IN the Ancient and Learned Ages, when it was the greatest Strife a­mongst Men, that Eternity shou'd accompany the Glory of Arts and Sciences, they were carried in a short time to the heighth of Learning; for [Page 2] the Romans emulated the Greeks, the Greeks the Aegyptians and both of them the Chaldaeans; but they all both imitated those who went before them, and were Examples to such as did follow: Only Epicurus gloried that he had no Master; and that he made the way for himself unto Truth; but that is the happiness of few People, and rarely falls out in our Times: We think it is excellent well for us, if we commendably follow; nor do we wonder that the things which are hidden deeply, shou'd be slowly discover'd; for such is the nature of our present Age, that Men avoid Difficulties, and treat lighter Matters with a slight hand, and are ignorant of very many things which they think they know, not so much thro' weakness of Judgment as Laziness. 'Tis apparent, almost to all Men, not only to Philosophers, but Unlearned, that the Sun, the Moon, and other Stars of this visible World, keep the Course which the Wisdom of the Supreme Dei­ty ordered from the beginning; and no body is so silly as not to understand, that at set times they return to illumi­nate the several Parts of the World; for [Page 3] it is well known, that the Earth some­times is torpid with the sharpest Cold, and bound together with the hard Frost; and sometimes in one and the same place of the World is inflam'd with the burning Heat of the Weather, and thereupon undergoes its various Vi­cissitudes; and Experience joyned to Reason doth sufficiently, and too much confirm, that no other Cause can be as­sign'd of that Matter, than the departure of the Sun, its return, and various Scitua­tion; but that some Countries shou'd burn with the continual Heat of Heaven, and others grow hard with a perpetual Cold, and yet equally afford Advanta­ges to their Inhabitants, is that which many Philosophers have call'd into Que­stion; and is not at this Day believ'd, but by those who have found it by Ex­perience. It would be a pleasant sight to behold the Earth in an Abridgement, to view the Scituation of it, its Form, and Bounds; some Parts very well Peo­pled, whilst again some others are fre­quently void of Inhabitants, thro' the violence and extremity of Cold or Heat, for there are many altogether as great [Page 4] Strangers in their own, as Foreign Coun­tries; and if they know any thing by the Relation of others, yet they them­selves are almost Ignorant of the Matter; and hence it is, that very often they judge wrong of the Condition, both of their Native and other Countries: where­fore, seeing it is now long since, that it seemed ill for Men to be Ignorant both of their own and Outlandish Climates, by degrees a certain Desire seized upon No­ble Souls, by Voyages and Learned Stu­dies, to render this Knowledge familiar to them. Without this culture of the Mind no Person cou'd have easily and soon perswaded us, who live in the re­motest Northern Countries, that there are some People who have perpetually their Days and Nights equal; or these last, that we shou'd under­go so different Changes, to wit, that we shou'd be sometimes destin'd to a per­petual Night; and again, under our sometimes unsetting Sun, have no room left us for Darkness; but that they shou'd rather cry out,

The Industry of that Italian is to be commended, who not long since view'd our Northern Parts, with curious re­searches. I am willing here to make use of his Words, out of his Manuscript, that by his Example, we may confirm our own, and invite others to do the like Matters. In questa (saith he) Zona glaciale boreale, bisogna ammirar la Pro­videnza di Dio, nel vider il Sole, che per sei settimane resto sobre dell' Orizonte, formando a questa regione non arco ma Co­rona, e cosi la Luna e le Stelle; ma queste non apparono per hora, cedendo al primo luminare, e campeggiono poi altretanto tempo circa il Solstitio hiemale, cosi loro [Page 6] permettendo quello con la sua contenanza: Pare in un certo modo che sia degno di non minor osservatione e maraviglia in quest' effetto il sole, di quello che sarebbe se si vedesse arrestar il suo corso, come nel tempo di Josue, overo retrocedere, come in quello d' Ezechia, insegnando S. Agostino nel decimo della città di Dio, che: Quamvis miracula visibilium na­turarum videndi assiduitate viluerint: tamen cum ea semper intuemur, inusi­tatissimis rarissimisque majora sunt. Che se all hora fece il giorno alcune hore più longè dell' ordinario, che lo so per setti­mane e mosi, si come ho detto, onde pare che di questo specialmente si verifichi il detto del Salmo: Ordinatione tua perse­verat dies. So far he.

But our Weakness, not to say Lazi­ness, causes this difficulty of Believing in many; who are very seldom perswa­ded that the things are true, which our Countrymen, and the Inhabitants of this Kingdom, tho' of very good Repute, relate concerning the various Vicissitudes of the Year in distant places. Nothing certainly being a greater Impediment to a right understanding, than the prejudicate [Page 7] Opinions of our Infancy, which having suckt in with our Mother's Milk, and an ill Education, we can hardly at last lay aside in our Old Age; for who does not, that I may use this Example, per­swade himself that he lives in the upper part of the Earth, and the highest place of it; that others dwell on the sides, or if he can apprehend it, on the bottom of it? And yet 'tis certain, that some do Inhabit Countries farther distant from the Pole, and others live in places nearer to it. The Experience of those who Travel by Land or Sea, convinces us of this, which to deny or oppose, is the sign of a Mind either Distracted, or al­together Perverse. Hence it is, that of late more Credit is given to some illiterate Sailors, who having sail'd round the World, have asserted that it is round, than to those Ancient Divines and Phi­losophers, who contended that the Form of the Earth was not so, only that they might gain a greater Strength to their Authority and Doctrine. Certainly we admire, that Men eminent for Learning, at the very mentioning of whose great Names we pay respect, shou'd ever fall [Page 8] into so absurd Opinions. Tertullian and Austin thought that they were over-wise, who taught that there were any Anti­podes. Others Ridiculously.

And Posterity perhaps will be surprized, that we, at this time of Day, are igno­rant of many, and those not so difficult Matters neither.

And further, I do believe it is agreed amongst all Virtuoso's, and such as are given up to Ingenuous Studies, that from the first Moment the Creator of the World gave to the Sun, as to the Ruler and Governour of the Day, a motion so equal and constant to it self that every where by equal Circumvolutions, it makes also alike Courses; and produces sometimes equal, and sometimes inequal Shadows, and as much as in it lies in places alike, produces effects alike also; from whence it comes to pass, by the great Providence of God, that the Sun warping towards either Pole at set times, regulates the Days and Nights, and gives Light or Darkness to Countries, to be [Page 9] estimated by the Spaces of Hours, of Days, or of Months; and it ought to seem a Paradox to none, that the Peo­ple who dwell under the Equator, and have their Days and Nights perpetually equal, shou'd not have longer Days than those, who if they live under the very Poles, will reckon one Night to be of six Months, and the opposite Day to be equal to it; and that those who are scituated between the Aequator and the Poles, however they divide their time, reckon also so many Days and Nights to be measured in the same Spaces.

No Mathematician is ignorant, that those who live about the 65th. degree of Altitude, have their whole Day in the Summers Solstice of 24 Hours; or which is the same, at that time the Sun doth not set as well from Natural as Op­tick Causes, before the 66th. degree be compleated: But very few Mathema­ticians have drawn this Knowledge from the Experience of their own Eyes; from whence it comes to pass, that tho' the Inhabitants of the Country should assert this to be true, yet in this Point they wou'd not gain Credit from such as urge [Page 10] only Natural Causes; and besides, the Variety and Disagreement of the Rela­ters increases the obstinate doubts of the Incredulous, since, after the Vulgar way, some mix incredible Things with Truths. This Assertion mov'd the most Serene Prince Charles the 11th. the most Potent King of Sweden, Goths, and Vandals, and our most Gracious Sovereign, when the last Year he viewed these Regions; who, as he is endowed by the Supreme Deity with a truly Divine and Admirable Wit, and adorned with all the Gifts that are most proper for his Royal Post; so he delights to make the exactest Scrutiny into all things, and to discuss every one of them in particular, and to give as much credit to every Person as he de­serves; so being now desirous to try with his own Eyes, what Truth there was in the common Report of the Peo­ple, and whether they did really see in those Places a Sun which sets not: He was then in the City Torneo in Westro Botnia, scituated about 65° and 43′ of Latitude; whose Horizon, altho' it was in part hinder'd by Mountains and Woods, so that the Truth of this Matter [Page 11] cou'd scarcely be discovered upon the plain ground; and besides, it being some Days after the Summer Solstice, we might doubt the opportunity of seeing it was slipped; however the undaunted Heart of the most Invincible Monarch, never fatigu'd by any Labours, conquer'd all these Difficulties: A little Tower being show'd to us of about One hun­dred Foot high, on which the Bells of the Church of the City are hung; he gets up into it by Ladders, and those very steep, accompanied with some Eminent Persons, as Curious Wit­nesses of this Observation; amongst whom by Name, were Count Gustavus Douglas, Governor of the Northern Pro­vinces, Charles Piper, Secretary of State, and the Secretary of War, John Hoghu­sen: In the Year M DC XCIV. on the 14th. of June we view'd the same until Eleven a - Clock and 53 M. at Night; at which time a little Cloud covering the Sun by little and little, it disappear'd; but about the 12th. Hour, and 6th. Minute after Mid­night, or of our following Day, which was June the 15th the Sun passing again [Page 12] out of the small Cloud, shined out very brightly; from whence it is certain that it did not set in the mean time, but that Cloud was the only Cause why it was not discerned all Night long; the Ex­perience of the Inhabitants confirm it, who always at that time of the Year, when the Weather is clear, use to see the Sun all the Night long: The most Se­rene King himself did not disdain to put down with his own Hand into his Table-Book this Observation; which when the rest of the Company had neglected, they were surprized the next Day at the admirable Exactness of the King, in an Affair so foreign to Royal Concern­ments, and his most exact and Mathe­matical Diligence; and being asham'd for the Neglect of it, and that they were outdone by their King in so small a Share of Trouble, they humbly and submissively beseech'd the King, that they might have a Copy of his Observa­tion; His most Gracious Majesty readi­ly granted their Requests, and gave leave to all those who desired to take a Copy of it. This way the Royal Ob­servation came to the joyful Hands of [Page 13] his Subjects; and by the Care of the most Illustrious Governor of that Coun­try, Count Gustavus Douglas, may be read in Golden Letters upon a Table fast'ned to the Wall, near to the Altar of the Church in that City; and lest any thing should be wanting in our Te­stimonial, for the Credit of the Transcri­bers, behold a Confirmation.

