VARIATION

, of Quantities, in Algebra. See Changes, and Combination.

Variation

, in Astronomy.—The Variation of the Moon, called by Bulliald, the Reflection of her Light, is the third inequality observed in the moon's motion; by which, when out of the quadratures, her true place differs from her place twice equated. See Place, Equation, &c.

Newton makes the moon's variation to arise partly from the form of her orbit, which is an ellipsis; and | partly from the inequality of the spaces, which the moon describes in equal times, by a radius drawn to the earth.

To find the Greatest Variation. Observe the moon's longitude in the octants; and to the time of observation compute the moon's place twice equated; then the difference between the computed and observed place, is the greatest Variation.

Tycho makes the greatest Variation 40′ 30″; and Kepler makes it 51′ 49″.—But Newton makes the greatest Variation, at a mean distance between the sun and the earth, to be 35′ 10″: at the other distances, the greatest Variation is in a ratio compounded of the duplicate ratio of the times of the moon's synodical revolution directly, and the triplicate ratio of the distance of the sun from the earth inversely. And therefore in the sun's apogee, the greatest Variation is 33′ 14″, and in his perigee 37′ 11″; provided that the eccentricity of the sun be to the transverse semidiameter of the orbis magnus, as 16 15/16 to 1000. Or, taking the mean motions of the moon from the sun, as they are stated in Dr. Halley's tables, then the greatest Variation at the mean distance of the earth from the sun will be 35′ 7″, in the apogee of the sun 33′ 27″, and in his perigee 36′ 51″. Philos. Nat. Princ. pr. 29, lib. 3.

Variation

, in Geography, Navigation, &c, a term applied to the deviation of the magnetic needle, or compass, from the true north point, either towards the east or west; called also the declination. Or the Variation of the compass is properly defined, the angle which a magnetic needle, suspended at liberty, makes with the meridian line on an horizontal plane; or an arch of the horizon, comprehended between the true and the magnetic meridians.

In the sea-language, the Variation is usually called north-easting, or north-westing.

All magnetic bodies are found to range themselves, in some sort, according to the meridian; but they seldom agree precisely with it: in one place they decline, from the north toward the east, in another toward the west; and that too differently at different times.

The Variation of the compass could not long remain a secret, after the invention of the compass itself: accordingly Ferdinand, the son of Columbus, in his life written in Spanish, and printed in Italian at Venice in 1571, asserts, that his father observed it on the 14th of September 1492: though others seem to attribute the discovery of it to Sebastian Cabat, a Venetian, employed in the service of our king Henry VII, about the year 1500.—It now appears however, that this Variation or declination of the needle was known even some centuries earlier, though it does not appear that the use of the needle itself in navigation was then known. For it seems there is in the library of the university of Leyden, a small manuscript tract on the Magnet, in Latin, written by one Peter Adsiger, bearing date the 8th of August 1269; in which the declination of the needle is particularly mentioned. Mr. Cavallo has printed the chief part of this letter in the Supplement to his Treatise on Magnetism, with a translation; and I think it is to be wished he had printed the whole of so curious a paper. The curiosity of this letter, says Mr. Cavallo, consists in its containing almost all that is at present known of the subject, at least the most remarkable parts of it, mixed however with a good deal of absurdity. The laws of magnetic attraction, and of the communication of that power to iron, the directive property of the natural magnet, as well as of the iron that has been touched by it, and even the declination of the magnetic needle, are clearly and unequivocally mentioned in it.

As this Variation differs in different places, Gonzales d'Oviedi found there was none at the Azores; from whence some geographers thought fit in their maps to make the first meridian pass through one of these islands: it not being then known that the Variation altered in time. See Magnet; also Gilbert De Magnete, Lond. 1600, p. 4 and 5; or Purchas's Pilgrims, Lond. 1625, book 2, sect. 1.

Various are the hypotheses that have been framed to account for this extraordinary phenomenon: we shall only notice some of the latter, and more probable: just premising, that Robert Norman, the inventor of the Dipping needle, disputes against Cortes's notion, that the Variation was caused by a point in the heavens; contending that it should be sought for in the earth, and proposes how to discover its place.

The first is that of Gilbert (De Magnete, lib. 4, p. 151 &c), which is followed by Cabeus, &c. This notion is, that it is the earth, or land, that draws the needle out of its meridian direction: and hence they argue, that the needle varied more or less, as it was more or less distant from any great continent; and consequently that if it were placed in the middle of an ocean, equally distant from equal tracts of land on each side, eastward and westward, it would not decline either to the one or the other, but point exactly north and south. Thus, say they, in the Azores islands, which are equally distant from Africa on the east, and America on the west, there is no Variation: but as you sail from thence towards Africa, the needle begins to decline toward the east, and that still more and more till you reach the shore. If you proceed still farther eastward, the declination gradually diminishes again, by reason of the land left behind on the west, which continues to draw the needle. The same holds till you arrive at a place where the tracts of land on each side are equal; and there again the Variation will be nothing. But the misfortune is, the law does not hold universally; for multitudes of observations of the Variation, in different parts, made and collected by Dr. Halley, overturn the whole theory.

