On the finding of the amount of variation: how great _is the arc of the Horizon from its arctick or antarctick_ intersection of the meridian, to the point _respective of the magnetick needle_.

Virtually the true meridian is the chief foundation of the whole matter: when that is accurately known, it will be easy by a mariners' compass (if its construction and the mode of attachment of the magnetick iron works are known) or by some other larger horizontal versorium to exhibit the arc of variation on the Horizon. By means of a sufficiently large nautical variation compass (two equal altitudes of the sun being observed before and after midday), the variation becomes known from the shadow; the altitude of the sun is observed either by a staff or by a rather large quadrant.

On land the variation is found in another way which is easier, and because of the larger size of the instrument, more accurate. Let a thick squared board be made of some suitable wood, the surface of which is two feet in length and sixteen inches in width: describe upon it some semicircles as in the following figure, only more in number. In the centre let a brass style be reared perpendicularly: let there be also a movable pointer reaching from the centre to the outmost semicircle, and a magnetick versorium in a cavity covered over with glass: then let the board be exactly adjusted to the level of the Horizon by the plane instrument with its perpendicular; and turn the lily of the instrument toward the north, so that the versorium may rest truly over the middle line of the cavity, which looks toward the point of variation on on the Horizon. Then at some convenient hour in the morning (eight or nine for instance) observe the apex of the shadow thrown by the style when it reaches the nearest semicircle and mark the place of the apex of this shadow with chalk or ink: then bring round the movable index to that mark, and observe the degree on the Horizon numbered from the lily, which the index shows. In the afternoon see when the end of the shadow shall again reach the periphery of the same semicircle, and, bringing the index to the apex of the shadow, seek for the degree on the other side of the lily. From the difference of the degrees becomes known [Illustration] {172} the variation; the less being taken from the greater, half the remainder is the arc of variation. The variation is sought by many other instruments and methods in conjunction with a convenient mariners'

compass; also by a globe, by numbers, and by the ratios of triangles and sines, when the latitude is known and one observation is made of the sun's altitude: but those ways and methods are of less use, for it is superfluous to try to find in winding and roundabout ways what can be more readily and as accurately found in a shorter one. For the whole art is in the proper use of the instruments by which the sun's place is expeditiously and quickly taken (since it does not remain stationary, but moves on): for either the hand trembles or the sight is dim, or the instrument makes an error. Besides, to observe the altitude on both sides of the meridian is just as expeditious as to observe on one side only and at the same time to find the elevation of the pole. And he who can take one altitude by the instrument can also take another; but if the one altitude be uncertain, then all the labour with the globe, numbers, sines and triangles is lost; nevertheless those exercises of ingenious mathematicians are to be commended. It is easy for anyone, if he stand on land, to learn the variation by accurate observations and suitable instruments, especially in a nearly upright sphere; but on the sea, on account of the motion and the restlessness of the waters, exact experiments in degrees and minutes cannot be made: and with the usual instruments scarcely within the third or even the halt of a rumbe, especially in a higher latitude; hence so many false and bad records of the observations of navigators. We have, however, taken care for the finding of the deviation by a sufficiently convenient and ready instrument, by means of the rising of certain stars, by the rising or setting of the sun, and in northern regions by the Pole Star: for the variation is learned with greater certainty even by the skilful with an instrument which is at once simple and less sensitive to the waves of the sea. Its construction is as follows.