Certainly a Monument fit for Poste­rity to admire, and to propose to them­selves the Sedulity, Care, Vigilance, and incredible enduring of Toils of so great a Prince; for who being intent, and ex­posed to mighty, not to say Royal Fa­tigues, can endure to descend to so mi­nute, so unusual Matters? And ye Sons of the Mathematicks whose Talent it was to fetch such things out of their [Page 14] secret Places, and to demonstrate them; You, I say, ought to blush, and pub­lickly acknowledge that your Science hath received this Improvement, not from your selves, but from the most Potent King.

Our most Gracious King having viewed these Countries, as he designed; and having travelled some Tracts of Land, inhabited by such People as ei­ther speak, or understand the Sweedish Language; and at length being come amongst other Nations, using only the Finland, or Lapland Tongue, used by few in the World, returned with great speed according to his usual Custom. After his Return, amongst other things, he relates to his Subjects, who enjoy a milder Air, and more fertile Soil, the incredible Varieties of Days and Nights, which he had seen in the most Northern Parts of his Kingdom; not only where the day at that time is continual by the Presence of the Sun, but also where they live in Summer-time without any Night, by the perpetual Twilights; and affir­med that he had spent a continued Day [Page 15] without any Night, a thing before heard, but not at all believed by him; and when that Business, known to very few, render'd all of them doubtful who were so attentive to his Majesty's Discourse, several Questions were started, which exercised the Belief of some, and the Judgment of others: Thereupon our Mathematicians are consulted, whether really under that Elevation of the Pole, such Phaenomena's were to be expected; and which were the true Causes, why in those Places the Body of the Sun did not set: But they most humbly an­swer'd, they believed it might be so through divers Natural Reasons to be determined by the Scituation of Places, Temper of Air, and other Changes; but as yet not at all understood by them, having never lived under that Elevation of the Pole, but only giving Credit to their Land-Maps; which being often made and corrected, cannot always me­rit our undoubted Belief in all things; but that every Astronomical Observation should be so made, as to answer the Ce­lestial Observations, and besides illu­strate them; and they all to be confir­med [Page 16] by Geometrical Demonstrations, that they may shew their Readers such Reasons, as do not perswade, but force them. By this means the Science of Astronomy had its Rise, Progress, and no ordinary Increase, first from the Asia­ticks, then from the Europaeans for many Ages, by the indefatigable Labour of the Observer. In the Northern World, the Inhabitants being studious of War, and Arms, that Science did not lye al­together neglected, as appears from the Grave-stones, and Runick Calendars, with other very Ancient Monuments; however it was not cultivated with a Care that might equal that of the Chal­daeans, or the Ancient Mathematicians in Greece: Nevertheless, by the Grace of God, these Ages owe their Happiness ever since the most Blessed Times of the Reformed Religion, to Kings of Pious and most Glorious Memory; and espe­cially to His most Serene Royal Maje­sty, which by a Paternal Affection, and truly Majestick Love for Learning, and Men of Letters, by his incredible and inexhausted Magnificence to them, hath brought not only the Mathematicks; [Page 17] but all sorts of Sciences to that pitch, as neither we cou'd hope, or Foreigners believe, they cou'd ever attain to; and yet a great deal of Work is still remaining, and there will never want an occasion to any who shall be born a thousand Ages hence to add something. For many things, according to the Con­jecture of the wise Roman, are reserved for future Ages, when the very Memo­ry of us shall be worn out: These things and others of the like Nature, discoursed they, not without Pleasure, before His most Serene Majesty; who, after con­sidering them more deeply, carefully weighs with himself the Force and Ef­fects of Nature; and tho' he did not distrust his own Eyes in the Observa­tions once made, yet that he might gain the Consent and Confession of all, and lay open the true Series of Causes, re­solveth to send thither some Mathema­ticians about the same time of the fol­lowing Year, that so they might note every thing distinctly, and duly observe the differences of Motions, with the true Risings, and Settings of the Sun, and what they were with Refraction [Page 18] or without it. In the mean time, his loyal Subjects made a Medal to the most grateful Memory of that so fortunate Royal Expedition, with the Picture of the King, and an agreeable Emblem.

NOW therefore in the present Year, 1695. in the Month of April, this Charge is committed to me by His most Serene Royal Majesty, that I should undertake the Journey, toge­ther with the most Illustrious Person, Mr. Andrew Spole, the most ingenious Mathematick Professor in the University of Upsal, and now almost superannuated, my Companion and Associate in the Jour­ney, and formerly for eleven Years my most pleasant Collegue in this sort of Studies; and that we shou'd omit no­thing that might conduce for the ma­king of these Experiments, or any other of this Nature; and above all we were injoined so to hasten our Journey, that we might be in the City Torneo, where [Page 20] the King's Observation was made, not only some days before the Summer-Sol­stice, but also that we shou'd go farther to the Northward, where we might see the Sun higher above the Horizon in the North Meridian, by reason of the greater Latitude of the Place: Thus we departed from Upsal with Hearts and Souls resolutely fixed, on the 21st. Day of May, Old Stile, which is used in our Country, at a Season unusual, and not yet fixed, by reason of the Unsea­sonableness and Rigour of the Weather; and therefore with great Difficulty we passed through Upland, Gestricland, Hol­singland, Medelpadia, Angirmarnland, and West Bothnia, being for the most part in these last Countries detained by Ice and Snow; especially in passing over Ri­vers, and Arms of the Sea, which are there in great Plenty, and sometimes so wide, as to be 1000 Paces over; in which not only the Rapidity of the Ri­vers, and Fierceness of the Winds, but also the Ferry-Boats are to be minded, least they be severed asunder; for two Boats placed at a certain distance from one another, make a Ponton, into which [Page 21] a Charriot is to be so put with Horses, that the sore-wheels rest upon one Boat, and the hind-wheels on the other; the Oars being fitted on both sides: And in the high way the ground being some­times slippery, and the Horses and Charriots sticking in dirty Places, crea­ted us great Trouble, where the Cold being partly dissipated, yet the Earth did not return to its former Solidity and Firmness; for at this Season the Creeks nearest the Shore being hardn'd with Frost and Ice, and many Pines being cut down, and disposed into order, did even then represent a Winter-Journey, the Frost being melted, and thawing near the Bank-side only, so that no body cou'd go any further of the Journey with Safety; and therefore almost all by Land, the way being as yet not well beaten; wherein being tossed by divers Fortunes, at length we happily arrived at Torneo on the 6th. of June, having made a most hazardous Voyage in six­teen Days, in Charriots, Boats, or on Hor­ses, and a-foot by turns.

[Page 22] The City Torneo is situated by the Ri­ver Torneo, rising in Lapland, a very pleasant Place, which the River makes, by parting it self into two Arms, and joining again where it discharges it self into the Sea, from which Island the Citizens assert the City to have received its Name at the time of its Building: But it was founded in this Island in the Year of our Lord M DC XX. when before it was the Seat of Inhabitants, who dwelt some Furlongs from it to the South, where there is still an old Stone-Church; for they have a wooden one in that City, and that curiously built, as generally is usual in other Cities of that Country, not long rebuilded. This City trades chiefly with the Finns and Laplanders, whose Language the Ci­tizens understand well: In the Winter they likewise give them a Visit with their Ram Deer; and for the Merchan­dize which they carry with them, re­ceive others from the Laplanders of equal Value: They have also no incon­siderable Commerce with the Mosco­vites, who yearly sell their Goods to them, and part with them at a very [Page 23] reasonable Price; since those which are brought out of the City Archangel, lie them in less, when the Concourse of the Hollanders is the greatest. The same Evening that we came to Torneo, we ob­serv'd the Sun above the Horizon, no­ting the Time by the going of a most exact Clock, which shew'd Minutes and Seconds, which I had for that use, by the Favour of the most excellent Count, and Royal Senator, Nicolas Gyldenstolp, by this at 11 h. 15′, 45″, the Sun was hidden in a little Cloud, passing over it, and appeared that Night no more to us.

On the 7th of June we sound the Al­titude of the Sun, by two Brass Astro­labes, exactly divided into Deg. and Min. One of which we wou'd have to be loose, and the other fixed with the Perpendi­cular, by which the Errors which arise by the Disposition, might be the more easily detected; and by this Means we took Care that the very least difference of them shou'd not escape us; nor was any Calculation made by us, except the Instruments agreed most exactly. The same day in our first Observation, we [Page 24] found the greatest Altitude of the Sun to be 47°. 48′. On the 8th Day we found the Meridian Altitude to be 47°. 49′. The 9th Day was Cloudy. On the 10th it was 47°. 50′. from which re­peated Observations, and another more made in the same place at our return, on the 18th of June, when the Suns Meri­dian heighth had decreased to 47°. 45′. we gathered by an Astronomical Calcu­lation, the true Motion of the Sun be­ing consider'd, and the just Parallax added, that the Elevation of the Pole in that City is not so much, as is laid down in some Geographical Tables, especially those of Foreigners, being but 65°. 43′. but no account ought to be had of the Refraction in these Observations, the Body of the Sun being elevated beyond that degree where they cease; we desi­red truly to confirm these Diurnal Ob­servations by the fixed Stars; because to those who observe by the Circumpolar Stars, the Altitude of the Pole uses to come out less; and the Winter and Sum­mer Declinations of the Sun being other­wise equal, the Hypothesis of the fixed Obliquity of the Ecliptick being granted; [Page 25] but amongst the more Northerly, at se­veral Times are render'd inequal by rea­son of their Refractions; but at that time the Light of the Sun, and its con­tinual Presence saved us that trouble.

