Instrument for finding the amplitude at rising on the horizon.
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.
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 deLagos 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.
In 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.
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 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, byCape 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.
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 difficultythat 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.
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 æquator. In a higher latitude up to 45 deg. the variation is greater than near the æquator; 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 æquator 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.
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 "græcizes," 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 sidetoward 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.
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.
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 Brandöe 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 ofMosambique the versorium inclines ¼ rumbe or even more to the south-west. Very wrongly also beyond the æquator in the course to Goa they make the little compass incline by 1½ 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 ½ 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 æquinoctial more than is commonly described on maps and globes.
In the middle of great and continent lands there is no variation. Nor, generally, in the middle of very great seas. On the margin of those lands and seas the variation is often ample, yet not so great as at a little further distance on the sea. As, for example, near Cape St. Augustine the compass varies; but at 50 miles from land toward the East it varies more; and 80 miles off it varies still more; and yet still more at a distance of 100 miles. But from a distance of 100 miles the diminutions of deviation are slower, when they are navigating toward the mainland, than at a distance of 80 miles, and at a distance of 80 miles than at 50: for the deviations change and are diminished rather more swiftly the more they approach and draw near land than when at a great distance off. As, for instance, navigating toward Newfoundland the change of variation is more rapid (that is, it decreases a degree in a smaller arc of the course on the parallel) when they are not far from land than when they are a hundred miles distant: but when travelling on land toward the interiors of regions the changes are slower in the first parts of the journey than when they come more into the interior.
The ratio of the arcs on a parallel circle, when a versorium is moved toward continents which extend to the pole, corresponds with the degrees of variation. Let A be the pole; B the eminences of the dominant lands; at C there is no variation caused by B, for it is too far away; at D the variation is very great because the versorium is allured or turned by the whole earth toward the eminentland B; and moreover it is not hindered, or restrained or brought back to the pole by the verticity of the earth; but, tending of its own nature to the pole, it is nevertheless deflected from it by reason of the site, or position, and convenient distance of the dominant and high lands.
Change in variation with position.
Now from C toward D the variation increases; the versorium, however, does not deviate so rapidly in the first spaces as near D: for more miles are traversed on the parallel circle C D, near C, in order that the versorium may deviate by one degree from the pole A, than near D. So also in order that the variation may be diminished from D toward E more miles are required near D than near E. Thus the deviations become equal in unequal courses, whether the variation be increasing or decreasing; and yet the variation decreases by lesser intervals than it increases. There intervene, however, many other causes which perturb this proportion.
Decoration.
In due course we have now come to that notable experiment, and remarkable motion of magnetick bodies dipping below the horizon by their own rotatory nature; by the knowledge of which is revealed a unity, a concordancy, and a mutual agreement between the terrestrial globe and the loadstone (or the magnetick iron), which is wonderful in itself, and is made manifest by our teaching. This motion we have made known in many striking experiments, and have established its rules; and in the following pages we shall demonstrate the causes of it, in such a way that no sound, logical mind can ever rightly set at nought or disprove our chief magnetick principles. Direction, as also variation, is demonstrated in a horizontal plane, when a balanced magnetick needle comes to rest at some definite point; but declination is seen to be the motion of a needle, starting from that point of the horizon, first balanced on its own axis, then excited by a loadstone, one end or pole of it tending toward the centre of the earth. And we have found that it takes place in proportion to the latitude of each region. But that motion arises in truth, not from any motion from the horizon toward the centre of the earth, but from the turning of the whole magnetick body toward the whole of the earth, as we shall show hereafter. Nor does the iron dip from the horizontal in some oblique sphere, according to the number of degrees of elevation of the pole in the given region, or by an equal arc in the quadrant, as will appear hereafter.
Instrument of the Declination
Instrument of the Declination.
