Decoration.
Direction has hitherto been spoken of as if in nature there were no variation; for in the preceding natural history we wished to omit and neglect this, inasmuch as in a terrestrial globe, perfect and in every sense complete, there would be none. Since, however, in fact, the earth's magnetick direction, owing to some fault and slip, deviates from its right course and from the meridian, we must extract and demonstrate the obscure and hidden cause of that variance which has troubled and sore racked in vain the minds of many. Those who before us have written on the magnetick movements have made no distinction between direction and variation, but consider the motion of magnetick iron to be uniform and simple. Now true direction is the motion of the magnetick body to the true meridian and its continuance therein with its appropriate ends towards the poles. But it very often happens at sea and on land that the magnetick iron does not point to the true pole, and that not only a versorium and magnetick pieces of iron, and the needle of a compass, or a mariners' compass, but also a terrella in its boat, as well as*iron ore, iron stones, and magnetick earths, properly prepared, are drawn aside and deviate towards some point of the Horizon very near to the meridian. For they with their poles frequently face termini away from the meridian. This variation(observed by means of instruments or a nautical variation compass) is therefore the arc of the horizon between the common point of intersecion of it with the true meridian, and the terminus of the deflecion on the horizon or projection of the deviating needle. That arc varies and differs with change of locality. To the terminus of the variation is commonly assigned a great circle, called the circle of variation, and also a magnetick meridian passing through the zenith and the point of variation on the horizon. In the northern regions of the earth this variation is either from the north toward the east or from the north toward the west: similarly in the southern regions it is from the south toward the east or toward the west. Wherefore one should observe in the northern regions of the earth*that end of the versorium or compass which turns toward the North; but in the southern regions the other end looking to the south—which seamen and sciolists for the most part do not understand, for in both regions they observe only the boreal lily of the compass (that which faces North). We have before said that all the motions of the magnet and iron, all its turning, its inclination, and its settlement, proceed from bodies themselves magnetical and from their common mother the earth, which is the source, the propagatrix, and the origin of all these qualities and properties. Accordingly the earth is the cause of this variation and inclination toward a different point of the horizon: but how and by what powers must be more fully investigated. And here we must at the outset reject that common opinion of recent writers concerning magnetick mountains, or any magnetick rock, or any phantasmal pole distant from the pole of the earth, by which the motion of the compass or versorium is controlled. This opinion, previously invented by others, Fracastorio himself adopted and developed; but it is entirely at variance with experience. For in that case in different places at sea and on land the point of variation would change toward the east or west in proportion and geometrical symmetry, and the versorium would always respect the magnetick pole: but experience teaches that there is no such definite pole or fixed terminus on the earth to account for the variation. For the arcs of*variation are changed variously and erratically, not only on different meridians but on the same meridian; and when, according to this opinion of the moderns, the deviation should be more and more toward the east, then suddenly, with a small change of locality, the deviation is from the north toward the west as in the northern regions near Nova Zembla. Moreover, in the southern regions, and at sea at a great distance from the æquator towards the antarctick pole, there are frequent and great variations, and not only in the northern regions, from the magnetick mountains. But the cogitations of others are still more vain and trifling, such as that of Cortes about a moving influence beyond all the heavens; that ofMarsilius Ficinus about a star in the Bear; that of Peter Peregrinus about the pole of the world; that of Cardan, who derives it from the rising of a star in the tail of the Bear[218]; of Bessardus, the Frenchman, from the pole of the Zodiack; that of Livio Sanuto from some magnetick meridian; that of Franciscus Maurolycus from a magnetical island; that of Scaliger from the heavens and mountains; that of Robert Norman, the Englishman, from a point respective. Leaving therefore these opinions, which are at variance with common experience or by no means proved, let us seek the true cause of the variation. The great magnet or terrestrial globe directs iron (as I have said) toward the north and south; and excited iron quickly settles itself toward those termini. Since, however, the globe of the earth is defective and uneven on its surface and marred by its diverse composition, and since it has parts very high and convex (to the height of some miles), and those uniform neither in composition nor body, but opposite and dissimilar: it comes to pass that the whole of that force of the earth diverts magnetical bodies in its periphery toward the stronger and more prominent connected magnetick parts. Hence on the outermost surface of the earth magnetical bodies are slightly perverted from the true meridian. Moreover, since the surface of the globe is divided into high lands and deep seas, into great continental lands, into ocean and vastest seas, and since the force of all magnetical motions is derived from the constant and magnetick terrestrial nature which is more prevalent on the greater continent and not in the aquæous or fluid or unstable part;[219]it follows that in certain parts there would be a magnetick inclination from the true pole east or west away from any meridian (whether passing through seas or islands) toward a great land or continent rising higher, that is, obviously toward a stronger and more elevated magnetick part of the terrestrial globe. For since the diameter of the earth is more than 1,700 German miles, those large lands can rise from the