The Latitude of Torneo being found, we were solicitous to find out the true Longitude of it; but seeing that cou'd not be Astronomically obtain'd, by any direct Journey, by reason of the Situa­tion of Places, we were forced to be sa­tisfied with the Reports of the Land-Surveyers, who have so exactly describ'd the Measures of the Ways, and the Si­tuation of all the Countries and Coun­ties, by the Command of His most Se­rene Royal Majesty, and because a­mongst the several Ways of finding out the Longitude of Places, especially at Sea, for which the States of the United Provinces promised so great a Reward to the finder of it, all Eyes being intent upon this Victory, which is not as yet obtain'd: I say, amongst so many ways, no Invention hath yet appeared more excellent than that which is performed by the help of a Pendulum; of which that Noble Hollander, Christianus Con-stantine [Page 26] Huygens, was the Inventer and Author; a Person, as well for his other Famous Works, as for the sake of this, most worthy of Immortality. And here it came into our Heads to admire the great Constancy of these Portable Clocks, made after that Example, two of which I brought with me from home, accurately distinguished with an Hori­zontal Pendulum, and divided into Mi­nutes; but the Third, having also Se­conds, was added to them at Stockholm. Before our departure I so dispos'd these Two for three Weeks together, to the Motion and Measure of a most correct, exact Pendulum of three Foot, which was such a Rule for me, that I cou'd scarce doubt of their Exactness; since in the whole Journey they went so equally, that they did not differ from one ano­ther so much as one Minute at the same time. But it moved me more than I can express, in the first Observation at Torneo, when the Suns greatest Altitude, and from thence the true place of the South was known to us, all these Three Clocks wanted only 18 Minutes of this Point; to wit, the Automaton shewed [Page 27] the Hour of the Day of the Meridian from whence I came, and to which I was joined when I departed at Twelve a Clock, and yet cou'd not rightly show us the Meridian of Torneo; or to agree with it, because that City is judged to be some Degrees more Easterly than Stockholm. For of the Mapps which I now have, one of them, which Aegidius Valkenier put forth in a lesser Form, makes the Longitude of Stockholm 35 Degrees, and 30 Minutes, but of Torneo 40°. 0′. this difference of the Meridians, 4°. 30′. gives the Intervals of Time 18′ Astronomically computed: The other of Fred. de Witt makes the Longitude of Stockholm, 36°. 20′. but of Torneo 41°. 10′. This difference of the Meri­dians 4°. 50′. makes the measure of Time betwixt them 19′. 20″. A third of Scandinavia, by the same De Witt makes the Longitude of Stockholm 39°. 00. but that of Torneo precisely 44°. 00. which is the greatest, and produces the difference of the Meridians of five Degrees; whence also in Time the difference of Meridians is given 20 Minutes. But which of these two Tables is the latter [Page 28] and truer is not certain; for in Maps and Clocks the Age of them is not ex­pressed, on purpose that so they may al­ways seem to be New; but howsoever it was, these three Maps did not differ so very much from one another, nor from the Scope which I proposed to demon­strate; for if the first Map please, that agrees exactly with my Clocks, which were so much too slow; and it is plain, that the second differs only in one Mi­nute, and twenty Seconds; the third differs two Minutes; which equality of Motion and Agreement is certain­ly to be mightily admir'd in so little and portable Machines; nor did I think that it cou'd by any Accident happen, that for so long a time they shou'd mutually answer one another in the same Laws of Motion; and it is pleasant to be em­ploy'd in so delightful a Speculation; now therefore, if any shall desire a fur­ther Scrutiny into it; let him also know that in winding; up the Clock I daily lost five Seconds; for that hath been long observ'd by me; as likewise, that 72 Beats of the Pulse of the Artery, be­ing Fasting, answer also to one Minute, [Page 29] when the Body is in Health, and neither bound up with too much Cold, nor in­flamed with vehement Heat; which Ex­perience, and that is wonderful, never failed me for fifteen Years together. Therefore, since these five Seconds 12 times reckon'd, make one Minute, the Clock also in twelve Days was too slow by one Minute. Now, because we got to Torneo in sixteen Days, add for those four Days twenty Seconds, that so the number of the lost may be 1′ 20″ which added to 18′ wanting at Torneo, makes the Sun 19′ 20″ which agrees excellently well with the second Maps, as is above showed; they requiring in that time the difference of so many Minutes. But many will be of Opinion, that the ine­quality of Natural Days doth much op­pose this Calculation; for the Apogae­ums and Perigaeums teach us, that the daily Motion in which the Sun returns from one Meridian again into it, is sometimes slower, and sometimes swifter; and that the Anomalies of the Plane of the Ecliptick, lying inclin'd to the E­quator, may beget some difference of Ascensions; but as these are very little [Page 30] every Day, and that we use only the Mean, we neglect such a small Time as a thing of lesser Consequence; but when it is necessary we also correct them by Tables of mean Motions made for this Purpose. The Companions of our Journey know that these things are nei­ther precariously asserted, nor rashly re­lated by me; and they can honestly certifie, that I have often mentioned this Certainty, not without Admiration; and I will show in the following Pro­blem, why I have been so long on this Subject, for the sake of those who do not understand it; why the difference of Time in two distant Places ought to be equal to the difference of Longitudes betwixt them.

Let P. be the Pole of the World in this Diagram, A. C. the Aequinoctial Circle, G. E. some Paralle, B. S. the Meridian of Stockholm, D. T. the Me­ridian at Torneo; therefore because the Sun, by its Diurnal Motion daily runs through the Aequinoctial Circle, A. C. and in it every Hour spends 15 Degrees, and by consequence 360 in its entire [Page]

[Page]

[Page 33] Circumvolution, in the space of 24 Hours. Let these two Places in the Question Stockholm, S. and Torneo, T. be either of them under their Meridians; now let there be taken out of that mid­dle Map aforementioned, the distance of these Places, 4°. 50′. when the Sun was in the Meridian, D. T. it was 12 of the Clock at Torneo, 19′ and 20″, after that the Sun comes to the Meridian at Stockholm, B. S. at which time it was Twelve a Clock there; but at the same time at Torneo it was Twelve a Clock, 19′ 20″, since Torneo is more Easterly by so many Minutes than Stockholm; and therefore it is manifest that the Arch B. D. and also every one of the Parallels with it to be 4°. 50′. and so much to be the difference of Longitude between Stockholm and Torneo, therefore the Horary difference is equal to the dif­ference of Longitude, Q. E. D.

[Page 34] This is the true cause why those who go Westerly have longer Days than those who go to the Eastward; for whosoever by going from the East to the West, after some Days passes into a different Meridian, hath a longer Day than if he had stayed in the same Meridian; but it matters not whether the Latitude be the same or different, because in every Lati­tude it is Noon when the Sun is in the Meridian; wherefore those who go from Torneo to Stockholm have the Day of 24 Hours, and almost 20 Minutes; as on the contrary those who go from Stock­holm to Torneo lose so many Minutes in a whole Day.

It is manifest from their Journals, that these Variations was the greatest ad­miration to the Spaniards and Portu­gueze; for these Sailing to the Philip­pine Islands with an Easterly Course, almost a Semicircle, gain'd Twelve Hours of the Europeans; but those with a Westerly Course had so many Hours of Day later. Wherefore if two Ships Sailing out of the same Port, go to the same Places, by contrary Courses, the one to the Eastward, and the other [Page 35] to the Westward, having Sailed a Semi­circle of the Earth, at their meeting, their Accounts do differ a whole Day from one another; but having Sailed a­bout the whole Earth, at their return Home will find two Days difference in their Journals. It is clear from Pliny, that the Ancients did not want this Knowledge, who proves it by many Ex­periments. But especially that those who Sail to the Westward, although on the Shortest Day, can Sail faster than those who Sail in the Night, as having the Sun it self for their Companion.

I thought it necessary to Treat more largely of these very well known Mat­ters; not that I can, by my own Clocks, prove any certain Longitudes to be found out, but that in Land Journeys, they may be this way most easily ob­served. But how much we exceed the Skill of the Ancients in this Machine, no body is so Ignorant in Letters as not to understand; for the Ancients had no other way of distinguishing Times, but by Shadows, and Water-Glasses; the more ancient way was used amongst the Chal­deans and Aegyptians, and at last brought [Page 36] down to the Greeks; but at Rome they Learned it latelier, as we may see by the same Plinius Secundus: For Scipio Nasica first of all divided the Hours, as well of Nights as of Days, and set up an Hour-Glass in his House in the Year, U. C. 595. which falls out 155 Years before the Birth of our Saviour. So long, says he, the Romans had divisions of Time; but at length in Octavius Au­gustus's Time, the manner of making Dials was taken from Vitruvius, which afterwards made so great Improvements, that now all Europe, which before had gotten the Victory from the other Parts of the World (whose Inhabitants much admire the Industry of the Europeans) daily strive amongst themselves by new Inventions of this Machine.

