A Voyage to Terra Australis/Volume 1/Appendix

by Matthew Flinders

 

APPENDIX.

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 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.

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.

4th. The reduced distance, found as above, has been corrected to the spheroidal figure of the earth, according to the theory explained in the Philosophical Transactions of the Royal Society of 1797; and for doing which, rules are given by Mr. Mendoza with his Nautical Tables of 1801. This calculation is tedious, and the correction, more especially in low latitudes, too small to be necessary in common cases.

5th. In the nautical almanack the distances are given to every three hours, but the irregularities of the moon's motion being such as to cause some inequality in the different parts of this interval, the distance at the hour preceding, and at the hour following the time of observation, was found by interpolation from the two nearest given on each side; and having the distances at Greenwich for each hour, the observed distance can never fall more than half an hour from one of them; and the moon's inequalities do not then produce any sensible error in the corresponding time, as obtained from common proportion. The correction arising from this process is seldom so important as to be necessary in sea observations.

6th. The longitude deduced from a comparison of the true distance at observation with the hourly distances at Greenwich, is contained in the following tables under the head of Longitude from Nautical Almanack. But as it frequently happened, that the observation was not taken exactly in the place which it is intended to fix, this longitude is reduced to that place by the application of the difference shown by the time keepers to have existed between the two situations. In ascertaining this difference, the rates of going allowed to the time keepers are generally those found at the place which is to be fixed; whether applied to observations taken before arriving, or after quitting that place. This, however, could be done only at those stations where rates had been observed; at the intermediate points, where the result of lunar distances is given principally as an object of comparison with the time keepers, the rates allowed in the reduction are those found at the station previously quitted; but then the difference of longitude is corrected by the quantity consequent on the following supposition: that the time keepers altered their rates from those at the previous, to those at the following station, in a ratio augmenting in arithmetic progression. The difference of longitude, thus corrected when necessary, is given under the head of Reduction by time keepers; and the longitudes reduced by it to the place intended to be fixed, are taken to be of equal authority with those resulting from observations made in the place itself.

7th. But these longitudes, whether reduced to, or observed in, the place to be fixed, still require a correction which is of more importance than any of those before mentioned. The theories of the solar and lunar motions not having reached such a degree of perfection as to accord perfectly with actual observation at Greenwich, the distances calculated from those theories and given in the almanack become subject to some error; and consequently so do the longitudes deduced from them. The quantities of error in the computed places of the sun and moon, have been ascertained at Greenwich as often as those luminaries could be observed; and Mr. Pond, the astronomer royal, having permitted access for this purpose to the table of errors kept in the Observatory, Mr. Crosley has calculated the corresponding effects on the longitude, and proportioned these to the time when our observations were taken. The combined effect of the two errors forms a correction to the longitudes obtained from the sun and moon; but when the moon was observed with a star, then the moon's error alone gives the correction. But it has sometimes happened, that there were many days interval between the observations of the moon at Greenwich, and that the errors preceding and following are so extremely irregular, that no accuracy could be expected in reducing them by proportion; in these unfortunate cases, that part of the error belonging to the moon has been taken absolute, such as it was found on the day nearest to the time of observation; but the sun's error is always from proportion. These corrections, with the interval in the Greenwich observations of the moon, are given under their proper heads.

8th. The longitudes thus computed, reduced to the intended point, and corrected, are placed under each other; and the mean of the whole is taken to be the true longitude of that point, unless in certain cases where it is otherwise expressed. The mean is also given of the longitudes uncorrected for the errors of the sun and moon's places, that the reader may have an opportunity of comparing them; and some sea officers who boast of their having never been out more than 5′, or at most 10′, may deduce from the column of corrections in the different tables, that their lunar observations could not be entitled to so much confidence as they wish to suppose; since, allowing every degree of perfection to themselves and their instruments, they would probably be 12′, and might be more than 30′ wrong.

In the nautical almanacks for 1814 and 1815, the distances are computed from the new tables of Burg for the moon, and of Delambre for the sun; and it is to be hoped that the necessity of correcting for errors in the distances at Greenwich will have ceased, or be at least greatly diminished. Should the computed places of the sun and moon be happily found to agree with actual observation, and supposing that our results may be taken as the average of what practised observers with good instruments will usually obtain when circumstances are favourable, then lunar observations taken in 1814 and afterwards, may be entitled to confidence within the following limits:

From one set of distances, consisting of six independent sights, the error in longitude may be 30′ on either side; but will probably not exceed 12′.

