Transcriber's Note.

Apparent errors in mathematical expressions have been retained, although apparent typographical errors elsewhere in the text have been corrected. Inconsistencies in hyphenation have been retained.

The decimal point may be indicated by a "." or "," while illustrations are referred to as a "Plate" or a "Tab."

The frontispiece probably depicts Charles II.

The Table of Discourses has been amended to include one omitted title and to correct erroneous page numbers.

Fifth roots and "nth" roots are indicated by 5√ and n√ respectively.

M: V^er Gucht Sculp:

Miscellanea Curiosa.

CONTAINING A

COLLECTION

Of some of the Principal

PHÆNOMENA
IN
NATURE

Accounted for by the Greatest Philosophers of this Age;

BEING THE

Most Valuable Discourses, Read and Delivered to the Royal Society, for the Advancement of Physical and Mathematical Knowledge.

As also a Collection of Curious Travels, Voyages, Antiquities, and Natural Histories of Countries; Presented to the same Society.

In Three VOLUMES.

The Second Edition; To which is added, A Discourse of the Influence of the Sun and Moon on Humane Bodies, &c. By R. MEAD, M. D. F. R. S. And also Fontenelle's Preface of the Usefulness of Mathematical Learning.

VOL. I.

LONDON:

Printed by F. M. for R. Smith, at the Bible under the Piazza of the Royal Exchange in Cornhill. 1708.

TO THE
READER.

SOME of the Principal Discoveries and Enquiries, both in Physical and Mathematical Learning, being register'd in the Voluminous Journals of the Royal Society, are amongst a multitude of less useful Matters, so Obscurely hid, that but very few inquisitive Gentlemen ever so much as heard of them.

The Design therefore of the ensuing Collection, is to digest in a convenient Method, all the most curious Philosophical and Mathematical Discoveries, as they are to be met with, which may any way tend to the Use of Life or Advancement of Arts and Sciences.

And on this Occasion, it will be convenient to intimate to the Reader;

First, That the Theories and Discourses here collected, have already past the Censure of the Learned World: Who have acknowleg'd them the most satisfactory Accounts of Nature's Proceedings, wherein some of her greatest Depths are fathom'd, and a Foundation laid for Posterity to build an infinite Superstructure.

Secondly, That they are related (Verbatim) just as they were delivered in, or read before the Royal Society: For it has been the Opinion of the most Judicious among those Honourable Members, that it is impossible so to abridge them, (which are but Abridgments themselves) as not to render them obscure and unintelligible.

A Translation of Part of Monsieur Fontenelle's Preface to the Memoirs of the Royal Academy at Paris, in the Year 1699. treating of the Usefulness of Mathematical Learning.

BUT to what purpose should People become fond of the Mathematicks and Natural Philosophy. Of what use are the Transactions of the Academy? These are common Questions, which most do not barely propose as Questions; and it will not be improper to clear them.

People very readily call useless, what they do not understand. It is a sort of Revenge; and as the Mathematicks and Natural Philosophy are known but by few, they are generally look'd upon as useless. The reason of this is; because they are crabbed and not easily learnt.

We have a Moon to light us in the Night; What is it to us, say they, whether Jupiter hath four? Why so many laborious Observations, so many tedious Calculations to know exactly their Course? They'll not afford us the more Light for it; and Nature, which hath plac'd these little Planets without the reach of our Eyes, doth not seem to have made them for us. According to this plausible Argument they ought not to have been observ'd with a Telescope, nor study'd. But it is certain, that we had been considerable Loosers by it: For those who have some insight into the Principles of Geography and Navigation know, that since these four Moons about Jupiter have been discover'd, they have been more useful to those Sciences than our own Moon; and that they serve, and shall more and more serve to make new Sea-Charts, infinitely more exact than the Old; and are likely to save the Lives of a vast many Seamen. Did we reap no other advantage from Astronomy than this from these Satellites of Jupiter, that wou'd be sufficient to justifie those prodigious Calculations, those assiduous and nice Observations, this great number of elaborate Instruments, and this Noble Edifice built only for this Science. However the greatest part of Mankind know nothing of these Satellites of Jupiter, unless perhaps by hear-say, and that too confusedly; or else they are ignorant of what Affinity they have with Navigation, or of the great Improvements which have been lately made in it.

This is the Fate of Sciences, which are study'd and improv'd by few. Most People are not sensible of their Progress, and especially when made in some mean Callings. But what doth it signifie, that we can now more easily direct the Course of Rivers, cut out Canals, and settle new Navigations; because our Method of taking the Level and making Sluces is infinitely better than heretofore? Some Masons and Seamen have thereby found their Business easier, but they themselves were not sensible of the Skill of the Geometrician who directed them. They were mov'd, as the Body by a Soul, it doth not know. Others are yet less sensible of the Genius that presided over the Undertaking; and the World is the better for its succeeding well, but not altogether free from Ingratitude.

Anatomy, which is some time since so carefully study'd, can't become more exact, but Chyrurgical Operations must also be more sure. Surgeons know this; but those who receive the Benefit of their Art know nothing of it. And indeed how should they? They would be oblig'd to compare Old with Modern Surgery; and this wou'd take too much Time, and go against the Grain: So that since the Operation hath succeeded well, they do not think it material to know whether it had succeeded as well in another Century.

It is strange that so many things are before our Eyes, and that we do not see them. Your Handycraft Shops are full of ingenious Works; but yet we hardly mind them: And very useful and well contriv'd Instruments and Experiments want Spectators, who wou'd be wonderfully pleas'd, wou'd they take the pains to admire them.

If a Learned Society have made some Improvements in Geometry, Anatomy, Mechanicks, or any other useful Science, it must not be expected, that the World will go back to so remote a Spring to thank and applaud them for the Usefulness of their Productions: For it will be more easie to enjoy the Benefit of their Discoveries and Improvements than to know them. The Determination of Longitude by the Satellites, the Discovery of the Ductus Thoracicus, a more convenient, and more exact Level, are not Novelties so fit to make a noise as a pleasant Poem, or a handsome Piece of Oratory.

Altho' the Usefulness of Mathematicks and Natural Philosophy is obscure, yet it is real. To consider Mankind in their Natural State, nothing is more useful to them, than what may preserve their Lives, and produce those Arts, which are both great Helps and Ornaments to Publick Societies.

As for what concerns the Preservation of Life, it peculiarly belongs to Physick; which for that reason is divided in the Academy into three Branches, which make three different sorts of Members of this Society, Anatomy, Chymistry, and Botanicks. Every Body knows of what Importance it is to have an exact Knowledge of Human Body, and of what Medicines may be extracted from Minerals and Plants.

As for Arts, too tedious to be reckon'd, they depend some upon Natural Philosophy, others upon Mathematicks.

One wou'd think at first, that if the Mathematicks were to be confin'd to what is useful in them, they ought only to be improv'd in those things, which have an immediate and sensible affinity with Arts, and the rest ought to be neglected as a Vain Theory. But this wou'd be a very wrong Notion. As for Instance, the Art of Navigation hath a necessary Connexion with Astronomy, and Astronomy can never be too much improv'd for the Benefit of Navigation. Astronomy cannot be without Opticks by reason of Perspective Glasses; and both, as all other Parts of Mathematicks, are grounded upon Geometry, and to go as far as you can, even upon Algebra.

Geometry, and especially Algebra, are the Keys of all the Inquiries, that can be made concerning Magnitude. These Sciences which are only conversant about abstruse Relations, and simple Ideas, may seem dry and barren, whilst they keep within the Verge of the Intellectual World; but mixt Mathematicks, which stoop to Matter, and consider the Motion of the Stars, the Augmentation of moving Forces, the different Passages of the Rays of Light through different Mediums; the different Effects of Sound by the Vibration of Things; to conclude all those Sciences, which discover the particular Relations of Sensible Magnitudes go on farther and more securely, when the Art of discovering Relations in General is more perfect. The Universal Instrument cannot be too extensive, too handy, or too easily apply'd: It is useful to all the Sciences, and they cannot be without it: And therefore among the Mathematicians of the Academy, who are design'd to be useful to the Publick, the Geometricians and Algebrists make a Class, as well as the Astronomers and Mechanicks.

However, it is certain, that Speculations purely of Geometry, or of Algebra, are not about useful things: But it is certain too, that those that are not, either lead or belong to those that are. It is in it self a very barren thing to know, that in a Parabola a Subtangant is double the corresponding Abscissæ; but yet it is a Degree of Knowledge necessary to the Art of throwing Bombs, so exactly as they can do now. There are not by far so many evident Uses as Propositions or Truths in the Mathematicks: Yet it is enough if the Concourse of several Truths is generally of some use.

Farther, a Geometrical Speculation, which was not at first applicable to any use, becomes so afterwards. When the greatest Geometricians in the Seventeenth Century set about to study a new Curve, which they call'd a Cycloide, they only engag'd themselves in a meer Speculation out of Vanity, striving to outdo one another by the Discovery of difficult Theorems. They did not even pretend that this was for the Publick Good; however by diving into the Nature of the Cycloide it was found, that it was destin'd to make Pendulums as perfect as may be, and carry the Measure of Time as far as it can go.

It is the same thing with Natural Philosophy as with Geometry. The Anatomy of Animals seems insignificant; and it only concerns us to know that of Human Body. But yet some Parts of it, which are of so nice, or so confus'd a Make, that they are invisible, are sensible and manifest in the Body of an Animal. Hence it is, that Monsters themselves are not to be neglected. The Mechanism conceal'd in a particular Kind or in a common Make, is unfolded in another kind, or in an extraordinary Make; and one wou'd be almost apt to say, that Nature by multiplying and varying so much her Works, can't sometimes forbear betraying her Secrets. All that the Antients knew of the Load-stone, was, that it attracts Iron. But whether they did not value a Curiosity, which promis'd them nothing; or that their Genius did not lead them to make Experiments, they have not examin'd this Stone as carefully as they might. One Experiment taught them, that it turns of its self towards the Poles of the World, and did put into their Hands the inestimable Treasure of the Mariners Compass. They might easily have made this Discovery important, and yet they did not do it; and if they had spent a little more time upon a Curiosity which seem'd useless to them, the Latent use of it had soon appear'd.

Let us always make a Collection of Mathematical and Physical Truths; happen what it will we can't hazard much by it. It is certain, that they shall be drawn from Springs, whence a great many useful ones have already been drawn. We have reason to presume, that we shall draw from thence, some that shall shine as soon as they are discover'd, and convince us of their Usefulness. Other Truths shall stay some time till a piercing Meditation, or some happy Accident discovers their Use. Some Truths being consider'd by themselves shall be barren, till they are consider'd with reference to one another. Lastly, let the worse come to the worse, some shall be eternally useless.

I mean useless with reference to sensible and gross Uses; for otherwise they shall not be so. An Object upon which alone you cast your Eyes is the clearer and brighter, when the neighbouring Objects, which however you do not look upon, are also enlighten'd; because it hath the Benefit of the Rays, which are reflected from them. Thus those Discoveries, which are palpably useful, and deserve our chiefest Attention, are in some measure enlighten'd by those, which may be call'd useless. For all Truths make one another more lucid.

It is always useful to have right Notions, even of useless Subjects. And tho' we cou'd reap no benefit by the Knowledge of Numbers and Sines, yet it wou'd still be the only certain Knowledge granted to our Natural Light, and they wou'd serve to give our Reason the first Habit of and Inclination to Truth. They wou'd teach us to operate upon Truths; to take the Thread of them, which is generally very fine and almost imperceptible; and to follow it as far as it reaches: In a word, they wou'd make Truth so familiar, that we might on other Occasions know it at first sight, and almost by Instinct.

A Geometrical Genius is not so confin'd to Geometry, but that it may be capable of learning other Sciences. A Tract of Morality, Politicks, or Criticism, and even a Piece of Oratory, supposing the Author qualify'd otherwise for those Performances, shall be the better for being compos'd by a Geometrician. That Order, Perspicuity, Precision and Exactness, which some time since are found in good Books, may originally proceed from that Geometrical Genius, which is now more common than ever, and in some manner is communicated by one Relation to another, nay even to those that do not understand Geometry. Sometimes a Great Man draws all his Cotemporaries after him; and he who hath the justest Claim to the Glory of having settled a new Art of Arguing, was an Excellent Geometrician.

Lastly, whatever raises us to Great and Noble Reflexions, tho' they be purely Speculative, afford a Spiritual and Philosophical Utility. The Wants of the Mind are perhaps as many as those of the Body. She desires to extend her Knowledge: All that can be known, is necessary to her, and there can be no better Proof than this, that she is design'd for Truth. Nothing perhaps can redound more to her Glory, than the Pleasure that is felt sometimes, in spight of ones self, in the dry and crabbed Questions of Algebra.

But without running counter to the common Notions, and recurring to Advantages which may seem too far fetch'd and refin'd, it may fairly be own'd, that the Mathematicks and Natural Philosophy have some things which are only subservient to Curiosity; and so have those Sciences which are most generally acknowledg'd to be useful, as History, &c.

History doth not in every Part of it supply us with Examples of Vertue and Rules for our Behaviour. For besides these, therein you have a View of the perpetual Revolutions of Human Affairs, of the Beginning and Fall of Empires, of Manners, Customs, and Opinions which continually succeed one another; and in a word, of all that rapid, tho' insensible, Motion that carries all before it, and incessantly alters the Face of the Earth.

Had we a mind to oppose Curiosity to Curiosity, we shou'd find that instead of the Motion, which agitates Nations, and gives birth to, and destroys States; Natural Philosophy considers that Great and Universal Motion, which hath put the whole Frame of Nature in Order, and suspended the Cœlestial Bodies in several Spheres, and which illuminates and extinguishes some Stars; and by following always unalterable Laws, diversifies its effects ad infinitum. If the surprising difference of Manners and Opinions of Mankind is so entertaining; there is too a great deal of Pleasure to study the prodigious diversity of the Structure of the different Species of Animals, with reference to their different Functions, to the Elements they live in, to the Climates they inhabit, and the Aliments they are to take, &c. The most curious strokes of History shall hardly be more curious than the Phosphorus, the cold Liquors which being mixt together, break out into a flame; Silver Trees, the almost Magical Operations of the Load-Stone, and a vast number of Secrets, which Art hath discover'd by a near and diligent Scrutiny of Nature.

Lastly, Natural Philosophy doth as much as it is possible unravel the Footsteps of that Infinite Intellect and Wisdom, who hath made all things: Whereas the Object of History are the disorderly Effects of the Passion, and of Humane Caprices; and so odd a Series of Events, that some formerly fancy'd that a Blind and Senseless Deity had the Direction of them.