Others therefore have recourse to the frame and compages of the earth, considered as interspersed with rocks and shelves, which being generally found to run towards the polar regions, the needle comes to have a general tendency that way; but it seldom happens that their direction is exactly in the meridian, and the needle has consequently, for the most part, some Variation.

Others hold that divers parts of the earth have different degrees of the magnetic virtue, as some are more intermixed with heterogeneous matters, which prevent the free action or effect of it, than others are.

Others again ascribe all to magnetic rocks and iron mines, which, affording more of the magnetic matter than other parts, draw the needle more. |

Lastly, others imagine that earthquakes, or high tides, have disturbed and dislocated several considerable parts of the earth, and so changed the magnetic axis of the globe, which was originally the same with the axis of the earth itself.

But none of these theories can be the true one; for still that great phenomenon, the Variation of the Variation, i. e. the continual change of the declination, in one and the same place, is not accountable for, on any of these foundations, nor is it even consistent with them.

Doctor Hook communicated to the Royal Society, in 1674, a theory of the Variation; the substance of which is, that the magnet has its peculiar pole, distant 10 degrees from the pole of the earth, about which it moves, so as to make a revolution in 370 years: whence the Variation, he says, has altered of late about 10 or 11 minutes every year, and will probably so continue to do for some time, when it will begin to proceed slower and slower, till at length it become stationary and retrograde, and so return back again. Birch's Hist. of the Royal Society, vol. 3, p. 131.

Dr. Halley has given a new system, the result of numerous observations, and even of a number of voyages made at the public expence on this account. The light which this author has thrown upon this obscure part of natural history, is very great, and of important consequence in navigation, &c. In this system he has reduced the several Variations in divers places to a precise rule, or order, which before appeared all precarious and arbitrary.

His theory will therefore deserve a more ample detail. The observations it is built upon, as laid down in the Philos. Trans. number 148, or Abr. vol. 2, p. 610, are as follow:

Observed Variations of the Needle in divers places, and at divers times.
		Longitude			Year of	Variation			Longitude			Year of	Variation
Places observed at.	from	Latitude	Obser-	Places observed at.	from	Latitude	Obser-
		London.			vation.	observed.			London.			vation.	observed.
		°	′	°	′		°	′			°	′	°	′		°	′
London		0	0	51	31 n	1580	11	15 e	Baldivia		73	0 w	40	0 s	1670	8	10 e
						1622	6	0 e	Cape Aguillas		16	30 e	34	50 s	1622	2	0 w
						1634	4	5 e							1675	8	0 w
						1672	2	30 w	At Sea		1	0 e	34	30 s	1675	0	0
						1683	4	30 w	At Sea		20	0 w	34	0 s	1675	10	30 e
Paris		2	25 e	48	51 n	1640	3	0 e	At Sea		32	0 w	24	0 s	1675	10	30 e
						1666	0	0	St. Helena		6	30 w	16	0 s	1677	0	40 e
						1681	2	30 w	Isle Ascension		14	30 w	7	50 s	1678	1	0 e
Uraniburg		13	0 e	55	54 n	1672	2	35 w	Johanna		44	0 e	12	15 s	1675	19	30 w
Copenhagen		12	53 e	55	41 n	1649	1	53 e	Mombasa		40	0 e	4	0 s	1675	16	0 w
						1672	3	45 w	Zocatra		56	0 e	12	30 n	1674	17	0 w
Dantzick		19	0 e	54	23 n	1679	7	0 w	Aden, Mouth	}	47	30 e	13	0 n	1674	15	0 w
Montpelier		4	0 e	43	37 n	1674	1	10 w	of Red Sea
Brest		4	25 w	48	23 n	1680	1	45 w	Diego Roiz		61	0 e	20	0 s	1676	20	30 w
Rome		13	0 e	41	50 n	1681	5	0 w	At Sea		64	30 e	0	0	1676	15	30 w
Bayonne		1	20 w	43	30 n	1680	1	20 w	At Sea		55	0 e	27	0 s	1676	24	0 w
Hudson's Bay		79	40 w	51	0 n	1668	19	15 w	Bombay		72	30 e	19	0 n	1676	12	0 w
In Hudson's	}	57	0 w	61	0 n	1668	29	30 w	Cape Comorin		76	0 e	8	15 n	1680	8	48 w
Straits	Ballasore		87	0 e	21	30 n	1680	8	10 w
Beffin's Bay,	}	80	0 w	78	0 n	1616	57	0 w	Fort St. George		80	0 e	13	15 n	1680	8	10 w
Sir T. Smith's	West Point of	}	104	0 e	6	40 s	1676	3	10 w
Sound	Java
At Sea		57	0 w	38	40 n	1682	7	30 w	At Sea		58	0 e	39	0 s	1677	27	30 w
At Sea		31	30 w	43	50 n	1682	5	30 w	I. St. Paul		72	0 e	38	0 s	1677	23	30 w
At Sea		42	0 w	21	0 n	1678	0	40 e	At Van Diemen's		142	0 e	42	25 s	1642	0	0
Cape St. Au-	}	35	30 w	28	0 s	1670	5	30 e	At New Zea-	}	170	0 e	40	50 s	1642	9	0 e
gustine	land
Off the mouth	}	53	0 w	39	30 s	1670	20	30 e	Three - kings	}	169	30 e	34	35 s	1642	8	40 e
of River Plate	Isle in ditto
Cape Frio		41	10 w	22	40 s	1670	12	10 e	I. Rotterdam in	}	184	0 e	20	15 s	1642	6	20 e
Entrance of	}	68	0 w	52	30 s	1670	17	0 e	the South Sea
Magellan's	Coast of New	}	149	0 e	4	30 s	1643	8	45 e
Straits	Guinea
West Entrance	}	75	0 w	53	0 s	1670	14	10 e	West Point of	}	126	0 e	0	26 s	1643	5	30 e
of ditto	ditto

