Why the variation from that lateral cause is not greater than has hitherto been observed, having been rarely seen to reach two points of the mariners' compass, except near the pole.
T he earth, by reason of lateral eminences of the stronger globe, diverts iron and loadstone by some degrees from the true pole, or true meridian. As, for example, with us English at London it varies eleven degrees and ⅓: in some other places the variation is a little greater, but in no other region is the end of the iron ever moved aside very much more from the meridian. For as the iron is always directed by the true verticity of the earth, so the polar nature of the continent land (just as of the whole terrene globe) acts toward the poles: and even if that mass divert magnetick bodies from the meridian, yet the verticity of those lands (as also of the whole earth) controls and disposes them so that they do not turn toward the East by any greater arc. But it is not easy to determine by any general method how great the arc of variation is in all places, and how many degrees and minutes it subtends on the horizon, since it becomes greater or less from diverse causes. For both the strength of true verticity of the place and of the elevated regions, as well as their distances from the given place and from the poles of the world, must be considered and compared; which indeed cannot be done exactly: nevertheless by our method the variation becomes so known that no grave error will perturb the course at sea. If the positions of the lands were uniform and straight along meridians, and not defective and rugged, the variations near lands would be simple; such as appear in the following figure.
This is demonstrated by a long loadstone the poles of which are in the ends A B; let C D be the middle line and the æquinoctial, and let G H and E F (the lines) be for meridians on which versoria are disposed, the variations of which are greater at a greater distance from the æquator. But the inequalities of the maritime parts of the habitable earth, the enormous promontories, the very wide gulfs, the mountainous and more elevated regions, render the variations more unequal, or sudden, or more obscure; and, moreover, less certain and more inconstant in the higher latitude.
On the construction of the common mariners' compass225, and on the diversity of the compasses of different nations.
I n a round226 hollow wooden bowl, all the upper part of which is closed with glass, a versorium is placed upon a rather long pin which is fixed in the middle. The covering prevents the wind, and the motion of air from any external cause. Through the glass everything within can be discerned. The versorium is circular, consisting of some light material (as card), to the under part of which the magnetick pieces of iron are attached. On the upper part 32 spaces (which are commonly called points) are assigned to the same number of mathematical intervals in the horizon or winds which are distinguished by certain marks and by a lily indicating the north. The bowl is suspended in the plane of the horizon in æquilibrium in a brass ring which also is itself suspended transversely in another ring within a box sufficiently wide with a leaden weight attached; hence it conforms to the plane of the horizon even though the ship be tossed to and fro by the waves. The iron works are either a pair with their ends united, or else a single one of a nearly oval shape with projecting ends, which does its work more certainly and more quickly. This is to be fitted to the cardboard circle so that the centre of the circle may be in the middle of the magnetick iron. But inasmuch as variation arises horizontally from the point of the meridian which cuts the horizon at right angles, therefore on account of the variation the makers in different regions and cities mark out the mariners' compass in different ways, and also attach in different ways the magnetick needles to the cardboard circle on which are placed the 32 divisions or points. Hence there are commonly in Europe 4 different constructions and forms. First that of the States on the Mediterranean Sea, Sicily, Genoa, and the Republick of Venice. In all these the needles are attached under the rose or lily on the cardboard versorium, so that (where there is no variation) they are directed to the true north and south points. Wherefore the north part marked with the lily always shows exactly the point of variation when the apex itself of the lily on the movable circle, together with the ends of the magnetick wires attached below, rests at the point of variation. Yet another is that of Dantzig, and throughout the Baltic Sea, and the Belgian provinces; in which the iron works fixed below the circle diverge from the lily ¼ of a rumbe to the east. For navigation to Russia the divergency is ⅔. But the compasses which are made at Seville, Lisbon, Rochelle, Bordeaux, Rouen, and throughout all England have an interval of ½ a rumbe. From those differences most serious errors have arisen in navigation, and in the marine science. For as soon as the bearings of maritime places (such as promontories, havens, islands) have been first found by the aid of the mariners' compass, and the times of sea-tide or high water determined from the position of the moon over this or that point (as they say) of the compass, it must be further inquired in what region or according to the custom of what region that compass was made by which the bearings of those places and the times of the sea-tides were first observed and discovered. For one who should use the British compass and should follow the directions of the marine charts of the Mediterranean Sea would necessarily wander very much out of the straight course. So also he that should use the Italian compass in the British, German, or Baltic Sea, together with marine charts that are made use of in those parts, will often stray from the right way. These different constructions have been made on account of the dissimilar variations, so that they might avoid somewhat serious errors in those parts of the world. But Pedro Nuñez seeks the meridian by the mariners' compass, or versorium (which the Spanish call the needle), without taking account of the variation: and he adduces many geometrical demonstrations which (because of his slight use and experience in matters magnetical) rest on utterly vicious foundations. In the same manner Pedro de Medina, since he did not admit variation, has disfigured his Arte de Navegar with many errors.