We must not look upon the Sublime Reflexions which Natural Philosophy leads us to make concerning the Author of the Universe, as meer Curiosities. For this stupendous Work, which appears always more wonderful the more we know it, gives us such exalted Notions of its Maker, that they fill our Minds with Admiration and Respect. But above all, Astronomy and Anatomy are the two Sciences which more palpably lay before us two grand Attributes of our Creator; one his Immensity by the distance, Magnitude and Number of Cœlestial Bodies; the other his Infinite Knowledge by the Mechanism of Animals. True Natural Philosophy is a kind of Theology.

The different views of Humane Understanding are almost infinite; and Nature is really so. So that we may every day expect some Discoveries, either in Mathematicks or Natural Philosophy, which shall be of a new sort of Utility or Curiosity. Make a Collection of all the different Advantages which the Mathematicks afforded a Hundred Years ago, and you'll find nothing to be compar'd to the Perspective Glasses they have furnish'd since that time, and which are a new Organ to the Sight, and cou'd not be expected from Art. How surpriz'd had the Ancients been, if they had been told that their Posterity, by the help of some Instruments, shou'd one day see a vast number of Objects which they did not see; a Heaven that was unknown to them; and Plants and Animals they did not even suspect it was possible to exist. Naturalists had already a great many curious Experiments; but within about half a Century, the Air-Pump hath produced a prodigious quantity of them wholly new, and which by shewing Bodies in a Space void of Air, shews them as transported in a World different from ours, where they undergo Alterations whereof we had no Notion. The Excellency of Geometrical Methods, which are every day invented and improv'd, may perhaps at last exhaust Geometry; that is, The Art of making Geometrical Discoveries, and that is all: Whereas Natural Philosophy, which contemplates an Object of an unlimited Variety, and Fæcundity, shall always find room for new Observations, and opportunities to increase its vast Stock, and shall have the Advantage of never being a compleat Science.

There are so many things to be discover'd, whereof a great part, in all likelyhood shall never be known; that they give an opportunity to those who will not encounter with the Thorns and Difficulties of Natural Philosophy, to affect a sort of Discouragement. A great many to vilify this Natural Science, pretend a mighty veneration for the works of Nature, and that they are absolutely incomprehensible. However, Nature is never so admirable, nor so admir'd as when known. True it is, that what is known is inconsiderable in comparison of what is not yet known. Nay, Sometimes what is not known, is exactly what seems shou'd be the soonest known. As for instance, it is not at least certainly known, why a Stone thrown up into the Air falls down again; but we certainly know the cause of the Rainbow, why it doth not exceed a certain height; why its breadth is always the same; why when there are two Rainbows at the same time, the Colours of the one are overset with reference to the Colours of the other; and yet the fall of a Stone in the Air appears a more simple Phænomenon, than the Rainbow. But in a word, altho' we do not know every thing, we are not neither ignorant of every thing. And altho' we are ignorant of the most simple Events, yet we have a knowledge of what seems the most Complex. So that if we have on the one hand reason to fear, lest our Vanity shou'd flatter us with the hopes of attaining to the knowledge of things above our reach; on the other we ought to dread, lest our Slothfulness should also flatter us that we are condemn'd to a greater degree of Ignorance than really we are.

People may think that the Sciences do not begin to exert themselves, either because they cou'd be but imperfect among the Ancients; or because we have almost lost the Footsteps of them during the gloomy Darkness of Barbarity; or because a better method hath been taken about 100 Years ago. Was the Progress Historically examin'd, they have already made in so short a time, notwithstanding the strong, but false Prejudices they had long to encounter with, even sometimes the foreign Obstacles they have met with from Authority and Power; the want of Zeal for Sciences so remote from common use, those few who apply'd themselves to this Work, and the weak Motives which engag'd them in it; a Man would wonder at the Greatness and Rapidity of the Progress of the Sciences, and even we might observe some new ones to start out of nothing, and perhaps be tempted to have too great hopes of future Improvements.

The greater reason we have of future Success, the greater we have to look upon the Sciences as in their Cradles, at least Natural Philosophy. And therefore the Academy is only now employ'd to make an ample Provision of Observations, and Facts well attested, which may one day be the foundation of a System. For before the Systematical Natural Philosophy can raise solid Edifices; Experimental Natural Philosophy must be in a condition to supply it with good Materials.

None but Societies, of those too countenanc'd and encourag'd by the Prince, can successfully make and prepare this Collection of Materials. All the Learning, Care, Life and Wealth of one Private Man can never answer this Design. There are too many different Experiments to be made, which are to be too much vary'd, and a long time prosecuted with the same Temper and Mind. The Cause of the least Effect is so wrap'd up, that unless you very carefully open all the various Foldings, you cannot come at it.

Hitherto the Academy of Sciences hath consider'd Nature but by parcels: They have fix'd upon no general System, for fear of falling into the inconveniency of hasty Systems, which are very grateful to the impatience of Humane Understanding; and being once settled, are Obstacles to what Truths are afterwards discover'd. This day we are sure of a Fact, to morrow we shall be sure of another that hath no relation with the former. However some Conjectures are ventur'd at upon Causes; but they are only Conjectures. So that this Collection, which the Academy gives to the Publick, is compos'd of separate Fragments, independant of one another; whereof every one who is the Author, warrants the Facts and Experiments; and whose Arguments are approv'd by the Academy, but with Restrictions becoming Wise and Wary Scepticks.

Time perhaps will come, when these scatter'd Fragments shall be united into one regular Body; and if they be such as they are wish'd, they may of themselves Unite. A great many Truths, when their Numbers is considerable, shew so near a Relation to, and so mutual a Dependance upon one another, that it seems, that notwithstanding their violent Separation, they have a natural Tendency to be re-united.

A
TABLE
OF THE
Discourses contain'd in this Volume.

Miscellanea Curiosa.

An Estimate of the Quantity of the Vapours raised out of the Sea derived from Experiment: Together with an Account of the Circulation of the watry Vapours of the Sea, and of the Cause of Springs, presented to the Royal Society. By Mr. E. Halley, F. R. S.

THAT the Quantity of Aqueous Vapours contain'd in the Medium of the Air, is very considerable, seems most evident from the great Rains and Snows which are sometimes observ'd to fall, to that degree, that the Water thus discharg'd out of the Interstices of the Particles of Air, is in weight a very sensible part of the incumbent Atmosphere: But in what proportion these Vapours rise, which are the Sources not only of Rains, but also of Springs or Fountains (as I design to prove) has not, that I know of, been any where well examin'd, tho' it seem to be one of the most necessary Ingredients of a Real and Philosophical Meteorology, and, as such; to deserve the Consideration of this Honourable Society. I thought it might not be unacceptable to attempt by Experiment to determine the Quantity of the Evaporations of Water, as far as they arise from Heat, which upon Trial succeeded as follows.

We took a Pan of Water, about 4 inches deep, and 7 Inches ⁹⁄₁₀ Diameter, in which we placed a Thermometer, and by means of a Pan of Coals, we brought the Water to the same degree of Heat, which is observed to be that of the Air in our hottest Summer; the Thermometer nicely shewing it: This done, we affixed the Pan of Water, with the Thermometer in it, to one end of the Beam of a Pair of Scales, and exactly counterpois'd it with weights in the other Scale; and by the application or removal of the Pan of Coals, we found it very easie to maintain the Water in the same degree of Heat precisely. Doing thus we found the weight of the Water sensibly to decrease; and at the end of two hours we observed that there wanted half an Ounce Troy, all but 7 grains, or 233 grains of Water, which in that time had gone off in Vapour; tho' one could hardly perceive it smoke, and the Water were not sensibly warm. This Quantity in so short a time seem'd very considerable, being little less than 6 ounces in 24 hours, from so small a Surface as a Circle of 8 inches Diameter. To reduce this Experiment to an exact Calculus, and determine the thickness of the Skin of Water that had so evaporated, I assume the Experiment alledg'd by Dr. Edward Bernard to have been made in the Oxford Society, viz. That the Cube-foot English of Water weighs exactly 76 Pounds Troy; this divided by 1728, the number of Inches in a Foot, will give 253⅓ grains, or ½ ounce 13⅓ grains for the weight of a Cube-inch of Water; wherefore the weight of 233 grains is ²³³⁄₂₅₃ or 35 Parts of 38 of a Cube-inch of Water. Now the Area of the Circle whose Diameter is 7⁹⁄₁₀ Inches, is 49 square Inches: by which dividing the Quantity of Water evaporated, viz. ³⁵⁄₃₈ of an Inch, the Quote ³⁵⁄₁₈₆₂ or ¹⁄₅₃ shews that the thickness of the Water evaporated was the 53d part of an Inch; but we will suppose it only the 60th part, for the Facility of Calculation. If therefore Water as warm as the Air in Summer, exhales the thickness of a 60th part of an Inch in two hours from its whole Surface, in 12 hours it will exhale the ⅒ of an Inch; which Quantity will be found abundantly sufficient to serve for all the Rains, Springs, and Dews; and account for the Caspian Sea, being always at a stand, neither wasting nor overflowing; as likewise for the Current said to set always in at the Streights of Gibralter, tho' those Mediterranean Seas receive so many and so considerable Rivers.

To estimate the Quantity of Water arising in Vapours out of the Sea, I think I ought to consider it only for the time the Sun is up, for that the Dews return in the Night, as much if not more Vapours than are then emitted; and in Summer the Days being no longer than 12 hours, this Excess is ballanc'd by the weaker Action of the Sun, especially when rising before the Water be warmed: So that if I allow ⅒ of an Inch of the Surface of the Sea, to be raised per diem in Vapours, it may not be an improbable Conjecture.

Upon this Supposition, every 10 square Inches of the Surface of the Water, yields in Vapour per diem a Cube-inch of Water; and each square Foot half a Wine-pint; every Space of 4 Foot square, a Gallon; a Mile square, 6914 Tons; a square Degree suppose of 69 English Miles, will evaporate 33 Millions of Tons: And if the Mediterranean be estimated at forty degrees long and four broad, allowances being made for the Places where it is broader, by those where it is narrower (and I am sure I guess at the least) there will be 160 Square degrees of Sea; and consequently, the whole Mediterranean must lose in Vapour, in a Summer's day, at least 5280 Millions of Tons. And this Quantity of Vapour, tho' very great, is as little as can be concluded from the Experiment produced: And yet there remains another Cause, which cannot be reduced to Rule, I mean the Winds, whereby the Surface of the Water is licked up some times faster than it exhales by the heat of the Sun; as is well known to those that have consider'd those drying Winds which blow sometimes.

To estimate the Quantity of Water, the Mediterranean Sea receives from the Rivers that fall into it, is a very hard Task, unless one had the Opportunity to measure their Chanels and Velocity; and therefore we can only do it by allowing more than enough; that is, by assuming these Rivers greater than in all probability they be, and then comparing the Quantity of Water voided by the Thames, with that of those Rivers, whose Waters we desire to compute.

The Mediterranean receives these considerable Rivers; the Iberus, the Rhone, the Tiber, the Po, the Danube, the Neister, the Borystenes, the Tanais, and the Nile; all the rest being of no great Note, and their Quantity of Water inconsiderable: These nine Rivers, we will suppose each of them to bring down ten times as much Water as the River Thames; not that any of them is great in reality, but to comprehend with them all the small Rivulets that fall into the Sea, which otherwise I know not how to allow for.

To calculate the Water of the Thames, I assume that at Kingston Bridge where the Flood never reaches, and the Water always runs down, the breadth of the Chanel is 100 Yards, and its Depth 3, it being reduced to an Equality (in both which Suppositions I am sure I take with the most) hence the Profil of the Water in this Place is 300 square Yards: This multiplied by 48 Miles (which I allow the Water to run in 24 hours, at 2 Miles an hour) or 84480 Yards, gives 25344000 Cubick-yards of Water to be evacuated every Day; that is, 20300000 Tons per diem; and I doubt not, but in the excess of my Measures of the Chanel of the River, I have made more than sufficient allowance for the Waters of the Brent, the Wandel, the Lea, and Darwent, which are all worth notice, that fall into the Thames below Kingston.

Now if each of the aforesaid 9 Rivers yield 10 times as much Water as the Thames doth, 'twill follow that each of them yields but 203 Millions of Ton per diem, and the whole 9, but 1827 Millions of Tons in a day; which is but little more than ⅓ of what is proved to be raised in vapour out of the Mediterranean in 12 hours time. Now what becomes of this Vapour when rais'd, and how it comes to pass that the Current always sets in at the Mouth, of the Streights of Gibralter, shall immediately be shew'd: But first it is necessary to advertise the Reader, that in making the Experiment herein mention'd, the Water used had been salted to the same degree as is the common Sea-water, by the Solution of about a 40th part of Salt.

HAving thus shew'd by Experiment the Quantity of Water raised in Vapour from the Surface of the Sea in a Days time, which was so far approv'd of by some Honourable Members of this Society, that I receiv'd their Commands to prosecute these Enquiries; and particularly, in relation to the Method used by Nature, to return the said Vapours again into the Sea; which is so justly perform'd, that in many hundred of Years we are sufficiently assured that the Sea has not sensibly decreased by the loss in Vapour; nor yet abounded by the immense Quantity of fresh it receives continually from the Rivers. To demonstrate this Equilibre of Receipt and Expence in the whole Sea, is a Task too hard for me to undertake, yet in obedience to those whom I have the Honour to serve, I shall here offer, what to me has hitherto seem'd the most satisfactory Account of this grand Phænomenon: I have in another place attempted to explain the manner of the rising of Vapour by Warmth, by shewing, that if an Atom of Water were expanded into a Shell or Bubble, so as to be ten times as big in Diameter as when it was Water; such an Atom would become specifically lighter than Air, and rise so long as that Flatus or warm Spirit that first separated it from the Mass of Water, shall continue to distend it to the same Degree; and that Warmth declining, and the Air growing cooler and also specifically lighter, the Vapours consequently shall stop at a certain Region of the Air, or else descend, which may happen upon several accounts, as I shall by and by endeavour to make out; yet I undertake not that this is the only principal of the rise of Vapours, and that there may not be a certain sort of Matter, whose Conatus may be contrary to that of Gravity; as is evident in Vegetation, where in the Tendency of the Sprouts is directly upwards, or against the Perpendicular. But what ever is the true Cause, it is in Fact certain, that warmth does separate the Particles of Water, and emit them with a greater and greater Velocity, as the heat is more and more intense; as is evident in the Steam of a boiling Cauldron, wherein likewise the Velocity of the ascent of the Vapours does visibly decrease till they disappear, being dispersed into and assimulated with the Ambient Air. Vapours being thus raised by warmth, let us for a first Supposition put, that the whole Surface of the Globe were all Water very deep, or rather that the whole Body of the Earth were Water, and that the Sun had its diurnal course about it: I take it, that it would follow, that the Air of it self would imbibe a certain Quantity of aqueous Vapours, and retain them like Salts dissolved in Water; that the Sun warming the Air, and raising a more plentiful Vapour from the Water in the day-time, the Air would sustain a greater proportion of Vapour, as warm Water will hold more dissolved Salts, which upon the absence of the Sun in the Nights would be all again discharged in Dews, analogous to the Precipitation of Salts on the cooling of the Liquors; nor is it to be believed that in such Case there would be any diversity of Weather, other than periodically, every Year alike; the mixture of all terrestrious, saline, heterogenious Vapours being taken away, which as they are variously compounded and brought by the Winds, seem to be the Causes of those various Seasons which we now find. In this case the Aiery Regions every where, at the same height, would be equally replenished with the Proportion of Water it could contain, regard being only to be had to the different degree of warmth, from the nearness or distance of the Sun; and an eternal East-wind would blow all round the Globe, inclining only to the same side of the East, as the Latitude doth from the Equator; as is observed in the Ocean between the Tropicks.