|

Upon these observed Variations Dr. Halley makes several remarks, as to the Variation in different parts of the world at the time of his writing, eastward and westward, and the situation and direction of the lines or places of no Variation: from the whole he deduces the following theory.

Dr. Halley's Theory of the Variation of the Needle. That the whole globe of the earth is one great magnet, having four magnetical poles, or points of attraction; near each pole of the equator two; and that in those parts of the world which lie nearly adjacent to any one of these magnetic poles, the needle is governed by it; the nearest pole being always predominant over the more remote.

The pole which at present is nearest to us, he conjectures to lie in or near the meridian of the Land's-end of England, and not above 7° from the north pole: by this pole, the Variations in all Europe and Tartary, and the North Sea, are chiefly governed; though still with some regard to the other northern pole, whose situation is in the meridian passing about the middle of California, and about 15° from the north pole of the world, to which the needle has chiefly respect in all North America, and in the two oceans on either side of it, from the Azores westward to Japan, and farther.

The two southern magnetic poles, he imagines, are rather more distant from the south pole of the world; the one being about 16° from it, on a meridian 20° to the westward of the Magellanic Streights, or 95° west from London: this pole commands the needle in all South America, in the Pacific Ocean, and the greatest part of the Ethiopic Ocean. The other magnetic pole seems to have the greatest power, and the largest dominion of all, as it is the most remote from the pole of the world, being little less than 20° distant from it, in the meridian which passes through New Holland, and the island Celebes, about 120° east from London: this pole is predominant in the south part of Africa, in Arabia, and the Red Sea, in Persia, India, and its islands, and all over the Indian sea, from the Cape of Good Hope eastward, to the middle of the Great South Sea that divides Asia from America.

Such, he observes, seems to be the present disposition of the magnetic virtue thoughout the whole globe of the earth. It is then shewn how this hypothesis accounts for all the Variations that have been observed of late, and how it answers to the several remarks drawn from the table.

It is there inferred that from the whole it appears, that the direction of the needle, in the temperate and frigid zones, depends chiefly upon the counterpoise of the forces of two magnetic poles of the same nature: as also why, under the same meridian, the Variation should be in one place 29 1/2 degrees west, and in another 20 1/2 degrees east.

In the torrid zone, and particularly about the equator, respect must be had to all the four poles, and their positions must be well considered, otherwise it will not be easy to determine what the Variation should be, the nearest pole being always strongest; yet so however as to be sometimes counterbalanced by the united forces of two more remote ones. Thus, in sailing from St. Helena, by the isle of Ascension, to the equator, on the north-west course, the Variation is very little easterly, and unalterable in that whole track; because the South-American pole (which is much the nearest in the aforesaid places), requiring a great easterly variation, is counterpoised by the contrary attraction of the North-American and the Asiatic south poles; each of which singly is, in these parts, weaker than the American south pole; and upon the north-west course the distance from this latter is very little varied; and as you recede from the Asiatic south pole, the balance is still preserved by an access towards the North-American pole. In this case no notice is taken of the European north pole; its meridian being a little removed from those of these places, and of itself requiring the same Variations which are here found.