centre of the earth more than four miles above the depth of the ocean bottom, and yet the earth will retain the form of a globe although somewhat uneven at the top. Wherefore a magnetical body is turned aside, so far as the true verticity, when disturbed, admits, and departs from its right (the whole earth moving it) toward a vast prominent mass of land as though toward what is stronger. But the variation does really take place, not so much because of the more prominent and imperfect terrestrial parts and continent lands as because of the inæquality of the magnetick globe, and because of the real earth, which stands out more under the continent lands than under the depths of the seas. We must see, therefore, how theapodixisof this theory can be sustained by more definite observations. Since throughout all the course from the coast of Guinea to Cape Verde, the Canary Isles, and the border of the kingdom of Morocco, andthence along the coasts of Spain, France, England, Belgium, Germany, Denmark, and Norway, there lie on the right hand and toward the east a continent and extensive connected regions, and on the left extensive seas and a vast ocean lie open far and wide, it is consonant with the theory (as has been carefully observed by many) that magnetical bodies should turn slightly to the East from the true pole toward the stronger and more remarkable elevations of the earth. But it is far otherwise on the eastern shores of northern America; for from Florida by Virginia and Norumbega to Cape Race and away to the north the versorium is turned toward the west. But in the middle spaces, so to speak, as in the more westerly Azores, it looks toward the true pole. That any magnetick body turns itself similarly to the same regions of the earth is not, however, because of that meridian or because of the concordancy of the meridian with any magnetick pole, as the crowd of philosophizers reckon, for it is not so throughout the whole of that meridian. For on the same meridian*near Brazil something very different occurs, as we will show further on. The variation (cæteris paribus) is always less near the æquator, greater in higher latitudes, with the limitation that it be not very near the pole itself. Hence the variation is greater on the coast of*Norway and Belgium than on the coast of Morocco or Guinea: greater also near Cape Race than in the harbours of Norumbega or of Virginia. On the coast of Guinea magnetick implements deviate by a third part of one rumbe to the East: in Cape Verde Islands by a half: on the coast of Morocco by two thirds: in England at the mouth of the Thames by a whole rumbe: and at London by nearly eleven degrees and one third. For indeed the moving magnetick virtue is stronger in a higher latitude; and the larger regions extending toward the poles dominate the more, as is easily apparent anywhere on a terrella. For as in the case of true Direction magnetick bodies tend toward the pole (namely, toward the stronger end, the whole earth causing the motion), so also do they incline a little toward the stronger and higher parts by the action of the whole along with the conjoint action of iron bodies.
Demonstration of this may manifestly be madeVariation on imperfect terrella.*by means of a terrella in the following way: let there be a round loadstone somewhat imperfect in some part, and impaired by decay (such an one we had with a certain part corroded to resemble the Atlantick or great Ocean): place upon it some fine iron wire of the length of two barleycorns, as in the following figure. A B, a Terrella in certain parts somewhat imperfect and of unæqual virtue on the circumference. The versoria E, F, do not vary, but look directly to the pole A; for they are placed in the middle of the firm and sound part of the terrella and somewhat distant from the imperfect part: that part of the surface which is distinguished by dots and transverse lines is the weaker. The versorium O also does not vary (because it is placed in the middle of the imperfect part), but is directed toward the pole,just as near the western Azores on the earth. The versoria H and L do vary, for they incline toward the sounder parts very near them. As this is manifest in a terrella whose surface is sensibly rather imperfect, so also is it in others whole and perfect, when often one part of the stone has stronger external parts, which nevertheless do not disclose themselves manifestly to the senses. In such a terrella the demonstration of the variation and the discovery of the stronger parts is on this wise.Terrella with stronger regions.*Let A be the pole, B the place of the variation, C the stronger regions; then the horizontal versorium at B varies from the pole A toward C: so that both the variation is shown and the stronger places of the loadstone recognized. The stronger surface is also found by a fine iron wire of the length of two barleycorns: for since at the pole of the terrella it rears up perpendicularly, but in other places inclines toward the æquator, if in one and the same parallel circle it should be more erect in one place than in another; where the wire is raised more upright, there the part and surface of the terrella is stronger. Also when the iron wire placed over the pole inclines more to one part than to another.Wire will not rest in certain directions.*Let the experiment be made by means of a fine iron wire of three digits length placed over the pole A, so that its middle lies over the pole. Then one end is turned away from B toward C, and is not willing to lie quietly toward B; but on a terrella which is perfect[220]all round and even it rests on the pole directed toward any point of the æquator you please. Otherwise, let there be two*Unequal raising of wires.meridians meeting in the poles A B, let iron wires be reared just at the ends D and C of the equal arcs D A and C A; then the wire at D (the stronger region) will be more raised up than that at C, the weaker. And thus the sounder and stronger part of the loadstone is recognized, which otherwise would not be perceived by the touch. In a terrella which is perfect, and even, and similar in all its parts, there is, at equal distances from the pole, no variation[221]. Variation is shown by means of a terrella, a considerable part of which, forming a surface a little higher than the rest, does, although it be not decayed and broken, allure the versorium from the true*direction (the whole terrella co-operating).
