The Latitude of the tents in Princess-Royal Harbour, from three meridian zenith distances of the sun, observed with Ramsden's universal theodolite, was 35° 2' 5" south.
Longitude from thirty-one sets of distances of the sun east and west of the moon, of which the particulars are given in [Table I] of the Appendix to this volume, 117° 53' 10" east.
These being reduced by the survey to BALD HEAD, at the entrance of the sound, will place it in
Latitude 35° 6' 15" south.
Longitude 118° 0' 45" east.*
The mean rates of the time keepers, deduced from equal altitudes taken on and between Dec. 15 and Jan. 1, and their errors from mean time at Greenwich, at noon there on the last day of observation, were as under:
h ' " "
Earnshaw's No. 543, slow 0 21 46,69 and losing 6,46 per day.
No. 520, 0 51 2,81 16,72
Arnold's No. 176, 1 0 45,46 9,26
No. 82 went too irregularly to be worth taking.
The longitude of the tents given by the time keepers on the first day of observation, with the Cape rates, was as follows:
Earnshaw's No. 543, 118° 14' 49" east.
520, 117 59 22
Arnold's 176, 118 1 14
The two first, which generally throughout the voyage showed themselves to be the best time keepers, were on a mean 13' 56" to the east of the lunar observations; but by using rates accelerating in arithmetic progression from those of the Cape of Good Hope to the new ones of King George's Sound, the mean of Earnshaw's two time keepers will then differ only 8' 19" to the east in forty-four days. In fixing the position of places from Cape Leeuwin to the Sound, these accelerating rates have been used; and the longitude has been further corrected by allowing an equal proportion of the error, 8' 19", according to the number of days after Nov. 1, when the last observations were made at the Cape of Good Hope. In the Appendix, the nature of these corrections is more particularly explained.
[* The situation of Bald Head, in captain Vancouver's chart, is 35° 6' 40" south, and 118° 16' 30" east from lunar observations which were not corrected for the errors of the astronomical tables. The situation assigned to Bald Head in the voyage of the French admiral D'Entrecasteaux, is 35° 10' south, and 118° 2' 40" east; but since the admiral passed it at six in the evening, and in blowing weather, an error of a few minutes may have entered into both latitude and longitude.]