How great the Variation of the Nee­dle is in these Northerly Countries is not to be rashly determin'd; for we by a Meridian Line found in the Town of Torneo, find its Declination from the N. to the W. to be about seven Degrees; for the great incertainty of the Weather hinder'd us to determine it precisely, which seldom permitted us to see the [Page 37] Light of the Sun, either before or after Noon; and that scarcely except a­mongst the Clouds; so that a shadow cou'd scarcely be distinguish'd from a Penumbra; tho' it is to be confessed, that the time of the Solstices is least fit for this purpose: For if that matter of moment is to be sought either from the greatest heighth of the Sun, in which the Meridian Line may be had exactly; or from an upright Gnomon perpendicu­larly erected, that Observation may nevertheless be liable to Error, unless it be frequently repeated in the same place, because the Shadows of the Sun nearest about Noon are sensibly neither increased or decreased: The Sun however in the mean time making its Progress in its own Parallel.

BUT let us return to our Sun seen by Night; in consideration of which, the chiefest part of our Labour was undertaken; in vain for some Nights did we watch in the Observation of it; the Sky being always fill'd with Rain and Clouds; but at length in the Night between the 10th and 11th of June, an happy Season broke forth, which beyond our Expectation dispersed the former Clouds; and that was the first opportunity we had to enjoy a clear Night; we therefore saw three Parts (almost four) of the Suns Body above the Horizon, one fourth only being un­der it; So that the Center of the Sun did really appear above the Horizon: We therefore Congratulated our selves [Page 39] in the Affair, for a long time believed, but before not usual to our Eyes. Being excited by that occasion, I joyfully com­posed the Day after the following Epi­gram, before we proceeded any further upon the Memory and Confirmation of the Royal Observation; and such as it was, sent it to Stockholm, to the most Illustrious and excellent Count Nicholas Guldenstolp, that so before our return, it might appear what might be expected in that business.

[Page 40] In our Observation we used the same Turret, in which His most Serene Roy­al Majesty observed the Sun; but lest any one might think that small heighth to be the reason why so much of the Sun was discerned, we chose a Place some Paces from thence, not far from a Gallows, where there was a free Pro­spect from the Northern Quarter; and there we found the Appearance to be no other, than out of the Turret, being satisfied with this clear and distinct Ob­servation when the Sun was so very few hours from the Solstice, which on the following Day, June the 11th. by an Astronomical Calculation falls out 9 h. 39 before Noon. And now we thought it our business to prosecute our Journey farther to the Northward; and to look out for a Place, where abating the Re­fraction, the whole Body of the Sun might be discerned, since it was clear that all that which appeared here of the Body of the Sun did appear by Re­fraction only; since beyond our Opini­on and Calculation, according to the late found out Elevation of the Pole, [Page 41] more of the Sun it self was seen than ought to have been.

So we likewise being to pass to the cold Northern Parts, did not trust to swift Wings, but to Boats very slender­ly fast'ned together; for from hence as we go farther to the Northward, there is no more Use of Chariots, or Horses; wherefore quitting our Journey by Land, we desired the help of Pilots, whose Lan­guage we understood no more than those who are most ignorant of it; and ent'ring into their Boats, were to strive against the Stream of the River, which wou'd suffer us neither to row nor sail, but amongst Stones and Rocks which lay in our way, which requires only a diligent help of Boats, Poles, and strong Arms to make use of them: Thus our Seamen passed along the Banks of this rocky River; and in some Places with their most vigorous Endeavours, they [Page 42] seemed scarcely to get a Foot forward; and for several Hours to advance but so many Paces; and sometimes by long bendings and turnings of the River they were forced to go ashore, and hale their Boats out of the violence of the River, where nothing else cou'd be o­therwise expected by Humane Assistance; but it seemed very hard, and strangely unusual to us, that on the Bank-side there was no room between the Thorns and Brambles, and heaps of Stones where we cou'd set our Feet; since being wearied with the Fatigue of this Haling, we at­tempted rather to make our Journey a-Foot, and by that means make the Boat somewhat quicker and lighter. And as an addition to these our Troubles, Moun­tains of Ice of twenty Cubits and more being driven together by the force of the Waters, cover'd both sides of the River, and they also so sloping and craggy, that every moment we dreaded their fall, to­gether with our own Ruine: Neither was there any help for us, clinging con­stantly with the Poles of our Boats to the Shore, had not God by his special Favour vouchsafed to avert the Mischief; [Page 43] but if it did any where happen, that the course of these Mountains was inter­rupted we joyfully leaped Ashore, admi­ring the Nature of the Country, which not without great Pleasure to the Spe­ctators, amongst Snows and heaps of Ice produced green Herbs and Flowers, a­mong which was a great plenty of the Lilies of the Vallies.

Amidst these Wonders of Nature we looked for Men; and at length, as in­deed we met with very few Houses of the Finns, we were carried to a certain Countrymans Cottage, which in their Language was called Pello. 'Tis said to be Ten old Miles distant from the City Torneo; and there was an Inn in which we might lie on Rain Dear Skins, for they make use of no other Bedding. How­ever, amongst other Inconveniencies, this was our Comfort, that in the said place, neither Mountains or Woods hin­der'd our prospect from the Northern Board, whereby the Sun might all Night be the less discerned; and it was a parti­cular Gift of God that the same Night was free from Clouds; since in our whole Journey we had ever a doubtful and [Page 44] lowering Sky; therefore 'twas here that we beheld, with much pleasure, the whole Body of the Sun, not only entire, but elevated more than two Diameters of its Body; and when we had tryed sufficiently in this place, with no less difficulty we performed the rest of our Journey; and on the 14th of June we Arrived at the Work-Houses of Iron and Copper at Kengis. That Night likewise favour'd our purpose; and we saw the Sun from our Boats on the River, three Diameters of its Body above the Hori­zon.

The Situation of this place is betwen the Confluence of both Rivers, whose right Branch owes its rise to the Lakes, Streams, and Moorish Places in Lapland, and thence from Swadawara, and per­haps further by several bendings thro' Monier and Kengis; but the left is ex­cluded from the Western side, and the Lake Torne, situate almost in the Con­fines of Norway, and is here precipitated with that violence thro' the tops of Mountains and broken Rocks, that the fall of the Waters near these Work-Hou­ses for Metals, is esteemed to be 36 Feet [Page 45] high, and that with extraordinary Noise, and vehement Impetuosity; but it gives an excellent advantage to the said Work-Houses, which are so placed, that where the River hath a turning to the Western Bank, it is not restrained with the Wears, tho' they be of considerable bigness; nor can it go over the top of them, but runs with a free Course, without any Cata­racts to the opposite Bank. On the 15th Day, being troubled with vehe­ment Cold Winds, and most boisterous Weather, we took the heighth of the Sun, amongst the interspersed Clouds, with an Astrolabe; and at length, at Ten of the Clock 15′ looking for its Altitude with an Astrolabe, the Calculation be­ing taken off, we guessed the Latitude of the Place to be scarcely more than 66° and 45′, altho' the Sun there in the Night Time shows it self so largely a­bove the Horizon, and makes its Day long enough, and with an ample Cir­cuit. And here, when we were design­ing to go further into Lapland, by the right Branch of the River, which seems to lead strait to the Northward, the In­habitants declared, that it was not in [Page 46] the Power of Man to perform such a Journey in Summer; for all Journeys into North Lapland ought to be made in Winter; but altho' the left side of the River was alike open, as before for the Boats; yet it seem'd to us to incline too much to the Western Shore; so that it was of very little use to us, from that side, to proceed one degree further; therefore supposing what we had already found out to be sufficient for the Lovers of Astronomy; and considering the ac­count of our Time, because we were stinted to narrow Limits in the Journey, and had not as yet perform'd all that was to be done, we resolved to take our Course homeward.

At our going away we had great plenty of Metals, which with great Care are drawn out of the Metallick Veins of Lapland; and those rich enough in Cop­per and Iron, and yet not carried out [Page 47] without great Charges, and very mighty Risques, thro' the Precipices of Waters

And some pieces of the Magnet were presented to us, taken out of the same Iron Mines, which we carried home with us. The Loadstones there have very little force; and yet in one of them, which I still keep, I perceive it daily encreases, and I hope that they will augment in time, being arm'd.

