirely vanish in their combined results. I do not apprehend, therefore, any material error from the declination of the principal stars observed at Greenwich; but with respect to the stars which are not in that list, viz. ♪ Ursae Minor, y Cephei, and & Equulei, for which I have not been able to obtain determinations supported by valid authorities, the case is quite different; and as it is evident from the observations that the declination of 7 Cephei is considerably too small-that of Ursa Minor. and y Equulei somewhat too great, the results deduced from those three stars must be excluded, until more accurate determinations of their declinations can be obtained. α 2nd. The refraction may not be accurately known, and consequently produce errors. It seems to be allowed by all, that the French tables calculated by Laplace's Formula on Delambre's Observations is the one which satisfies best, and these tables were constantly used in the reduction of all the observations. It is, however, possible, and has been proved in some cases, that the local situation of a place may have an influence on the refraction. This influence, however, is only of great consequence towards the horizon, and is less to be feared on stars which have considerable altitude. No stars have been observed which have less than 29° of altitude, ß Ursa Minor. the lowest star that was observed, having in its lower passage a little more than that; and as the results of an equal number of observations of Polaris andß Ursa Minor. on the last station agree so nearly, it is not probable that there is any great error in this part of the reduction of the observations. The southern stars seem, indeed, to give rather a greater result, which might be attributed to too great refractions being used, but may also arise from other causes. An equal number of observations of southern and northern stars of equal altitudes would perfectly destroy any error of this kind, as in the calculation of latitude the refraction has different signs for the northern and southern stars; but it is not well possible to find enough well-determined stars for this purpose. 3rd. The instruments may have constant errors which cannot be avoided. Although the repeating circle of Borda corrects almost all the errors to which common instruments are liable, yet it has been found by experience, that different repeating circles, principally those of smaller dimensions, have not given the same result; although the number of observations and their agreement among themselves was such, that the probable error of the result obtained by each seemed to fall much short of the actual difference found in their results; and it is well known that Delambre, one of the greatest practical astronomers, obtained, from a long and most satisfactory set of observations of Polaris and Ursa Minor. a result which was afterwards found to deviate more than three seconds from the truth. In order to avoid such an error, it would again be desirable to have an equal number of northern and southern stars of equal altitudes, as the observed altitudes are applied with contrary signs in the calcution of the latitude; and a constant error would therefore disappear, in taking J. L. tronomer's Report. α Appendix. the mean of the results of northern and southern stars. It was for this reason that y Cephei, which in latitude 45° has nearly the same altitude with « and Tiarks, H. Pegasi, was observed; and if the accurate declination could have been obB. M. As tained, the observations of that star would have been important. It may not be improper to remark here, that this consideration is, in the present case, of still greater importance than in most others, as an absolute latitude is to be established. In the measurement of the length of an arc of the meridian, for example, it is more the comparative latitude that is required; and the same star, observed at the different stations, may give the correct difference of latitude, and yet the absolute latitudes may not be correct. Although the number of northern stars is considerably less than that of southern stars, on account of the necessary exclusion of a Ursae Minor. and r Cephei, yet, generally, the results of both northern and southern stars are so nearly alike, that that small excess of latitude which the southern stars sometimes seem to give, cannot be of great moment in the final result. The result of the northern stars alone has been given; and it will be observed, that the final result of all observations never differs considerably from it, except at St. Regis. All which is most respectfully submitted. J. L. TIARKS, Astronomer, on the part of His Britannic Majesty, under the 5th, 6th, and 7th Articles of the Treaty of Ghent. To the Honourable the Commissioners under |