A Voyage to Terra Australis/Volume 2/Appendix 2

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A Voyage to Terra Australis, Volume 2 (1814)
by Matthew Flinders

Appendix II

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3999297A Voyage to Terra Australis, Volume 2 — Appendix II1814Matthew Flinders

No. II.

On the errors of the compass arising from attractions within the ship, and others from the magnetism of land; with precautions for obviating their effects in marine surveying.

Several instances have been mentioned in the course of this voyage, where the compass showed a different variation on being removed from one part of the ship to another; thus observations on the binnacle gave 29½° off the Start, where the true variation was about 25½° west, whilst others taken upon the booms before the main mast, sixty-eight miles lower down Channel, gave only 24°; and in the experiments made with five compasses, Vol. I. p. 18, the mean variation at the binnacle was 4° 37′ greater than on the booms. Finding that the situation of the compass was an object of importance, I determined very early in the voyage to place it always upon the binnacle; both when taking bearings for the survey, and when observing azimuths or amplitudes; nor in any observations taken by myself, was it ever displaced except by way of experiment; but the officers occasionally observed from different parts of the ship, when the sun could not be seen from the binnacle, until they were convinced that such observations were of no utility, either to the survey, or for ascertaining the true variation.

It soon became evident, however, that keeping the compass to one spot was not sufficient alone to insure accuracy; a change in the direction of the ship's head was also found to make a difference in the needle, and it was necessary to ascertain the nature and proportional quantity of this difference before a remedy could be applied. This inquiry was attended with many difficulties, and no satisfactory conclusion could be drawn until a great variety of observations were collected; it then appeared, that when the ship's head was on the east side of the meridian the differences were mostly one way, and when on the west side they were the contrary, whence I judged that the iron in the ship had an attraction on the needle, and drew it forward; but there was this remarkable distinction,—in the northern hemisphere it was the north end of the needle which was attracted, and in the southern hemisphere it was the south end. In the instance off the Start before cited, when the ship's head was West, the north end of the needle had been drawn forward, or to the left of North, nearly 4°, and the west variation thereby increased to 29½°; with the head East, it would be drawn to the right of its natural position, and the variation diminished to about 21½°; but at North, the attraction in the ship was in the same line with the magnetic poles of the earth, and would therefore produce no change. The same thing took place at South, for the two attractions were still in the same continued line, though on opposite sides of the compass; and throughout the voyage I found, that variations taken with the head at North and South agreed very nearly in themselves and with the observations on shore near the same place, when such observations were not affected by local attractions.

But although the errors were always the same way in the same hemisphere, when the head was at West, and when it was East they were always the contrary, yet the quantities varied with the situation of the ship, being greater in high, and less in low latitudes; and yet they did not increase and diminish in proportion to the latitude. After much examination and comparison of the observations, and some thinking on the subject, I found that the errors had a close connexion with the dip of the needle. When the north end of the needle had dipped, it was the north point of the compass which had been attracted by the iron in the ship; and as that dip diminished, so had the attraction, until, at the magnetic equator, where the dipping needle stands horizontal, there seemed to be no attraction. After passing some distance into the southern hemisphere, and the south end of the needle dipped, our observations again showed errors in the compass; but the west variation was now too great when the ship's head was eastward. These errors increased as the dip augmented; and in Bass' Strait, where the south dip is nearly as great as the north dip in the English Channel, the attraction produced almost as much error as when we left England, but it was of an opposite nature. On turning northward again, along the east coast of New South Wales, the dip of the south end of the needle and the attraction of the iron upon the south point of the compass diminished together, as nearly in equal proportions as the accuracy of our observed variations could be depended on; and I therefore considered the connexion between them to be so far certain, as to make the dip one datum in reducing the observed to the true variations.

Another point of equal importance remained to be known: the compass stood right in both hemispheres when the ship's head was at North or South, and erred most on one side when the head was West and on the other when it was at East; but what was the proportion of error at the intermediate points, between the magnetic meridian and East and West? Unfortunately, the direction of the ship's head when observations were taken, had not been particularly marked in the first part of the voyage, nor always in the latter part; and in gathering it from the courses steered when under way, and from the direction of the winds and tides when at anchor, there was often a good deal of uncertainty; but it was evident, that the quantity of error increased as the angle between the ship's head and the magnetic meridian became greater. After some consideration, it appeared to me that the magnetism of the earth and the attraction forward in the ship must act upon the needle in the nature of a compound force; and that the errors produced by the attraction should be proportionate to the sines of the angles between the ship's head and the magnetic meridian. I tried this upon many observations where the direction of the head was least doubtful, and found the differences to correspond as nearly as could be expected, and sometimes exactly; it therefore seemed probable that the error produced at any direction of the ship's head, would be to the error at East or West, at the same dip; as the sine of the angle between the ship's head and magnetic meridian, was to the sine of eight points, or radius. According to this, when the error was ascertained at any given direction, more especially at East or West where it was greatest, it might be found at any direction required, by inspection in the Traverse Table.

Soon after my arrival in England, application was made to the Lords Commissioners of the Admiralty to have experiments tried on board some of His Majesty's ships, that this law might be verified; and they were pleased to order them at Sheerness, Portsmouth, and Plymouth. I was present at the two first ports, when a series of observations were made in five different vessels; and the general results, so far as they are necessary to the present explanation, were these.

