A VOYAGE Of the Late King of Sweden, And another of MATHEMATICIANS, Sent by Him: In which are discovered The Refraction of the Sun, which sets not in the Northern Parts, at the Time of the Summer Solstice, Variation of the Needle, Latitudes of Places, Seasons, etc. of those Countries. By Command of the Most Serene, and Most Mighty Prince, Charles' XI. King of Swedes, Goths, and Vandals.  
Faithfully Rendered into English.  
LONDON, Printed for Edward Castle, next Scotland-Yard-Gate, by Whitehall, 1698.   

TO THE Most Serene, and Most Mighty Prince and Lord Charles XI. King of Sweden, Goths, and Vandals; Great Prince of Finland; Duke of Schonen, Estland, Lifland, Carelen, Bremen, Verden, Stetin, Pomerania, Cassuben, and Vandalia; Prince of Rugen; Lord of Ingria, and Wismar; Palsgrave of the Rhine; Duke of Bavaria, Juliers, Cleves, and Mons, etc. etc.  
My most Gracious King and Master. Most Serene KING, AND MY Most Gracious LORD,  
BECAUSE it Pleased Your Majesty, most Serene Prince, to lay Your Commands upon me, to Write both in our own Language and Latin, what we observed in a late Northern Journey, concerning the Elevation of the Pole, and other things of that Nature, I have therefore for a few Weeks past, since our Return, daily deducted somewhat from my Public Concerns, that thereby I might most humbly Obey the Commands of Your Most Serene and Royal Majesty. But as the Nature of Mathematical Sciences is such, that they depend upon Easie Use and Exercise, but require a more difficult Invention and Demonstration; so our Observations are made in fewer Hours than Demonstrated. The distinction of the little Wheel into its known Parts, gives but small Trouble to the Clockmaker; but the manner of dividing is not his, and but difficultly Invented. Even Boys at present do mutually teach one another Arithmetic; but the Practice of it hath been Intricate, the Rules being altogether drawn from the very depths of Mathematics. The Masters of that Art will peradventure wonder, that at this day the Mathematicians solve the more difficult Problems by the help of Addition solely; but when they have gotten the Key they will cease any further to admire it. For the Ignorant Ploughman will play you upon his Instrument any French Air, just as well as the most excellent Musician, provided he have but the Key of it. In a word, all Artifices which owe their Births properly to Mathematics, are of the same Nature. And because very many not well skilled in this Learning; and not sufficiently accustomed to distinguish the Truth of Sense and Reason, have rendered Philosophy only sensible; and by this Error of theirs, have rendered the way to solid Learning in other Sciences also very abstruse and difficult; therefore Mathematicians have resolved never to admit of any thing whatsoever, without clear and perspicuous Demonstration. How imperfect the knowledge of our Senses is, when destitute of Reason, the Sun being elevated above the Horizon in the whole World may teach us; which yet reason dictates to be otherwise placed. I have therefore expounded the Doctrine of Refraction, and other things not altogether so unknown more at large than was absolutely needful. And it is well that our Observations come forth in both Languages, tho' our Mother-Tongue might have been sufficient for our Countrymen; as it is now usual for the French, English, and other Nations of Europe, to express Arts and Sciences to their Countrymen. And yet because very many Foreigners have laid the Seat of their Fortunes in Swedeland; and, besides that, there be divers People of the Subjects of Your Most Serene Majesty, who speak a Language only proper to themselves; the Latin Tongue being familiar to all in the European World, will best fit every one of them in Particular.  
Lastly, because Foreigners born under another Climate and Soil, have a desire to learn such things from us; as not long since, both the French and Italians undertook this Journey, not without the greatest labour; so, Great King, something will redound to the Immortality of your Name, from this Observation not only begun, but likewise perfected under the Auspicious Influences of your most Serene Majesty. The World is not ignorant, that God hath adorned and accumulated your Majesty with Endowments of all sorts, which we falling into the other Extreme do more sparingly commend; whilst studiously shunning the Mob of Flatterers so much detested by your Majesty, with a tacit Veneration only honour every Perfection drawn from the heap of your Imperial Virtues: Outlandish Men will not be silent in it; nor shall after-Ages neglect to extol it to Heaven with the justest Praises. As for what concerns this little Work, I ought not to conceal that it is not only below Mediocrity, but I am sensible will be far beneath the Hopes of your most Serene Majesty: For since the Time that your Majesty unexpectedly imposed the Province upon me of a most different Nature from this Affair; for some Years together I threw away the Rule and Compass, as unprofitable Instruments for the Course of Life which was then to be taken; and hid those old Masters in a certain Corner of my Library, which still fills up a little Room in my House at Upsal; but now endeavouring to wipe off that filthy Rust from my Mathematical Instruments, which they had contracted by lying by, I have made it my Business, that rather Power than Will should be wanting in me so far distant from my Books; and because a great Strife amongst your Subjects in the Veneration of your Serene Royal Majesty grows daily warmer; as for me, the least share of them, if I cannot act equally to the rest, yet certainly will never suffer myself to be outdone by any in Obedience, Reverence, Observance, submissive Respects, and a devoted Disposition. To the very last I will humbly implore the Divine Majesty of the Supreme God, that he will vouchsafe perpetually to preserve your Majesty, the Glory of Kings, (given from Heaven to promote his Honour, and conserve our Country) healthful, vigorous, undisturbed, and cheerful to us, and to them that are, and shall be born of us: So wishes, and will ever pray,  
Of Your most Serene and Royal Majesty, The Eternally, most Devoted Servant, John Bilberg.   