A terrella uneven in surface.
A terrella uneven in surface.
It is shown by a small spike placed over a terrella or by a small versorium; for they are turned by the terrella toward the mass that stands out and toward the large eminences. In the same way on the earth the verticity is perturbed by great continents, which are mostly elevated above the depths of the seas and make the versorium deviate sometimes from the right tracks (that is, from the true meridians). On a terrella it is thus demonstrated: the end of the versorium A is not directed straight to the pole P, if there be a large protuberance B on the terrella; so also the cusp C deviates from the pole because of the eminence F. In the middle between the two eminences the versorium G collimates to the true pole because, being at equal distances from the two eminences B and F, it turns aside to neither, but observes the true meridian, especially when the protuberances are of equal vigour. But the versorium N on the other side varies from the pole M toward the eminences H, and is not held back, stopped, or restrained by the small eminence O on the terrella (as it were, some island of land in the ocean). L, however, being unimpeded, is directed to the pole M. The variation is demonstrated in another way on a terrella, just as on the earth. Let A be the pole of the earth, B the equator, C the parallel circle of latitude of 30 degrees, D a great eminence spread out toward the pole, E another eminence spread out from the pole toward the æquator. It is manifest that in the middle of D the versorium Fdoes not vary; while G is very greatly deflected: but H very little, because it is further removed from D. Similarly also the versorium I placed directly toward E does not deviate from the pole: but L and M turn themselves away from the pole A toward the eminence E.
Terrella with great eminences.
Inclination of a versorium toward a second magnet.
Vnless there should be a great dissolution of a continent and a subsidence of the land such as there was of the region Atlantis of which Plato and the ancients tell, the variation will continue perpetually immutable; the arc of the variation remains the same in the same place or region, whether it be at sea or on land, as in times past a magnetick body has declined toward the East or the West. The constancy of the variation and the pointing of the versorium to a definite point on the horizon in individual regions is demonstrated by a small versorium placed over a terrella the surface of which is uneven: for it always deviates from the meridian by an equal arc. It is also shown by the inclination of a versorium toward a second magnet; although in reality it is by the turning power of the whole, whether in the earth or in a terrella. Place upon a plane a versorium whose cusp is directed toward the north A: place beside it a loadstone, B, at such a distance that the versorium may turn aside toward B to the point C, and not beyond. Then move the needle of the versorium as often as you will (the box and the loadstone not being moved), and it will certainly always return to the point C. In the same manner, if youplaced the stone so that it may be truly directed toward E, the cusp always reverts to E, and not to any other point of the compass. Accordingly, from the position of the land and from the distinctive nature of the highest parts of the earth (certain terrene and more magnetick eminences of the regions prevailing), the variation indeed becomes definite in one and the same place, but diverse and unæqual from a change of place, since the true and polar direction originating in the whole terrestrial globe is diverted somewhat toward certain stronger eminences on the broken surface.
In the open sea, when a vessel is borne by a favourable wind along the same parallel, if the variation be changed by one degree in the course of one hundred miles, the next hundred miles do not therefore lessen it by another degree; for the magnetick [needle] varies erratically as respects position, form, and vigour of the land, and also because of the distance. As, for example, when a course from the Scilly Isles to Newfoundland has proceeded so far that the compass is directed to the true pole, then, as the vessel proceeds, in the first part of the course the variation increases toward the north-west[222], but rather indistinctly and with small difference: thence, after an equal distance, the arc is increased in a greater proportion until the vessel is not far from the continent: for then it varies most of all. But before it touches actual land or enters port, then at a certain distance the arc is again slightly diminished. But if the vessel in its course should decline greatly from that parallel either toward the south or the north, the magnetick [needle] will vary more or less, according to the position of the land and the latitude*of the region. For (cæteris paribus) the greater the latitude the greater the variation.