Magnets are found in the Iron Mines of Sweden, and elsewhere; but those of Lapland excell in Force all that ever I had the Fortune to meet with. I pass by other things, which we saw, or were related to us, lest I shou'd seem to give an History of the People, which others have before written: And now being gotten into our Boats, we no longer, as before with our Boat Poles and Spreads, follow'd the Course of the Shore, but keeping the middle of the River, where it was most Rapid; the Rowers doubling their Strokes, we strove at least to emu­late, [Page 48] if not to outdo, the swiftness of the Waters; this was absolutely necessary, lest the Impetuosity being swifter than the Boats Course, shou'd fill our Boat with Water, and so drown it with its Waves, especially when the Waters a head of us, being roll'd with the greatest violence amongst the sharpest Rocks, Whirlpools, and deepest Gulfs, returning with like force, shou'd meet the Head of the Boat, and so detaining it as it were in a Whirl­pool, shou'd appear altogether to over­set it. In these Streights we were sen­sible

By so much more was the safety placed in the Pilots of our Boats; for they Steered with that Skill amongst the un­seen Shoals, that we were so amazed and astonish'd, that when we were deli­ver'd from Dangers, we cou'd scarcely believe our selves to be in Safety; but their Art appeared still more, and espe­cially in some certain Places. Those [Page 49] that are the most Experienc'd in this Voyage will witness, that there are some Precipices of this River, where the Boat is tossed up into the Air for the space of some Feet, the Pilot Steering in the same manner, until it is again in the Water. And this whole Voyage from Kengis to the City Torneo, which flows with one continued Channel, re­ceives 29 Rivers, one of which makes a whole Swedish Mile in breadth; the o­ther being less, recompence their small­ness by the violence and rapidity of their Waves. Neither can they be passed at any time, except by the most able Boat­men of the Place; and in one of the Ri­vers, altho' the Passengers are expert, yet they Hire an Inhabitant to be Pilot, but which is wonderful, for two Far­things only, venturing his Life; certain­ly a great hazzard, as we have some­times beheld from the Shore with hor­ror; but necessity imposed that Law on them, for this is the King's High-way, and the only one for those who pass into Lapland for sometime in the Summer; but the Inhabitants who dwell near the River side, and those but very few, as they [Page 50] live for the most part by catching of Fish, never Inhabit in any other place, since beyond the Shore side, for a long Tract, all the Lands are uncultivated and horrid; and they are contented with a little Ground, where-ever any place is found fit to be sowed; neither do they break it up with a Plough, or Plough with Oxen or Horses, but by digging and Spades temper and bring the Soil into order by the Labour of their Hands. But at our return, we were carried by so swift a Course, that we came from Kengis to Torneo, a Voyage of 16 Miles, in less than a day and halfs time. There we immediately observed the Diurnal and Nocturnal Sun, trying whether the Observations again made did agree with the former; but because it was many Days after the Solstice, this after Care was of little advantage. Having therefore once observed the Meridan Altitude of the Sun on the 18th of the Month, we perceived it to have decreased to 47°. 45′. and yet from the declination of that time gave the same elevation of the Pole with our former Observations.

[Page 51] And now, Courteous Reader, you have wherewith you may exercise your Wit, by enquiring into the true Causes of these Apparitions. We have given you Materials, make use of them as seems fit to your Judgments; but by your leave we interpose ours also, most freely suffering every one to abound in his own sence. What therefore apper­tains to our Nocturnal Observations, and the true ascension of the Sun above the Horizon, because it cannot be under­stood by all without the premised Do­ctrine of Refraction, which is the most subtil part of the Science of Opticks, we will briefly lay down some things for the use of Students, whereby they may with greater ease take our Demonstrati­ons.

MAny are the Arts and Sciences which owe their beginnings to Chance and Fortune; which wou'd be long and difficult to reckon, since their first Originals are unknown, and their Progress made by little and little, which renders us doubtful both of the Order and Manner in which they began. First of all it is very certain, that we learn by Experience, that the Rays which proceed from any visible Body, if they fall from a more dense Body upon a more rare, or on the contrary (which Philosophers use to term a different Me­dium) [Page 53] at this Entry the Ray proceeds no more strait forward, but is Refracted, and in its passage gets another way dif­ferent from the former. This Assertion is proved many ways; but leaving the more subtil, we will explain it in a vul­gar way not unknown to all People. Let some bright Piece be put into an empty Vessel, as Gold or Silver Money; whereby the splendid Ray may more easily represent the image to the Eye; then let him that makes the Experiment go so far from the empty Vessel that the Money being at the bottom is so covered with the Edges of the Vessel, that it cannot be discerned, let him stay in that place, and order Water to be poured out of a­nother into this Vessel; which being done, the Money will appear through the Water to him in that Posture, being inconspicuous before; and that so much the higher as the Water is put in in grea­ter plenty, by which it may be under­stood, that this visive Ray between the Money and the Eye is only Refracted in the highest Superficies of the Water, since a right Ray cannot be carried to [Page 54] the Eyes, remaining in the same Posture, from the Money, by the Opake sides of the Vessel: The reason is the same, when an Oar seems to be broken in the Water, where no other Cause can be given of this Fallacy of the sight, than the Incli­nation of the Ray of the things seen, from that side in which it enters a diffe­rent Medium. Wherefore since the Solar Rays are right Lines, it is doubted, not without cause, if the Sun, and o­ther Lucid Bodies in Heaven, be any where or every where discerned in their true places; but since it is for certain observed in the Eclipses of the Lumina­ries, that the places of the hidden Bo­dies, both true and apparent, are diffe­rent not only by reason of the Paral­laxes, but also Refractions, the strongest Argument of Astronomical Truth, and besides, some other Observations most deserving Credit, takes away all Doubts.

Since therefore, by consent of all Men, it is evinced, that the Air is nearest the Earth, whose Particles going out from the Earth are the Causes almost of all [Page 55] the Vicissitudes which happen to it from natural Motions; and we think do scarce­ly exceed, or not much transcend, the highest tops of Mountains (and that is it which we call the Atmosphere) but next to this the Aetherial Air succeeds, diffus'd through the whole Universe, in which the Sun, and fixed Stars, and all Planets are moved; and yet there is not the same tenuity and purity of both of them: For the Aetherial Region (the spaces of Shadows which proceed either from the Earth, the Moon, or Planets, or Comets excepted) is wholly in the Rays of the Sun, and Stars; and is so splendid, that at Night its splendor may be perceived by us, dwelling in the sha­dow of the Earth, altho' the Interval be­twixt us and the fixed Stars be inestima­ble, by which this Splendor, with the difference also of Colour, is transmitted to us, but is always open to the Rays of them, except when 'tis obscured by the Atmosphere, but the Air swelling with smoaky and thick Exhalations, drawn from the Terrestrial Globe by the help of the Sun, and subterraneous Fire, ac­cording [Page 56] to the measure of the Matter is sometimes thicker and sometimes thin­ner, both in divers, and in one and the same place, but at divers times, to wit, that Matter, being rarified or compres­sed, which perpetually ascends from the Sea or Earth, and its Superficies some­times takes up a greater, sometimes a lesser part of Aether, which Vicissitudes we prove by several Mechanical Instru­ments, Hygrometrical and Barometrical, and from thence also determine its true Altitude; and we daily perceive by the disposition of our Bodies (the sick and weakly especially, and who have any crude Wounds, confirm this Truth more certainly than any Almanack) that the Ray entring into the Atmosphere is vari­ously determin'd, nor cannot go for­ward in strait way, according to its thickness and condensation, no other­wise than a Leaden-Ball obliquely shot into the Water, on its Superficies, re­cedes from its first direction, losing some of its strength in passing through a dif­ferent Medium; or as a Nail driven through two Boards, not contiguous e­nough, [Page 57] acquires one determination in the intermediate Air at the end of one, and another at the entrance of the other Board; these things being more largely Premised than was intended, we will, by a rude Scheme, delineate the Re­fraction of the Sun.

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[Page 59] Let T. be the Center of the Earth, O. the Eye on the Plane of the Earth, A. B. C. the Superficies of the Atmo­sphere, where the more gross Air is se­parated from the thinner Aether. E. D. G. the Orbit of the Sun. O. B. D. the right Horizontal Ray to the Sun ap­pearing in D. Now it is certain that no Coelestial Body can appear to the Eye, placed in O. before it shall come to the Point D. And further, because Ex­perience teaches us, that it appears be­low O. B. D. that cannot be done ex­cept by a Ray Refracted; for this Ray wou'd fall sooner on the Convex of the Earth's Globe, than upon the Horizon­tal Line O. B. D. and so that Body wou'd remain inconspicuous, the Ray S. B. falling from the Aether into a more dense Medium, to wit, the Atmo­sphere A. B. C. is Refracted, and in one part of it represents the Line B. O. when otherwise it wou'd have been pro­duced to R. if the Medium had been the same, but not to the Eye, O. Hence it is certainly concluded, that the Sun appears on the Earth, sometimes before its Rising, when it seems to be discern­ed [Page 60] by us in an Horizontal Line, Q. E. D.

But because it is manifest, that the nature of Refractions is divers, and that the Rays falling perpendicularly upon the Superficies of a different Medium are not Refracted, as if the Ray from E. shou'd fall upon the Atmosphere A. it reaches to the Eye O, directly and with­out any Refraction; but those which fall obliquely, are by so much the more Refracted, by how much the more they recede from the Perpendicular; hence it is manifest, that the Coelestial Bodies, nearer to the Horizon, appear under a greater Refraction, and therefore appear higher than the more remote, which come nearer to the Perpendicular. Hence the Rules of Refraction are by the Ma­thematicians derived to a certain De­gree, for the Sun and Moon, even to the Degree of 38 Altitude; but for the fixed Stars, but to the Degree of 20. which Rules would never fail, if the disposition of the Atmosphere was every­where the same; but this variety is not [Page 61] in the least to be neglected, because that Refraction cannot in all Parts of the Earth be equal, but is found to be grea­ter in places nearer to the Pole than that which is in the more remote, which may be confirmed by the sole Experi­ence of the Hollanders; and that Ex­ample is wont to be produced, as most true, by all, even the most excellent of Mathematicians, since there are but a few Observations in places near to the Pole, which we may use in examining the Phaenomena; for the Dutch Win­tering in Nova Zembla saw the Body of the Sun above the Horizon, at the time when it shou'd have been four Degrees below the Horizon, which certainly is a Paradox; for by this reason the Hori­zontal Refraction encreased too much be­yond the quantity commonly allowed in the Tables of Refractions.