Next let us suppose this Ocean interspersed with wide and spacious Tracts of Land, with high Ridges of Mountains, such as the Pyrenean, the Alps, the Apennine, the Carpathian in Europe, Taurus, Caucasus, Imaus, and several others in Asia; Atlas and the Montes Lunæ, with other unknown Ridges in Africa, whence came the Nile, the Nigre, and the Zaire: And in America, the Andes and the Apalatean Mountains; each of which far surpass the usual height to which the Aqueous Vapours of themselves ascend, and on the tops of which the Air is so cold and rarified, as to retain but a small part of those Vapours, that shall be brought thither by Winds. Those Vapours therefore that are raised copiously in the Sea, and by the Wind, are carried over the low Land to those Ridges of Mountains, are there compelled by the Stream of the Air to mount up with it to the tops of the Mountains, where the Water presently precipitates, gleeting down by the Crannies of the Stone; and part of the Vapour entering into the Caverns of the Hills, the Water thereof gathers as in an Alembick into the Basons of Stone it finds; which being once fill'd, all the overplus of Water that comes thither runs over by the lowest place, and breaking out by the sides of the Hills, forms single Springs. Many of these running down by the Valleys or Guts between the Ridges of the Hills, and coming to unite, form little Rivulets, or Brooks: Many of these again, meeting in one common Valley and gaining the plain Ground, being grown less rapid, become a River; and many of these being united in one common Channel, make such Streams as the Rhine, the Rhone, the Danube; which latter, one would hardly think the Collection of Water condensed out of Vapour, unless we consider how vast a Tract of Ground that River drains, and that it is the Sum of all those Springs which break out on the South side of the Carpathian Mountains, and on the North side of the immense Ridge of the Alps, which is one continued Chain of Mountains from Switzerland, to the Black-Sea. And it may almost pass for a Rule, that the magnitude of a River, or the quantity of Water it evacuates, is proportionable to the length and height of the Ridges from whence its Fountains arise. Now this Theory of Springs is not a bare Hypothesis, but founded on Experience, which it was my luck to gain in my abode at St. Helena, where in the Night-time, on the tops of the Hills, about 800 Yards above the Sea, there was so strange a condensation, or rather precipitation of the Vapours, that it was a great Impediment to my Cœlestial Observations; for in the clear Sky, the Dew would fall so fast, as to cover, each half quarter of an Hour, my Glasses with little drops; so that I was necessitated to wipe them so often, and my Paper on which I wrote my Observations would immediately be so wet with Dew, that it would not bear Ink: By which it may be suppos'd how fast the Water gathers in those mighty high Ridges I but now nam'd.

Thus is one part of the Vapours blown upon the Land return'd by the Rivers into the Sea, from whence they came; another part by the cool of the Night falls in Dews, or else in Rains, again into the Sea before it reaches the Land, which is by much the greatest part of the whole Vapours, because of the great extent of the Ocean, which the motion of the Wind does not traverse in a very long space of Time; and this is the Reason why the Rivers do not return so much into the Mediterranean, as is extracted into Vapour. A third part falls on the Low-Lands, and is the Pabulum of Plants, where yet it does not rest, but is again exhaled in Vapour by the action of the Sun, and is either carried by the Winds to the Sea to fall in Rain or Dew there, or else to the Mountains to be there turn'd into Springs; and tho' this does not immediately come to pass, yet after several Vicissitudes of rising in Vapour, and falling in Rain or Dews, each Particle of the Water is at length return'd to the Sea from whence it came. Add to this, that the Rain-waters after the Earth is fully sated with moisture, does, by the Vallies or lower parts of the Earth, find its way into the Rivers, and so is compendiously sent back to the Sea. After this manner is the Circulation perform'd, and I doubt not but this Hypothesis is more reasonable than that of those who derive all Springs from the Rain-waters, which yet are perpetual and without diminution, even when no Rain falls for a long space of time; or that derive them from a Filtration or Percolation of the Sea-waters, thro' certain imaginary Tubes or Passages within the Earth wherein they lose their Saltness. This, besides many others, labouring under this principal Absurdity, that the greatest Rivers have their most copious Fountains farthest from the Sea, and whether so great quantities of fresh Water cannot reasonably be deriv'd any other way than in Vapour. This, if we may allow final Causes, seems to be the design of the Hills, that their Ridges being plac'd thro' the midst of the Continents, might serve, as it were, for Alembicks to distil fresh Water for the use of Man and Beast, and their heights to give a descent to those Streams to run gently, like so many Veins, of the Macrocosm to be the more beneficial to the Creation. If the difference between Rain and Dew, and the cause why sometimes 'tis Cloudy, at other times Serene, be inquir'd, I can offer nothing like a proper Solution thereof, only with submission to propose Conjectures, which are the best I can find, viz. That the Air being heaped up by the meeting of two contrary Winds, when the Mercury is high, the Vapours are the better sustain'd and kept from Co-agulating or Condensing into Drops, whereby Clouds are not so easily generated, and the Night the Vapours fall down single, as they rose in imperceptible Atoms of Water: Whereas, when the Mercury is low, And the Air rarified by the Exhaustion thereof, by two contrary Winds blowing from the place; the Atoms of Air keep the Vapours not so well separated, and they coalesce into visible Drops in the Clouds, and from thence are easily drawn into greater Drops of Rain; to which 'tis possible and not improbable, that some sort of Saline or Angular Particles of Terrestrial Vapour being immix'd with the Aqueous, which I take to be Bubbles, may cut or break their Skins or Coats, and so contribute to their more speedy Condensation into Rain.

The True Theory of the Tides, extracted from that admired Treatise of Mr. Isaac Newton, Intitled, Philosophiæ Naturalis Principia Mathematica; Being a Discourse presented with that Book to the late King James, by Mr. Edmund Halley.

IT may, perhaps, seem strange, that this Paper, being no other than a particular Account of a Book long since published, should now appear here; but the Desires of several honourable Persons, which could not be withstood, have obliged us to insert it here, for the sake of such, who being less knowing in Mathematical Matters, and therefore not daring to adventure on the Author himself, are notwithstanding, very curious to be inform'd of the Causes of Things; particularly of so general and extraordinary Phænomena, as are those of the Tides. Now this Paper having been drawn up for the late King James's Use, (in whose Reign the Book was publish'd) and having given good Satisfaction to those that got Copies of it; it is hoped the Savans of the higher Form will indulge us this Liberty we take to gratifie their Inferiours in point of Science; and not be offended, that we here insist more largely upon Mr. Newton's Theory of the Tides, which, how plain and easie soever we find, is very little understood by the common Reader.

THE sole Principle upon which this Author proceeds to explain most of the great and surprizing Appearances of Nature, is no other than that of Gravity, whereby in the Earth all Bodies have a tendency towards its Centre; as is most evident: And from undoubted Arguments it's proved, that there is such a Gravitation towards the Centre of the Sun, Moon, and all the Planets.

From this Principle, as a necessary Consequence, follows the Sphærical Figure of the Earth and Sea, and of all the other Cœlestial Bodies: And tho' the tenacity and firmness of the Solid Parts, support the Inequalities of the Land above the Level; yet the Fluids, pressing equally and easily yielding to each other, soon restore the Æquilibrium, if disturbed, and maintain the exact Figure of the Globe.

Now this force of Descent of Bodies towards the Centre, is not in all places alike, but is still less and less, as the distance from the Center encreases: And in this Book it is demonstrated, that this Force decreases as the Square of the distance increases; that is, the weight of Bodies, and the Force of their Fall is less, in parts more removed from the Center, in the proportion of the Squares of the Distance. So as for Example, a Ton weight on the Surface of the Earth, if it were raised to the height of 4000 Miles, which I suppose the Semidiameter of the Earth, would weigh but ¼ of a Ton, or 5 Hundred weight: If to 12000 Miles, or 3 Semidiameters from the Surface, that is 4 from the Center, it would weigh but ¹⁄₁₆ part of the Weight on the Surface, or a Hundred and Quarter: So that it would be as easie for the Strength of a Man at that height to carry a Ton weight, as here on the Surface a 100¼. And in the same Proportion does the Velocities of the fall of Bodies decrease: For whereas on the Surface of the Earth all things fall 16 Foot in a second; at one Semidiameter above, this fall is but four Foot; and at three Semidiameters, or four from the Centre, it is but ¹⁄₁₆ of the Fall at the Surface, or but one Foot in a second: And at greater Distances both Weight and Fall become very small, but yet at all given Distances is still some thing, tho' the Effect become insensible. At the distance of the Moon (which I will suppose 60 Semidiameters of the Earth) 3600 Pounds weigh but one Pound, and the fall of Bodies is but of ¹⁄₃₆₀₀ a Foot in a second, or 16 Foot in a Minute; that is, a Body so far off descends in a Minute no more than the same at the Surface of the Earth would do in a Second of Time.

As was said before, the same force decreasing after the same manner is evidently found in the Sun, Moon, and all the Planets; but more especially in the Sun, whose Force is prodigious; becoming sensible even in the immense distance of Saturn: This gives room to suspect, that the force of Gravity is in the Cœlestial Globes proportional to the quantity of Matter in each of them: And the Sun being at least ten Thousand times as big as the Earth, its Gravitation or attracting Force, is found to be at least ten Thousand times as much as that of the Earth, acting on Bodies at the same distance.

This Law of the decrease of Gravity being demonstratively proved, and put past contradiction; the Author with great Sagacity, inquires into the necessary Consequences of this Supposition; whereby he finds the genuine Cause of the several Appearances in the Theory of the Moon and Planets, and discovers the hitherto unknown Laws of the Motion of Comets, and of the Ebbing and flowing of the Sea. Each of which are Subjects that have hitherto taken up much larger Volumes; but Truth being uniform, and always the same, it is admirable to observe how easily we are enabled to make out very abstruse and difficult Matters, when once true and genuine Principles are obtain'd: And on the other hand it may be wondred; that, notwithstanding the great facility of truth, and the perplexity and nonconsequences that always attend erroneous Suppositions, these great Discoveries should have escaped the acute Disquisitions of the best Philosophical Heads of all past Ages, and be reserv'd to these our Times. But that wonder will soon cease, if it be consider'd how great improvements Geometry has receiv'd in our Memory, and particularly from the profound Discoveries of our incomparable Author.

The Theory of the Motion of the primary Planets is here shewn to be nothing else, but the contemplation of the Curve Lines which Bodies cast with a given Velocity, in a given Direction, and at the same time drawn towards the Sun by its gravitating Power, would describe. Or, which is all one, that the Orbs of the Planets are such Curve Lines as a Shot from a Gun describes in the Air, being cast according to the direction of the Piece, but bent in a crooked Line by the supervening Tendency towards the Earths Centre: And the Planets being supposed to be projected with a given Force, and attracted towards the Sun, after the aforesaid manner, are here proved to describe such Figures, as answer punctually to all that the Industry of this and the last Age has observed in the Planetary Motions. So that it appears, that there is no need of solid Orbs and Intelligences, as the Antients imagin'd, nor yet of Vortices or Whirlpools of the Cœlestial Matter, as Des Cartes supposes; but the whole Affair is simply and mechanically performed, upon the sole Supposition of a Gravitation towards the Sun; which cannot be denied.

The Motion of Comets is here shewn to be compounded of the same Elements, and not to differ from Planets, but in their greater swiftness, whereby overpowering the Gravity that should hold them to the Sun, as it doth the Planets, they flie off again, and distance themselves from the Sun and Earth, so that they soon are out of our sight. And the imperfect Accounts and Observations Antiquity has left us, are not sufficient to determine whether the same Comet ever return again. But this Author has shewn how Geometrically to determine the Orb of a Comet from Observations, and to find his Distance from the Earth and Sun, which was never before done.

The third thing here done is the Theory of the Moon, all the Inequalities of whose Motion are proved to arise from the same Principles, only here the effect of two Centers operating on, or attracting a projected Body, comes to be considered; for the Moon, though principally attracted by the Earth, and moving round it, does together with the Earth, move round the Sun once a Year, and is, according as she is nearer or farther from the Sun, drawn by him more or less than the Center of the Earth, about which she moves; whence arise several Irregularities in her Motion, of all which, the Author in this Book, with no less Subtility than Industry, has given a full account. And though by reason of the great Complication of the Problem, he has not yet been able to make it purely Geometrical, 'tis to be hoped, that in some farther Essay he may surmount the difficulty: And having perfected the Theory of the Moon, the long desir'd Discovery of the Longitude (which at Sea is only practicable this way) may at length be brought to light, to the great Honour of your Majesty, and Advantage of your Subjects.

All the surprising Phænomena of the Flux and Reflux of the Sea, are in like manner shewn to proceed from the same Principle; which I design more largely to insist on, since the Matter of Fact is in this Case much better known to your Majesty than in the foregoing.

If the Earth were alone, that is to say, not affected by the Actions of the Sun and Moon, it is not to be doubted, but the Ocean, being equally press'd by the force of Gravity towards the Center, would continue in a perfect Stagnation, always at the same height, without either Ebbing or Flowing; but it being here demonstrated, that the Sun and Moon have a like Principle of Gravitation towards their Centers, and that the Earth is within the Activity of their Attractions, it will plainly follow, that the Equality of the pressure of Gravity towards the Center will thereby be disturb'd; and though the smallness of these Forces, in respect of the Gravitation towards the Earth's Center, renders them altogether imperceptible by any Experiments we can devise, yet the Ocean being fluid and yielding to the least force, by its rising shews where it is less press'd, and where it is more press'd by its sinking.