1st. At or near the binnacle, the north point of the compass was attracted forward in all the ships; but the quantity of error produced, on one side when the head was East, and on the other when West, varied from 6½° to 0° 21′.

2nd. When the compass was placed in other parts of the different ships, the attraction was sometimes forward and sometimes aft; but always aft from the forecastle. The error at some of the stations was greater than at the binnacle, and at others less.

3rd. The errors were least when the ship's head was at, or near to North or South, and greatest at, or near to East or West; and as the head was made to deviate from the points of least error towards the greatest, the increase of error was found to be in proportion to the sines of the angles of deviation.

This last was the particular subject of my anxiety; and being then satisfied that the law before deduced from analogy was certain, I employed it to find a standard correction for all my observations in the Investigator. For this purpose a selection of them was made where the ship's head was in the most opposite points and furthest from the meridian, and where the true variation could be ascertained within a small quantity; the difference between the observed and true variations gave the errors, and when the head had not been at East or West, they were proportioned to eight points or radius by the sines of the angles. These observations were collected into tables, one for the north, and another for the southern magnetic hemisphere, and classed according to the dips of the needle; and the error for eight points at each dip being reduced to parts of that dip, a medium of the whole was taken, and considered to be the standard radius applicable to all situations. The two tables are here inserted for the satisfaction of naval and philosophical readers; and no further explanation of them seems requisite, than that when the errors of observation were to the right they are marked +, and − when to the left.

Observations taken at different dips of the needle in the Northern magnetic Hemisphere, from which are deduced the errors of variation at the Investigator's binnacle when the ship's head was at East or West.

Time 1801.	Lat. N.	Lon. W.	Az. or Amp.	Comps.	Observers	Ship's Hd.	Variat. Observ. West.	Variat. suppᵈ true.	Errors of observⁿ.		Errors at 8 points.		Dip Nᵒ.	Remarks.
July	° ′	° ′					° ′	° ′	° ′			° ′	°
p.m. 20	49 50	3 52	Az.	No. 1,2	T	West.	29 34	25 40	3 54	−	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	3 52	72	Off the Start.
—	49 48	4 2	Amp.	No. 1	—	—	29 30	—	3 50	−		3 52	72	Off the Start.
August a.m. 29	5 38	16 50	Az.	No. 1,2	F	S.E. by S.	12 18	13 15	0 57	+		1 43	32	Off the African Coast.
Sept. a.m. 5	2 21	14 15	—	—	T	W.S.W.	14 54	13 40	1 14	−		1 20	26	Off the African Coast.

At dip	72°,	error for 8 points	3°	52′,	or in parts of the dip	,0537
	29 ,	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	1	31½	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	,0526
Mean error for eight points in parts of the dip						,0531

These are all the observations taken in the northern hemisphere, where there was any certainty of knowing the true variation; for not being then aware of the difference which changing the direction of the ship's head produced, I did not seek to multiply the observations, nor to take them at opposite points.^[1] In the southern hemisphere, the survey of Terra Australis required the variation to be frequently observed, and it will be seen in the following table what considerable differences arose on the direction of the ship's head being changed; it will also be remarked, that the errors were of an opposite nature to those in the northern hemisphere, and decreased with the dip of the needle.

Observations taken at different dips of the needle in the Southern magnetic Hemisphere, from which are deduced the errors of variation at the Investigator's binnacle when the ship's head was at East or West