After the same manner may the Variations in other places about the equator be accounted for, upon Dr. Halley's hypothesis.

To observe the Variation of the Needle. Draw a meridian line, as directed under Meridian; then a stile being erected in the middle of it, place a needle upon it, and draw the right line which it hangs over. Thus will the quantity of the Variation appear.

Or thus: As the former method of finding the Variation cannot be applied at sea, others have been devised, the principal of which are as follow. Suspend a thread and plummet over the compass, till the shadow pass through the centre of the card; observe the rhumb, or point of the compass which the shadow touches when it is the shortest. For the shadow is then a meridian line; and consequently the Variation is shewn.

Or thus: Observe the point of the compass upon which the sun, or some star, rises and sets; bisect the arch intercepted between the rising and setting, and the line of bisection will be the meridian line; consequently the Variation is had as before. The same may also be obtained from two equal altitudes of the same star, observed either by day or night. Or thus: Observe the rhumb upon which the sun or star rises and sets; and from the latitude of the place find the eastern or western amplitude: for the difference between the amplitude, and the distance of the rhumb observed, from the eastern rhumb of the card, is the Variation sought.

Or thus: Observe the altitude of the sun, or some star S, whose declination is known; and note the rhumb in the compass to which it then corresponds. Then in the triangle ZPS, are known three sides, viz, PZ the colatitude, PS the codeclination, and ZS the coaltitude; the angle PZS is thence found by spherical trigonometry; the supplement to which, viz AZS, is the azimuth from the south. Then the difference between the azimuth and the observed distance of the rhumb from the south, is the Variation sought. See Azimuth Compass.

The use of the Variation is to correct the courses a ship has steered by the compass, which must always be done before they are worked, or calculated. |

Variation of the Variation, is a gradual and continual change in the Variation, observed in any place, by which the quantity of the Variation is found to be different at different times.

This Variation, according to Henry Bond (in his Longitude found, Lond. 1670, pa. 6) “was first found to decrease by Mr. John Mair; 2dly, by Mr. Edmund Gunter: 3dly, by Mr. Henry Gellibrand; 4thly, by myself (Henry Bond) in 1640; and lastly, by Dr. Robert Hook, and others, in 1665;” which they found out by comparing together observations made at the same place, at different times. The discovery was soon known abroad; for Kircher, in his treatise intitled Magnes, first printed at Rome in 1641, says that our countryman Mr. John Greaves had informed him of it, and then he gives a letter of Mersenne's, containing a distinct account of it.

This continual change in the Variation, is gradual and universal, as appears by numerous observations. Thus, the Variation was,

At Paris, according to Orontius Finæus,

in 1550	8°	0′E.
in 1640	3	0 E.
in 1660	0	0
in 1681	2	2 W.
in 1759	18	10 W.
in 1760	18	20 W.

M. De la Lande (Exposition du Calcul Astronomique) observes, that the Variation has changed, at Paris, 26° 20′ in the space of 150 years, allowing that in 1610 the Variation was 8° E: and since 1740 the needle, which was always used by Maraldi, is more than 3° advanced toward the west, beyond what it was at that period; which is a change after the rate nearly of 9′1/2 per year.

At Cape d'Agulhas, in 1600, it had no Variation; (whence the Portuguese gave it that name);

in 1622	it was	2°W.
in 1675	"	8 W.
in 1692	"	11 W.

which is a change of nearly 8′ per year.

At St. Helena, the Variation, in 1600	was 8°	0′E.
in 1623	" 6	0 E.
in 1677	" 0	40 E.
in 1692	" 1	0 W.

which is a change of nearly 5′1/2 per year.

At Cape Comorin, the Variation,

in 1620	was 14°	20′W.
in 1680	" 8	44 W.
in 1688	" 7	30 W.

which is a change of nearly 6′1/2 per year.

At London, the Variation, in 1580	was 11°	15′E.
in 1622	" 6	0 E.
in 1634	" 4	5 E.
in 1657	" 0	0
in 1672	" 2	30 W.
in 1692	" 6	0 W.
in 1723	" 14	17 W.
in 1747	" 17	40 W.
in 1780	" 22	41 W.

which is a change after the rate of 10′ per year, upon a course of exactly 200 years. See Philos. Trans. No. 148 and No. 383, or Abr. vol. 2, p. 615, and vol. 7, p. 290; and Philos. Trans. vol. 45, p. 280, and vol. 66, p. 393. On the subject of the Variation, see also Norman's New Attractive 1614; Burrows's Discovery of the Variation 1581; Bond's Longitude found, 1676; &c.