From six sets on one side of the moon, each set consisting as above, the error may be 20′; but not probably more than 8′.

Twelve sets of distances, of which six on each side of the moon, are not likely to err more than 10′ from the truth; and may be expected to come within 5′.

The error in sixty sets, taken during three or four lunations, and one half on each side of the moon, will not, I think, be wrong more than 5′; and will most probably give the longitude exact to 1′ or 2′. This degree of accuracy is far beyond what the hopes of the first proposers of the lunar method ever extended, and even beyond what astronomers accustomed only to fixed observatories will be disposed to credit at this time; but in thinking it probable that sixty sets of lunar distances will come within 1′ or 2′ of the truth, when compared with correct tables, I conceive myself borne out by the following facts.

In Port Lincoln, I observed an eclipse of the sun with refracting telescope of forty-six inches focus, and a power of about two hundred. It was recalculated by Mr. Crosley from Delambre's and Burckhardt's tables, the one made four and the other ten years afterwards. The longitude deduced from the beginning differed only 1′ 31″,5 from that at the end, and the mean of both only 1′ 17″ from thirty sets of lunar distances corrected for the errors of the tables.

The Spanish admiral D'Espinosa observed emersions of the first and second satellites of Jupiter in 1793, at Port Jackson, and also an eclipse of the sun which he recalculated by the tables of Burg. He deduces from thence the longitude of Sydney Cove to be 151° 12′ 45″; and from forty-four sets of lunar distances by lieutenant Flinders, it would be 151° 11′ 49″ east.

At Port Louis in the Isle Mauritius, the Abbé de la Caille observed an eclipse of the sun, the transit of mercury over the sun's disk, and various occultations of Jupiter's satellites; M. d'Après also observed several occultations; and this place should therefore be well determined. Its longitude in the Requisite Tables is 57° 29′ 15″ east; and from twenty-seven sets of distances taken whilst a prisoner there, I made it, when corrected for the errors of the tables, 57° 29′ 57″ east.

In appreciating the degrees of accuracy to which a small or larger number of lunar distances may be expected to give the longitude, I suppose the observer to be moderately well practised, his sextant or circle, and time keeper to be good, and his calculations to be carefully made; and it is also supposed, that the distances in the nautical almanack are perfectly correct. As, however, there may still be some errors, notwithstanding the science and the labour employed to obviate them, it cannot be too much recommended to sea officers to preserve all the data of their observations; more especially of such as may be used in fixing the longitudes of places but little, or imperfectly known. The observations may then be recalculated, if requisite; the corrections found to be necessary may be applied; and the observer may have the satisfaction of forwarding the progress of geography and navigation, after having contributed to the safety of the ship, and benefit of the particular service in which he may happen to have been engaged.

 

TABLE I. (Reference from p. 69.)

Longitude of the Observatory in Princess Royal Harbour, King George's Sound.