Now how much it dips at every horizon may be ascertained in the first place by a contrivance, which, however, is not so easily made as is that in dials for measuring time, in which the needle turns to the points of the horizon, or in the mariners' compass. From a plank of wood let a smooth and circular instrument be prepared, at least six digits in diameter, and affix this to the side of a square pillar, which stands upright on a wooden base. Divide the periphery of this instrument into 4 quadrants: then each quadrant into 90 degrees. At the centre of the instrument let there be placed a brass peg, at the centre of the end of which let there be a small hollow, well polished. To this wooden instrument let a brass circle or ring be fixed, about two digits in width, with a thin plate or flat rod of the same metal, representing the horizon, fixed across it, through the middle of the circle. In the middle of the horizontal rod let there be another hollow, which shall be exactly opposite the centre of the instrument, where the former hollow was made. Afterward let a needle be fashioned out of steel, as versoria are accustomed to be made. Divide this at right angles by a thin iron axis (like a cross) through the very middle and centre of the wire and the cross-piece. Let this dipping-needle be hung (with the ends of the cross resting in the aforesaid holes) so that it can move freely and evenly on its axis in the most perfect æquilibrium, so accurately that it turns away from no one point or degree marked on the circumference more than from another, but that it can rest quite easily at any. Let it be fixed upright to the front part of the pillar, whilst at the edge of the base is a small versorium to show direction. Afterward touch the iron, suspended by this ingenious method, on both ends with the opposite ends of a loadstone, according to the scientifick method, but rather carefully, lest the needle be twisted in any way; for unless you prepare everything very skilfully and cleverly, you will secure no result. Then let another brass ring be prepared, a little larger, so as to contain the former one; and let a glass or a very thin plate of mica be fitted to one side of it. When this is put over the former ring, the whole space within remains inclosed, and the versorium is not interfered with by dust or winds. Dispose the instrument, thus completed, perpendicularly on its base, and with the small versorium horizontal, in such a way that, while standing perpendicularly, it may be directed toward the exact magnetical point respective. Then the end of the needle which looks toward the north dips below the horizon in northern regions, whilst in southern regions the end of the needle which looks toward the south tends toward the centre of the earth, in a certain proportion (to be explained afterward) to the latitude of the district in question, from the æquator on either side. The needle, however, must be rubbed ona powerful loadstone; otherwise it does not dip to the true point, or else it goes past it, and does not always rest in it. A larger instrument may also be used, whose diameter may be 10 or 12 digits; but in such an instrument more care is needed to balance the versorium truly. Care must be taken that the needle be of steel; also that it be straight; likewise that both ends of the cross-piece be sharp and fixed at right angles to the needle, and that the cross-piece pass through the centre of the needle. As in other magnetical motions there is an exact agreement between the earth and the stone, and a correspondence manifestly apparent to our senses by means of our experiments; so in this declination there is a clear and evident concordance of the terrestrial globe with the loadstone. Of this motion, so important and so long unknown to all men, the following is the sure and true cause. A magnet-stone is moved and turned round until one of its poles being impelled toward the north comes to rest toward a definite point of the horizon.[231]This pole, which settles toward the north (as appears from the preceding rules and demonstrations), is the southern, not the boreal; though all before us deemed it to be the boreal, on account of its turning to that point of the horizon. A wire or versorium touched on this pole of the stone turns to the south, and is made into a boreal pole, because it was touched by the southern terminal of the stone. So if the cusp of a versorium be excited in a similar manner, it will be directed toward the southern pole of the earth, and will adjust itself also to it; but the cross (the other end) will be southern, and will turn to the north of the earth (the earth itself being the cause of its motion); for so direction is produced from the disposition of the stone or of the excited iron, and from the verticity of the earth. But declination takes place when a magnetick is turned round toward the body of the earth, with its southern end toward the north, at some latitude away from the æquator. For this is certain and constant, that exactly under the cœlestial æquator, or rather over the æquator of the terrestrial globe, there is no declination of a loadstone or of iron; but in whatever way the iron has been excited or rubbed, it settles in the declination instrument precisely along the plane of the horizon, if it were properly balanced before. Now this occurs thus because, when the magnetick body is at an equal distance from either pole, it dips toward neither by its own versatory nature, but remains evenly directed to the level of the