Time 1802.	Lat. S.	Lon. E.	Az. or Amp.	Comps.	Observ.^[2]	Ship's Head.	Var. Obs.		Variat. supposed true.		Errors of observation.			Errˢ. at 8 points.	Dip Sᵒ.	Remarks.
April.	° ′	° ′					° ′		° ′		° ′			° ′	°
a.m. 10	35 48	139 3	Amp.	Nᵒ. 3	C	W. by S.	5 11	E.	1 41	E.	3 30	+	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	3 34	66	Encounter Bay
p.m. —	35 49	139 12	Az.	—	—	S.E.	0 50	W.	—		2 31	−		3 34	66	Encounter Bay
p.m. 12	36 42	139 50	—	—	—	S.S.E. ½ E.	1 25	E.	3 0		1 35	−	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \\\ \ \end{matrix}}\right\}\,}$	3 23	67	Off C. Buffon
a.m. 15	37 30	139 40	Amp.	—	—	South	4 8
a.m. 16	37 50	139 41	—	—	—	S.E. by S.	2 39		4 8	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$	1 54	−
—	37 56	139 41	Az.	—	—	S.S.E.	2 2		—
p.m. —	37 55	139 48	—	—	—	N.Eᵗˡʸ.	2 2		—
a.m. 22	39 38	144 40	—	—	—	W.S.W.	11 52		8 30		3 22	+	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,}$	3 26	68	Bass' Strait
a.m. 24	39 38	144 1	—	—	—	South	7 59
p.m. 25	38 36	144 20	—	—	—	N.E. by E. ½ E.	3 41		7 30	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	2 16	−
p.m. 26	38 38	144 30	Amp.	—	—	N.N.E. ½ E.	6 48		—		2 16	−
											Means			3 28	67
1802 Jan.	° ′	° ′					° ′		° ′		° ′			° ′	°
a.m. 16	34 5	123 9	Az.	Nᵒ. 3	C	W.S.W.	0 54	W.	3 30	W.	2 36	+	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$	12 45	64	At anchor in Goose-I. Bay
1803 May. p.m. 20	34 4	123 10	—	Nᵒ. 1	—	East	6 10		—		2 40	−		12 45	64	At anchor in Goose-I. Bay
1802 Feb. p.m. 15	34 5	135 9	—	—	—	S.E. by E.	1 33		1 11½	E	2 44½	−	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	3 18	—	Off Pᵗ Drummᵈ
—	34 6	135 9	Amp.	—	—	S.W. by W.	3 56	E.	—		2 44½	+		3 18	—	Off Pᵗ Drummᵈ
Mar. p.m. 16	34 7	137 19	—	—	—	S.W. by S.	4 38		2 50	E.	1 48	+	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,}$	3 18	—	Off Point Pearce Spencer's G.
a.m. 17	34 16	137 16	Az.	—	F	E. by N.	0 10	W.	—		3 0	−
p.m. 17	34 22	137 21	—	—	C	S.E.	0 35		2 0		2 35	−
p.m. 18	34 42	137 14	Amp.	—	—	S.S.W.	3 15	E.	—		1 15	+
p.m. 28	34 36	138 18	—	—	—	S. by W.	5 22									At anchor, G. of St. Vincent.
a.m. 29	—	—	Az.	—	—	S.Eᵗˡʸ.	2 27		4 45		2 18	−		3 15	—	At anchor, G. of St. Vincent.
											Means			3 9	64
1802 Jan.	° ′	° ′					° ′		° ′		° ′			° ′	°
p.m. 19	32 40	125 25	Az.	Nᵒ. 1	C	E. by N.	7 15	W.	4 30	W.	2 45	−	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \\\ \ \end{matrix}}\right\}\,}$	2 48	62	Off South Coast
p.m. 20	32 30	125 40	—	Nᵒ. 1,2,3	C & T	South	4 26
p.m. 21	32 32	125 54	—	Nᵒ. 1	C	N.E.	6 13		4 15		1 58	−
p.m. 22	32 24	126 23	Amp.	—	—	S. by E.	4 18
a.m. 24	32 7	126 23	Az.	—	—	E. by N.	6 4		3 0		3 4	−		3 8	—	—
p.m. 25	32 17	128 2	—	Nᵒ. 1,2,3	F	S. by E.	3 8
a.m. 31	32 15	132 39	—	Nᵒ. 1	—	E. by N.	2 49		0 0		2 49	−		2 52	—	Nuyts' Archip.
Feb. a.m. 2	32 23	132 56	—	—	C	S. ½ W.	0 19	E.
											Means			2 56	62
a.m. 28	25 0	153 23	Amp.	No. 3	C	N.W. by N.	9 39	E.	8 12	E.	1 27	+	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	2 36	53½	Off Indian Head.
a.m. 29	24 43	153 27	—	—	F	S.E. ½ S.	6 33		—		1 39	−		2 36	53½	Off Indian Head.
Sept.
a.m. 3	22 23	150 16	Az.	No. 1	—	S.E. by E.	6 31		8 45		2 14	−	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	2 41	50½	Shoal-water B.
—	—	—	—	No. 2,3	—	W.N.W.	11 15		—		2 30	+		2 41	50½	Do. ship swung.
											Means			2 39	52
1802 Nov.	° ′	° ′					° ′		° ′		° ′			° ′	°
p.m. 21	17 7	139 43	Amp	No. 3	C	E.N.E.	2 28	E.	4 30		2 2	−		2 12	44½	Investigˢ. Road.
p.m. 22	—	—	—	—	F	Northerly	4 30									(G. of Carpent.)
December
p.m. 8	16 41	138 27	—	—	C	N.W.	4 10		2 40		1 30	+	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	2 7	43½	S. side of Gulph.
p.m. 10	16 16	137 57	—	—	—	W. by N.	4 45		—		2 5	+		2 7	43½	S. side of Gulph.
1803 Jan.
p.m. 2	14 19	136 1	—	—	—	E. by S.	0 43		—		1 57	−	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	2 4	41½	Near Groote Eyl.
p.m. 6	14 19	136 23	—	—	—	S.E.	1 9		—		1 31	−		2 4	41½	Near Groote Eyl.
											Means			2 8	43

At dip	67°,	error for eight points	3°	28′,	or in parts of the dip	,0517
	64	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	3	9	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	,0492
	62	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	2	56	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	,0473
	52	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	2	39	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	,0510
	43	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	2	8	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	,0496
		Mean error for eight points in parts of the dip				,0498

The medium error for eight points deviation of the Investigator's head on either side of the magnetic meridian, was therefore very nearly one-twentieth part of the dip; and (,0498 called) ,05, the decimal expression of it, is the common multiplier to the dip for obtaining the radius of error at any situation in the southern hemisphere; as the (,0531 called) ,053 from the first table, is the common multiplier from England to the magnetic equator. Had the observations in both hemispheres been equally numerous, the multipliers might perhaps have been exactly the same; but it is also possible that they might have been more different, for the removing of four guns from the quarter deck into the hold, which was done after the northern observations were taken, was likely to make some change in the attraction of the iron in the ship.

In correcting the variations given in this and the preceding volume, to what it is presumed they would have been if observed with the ship's head in the magnetic meridian, the following plan was used. With the dip of the needle, as near as it could be known, and the common multiplier, the radius, or error for eight points was obtained; with this, taken as a distance, and the direction of the ship's head as a course, the correction was found in the departure column of the Traverse Table; and being applied to the observed variation, either to the right or left, according as the dip was north or south and the head on the east or west side of the meridian, it gave the true variation.