Whether the terrestrial longitude can be found from the variation.
G rateful would be this work to seamen, and would bring the greatest advance to Geography. But B. Porta in chap. 38 of book 7 is mocked by a vain hope and fruitless opinion. For when he supposes that the magnetick needle would follow order and proportion in moving along meridians, so that "the neerer it is to the east, the more it will decline from the Meridian line, toward the east; and the neerer it comes to the west, the point of the needle will decline the more to the west" (which is totally untrue), he thinks that he has discovered a true index of longitude. But he is mistaken. Nevertheless, admitting and assuming these things (as though they were perfectly true), he makes a large compass indicating degrees and minutes, by which these proportional changes of the versorium might be observed. But those very principles are false, and ill conceived, and very ill considered; for the versorium does not turn more to the east because a journey is made toward the east: and although the variation in the more westerly parts of Europe and the adjoining ocean is to the east and beyond the Azores is changed a little to the west, yet the variation is, in various ways, always uncertain, both on account of longitude and of latitude, and because of the approach toward extensive tracts of land, and also because of the form of the dominant terrestrial eminences; nor does it, as we have before demonstrated, follow the rule of any particular meridian. It is with the same vanity also that Livio Sanuto so greatly torments himself and his readers. As for the fact that the crowd of philosophizers and sailors suppose that the meridian passing through the Azores marks the limits of variation, so that on the other and opposite side of that meridian a magnetick body necessarily respects the poles exactly, which is also the opinion of Joannes Baptista Benedictus and of many other writers on navigation, it is by no means true. Stevinus (on the authority of Hugo Grotius) in his Havenfinding Art distinguishes the variation according to the meridians: "It may be seene in the Table of variations, that in Coruo the Magneticall needle pointeth due North: but after that, the more a man shal goe towards the East, so much the more also shall he see the needle varie towards the East , till he come one mile to the Eastward from Plimouth, where the variation comming to the greatest is 13 degr. 24 min. From hence the Northeasting beginneth to decrease, til you come to Helmshude (which place is Westward from the North Cape of Finmark) where againe the needle pointeth due North. Now the longitude from Coruo to Helmshude is 60 degr. Which things being well weighed, it appeareth that the greatest variation 13 degr. 24 minutes at Plimmouth (the longitude whereof is 30 degr.) is in the midst betweene the places where the needle pointeth due North." But although this is in some part true in these places, yet it is by no means true that along the whole of the meridian of the island of Corvo the versorium looks truly to the north; nor on the meridian of Plymouth is the variation in other places 13 deg. 24 min. — nor again in other parts of the meridian of Helmshuda does it point to the true pole. For on the meridian passing through Plymouth in Latitude 60 degrees the North-easterly variation is greater: in Latitude 40 deg. much less; in Latitude 20 deg. very small indeed. On the meridian of Corvo, although there is no variation near the island, yet in Latitude 55 degrees the variation is about ½ a rumbe to the North-west; in Latitude 20 deg. the versorium inclines ¼ of a rumbe toward the East. Consequently the limits of variation are not conveniently determined by means of great circles and meridians, and much less are the ratios of the increment or decrement toward any part of the heavens properly investigated by them. Wherefore the rules of the abatement or augmentation of Northeasting or Northwesting, or of increasing or decreasing the magnetick deviation, can by no means be discovered by such an artifice. The rules which follow later for variation in southern parts of the earth investigated by the same method are altogether vain and absurd. They were put forth by certain Portuguese mariners, but they do not agree with the observations, and the observations themselves are admitted to be bad. But the method of haven-finding in long and distant voyages by carefully observed variation (such as was invented by Stevinus, and mentioned by Grotius) is of great moment, if only proper instruments are in readiness, by which the magnetick deviation can be ascertained with certainty at sea.
