Account of the observations by which the Longitudes of places on the south coast of Terra Australis have been settled.
The lunar distances and other observations taken in the Investigator's voyage having been ordered by the Commissioners of the Board of Longitude to be recalculated by a professed astronomer, with every degree of correctness which science has hitherto been able to point out as necessary, this delicate, but laborious task was assigned to Mr. John Crosley, formerly assistant at the Royal Observatory at Greenwich; a gentleman who formed part of the expedition as far as the Cape of Good Hope, but whose ill health had then made it necessary to relinquish the voyage and return to England. The data and results of all the observations will probably be made public, by order of the Commissioners; but in the mean time, for the satisfaction of the geographer, and more especially for that of the seaman, whose life and property may be connected with the accuracy of the charts., the results of the lunar distances observed upon each coast are added in the form of an Appendix to the volume wherein that coast is described. It is by these results that the time keepers have been regulated; and the longitudes used in the construction of the charts are taken from the time keepers.
To appreciate the degree of confidence to which these results may be entitled, it is necessary to know under what circumstances the observations were taken; also the method used in the calculations, and the corrections which have been applied beyond what is usual in the common practice at sea: of these the following is a general statement.
1st. The instruments used in taking the distances, were a nine-inch sextant by Ramsden, and three sextants of eight inches radius by Troughton, the latter being made in 1801, expressly for the voyage. On board the ship, the sextant was necessarily held in the hand, and the distances were sometimes so taken on shore; but in most of the latter cases, it was fixed on a stand admitting of the sextant being turned easily in any direction. The telescopes were of the largest magnifying powers which the motion of the ship, or state of the atmosphere could admit, and each longitude is the result of a set of observations, most generally consisting of six independent sights. They were taken either by lieutenant Flinders or by myself; those by him being designated in the column of Observers by the letter F, the others by C.
2nd. Preparatory to the reduction of the apparent to the true distance, the four following corrections have been applied.
From the sun's semi-diameter, as given in the nautical almanack, 3" have been subtracted. In the almanacks of the years comprehending our observations, the semi-diameter was stated from Mayer's tables, which gave it 3" too great; owing to the imperfection of the telescope with which Mayer observed.
The semi-diameters of the sun and moon being less in the vertical, than in the horizontal direction, on account of the differences in the refraction, they have been reduced proportionally to these differences and to the angles at the points of contact in measuring the distance. This correction is called contraction of the semi-diameter.
Before using the moon's horizontal parallax in the nautical almanack, where it is calculated for the equator, it has been corrected (printed as 'diminished', and corrected in the errata) by a number of seconds depending upon the latitude of the place, and upon this assumed position: that the earth is a regular spheroid, whose polar axis is to the equatorial axis, as 320 to 321. This, and the preceding correction are unnecessary, unless where great exactness may be required.
The refraction of the heavenly bodies given in the tables, being calculated for a mean height of 50° of Fahrenheit's thermometer, and 29.6 inches of the barometer, it has been corrected for the difference between these means and what was the state of the atmosphere at the time of observation.
3rd. In reducing the apparent to the true distance, Mr. Crosley has used the method of Joseph Mendoza de Rios, Esq., F. R. S., given with his Nautical Tables, second edition, 1809; and the tables from which the corrections were taken and the computations made, are those of the same valuable work.