Now if we suppose the force of the Moon's Attaction to decrease as the Square of the Distance from its Center increases (as in the Earth and other Cœlestial Bodies) we shall find, that where the Moon is perpendicularly either above or below the Horizon, either in Zenith or Nadir, there the force of Gravity is most of all diminished, and consequently that there the Ocean must necessarily swell by the coming in of the Water from those parts where the Pressure is greatest, viz. in those places where the Moon is near the Horizon: But that this may be the better understood, I thought it needful to add the following Figure, (Vide Fig. 1. Plate 1.) where M is the Moon, E the Earth, C its Center, and Z the place where the Moon is in the Zenith, N where in the Nadir.

Now by the Hypothesis it is evident, that the Water in Z, being nearer, is more drawn by the Moon, than the Center of the Earth C, and that again more than the Water in N; wherefore the Water in Z hath a tendency towards the Moon, contrary to that of Gravity, being equal to the excess of the Gravitation in Z, above that in C: And in the other case, the Water in N, tending less towards the Moon than the Center C, will be less pressed, by as much as is the difference of the Gravitation towards the Moon in C and N. This rightly understood, it follows plainly, that the Sea, which otherwise would be Spherical, upon the Pressure of the Moon, must form it self into a Spheroidal or Oval Figure, whose longest Diameter is where the Moon is vertical, and shortest where she is in the Horizon; and that the Moon shifting her Position as she turns round the Earth once a Day, this Oval of Water shifts with her, occasioning thereby the two Floods and Ebbs observable in each 25 Hours.

And this may suffice, as to the general Cause of the Tides; it remains now to shew how naturally this Motion accounts for all the Particulars that have been observ'd about them; so that there can be no room left to doubt, but that this is the true cause thereof.

The Spring Tides upon the New and Full Moons, and Neap Tides on the Quarters, are occasion'd by the attractive Force of the Sun in the New and Full, conspiring with the Attraction of the Moon, and producing a Tide by their united Forces: Whereas in the Quarters, the Sun raises the Water where the Moon depresses it, and the contrary; so as the Tides are made only by the difference of their Attractions. That the force of the Sun is no greater in this Case, proceeds from the very small Proportion the Semi-diameter of the Earth bears to the vast distance of the Sun.

It is also observ'd, that cæteris paribus, the Æquinoctial Spring Tides in March and September, or near them, are the Highest, and the Neap Tides the lowest; which proceeds from the greater Agitations of the Waters, when the fluid Spheroid revolves about a great Circle of the Earth, than when it turns about in a lesser Circle; it being plain that if the Moon were constituted in the Pole, and there stood, that the Spheroid would have a fix'd Position, and that it would be always high Water under the Poles, and low Water every where under the Æquinoctial: And therefore the nearer the Moon approaches the Poles, the less is the agitation of the Ocean, which is of all the greatest, when the Moon is in the Æquinoctial, or farthest distant from the Poles. Whence the Sun and Moon, being either conjoined or opposite in the Æquinoctial, produce the greatest Spring Tides; and the subsequent Neap Tides, being produc'd by the Tropical Moon in the Quarters, are always the least Tides; whereas in June and December, the Spring Tides are made by the Tropical Sun and Moon, and therefore less vigorous; and the Neap Tides by the Æquinoctial Moon, which therefore are the stronger: Hence it happens, that the difference between the Spring and Neap Tides in these Months, is much less considerable than in March and September. And the reason why the very highest Spring Tides are found to be rather before the Vernal and after the Autumnal Equinox, viz. in February and October, than precisely upon them, is, because the Sun is nearer the Earth in the Winter Months, and so comes to have a greater effect in producing the Tides.

Hitherto we have consider'd such Affections of the Tides as are Universal, without relation to particular Cases; what follows from the differing Latitudes of places, will be easily understood by the following Fig. (Vide Fig. 2. Plate 1.)

Let ApEP be the Earth cover'd over with very deep Waters, C its Center, P, p, its Poles, AE the Æquinoctial, F, f, the parallel of Latitude of a Place, D, d, another Parallel at equal distance on the other side of the Æquinoctial, H, h, the two Points where the Moon is vertical, and let K, k, be the great Circle, wherein the Moon appears Horizontal. It is evident, that a Spheroid describ'd upon Hh, and Kk, shall nearly represent the Figure of the Sea, and Cf, CD, CF, Cd, shall be the heighths of the Sea in the places f, D, F, d, in all which it is High-water: And seeing that in twelve Hours time, by the diurnal Rotation of the Earth, the Point F is transferr'd to f, and d to D: The height of the Sea CF will be that of the High-water when the Moon is present, and Cf that of the other High-water, when the Moon is under the Earth: Which in the case of this Figure is less than the former CF. And in the opposite Parallel Dd, the contrary happens. The Rising of the Water being always alternately greater and less in each place, when it is produc'd by the Moon declining sensibly from the Æquinoctial; that being the greatest of the two High-waters in each diurnal Revolution of the Moon, wherein she approaches nearest either to the Zenith or Nadir of the place: Whence it is, that the Moon in the Northern Signs, in this part of the World, makes the greatest Tides when above the Earth, and in Southern Signs, when under the Earth; the Effect being always the greatest where the Moon is farthest from the Horizon, either above or below it. And this alternate Increase and Decrease of the Tides has been observ'd to hold true on the Coast of England, at Bristol by Captain Sturmy, and at Plymouth by Mr. Colepresse.

But the Motions hitherto mentioned are somewhat alter'd by the Libration of the Water, whereby, though the Action of the Luminaries should cease, the Flux and Reflux of the Sea would for some time continue: This Conservation of the impress'd Motion diminishes the differences that otherwise would be between two consequent Tides, and is the reason why the highest Spring-Tides are not precisely on the New and Full Moons, nor the Neaps on the Quarters; but generally they are the third Tides after them, and sometimes later.

All these things would regularly come to pass, if the whole Earth were cover'd with Sea very deep; but by reason of the shoalness of some places, and the narrowness of the Streights, by which the Tides are in many cases propagated, there arises a great diversity in the Effect, and not to be accounted for, without an exact Knowledge of all the Circumstances of the Places, as of the Position of the Land, and the Breadth and Depth of the Channels by which the Tide flows; for a very slow and imperceptible Motion of the whole Body of the Water, where it is (for Example) 2 Miles deep, will suffice to raise its Surface 10 or 12 Feet in a Tides time; whereas, if the same quantity of Water were to be convey'd up a Channel of 40 Fathoms deep, it would require a very great Stream to effect it, in so large Inlets as are the Channel of England, and the German Ocean; whence the Tide is found to set strongest in those places where the Sea grows narrowest; the same quantity of Water being to pass through a smaller Passage: This is most evident in the Streights, between Portland and Cape de Hague in Normandy, where the Tide runs like a Sluce; and would be yet more between Dover and Calais, if the Tide coming about the Island from the North did not check it. And this force being once impress'd upon the Water, continues to carry it above the level of the ordinary height in the Ocean, particularly where the Water meets a direct Obstacle, as it is at St. Malo's; and where it enters into a long Channel, which running far into the Land, grows very streight at its Extremity; as it is in the Severn-Sea at Chepstow and Bristol.

This shoalness of the Sea, and the intercurrent Continents are the reason, that in the open Ocean the time of High water is not at the Moons appulse to the Meridian, but always some Hours after it; as it is observ'd upon all the West Coast of Europe and Africa, from Ireland to the Cape of Good Hope: In all which a S. W. Moon makes High-water, and the same is reported to be on the West side of America. But it would be endless to account all the particular Solutions, which are easie Corollaries of this Hypothesis; as why the Lakes, such as the Caspian Sea, and Mediterranean Seas, such as the Black Sea, the Streights and Baltick, have no sensible Tides: For Lakes having no Communication with the Ocean, can neither increase nor diminish their Water, whereby to rise and fall; and Seas that communicate by such narrow Inlets, and are of so immense an Extent, cannot in a few Hours time receive or empty Water enough to raise or sink their Surface any thing sensibly.

Lastly, to demonstrate the Excellency of this Doctrine, the Example of the Tides in the Port of Tunking in China, which are so extraordinary, and differing from all others we have yet heard of, may suffice. In this Port there is but one Flood and Ebb in 24 Hours; and twice in each Month, viz. when the Moon is near the Æquinoctial there is no Tide at all, but the Water is stagnant; but with the Moons Declination there begins a Tide, which is greatest when she is in the Tropical Signs: Only with this difference, that when the Moon is to the Northward of the Æquinoctial, it Flows when she is above the Earth, and Ebbs when she is under, so as to make High-water at Moons-setting, and Low-water at Moons-rising: But on the contrary, the Moon being to the Southward, makes High-water at rising, and Low-water at setting; it Ebbing all the time she is above the Horizon. As may be seen more at large in the Philosophical Transactions, Numb. 162.

The Cause of this odd Appearance is propos'd by Mr. Newton, to be from the concurrence of two Tides; the one propagated in six Hours out of the great South-Sea along the Coast of China; the other out of the Indian-Sea, from between the Islands in twelve Hours, along the Coast of Malacca and Cambodia. The one of these Tides, being produc'd in North Latitude, is, as has been said, greater, when the Moon being to the North of the Equator is above the Earth, and less when she is under the Earth. The other of them, which is propagated from the Indian Sea, being raised in South-Latitude, is greater when the Moon declining to the South, is above the Earth, and less when she is under the Earth: So that of these Tides alternately greater and lesser, there comes always successively two of the greater and two of the lesser together every Day; and the High-water falls always between the times of the arrival of the two greater Floods; and the Low-water between the arrival of the two lesser Floods. And the Moon coming to the Æquinoctial, and the alternate Floods becoming equal, the Tide ceases, and the Water stagnates: But when she has pass'd to the other side of the Equator, those Floods which in the former Order were the least, now becoming the greatest, that That before was the time of High-water, now becomes the Low-water, and the Converse. So that the whole appearance of these strange Tides, is without any forcing naturally deduc'd from these Principles, and is a great Argument of the Certainty of the whole Theory.

A Theory of the Variation of the Magnetical Compass. By Mr. Ed. Halley, Fellow of the Royal Society.

THE Variation of the Compass (by which I mean the Deflection of the Magnetical Needle from the true Meridian) is of that great Concernment in the Art of Navigation, that the neglect thereof, does little less than render useless one of the noblest Inventions Mankind ever yet attained to. And for this cause all Ships of Consequence (especially those bound beyond the Equator) carry with them Instruments on purpose to observe this Variation: That so the Course steer'd by the Compass, may be reduc'd to the true Course in respect of the Meridian.

Now although the great utility that a perfect Knowledge of the Theory of the Magnetical Direction would afford to Mankind in general, and especially to those concern'd in Sea Affairs, seems as sufficient incitement to all Philosophical and Mathematical Heads, to take under serious Consideration the several Phænomena, and to endeavour to reconcile them by some general Rule: Yet so it is; that almost all the Authors, from whom a Discourse of this kind ought to have been expected, pass by in silence the Difficulties they here Encounter. And those that mention this Variation: By affirming it to proceed from Causes altogether uncertain (as are the casual lying of Iron Mines and Loadstones in the Earth) put a stop to all further Contemplation; and give discouragement to those that would otherwise undertake this Enquiry. 'Tis true, that not long since one Mr. Bond, an old Teacher of Navigation, put forth a small Treatise, wherein he pretends to calculate the Variation: But he limits his Hypothesis to the City of London, affirming himself (as he had a great deal of reason) that the same Calculus is not sufficient for other Places; whereby it appears that this Rule is far short of the so much desir'd general one.

Now although (through want of sufficient Observations, and some other Difficulties, which I shall anon shew) I cannot pretend perfectly to establish the Numbers and Rules of a Calculus, which shall precisely answer to the Variations of all parts of the World: Yet I suppose it will not be unacceptable to the Curious to propose something of a Light into this abstruse Mystery; which, if no other, may have this good Effect, to stir up the Philosophical Genii of the Age to apply themselves more attentively to this useful Speculation. But before I proceed, 'twill be necessary to lay down the Grounds upon which I raise my Conclusions; and at once to give a Synopsis of those Variations, which I have reason to look upon as sure, being mostly the Observations of Persons of good Skill and Integrity.

A
TABLE
OF
VARIATIONS.

Tho' I could wish we could obtain from the Spaniards what Variations they find in their Voyages from the Manilhas towards Acapulco, through the North part of the South Sea; as likewise what it is at Japan from the Dutch: Yet (considering the number of these Observations I have collected, and that they are made in parts of the World so remote from Europe, and from one another) I suppose that the Theory that answers these will scarce fail in those Regions from whence we have as yet no account. But first we must make some Remarks upon the foregoing Table: And, First,

That in all Europe the Variation at this time is West, and more in the Eastern Parts thereof than the Western: As likewise, that it seems throughout to be upon the increase that way.

Secondly, That on the Coast of America, about Virginia, New-England and New-Foundland, the Variation is likewise Westerly; and that it increases all the way as you go Northerly along the Coast, so as to be above 20 Degrees at New-Found-Land, nearly 30 gr. in Hudson's Straights, and not less than 57 Degrees in Baffin's Bay; also, that as you Sail Eastward from this Coast, the Variation diminishes. From these two it is a Legitimate Corollary: That Somewhere between Europe, and the North part of America, there ought to be an Easterly Variation, or at least no Westerly. And so I conjecture it is about the Eastermost of the Tercera Islands.

Thirdly, That on the Coast of Brasile there is East Variation, which increases very notably as you go to the Southward, so as to be 12 Degrees at Cape Frio, and over against the River of Plate 20½ Degrees: And from thence Sailing South-Westerly to the Straits of Magellan it decreases 17 Degrees, and at the West Entrance but 14 Degrees.

Fourthly, That at the Eastward of Brasile, properly so call'd, this Easterly Variation decreases, so as to be very little at St. Helena and Ascension, and to be quite gone, and the Compass Point true about 18 Degrees of Longitude West from the Cape of Good-hope.

Fifthly, That to the Eastward of the aforesaid Places a Westward Variation begins, which Reigns in the whole Indian Sea, and arises to no less than Eighteen Degrees under the Equator it self, about the Meridian of the Northern part of Madagascar; and near the same Meridian, but in 39 Degrees South Latitude it is found full 27½ Degrees: From thence Easterly the West Variation decreases, so as to be little more than eight Degrees at Cape Comorin, and than three Degrees upon the Coast of Java; and to be quite extinct about the Molucca Islands, as also a little to the Westwards of Van Diemens Land found out by the Dutch in 1642.

Sixthly, That to the Eastward of the Molucca's and Van Diemens Land in South Latitude there arises another Easterly Variation, which seems not so great as the former, nor of so large Extent; for that at the Island Rotterdam it is sensibly less than upon the East Coast of New Guinea; and, at the rate it decreases, it may well be suppos'd, that about 20 Degrees farther East, or 225 Degrees East Longitude from London, in the Latitude of 20 Degrees South, a Westerly Variation begins.