Example. The dip being 66° south, and the ship's head W. by S., the variation was observed to be 5° 11′ east; required the true variation?

Dip 66° × ,05 = error for eight points 3°,30 = (3° 18′ =) 198′.

Course 7 points and distance 198′ = departure 194′, or 3° 14′ correction. Then, as in south dip the south end of the needle was drawn forward, or in this case to the West, and the north end went to the East, the east variation observed was too great, and must be reduced 3° 14′; and 5° 11′ observed, −3° 14′ correction, =1° 57′ east, the true variation.^[3] Had the north end of the needle dipped, and all other circumstances been the same, the correction 3° 14′ would have been additive; as it would also, had the head been E. by N. or E. by S., instead of W. by S.

To ascertain the proper variation to be allowed on bearings for the survey, I was obliged to go through a double process; unless where variations happened to have been observed with the ship's head in the same direction, or at an equal number of points on the same side of the magnetic meridian, in which case the variation observed was allowed upon the beatings. But in all other cases it was necessary to find, first what was the true variation, and second what it would be with the ship's head in the given direction.

Example. Suppose that with the ship's head W.S.W., the variation was observed to be 29° 12′ west in the English Channel, where the dip is 72° north; and I wished to know what variation is to be allowed upon a set of bearings taken when the head was N.E. ½ E.

1st. To find the true variation.

Dip 72 × ,053 = error for eight points 3°,816 = (3° 49′ =) 229′. Course 6 points, distance 229′ = departure 212′, or 3° 32′ correction. Being in north dip, the north end of the needle was drawn forward, that is westward in this case, and the west variation observed was too great; therefore 29° 12′ observed, −8° 32′ correction = 25° 40′ the true west variation.

2nd. To find from thence what is to be allowed with the head at N.E. ½ E.

Course 4½ points, distance 229′ = departure 177′, or 2° 57′ correction. With the head N.E. ½ E., the north end of the needle at the binnacle would be drawn eastward, and the west variation be less than the true; therefore, true variation 25° 40′ − 2° 57′ = 22° 43′ to be allowed, deduced from 29° 12′ observed.

This operation will at first seem complex and tedious to the seaman; but when a common multiplier is once obtained and the principle of its use understood, it will be found not more troublesome than working a meridian altitude for the latitude; and the accuracy required is generally much less.

Some persons will be disposed to doubt whether the differences found in the azimuths and amplitudes on changing the direction of the ship's head, really took place in the bearings themselves; a few instances are therefore subjoined, in which bearings were taken the instant before tacking from the shore, and so soon as the ship was round and compass steady, the same objects were again set. Differences took place without exception, and always the same way; but some of the objects being too near for the bearing not to be affected by a small change in the ship's place, those only are selected whose distance was more considerable. The first examples occurred whilst beating along that part of the south coast of Terra Australis discovered by the French, where the dip is nearly 67°; and that it may be seen how near the bearings coincided with the azimuths and amplitudes, the differences which should result from the common multiplier and sines of the angles are added to the table.

Objects set.	Before tacking.			After tacking.				Increase of E. Var.
Objects set.	Bearings.		Ship's Head.	Bearings.		Ship's Head.		From Bearings	From Multipl.
C. Jaffa, outer part	N. 4°	W.	E.S.E.	N. 9°	W.	S.W. by W.	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	6° 30′	5° 53′
C. Lannes, the point	S. 32	E.	——	S. 40	E.	——		6° 30′	5° 53′
Hummock	N. 35½	E.	S.E. by E.	N. 33½	E.	S.W. by W.	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	5 0	5 34
Furthest extreme	S. 36	E.	——	S. 44	E.	——		5 0	5 34
C. Lannes, north extreme	N. 39	E	S.E by E.	N. 30	E.	West.	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	6 30	6 8
Furthest extreme	S. 51	E.	——	S. 55	E.	——		6 30	6 8
C. Lannes, western part	N. 15	W.	E.N.E.	N. 21	W.	S.W. by S.	$\scriptstyle {\left.{\begin{matrix}\ \\\\\ \ \end{matrix}}\right\}\,}$
Sandy hummock	N. 19	E.	——	N. 15	E.	——		6 0	4 57
Furthest extreme	S. 53	E.	——	S. 61	E.	——
The sandy hummock	N. 12	W.	East.	N. 18	W.	S.W. by S.	$\scriptstyle {\left.{\begin{matrix}\ \\\ \end{matrix}}\right\}\,}$	5 30	5 13
Projecting part of the coast	S. 59	E.	——	S. 64	E.			5 30	5 13
Mean increase								5 54	5 33

Another example occurred whilst working up to King's Island, in Bass' Strait, where the dip is 68°; on changing the ship's head from West to S.E. ½ S., the decrease of east variation from five bearings was 4° 48′; from the common multiplier it would be 5° 33′.

The bearings therefore showed differences the same way, and nearly the same in quantity as did the azimuths and amplitudes: that they should do so exactly, is not to be expected; for if azimuths, and especially amplitudes taken at sea with the present compasses, cannot be depended upon nearer than to half a degree on either side, as I believe they cannot, even under the most favourable circumstances, the best bearings set by hand are likely to err a degree on either side, and two degrees where there is much motion; and it is only by taking the medium of several differences, that any thing like an accurate comparison can be established.