In Solstitium aestivum à Serenissimo, Potentissimoque PRINCIPE, CAROLO UNDECIMO, Suecorum, Gothorum, Vandalorumque REGE, In TORNEA Urbe spectatum expositumque à Celeberrimo Viro JOANNE BILBERG.  
TOrna, vetus septem sed nunc nova fama Trionum,  
Ultima Botniaci quam maris unda ferit:  
Grande tibi cessit, praesens quod suspicit aevum,  
Quodque canent semper postera secla, decus.  
Nuper Hyperboreum propius cum viserit axem  
CAROLUS, Augusti sideris instar habens;  
Quaque iit, in plausus sese utraque solveret Arctos,  
Et nova conciperet gaudia totus apex:  
In te, pervigilem, nocturno tempore, Phaebum  
Vidit, pro patria pervigil ipse sua:  
Vidit inocciduo radiantem lumine vultum,  
Perpetuoque die tum sua Regna frui.  
I nunc, quicunque es, nostris atque objice terris  
Aeternumque gelu, Cimmeriumque chaos.  
Haec lege, quae narrat Bilbergius, (Is quoque tantae  
Spectator lucis, Rege jubente, fuit)  
Cognosces quanto fulgore hic ferveat aestas;  
Quantaque naturae munera mitis alat.  
Cognosces, quam pura fluat, qua vescimur, aura;  
Quam fit, quod colimus, non sibi segne solum.  
Ut nulli faveat Titan impensius orae;  
Majores nusquam ducat ut ille moras.  
Hibernae noctes tolerentur, & aspera brumae  
Omnia nam redimit solstitiale jubar.   

THE CONTENTS.  

Chap. 1. THE Observation of His most Serene Royal Majesty. Page 1.  
Chap. 2. An Account of the Longitude of Places. Page 19  
Chap. 3. Diurnal and Nocturnal Observations of the Sun. Page 38  
Chap. 4. The Doctrine of Refractions. Page 52  
Chap. 5. The Constitution of the Frigid Zone. Page 75  
Chap. 6. The Latitudes of Places observed in our Return. Page 83  
Chap. 7. The Figure of the Earth, Variation of the Needle, and difference of Refractions under the Role, and Aequator. Page 96    
A VOYAGE Of the Late King of SWEDEN, etc.  

CHAP. I. The Observation of His most Serene Royal Majesty.  
IN the Ancient and Learned Ages, when it was the greatest Strife amongst Men, that Eternity should accompany the Glory of Arts and Sciences, they were carried in a short time to the height of Learning; for the Romans emulated the Greeks, the Greeks the Egyptians 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, should be slowly discovered; 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 through weakness of Judgement 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 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 inflamed with the burning Heat of the Wether, and thereupon undergoes its various Vicissitudes; and Experience joined to Reason doth sufficiently, and too much confirm, that no other 'Cause can be assigned of that Matter, than the departure of the Sun, its return, and various Situation; but that some Countries should 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 called into Question; and is not at this Day believed, 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 Situation of it, its Form, and Bounds; some Parts very well Peopled, whilst again some others are frequently void of Inhabitants, through the violence and extremity of Cold or Heat, for there are many altogether as great 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 could have easily and soon persuaded 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 should undergo so different Changes, to wit, that we should be sometimes destined to a perpetual Night; and again, under our sometimes unsetting Sun, have no room left us for Darkness; but that they should rather cry out,  