Seventhly, That the Variations observ'd by the Honourable Sir John Norborough at Baldivia, and at the West Entrance of the Straights of Magellan do plainly shew, that That East Variation, noted in our third Remark, is decreasing apace; and that it cannot reasonably extend many Degrees into the South Sea from the Coast of Peru and Chili, leaving room for a small Westerly Variation, in that Tract of the unknown World that lies in the mid-way between Chili and New-Zealand, and between Hounds-Island and Peru.

Eighthly, That in Sailing North-West from St. Helena by Ascension, as far as the Equator, the Variation continues very small East, and as it were constantly the same: So that in this part of the World the Course, wherein there is no Variation, is evidently no Meridian, but rather North-West.

Ninthly, That the Entrance of Hudson's Straights, and the Mouth of the River of Plate, being nearly under the same Meridian, at the one place the Needle varies 29½ Degrees to the West; at the other 20½ Degrees to the East. This plainly demonstrates the impossibility of reconciling these Variations by the Theory of Bond; which is by two Magnetical Poles and an Axis, inclin'd to the Axis of the Earth; from whence it would follow, That under the same Meridian the Variation should be in all places the same way.

These things being premised may serve as a sure Foundation to raise the Superstructure of a Theory upon. But first it would not be amiss to shew hereby the mistake of Gilbert and Des Cartes: The first whereof supposes, that the Earth it self being in all its parts Magnetical, and the Water not; wheresoever the Land is, thither also should the Needle turn, as to the greater quantity of Magnetical Matter. But this in many Instances is not true; but most remarkably upon the Coast of Brazile, where the Needle is so far from being attracted by the Land, that it turns the quite contrary way, leaving the Meridian to lye N b E, which is just along the Coast. As to the Position of Des Cartes, that the Iron and Loadstones hid in the Bowels of the Earth and the Bottom of the Sea, may be the Causes that the Needle varies; if we consider for how great a part of the Earths Surface, ex. gr. in the whole Indian Sea, the Needle declines the same way, and that regularly, 'twill follow that the attracting Substance that occasions it, must be very far distant. Now by Experience we find the little force that Iron Guns have upon the Compass in Ships (their Vertue, though they be Demiculverin, or greater Cannon, being not perceptible at four or five Yards distance) and the Experiments now before the Royal Society do plainly shew, how little a Magnetism there is in most crude Iron Oars: What quantity thereof must be then suppos'd to make so powerful a Diversion at two or three Thousand Miles distance? Yet I cannot deny that in some places near the Shoar, or in Shoal-Water, the Needle may be irregularly directed from the aforesaid Causes, and that not a little, as Gassendus gives a notable instance of the Island Elba in the Mediterranean Sea: But these differences from the general Direction are always signs of the nearness of those Magnetical Substances, for the Production whereof that Island Elba has been famous from all Antiquity. Besides, against both Des Cartes and Gilbert, the change of the Variation, which has been within these Hundred Years last past more than 15 gr. at London, is an entire Demonstration; tho' Des Cartes does not stick to say, that the transportation of Iron from place to place, and the growth of new Iron within the Earth, where there was none before, may be the cause thereof. The same holds likewise against the Hypothesis of Magnetical Fibres, which Kircher maintains.

Now to propose something that may answer the several appearances, and introduce nothing strange in Philosophy, after a great many close Thoughts, I can come to no other Conclusion than that, The whole Globe of the Earth is one great Magnet, having four Magnetical Poles, or Points of Attraction, near each Pole of the Equator. Two; and that, in those parts of the World which lie near adjacent to any one of those Magnetical Poles, the Needle is govern'd thereby, the nearest Pole being always predominant over the more remote. The parts of the Earth wherein these Magnetical Poles lie, cannot as yet be exactly determin'd for want of sufficient Data to proceed Geometrically; but, as near as Conjecture can reach, I reckon that the Pole, which is at present nearest to us, lies in or near the Meridian of the Lands-end of England, and not above seven Degrees from the Pole Arctick; by this Pole the Variations in all Europe and Tartary, and the North Sea are principally govern'd, though with regard to the other Northern Pole, whose situation is in a Meridian passing about the middle of California, and about 15 gr. from the North Pole of the World; to this the Needle has chiefly respect in all the North America, and in the two Oceans on either side thereof, from the Azores Westward to Japan, and farther. The two Southern Poles are rather farther distant from the South Pole of the World: The one about sixteen Degrees therefrom, is in a Meridian, some twenty Degrees to the Westward of Magellan Straights, or ninety five Degrees West from London: This commands the Needle in all the South-America, in the Pacifick Sea, and the greatest part of the Ethiopick Ocean. The Fourth and last Pole seems to have the greatest Power, and largest Dominions of all, as it is the most remote from the Pole of the World, being little less than 20 Degrees distant therefrom in the Meridian, which passes through Hollandia Nova, and the Island Celebes about one hundred and twenty Degrees East from London; this Pole is predominant in the South part of Africa, in Arabia and the Red Sea, in Persia, India, and its Islands, and all over the Indian Sea, from the Cape of Good-Hope Eastwards to the middle of the great South Sea, that divides Asia from America. This seems to be the present Disposition of the Magnetical Vertue throughout the whole Globe of the Earth; it remains to shew how this Hypothesis makes out all the Variations that have been observ'd of late; and how it answers to our several Remarks drawn from the Table. And first it is plain, that (our European North Pole being in the Meridian of the Lands-end of England) all places more Easterly than that will have it on the West side of their Meridian, and consequently the Needle, respecting it with its Northern Point, will have a Westerly Variation, which will still be greater as you go to the Eastwards, till you come to some Meridian of Russia, where 'twill be greatest, and from thence decrease again. Thus at Brest the Variation is but 1¾ Degrees, at London 4½ Degrees; but at Dantzick seven Degrees West. To the Westward of the Meridian of the Lands-end, the Needle ought to have an Easterly Variation; were it not that (by approaching the American Northern Pole, which lies on the West side of the Meridian, and seems to be of greater force than this other) the Needle is drawn thereby Westwards, so as to counterballance the Direction given by the European Pole, and to make a small West Variation in the Meridian of the Lands-end it self. Yet I suppose that about the Meridian of the Isle Tercera, our nearest Pole may so far prevail as to give the Needle a little turn to the East, though but for a very small space: The Counterballance of those two Poles permitting no considerable Variation in all the Eastern Parts of the Atlantick Ocean; nor upon the West Coasts of England and Ireland, France, Spain and Barbary. But to the Westwards of the Azores the Power of the American Pole overcoming that of the European, the Needle has chiefly respect thereto, and turns still more and more towards it as you approach it. Whence it comes to pass, that on the Coast of Virginia, New-England, New-found-Land, and in Hudson's-Straights the Variation is Westward; that it decreases as you go from thence towards Europe, and that it is less in Virginia and New-England, than in New-found-Land, and Hudson's-Straights. This Westerly Variation again decreases, as you pass over the North America; and about the Meridian of the middle of California the Needle again points due North; and from thence Westward to Yedzo and Japan, I make no doubt but the Variation is Easterly, and half the Sea over no less than fifteen Degrees, if there be any truth in this Hypothesis of mine. Therefore I propose this as a Trial, that the whole may be scann'd thereby; and I conceive it will not be hard to know of the Spaniards how it is, who so frequently sail through that Ocean, in their return from the Manilha Isles. This East Variation extends over Japan, Yedzo, East-Tartary, and part of China, till it meet with the Westerly, which is govern'd by the European North Pole, and which I said was greatest some where in Russia.

Towards the Southern Pole the effect is much the same, only that here the South Point of the Needle is attracted. Hence it will follow, that the Variation on the Coast of Brazile, at the River of Plate, and so on to the Straights of Magellan, should be Easterly (as in our third Remark); if we suppose a Magnetical Pole situate about twenty Degrees more Westerly than the Straights of Magellan. And this Easterly Variation doth extend Eastward over the greatest part of the Ethiopick Sea, till it be counterpoised by the Vertue of the other Southern Pole; as it is about mid-way between the Cape of Good-Hope, and the Isles of Tristan d' Acuntia. From thence Eastwards, the Asian South Pole (as I must take the liberty to call it) becoming prevalent, and the South point of the Needle being attracted thereby, there arises a West Variation, very great in quantity and extent, because of the great distance of this Magnetical Pole of the World. Hence it is, that in all the Indian Sea as far as Hollandia Nova, and farther, there is constantly West Variation; at that under the Equator it self it arises to no less than eighteen Degrees, where 'tis most. About the Meridian of the Island Celebes, being likewise that of this Pole, this Westerly Variation ceases, and an Easterly begins; which reaches, according to my Hypothesis, to the middle of the South-Sea, between Zelandia Nova, and Chili, leaving room for a small West Variation govern'd by the American South Pole, which I shew'd to be in the Pacifick Sea, in the sixth and seventh Remark.

What I have now said, does plainly shew the sufficiency of this Hypothesis for solving the Variations that are at this time observ'd in the temperate and frigid Zones, where the Direction of the Needle chiefly depends upon the Counterpoise of the forces of two Magnetical Poles of the same Nature; and I suppose I have shewn how it comes to pass, that under the same Meridian the Variation should be in one place 29½ West, and another 20½ East; as I have noted in my ninth Remark.

In the Torrid Zone, and particularly under the Equinoctial, respect must be had to all four Poles, and their Positions well consider'd, otherwise it will not be easie to determine what the Variations shall be; the nearest Pole being always the strongest; yet not so, as not to be counterballanc'd sometimes by the united forces of two more remote; a notable Instance whereof is in our eighth Remark, where I took notice, that in sailing from St. Helena by the Isle of Ascension, to the Equator, on a N. W. Course, the Variation is very little Easterly, and in that whole Tract unalterable; for which I give this Reason, That the South American Pole (which is considerably the nearest in the aforesaid Places) requiring a great Easterly Variation, is counterpoised by the contrary Attraction of the North-American and the Asian-South-Pole; each whereof singly are in these Parts, weaker than the American-South-Pole; and upon the North West Course, the Distance from this latter is very little varied; and as you recede from the Asian-South-Pole, the Ballance is still preserv'd by the access towards the North-American-Pole. I mention not in this Case the European-North-Pole, its Meridian being little remov'd from those of these places; and of it self requiring the same Variations we here find. After the same manner we might proceed to conclude the Variations in other places under and near the Equator; but I purposely leave it for an Exercise to the Thoughts of the serious Reader, who is desir'd to help his Imagination, by having before him a Map or Globe of the Earth: And to mark thereon the Magnetical Poles in the Longitudes and Latitudes I assign them. (Vide Plate 2.)

Thus, I hope, I have not lost my Pains and Study in this difficult Subject; believing that I have put it past doubt, That there are in the Earth four such Magnetical Points or Poles, which occasion the great variety and seeming irregularity which is observed in the Variations of the Compass. But to calculate exactly what it is, in any place assign'd, is what I dare not yet pretend to, though I could wish it were my happiness to be able to oblige the World with so useful a piece of Knowledge; there are Difficulties that occur, that render the thing as yet not feasible; for first there are a great many Observations requisite, which ought to be made at the same time; not at Sea, but ashore, with greater Care and Attention than the generality of Sailors apply. And besides, it remains undetermin'd in what proportion the attractive Power decreases, as you remove from the Pole of a Magnet, without which it were a vain attempt to go about to calculate. There is yet a further Difficulty, which is the Change of the Variation, one of the Discoveries of this last Century; which shews, that it will require some hundreds of Years to establish a compleat Doctrine of the Magnetical System. From the foregoing Table it should seem, that all the Magnetical Poles had a motion Westward: But if it be so, 'tis evident, that it is not a Rotation about the Axis of the Earth; for then the Variations would continue the same, in the same parallel of Latitude (the Longitude only chang'd) as much as is the motion of the Magnetical Poles, but the contrary is found by Experience; for there is no where in the Latitude of 15½ North between England and America, a Variation of eleven Degrees East at this time; as it was once here at London; it seems therefore, that our European Pole is grown nearer the Pole Arctick than it was heretofore, or else that it has lost part of its Vertue. But whether these Magnetical Poles move altogether with one motion, or with several; whether equally or unequally; whether Circular or Libratory: If Circular, about what Center; if Libratory, after what manner; are Secrets as yet utterly unknown to Mankind, and are reserv'd for the Industry of future Ages.

An Account of the Cause of the Change of the Variation of the Magnetical Needle, with an Hypothesis of the Structure of the Internal Parts of the Earth; as it was proposed to the Royal Society in one of their late Meetings. By Mr. Edmund Halley.

HAving in the precedent Discourse delivered a Theory of the Variation of the Magnetical Compass, wherein I did collect as many Observations as at that time I could procure, and having carefully compar'd them together, I came at length to this general conclusion, That the Globe of the Earth might be supposed to be one great Magnet, having four Magnetical Poles or Points of Attraction, near each Pole of the Equator two; and that in those parts of the World which lie near adjacent to any one of those Magnetical Poles, the Needle is chiefly govern'd thereby; the nearest Pole being always predominant ever the more remote. And I there have endeavour'd to state and limit the present Position of those Poles in the Surface of our Globe, which the Reader pleasing to consult, will save us the pains of repeating. But after all, tho' that Discourse was favourably receiv'd both at home and abroad, as seeming to render a tolerable account of the observ'd Variations, yet I found two Difficulties not easie to surmount; the one was, that no Magnet I had ever seen or heard of, had more than two opposite Poles, whereas the Earth had visibly four, and perhaps more. And secondly, it was plain that these Poles were not, at least all of them, fixt in the Earth, but shifted from place to place, as appear'd by the great Changes in the Needles Direction within this last Century of Years, not only at London, (where this great Discovery was first made) but almost all over the Globe of Earth; whereas it is not known or observ'd that the Poles of a Load-stone ever shifted their place in the Stone, nor (considering the compact hardness of that Substance) can it easily be suppos'd; though the Matter of Fact be too notorious and universal, not to be accounted for.

These Difficulties had wholly made me despond, and I had long since given over an Inquiry I had so little hopes of, when in accidental Discourse, and least expecting it, I stumbl'd on the following Hypothesis; in delivering whereof, if I shall seem to advance any thing that looks like Extravagant or Romantick, the Reader is desir'd to suspend his Censure, till he have consider'd the force and number of the many Arguments which concur to make good so new and so bold a Supposition.

Though it be sufficiently known and allow'd, that the Needles Variation changes, it will be necessary however to give a few Instances, whereby it may appear that this Change is gradual and universal, and the effect of a great and permanent motion: For which take the following Examples.