Mr. Thomas Harding, in the Transactions of the Royal Irish Academy, vol. 4, has given observations on the Variation of the magnetic needle, at Dublin, which are rather extraordinary. He says the change in the Variation at that place is uniform. That from the year 1657, in which the Variation was nothing (the same as at London in that year), it has been going on at the medium rate of 12′ 20″ annually, and was in May 1791, 27° 23′ west: exceeding that at London now by 3 or 4 degrees. He brings proof of his assertion of the uniformity of the Variation, from different authentic records, and states the operations by which it is calculated. He concludes with recommending accuracy in marking the existing Variation when maps are made, as not only conducing to the exact definition of boundaries, but as laying the best foundation for a discovery of the longitude by sea or land.

Theory of the Variation of the Variation. According to Dr. Halley's theory, this change in the Variation of the compass, is supposed owing to the difference of velocity in the motions of the internal and external parts of the globe. From the observations that have been cited, it seems to follow, that all the magnetical poles have a motion westward, but yet not exactly round the axis of the earth, for then the Variations would continue the same in the same parallel of latitude, contrary to experience.

From the disagreement of such a supposition with experiments therefore, the learned author of the theory invented the following hypothesis: The external parts of the globe he considers as the shell, and the internal as a nucleus, or inner globe; and between the two he conceives a fluid medium. That inner earth having the same common centre and axis of diurnal rotation, may revolve with our earth every 24 hours: Only the outer sphere having its turbinating motion somewhat swifter or slower than the internal ball; and a very minute difference in length of time, by many repetitions, becoming sensible; the internal parts will gradually recede from the external, and they will appear to move, either eastward or westward, by the difference of their motions.

Now, supposing such an internal sphere, having such a motion, the two great difficulties in the former hypothesis are easily solved; for if this exterior shell of earth be a magnet, having its pole at a distance from the poles of diurnal rotation; and if the internal nucleus be likewise a magnet, having its poles in two other places, distant also from the axis; and these latter, by a slow gradual motion, change their place in respect of the external, a reasonable account may then be given of the four magnetical poles before mentioned, and also of the changes of the needle's Variation.

The author thinks that two of these poles are fixed, and the other two moveable; viz, that the fixed poles are the poles of the external cortex or shell of the | earth; and the other the poles of the magnetical nucleus, included and moveable within the former. From the observations he infers, that the motion is westwards, and consequently that the nucleus has not precisely attained the same velocity with the exterior parts in their diurnal rotation; but so very nearly equals it, that in 365 revolutions the difference is scarcely sensible.

That there is any difference of this kind, arises from hence, that the impulse by which the diurnal motion was impressed on the earth, was given to the external parts, and from thence in time communicated to the internal; but so as not yet perfectly to equal the velocity of the first motion impressed on the superficial parts of the globe, and still preserved by them.

As to the precise period, observations are wanting to determine it, though the author thinks we may reasonably conjecture that the American pole has moved westward 46° in 90 years, and that its whole period is performed in about 700 years.

Mr. Whiston, in his New Laws of Magnetism, raises several objections against this theory. See MAGNETISM.

M. Euler, too, the son of the celebrated mathematician of that name, has controverted and censured Dr. Halley's theory. He thinks, that two magnetic poles, placed on the surface of the earth, will sufficiently account for the Variation: and he then endeavours to shew, how we may determine the declination of the needle, at any time, and on every part of the globe, from this hypothesis. For the particulars of this reasoning, see the Histoire de l'Academie des Sciences & Belles Lettres of Berlin, for 1757; also Mr. Cavallo's Treatise on Magnetism, p. 117.

Variation of the Needle by Heat and Cold.—There is a small Variation of the Variation of the magnetic needle, amounting only to a few minutes of a degree in the same place, at different hours of the same day, which is only discoverable by nice observations. Mr. George Graham made several observations of this kind in the years 1722 and 1723, professing himself altogether ignorant of the cause of the phenomena he observed. Philos. Trans. No. 383, or Abr. vol. 7, p. 290.

About the year 1750, Mr. Wargentin, secretary of the Swedish Academy of Sciences, took notice both of the regular diurnal Variation of the needle, and also of its being disturbed at the time of the aurora borealis, as recorded in the Philos. Trans. vol. 47, p. 126.

About the year 1756, Mr. Canton commenced a series of observations, amounting to near 4000, with an excellent Variation-compass, of about 9 inches diameter. The number of days on which these observations were made, was 603, and the Diurnal Variation on 574 of them was regular, so as that the absolute Variation of the needle westward was increasing from about 8 or 9 o'clock in the morning, till about 1 or 2 in the afternoon, when the needle became stationary for some time; after that, the absolute Variation westward was decreasing, and the needle came back again to its former situation, or nearly so, in the night, or by the next morning. The Diurnal Variation is irregular when the needle moves slowly eastward in the latter part of the morning, or westward in the latter part of the afternoon; also when it moves much either way after night, or suddenly both ways in a short time. These irregularities seldom happen more than once or twice in a month, and are always accompanied, as far as Mr. Canton observed, with an aurora borealis.