Triste solum, sterilis, sine fruge, sine arbore tellus,  
Frigus iners, illic habitant, pallorque tremorque,  
Et jejuna fames.—   

Sad Soil, Earth barren, without Fruit or Tree,  
Cold, Paleness, Shivering do Inhabit thee,  
And meager Hunger.—   
The Industry of that Italian is to be commended, who not long since viewed 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 sober 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 permettendo quello con la sua contenanza: Pair in un certo modo che sia degno di non minor osservatione e maraviglia in quest' effetto i'll 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 persuaded 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 prejudicated Opinions of our Infancy, which having sucked 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, persuade 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 sailed 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, should ever fall 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 surprised, 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 Governor of the Day, a motion so equal and constant to itself 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 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, should 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 situated 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 Summer's Solstice of 24 Hours; or which is the same, at that time the Sun doth not set as well from Natural as Optic Causes, before the 66th. degree be completed: 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 would not gain Credit from such as urge 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 moved 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, situated about 65° and 43′ of Latitude; whose Horizon, altho' it was in part hindered by Mountains and Woods, so that the Truth of this Matter could 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 fatigued by any Labours, conquered all these Difficulties: A little Tower being showed 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 viewed 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 disappeared; but about the 12th. Hour, and 6th. Minute after Midnight, or of our following Day, which was June the 15th the Sun passing again 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 Wether 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 surprised 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 ashamed for the Neglect of it, and that they were outdone by their King in so small a Share of Trouble, they humbly and submissively beseeched 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 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 fastened 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.  
IVnderwritten do testify this Description wholly to agree with the Observation of his most Serene Majesty, written with his own Hand,  
Torneo, June 15. 1694. John Hoghusen.  
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 Mathematics whose Talon it was to fetch such things out of their secret Places, and to demonstrate them; You, I say, aught to blush, and publicly acknowledge that your Science hath received this Improvement, not from yourselves, but from the most Potent King.  
Our most Gracious King having viewed these Countries, as he designed; and having traveled 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 Summertime without any Night, by the perpetual Twilights; and affirmed that he had spent a continued Day without any Night, a thing before heard, but not at all believed by him; and when that Business, known to very few, rendered 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 Judgement 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 answered, they believed it might be so through divers Natural Reasons to be determined by the Situation 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 by Geometrical Demonstrations, that they may show their Readers such Reasons, as do not persuade, but force them. By this means the Science of Astronomy had its Rise, Progress, and no ordinary Increase, first from the asiatics, 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 lie 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 Majestic Love for Learning, and Men of Letters, by his incredible and inexhausted Magnificence to them, hath brought not only the Mathematics; but all sorts of Sciences to that pitch, as neither we could hope, or Foreigners believe, they could 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 Setting of the Sun, and what they were with Refraction 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.   

CHAP. II. An Account of the Longitude of Places.  
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 Mathematic 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 Colleague in this sort of Studies; and that we should omit nothing that might conduce for the making of these Experiments, or any other of this Nature; and above all we were enjoined so to hasten our Journey, that we might be in the City Torneo, where the King's Observation was made, not only some days before the Summer-Solstice, but also that we should 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 Style, which is used in our Country, at a Season unusual, and not yet fixed, by reason of the Unseasonableness and Rigour of the Wether; 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, lest they be severed asunder; for two Boats placed at a certain distance from one another, make a Ponton, into which a Chariot 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 Chariots 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 hardened 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 Bankside only, so that no body could 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 Chariots, Boats, or on Horses, and afoot by turns.  
The City Torneo is situated by the River Torneo, rising in Lapland, a very pleasant Place, which the River makes, by parting itself into two Arms, and joining again where it discharges itself 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 dwelled 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 Merchandise 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 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 observed the Sun above the Horizon, noting the Time by the going of a most exact Clock, which showed 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 would 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 lest difference of them should not escape us; nor was any Calculation made by us, except the Instruments agreed most exactly. The same day in our first Observation, we 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 Sun's Meridian height had decreased to 47°. 45′. we gathered by an Astronomical Calculation, the true Motion of the Sun being considered, 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 Ecliptic being granted; but amongst the more Northerly, at several Times are rendered 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 could not be Astronomically obtained, 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 described 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 obtained: 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 Huygens, was the Inventor 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 disposed 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 could 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 Sun's 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 showed 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 could 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 Maps 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 Meridian's, 4°. 30′. gives the Intervals of Time 18′ Astronomically computed: The other of Fred. de Wit makes the Longitude of Stockholm, 36°. 20′. but of Torneo 41°. 10′. This difference of the Meridian's 4°. 50′. makes the measure of Time betwixt them 19′. 20″. A third of Scandinavia, by the same De Wit makes the Longitude of Stockholm 39°. 00. but that of Torneo precisely 44°. 00. which is the greatest, and produces the difference of the Meridian's of five Degrees; whence also in Time the difference of Meridian's is given 20 Minutes. But which of these two Tables is the latter 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 admired in so little and portable Machine's; nor did I think that it could by any Accident happen, that for so long a time they should mutually answer one another in the same Laws of Motion; and it is pleasant to be employed 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 observed by me; as likewise, that 72 Beats of the Pulse of the Artery, being Fasting, answer also to one Minute, 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 reckoned, 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 Ecliptic, lying inclined to the Equator, may beget some difference of Ascensions; but as these are very little 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 certify, 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.  
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, gained 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 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 itself 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 Egyptians, and at last brought 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 Hourglass 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' Time, the manner of making Dial's 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 determined; 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 Wether hindered us to determine it precisely, which seldom permitted us to see the Light of the Sun, either before or after Noon; and that scarcely except amongst the Clouds; so that a shadow could scarcely be distinguished 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 height 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.   