At London, in the Year 1580, the Variation was observ'd by Mr. Burrows to be 11° 15' East. In Anno 1622, the same was found by Mr. Gunter to be but 6° 0' East. In the Year 1634, Mr. Gellibrand found it 4° 5' East. In 1657, Mr. Bond observ'd that there was no Variation at London. Anno 1672, my self observ'd it 2° 30' to the West; and in the Year 1692, I again found it 6° 00' West. So that in 112 Years the Direction of the Needle has chang'd no less than seventeen Degrees.

At Paris, Orontius Finæus about the Year 1550, did account it about eight or nine Degrees East Variation. Anno 1640, it was found three Degrees East. Anno 1660, there was no Variation there, and Anno 1681, I found it to be 2° 30' to the West.

At Cape d' Agulhas, the most Southerly Promontary of Africa, about the Year 1600, the Needle pointed due North and South without Variation, whence the Portugueze gave its name. Anno 1622, there was two Degrees West Variation. Anno 1675, it was 8° 50' West; and in the Year 1691, it was curiously observ'd not less than eleven Degrees West.

At St. Helena, about the Year 1600, the Needle declin'd eight Degrees to the East. Anno 1623, it was but 6° 0' East. Anno 1677, when I was there, I observ'd it accurately on Shoar to be 0° 40' East; and in 1692 it was found about 1° to the Westward of the North.

At Cape Comorine in India, in the Year 1620, there was 14° 20' West Variation. In the Year 1680, there was 8° 48', but now lately in the Year 1688, it was no more than 7° 30', so that here the Needle has return'd to the East about seven Degrees in seventy Years.

In all the other Examples the Needle has gradually mov'd towards the West, and the places are too far asunder to be influenc'd by the removal of any Magnetical Matter, which may by accident be transplac'd within the Bowels, or on the Surface of the Earth. If more Examples are desir'd, the Reader may be furnished with them in the Portugueze Routier of Aleixo de Motta (written about the Year 1600) and in the Voyage of Beaulieu, both publish'd in Mr. Thevenot's first Collection of curious Voyages, Printed at Paris, Anno 1663; which he is to compare with the Journals of our late East India Voyagers, and I am assur'd, that it will be thereby evident, that the Direction of the Needle is in no place fix'd and constant, tho' in some it change faster than in others: And where for a long time it has continu'd as it were unalter'd, it is there to be understood, that the Needle has its greatest Deflection, and is become Stationary in order to return, like the Sun, in the Tropick. This, at present, is in the Indian Sea, about the Island Mauritius, where is the highest West Variation, and in a Tract tending from thence into the N. N. W. towards the Red-Sea and Egypt. And in all Places to the Westward of this Tract, all over Africa and the Seas adjoining, the West Variation will be found to have encreas'd; and to the Eastwards thereof as in the Example of Cape Comorine, to have decreased, viz. all over the East-Indies, and the Islands near it.

After the like manner in that Space of East Variation, which, beginning near St. Helena, is found all over the South America, and which at present is highest about the Mouth of Rio de la Plata, it has been observ'd, that in the Eastern Parts thereof, the Variation of the Needle gradually decreases; but whether on the contrary it increases in those places which lie more Westerly than that Tract wherein the highest East Variation is found; or how it may be in the vast Pacifick Sea, we have not Experience enough to ascertain, only we may by Analogy infer, that both the East and West Variations therein do gradually increase and decrease after the same Rule.

These Phænomena being well understood and duly consider'd, do sufficiently evince, That the whole Magnetical System is by one, or perhaps more motions translated, whether Eastwards or Westwards, I shall anon discuss; that this moving thing is very great, as extending its effects from Pole to Pole, and that the motion thereof is not per saltum, but a gradual and regular motion.

Now considering the Structure of our Terraqueous Globe, it cannot be well suppos'd that a very great part thereof can move within it, without notably changing its Center of Gravity and the Equilibre of its Parts, which would produce very wonderful Effects in changing the Axis of diurnal Rotation, and occasion strange alteration in the Seas Surface, by Inundations and Recesses thereof, such as History never yet mention'd. Besides, the solid parts of the Earth are not to be granted permeably by any other than fluid Substances, of which we know none that are any ways Magnetical. So that the only way to render this motion intelligible and possible, is to suppose it to turn about the Center of the Globe, having its Center of Gravity fix'd and immoveable in the same common Center of the Earth: And there is yet requir'd, that this moving internal Substance be loose and detached from the external Parts of the Earth whereon we live; for otherwise, were it affix'd thereto, the whole must necessarily move together.

So then the External Parts of the Globe may well be reckon'd as the Shell, and the Internal as a Nucleus or inner Globe, included within ours, with a fluid Medium between, which having the same Common Center and Axis of diurnal Rotation, may turn about with our Earth each twenty four Hours; only this outer Sphere having its turbinating motion some small matter either swifter or slower than the internal Ball: And a very minute Difference in length of time, by many Repetitions becoming sensible, the Internal Parts will by degrees recede from the External, and not keeping pace with one another, will appear gradually to move either Eastwards or Westwards by the difference of their motions.

Now supposing such an Internal Sphere having such a motion, we shall solve the two great Difficulties we encounter'd in my former Hypothesis: For if this exteriour Shell of Earth be a Magnet, having its Poles at a distance from the Poles of diurnal Rotation; and if the Internal Nucleus be likewise a Magnet, having its Poles in two other places, distant also from the Axis; and these latter by a gradual and slow motion change their place in respect of the External; we may then give a reasonable account of the four Magnetical Poles I presume to have demonstrated before; as likewise of the Changes of the Needles Variations, which till now hath been unattempted.

The Period of this Motion being wonderful great, and there being hardly an hundred Years since these Variations have been duly observ'd, it will be very hard to bring this Hypothesis to a Calculus, especially since, though the Variations do increase and decrease regularly in the same place, yet in differing places, at no great distance, there are found such casual Changes thereof as can no ways be accounted for by a regular Hypothesis; as depending upon the unequal and irregular distribution of the Magnetical Matter within the Substance of the External Shell or Coat of the Earth, which deflect the Needle from the Position it would acquire from the effect of the general Magnetism of the whole. Of this the Variations at London and Paris give a notable Instance, for the Needle has been constantly about 1°½ more Easterly at Paris than at London; though it be certain that according to the general effect, the Difference ought to be the contrary way: Notwithstanding which, the Variations in both places do change alike.

Hence, and from some other of like Nature, I conclude, That the two Poles of the External Globe are fixt in the Earth, and that if the Needle were wholly govern'd by them, the Variations thereof would be always the same, with some little Irregularities upon the account I but just now mention'd: But the Internal Sphere having such a gradual translation of its Poles, does influence the Needle, and direct it variously, according to the result of the attractive or directive Power of each Pole; and consequently there must be a Period of the Revolution of this Internal Ball, after which the Variations will return again as before. But if it shall in future Ages be observ'd otherwise, we must then conclude that there are more of these Internal Spheres, and more Magnetical Poles than Four, which at present we have not a sufficient number of Observations to determine, and particularly in that vast Mar del Zur, which occupies so great a part of the whole Surface of the Earth.

If then two of the Poles be fixt and two moveable, it remains to ascertain which they are that keep their place; and though I could wish we had the Experience of another Century of Years to found our Conclusions upon, yet I think we may safely determine, That our European North Pole (which in the precedent Discourse I suppos'd near the Meridian of the Lands-end of England, and about seven Degrees therefrom) is that That is moveable of the two Northern Poles, and that That has chiefly influenc'd the Variations in these parts of the World: For in Hudson's Bay, which is under the Direction of the American Pole, the Change is not observ'd to be near so fast as in these parts of Europe, though that Pole be much farther remov'd from the Axis.

As to the South Poles, I take the Asian Pole, which I place about the Meridian of the Island Celebes to be the fixt, and consequently the American Pole to move; from the like Observation of the slow Decrease of the Variation on the Coast of Java, and near the Meridian of the Asian Pole; though I must confess to have no account of the effects of the other beyond Magellan's Streights.

If this be allow'd me, 'tis plain that the fixt Poles are the Poles of this External Shell or Cortex of the Earth, and the other two the Poles of a Magnetical Nucleus included and moveable within the other. It likewise follows, that this Motion is Westwards, and by consequence that the aforesaid Nucleus has not precisely attained the same degree of Velocity with the exteriour Parts in their diurnal Revolution; but so very nearly equals it, that in 365 Revolves the difference is scarce sensible. This I conceive to arise from the Impulse whereby this diurnal Motion was imprest on the Earth, being given to the External Parts, and from thence in time communicated to the Internal; but not so as perfectly to equal the Velocity of the first Motion impress'd on, and still conserv'd by the superficial Parts of the Globe.

As to the quantity of this Motion it is almost impossible to define it, both from the Nature of this kind of Observation, which cannot be very accurately perform'd, as also from the small time these Variations have been observ'd, and their Change discover'd. It appears by all Circumstances, that its Period is of many Centuries of Years, and as far as may be collected from the Change of the Place, where there was no Variation, by reason of the Equilibre of the two Southern Magnetical Poles, viz. from Cape d' Agulhas to the Meridian of St. Helena (which is about 23 degr. in about ninety Years) and of the place where the Westerly Variation is in its ἀκμὴ or greatest Deflection, being about half so much, viz. from the Isle of Diego Roiz to the South West Parts of Madagascar. We may with some Reason conjecture, that the American Pole has mov'd Westwards forty six Degrees in that time, and that the whole Period thereof is perform'd in seven hundred Years, or thereabouts; so that the nice Determination of this, and of several other Particulars in the Magnetick System is reserv'd for remote Posterity; all that we can hope to do, is to leave behind us Observations that may be confided in, and to propose an Hypothesis which after Ages may examine, amend or refute. Only here I must take leave to recommend to all Masters of Ships, and all others, Lovers of Natural Truths, that they use their utmost Diligence to make, or procure to be made, Observations of these Variations in all parts of the World, as well in the North as South Latitude (after the laudable Custom of our East India Commanders) and that they please to communicate them to the Royal Society, in order to leave as compleat a History as may be to those that are hereafter to compare all together, and to compleat and perfect this abstruse Theory.

And by the way it will not be amiss to amend a receiv'd Error in the Practice of observing the Variation, which is, to take it by the Amplitude of the Rising and Setting Sun, when his Center appears in the visible Horizon; whereas he ought to be observ'd when his under Limb is still above the Horizon about ⅔ of his Diameter, or twenty Minutes, upon the score of the Refraction, and the height of the Eye of the Observer above the Surface of the Sea: Or else they are to work the Amplitudes as they do the Azimuth, reckoning the Suns Distance from the Zenith 90° 36': This, though it be of little consequence near the Æquinoctial, will make a great Error in high Latitudes, where the Sun rises and sets obliquely.

But to return to our Hypothesis, In order to explain the Change of the Variations, we have adventur'd to make the Earth hollow, and to place another Globe within it; and I doubt not but this will find Opposers enough. I know 'twill be Objected, That there is no Instance in Nature of the like thing; that if there was such a middle Globe it would not keep its place in the Center, but be apt to deviate therefrom, and might possibly chock against the Concave Shell, to the ruin, or at least endammaging thereof; That the Water of the Sea would perpetually leak through, unless we suppose the Cavity full of Water; That were it possible, yet it does not appear of what use such an inward Sphere can be of, being shut up in Eternal Darkness, and therefore unfit for the Production of Animals or Plants; with many more Objections, according to the Fate of all such new Propositions.

To these, and all other that I can foresee, I briefly Answer, That the Ring environing the Globe of Saturn is a notable Instance of this kind, as having the same common Center, and moving along with the Planet, without sensibly approaching him on one side more than the other. And if this Ring were turn'd on one of its Diameters, it would then describe such a Concave Sphere as I suppose our External one to be. And since the Ring, in any Position given, would, in the same manner, keep the Centre of Saturn in its own, it follows, that such a Concave Sphere may move with another included in it, having the same common Centre. Nor can it well be suppos'd otherwise, considering the Nature of Gravity; for should these Globes be adjusted once to the same common Centre, the Gravity of the parts of the Concave would press equally towards the Centre of the inner Ball, which equality must necessarily continue till some External Force disturb it, which is not easie to imagine in our Case. This perhaps I might more intelligibly express, by saying that the inner Globe being posited in the Centre of the Exteriour, must necessarily ascend which way soever it move; that is, it must overcome the force of Gravity pressing towards the common Centre, by an impulse it must receive from some outward Agent; but all outward Efforts being sufficiently fenc'd against by the Shell that surrounds it, it follows, that this Nucleus being once fixt in the common Centre, must always there remain.

As to the leaking of the Water through this Shell, when once a passage shall be found for it to run through, I must confess it is an Objection seemingly of weight; but when we consider how tightly great Beds of Chalk or Clay, and much more Stone do hold Water, and even Caves arch'd with Sand; no Man can doubt but the Wisdom of the Creator has provided for the Macrocosm by many more ways than I can either imagine or express, especially since we see the admirable and innumerable Contrivances wherewith each worthless Individual is furnish'd both to defend it self, and propagate its Species. What Curiosity in the Structure, what Accuracy in the Mixture and Composition of the parts, ought not we to expect in the Fabrick of this Globe, made to be the lasting Habitation of so many various Species of Animals, in each of which there want not many Instances that manifest the boundless Power and Goodness of their Divine Author; and can we then think it a hard Supposition, that the Internal Parts of this Bubble of Earth should be replete with such Saline and Vitriolick Particles as may contribute to Petrefaction, and dispose the transuding Water to shoot and coagulate into Stone, so as continually to fortifie, and, if need were, to consolidate any breach or flaw in the Concave Surface of the Shell.

And this perhaps may not without Reason be suppos'd to be the final Cause of the admixture of the Magnetical Matter in the Mass of the Terrestrial parts of our Globe, viz. To make good and maintain the Concave Arch of this Shell: For by what the Excellent Mr. Newton has shewn in his Principia Philosophiæ, it will follow, that according to the general Principle of Gravity, visible throughout the whole Universe, all those Particles that by length of time, or otherwise, shall moulder away, or become loose on the Concave Surface of the External Sphere, would fall in, and with great force descend on the Internal, unless those Particles were of another sort of Matter capable by their stronger tendency to each other, to suspend the force of Gravity; but we know no other Substances capable of supporting each other by their mutual Attraction but the Magnetical, and these we see miraculously to perform that Office, even where the Power of Gravity has its full effect, much more within the Globe where it is weaker. Why then may we not suppose these said Arches to be lin'd throughout with a Magnetical Matter, or rather to be one great Concave Magnet, whose two Poles are the Poles we have before observ'd to be fixt in the Surface of our Globe.