Mr. Canton lays down and evinces, by experiment, the following principle, viz, that the attractive power of the magnet (whether natural or artificial) will decrease while the magnet is heating, and increase while it is cooling. He then proceeds to account for both the regular and irregular Variation. It is evident, he says, that the magnetic parts of the earth in the north, on the east side, and on the west side of the magnetic meridian, equally attract the north end of the needle. If then the eastern magnetic parts be heated faster by the sun in the morning, than the western parts, the needle will move westward, and the absolute Variation will increase: when the attracting parts of the earth on each side of the magnetic meridian have their heat increasing equally, the needle will be stationary, and the absolute Variation will then be greatest; but when the western magnetic parts are either heating faster, or cooling slower, than the eastern, the needle will move eastward, or the absolute Variation will decrease; and when the eastern and western magnetic parts are cooling equally fast, the needle will again be stationary, and the absolute Variation will then be least.

By this theory, the Diurnal Variation in the summer ought to exceed that in winter; and accordingly it is found by observation, that the Diurnal Variation in the months of June and July is almost double of that in December and January.

The irregular Diurnal Variation must arise from some other cause than that of heat communicated by the sun; and here Mr. Canton has recourse to subterranean heat, which is generated without any regularity as to time, and which will, when it happens in the north, affect the attractive power of the magnetic parts of the earth on the north end of the needle. That the air nearest the earth will be most warmed by the heat of it, is obvious; and this has been often noticed in the morning, before day, by means of thermometers at different distances from the ground. Philos. Trans. vol. 48, pa. 526.

Mr. Canton has annexed to his paper on this subject, a complete year's observations; from which it appears, that the Diurnal Variation increases from January to June, and decreases from June to December. Philos. Trans. vol. 51, pa. 398.

It has also been observed, that different needles, especially if touched with different loadstones, will differ a few minutes in their Variation. See Poleni Epist. Phil. Trans. num. 421.

Dr. Lorimer (in the Supp. to Cavallo's Magnetism) adduces some ingenious observations on this subject. It must be allowed, says he, according to the observations of several ingenious gentlemen, that the collective magnetism of this earth arises from the magnetism of all the ferruginous bodies contained in it, and that the magnetic poles should therefore be considered as the centres of the powers of those magnetic substances. These poles must therefore change their places according as the magnetism of such substances is affected, and if | with Mr. Canton we allow, that the general cause of the Diurnal Variation arises from the sun's heat in the forenoon and afternoon of the same day, it will naturally occur, that the same cause, being continued, may be sufficient to produce the general Variation of the magnetic needle for any number of years. For we must consider, that ever since any attentive observations have been made on this subject, the natural direction of the magnetic needle in Europe has been constantly moving, from west to east, and that in other parts of the world it has continued its motion with equal constancy.

As we must therefore admit, says Dr. Lorimer, that the heat in the different seasons depends chiefly on the sun, and that the months of July and August are commonly the hottest, while January and February are the coldest months of the year; and that the temperature of the other months falls into the respective intermediate degrees; so we must consider the influence of heat upon magnetism to operate in the like manner, viz, that for a short time it scarcely manifests itself; yet in the course of a century, the constancy and regularity of it becomes sufficiently apparent. It would therefore be idle to suppose, that such an influence could be derived from an uncertain or fortuitous cause. But if it be allowed to depend upon the constancy of the sun's motion, and this appears to be a cause sufficient to explain the phenomena, we should (agreeably to Newton's first law of philosophizing) look no farther.

As we therefore consider, says he, the magnetic powers of the earth to be concentrated in the magnetic poles, and that there is a diurnal Variation of the magnetic needle, these poles must perform a small diurnal revolution proportional to such Variation, and return again to the same point nearly. Suppose then that the sun in his diurnal revolution passes along the northern tropic, or along any parallel of latitude between it and the equator, when he comes to that meridian in which the magnetic pole is situated, he will be much nearer to it, than in any other; and in the opposite meridian he will of course be the farthest from it. As the influence of the sun's heat will therefore act most powerfully at the least, and less forcibly at the greatest distance, the magnetic pole will consequently describe a figure something of the elliptical kind; and as it is well known that the greatest heat of the day is some time after the sun has passed the meridian, the longest axis of this elliptical figure will lie north easterly in the northern, and south-easterly in the southern hemisphere. Again, as the influence of the sun's heat will not from those quarters have so much power, the magnetic poles cannot be moved back to the very same point, from which they set out; but to one which will be a little more northerly and easterly, or more southerly and easterly, according to the hemispheres in which they are situated. The figures therefore which they describe, may more properly be termed elliptoidal spirals.