After this exposition of the errors produced in the Investigator's compasses by the attraction of the iron, and of the method employed to obviate their effects on the survey, it will be asked whether any thing similar has been found in other ships, especially in those sent on discovery; and if so, whether their observed variations and survey bearings were submitted to any regular system of correction? It does appear that similar errors have been noticed in ships employed on discovery, as also in others, and that they probably exist in all ships, in a greater or less degree; but as they were not perceived to follow any regular laws, no correction had hitherto been applied; and it naturally follows, that there should be frequent discordance between the bearings given in Captain Cook's voyages and others, and the charts which accompany them. There are few experienced seamen who have not remarked occasional differences in the compass; but the most general result of their observations seems to have been an opinion, that within some undefined and variable limits this instrument was radically imperfect; and it has been not unusual, when an observed variation differed much from what was thought to be the truth, to reject it, as having been either erroneously taken or bad from some unknown cause, and it is not entered in the journal. To this injudicious practice, than which nothing can more tend to stifle inquiry, and consequently prevent the advancement of knowledge, there are however many honourable exceptions; and at the head of these must be placed the immortal Cook. In the introduction to the Astronomical Observations made in his second voyage, page 49, is the following passage from the pen of Mr. Wales, astronomer on board the Resolution.

"In the Channel of England, the extremes of the observed variations were from 19½° to 25°: and all the way from England to the Cape of Good Hope, I frequently observed differences nearly as great, without being able, any way, to account for them; the difference in situation being by no means sufficient. These irregularities continued after leaving the Cape, which, at length, put me on examining into the circumstances under which they were made. In this examination it soon appeared, that when most of those observations were made, wherein the greatest west variations had happened, the ship's head was North and Easterly; and that when those, where it was least, had been observed, it was South and Westerly." (The greatest west variations in the southern hemisphere were observed with the head East, on board the Investigator, and the least with the head West.) "I mentioned this to captain Cook, and some of the officers, who did not at first seem to think much of it; but as opportunities happened, some observations were made under those circumstances, and very much contributed to confirm my suspicions; and throughout the whole voyage I had great reasons to believe, that variations observed with a ship's head in different positions, and even in different parts of her, will differ very materially from one another; and much more will variations observed on board different ships, which I now find fully verified, on comparing those made on board the Adventure with my own, made about the same time" in the Resolution.

Mr. Wales did not quit the subject here. In the introduction to captain Cook's third voyage, published in 1785, is a paper from the same careful observer, citing a variety of cases wherein differences were found in the variation of the compass. These cases are as follow.

1st. Putting the ship's head a contrary way: differences 3° to 6°, and even 10°.

2nd. At different times of the same day: differences 3° to 7°.

3d. Being under sail, and at anchor in a road-stead: difference 5°.

4th. On board different ships: differences 3° to 5°.

5th. Near the same place; at different times in the voyage: 4° and 5°, or upwards.

6th. In different compasses: 3° to 6°.

That the variation should be different on changing the direction of the ship's head or the place of the compass, and also on board different ships, is perfectly reconcileable to the explanation I have given; but that it should vary so much at different times of the same day or year,—when under sail and at anchor,—or even in different compasses, much surprised me, if all other circumstances were the same. I was therefore induced to examine the instances quoted under each case; and found great reason to believe, not only that the direction of the head was changed in most, if not all of those where great differences had been observed, but also that the differences themselves were conformable to what had taken place upon the binnacle of the Investigator.

Mr. Wales goes on to observe, "It is not necessary to account for these differences in the observed variations in this place, nor yet to point out the reasons why such anomalies have not been noticed in observations of this kind before. I shall however remark, that I have hinted at some of the causes in my introduction to the observations which were made in captain Cook's second voyage; and many others will readily offer themselves to persons who have had much practice in making these observations, and who have attentively considered the principles upon which the instruments are constructed, and the manner in which they are fabricated. Nor is it at all surprising, that the errors to which the instruments and observations of this kind are liable, should not have been discovered before; since no navigators before us ever gave the same opportunity, by multiplying their observations, and making them under such a variety of circumstances as we did."

That the compasses, even in the Royal Navy and to this day, are the worst constructed instruments of any carried to sea, and often kept in a way to deteriorate, rather than to improve their magnetism, cannot be denied; but errors arising from the badness of compasses would not be reducible to regular laws as those were in the Investigator, and appear to be in the three ships commanded by captain Cook. It seems indeed extraordinary, that with the attention paid by Mr. Wales to the subject, he should not have discovered, or suspected, that the attraction of the iron in the ship was the primary and general cause of the differences so frequently observed; nor have perceived that the differences varied proportionally to the direction of the ship's head and to the dip of the needle, and were of an opposite nature in the two hemispheres. But it should be recollected, that the apparently contradictory phenomena which occur in most branches of science, frequently bewilder the inquirer in a labyrinth where pursuit seems to be hopeless; and that when one general cause is found to explain all the contradictions, to have hit upon the clue appears so easy that any one might have perceived it: the inquirer himself is not less surprised that it should have escaped him so long, than pleased at his final success.