Appt. Greenwich time of the observations.		Place.	Longit. E. from Naut. Alm.			Reduction by two time keepers.			E. Longitude of the Observatory.			Correction		Correct Longit. of the Observatory.			Whence deduced.	Observer.
												for errors in tables	Interv. of ☾'s error.
1801 Nov.⁠			º	′	″	º	′	″	º	′	″	′⁠ ″		º	′	″
ʰ ⁠′  28 at 17 30	$\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$	At sea. —	90  91	56  6	0 15	+27	20 —	49	118 118	16 27	49  4	−29 45 —	One day —	117 117	47 57	4 19	ʘ E. ☾ —	C —
29 at 17 50	$\scriptstyle {\left\{{\begin{matrix}\ \\\ \end{matrix}}\right.}$	— —	95  95	50 47	45 45	+22	39 —	7	118 118	29 26	52 52	−29  0 —	Two days —	118 117	0 57	52 52	Ditto. —	— —
30 at 17 23		—	97	51	0	+20	20	18	118	11	18	−28 30	—	117	42	48	—	F
December.⁠ ʰ ⁠′  11 at 17 24	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	Anchorage in Princess Royal Harbour.	118 118 118 118 118	4  4  7  9  1	30 30 30 45  0				118 118 118 118 118	4  4  7  9  1	30 30 30 45  0	− 5 30 — — — —	One day — — — —	117 117 118 118 117	59 59  2  4 55	0  0  0 15 30	ʘ W. ☾ — — — —	C — F — —
12 at 21 47	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	At Observatory. — — —	117 117 117 117 117	56 59 55 54 58	45 15 45 30 45				117 117 117 117 117	56 59 55 54 58	45 15 45 30 45	− 9 30 — — — —	One day — — — —	117 117 117 117 117	47 49 45 44 49	15 45 15  0 15	Ditto. — — — —	C — F — —
31 at 13 32	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$	Ditto. — — — — — — — — —	118 118 117 117 117 117 118 118 117 117	2  6 58 56 55  8  4 50 52 51	45 30  0 45  0  0 30  0 30  0				118 118 117 117 117 117 118 118 117 117	2  6 58 56 55  8  4 50 52 51	45 30  0 45  0  0 30  0 30  0	−13 0 — — — — — — — — —	One day — — — — — — — — —	117 117 117 117 117 117 117 117 117 117	47 53 45 43 42 55 51 37 39 38	45 30  0 45  0  0 30  0 30  0	ʘ E. ☾ — — — — — — — — —	C — F — — C — F — —
1802 Jan.⁠ ʰ ⁠′  11 at 17 56	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$	On shore at Lucky Bay. — — — —	122 122 122 122 122 122	30 29 33 34 38 41	45 30 15 45 45 15	− 4	22 — — — — —	38	118 118 118 118 118 118	8  6 10 12 16 18	7 52 37  7  7 37	− 6 15 — — — — —	One day — — — — —	118 118 118 118 118 118	1  0  4  5  9 12	52 37 22 52 52 22	ʘ W. ☾ — — — — —	C — — — — —
Longitude from thirty-one sets of lunar distances,				$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	Uncorrected				118	5	41,8	Corrected		117	53	9,9	and taken

 

From observations	east of the moon alone	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	117°	48′	3,7″
	west of the moon alone	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	117	57	57
		Mean	117	53	0,3	east.

 

TABLE II. (Reference from p. 84.)

Longitude of the south point of Lucky Bay, Archipelago of the Recherche.

Appt. Greenwich time of the observations.		Place.	Longit. E. from Naut. Alm.			Reduction by two time keepers.			E. Longitude of Lucky Bay.			Correction			Correct Longit. of Lucky Bay.			Whence deduced.	Observer.
												for errors in tables		Interv. of ☾'s error.
			°	′	″				°	′	″	'	″		°	′	″
1802 Jan.⁠ ʰ    ′ 9 at 17 56	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	On the South Pt. — — — —	122 122 122 122 122 122	30 29 33 34 38 41	45 30 15 45 45 15				122 122 122 122 122 122	30 29 33 34 38 41	45 30 15 45 45 15	−6 — — — — —	15	One day — — — — —	122 122 122 122 122 122	24 28 27 28 32 35	30 15  0 30 30  0	ʘ W. ☾ — — — — —	C — — — — —
27 at 13 28	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	At sea. — — — — —	132 131 131 131 131 131	0 51 51 47 50 52	45 15  0  0 15 45	° − 9	' 30 — — — — —	" 55	122 122 122 122 122 122	29 20 20 16 19 21	50 20  5  5 20 50	−8 — — — — —	45	As on 27th there being no other obs. until Feb 5. —	122 122 122 122 122 122	21 11 11  7 10 13	5 35 20 20 35  5	ʘ E. ☾ — — — — —	C — — — — —
28 at 14 42	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	On shore at Fowler's Bay. —	132 132 132 132	30 24 19 19	45 30 30 15	−10	13 — — —	38	122 122 122 122	17 10  5  5	7 52 52 37	−8 — — —	30	Ditto. — — —	122 122 121 121	8  2 57 57	37 22 22  7	Ditto. — — —	F — — —
Longitude from sixteen sets of lunar distances,			$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	Uncorrected		122	23	27,1	Corrected						122	15	42,1

 

Longitude of the south point from the two time keepers.
On Jan. 9 at 15ʰ 51′ of Greenwich time, and using the King-George's-Sound rates, the mean longitude was	122°	15″	48″
Correction for variation in the rates found at Pt Lincoln,		−0	24,1
Correction for supplemental error during 9 days,		−1	10,2
Corrected longitude, taken preferably to that above,	122	14	13,7	east

 

TABLE III. (Reference from p. 105.)