In this manner the Variation of the magnetic needle in the northern hemisphere may be accounted for. But with respect to the southern hemisphere we must recollect, that though the lines of declination in the northern hemisphere have constantly moved from west to east, yet in the southern hemisphere, it is equally certain that they have moved from east to west, ever since any observations have been made on the subject. Hence then the lines of magnetic declination, or Halleyan curves, as they are now commonly called, appear to have a contrary motion in the southern hemisphere, to what they have in the northern; though both the magnetic poles of the earth move in the same direction, that is from west to east.

In the northern hemisphere there was a line of no Variation, which had east Variation on its eastern side, and west Variation on its western side. This line evidently moved from west to east during the two last centuries; the lines of east Variation moving before it, while the lines of west Variation followed it with a proportional pace. These lines first passed the Azores or Western Islands, then the meridian of London, and after a certain number of years still later, they passed the meridian of Paris. But in the southern hemisphere there was another line of no Variation, which had east Variation on its western side, and west Variation on its eastern; the lines of east Variation moving before it, while those of the west Variation followed it. This line of no Variation first passed the Cape des Aiguilles, and then the Cape of Good Hope; the lines of 5°, 10°, 15°, and 20° west Variation following it, the same as was the case in the northern hemisphere, but in the contrary direction.

We may just farther mention the idea of Dr. Gowin Knight, which was, that this earth had originally received its magnetism, or rather that its magnetical powers had been brought into action, by a shock, which entered near the southern tropic, and passed out at the northern one. His meaning appears to have been, that this was the course of the magnetic fluid, and that the magnetic poles were at first diametrically opposite to each other. Though, according to Mr. Canton's doctrine, they would not have long continued so; for from the intense heat of the sun in the torrid zone, according to the principles already explained, the north pole must have soon retired to the north-eastward, and the south pole to the south-eastward. It is also curious to observe, that on account of the southern hemisphere being colder upon the whole than the northern hemisphere, the magnetic poles would have moved with unequal pace: that is, the north magnetic pole would have moved farther in any given time to the north-east, than the south magnetic pole could have moved to the south-east. And, according to the opinions of the most ingenious authors on this subject, it is generally allowed, that at this time the north magnetic pole is considerably nearer to the north pole of the earth, than the south magnetic pole is to the south pole of the earth.

It may farther be added, that several ingenious sea officers are of opinion, that in the western parts of the English Channel the Variation of the magnetic needle has already begun to decrease; having in no part of it ever amounted to 25°. There are however other persons who assert that the Variation is still increasing in the Channel, and as far westward as the 15th degree of longitude and 51° of latitude, at which place they say that it amounts to about 30°.

Of the Variation Chart. Doctor Halley having collected a multitude of observations made on the Variation of the needle in many parts of the world, was hence enabled to draw, on a Mercator's chart, certain lines, shewing the Variation of the compass in all those | places over which they passed, in the year 1700, when he published the first chart of this kind, called the Variation Chart.

From the construction of this chart it appears, that the longitude of any of those places may be found by it, when the latitude and the Variation in that place are known. Thus, having found the Variation of the compass, draw a parallel of latitude on the chart through the latitude found by observation; and the point where it cuts the curved line, whose Variation is the same with that observed, will be the ship's place. A similar project of thus finding the longitude, from the known latitude and inclination or dip of the needle, was before proposed by Henry Bond, in his treatise intitled, The Longitude Found, printed in 1676.

This method however is attended with two considerable inconveniences: 1st, That wherever the Variation lines run east and west, or nearly so, this way of finding the longitude becomes imperfect, as their intersection with the parallel of latitude must be very indesinite: and among all the trading parts of the world, this imperfection is at present found chiefly on the western coasts of Europe, between the latitudes of 45° and 53°; and on the eastern shores of North America, with some parts of the Western Ocean and Hudson's Bay, lying between the said shores: but for the other parts of the world, a Variation Chart may be attended with considerable benefit. However, the Variation curves, when they run east and west, may sometimes be applied to good purpose in correcting the latitude, when meridian observations cannot be had, as it often happens on the northern coasts of America, in the Western Ocean, and about Newfoundland; for if the Variation can be obtained exactly, then the east and west curve, answering to the Variation in the chart, will shew the latitude.