It appears that differences, probably similar to those in the Investigator, were also observed on board La Recherche, one of the ships with which the French admiral D'Entrecasteaux went in search of the unfortunate La Pérouse. Monsieur Beautemps-Beaupré, the able surveyor to the expedition, found so much uncertainty in compass bearings that he abandoned, as far as was possible, the use of them; substituting the sun's azimuth and angular distance from some one point, and measuring the angles from that point to other objects. He says of the compass, "We found by a great number of observations, but principally by the differences between the bearings of points set with each other from opposite directions, that no confidence could be had in bearings taken with the compass from the deck of a large vessel, nearer than to 3°, even under the most favourable circumstances. For instance, it has often happened that from one position, as C, the cape A has been set in a line with cape B; and afterwards, from another position, D, cape B has been set with A; and that we have found considerable differences in the results of the two observations.^[4] We also remarked, that the compass showed differences of several degrees in variations at sea, though observed with the greatest care and within the space of a few minutes." (Voyage de D'Entrecasteaux, par M. de Rossel. Vol. I. p. 600. A Paris, 1808.)

I do not find any other distinct mention of differences found in the variation, from changing the direction of the ship's head or the place of the compass; but it appears from the following extract, that the Investigator was not singular in having a variation of 4° greater than the truth in the English Channel. Captain Vancouver, in his passage towards Madeira, says (Vol. I. p. 6.), "The error in reckoning, amounting almost to a degree (of longitude), seemed most likely to have been occasioned by our not having made sufficient allowance for the variation of the compass on our first sailing; as, instead of allowing from 22° to 25°, which was what we esteemed the variation, our observations for ascertaining this fact, when the ship was sufficiently steady, shewed the variation to be 28° and 29½° westwardly."

Besides the errors which the attraction of the iron produced in the compasses at the binnacle of the Investigator, differences are frequently mentioned in the course of this voyage as having been found in the magnetic needle on shore, and on board the ship in the vicinity of land. That there are few masses of stone totally devoid of iron, and that all iron which has long remained in the same position will acquire magnetism, or a power of attracting one end of the magnetic needle towards one part of it, and the opposite end towards another, is, I believe, generally admitted. The kinds of stone which I have observed to exert the greatest influence on the needle, are iron ore, porphyry, granite, and basaltes; and the least, are sand or free stone, and calcareous rock, and the argillaceous earths very little.

The iron in the ship attracted the south end of the needle in the southern hemisphere, and in the same part of the world it was the same end of the needle upon which the land had an attraction. The following are some instances:

In King George's Sound, the west variation was 6° greater on the western head of Michaelmas Island, than it was on the east side of a flat rock in the sound. The stone here is granite.

On approaching the granite islands of the Archipelago of the Recherche, from the west, the corrected variation on board the ship was increased from 5° 25′ to 6° 22′ west, contrary to the regular order; but when Termination Island bore nearly West, and the principal cluster N.N.W., the corrected variation was no more than 0° 51′; and after clearing the Archipelago some distance, it again increased to 4½° west.^[5] Near the west side of Yorke's Peninsula, the corrected east variation was 3° less than on the east side, although the places of observation were not more than forty-eight miles asunder: the uncorrected observations differed 6°.

Upon the east side of the high hills behind Memory Cove, the east variation was 1° 40′ greater than at the granitic summit of the same hills.

In Shoal-water Bay, at anchor near the eastern shore, the corrected east variation was 1° 25′ less than near the west shore; at Broad Sound also, it was 1° less on the east than on the west side. These effects were correspondent to the former, though the expression of the situations be unavoidably different.

In the Investigator's Road, Gulph of Carpentaria, the east variation was full 1° more on the east side of Bentinck's than on the west side of Sweers' Island. The rock here is partly iron ore.

Near the east side of Pellew's Group, the east variation appeared from the bearings to be increased 2° from what it had been at a further distance, though in regular course it should have diminished; and at stations on the east sides of the different islands, I found it necessary to allow 1° degree more than on the west sides.

There were several other examples where the south end of the magnetic needle was drawn towards the nearest land; but only two where the contrary attraction seemed to have been exerted. These were both on shore, and probably might not be exceptions to the rule if all the circumstances were known; for although the body of an island may lie to the west, a single block of stone near the theodolite on the other side might do more than counteract the opposite attraction.

To arrive at the cause why both the iron in the ship and also the land should preferably attract the south end of the compass needle in the southern hemisphere, it seems necessary to refer to the direction of the dipping needle; for the unobstructed magnetism in a mass of iron will lie as nearly in that direction as the form of the mass will admit. Where the south end of the needle dips 60°, the north end will necessarily be no more than 30° from standing perpendicularly upright; and it is to be supposed, that the upper ends or parts of the different pieces of iron in the ship will possess the same attraction as the north end of the dipping needle, and the same with the upper parts of magnetic lands in the southern hemisphere. But it is an universal law in magnetics, that powers of the same quality repulse, and dissimilar powers attract each other; therefore the upper parts, both of the iron in the ship and of the land, should, like the north end of the dipping needle, repulse the north and attract the south end of the compass needle. Now the compass in, or upon the binnacle of a ship is raised above the greater part of the iron, and therefore more in a situation to be attracted by the upper, than the lower parts of the different pieces. The same will generally be the case with respect to the land; its southern polarity must often be lower than the depths of the sea, whilst the upper part, which attracts the south end of the compass needle, will be nearly on a level with, sometimes a few degrees above the ship.

This reasoning from abstract principles is consistent with my observations on and near the coasts of Terra Australis; and if it be just, the contrary effects must take place in the northern hemisphere, at least in high latitudes: the upper parts, both of the iron in a ship and of land possessing magnetism, will attract the north end of the compass needle. That it is the north point of a compass on the binnacle which is attracted by the iron of a ship in the northern hemisphere, has already been shown; but whether the land do generally attract the same point, I have no knowledge from experience: answers to the following queries would probably be useful in the determination.