Very many therefore not undeser­vedly suspected this Observation of the Hollanders, and yet they themselves are compelled to confess that those Obser­vers were Learned in Astronomy, so that they cou'd not commit so great an [Page 62] Error in their Observation. Certainly the exact noting of the Time by a cor­rected Clock; and that hindered by the Frost, by an Hour-Glass of Twelve Hours; as also the conjunction of the Moon and Jupiter, observed by them, by which compared with Ephemerides, they found out the Longitude of the Place. This they related more at large, say they, lest any shou'd doubt of the Truth of the Observations, since they all seemed to oppose the Opinion of the Ancients and Moderns, the Order of Na­ture, the roundness of the Earth and Heaven. From which the more celebra­ted Mathematicians gather, that Re­fractions are greater or lesser in the very same Horizon, according to the density or rarity of Vapours, and especially a­bout the Northern side of the World, they increase and augment by reason of the thicker Air. I shall not uneasily give my assent to their Opinions; for in our Nocturnal Observation somewhat hap­pened altogether like it, for let the found-out Elevation of the Pole at Torneo, 65°. 17′. that being taken from a Qua­drant [Page 63] 90°. gives the Complement of the Elevation of the Pole, 24°. 17′. now because the Observation was made about the time of the Solstice, the Sun being in the beginning of Cancer, if the Declina­tion of the Ecliptick, which is commonly 23°. 30′. be taken from it, the residue will be 47′ for the place of the Sun be­low the Horizon.

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[Page] In [...] [...] L Q. be [...]he M [...]ridian at [...] [...] this Diagram, P L. the Axis of the World, AE Q. the Aequator, H R. the Horizon, E C. the Eccliptick, the Angle P. O. R. the Elevation of the Pole, R O Q. its Complement, C O Q. shall be the Declination of the Eccliptick R O Q.—C O Q. = R O C. that is to say, the place of the Sun shall be 47′ be­low the Horizon, Q E D.

Now because the Diameter of the Sun, at that time of the Year is supposed by us, about 30′. to which the Horizontal Refraction may be equal in the Opinion of those who think the Tychonick Tables of Refractions are greater than they ought, by reason of his assuming the Suns Parallax too bigg. Let it be either by his Table, or that of Lansberg, 34′ for the difference is small in either of them, the Sun shall be still depressed be­low the Horizon, altho' it shou'd ap­pear in its Center, being Elevated above the Horizon, three fourth Parts of its Body, to wit, 22′ 30″. Since there­fore [Page 66] there is so great a difference be­tween Diurnal and Nocturnal Observa­tion, it follows, that here the Hori­zontal Refractions are far greater than in those Places where the foresaid Tables were made; but to form an exact Rule for them is an hard Work, and of no few Years, as we learn from Tycho's Tables, composed by a long use from the Risings, Sittings, and Culminations of the fixed Stars.

And further it appears from this our Observation, that they who place Torneo beyond the 66 Degree of Lati­tude are mistaken. For if it be laid down to be only 66° 30′. then 66° 30′. = 90°—23° 30′. But when this num­ber is the Declination it self of the Ec­cliptick, by this Hypothesis the Sun will also be Elevated one half above the Horizon, without Refraction, when its Center is in the Horizon it self; but ad­ding the usual Refraction, the inferiour Limb will be Elevated at Torneo, a­bove 19′ which yet contradicts Obser­vations.

[Page 67] In the little Cottage Pello, where we saw the Sun at Night two Diame­ters, or 60 Minutes above the Horizon, by Tycho's Rule of Refractions, which makes the Refraction 34′ in the Hori­zon, and in one Degree above the Hori­zon 26′, it is easily concluded, that the Sun is discerned in its whole Body with­out Refraction, for the Sun being eleva­ted two Diameters or 60 Minutes above the Horizon, its Center will possess 45′. But in that Altitude let the Refraction be proportionable to 34′ and 26′ or 30= to the Diameter of the Sun, therefore its lower Limb will appear without Re­fraction 15′ above the Horizon; but if we assume, as it is fit, a greater Refraction some Particles of the Solar Body will also be elevated in this place by Refra­ction: But at Kengis, where it was discerned in three Diameters of its Bo­dy, it appears by what hath been de­monstrated, that the Sun was seen with­out any Refraction at all, to which end we are willing to delineate in one Scheme, the Nocturnal Observations, [Page 68] which we had at that Season in three Places, that the inexperienced in Ma­thematicks may judge more rightly of them, and understand their true and genuine Sense.

Let T. be the Globe of the Earth, B F G. the Horizontal Line, K A B C I. the Suns Orbit, F E D H. the Quadrant of the Atmosphere, G. the Eye in an Horizontal Plane, C D G B E G. A E G. the Refracted Rays, A G F. the Angle of 47 Minutes, the rest successively lesser; for the first of the Sun observed at Torneo is under the greatest Refraction; the second at Pello a little less; the last at Kengis, least of all; whence it follows, that the Sun seen by Refracted Rays in the Points A. B. C. does not make the Lines F A. E B. D C. drawn from the Points of Refractions Parallel, further it is clear that the Sun at Torneo in D. was below the Horizon by Refraction at A. but being Refracted at Pello from E. to B. some part of its Body was really still be­neath the Horizon, altho' it appeared [Page]

[Page 70] two Diameters, or a whole Degree a­bove it in E. Lastly, being Refracted at Kengis from F. to C. it was really a­bove the Horizontal Line; the Experi­ence of the Inhabitants confirms this Opinion, who there also, for the first Days of July, confess that the Sun sets not; which Argument I do not bring, but only as probable; for it is known from the foresaid Observation of the Hollanders in Nova Zembla, that they in the same Altitude did not yet see the Sun for so many Days after it ceased to rise; and therefore this appearance might be drawn from the thickness of the Air; for (as different Liquors make different Refractions, and a greater plenty also of them encreases the Refraction) a more rare or more dense will make a diversity of Refractions. How much the Hol­landers admired this, their Words prove in their Voyage to the Northward, on the 24th Day of January, 1597. but, say they, as for what relates to the Matter it self, as God is wonderful in his Works, so we refer it to his Omni­potence, and leave it to be discussed by [Page 71] others, viz. That the Sun under the foresaid Altitude of 76 Degrees disap­peared to us on the fourth of November, and on the 24th of January was again seen by us. For the rest, there is no doubt but a right Judgment may be made Astronomically from the Altitude of the Sun of its stay above the Horizon, even not attending to Refractions, which alike dispatch this business; al­tho' in the determination of Climates, I do not still deny that it is Controver­ted amongst the Mathematicians, whe­ther any notice is to be taken of Paral­laxes and Refractions, some asserting, and others denying it. But waving these things, and neglecting Refraction, the longest Day in Kengis is found to be of about 30 of our Days, by the sole Calculation of Climates.

[Page 72] In this Diagram, let the Pole be A, the Elevation of it A. B., B. C. the last Parallel in which the Sun is car­ried above the Horizon; H. I. the Ae­quator B. N. the Horizon, B. L. H. the Angle of the Complement, E. L. of the Pole, E. F. the Tropick of Cancer, G. K. the Tropick of Capricorn, E. G. the Eccliptick, D. the Point where the Eccliptick cuts the Parallel B. C. which Arch being doubled, gives the place in which whilst the Sun tar­ries, by ascending to the Tropick, and again descending to the Parallel, it does not reach the Horizon, but that whole Line will not set.

The reason is the same of any place within the Arctick Circle, according to its different Latitude, even to the Ar­ctick Pole, that the Sun Yearly does not rise or set for some Days; and by so much the more as the Places are nearer to the Pole; so that in the place of the Pole it self it does not set for an whole half Year, and does not rise all that [Page]

[Page 74] time in the place opposite to it, but in the furthest places follows the Course of the Tropicks; for the Sun being in the beginning of Cancer, as it does not set there, so in the beginning of Capricorn it doth not rise, but only sweeps the Ho­rizon; but it will rise or set in all other Points of the Eccliptick, all which may be easily understood from what is be­fore said.

LAstly, We must not omit, that all the time we were at Torneo, and the further places, we were Periscii; for so long as the Sun did not set to us, the Shadow was carried about into all Parts; and the Sun being in the upper Semicircle of the Meridian, it was ex­tended towards the North; but being in the lower towards the South, but in so little an Elevation of it to the North, the Light of the Sun cou'd not show the Hour of the Night on our Dials: Without doubt as well by reason of the Parallelism, with the place of the Dial, because it was scarce above its Plane; as also because of the thicker Vapours about the Horizon. There [Page 76] is some difference between Observati­ons made at Land and at Sea; so that even they who are in a less Latitude of place, see the Sun all the Night, which very many Inhabitants of We­stern Bothnia confirm to be true to their Knowledge, in the Cities of Bithea and Buhlea, and other Mari­tine Places; for besides that, the Hori­zon seen upon the Waters is even, be­ing hinder'd by no Inequalities, which at Land the Mountains or Trees use to make. I also think, that Reflection comes nearest to Refraction, which be­ing joined in a double manner, repre­sents the Species of the Solar Body, no otherwise than happens in Looking-Glasses, where the first Reflection with­out Refraction, is made in the polished Superficies of the Glass, but the other in the bottom of it, in its filed bot­tom, but with Refraction; which Com­position, except you take heed, shows to you one thing sometimes falsly, un­der a double Image, or somewhat grea­ter than it shou'd be; and further, ma­ny things may be Objected about the [Page 77] Maritine Observations of Peasants; and we very often want the Confirmation of Fishermens Sayings, who being ac­customed to spread Probabilities for Certainties, sometimes both egregiously deceive, and are deceived; yet we will admire it the less, because Mathemati­cians, as well in their Coelestial as Ter­restrial Observations have something that is Human in them.