2dly, As the deviation of the magnetical meridian, from the true one, is subject to continual alteration, therefore a chart to which the Variation lines are fitted for any year, must in time become useless, unless new lines, shewing the state of the Variation at that time, be drawn on the chart: but as the change in the Variation is very slow, therefore new Variation Charts published every 7 or 8 years, will answer the purpose tolerably well. And thus it has happened that Halley's Variation Chart has become useless, for want of encouragement to renew it from time to time.

However, in the year 1744, Mr. William Mountaine and Mr. James Dodson published a new Variation Chart, adapted for that year, which was well received; and several instances of its great utility having been communicated to them, they fitted the Variation lines anew for the year 1756, and in the following year published the 3d Variation Chart, and also presented to the Royal Society a curious paper concerning the Variation of the magnetic needle, with a set of tables annexed, containing the result of upwards of 50 thousand observations, in six periodical reviews, from the year 1700 to 1756 inclusive, and adapted to every 5 degrees of latitude and longitude in the more frequented oceans; which paper and tables were printed in the Transactions for the year 1757.

From these tables of observations, such extraordi- nary and whimsical irregularities occur in the Variation, that we cannot think it wholly under the direction of one general and uniform law; but rather conclude, with Dr. Gowen, in the 87th prop. of his Treatise upon Attraction and Repulsion, that it is influenced by various and different magnetic attractions, perhaps occasioned by the heterogeneous compositions in the great magnet, the earth.

Many other observations on the Variation of the magnetic needle, are to be found in several volumes of the Philos. Trans. See particularly vol. 48, p. 875; vol. 50, p. 329; vol. 56, p. 220; and vol. 61, p. 422.

Variation Compass. See Compass.

Variation of Curvature, in Geometry, is used for that inequality or change which takes place in the curvature of all curves except the circle, by which their curvature is more or less in different parts of them. And this Variation constitutes the quality of the curvature of any line.

Newton makes the index of the inequality, or Variation of Curvature, to be the ratio of the fluxion of the radius of curvature to the fluxion of the curve itself: and Maclaurin, to avoid the perplexity that different notions, connected with the same terms, occasion to learners, has adopted the same definition: but he suggests, that this ratio gives rather the Variation of the ray of curvature, and that it might have been proper to have measured the Variation of Curvature rather by the ratio of the fluxion of the curvature itself to the fluxion of the curve; so that, the curvature being inversely as the radius of curvature, and consequently its fluxion as the fluxion of the radius itself directly, and the square of the radius inversely, its Variation would have been directly as the measure of it according to Newton's definition, and inversely as the square of the radius of curvature.

According to this notion, it would have been measured by the angle of contact contained by the curve and circle of curvature, in the same manner as the curvature itself is measured by the angle of contact contained by the curve and tangent. The reason of this remark may appear from this example: The Variation of curvature, according to Newton's explication, is uniform in the logarithmic spiral, the fluxion of the radius of curvature in this figure being always in the same ratio to the fluxion of the curve; and yet, while the spiral is produced, though its curvature decreases, it never vanishes; which must appear a strange paradox to those who do not attend to the import of Newton's definition. Newton's Method of Fluxions and Inf. Series, pa. 76. Maclaurin's Flux. art. 386. Philos. Trans. num. 468, pa. 342.

The Variation of curvature at any point of a conic section, is always as the tangent of the angle contained by the diameter that passes through the point of contact, and the perpendicular to the curve at the same point, or to the angle formed by the diameter of the section, and of the circle of curvature. Hence the Variation of curvature vanishes at the extremities of either axis, and is greatest when the acute angle, contained by the diameter, passing through the point of contact and the tangent, is least.

When the conic section is a parabola, the Variation is | as the tangent of the angle, contained by the right line drawn from the point of contact to the focus, and the perpendicular to the curve. See Curvature.

From Newton's definition may be derived practical rules for the Variation of curvature, as follows:

1. Find the radius of curvature, or rather its fluxion; then divide this fluxion by the fluxion of the curve, and the quotient will give the Variation of curvature; exterminating the fluxions when necessary, by the equation of the curve, or perhaps by expressing their ratio by help of the tangent, or ordinate, or subnormal, &c.

2. Since z^.3/-x^.y^.., or z^.3/-y^.. (putting x^. = 1) denotes the radius of curvature of any curve z, whose absciss is x, and ordinate y; if the fluxion of this be divided by z^., and z^. and z^.. be exterminated, the general value of the Variation will come out (-3y^.y^..2 + y^∴ (1 + y^.2))/y^..2; then substituting the values of y^., y^.., y^∴ (found from the equation of the curve) into this quantity, it will give the Variation sought.

Ex. Let the curve be the parabola, whose equation is , the Variation sought. Emerson's Flux. pa. 228.