Longitude of the Anchorage in Fowler's Bay.

Appt. Greenwich time of the observations.		Place.	Longit. E. from Naut. Alm.			Reduction by two time keepers.			East Longit. of the Anchorage.			Correction			Corr. Longit. of the Anchorage.			Whence deduced.	Observer.
												for errors in tables		Interv. of ☾'s error.
			°	′	″	°	′	″	°	′	″	'	″		°	′	″
1802 Jan.⁠ ʰ    ′ 9 at 17 56	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	On shore at Lucky Bay. — — —	122 122 122 122 122 122	30 29 33 34 38 41	45 30 15 45 45 15	+10	13 — — — — —	38	132 132 132 132 132 132	44 43 46 48 52 54	23  8 53 23 23 53	− 6 — — — — —	15	One day — — — — —	132 132 132 132 132 132	38 36 40 42 46 48	8 53 38  8  8 38	ʘ W. ☾ — — — — —	C — — — — —
27 at 13 28	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	At sea. — — — — —	132 131 131 131 131 131	0 51 51 47 50 52	45 15  0  0 15 45	+ 0	42 — — — — —	43	132 132 132 132 132 132	43 33 33 29 32 35	28 58 43 43 58 28	− 8 — — — — —	45	As on 27th there being no other obs. until Feb 5. —	132 132 132 132 132 132	34 25 24 20 24 26	43 13 58 58 13 43	ʘ E. ☾ — — — — —	C — — — — —
28 at 14 42	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	On shore at Fowler's Bay. —	132 132 132 132	30 24 19 19	45 30 30 15				132 132 132 132	30 40 38  5	7 52 52 37	− 8 — — —	30	Ditto. — — —	132 132 132 132	22 16 11 10	15  0  0 45	Ditto. — — —	F — — —
February ʰ    ′ 15 at 1 26	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	At sea. — — — — —	135 135 135 135 135 135	8 18 16 44 31 21	0 15 30 15 15 30	− 2	37 — — — — —	43	132 132 132 132 132 132	30 40 38  6 53 43	17 32 47 32 32 47	−19 — — −19 — —	45     15	Two days — — — — —	132 132 132 132 132 132	10 20 19 47 34 24	32 47  2 17 17 32	* Aldeb. W. ☾ — * Sp. Virg. E. ☾ —	C — — — — —
Longitude from twenty-two sets of lunar distances,				$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	Uncorrected				132	39	24	Corrected			132	28	26,7

 

Longitude of the Anchorage from the two time keepers.
On Jan. 28 at 11ʰ 14′ of Greenwich time, and using the King-George's-Sound rates, the mean longitude was	132°	32′	37″
Correction for variation in the rates found at Pt. Lincoln,		−3	34,4
Correction for supplemental error during 27,8 days,		−3	36,8
Corrected longitude, taken preferably to that above,	132	25	25,8	east.

 

TABLE IV. (Reference from p. 148.)

Longitude of the Tents, at the head of Port Lincoln.