Another Argument, favouring this Hypothesis, is drawn from a Proposition of the same Mr. Newton, where he determines the force wherewith the Moon moves the Sea in producing the Tides: His Words are, Densitas Lunæ est ad densitatem Terra ut 680 ad 387 seu 9 ad 5 quamproximé. Est igitur corpus Lunæ densius ac magis terrestre quam Terra nostra, p. 466. Now if the Moon be more solid than the Earth, as 9 to 5, why may we not reasonably suppose the Moon, being a small Body, and a secondary Planet, to be solid Earth, Water, Stone, and this Globe to consist of the same Materials, only four Ninths thereof to be Cavity, within and between the Internal Spheres; which I would render not improbable.

To those that shall enquire of what use these included Globes can be, it must be allow'd, that they can be of very little service to the Inhabitants of this outward World, nor can the Sun be serviceable to them, either with his Light or Heat. But since it is now taken for granted, that the Earth is one of the Planets, and they all are with Reason suppos'd Habitable, though we are not able to define by what sort of Animals; and since we see all the parts of the Creation abound with Animate Beings, as the Air with Birds and Flies, the Water with the numerous varieties of Fish, and the very Earth with Reptiles of so many sorts; all whose ways of Living would be to us incredible did not daily Experience teach us. Why then should we think it strange that the prodigious Mass of Matter, whereof this Globe does consist, should be capable of some other improvement than barely to serve to support its Surface? Why may not we rather suppose that the exceeding small quantity of solid Matter, in respect of the fluid Æther, is so dispos'd by the Almighty Wisdom, as to yield as great a Surface for the use of living Creatures, as can consist with the conveniency and security of the whole? We our selves, in Cities where we are pressed for Room, commonly build many Stories one over the other, and thereby accommodate a much greater multitude of Inhabitants.

But still it will be said, That without Light there can be no living, and therefore all this apparatus of our inward Globes must be useless: To this I Answer, That there are many ways of producing Light which we are wholly ignorant of; the Medium it self may be always luminous after the manner of our Ignes fatui. The Concave Arches may in several places shine with such a Substance as invests the Surface of the Sun; nor can we, without a boldness unbecoming a Philosopher, adventure to assert the impossibility of peculiar Luminaries below, of which we have no sort of Idea. I am sure the Poets Virgil and Claudian have gone before me in this Thought, inlightning their Elysian Fields with Sun and Stars proper to those infernal, or rather internal Regions. Virg. Æneid. 6.

Largior hic compos Æther & lumine vestit

Purpureo; Solemque suum sua Sidera norunt.

And Claudian lib 2. De Raptu Proserpinæ.

Amissum ne crede diem, sunt altera nobis

Sidera, sunt orbes alii, luménque videbis

Purius, Elysiumque magis mirabere Solem.

And though this be not to be esteem'd as an Argument, yet I may take the liberty I see others do, to quote the Poets when it makes for my purpose.

Lastly, To explain yet farther what I mean, I have adventur'd to adjoin the following Scheme, (Tab. 1. Fig. 3) wherein the Earth is represented by the outward Circle, and the three inward Circles are made nearly proportionable to the Magnitudes of the Planets Venus, Mars and Mercury, all which may be included within the Globe of Earth, and all the Arches more than sufficiently strong to bear their weight. The Concave of each Arch, which is shaded differently from the rest, I suppose to be made up of Magnetical Matter; and the whole to turn about the same common Axis pp, only with this difference, that the Outer Sphere still moves somewhat faster than the Inner. Thus the Diameter of the Earth being about eight thousand English Miles, I allow five hundred Miles for the thickness of its Shell, and another space of five hundred Miles for a Medium between, capable of an immense Atmosphere for the use of the Globe of Venus: Venus again I give a Shell of the same thickness, and leave as great a space between her Concave and Mars; so likewise from Mars to Mercury, which latter Ball we will suppose solid, and about two thousand Miles Diameter. Thus I have shew'd a possibility of a much more ample Creation, than has hitherto been imagin'd; and if this seem strange to those that are unacquainted with the Magnetical System, it is hop'd that all such will endeavour, first, to inform themselves of the Matter of Fact, and then try if they can find out a more simple Hypothesis, at least a less absurd, even in their own Opinions. And whereas I have adventur'd to make these Subterraneous Orbs capable of being Inhabited, 'twas done designedly for the sake of those who will be apt to ask cui bono, and with whom Arguments drawn from Final Causes prevail much. If this short Essay shall find a kind Acceptance, I shall be encourag'd to enquire farther, and to Polish this rough Draft of a Notion till hitherto not so much as started in the World, and of which we could have no Intimation from any other of the Phænomena of Nature.

Since this was written, a Discovery I have made in the Cœlestial Motions, seems to render a farther Account of the Use of the Cavity of the Earth, viz. To diminish the Specifick Gravity thereof, in respect of the Moon; for I think I can demonstrate that the Opposition of the Æther to the Motions of the Planets in long time becomes sensible; and consequently the greater Body must receive a less Opposition than the smaller, unless the Specifick Gravity of the smaller do proportionably exceed that of the greater, in which case only they can move together; so that the Cavity I assign in the Earth, may well serve to adjust its weight to that of the Moon, for otherwise the Earth would leave the Moon behind it, and she become another Primary Planet.

An Historical Account of the Trade Winds and Monsoons, observable in the Seas between and near the Tropicks, with an attempt to assign the Physical Cause of the said Winds, by Mr. Ed. Halley.

AN exact Relation of the constant and periodical Winds, observable in several Tracts of the Ocean, is a part of Natural History not less desireable and useful, than it is difficult to obtain, and its Phænomena hard to explicate: I am not ignorant that several Writers have undertaken this Subject, and although Varenius (Lib. 1. Chap. 21. Geo. Gen.) seems to have endeavour'd after the best information from Voyagers, yet cannot his Accounts be admitted for accurate, by those that shall attentively consider and compare them together, and some of them are most evident Mistakes; which, as near as I can, I shall attempt to rectify, having had the opportunity of conversing with Navigators, acquainted with all parts of India, and having liv'd a considerable time between the Tropicks, and there made my own Remarks.

The Substance of what I have collected is briefly as follows.

The Universal Ocean may most properly be divided into three Parts, viz. 1. The Atlantick and Æthiopick-Sea. 2. The Indian Ocean. 3. The Great South Sea, or the Pacifick Ocean; and though these Seas do all communicate by the South, yet as to our present purpose of the Trade Winds, they are sufficiently separated by the interposition of great Tracts of Land; the first lying between Africa and America, the second between Africa and the Indian Islands, and Hollandia Nova; and the last between the Phillipine Isles, China, Japan and Hollandia Nova on the West, and the Coast of America on the East. Now following this natural division of the Seas, so will we divide our History into three parts in the same order.

I. In the Atlantick and Æthiopick Seas between the Tropicks, there is a general Easterly Wind all the Year long, without any considerable Variation, excepting that it is subject to be deflected therefrom, some few Points of the Compass towards the North or South, according to the Position of the place. The Observations which have been made of these Deflections, are the following.

1. That near the Coast of Africa, as soon as you have pass'd the Canary Isles, you are sure to meet a fresh Gale of North East Wind, about the Latitude of 28 Degrees North, which seldom comes to the Eastwards of the East North-East, or passes the North North-East. This Wind accompanies those bound to the Southward, to the Latitude of ten North, and about a hundred Leagues from the Guinea Coast, where, till the fourth Degree of North Latitude, they fall into the Calms and Tornadoes; of which more hereafter.

2. That those bound to the Caribbee Isles, find, as they approach the American side, that the aforesaid North-East Wind becomes still more and more Easterly, so as sometimes to be East, sometimes East by South, but yet most commonly to the Northward of the East a Point or two, seldom more. 'Tis likewise observ'd, that the strength of these Winds does gradually decrease, as you sail to the Westwards.

3. That the limits of the Trade and variable Winds, in this Ocean, are farther extended on the American side than the African; for whereas you meet not with this certain Wind till after you have pass'd the Latitude of twenty eight Degrees on this side; on the American side it commonly holds to thirty, thirty one, or thirty two Degrees of Latitude; and this is verified likewise to the Southwards of the Æquinoctial, for near the Cape of Good-Hope the limits of the Trade Winds, are three or four Degrees nearer the Line, than on the Coast of Brazile.

4. That from the Latitude of four Degrees North, to the aforesaid Limits on the South of the Æquator, the Winds are generally and perpetually between the South and East, and most commonly between the South-East and East, observing always this Rule, That on the African side they are more Southerly, on the Brazilian more Easterly, so as to become almost due East, the little deflection they have being still to the Southwards. In this part of the Ocean it has been my fortune to pass a full Year, in an Employment that oblig'd me to regard more than ordinary the Weather, and I found the Winds constantly about the South-East, the most usual Point S E b E; when it was Easterly, it generally blew hard, and was gloomy, dark, and sometimes rainy Weather; if it came to the Southwards it was generally Serene, and a small Gale next to a Calm, but this not very common. But I never saw it to the Westwards of the South, or Northwards of the East.

5. That the Season of the Year has some small effect on these Trade Winds, for that when the Sun is considerable to the Northwards of the Æquator, the South-East Winds, especially in the Straight of this Ocean (if I may so call it) between Brazile and the Coast of Guinea, do vary a Point or two to the Southwards, and the North-East become more Easterly; and on the contrary, when the Sun is towards the Tropick of Capricorn the South-Easterly Winds become more Easterly, and the North-Easterly Winds on this side the Line veere more to the Northwards.

6. That as there is no general Rule that admits not of some Exception, so there is in this Ocean a Tract of Sea wherein the Southerly and South-West Winds are perpetual, viz. all along the Coast of Guinea, for above five hundred Leagues together, from Sierra Leona to the Isle of St. Thomas; for the South-East Trade Wind having pass'd the Line, and approaching the Coast of Guinea within eighty or 100 Leagues, inclines towards the Shore, and becomes S. S. E. and by Degrees, as you come nearer, it veeres about to South, S. S. W. and in with the Land South-West, and sometimes West South-West; which Variation is better express'd in the Mapp hereto annexed, (Vide Plate 2) than it can well be in Words. These are the Winds which are observ'd on this Coast when it blows true, but there are frequent Calms, violent sudden Gusts call'd Tornado's, from all Points of the Compass, and sometimes unwholsome foggy Easterly Winds, call'd Hermitaa by the Natives, which too often infest the Navigation of these parts.

7. That to the Northwards of the Line, between four and ten Degrees of Latitude, and between the Meridians of Cape Virde, and of the Eastermost Islands that bear that Name, there is a Tract of Sea wherein it were improper to say there is any Trade Wind, or yet a Variable; for it seems condemn'd to perpetual Calms, attended with terrible Thunder and Lightning, and Rains so frequent, that our Navigators from thence call this part of the Sea the Rains; the little Winds that are, be only some sudden uncertain Gusts, of very little Continuance and less Extent; so that sometimes each Hour you shall have a different Gale, which dies away into a Calm before another succeed, and in a Fleet of Ships in sight of one another, each shall have the Wind from a several Point of the Compass; with these weak Breezes Ships are oblig'd to make the best of their way to the Southward through the aforesaid six Degrees, wherein 'tis reported some have been detain'd whole Months for want of Wind.

From the three last Observables is shewn the Reason of two notable Occurents in the East-India and Guinea Navigations: The one is, why, notwithstanding the narrowest part of the Sea between Guinea and Brazile be about five hundred Leagues over, yet Ships bound to the Southward, sometimes, especially in the Months of July and August, find a great difficulty to pass it. This happens because of the South-East Winds, at that time of the Year commonly extending some Degrees beyond the ordinary limit of four Degrees North Latitude, and withal they come so much Southerly, as to be sometimes South, sometimes a Point or two to the West; there remains then only to ply to Windward, and if on the one side they stand away W. S. W. they gain the Wind still more and more Easterly; but there is danger of not weathering the Brazilian Shoar, or at least the Shoals upon that Coast. But if upon the other Tack they go away E. S. E. they fall into the Neighbourhood of the Coast of Guinea, from which there is no departing without running Easterly, as far as the Isle of St. Thomas, which is the constant practice of all the Guinea Ships, and which may seem very strange, without the consideration of the sixth Remark, which shews the Reason of it: For being in with the Coast, the Wind blows generally at S. W. and W. S. W. with which Winds they cannot go to the Northward for the Land; and on the other Tack they can lie no nearer the Wind than S. S. E. or South; with these Courses they run off the Shoar, but in so doing they always find the Winds more and more contrary; so that when near the Shoar they could lie South, at a greater distance they can make their way no better than S. E. and afterwards E. S. E. with which Courses they fetch commonly the Isle of St. Thomas and Cape Lopez, where finding the Winds to the Eastward of the South, they keep them favourable, by running away to the Westward in the South Latitude, of three or four Degrees, where the S. E. Winds are perpetual.

For the sake of these general Winds, all those that use the West-Indian Trade, even those bound to Virginia, count it their best Course to get as soon as they can to the Southwards, that so they may be certain of a fair and fresh Gale to run before it to the Westwards; and for the same Reason those homewards bound from America, endeavour to gain the Latitude of thirty Degrees, as soon as possible, where they first find the Winds begin to be variable; tho' the most ordinary Winds in the Northern part of the Atlantick Ocean come from between the South and West.

As to those furious Storms call'd Hurricanes, which are, as it were, peculiar to the Caribbee Isles; and which so dreadfully afflict them in the Month of August, or not much before or after, they do not so properly belong to this place, both by Reason of their small continuance and extent, as likewise because they are not Anniversary, some Years having more than one, and sometimes for several Years together there being none at all. But their Violence is so unconceivable, and their other Phænomena so surprising, that they merit well to be consider'd apart.

What is here said, is to be understood of the Sea Winds at some distance from the Land; for upon and near the Shoars, the Land and Sea Breezes are almost every where sensible; and the great Variety which happens in their Periods, Force and Direction, from the situation of the Mountains, Vallies and Woods, and from the various Texture of the Soil, more or less capable of retaining and reflecting Heat, and of exhaling or condensing Vapours, is such, that it were an endless task, to endeavour to account for them.

II. In the Indian Ocean, the Winds are partly general, as in the Æthiopick Ocean, partly Periodical; that is, half the Year they blow one way, and the other half near upon the opposite Points; and these Points and Times of shifting are different in different parts of this Ocean; the limits of each Tract of Sea, subject to the same Change or Monsoon, are certainly very hard to determine, but the diligence I have used to be rightly inform'd, and the care I have taken therein, has, in a great measure, surmounted that Difficulty; and I am perswaded that the following Particulars may be relied upon.