Islands, although they be more magnetick than the sea, yet do not change the magnetick directions or variations. For since direction is a motion derived from the power of the whole earth, not from the attraction of any hill but from the disposing and turning power of the whole; so variation (which is a perturbation of the direction) is an aberration of the real turning power arising from the great inequalities of the earth, in consequence of which it, of itself, slightly diverts movable magneticks toward those which are the largest and the more powerful. The cause now shown may suffice to explain that which some so wonder at about the Island of Elba (and although this is productive of loadstone, yet the versorium (or mariners' compass) makes no special inclination toward it whenever vessels approach it in the Tyrrhenian sea); and the following causes are also to be considered, viz.: that the virtue of smaller magnetick bodies extends scarcely or not at all of itself beyond their own mines: for variation does not occur because of attraction, as they would have it who have imagined magnetick poles. Besides, magnetick mines are only agnate to the true earth, not innate: hence the whole globe does not regard them, and magneticks are not borne to them, as is demonstrated by the diagram of eminences.
Owing to the loadstone being supposed (amongst the crowd of philosophizers) to seize and drag, as it were, magnetick bodies; and since, in truth, sciolists have remarked no other forces than those so oft besung of attractive ones, they therefore deem every motion toward the north and south to be caused by some alluring and inviting quality. But the Englishman,Robert Norman, first strove to show that it is not caused by attraction: wherefore, as if tending toward hidden principles, he imagined apoint respective[224], toward which the iron touched by a loadstone would ever turn, not apoint attractive; but in this he erred greatly, although he effaced the former error about attraction. He, however, demonstrates his opinion in this way:
Robert Norman's demonstration.
Let there be a round vessel filled with water: in the middle of the surface of the water place a slender iron wire on a perfectly round cork, so that it may just float in æquilibrium on the water; let the wire be previously touched by a magnet, so that it may more readily show the point of variation, the point D as it were: and let it remain on the surface for some time. It is demonstrable that the wire together with the cork is not moved to the side D of the vessel: which it would do if an attraction came to the iron wire by D: and the cork would be moved out of its place. This assertion of the Englishman, Robert Norman, is plausible and appears to do away with attraction because the iron remains on the water not moving about, as well in a direction toward the pole itself (if the direction be true) as in a variation or altered direction; and it is moved about its own centre without any transference to the edge of the vessel. But direction does not arise from attraction, but from the disposing and turning power which exists in the whole earth, not in the pole or in some other attracting part of the stone, or in any mass rising above the periphery of the true circle so that aThe magnetick force exists in the whole.variation should occur because of the attraction of that mass. Moreover, it is the directing power of the loadstone and iron and its natural power of turning around the centre which cause the motion of direction, and of conformation, in which is included also the motion of the dip. And the terrestrial pole does not attract as if the terrene force were implanted only in the pole, for the magnetick force exists in the whole, although it predominates and excels at the pole. Wherefore that the cork should rest quiescent in the middle and that the iron excited by a loadstone should not be moved toward the side of the vessel are agreeable to and in conformitywith the magnetick nature, as is demonstrated by a terrella: for an iron spike placed on the stone at C clings on at C, and is not pulled*further away by the pole A, or by the parts near the pole: hence it persists at D, and takes a direction toward the pole A; nevertheless it clings on at D and dips also at D in virtue of that turning power by which it conforms itself to the terrella: of which we will say more in the partOn Declination.
The 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 lessfrom 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.
If only lands were like this...
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.
In a round[226]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 calledpoints) 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 hisArte de Navegarwith many errors.
Grateful 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, thepoint 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 hisHavenfinding Artdistinguishes the variation according to the meridians: "It may be seene in the Table of variations, that inCoruothe 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 [ἀνατολίζειν], till he come one mile to the Eastward fromPlimouth, where the variation comming to the greatest is 13 degr. 24 min. From hence the Northeasting [Anatolismus] beginneth to decrease, til you come toHelmshude(which place is Westward from the North Cape of Finmark) where againe the needle pointeth due North. Now the longitude fromCoruotoHelmshudeis 60 degr. Which things being well weighed, it appeareth that the greatest variation [Chalyboclysis] 13 degr. 24 minutes atPlimmouth(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 theisland, 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.
Variations 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:[227]at 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 theversorium; 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 bookOn 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.
One 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.
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 knownInstrument to find variationthe 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,Another instrument to find variationthrough 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 [prostaphæresis][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.
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.