[228]Let an instrument be made of the form of a true and meridional mariners' compass of at least one foot in diameter (with a versorium which is either nude or provided with a cardboard circle): let the limb be divided into four quadrants, and each quadrant into 90 degrees. The movable compass-box (as is usual in the nautical instrument) is to be balanced below by a heavy weight of sixteen pounds. On the margin of the suspended compass-box, where opposite quadrants begin, let a half-ring rising in an angular frame in the middle be raised (with the feet of the half-ring fixed on either side in holes in the margin) so that the top of the frame may be perpendicular to the plane of the compass; on its top let a rule sixteen digits in length be fastened at its middle on a joint like a balance beam, so that it may move, as it were, about a central axis. At the ends of the rule there are small plates with holes, {173} [Illustration] {174} through which we can observe the sun or stars. The variation is best observed and expeditiously by this instrument at the equinoxes by the rising or setting sun. But even when the sun is in other parts of the zodiack, the deviation becomes known when we have the altitude of the pole: that being known, one can learn the amplitude on the Horizon and the distance from the true east both of the sun and of the following fixed stars by means of a globe, or tables, or an instrument. Then the variation readily becomes known by counting from the true east the degrees and minutes of the amplitude at rising. Observe the preceding star of the three in the Belt of Orion as soon as it appears on the horizon; direct the instrument toward it and observe the versorium, for since the star has its rising in the true east about one degree toward the south, it can be seen how much the versorium is distant from the meridian, account being taken of that one degree. You will also be able to observe the arctick pole star when it is on the meridian, or at its greatest distance from the meridian of about three degrees (the pole star is distant 2 deg. 55 min. from the pole, according to the observations of Tycho Brahe), and by the instrument you will learn the variation (if the star be not on the meridian) by adding or subtracting, _secundum artem_, the proper reduction [_prostaphaeresis_][229] of the star's distance from the meridian. You will find when the pole star is on the meridian by knowing the sun's place and the hour of the night: for this a practised observer will easily perceive without great error by the visible inclination of the constellation: for we do not take notice of a few minutes, as do some who, when they toil to track the minutes of degrees at sea, are in error by a nearly whole rumbe. A practised observer will, in the rising of sun or stars, allow something for refraction, so that he may be able to use a more exact calculation.

Bright and conspicuous stars[230] which are _not far distant from the equator which it will be useful to observe at their rising and setting: the amplitude at the Horizon on rising being known from the altitude of the pole and from the declination of the stars, by means of a globe, or tables, or an instrument whence the variation is perceived by technical calculation._

{175}

_Right Ascension_ _Declination_ Oculus Tauri 62 55' 15 53' N Sinister humerus Orionis 72 24' 4 5' N Dexter humerus Orionis 83 30' 6 19' N Praecedens in cingulo Orionis 77 46' 1 16' S Canis major 97 10' 15 55' S Canis minor 109 41' 5 55' N Lucida Hydrae 137 10' 5 3' S Caput Geminorum australe 110 21' 28 30' N Caput boreale 107 4' 32 10' N Cor Leonis 146 8' 13 47' N Cauda Leonis 171 38' 16 30' N Spica Virginis 195 44' 8 34' S Arcturus 29 13' 21 54' N Cor Aquilae 291 56' 7 35' N

_An instrument for finding the amplitude at rising on the horizon._

Describe the circumference of a circle and let it be divided into quadrants by two diameters intersecting each other at right angles at its centre. One of these will represent the aequinoctial circle, the other the axis of the world. Let each of these quadrants be divided (in the accustomed way) into 90 degrees; on every fifth or tenth of which at each end of each diameter and on each side let marks (showing the numbers) be inscribed on the two limbs or margins made for that purpose outside the circumference. Then from each degree straight lines are drawn parallel to the aequator. You will then prepare a rule or alhidade equal to the diameter of that circle and divided throughout into the same parts into which the diameter of the circle representing the axis of the world is divided. Let there be left a small appendage attached to the middle of the rule, by which the middle of the fiducial line itself of the rule may be connected with the centre of the circle: but to every fifth or tenth part of that rule let numbers be attached proceeding from the centre toward each side. This circle represents the plane of the meridian; its centre the actual point of east or west, _i.e._, the common intersection of the horizon and aequator; all those lines aequidistant from the aequator denote the parallels of the sun and stars; the fiducial line of the rule or alhidade represents the horizon; and its parts signify the degrees of the horizon, beginning from the point of setting or of rising. {176}

[Illustration]

Therefore if the fiducial line of the rule be applied to the given latitude of the place reckoned from either end of that diameter which represents the axis of the world; and if further the given declination of the sun or of some star from the aequator (less than the complement of the latitude of the place) be found on the limb of the instrument; then the intersection of the parallel drawn from that point of the declination with the horizon, or with the fiducial line of the rule or alhidade, will indicate for the given latitude of the place the amplitude at rising of the given star or the sun.

{177} CHAP. XIII.

The observations of variation by seamen vary, for the _most part, and are uncertain: partly from error and inexperience_, and the imperfections of the instruments; and partly _from the sea being seldom so calm that the shadows or lights can remain quite steady on the instruments_.