Is the west variation on the coast of Holland and Germany considerably less than on the east coast of England and Scotland, in the same latitude?

Is it sensibly less at Holy Head than at Dublin; at Port Patrick than at Caricfergus?

Is the variation as much, or greater on the Yorkshire, than on the Lancashire coast?

And generally in the northern hemisphere, is the west variation greater, or east variation less on the east sides of islands and projecting points than on the west sides?

Observations made on ship-board for determining this or any other general question of magnetism, will require, when the head is not at North or South, to be divested of the error which the attraction of the iron in the ship may produce. In making them on land, it should be done on the open shore, so as that no attraction, purely local, may interfere; and if the direction of that shore be North and South, the experiment would be more satisfactory.

In an investigation of the cause why the attraction of the iron in a ship, and in some cases of the land, should decrease with the dip of the needle, and cease at the magnetic equator, the position of the dipping needle must again be consulted. At the equator it is horizontal; and therefore the line connecting the north and south polarities in each piece of iron in the ship, if it still possess magnetism, will also be horizontal, and the two attracting parts equally near to the level of the binnacle; and it should follow, that the attractions on the north and south points of the compass would be equal, and counteract each other. But it seems not improbable that stanchions and other upright pieces of iron, and perhaps the whole lose most, if not all their magnetism at the equator; from the rotatory motion of the ship not allowing any piece to have one end directed to the North, and the other end to the South, a sufficiently long time to acquire or retain magnetism. This was not the case where the dipping needle approached the perpendicular; for there, however the ship were turned, the upper part or end of each fixed piece of iron still remained the upper part; and the more nearly the needle stood to the perpendicular, the more strongly would the magnetism of the iron be concentrated at the upper and lower extremities, and consequently the more strong would be the attractive power on the compass. This I take to be the true cause of the errors increasing and decreasing in close connexion with the dip of the needle.

With respect to land near the magnetic equator, the analogy should not hold, because the magnetic vein or mass is not, like the iron in a ship, subject to a rotatory motion. Suppose that in the upper part of an island near the equator, there be a mass of iron ore, or other stone possessing magnetism; the north end of this mass will have a power of attracting the south point of the compass, and the south end, the north point; and it should follow, that when the centre of this island hears S.W. or N.E., at a little distance, the west variation should be less than when it bears S.E. or N.W. At the small island Trinidad, where the south end of the needle dipped about 18° only, I had some observations which countenance this supposition, though taken at too great a distance to afford a satisfactory proof.

Trinidad	S.S.W. 13 leagues, corrected variation	3°	58′	west.
	S.S.E. 6 leagues, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	4	15
	N.E. by E. 15 leagues, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	1	50

The attraction of land has here been supposed to be so far uniform, as that, in high dips of the needle, the upper part has the same kind of attraction as the magnetic pole of its hemisphere; and that near the magnetic equator, the north end of the land attracts the south point of the compass, and vice versa; but it must be evident, that not only should there be a regular gradation from one to the other, as the dip increases or diminishes, but also that local discordances may take place in both cases, where, instead of one extended magnetic substance pervading the whole land, there are many detached masses, veins, or blocks. Each one of these will possess a north and a south polarity; and contrary attractions may therefore be found at different degrees of elevation and in short intervals of space, without the supposition of the general attraction in land being thereby overturned.

That even, small differences in elevation may produce a change in the magnetic needle appears from some instances in this voyage, where observations were taken on shore, either in the same spot or a few feet from it, with the ship's azimuth compasses and with a theodolite. The compasses stood on the ground, the theodolite upon legs about four and a half feet high, and the variations were as under:

In	K.G.'s Sound, from three compasses	6°	23′,	from theodolite	8°	17′	W.
	Lucky Bay, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	2	35,	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	0	30	W.
	Kanguroo I., from one compass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	2	58,	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .	5	48	E.

Some part of these differences might arise from erroneous construction of the instruments, but only a small part; for they were scarcely sensible in other cases where no hills existed in the neighbourhood, or where the theodolite was placed on the highest land. It is to be remarked, that the compasses come nearer to what appeared to be the true variation than did the theodolite; which I should attribute to the attraction being more equal all round, upon the instrument placed on the earth, and to the theodolite being influenced by the neighbouring hills.

In some parts of this little discussion upon the attraction of land, I feel to have stepped out of my sphere; but if the hints thrown out should aid the philosopher in developing a system of magnetism applicable to the whole earth, or even be the means of stimulating inquiry, the digression will not have been useless. I conclude this article with copying some precautionary memoranda upon the use of the compass in marine surveying; they were made for myself, in case of being hereafter called upon to sail in another Investigator, and may not be without their use to other officers.

1. So soon as the guns are on board and the ship ready for sea, to nail small cleats on the binnacle for showing the place where the azimuth and surveying compass is to stand, when in use. To ascertain by repeated observations whether it be at North and South, or at what other opposite directions near them, that this compass gives exactly the same variation; and to note these as the Points of no difference.

2. Ascertain what the difference in variation is, when the head is placed at right angles to the points of no difference, on each side. Half this difference is the Error for eight points; which being divided by the dip, will give the common multiplier for that hemisphere, and perhaps for both.

3. To try the accuracy of the common multiplier as often as can conveniently be done, by observations taken at various ports where the dip of the needle is different; and more especially to ascertain whether observations in the southern hemisphere give the same multiplier as in the north.