horizon, as if it were resting on a pin or floating free and unhindered on water. But when the magnetick substance is at some latitude away from the æquator, or when either pole of the earth is raised (I do not say raised above the visible horizon, as the commonly imagined pole of the revolving universe in the sky, but above the horizon or its centre, or its proper diameter, æquidistant from the plane of the visible horizon, which is the true elevation of the terrestrial pole),Explanation of declination.then declination is apparent, and the iron inclines toward the body of the earth in its own meridian. Let A B, for example, be the visible horizon of a place; C D the horizontal through the earth, dividing it into equal parts; E F the axis of the earth; G the position of the place. It is manifest that the boreal pole E is elevated above the point C by as much as G is distant from the æquator. Wherefore, since at E the magnetick needle stands perpendicularly in its proper turning (as we have often shown before), so now at G there is a certain tendency to turn in proportion to the latitude (the magnetick dipping below the plane of the horizon), and the magnetick body intersects the horizon at unequal angles, and exhibits a declination below the horizon. For the same reason, if the declinatory needle be placed at G, its southern end, the one namely which is directed toward the North, dips below the plane of the visible horizon A B. And so there is the greatest difference between a right sphere[232]and a polar or parallel sphere, in which the pole is at the very Zenith. For in a right sphere the needle is parallel to the plane of the horizon; but when the cœlestial pole is vertically overhead, or when the pole of the earth is itself the place of the region, then the needle is perpendicular to the horizon. This is shown by a round stone. Let a small dipping-needle, of two digits length (rubbed with a magnet), be hung in the air like a balance, and let the stone be carefully placed under it; and first let the terrella be at right angles, as in a right sphere, and as in the first figure; for so the magnetick needle will remain in equilibrium. But in an oblique position of the terrella, as in an oblique sphere, and in the second figure, the needle dips obliquely at one end toward the near pole, but does not rest on the pole, nor is its dip ruled by the pole, but by the body and mass of the whole; for thedip in higher latitudes passes beyond the pole. But in the third position of the terrella the needle is perpendicular; because the pole of the stone is placed at the top, and the needle tending straight toward the body reaches to the pole. The cross in the preceding figures always turns toward the boreal pole of the terrella, having been touched by the boreal pole of the terrella; the cusp of the needle, having been touched by the southern pole of the stone, turns to the south. Thus one may see on a terrella the level, oblique, and perpendicular positions of a magnetick needle.*
Examples of declination on terrella.
Declinations of the magnetick needle.
As æquator let A B be taken, C the north pole, D the south, E G dipping-needles in the northern, H F in the southern part of the earth or of a terrella. In the diagram before us all the cusps have been touched by the true Arctick pole of the terrella.
Here we have the level position of the magnetick needle on the æquator of the earth and the stone, at A and B, and its perpendicular position at C, D, the poles; whilst at the places midway between, at a distance of 45 degrees, the crosses of the needle dip toward the south, but the cusps just as much toward the north. Of which thing the reason will become clear from the demonstrations that follow.
*Diagram of the rotation and declination of a terrellaconforming to the globe of the earth, for alatitude of 50 degrees north.
Declinations of the magnetick needle.
A is the boreal pole of the earth or of a rather large terrella, B the southern, C a smaller terrella, E the southern pole of the smaller terrella, dipping in the northern regions[233]. The centre C is placed on the surface of the larger terrella, because the smaller terrella shows some variation on account of the length of the axis; inappreciable, however, on the earth. Just as a magnetick needle dips in a regional latitude of 50 degrees, so also the axis of a stone (of a spherical stone, of course) is depressed below the horizon, and its natural austral pole falls, and its boreal pole is raised on thesouth toward the Zenith. In the same way also a circular disc of iron behaves, which has been carefully touched at opposite parts on its circumference; but the magnetical experiments are less clear on account of the feebler forces in round pieces of iron.
Variety in the declinations of iron spikes at various latitudes of a terrella.
Variety in the declinations of iron spikes.
The declination of a magnetick needle above a terrella is shown by means of several equal iron wires, of the length of a barleycorn, arranged along a meridian. The wires on the æquator are directed by the virtue of the stone toward the poles, and lie down upon its body along the plane of its horizon. The nearer they are brought to the poles, the more they are raised up by their versatory nature. At the poles themselves they point perpendicularly toward the very centre. But iron spikes, if they are of more than a due length, are not raised straight up except on a vigorous stone.
*
Indicatory instrument.
Description of the Instrument, and its use.