CHAP. III. Diurnal and Nocturnal Observations of the Sun.  
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 filled 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 Sun's Body above the Horizon, one fourth only being under it; So that the Centre of the Sun did really appear above the Horizon: We therefore Congratulated ourselves 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.  

Rex Carolus terras, quas Circulus Arcticus ambit,  
Dum peragrat, proprias atque tuetur opes:  
Miratur parere suis latissima sceptris,  
Sol ubi continua lampade lustrat humum.  
Hactenus & nostris haec sensibus invia, Princeps  
Nullus, ait, Phoebum vidit inocciduum.  
Substitit in votis Alphonsi gloria Regis;  
Curio se perpetuo lumine jactat Iber?  
Sobrietas sed enim, Pietas, vigilantia, cura,  
Sufficiunt Carolo munera tanta Dei.   
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 height 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, more of the Sun itself was seen than aught to have been.  

Daedalus, & fama est, fugiens Minoia regna,  
Praepetibus pennis ausu●●●e credere coelo,  
Insuetum per iter ge●●●as enavit ad Arctos.   
So we likewise being to pass to the cold Northern Parts, did not trust to swift Wings, but to Boats very slenderly fastened 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 would 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 seemed scarcely to get a Foot forward; and for several Hours to advance but so many Paces; and sometimes by long bend 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 could be otherwise expected by Humane Assistance; but it seemed very hard, and strangely unusual to us, that on the Bankside there was no room between the Thorns and Brambles, and heaps of Stones where we could set our Feet; since being wearied with the Fatigue of this Haling, we attempted rather to make our Journey afoot, 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, covered both sides of the River, and they also so sloping and craggy, that every moment we dreaded their fall, together with our own Ruin: 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; but if it did any where happen, that the course of these Mountains was interrupted we joyfully leapt 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 Valleys.  
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 Countryman's 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 hindered 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 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 tried 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 favoured 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 between 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 bend through Monier and Kengis; but the left is excluded from the Western side, and the Lake Torn, situate almost in the Confines of Norway, and is here precipitated with that violence through 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 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 Wether, we took the height 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 itself 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 straight to the Northward, the Inhabitants declared, that it was not in 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 seemed 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 performed all that was to be done, we resolved to take our Course homeward. 
Tum verò nautae incumbunt, & littore parvas  
Deducunt sur do naves; natat uncta carina.  At our going away we had great plenty of Metals, which with great Care are drawn out of the Metallic Veins of Lapland; and those rich enough in Copper and Iron, and yet not carried out without great Charges, and very mighty Risks, through 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 Lodestones there have very little force; and yet in one of them, which I still keep, I perceive it daily increases, and I hope that they will augment in time, being armed.  
Magnets are found in the Iron Mines of Sweden, and elsewhere; but those of Lapland excel 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 should 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, followed 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, if not to outdo, the swiftness of the Waters; this was absolutely necessary, lest the Impetuosity being swifter than the Boats Course, should fill our Boat with Water, and so drown it with its Waves, especially when the Waters a head of us, being rolled with the greatest violence amongst the sharpest Rocks, Whirlpools, and deepest Gulfs, returning with like force, should meet the Head of the Boat, and so detaining it as it were in a Whirlpool, should appear altogether to overset it. In these straits we were sensible 
Quantoque ratem qui temperat anteit  
Remigis officium; quanto Dux milite major.  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 astonished, that when we were delivered from Dangers, we could scarcely believe ourselves to be in Safety; but their Art appeared still more, and especially in some certain Places. Those that are the most Experienced 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, recompense their smallness by the violence and rapidity of their Waves. Neither can they be passed at any time, except by the most able Boat-men 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 hazard, as we have sometimes beheld from the Shore with horror; but necessity imposed that Law on them, for this is the King's Highway, 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 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, wherever 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.  
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 Judgements; but by your leave we interpose ours also, most freely suffering every one to abound in his own sense. 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 subtle part of the Science of Optics, we will briefly lay down some things for the use of Students, whereby they may with greater ease take our Demonstrations.   