After the variation of the compass had first been noticed, some more diligent navigators took pains to investigate in various ways the difference of aspect of the mariners' compass. Yet, to the great detriment of the nautical art, this has not been done so exactly as it ought to have been. For either being somewhat ignorant they have not understood any accurate method or they have used bad and absurd instruments, or else they merely follow some conjecture arising from an ill-formed opinion as to some prime meridian or magnetick pole; whilst others again transcribe from others, and parade these observations as their own; and they who, very unskilful themselves, first of all committed their observations to writing are, as by the prerogative of time, held in esteem by others, and their posterity does not think it safe to differ from them. Hence in long navigations, especially to the East Indies, the records by the Portuguese of the deviating compass are seen to be unskilful: for whoever reads their writings will easily understand that they are in error in very many things, and do not rightly understand the construction of the Portuguese compass (the lily of which diverges by half a rumbe from the needles toward the west), nor its use in taking the variation. Hence, while they show the variation of the compass in different places, it is uncertain whether they measure the deviation by a true meridional compass or by some other whose needles are displaced from the lily. The Portuguese (as is patent in their writings) make use of the Portuguese compass, whose magnetick needles are fixed aside from the lily by half of one rumbe toward the east. Moreover on the sea the observation of the variation is a matter of great difficulty, on account of the motion of the ship and the uncertainty of the deviation, even with the more skilful observers, if they use the best made instruments hitherto known and used. Hence there arise different opinions concerning the magnetick deviation: as, for instance, near the Island of St. Helena the Portuguese Rodriguez de {178} Lagos measures half a rumbe. The Dutch in their nautical log fix it at a whole rumbe. Kendall, the expert Englishman, with a true meridional compass admits only a sixth part of a rumbe. A little to the East of Cape Agullias Diego Alfonso makes no variation, and shows by an Astrolabe that the compass remains in the true meridian.

Rodriguez shows that the compass at Cape Agulhas has no variation if it is of Portuguese construction, in which the needles are inclined half a rumbe to the East. And there is the same confusion, negligence, and vanity in very many other instances.

CHAP. XIIII.

On the variation under the aequinoctial line, _and near it_.

In the North the magnetick needle varies because of the Boreal eminences of the continent; in the South because of the Austral; at the aequator, if the regions on both sides were equal, there would be no variation. But because this rarely happens some variation is often observed under the aequator; and even at some distance from the aequator of three or 4 degrees toward the North, there may be a variation arising from the south, if those very wide and influential southern continents be somewhat near on one side.

CHAP. XV.

The variation of the magnetick needle in the great aethiopick and American sea, beyond _the aequator_.

Discourse hath already been had of the mode and reason of the variation in the great Atlantick Ocean: but when one has advanced beyond the aequator off the east coast of Brazil the magnetick needle turns aside toward the mainland, namely, with that end of it which points to the south; so that with that end of the versorium it deviates from the true meridian toward the west; which navigators observe at the other end and suppose a variation to occur toward the east. But throughout the whole way from the first promontory on the east of Brazil, by {179} Cape St. Augustine and thence to Cape Frio, and further still to the mouth of the Strait of Magellan, the variation is always from the south toward the west with that end of the versorium which tends toward the antarctick pole. For it is always with the accordant end that it turns toward a continent. The variation, however, occurs not only on the coast itself, but at some distance from land, such as a space of fifty or sixty German miles or even more. But when at length one has progressed far from land, then the arc begins to diminish: for the magnetick needle turns aside the less toward what is too far off, and is turned aside the less from what is present and at hand, since it enjoys what is present. In the Island of St. Helena (the longitude of which is less than is commonly marked on charts and globes) the versorium varies by one degree or nearly two. The Portuguese and others taught by them, who navigate beyond the Cape of Good Hope to the Indies, set a course toward the Islands of Tristan d'Acunha, in order that they may enjoy more favourable winds; in the former part of their course the change of variation is not great; but after they have approached the islands the variation increases; and close to the islands it is greater than anywhere else in the whole course. For the end of the versorium tending to the south (in which lies the greatest source of the variation) is caught and allured toward the south-west by the great promontory of the southern land. But when they proceed onward toward the Cape of Good Hope the variation diminishes the more they approach it. But on the prime meridian in the latitude of 45 degrees, the versorium tends to the south-east: and one who navigates near the coast from Manicongo to the tropick, and a little beyond, will perceive that the versorium tends from the south to the east, although not much. At the promontory of Agulhas it preserves slightly the variation which it showed near the islands of d'Acunha, which nevertheless is very much diminished because of the greater remoteness from the cause of variation, and consequently there the southern end of the versorium does not yet face exactly to the pole.