Take a terrella of the best strong loadstone, and homogeneous throughout, not weakened by decay or by a flaw in any parts; let it be of a fair size, so that its diameter is six or seven digits; and let it be made exactly spherical. Having found its poles according to the method already shown, mark them with an iron tool; then mark also the æquinoctial circle. Afterwards in a thick squared block of wood, one foot in size, make a hemispherical hollow, which shall hold half of the terrella, and such that exactly one half of the stone shall project above the face of the block. Divide the limb close to this cavity (a circle having been drawn round it for a meridian) into 4 quadrants, and each of these into 90 degrees. Let the terminus of the quadrants on the limb be near the centre of a quadrant described on the block, also divided into 90 degrees. At that centre let a short, slender versorium (its other end being rather sharp and elongated like a pointer) be placed in æquilibrio on a suitable pin. It is manifest that when the poles of the stone are at the starting points of the quadrants, then the versorium lies straight, as if in æquilibrio, over the terrella. But if you move the terrella, so that the pole on the left hand rises, then the versorium rises on the meridian in proportion to the latitude, and turns itself as a magnetick body; and on the quadrant described on the flat surface of the wood, the degree of its turning or of the declination is shown by the versorium. The rim of the cavity represents a meridional circle, to which corresponds some meridian circle of the terrella, since the poles on both sides are within the circumference of the rim itself. These things clearly always happen on the same plan on the earth itself when there is no variation; but when there is variation, either in the direction or in the declination (a disturbance, as it were, in the true turning, on account of causes to be explained later), then there is some difference. Let the quadrant be near the limb, or have its centre on the limb itself, and let the versorium be very short, so as not to touch the terrella, because with a versorium that is longer or more remote, there is some error; for it has a motion truly proportionate to the terrella only on the surface of the terrella. But if the quadrant, being far distant from the terrella, were moved within the orbe of virtue of the terrella toward the pole on some circle concentrick with the terrella, then the versorium would indicate the degrees of declination on the quadrant, in proportion to and symmetrically with that circle, not with the terrella.
Declination being investigated on the earth itself by means of a declination instrument, we may use either a short or a very long versorium, if only the magnetick virtue of the stone that touches it is able to permeate through the whole of its middle and through all its length. For the greatest length of a versorium has no moment or perceptible proportion to the earth's semi-diameter. On a terrella, however, or in a plane near a meridian of a terrella, a short versorium is desirable, of the length, say, of a barleycorn; for longer ones (because they reach further) dip and turn toward the body of the terrella suddenly and irregularly in the first degrees of declination.Too long a versorium!For example, as soon as the long versorium is moved forward from the aequator A to C, it catches on the stone with its cusp (as if with a long extended wing), when the cusp reaches to the parts about B, which produce a greater rotation than at C. And the extremities of longer wires also and rods turn irregularly, just as iron wires and balls of iron and other orbicular loadstones are likewise turned about irregularly by a long non-orbicular loadstone. Just so magneticks or iron bodies on the surface of a terrella ought not to have too long an axis, but a very short one; so that they may make a declination on the terrella truly and naturally proportionate to that on the earth. A long versorium also close to a terrella with difficulty stands steady in a horizontal direction on a right sphere, and, beginning to waver, it dips immediately to one side, especially the end that was touched, or (if both were touched) the one which felt the stone last.
