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 diminished 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.