In the Frigid Zone, and its Neighbourhood, the stay of the Sun above the Horizon, brings this Advan­tage to the Inhabitants, that the Corn in those Places ripens in a short time; for as we have heard from the Husband­men in fertile and fruitful Years, not above six or seven Weeks are required amongst them, from the time of Sow­ing their Corn until Harvest, we made no difficulty to suffer our selves to be perswaded of it, when the first Sower, as we went, was in the City Torneo, and the Barley sown in the beginning of June, or the 16th Day of the same Month, was grown beyond Expectati­on; [Page 78] and the Grass, which as we passed by some places of Western Bothnia, in the beginning of June, had scarcely come out of its Stalk, at our return, after four Weeks was Mowed. But this Advantage is followed by another Disadvantage; for the Corn is liable to much danger from the Cold, in this so short a space of time; for if it do but happen about the time when it ripens, or when they hope it shou'd ripen, that the Dew or Frost falls upon it in the Morning, it hurts the Grain, and wholly destroys it, which Mischief they cannot other­wise prevent, than by cutting the Corn unripe, before it so suffer. Even then they did conjecture, that they shou'd experience this Year the same Damage, not without the greatest prejudice to them; and the event showed that they were not False Prophets; for altho' they saw the Cold to be near, yet the Corn was not then come to that Matu­rity, as it cou'd be exposed to any in­convenience by the violence of the Cold Weather.

[Page 79] But here is one thing which I wou'd have my Courteous Reader to observe, that the Nature of these Northern Countries is not altogether to be esti­mated from the Intemperateness of this Year, for the present Year exceeds all others that are past in the Memory of Man, for the severity of the Season; and there are very long lived Men in those Places, who sometimes live to an Hundred and more Years; but not one to be found amongst them who cou'd testifie that Thunder is so much as once heard in the Year, and especially in the middle of April, which now happened and seemed to presage some­thing unusual: And it is very remark­able, that when our most Serene King went to see these Places, the Year be­fore, the Inhabitants never saw a more pleasant Time, as if the Countenance of Heaven was composed for Mirth, the Lord of the Country being pre­sent.

[Page 80] As for what concerns the Islands of the Bothnick Sea, they underwent a different Fortune; for as we went from Torneo, to the Parish Calix, in our Voyage on the 19th of June; at our Arrival at some little Islands, we there perceived that the Soil was not yet freed from Cold; nor did the Birch-Trees, which are very many, in that place, show any sing of Green­ness; when yet in other Places be­yond Sea, they abounded with their ripe and full grown Leaves; and we know, that this is not also unusual in other Countries, since in Japan, whilst the sharpest Winter continues, and the Snows and Rains continually fall, other Countries of Asia and Eu­rope, situated under the same Climate, are not sensible of the same hardness of Winter.

[Page 81] And Nova Albion being situated a­bout Forty Two Degrees North Lati­tude, when Drake the English-Man first Arrived there, he found the Moun­tains covered with Snow; and the En­glish were so troubled with Cold in the Month of June, that they were forced to go from it. Other Islands also lying in the Ocean, are reported to be liable to these Inconveniencies.

At Night, between the Nineteenth and Twentieth Day we saw the Sun set­ting in Calix at Eleven a Clock and Twelve Minutes, tho' the Horizontal Plane, by reason of that unequal part, in which it looks to the North, scarce­ly permitted us to determine its true setting. We tryed the next Day to take the heighth of the Sun; but this hope vanish'd amongst the Clouds. As much as we can judge from our Journey, and the Sun's setting, the La­titude of that place can differ but little from Torneo, since the Church in Ca­lix, [Page 82] where the Observation was taken, seems to be situate directly to the Westward of it.

ON the 21st we observed in the Old Town Luhlea, the Meri­dian Altitude of the Sun, and thence gathered the Latitude of the Place to be 65 Degrees, and 25 Minutes. And the Declination of the Magnet from the North to the West, to be about Six Degrees. That City was founded in the Year M DC XX II. where there is still an Old Church, yielding to none in that Country, for Structure and Largeness; but for a more convenient Situation New Luhlea was Built nearer to the Sea, in the Year M DC XL II. [Page 84] but by the Carelesness of the Lapland­ers, kindling a Fire in the Neighbour­ing Wood, was Five Years after, toge­ther with the Wood, destroyed by Fire; nor was it Rebuilt more Fortu­nately after; for in the Year MDCLIII. it was again ruin'd by an accidental Fire, and from those Ruines, became such an one as we now see it.

On the 24th, in the Old City Bithea, we in vain hunted after the Meridian Altitude of the Sun, the Sky being thick set with Clouds, wholly hinder­ing our Design; and therefore we went the next Day into the Neighbourhood, to search for it. This Old City was Built in the Year M DC XX I. but af­ter it was casually by Fire reduced into Ashes in the Year M DC LX VI. for some time the Rebuilding of it was de­ferred, until some fresh Privileges and Immunities being granted by His Most Serene Royal Majesty, they might un­dertake the Business. But the New City then beginning to be Built, is di­stant half a Mile from the Old, being [Page 85] situated nearer to the Sea, for a more convenient Port, and convenience of exporting Merchandizes.

The next Day, in the Parish of Schelefta, near to the Church, we ob­served from the Meridian Altitude of the Sun, the Latitude of that place to be 64° 37′ and the variation of the Needle to be equal to the former.

On the 26th and 27th Days we did nothing, the Air being Cloudy, nor was there any thing which deserved the noting; except only that the Church of the Parish Bygde, seems to be the most ancient of all the Churches of the Norlands, provided the Inscription which appears in the Front of the Church, be genuine, and sets down the Year of Christ, 1169. Yet the Chronicle of those Times takes away the doubt, which clearly show, that it was Founded under the Reign of St. Erice, at which Time Religious Worship, altho' Infected with Old Po­pery, made extraordinary Progress; [Page 86] And besides, there was the Picture of a certain Religious Person which was placed in a Wood half a Mile and more from thence; where formerly those who were Remote from Church, are said to have met together to Prayers, on Holy-Days; but after the most hap­py Times of Religion being purged from the Heresies of Papists, as that sort of Worship ceased in our Country, so the Picture was laid up in a certain place of the Temple, in detestation of the Memory of that Matter.

On the 28th in Uhma, near the Old Temple, we observed the Meridian Altitude of the Sun, to be 48° 38′. And thence we computed the Latitude of the place to be 63° 48′ but the va­riation of the Needle not different from the former. That City is situated in a more convenient place towards the Sea, and is the first and chiefest of Western Bothnia; in which also is the Seat of the Governour of that Province.

[Page 87] On the 29th leaving that Place, and going thro' the Borders of Western Bothnia, which altho' it be more Nor­therly, yet is happy in a more conve­nient Soil than the Countries next to the South, which abound in Mountains, and give place to it in Fruitfulness; but the Mountain Scula in Angermannia, is Famous before all others, very crag­gy and broken, threatning Ruine, as it were to all who pass by it, for it is very near to the Highway. Many Stories are vulgarly reported about it, which relish only of Gentilism. Their only chief City is Hernosand, being fur­nished with a most convenient Haven, and is situated in the Island, where the Seat of the Super-Intendant is, and the Royal-School, the Seminary of the Youth of Norland. We stayed there three Days, hoping to find the Eleva­tion of the Pole; but this stay was to no purpose, as in several other Places, by reason of the Rains, and the Sky be­ing covered with perpetual Clouds.

[Page 88] On the 7th. of July in the Town Medelpadia Sundswald, we endeavou­red to find the Latitude of the Place; but Heaven also oppos'd it. When therefore all things seemed to thwart our Labours, which we cou'd not stick long to in one Place for our other Af­fairs; yet we still continued two days not far from this City in an Inn near the Church Niurunda, a Place fit for Observations, expecting but with lost labour the Light of the Sun; and this is the reason why at no Place in Anger­mannia or Medelpadia we made Obser­vations.

On the 10th. of July, coming to Hel­singland, first we sought for the Sun's heighth in Hudwikswald, a neat City of that Country conveniently situated near the mouth of the Sea; but without any Success, by reason of the imminent Tem­pest.

[Page 89] After that, on the 11th. day, we at length found the Elevation of the Pole to be 61° 12′ in another City of that Country, called Soderhamn, in a fa­mous Armoury built there. Thence by a crooked way, going to the Copper and Iron Mines, in our Passage we first observed the Elevation of the Pole of the City Gefle, being in the County of Gestrefland, 11 miles from Upsal, and is famous for being the Seat of the Go­vernor of that Country; and having a Royal School, the Altitude was 60° 31′.

On the 13th. at our coming into Dalecarle, or the mountainous Country, the Elevation of the Pole was found at our Inn Lomsheden, to be a little greater than before, by reason of our Journey's bending to the Northward, viz. 60° 41′ going thence through the Parish of Dalicarton Swerdsio, whose Church was first beautified with a Monument of a gilded Crown, by King Gustavus of most Glorious Memory: Some Antiqui­ties [Page 90] were produc'd here by the In­habitants; let those who please be­lieve them in a Matter so dubious, and not confirmed by any ancient Monu­ments.

On the 14th. we came to the City Fahlun, very famous and eminent for being the Seat of the Governour of that Country; and especially being the richest in Copper Mines, of so great An­tiquity, that the Original of it is very uncertain and doubtful. From this City which we arrived at with so many Windings and Turnings, we did not think it convenient to depart without an Observation; therefore staying there six days before the Sky was as agreeable as we wish'd, at last the grateful Light shone forth on the 20th. of July, by help of which we found the Meridian Alti­tude of the Sun, and by it the Places Latitude to be 60° 32′; and therefore perceived this City to lye almost in the same Latitude as Gefle.

[Page 91] After that designing to bring our Jour­ney to an end. (without any Observation because of Showers and Storms) we pas­sed the several Cities of Westmanland and Hedenore, so well known for its Mer­chandize, Agriculture, and Fairs; and then Afwestafors famous for Copper Mines of several sorts, and coining of Moneys; and then to Soleburg a very noble Place, and celebrated for one of the most precious and ancient Mines of Silver.