4. No change to be made in the disposition of the iron work or guns during the voyage; but if a change be indispensable, to ascertain as soon after as may be, what alteration it may have produced in the points of no difference, and in the multiplier.

5. The direction of the ship's head, by compass, to be noted to the nearest quarter point when the variation is observed, or bearings of land are taken; this to be considered an indispensable part of such observations, since without it the true variation cannot be known, nor the proper allowance made to the bearings.

6. On arriving upon the coast to be surveyed, to miss no opportunity of observing the variation, by azimuth if possible; and on passing from one side of a projecting cape or island to the other side, to remark if any difference arise in the compass. This is best done by azimuth; but it may be found roughly by the bearing of two well-defined heads or points set in a line from opposite directions. If, after the proper corrections are made according to the ship's head, the bearing be not the same, the difference will be seen.

These memoranda are mostly relative to a compass fixed on the binnacle; but the trouble of correction may be saved if a place can be found near the taffrel, where the attraction of the iron at the stern will counteract, by its greater vicinity, the more powerful attraction in the centre and fore parts of the ship; and should the after attraction be too weak, it may be increased by fixing one or more upright stanchions or bars of iron in the stern. If a neutral station can be found or made, exactly amidships, and of a convenient height for taking azimuths and bearings, let a stand be there set up for the compass; and if the stand must of necessity be moveable, make permanent marks, that the exact place and elevation may always be known. Observations taken here should never undergo any change from altering the direction of the ship's head, at any dip of the needle; but it will be proper to verify. occasionally, and to compare the azimuths and bearings with others taken on the binnacle. The course should also be marked from this compass, though the ship be steered by one before the wheel; a quarter or half point being allowed to the right or left, according as the two may be found to differ.

These precautions are not intended to supersede the taking of angles with a sextant or circle, from the sun to any chosen object, and from thence to others; but in using the compass on ship-board such are those I would employ, in order to arrive at the true variation and to know what should be allowed on each set of bearings. In surveying with a theodolite or circumferentor on shore, my memorandum is,—To observe azimuths with the same instrument, and in the same spot where each set of bearings is taken; unless where the back bearing can be had of some former station or of the ship, where the variation has been observed.

Had I been more early aware of the necessity of these precautions in the use of the magnetic needle, both on ship-board and on shore, much perplexing labour would have been saved; and although every existing datum has been employed to remedy the deficiences, the charts which accompany this work would then have presented a more correct delineation of the coasts of Terra Australis.

↑ The mean of two variations or bearings taken with the head in directly opposite points, will be the correct variation or bearing, however much the attraction in the ship may make them differ from each other.
↑

In the column of observers
C means Commander, F lieutenant Flinders, and T Mr. Thistle the master.
↑ This example is the first observation in the table for the Southern Hemisphere. The true variation is not there taken at 1° 57′, but at 1° 41′ east; for it could not be exactly known until the standard was fixed. Another observation, with the head S.E., was taken at two leagues from the same place, and gave variation 0° 50′ west; and from them both it was, that I judged the variation there to be 1° 41′ east: it appears to have been 1° 44′ east from the mean of both observations.
↑ In the sketch given for elucidation, the ship at the position C, is represented to be steering S.W., and at the position D, N. by E.; hence probably the difference of bearing.
↑ M. Beautemps-Beaupré (in Vol. I. p. 605, of the work before cited) gives the following instance of attraction in the stone of this Archipelago. The compass was placed upon one of the capes of the main land, to set the bearing of a point. "When the beating had been taken, the compass was removed six feet from its place, beyond a large stone; where the vane being by chance directed to the same point, a difference of four degrees was found in the bearing, although the object were so far distant that the change of place should scarcely have produced a difference of one minute. Fully persuaded that we had made an error, either in reading off the bearing or in writing it down, the first observation was verified; but we had the same result within a few minutes as had been marked on the paper, and it was certain that the stone near which the observation had been made, had solely caused this great error."

[1] The mean of two variations or bearings taken with the head in directly opposite points, will be the correct variation or bearing, however much the attraction in the ship may make them differ from each other.

[2] 

In the column of observers
C means Commander, F lieutenant Flinders, and T Mr. Thistle the master.

[3] This example is the first observation in the table for the Southern Hemisphere. The true variation is not there taken at 1° 57′, but at 1° 41′ east; for it could not be exactly known until the standard was fixed. Another observation, with the head S.E., was taken at two leagues from the same place, and gave variation 0° 50′ west; and from them both it was, that I judged the variation there to be 1° 41′ east: it appears to have been 1° 44′ east from the mean of both observations.

[4] In the sketch given for elucidation, the ship at the position C, is represented to be steering S.W., and at the position D, N. by E.; hence probably the difference of bearing.

[5] M. Beautemps-Beaupré (in Vol. I. p. 605, of the work before cited) gives the following instance of attraction in the stone of this Archipelago. The compass was placed upon one of the capes of the main land, to set the bearing of a point. "When the beating had been taken, the compass was removed six feet from its place, beyond a large stone; where the vane being by chance directed to the same point, a difference of four degrees was found in the bearing, although the object were so far distant that the change of place should scarcely have produced a difference of one minute. Fully persuaded that we had made an error, either in reading off the bearing or in writing it down, the first observation was verified; but we had the same result within a few minutes as had been marked on the paper, and it was certain that the stone near which the observation had been made, had solely caused this great error."

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