CHAP. IU. The Doctrine of Refraction.  
MAny are the Arts and Sciences which owe their beginnings to Chance and Fortune; which would 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) at this Entry the Ray proceeds no more straight 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 subtle, 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 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 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, diffused 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 splendour 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 Splendour, 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 smoky and thick Exhalations, drawn from the Terrestrial Globe by the help of the Sun, and subterraneous Fire, according 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 Almanac) that the Ray entering into the Atmosphere is variously determined, nor cannot go forward in straight 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 Board's, not contiguous enough, 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.  
Let T. be the Centre 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 Celestial 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 would fall sooner on the Convex of the Earth's Globe, than upon the Horizontal Line O. B. D. and so that Body would 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 would 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 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. should 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 Celestial 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 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 should have been four Degrees below the Horizon, which certainly is a Paradox; for by this reason the Horizontal Refraction increased 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 could not commit so great an Error in their Observation. Certainly the exact noting of the Time by a corrected Clock; and that hindered by the Frost, by an Hourglass of Twelve Hours; as also the conjunction of the Moon and Jupiter, observed by them, by which compared with Ephemerideses, they found out the Longitude of the Place. This they related more at large, say they, lest any should 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 foundout Elevation of the Pole at Torneo, 65°. 17′. that being taken from a Quadrant 90°. gives the Compliment 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 Ecliptic, which is commonly 23°. 30′. be taken from it, the residue will be 47′ for the place of the Sun below the Horizon.  
In ●● L Q. be ●he Meridian at 〈◊〉 〈◊〉 this Diagram, P L. the Axis of the World, A 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 Compliment, 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 Sun's Parallax too big. 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 should appear in its Centre, being Elevated above the Horizon, three fourth Parts of its Body, to wit, 22′ 30″. Since therefore 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 itself of the Eccliptick, by this Hypothesis the Sun will also be Elevated one half above the Horizon, without Refraction, when its Centre is in the Horizon itself; but adding the usual Refraction, the inferior Limb will be Elevated at Torneo, above 19′ which yet contradicts Observations.  
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 Centre 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 it's 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, which we had at that Season in three Places, that the inexperienced in Mathematics may judge more rightly of them, and understand their true and genuine Sense.  
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 Compliment, E. L. of the Pole, E. F. the Tropic of Cancer, G. K. the Tropic 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 Tropic, and again descending to the Parallel, it does not reach the Horizon, but that whole Line will not set.   

CHAP. V. Of the Constitution of the Frigid Zone.  
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 could not show the Hour of the Night on our Dial's: 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 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 hindered 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 filled bottom, but with Refraction; which Composition, except you take heed, shows to you one thing sometimes falsely, under a double Image, or somewhat greater than it should be; and further, many things may be Objected about the Maritine Observations of Peasants; and we very often want the Confirmation of fisher-men's 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 Celestial 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 ourselves to be persuaded 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; 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 should 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 than they did conjecture, that they should 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 could be exposed to any inconvenience by the violence of the Cold Wether.  
But here is one thing which I would 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 passed 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 could testify 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.  
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.  
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 tried the next Day to take the height of the Sun; but this hope vanished 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, where the Observation was taken, seems to be situate directly to the Westward of it.   