Happily returning to Upsal on the 24th. of July, the Situation and Anti­quities of which City being described by others, are well known to all People; but the Elevation of that Place's Pole is 59° 54′ for ten Years, and more at several times observed by me, and the Variation of the Compass about eight degrees.

[Page 92] Because we were sensible at our re­turn, that our most Serene King was at Kongsor, to Review his Army, to whom we were to give an Account of our Expedition, we thought fit to wait on His Most Serene Royal Majesty there; and therefore setting our Affairs in Or­der in two Days, on the 27th we passed thro' the City Enecopia in Upland, and the Cities of Arosia, Koping, and Westmanland.

On the 28th we came to Kongsor, in that most pleasant place of Suder­manland, to the Latitude of 59° 34′. si­tuated by a most pleasant River, where it empties it self into the Lake Galtem, and Malaren.

His Most Serene Royal Majesty re­ceived us at our Coming with a singu­lar Clemency; and as we gave him that Account of the demanded Expedition, hearkned to us with a Countenance full of Grace and Maje­sty; [Page 93] and the Most Serene Hereditary Prince, and some of the King's Council, and great Ministers of State being pre­sent, He enquired much about our De­monstrations; and would have the Rea­sons of the most minute Matters laid before him; but we wondred at no­thing more, than that the Most Serene King being loaded with such a weight of Empire, and perplexed with infinite Cares, shou'd, of all the things which he saw or heard the Year before, in the Northern Countries, forget no­thing; so that we but just returning from those Places, and doing no other Business, did not seem to have a fresh­er Memory of Things, Events, Places, Persons, and of the Names of Towns and Houses, which we beheld as if we were present, being just come from our Journey, and Instructed with our Jour­nals; but what need of our Testimony in a Thing so well known in our Coun­try? Those whom God hath Exalted upon Earth to so high a Place, he hath thought fit to endue with Divine Gifts; [Page 94] which certainly He hath bestowed with a full Hand on our Most Gracious Mo­narch.

The next Day being dismissed most favourably by His Most Serene Royal Majesty, we heartily Rejoyced that we had obtained the heighth of our Wishes, that our slight Labours seemed not to displease our Most Gracious Master; and now having dispatched this Business, every one went to his own Home.

Homer relates of his Ulysses;

But who can believe that we traver­sed so many Cities in this Journey; and Northerly waste Part of Sweden; going no more than Five Miles beyond Kongsor, thro' Holmia, before we came to Upsal. We saw besides the said Ci­ties Orebro, Arboga, Torshella, Strang­nans, Mariefred, Sodertelus, and Stock­holm. [Page 95] So that in all we passed thro' Twenty Four of them in a direct way.

NOW altho' in this Journey, but a little may seem to be Remark­ed, which may please a Curious Rea­der; yet there are some Things, which amongst Just and Learned Criticks, will at least Excuse, if not Commend our Labour; for as to what concerns Cho­rography, that by Command of His Most Serene Royal Majesty, is described with the greatest Care, by the Survey­ors [Page 97] of those Countries, who for some Time had the Charge of it. The Antiquities of the s [...]veral Provinces are not slightly discussed by the mo [...] Learn­ed Antiquaries of [...]e Kingdom, there­fore Astronomy was only our Point, in which if we have performed nothing else, we have really shown, that all those Places in which we made Obser­vations, being laid down too much to the Northward, both in our Maps and Charts, ought to be more Southerly. And this very Thing hath been be­fore observed by those who Sail to the Northern Parts about the Promon­tory of the Northern Cape; which in their Opinion is more Southerly, than is described in the Geographical Ta­bles.

As for the variation of the Compass, altho' by reason of the Imped [...]ments before expressed, we cou'd not describe it so exactly as we ought; yet we may assert for certain, that in all those Places we had the Fortune to go to, it was never found less than Six Degrees, [Page 98] which Experiment may be serviceable to Posterity who may observe the Constancy of its Declination; for it is very probable and agreeable to Na­tural Causes, that its Declination is changed with the Time; as the Ex­periments and Observations of Mathe­maticians made in very many places, many Years since, do abundantly teach us.

There yet remained one thing which rendered us very sollicitous, though in vain, of which we conceived an ample Hope at our departure, viz. That in these more Northerly Voyages, an oc­casion is given of enquiring into the true Figure of the Earth, which altho' no Body who hath a sound Head, at a Time of so great an Improvement of Mathematicks, will make to be Tri­angular or Cubical, since the Superfi­cies of the Water and Earth returning into it self hath long proved it to be Gibbous. Yet since there are sundry sorts of Gibbous which arise from a Cone or Cylinder, if it goes from a [Page 99] Circular, 'tis doubted to which of these it is to be chiefly referred.

We have spoke before of the Experi­ence of Sailors, to whose Credit and Relations we owe the asserting the Roundness of the Earth, but only to convince the obstinate Heads of some People, who trust more to their Sen­ses than Understanding. For Mathe­maticians have demonstrated this very Thing many Years ago, by other, and those most evident Reasons.

All know the Story that Ferdinand Magellanus Sailing out of Spain to­wards the West, and having passed the Atlantick Sea, by a strait he sound out, got into the Eastern Ocean, and by that way came to the Moluccos Islands; in which Voyage, when he had sufficiently view'd enough that Country, he might have return'd by the same way: But not contented with that Experiment, he went farther to the West, by a direct continued Course; at length returning as it were out of [Page 100] the East, by the Indian Ocean, and Atlantick; and lest any shou'd think, that the Face of the Continent is dif­ferent from that of the Waters, let him consider, that the Ocean is distinguish'd by Lands, from the East to the West; and on the contrary, by Seas be­twixt them; and again, slowing into the Northern Land, above and below Tartary, whence arise so many Conti­nents as if they were Islands, scarcely cohereing any where by the most narrow Isthmus which every where almost have the same heighth. For here is no Con­troversie about the Mountains or higher Places in the Earth, which no more hinder its being round, than the small Inequalities in an Apple; since we will grant to any, that its Superficies is not most exactly round; for Nature seldom makes Mathematical Circles in its Motion; but if the Motion of the Sun were altogether Sphaerical near the Aequator, which we know to be in­equal, altho' it is supposed to be equal; for the Earth is not the Center of that Motion; yet would it not follow, that a Sphere is formed by Motion, equally [Page 101] near the Poles, as the Aequator; for the Experience of Artists shows, that Cups turned, may imitate another Figure than Spherical.

It is not to no purpose therefore, that some in this Age doubt whether the Earth be equally Spherical near the Poles as the Aequator. Some of the Reasons which John Childrey brings in his Britannia Baconica, for the Oval Figure of the Earth, are not to be de­spised; altho' we do not much approve of that which is brought from the Snows being gathered together in a great heap near to the Poles, ever since the Creation of the World.

It is certainly true, that in Lapland very old Snows, of many Years stand­ing, are found in the Vallies between the Mountains; as may be gathered from their outward Coat Yearly re­maining: And yet, no doubt, some of this Heap is Yearly dissolved into Wa­ter. But those heaps of Snow make no more for taking away the Round­ness [Page 102] of the Earth, than the Risings of those Mountains we before mention'd; but besides, if this was true, there ought to be the same Accession of Snow every where about the whole Globe of the Earth, which the Industry of those who going to Eighty Degrees Latitude, sound Mountains crusted with Ice in that Sea: Tho' in time dissol­vable by the violence of a Tempest, forbids us to assert of Maritime Pla­ces.

Better Arguments might be brought from the Diurnal Motion, and the Na­ture of Coelestial Vortices, which per­adventure wou'd produce some variety in a Spherical Figure; so that this Hy­pothesis shou'd not seem to be altoge­ther neglected, especially since amongst Oval Figures, by reason of the small difference of Diameters, almost Parallel at the Section of a Cone or Cylinder, they do not much differ from the Fi­gure of a Circle. Caspar Eisenschmit hath therefore confirmed this Argument with great probability, and illustrated [Page 103] it with the Demonstrations that were needful. Of which at present we must say no more, since it requires a sepa­rate Work and Demonstration assuredly. In our Journey we long sought after some places of the Earth, situate in some Plain, stretching from South to North, by advantage of which we might Be more certain of the true measure of Degrees in Northern Latitudes, and by comparing them with the more Sou­therly, collected by the Pains of others, we also might give our Judgment of the Figure of the Earth; but the steep tops of Mountains, the Moorish Grounds, and inaccessible Woods, render'd our Desires unsuccessful.

Lastly, We hope that this our little Work will not be unacceptable to Ma­thematicians abroad; tho' it were only for that Doctrine of Refractions, light­ty attempted; from which occasion, they will not disapprove of our Opini­on to make Tables of them in the se­veral Parts of the World. For as we do not at all doubt that they increase [Page 104] according to the different Account of Elevations in places nearer to the Poles; so in those placed in the Aequator, and next to it; if there shall be any Re­fractions, we believe they will be very little. And from hence, when the Rea­son is asked, why the Polar Stars are not seen by those who Sail under the Aequinoctial; and yet it is probable, that the Stars placed in the Aequator may be discerned from the Poles, if there was any Observer. We think that, amongst other Reasons, this of Refractions is not of the least Mo­ment.

And if it be true which Mandeslo asserts in his Travels, in the Thir­teenth Chapter, that he saw not the Arctick Pole, except beyond the Sixth Degree, on this side of the Aequator; but the Antartick beyond the Eighth. It follows, besides other Reasons, that the Refraction from the Northern Part of the Earth; is greater than from the Southern, To Confirm which, we cou'd bring many probable Argu­ments, [Page 105] if the Matter was to our pur­pose.