In the universe of nature that marvellous provision of its Maker should be noticed, whereby the principal bodies are restrained within certain habitations and fenced in, as it were (nature controlling them). For this reason the stars, though they move and advance, are not thrown into confusion. Magnetical rotations also arise from a disposing influence, whether in greater and dominating quantity, or in a smaller, and compliant quantity, even though it be very small. For the work is not accomplished by attraction, but by an incitation of each substance, by a motion of agreement toward fixed bounds, beyond which no advance is made. For if the versorium dipped by reason of an attractive force, then a terrella made from a very strong magnetick stone would cause the versorium to turn toward itself more than one made out of an average stone, and a piece of iron touched with a vigorous loadstone would dip more. This, however, never happens. Moreover, an iron snout placed on a meridian in any latitude does not raise a spike more toward the perpendicular than the stone itself, alone and unarmed; although when thus equipped, it plucks up and raises many greater weights[234]. But if a loadstone be sharper toward one pole, toward the other blunter, the sharp end or pole allures a magnetick needle more strongly, the blunt, thick end makes it rotate more strongly; but an orbicular stone*makes it rotate strongly and truly, in accordance with magnetick rules and its globular form. A long stone, on the other hand, extended from pole to pole, moves a versorium toward it irregularly; for in this case the pole of the versorium always looks down on the pole itself. Similarly also, if the loadstone have been made in the shape of a circle, and its poles are on the circumference, whilst the body of it is plane, not globular, if the plane be brought near a versorium, the versorium does not move with the regular magnetick rotation, as on a terrella; but it turns looking always toward the pole of the loadstone, which has its seat on the circumference of the plane. Moreover, if the stone caused the versorium to rotate by attracting it, then in the first degrees of latitude, it would attract the end of a short versorium toward the body itself of the terrella; yet it does not so attract it that they are brought into contact and unite; but the versorium rotates just so far as nature demands, as is clear from this example.Dipping of a versorium.*For the cusp of a versorium placed in a low latitude does not touch the stone or unite with it, but only inclines toward it. Moreover, when a magnetick body rotates in dipping, the pole of the versorium is not stayed or detained by the pole of the earth or terrella; but it rotates regularly, and does not stop at any point or bound, nor point straight to the pole toward which the centre of the versorium is advancing, unless on the pole itself, and once only between the pole and the æquator; but it dips as it advances, according as the change of position of its centre gives a reason for its inclination in accordance with rules magnetical. The declination of a magnetick needle in water also, as demonstrated in the following pages, is a fixed quantity[235]; the magnetick needle does not descend to the bottom of the vessel, but remains steady in the middle, rotated on its centre according to its due amount of declination. This would not happen, if the earth or its poles by their attraction drew down the end of the magnetick needle, so that it dipped in this way.
Concerning the making of an instrument for finding declination, the causes and manner of declination, and the different degrees of rotation in different places, the inclination of the stone, and concerning an instrument indicating by the influence of a stone the degree of declination from any horizon we have already spoken. Then we spoke about needles on the meridian of a stone, and their rotation shown for various latitudes by their rise toward the perpendicular. We must now, however, treat more fully of the causes of the degree of that inclination. Whilst a loadstone and a magnetick iron wire are moved along a meridian from the aequator toward the pole, they rotate toward a round loadstone, as also toward the earth with a circular movement. On a right horizon (just as also on the æquinoctial ofthe stone) the axis of the iron, which is its centre line, is a line parallel to the axis of the earth. When that axis reaches the pole, which is the centre of the axis, it stands in the same straight line with the axis of the earth. The same end of the iron which at the æquator looks south turns to the north. For it is not a motion of centre to centre, but a natural turning of a magnetick body to a magnetick body, and of the axis of the body to the axis; it is not in consequence of the attraction of the pole itself that the iron points to the earth's polar point. Under the æquator the magnetick needle remains in æquilibrio horizontally; but toward the pole on either side, in every latitude from the beginning of the first degree right up to the ninetieth, it dips. The magnetick needle does not, however, in proportion to any number of degrees or any arc of latitude fall below the horizon just that number of degrees or a similar arc, but a very different one: because this motion is not really a motion of declination, but is inA magnetick body rotates mor quickly than the centre advances.reality a motion of rotation, and it observes an arc of rotation according to the arc of latitude. Therefore a magnetick body A, while it is advancing over the earth itself, or a little earth or terrella, from the æquinoctial G toward the pole B, rotates on its own centre, and halfway on the progress of its centre[237]from the æquator to the pole B it is pointing toward the æquator at F, midway between the two poles. Much more quickly, therefore, must the versorium rotate than its centre advances, in order that by rotating it may face straight toward the point F. Wherefore the motion of this rotation is rapid in the first degrees from the æquator, namely, from A to L; but more tardy in the later degrees from L to B, when facing from the æquator at F to C. But if the declination were equal to the latitude (i.e., always just as many degrees from the horizon, as the centre of the versorium has receded from the æquator), then the magnetick needle would be following some potency and peculiar virtue of the centre, as if itwere a point operating by itself. But it pays regard to the whole, both its mass, and its outer limits; the forces of both uniting, as well of the magnetick versorium as of the earth.*