CHAP. VI The Latitudes of Places observed in our Return.  
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. but by the Carelessness 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 ruined by an accidental Fire, and from those Ruins, 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 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; 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 holidays; 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 Governor of that Province.  
On the 29th leaving that Place, and going through the Borders of Western Bothnia, which altho' it be more Northerly, yet is happy in a more convenient Soil than the Country's 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, threatening Ruin, 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 Superintendent 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.  
On the 7th. of July in the Town Medelpadia Sundswald, we endeavoured to find the Latitude of the Place; but Heaven also opposed it. When therefore all things seemed to thwart our Labours, which we could 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 height 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.  
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 were produced 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 Governor 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 wished, 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 lie almost in the same Latitude as Gefle.  
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 Merchandise, 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.  
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 through 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 itself 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, harkened to us with a Countenance full of Grace and Majesty; 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 wondered at nothing more, than that the Most Serene King being loaded with such a weight of Empire, and perplexed with infinite Cares, should, 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; 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 Rejoiced that we had obtained the height 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; 
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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, through Holmia, before we came to Upsal. We saw besides the said Cities Orebro, Arboga, Torshella, Strangnans, Mariefred, Sodertelus, and Stockholm. So that in all we passed through Twenty Four of them in a direct way.   

CHAP. VII. The Figure of the Earth, Variation of the Needle, and difference of Refractions under the Pole and Aequator.  
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 Critics, 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 of those Countries, who for some Time had the Charge of it. The Antiquities of the several 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, aught 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 Impediments before expressed, we could 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, 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 solicitous, 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 Mathematics, will make to be Triangular or Cubical, since the Superficies of the Water and Earth returning into itself 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 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 Atlantic Sea, by a straight he sound out, got into the Eastern Ocean, and by that way came to the Moluccos Islands; in which Voyage, when he had sufficiently viewed enough that Country, he might have returned 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 the East, by the Indian Ocean, and Atlantic; and lest any should think, that the Face of the Continent is different from that of the Waters, let him consider, that the Ocean is distinguished 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 height. For here is no Controversy 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 Spherical near the Aequator, which we know to be inequal, altho' it is supposed to be equal; for the Earth is not the Centre of that Motion; yet would it not follow, that a Sphere is form by Motion, equally 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 Valleys 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 of the Earth, than the Risings of those Mountains we before mentioned; 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 Celestial Vortices, which peradventure would produce some variety in a Spherical Figure; so that this Hypothesis should 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 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 Judgement of the Figure of the Earth; but the steep tops of Mountains, the Moorish Grounds, and inaccessible Woods, rendered 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 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 Arctic Pole, except beyond the Sixth Degree, on this side of the Aequator; but the Antarctic 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 could bring many probable Arguments, if the Matter was to our purpose.  
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〈◊〉 〈◊〉 〈◊〉 〈◊〉 〈◊〉.   
FINIS.  

BOOKS Printed for, and Sold by Edward Castle NEAR WHITEHALL.  
I. THe Whole Works of that excellent Practical Physician, Dr. Thomas Sydenham.  
II. An Epitome of the whole Practical part of Physic, contained in the Works of the Learned Dr. Willis. With a Treatise of the Plague, its Nature and Cure, etc.  
III. A Letter to the Deists.  
IV. A List of all the Offices and Officers of England, both Civil and Military, in Church and State. With a Table for finding out any Office or Officer therein.  
V. Contemplations Moral and Divine. By Sir M. Hale, Knight, Late Lord Chief Justice of the King's-Bench.  
VI A Letter to the Right Reverend Edward Lord Bishop of Worcester, concerning some Passages relating to Mr. Locke's Essay of Humane Understanding. In a late Discourse of His Lordship's, in Vindication of the Trinity. By John Lock, Gent.  
VII. Mr. Locke's Reply to the Right Reverend the Lord Bishop of Worcester's Answer to his Letter, concerning some Passages relating to Mr. Locke's Essay of Humane Understanding. In a late Discourse of His Lordship's in Vindication of the Trinity.  
VIII. A Treatise of the Causes of Incredulity: Wherein are Examined the General Motives and Occasions which dispose Unbelievers to Reject the Christian Religion. With two Letters, containing a direct Proof of the Truth of Christianity. Translated from the French of Monsieur Le Clerc.  
IX. An Abridgement of Mr. Locke's Essay concerning Humane Understanding.  
X. The Reasonableness of Christianity, as it is delivered in the Scriptures. The Second Edition. To which is added, A Vindication of the same from Mr. Edward's Exceptions.  
XI. A Second Vindication of the Reasonableness of Christianity. By the Author of the Reasonableness of Christianity.  
XII. The Christians Pattern, or a Divine Treatise of the Imitation of Christ. Written in Latin by Thomas of Kempis, above 200 Years since. 8°.  
XIII. Historia Nuperae rerum mutationis in Anglia, in qua Res à Jacobo Rege, contra Leges Angliae, & Europae Libertatem, & ab Ordinibus Angliae contra Regem patratae, duobus Libris recensentur. Authore E. Burridge, A. M.