Appt. Greenwich time of the observations.		Place.	Longit. E. from Naut. Alm.			Reduction by two time keepers.	East Longitude of the Tents.			Correction		Correct Longit. of the Tents.			Whence deduced.	Observer.
										for errors of tables	Interv. of ☾'s error.
			°	′	″	°⁠′⁠″	°	′	″	′⁠″		°	′	″
1802 Feb.  ʰ    ′ 15 at 1 26	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	At sea. — — — — —	135 135 135 135 135 135	8 18 16 44 31 21	0 15 30 15 15 30	+0 44 58 — — — — —	135 136 136 136 136 136	52  3  1 29 16  6	58  3  1 29 16  6	−19 45 — — −19 45 — —	Two days. — — Ditto. — —	135 135 135 136 135 135	33 43 41  9 56 47	13 28 43 58 58 13	* Aldeb. W. of ☾ — * Sp. Virg. E. of ☾ —	C — — — — —
26 at 13 22	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	At the tents. — —	136 135 135	1 52 51	15 30 15		136 135 135	1 52 51	15 30 15	−4 30 — —	One day. — —	135 135 135	56 48 46	45  0 45	ʘ E. ☾ — —	F — —
March.⁠ ʰ⁠′  9 at 16 36	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	At anchor near the head of Spencer's Gulph. — —	138 138 138 138 138 137	14 30 13  5  4 59	30  0 45  0  0 30	−2  5  5 — — — — —	136 136 136 135 135 135	9 24  8 59 58 54	25 55 40 55 55 25	−15 30 — — — — —	Two days. — — — — —	135 136 135 135 135 135	53  9 53 44 43 38	55 25 10 25 25 55	ʘ W. ☾ — — — — —	F — — — — —
10 at 18 42	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	Ditto. — — — — —	138 138 138 138 137 137	4  2  3  4 55 57	30 15 45 15  0 15	Ditto. — — — — —	135 135 135 135 135 135	59 57 58 59 49 52	25 10 40 10 55 10	−16 30 — — — — —	Ditto. — — — — —	135 135 135 135 135 135	42 40 42 42 33 35	42 40 42 42 33 40	Ditto. — — — — —	F — — — — —
25 at 12 42	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	Under sail, Investigator's Strait. —	137 137 137 137	38 46 38 46	30 45 30 45	−1 47 34 — — —	135 135 135 135	50 59 50 59	56 11 56 11	−7 15 — — —	Five days. — — —	135 135 135 135	43 51 43 51	41 56 41 56	ʘ E. ☾ — — —	F — — —
26 at 13  6	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right.}$	Ditto. — — — —	137 137 137 137 137	43 41 39 41 47	0 15 45 15 30	−1 57 54 — — — —	135 135 135 135 135	45 43 41 43 49	6 21 51 21 36	−10 45 — — — —	Ditto. — — — —	135 135 135 135 135	34 32 31 32 38	21 36  6 36 51	Ditto. — — — —	F — — — —
Longitude from thirty sets of lunar distances,			$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	Uncorrected			135	58	21,6	Corrected		135	44	51,1	and taken

 

From observations west of the moon alone	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	135°	43′	56,6″
From observations east of the moon alone	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	135	45	45,5
	Mean	135	44	51,1	east.
Solar Eclipse of March 4, 1802, observed at the tents.
Longitude deduced from beginning	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	135	46	54
Longitude deduced from end	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	135	46	22,5
	Mean	135	46	8,2	east.

 

TABLE V. (Reference from p. 220.)

Longitude of Point Nepean at the entrance of Port Phillip.

Appt. Greenwich time of the observations.

Place.

Longitude E. from Naut. Alm.

Reduction by two time keepers.

East Longitude of Pt. Nepean.

Correction

Correct Longit. of Pt. Nepean.

Whence deduced.

Observer.

for errors of tables

Interv. of ☾'s error.

°

′

″

°⁠′⁠″

°

′

″

′⁠″

°

′

″

1802 April. ʰ   ′  16 at  0 42

$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$

At sea. — — — — —

140 140 140 140 139 139

6  6 10  2 55 52

45 15 15 15 45 30

+4 57 25 — — Ditto. — —

145 145 145 144 144 144

4  3  7 59 53 49

10 40 40 40 10 55

−21 45 — — −21 15 — —

Four days. — — Ditto. — —

144 144 144 144 144 144

42 41 45 38 31 28

25 55 55 25 55 40

* Antares. E. of ☾ — * Regulus. W. of ☾ —

C — — — — —

26 at 12 34

$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$

At 1st anchor in Port Phillip. — — — —

144 144 144 144 144 144 144

45 37 46 41 43 44 41

45 45  0 30  0  0 45

−0  8 10 by survey. — — — — —

144 144 144 144 144 144 144

37 29 37 33 34 35 33

35 35 50 20 50 50 35

−11 45 — — — — — —

8¼ days. (April 25, to May 4.) — — — —

144 144 144 144 144 144 144

25 17 26 21 23 24 21

50 50  5 35  5  5 20

ʘ E. ☾ — — — — — —

F — — — — — —

27 at 16 28

$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$

At 2nd anchor. in do. — — —

144 144 144 144 145

53 56 54 56  3

30 30 45 45  0

−0 13 25 by survey — — —

144 144 144 144 144

40 43 41 43 49

5  5 20 20 35

−11 15 — — — —

Ditto. — — — —

144 144 144 144 144

28 31 30 32 38

50 50  5  5 20

Ditto. — — — —

F — — — —

Longitude from eighteen sets of lunar distances,

$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$

Uncorrected

144

45

27,5

Corrected

144

30

35,8

 

Longitude of Point Nepean from the two time keepers.