CHAP. XVI.

On the variation in Nova Zembla.

Variations in parts near the pole are greater (as has been shown before) and also have sudden changes, as in former years the Dutch explorers observed not badly, even if those observations were not exact--which indeed is pardonable in them; for with the usual instruments it is with difficulty {180} that the truth becomes known in such a high latitude (of about 80 degrees). Now, however, from the deviation of the compass the reason for there being an open course to the east by the Arctick Ocean appears manifest; for since the versorium has so ample a variation toward the north-west, it is demonstrable that a continent does not extend any great distance in the whole of that course toward the east. Therefore with the greater hope can the sea be attempted and explored toward the east for a passage to the Moluccas by the north-east than by the north-west.

CHAP. XVII.

Variation in the Pacifick Ocean.

Passing the Strait of Magellan the deviation on the shore of Peru is toward the south-east, _i.e._, from the south toward the east. And a similar deflection would be continued along the whole coast of Peru as far as the aequator. In a higher latitude up to 45 deg. the variation is greater than near the aequator; and the deflection toward the south-east is in nearly the same proportion as was the deviation from the south toward the west on the eastern shore of South America. From the aequator toward the North there is little or no variation until one comes to New Galicia; and thence along the whole shore as far as Quivira the inclination is from the north toward the east.

CHAP. XVIII.

On the variation in the Mediterranean Sea.

Sicilian and Italian sailors think that in the Sicilian Sea and toward the east up to the meridian of the Peloponnesus (as Franciscus Maurolycus relates) the magnetick needle "graecizes," that is, turns from the pole toward what is called the greek wind or Boreas; that on the shore of the Peloponnesus it looks toward the true pole; but that when they have proceeded further east, then it "mistralizes," because it tends from the pole toward the mistral or north-west wind: which agrees with our rule for the variation. For as the Mediterranean Sea is extended toward the west from that meridian, so on the side {181} toward the east the Mediterranean Sea lies open as far as Palestine; as toward North and East lie open the whole Archipelago and the neighbouring Black Sea. From the Peloponnesus toward the north pole the meridian passes through the largest and most elevated regions of all Europe; through Achaia, Macedonia, Hungary, Transylvania, Lithuania, Novogardia, Corelia and Biarmia.

CHAP. XIX.

The variation in the interior of large _Continents_.

Most of the great seas have great variations; in some parts, however, they have none, but the true directions are toward the pole. On continents, also, the magnetick needle often deviates from the meridian, as on the edge of the land and near the borders; but it is generally accustomed to deviate by a somewhat small arc. In the middle, however, of great regions there are no variations. Hence in the middle lands of Upper Europe, in the interior of Asia, and in the heart of Africa, of Peru, and in the regions of North or Mexican America, the versorium rests in the meridian.

CHAP. XX.

Variation in the Eastern Ocean.

Variation in the Eastern Ocean throughout the whole voyage to Goa and the Moluccas is observed by the Portuguese; but they err greatly in many things, following, as they do, the first observers who note down variations in certain places with ill-adapted instruments, and by no means accurate observations, or by some conjectures. As, for instance, in Brandoe Island, they make the versorium deviate by 22 degrees to the north-west. For in no region or place in the whole world, of not greater latitude, is there so great a deviation; and, in reality, there the deviation is slight. Also when they make out that at Mosambique the compass deviates by one rumbe to the north-west, it is false; even though they use (as they are accustomed to do) the Portuguese compass: for beyond all doubt on the shore of {182} Mosambique the versorium inclines rumbe or even more to the south-west.

Very wrongly also beyond the aequator in the course to Goa they make the little compass incline by 1 rumbe to the west: whereas they should rather have said that in the first part of the course the Portuguese compass inclines by 1 rumbe: but that the true meridional compass inclines by rumbe only. In order that the amount of variation in the Eastern Ocean may be accurately settled in most places by our rules, there is needed a more exact and truer survey of the southern land, which spreads out from the south to the aequinoctial more than is commonly described on maps and globes.