Why in various places near the pole the variations are much more ample than in a lower latitude.
V ariations are often slight, and generally null, when the versorium is at or near the earth's æquator. In a higher Latitude of 60, 70 or 80 deg. there are not seldom very wide variations. The cause of this is to be sought partly from the nature of the earth and partly from the disposition of the versorium. The earth turns magnetick bodies and at the æquator directs them strongly toward the pole: 227at the poles there is no direction, but only a strong coition through the congruent poles. Direction is therefore weaker near the poles, because by reason of its own natural tendency to turn, the versorium dips very much, and is not strongly directed. But since the force of those elevated lands is more vigorous, for the virtue flows from the whole globe, and since also the causes of variation are nearer, therefore the versorium deflects the more from its true direction toward those eminences. It must also be known that the direction of the versorium on its pin along the plane of the Horizon is much stronger at the æquator than anywhere else by reason of the disposition of the versorium; and this direction falls off with an increase of latitude. For on the æquator the versorium is, following its natural property, directed along the plane of the horizon; but in other places it is, contrary to its natural property, compelled into æquilibrium, and remains there, compelled by some external force: because it would, according to its natural property, dip below the horizon in proportion to the latitude, as we shall demonstrate in the book On Declination. Hence the direction falls off and at the pole is itself nothing: and for that reason a feebler direction is easily vanquished by the stronger causes of variation, and near the pole the versorium deflects the more from the meridian. It is demonstrated by means of a terrella: if an iron wire of two digits length be placed on its æquator, it will be strongly and rapidly directed toward the poles along the meridian, but more weakly so in the mid-intervals; while near the poles one may discern a precipitate variation.
Cardan's error when he seeks the distance of the centre of the earth from the centre of the cosmos by the motion of the stone of Hercules; in his book 5, On Proportions.
O ne may very easily fall into mistakes and errors when one is searching into the hidden causes of things, in the absence of real experiments, and this is easily apparent from the crass error of Cardan; who deems himself to have discovered the distances of the centres of the cosmos and of the earth through a variation of the magnetick iron of 9 degrees. For he reckoned that everywhere on the earth the point of variation on the Horizon is always distant nine degrees from the true north, toward the east: and from thence he forms, by a most foolish error, his demonstrative ratio of the separate centres.
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.
V irtually 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 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.
228Let 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, 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 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 stars230 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.
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
Præcedens in cingulo Orionis
77° 46'
1° 16' S
Canis major
97° 10'
15° 55' S
Canis minor
109° 41'
5° 55' N
Lucida Hydræ
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 Aquilæ
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 æquinoctial 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 æquator. 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 æquator; all those lines æquidistant from the æquator 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.
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 æquator (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.
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.
A fter 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 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.
On the variation under the æquinoctial line, and near it.
I n the North the magnetick needle varies because of the Boreal eminences of the continent; in the South because of the Austral; at the æquator, 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 æquator; and even at some distance from the æquator 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.
The variation of the magnetick needle in the great Æthiopick and American sea, beyond the æquator.
D iscourse hath already been had of the mode and reason of the variation in the great Atlantick Ocean: but when one has advanced beyond the æquator 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 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.
On the variation in Nova Zembla.
V ariations 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 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.