 

On April 26 at 11ʰ 11′ of Greenwich time, and using the Kanguroo-I. rates, the mean longitude of first anchorage in Port Phillip was . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		144°	57′	49,5″
⁠	Difference of longitude by the survey to Point Nepean, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		−8	10
	Correction for variation in the rates found at Port Jackson, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		−0	53,8
	Correction for supplemental error during 21 days, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		−9	14,4
	Corrected longitude from first set of observations,	144	39	31,3
On May 2 at 11ʰ 46′ of Greenwich time, and using the Kanguroo-I. rates, the longitude of the ship (Pt. Nepean N. 1° W. 5½′) was . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		144	50	5
⁠	⁠Difference of Longitude to Point Nepean, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		−0	6
	Correction for variation in the rates found at Port Jackson, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		−1	28,1
	Correction for supplemental error during 27 days, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .		−11	52,8
	Corrected longitude from second set of observations,	144	36	38,1
	Mean longitude from both sets, preferred to that above, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	144	38	4,7	east.

 

TABLE VI. (Reference from p. 237.) Longitude of Cattle Point, Port Jackson.

Appt. Greenwich time of the observations.		Place.	Longitude E. from Naut. Alm.			Reduction by two time keepers.	East Longitude of Cattle Point.			Correction		Correct Longit. of Cattle Point.			Whence deduced.	Observer.
										for errors of tables	Interv. of ☾'s error.
			°	′	″	°⁠′⁠″	°	′	″	′⁠″		°	′	″
1802 April. ʰ   ′  26 at 12 34	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \\\ \ \end{matrix}}\right.}$	At 1st anchor. in Port Phillip. — — — —	144 144 144 144 144 144 144	45 37 46 41 43 44 41	45 45  0 30  0  0 45	+6 29 32 (From first rates found at Pt. Jackson.) — — —	151 151 151 151 151 151 151	15  7 15 11 12 13 11	17 17 32  2 32 32 17	−11 45 — — — — — —	8¾ days (April 25, to May 4.) — — — —	151 150 151 150 151 151 150	3 55  3 59  0  1 59	32 32 47 17 47 47 32	ʘ E. ☾ — — — — — —	F — — — — — —
27 at 16 28	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	At 2nd anchor. in Port Phillip. — —	144 144 144 144 145	53 56 54 56  3	30 30 45 45  0	+6 23  2 (From ditto.) — — —	151 151 151 151 151	16 19 17 19 26	32 32 47 47  2	−11 15 — — — —	Ditto. — — — —	151 151 151 151 151	5  8  6  8 14	17 17 32 32 47	Ditto. — — — —	F — — — —
May⁠ ʰ⁠′  24 at 14 15	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	On Cattle Point. — —	151 151 151 151	18 21 17 21	45 45 15  0		151 151 151 151	18 21 17 21	45 45 15  0	−11  0 — — —	Two days. — — —	151 151 151 151	7 10  6 10	45 45 15  0	Ditto. — — —	F — — —
27 at 16 28	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	Ditto. — — — — —	151 151 151 151 151 151	11 12  8 15 10 10	15 30 45  0  0  0		151 151 151 151 151 151	11 12  8 15 10 10	15 30 45  0  0  0	− 3 15 — — — — —	One day. — — — — —	151 151 151 151 151 151	8  9  5 11  6  6	0 15 30 45 45 45	Ditto — — — — —	F — — — — —
July⁠ ʰ⁠′  8 at 16 15	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \ \end{matrix}}\right.}$	Ditto. — — —	151 151 151 151	47 42 39 30	0  0 45 30		151 151 151 151	47 42 39 30	0  0 45 30	−12  0 — — —	8¼ days, (July 4th to 12th.) —	151 151 151 151	35 30 27 18	0  0 45 30	ʘ W. ☾. — — —	F — — —
9 at 16  0	$\scriptstyle {\left\{{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right.}$	Ditto. — — — — —	151 151 151 151 151 151	30 31 31 29 29 26	30 30 45 30 45 30		151 151 151 151 151 151	30 31 31 29 29 26	30 30 45 30 45 30	−10 45 — — — — —	Ditto. — — — — —	151 151 151 151 151 151	19 20 21 18 19 15	45 45  0 45  0 45	Ditto — — — — —	F — — — — —
Mean of forty-four sets: uncorrected							151	21	14,9	Corrected		151	11	49,	and taken
From observations			east of the moon alone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .					151°	5′	55,6″	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	Mean	151°	11′	49″	east.
			west of the moon alone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .					151	17	42,4

 

In addition to the tables of longitude for the south coast of Terra Australis, I subjoin, for the satisfaction of nautical and geographical readers, a table of the rates of the time keepers, to show their deviations and the errors in longitude during the several passages from one fixed point to another; commencing November 1, 1801, at the Cape of Good Hope, and ending May 9, 1802, at Port Jackson. From this table, the corrections for variation of rates and supplemental error, which have been applied to obtain the corrected longitudes by the time keepers, will be more distinctly seen.

 

TABLE VII.

Variations in rate and errors in longitude, made by Earnshaw's time keepers No. 543 and No. 520, between the Cape of Good Hope and Port Jackson.

 

Departure taken.

Rates of time keepers losing.

Variations in mean rate

Errors in long. on arriving

Daily part of supplemental errors.

Place.

Longit. East

No. 543

No. 520.

Mean.

During the passage.

Number of days.

Daily acceleration.

With rate before found.

With rate accelerated.

Cape of G. Hope King G. Sound Port Lincoln

°  18 117 136

′ 25 53 44

″  7 10 51

″   5,33 6,46 8,43

″   15,84 16,72 18,82

″    10,585 11,590 13,625

″    1,005 2,035

43,7 57

″     0,0230 0,0357

′ 13 22

″ 55,8 E. 10,2

′ S 7

″ 18,8 E. 25

″ 11 41 E  7,80

(The time keepers were let down at Kanguroo Island, previously to the following rates.)

Kanguroo Island Port Jackson

137 151

57 11

11 49

8,46 9,886

18,07 17,70

13,265 13,793

0,528

34

0,01553

17

16

14

57,4

26 40

(First rates on arriving.)

In altering their rates between one station and another, the time keepers are supposed to have done it, not suddenly, but gradually and uniformly, by the quantities marked in the column of daily acceleration; which quantities are the results of the variations in the mean rate during the passage, divided by the number of days. The daily acceleration; is not much in any case, yet it makes a material difference in the longitude after some time; and as the application of this difference has always diminished the error found on arriving at any station, it is a satisfactory proof that the accelerated rate is nearer to the true going of the time keepers on the passage, than the rate found at the commencement.

The difference of longitude produced by the acceleration at any given time, is the sum of all the terms of a series in arithmetic progression; of which the daily acceleration, turned into longitude, is both the first term and common difference; and the days elapsed form the number of terms. Therefore,

Daily accel. × 15, × number of days + 1, × half number of days, = the difference of longitude in seconds.

The differences thus obtained have been applied to the errors in longitude on arriving, as given by the rate before found; and the result is the error which remains with rate accelerated.

Had the time keepers been so far perfect machines, as that the change in their rates had been altogether gradual and uniform; and were the stations, as fixed by the lunar distances, perfectly exact; then the error on arriving, with rate accelerated, would have been 0′ 0″ in every case. But since neither the one nor the other may be perfect, and yet it is necessary to take one of them as being so, the difference which remains is considered to be the deviation of the time keepers from an uniformly accelerating rate; and this I call their supplemental error. It is generally impossible to fix upon the manner how, or time when this error was contracted; and therefore it is distributed equally throughout the whole passage, day by day, according to the quantities marked in the last column of the table.

To recapitulate briefly: The longitudes of places given in this first Book of the voyage, and used in the construction of the charts of the South Coast, are those resulting from the time keepers, corrected as above for the acceleration of their mean rate and the supplemental error. The exceptions are, King George's Sound, Port Lincoln, and Port Jackson, which are fixed by the lunar distances; and with the position of Simon's Town, Cape of Good Hope, constitute the basis of this chronometrical fabric.

 

END OF VOL. I.

 

London : Printed by W. Bulmer and Co.

Cleveland Row, St. James's.