1. That between the Latitudes of ten Degrees and thirty Degrees South, between Madagascar and Hollandia Nova, the general Trade Wind about the S. E. by E. is found to blow all the Year long, to all Intents and Purposes after the same manner as in the same Latitudes in the Æthiopick Ocean, as it is describ'd in the fourth Remark aforegoing.

2. That the aforesaid S. E. Winds extend to within two Degrees of the Æquator, during the Months of June, July, August, &c. to November; at which time between the South Latitudes of three and ten Degrees, being near the Meridian of the North end of Madagascar, and between two and twelve South Latitude, being near Sumatra and Java, the contrary Winds from the N. W. or between the North and West, set in and blow for half the Year, viz. from the beginning of December till May; and this Monsoon is observ'd as far as the Molucca Isles, of which more anon.

3. That to the Northward of three Degrees South Latitude, over the whole Arabian or Indian-Sea and Gulph of Bengall, from Sumatra to the Coast of Africa, there is another Monsoon, blowing from October to April upon the North East Points; but in the other half Year, from April to October, upon the opposite Points of S. W. and W. S. W. and that with rather more force than the other, accompanied with dark rainy Weather, whereas the N. E. blows clear; 'tis likewise to be noted, that the Winds are not so constant, either in strength or point in the Gulph of Bengall, as they are in the Indian-Sea, where a certain and steady Gale scarce ever fails. 'Tis also remarkable, that the S. W. Winds in these Seas are generally more Southerly on the African side, more Westerly on the Indian.

4. That as an Appendix to the last describ'd Monsoon, there is a Tract of Sea to the Southwards of the Æquator, subject to the same Changes of the Winds, viz. near the African Coast, between it and the Island Madagascar or St. Lawrence, and from thence Northwards as far as the Line; wherein from April to October there is found a constant fresh S. S. W. Wind, which, as you go more Northerly, becomes still more and more Westerly, so as to fall in with the W. S. W. Winds, mention'd before, in those Months of the Year to be certain to the Northward of the Æquator: What Winds blow in these Seas, for the other half Year, from October to April, I have not yet been able to obtain to my full satisfaction, for that our Navigators always return from India without Madagascar, and so are little acquainted in this Matter; the Account that has been given me is only this, that the Winds are much Easterly hereabouts, and as often to the North of the true East as to the Southwards thereof.

5. That to the Eastward of Sumatra and Malacca, to the Northwards of the Line, and along the Coast of Cambodia and China, the Monsoons blow North and South, that is to say, the N. E. Winds are much Northerly, and the S. W. much Southerly: This Constitution reaches to the Eastwards of the Philippine Isles, and as far Northerly as Japan. The Northern Monsoon setting in, in these Seas, in October or November, and the Southern in May, blowing all the Summer Months: Here it is to be noted, That the Points of the Compass, from whence the Wind comes in these Parts of the World, are not so fixt as in those lately describ'd; for the Southerly will frequently pass a Point or two to the Eastwards of the South, and the Northerly as much to the Westwards of the North, which seems occasion'd by the great quantity of Land, which is interspers'd in these Seas.

6. That in the same Meridians, but to the Southwards of the Æquator, being that Tract lying between Sumatra and Java to the West, and New Guinea to the East, the same Northerly Monsoons are observ'd, but with this difference, that the inclination of the Northerly is towards the N. West, and of the Southerly towards the S. E. but the plagæ venti are not more constant here than in the former, viz. variable five or six Points; besides the times of the Change of these Winds, are not the same as in the Chinese Seas, but about a Month or six Weeks later.

7. That these contrary Winds do not shift all at once, but in some places the time of the Change is attended with Calms, in others with variable Winds; and it is particularly remarkable, that the end of the Westerly Monsoon on the Coast of Coromandel, and the two last Months of the Southerly Monsoon in the Seas of China, are very subject to be tempestuous: The violence of these Storms is such, that they seem to be of the Nature of the West-India Hurricanes, and render the Navigation of these parts very unsafe about that time of the Year. These Tempests are by our Seamen usually term'd, The breaking up of the Monsoons.

By reason of the shifting of these Winds, all those that sail in these Seas, are oblig'd to observe the Seasons proper for their Voyages, and so doing they fail not of a fair Wind and speedy Passage; but if so be they chance to out-stay their time, till the contrary Monsoon sets in, as it frequently happens, they are forc'd to give over the hopes of accomplishing their intended Voyages, and either return to the Port from whence they came, or else put in to some other Harbour, there to spend the time till the Winds shall come favourable.

III. The third Ocean call'd Mare Pacificum, whose Extent is equal to that of the other two (it being from the West Coast of America to the Philippine Islands, not less than 150 Degrees of Longitude) is that which is least known to our own or the Neighbour Nations; that Navigation that there is on it, is by the Spaniards, who go Yearly from the Coast of New Spain to the Manilha's, but that but by one beaten track; so that I cannot be so particular here as in the other two. What the Spanish Authors say of the Winds they find in their Courses, and what is confirm'd by the old Accounts of Drake and Cavendish; and since by Schooten, who sail'd the whole breadth of this Sea in the Southern Latitude of fifteen or sixteen Degrees, is, that there is a great conformity between the Winds of this Sea, and those of the Atlantick and Æthiopick; that is to say, that to the Northwards of the Æquator, the predominant Wind is between the East and North-East; and to the Southwards thereof there is a constant steady Gale between the East and South-East, and that on both sides the Line with so much constancy, that they scarce ever need to attend the Sails, and Strength, that it is rare to fail of crossing this vast Ocean in ten Weeks time, which is about 130 Miles per diem; besides, 'tis said that Storms and Tempests are never known in these parts: So that here is the very best of Sailing; no want of a fresh fair Wind, and yet no danger of having too much: Wherefore some have thought it might be as short a Voyage to Japan and China, to go by the Streights of Magellan, as by the Cape of Good Hope.

The Limits of these general Winds are also much the same as in the Atlantick Sea, viz. about the thirtieth Degree of Latitude on both sides; for the Spaniards homewards bound from the Manilha's, always take the advantage of the Southerly Monsoon, blowing there in the Summer Months, and run up to the Northwards of that Latitude, as high as Japan, before they meet with variable Winds, to shape their Course to the Eastwards. And Schooten and others that have gone about by the Magellan Streights, have found the Limits of S. E. Winds, much about the same Latitude to the Southwards; besides a farther Analogy between the Winds of this Ocean, and the Æthiopick, appears in that, upon the Coast of Peru, they are always much Southerly, like as they are found near the Shoars of Angola.

Thus far Matter of Fact, wherein if the information I have receiv'd be not in all parts Accurate, it has not been for want of inquiry from those I conceiv'd best able to instruct me; and I shall take it for a very great Kindness if any Master of a Ship, or other Person, well inform'd of the Nature of the Winds, in any of the aforemention'd parts of the World, shall please to communicate their Observations thereupon; so that what I have here Collected may be either confirm'd or amended, or by the addition of some material Circumstances enlarg'd. It is not the work of one, nor of few, but of a multitude of Observers, to bring together the Experience requisite to compose a perfect and compleat History of these Winds; however I am not much doubtful that I have err'd in, or omitted any of the principal Observables, whatever lesser Particulars may have escaped my Knowledge.

To help the Conception of the Reader in a manner of so much difficulty, I believ'd it necessary to adjoin a Scheme, (Plate 2.) shewing at one view all the various Tracts and Courses of these Winds; whereby 'tis possible the thing may be better understood, than by any verbal Description whatsoever.

The Limits of these several Tracts are design'd every where by prickt Lines, as well in the Atlantick and Æthiopick, where they are the boundaries of the Trade and variable Winds, as in the Indian Ocean, where they also shew the Extent of the several Monsoons. I could think of no better way to design the Course of the Winds on the Map, than by drawing rows of stroaks in the same Line that a Ship would move going always before it; the sharp end of each little stroak pointing out that part of the Horizon, from whence the Wind continually comes; and where there are Monsoons, the rows of the stroaks run alternately backwards and forwards, by which means they are thicker there than elsewhere. As to the great South Sea, considering its vast Extent, and the little Variety there is in its Winds, and the great Analogy between them, and those of the Atlantick and Æthiopick Oceans; besides, that the greatest part thereof is wholly unknown to us; I thought it unnecessary to lengthen the Map therewith.

In the foregoing History are contained several Problems, that merit well the Consideration of our acutest Naturalists, both by reason of the constancy of the Effect, and of the immense Extent thereof; near half the Surface of the Globe being concerned. The chief of these Problems are, 1. Why these Winds are perpetually from the East in the Atlantic and Æthiopick; as likewise in the Pacifick Ocean, between the Latitudes of 30 North and South? 2. Why the said Winds extend no farther with constancy than to the Latitude of 30 Degrees? 3. Why there should be a constant South-Westerly Wind upon and near the Coast of Guinea? 4. Why in the North part of the Indian Ocean, the Winds, which for one half Year do agree with those of the other two Oceans, should change in other half Year, and blow from the opposite Points; whilst the Southern part of that Ocean follows the General Rule, and has perpetual Winds about S. E? 5. Why in these General Trade-Winds it should be always true, that to the Northward of the Æquator it is inclin'd to the Northwards of the East; and in South Latitudes, to the Southward thereof? 6. Why in these Seas of China there should be so great an Inclination from the East to the North, more than elsewhere? with many more, which it would be much easier to propose than answer.

But lest I should seem to propose to others, Difficulties which I have not thought worth my own Time and Pains, take here the result of an earnest Endeavour after the true reason of the aforesaid Phænomena; wherein if I am not able to account for all Particulars, yet 'tis hoped the Thoughts I have spent thereon, will not be judged wholly lost, by the Curious in Natural Enquiries.

Wind is most properly defined to be the Stream or Current of the Air, and where such a Current is perpetual and fixt in its Course, 'tis necessary that it proceed from a permanent un-intermitting Cause. Wherefore some have been inclin'd to propose the diurnal Rotation of the Earth upon its Axis, by which, as the Globe turns Eastwards, the loose and fluid Particles of the Air, being so exceeding light as they be, are left behind, so that in respect of the Earths Surface they move Westwards, and become a constant Easterly Wind. This Opinion seems confirm'd, for that these Winds are found only near the Æquinoctial, in those Parallels of Latitude where the diurnal Motion is swiftest; and I should readily assent to it, if the constant Calms in the Atlantick Sea, near the Æquator, the Westerly Winds near the Coast of Guinea; and the Periodical Westerly Monsoons under the Æquator in the Indian Seas, did not declare the insufficency of that Hypothesis. Besides the Air being kept to the Earth by the Principle of Gravity, would acquire the same degree of Velocity that the Earths Surface moves with, as well in respect of the diurnal Rotation, as of the Annual about the Sun, which is about thirty times swifter.

It remains therefore to substitute some other Cause, capable of producing a like constant Effect, not liable to the same Objections, but agreeable to the known Properties of the Elements of Air and Water, and the Laws of the Motion of fluid Bodies. Such an one is, I conceive, the Action of the Sun Beams upon the Air and Water, as he passes every Day over the Oceans, consider'd together with the Nature of the Soil, and Situation of the adjoining Continents: I say therefore, first, that according to the Laws of Staticks, the Air which is less rarified or expanded by heat, and consequently more ponderous, must have a Motion towards those parts thereof, which are more rarified, and less ponderous, to bring it to an Æquilibrium; and secondly, That the Presence of the Sun continually shifting to the Westwards, that part towards which the Air tends, by reason of the Rarifaction made by his greatest Meridian Heat, is with him carried Westward, and consequently the tendency of the whole Body of the lower Air is that way.

Thus a general Easterly Wind is formed, which being impressed upon all the Air of a vast Ocean, the Parts impel one the other, and so keep moving till the next return of the Sun, whereby so much of the Motion as was lost, is again restored, and thus the Westerly Wind is made perpetual.

From the same Principle it follows, that this Easterly Wind should on the North side of the Æquator, be to the Northwards of the East, and in South Latitudes to the Southwards thereof; for near the Line, the Air is much more rarified, than at a greater distance from it; because of the Sun twice in a Year Vertical, and at no time distant above 23 Degr. and a half; at which distance the Heat, being as the Sine of the Angle of Incidence, is but little short of that of the perpendicular Ray. Whereas under the Tropicks, though the Sun stay long Vertical, yet he is as long 47 Degr. off; which is a kind of Winter, wherein the Air so cools, as that the Summer-heat cannot warm it to the same degree with that under the Æquator. Wherefore the Air to the Northwards and Southwards, being less rarified than that in the middle, it follows, that from both sides it ought to tend towards the Æquator: This Motion compounded with the former Easterly Wind, answers all the Phænomena of the general Trade-winds; which, if the whole Surface of the Globe were Sea, would undoubtedly blow all round the World, as they are found to do in the Atlantick, and Æthiopick Oceans.

But seeing that so great Continents do interpose, and break the continuity of the Oceans, regard must be had to the Nature of the Soil, and the Position of the high Mountains, which I suppose the two principal Causes of the several Variations of the Winds, from the former general Rule: For if a Country lying near the Sun, prove to be flat, sandy, low Land, such as the Desarts of Lybia are usually reported to be, the Heat occasion'd by the Reflection of the Suns Beams, and the retention thereof in the Sand, is incredible to those that have not felt it; whereby the Air being exceedingly rarified, it is necessary that the cooler and more dense Air should run thitherwards to restore the Æquilibrium: This I take to be the cause, why near the Coast of Guinea the Wind always sets in upon the Land, blowing Westerly instead of Easterly, there being sufficient Reason to believe, that the Inland Parts of Africa are prodigiously hot, since the Northern Borders thereof were so intemperate, as to give the Ancients cause to conclude, that all beyond the Tropick, was made uninhabitable by excess of Heat: From the same Cause it happens, that there are so constant Calms in that part of the Ocean, called the Rains, (described in the 7th Remark on the Atlantick Sea) for this Tract being placed in the middle, between the Westerly Winds blowing on the Coast of Guinea, and the Easterly Trade-winds, blowing to the Westwards thereof, the tendency of the Air here, is indifferent to either, and so stands in Æquilibrio between both; and the weight of the incumbent Atmosphere being diminished by the continual contrary Winds blowing from hence, is the reason that the Air here holds not the copious Vapour it receives, but lets it fall into frequent Rains.

But as the cool and dense Air, by reason of its greater Gravity, presses upon the hot and rarified, 'tis demonstrative that this latter must ascend in a continued Stream as fast it rarifies; and that being ascended, it must disperse it self to preserve the Æquilibrium: that is, by a contrary Current, the upper Air must move from those Parts where the greatest Heat is: So by a kind of Circulation, the North-East Trade-Wind below, will be attended with a South-Westerly above, and the South-Easterly with a North-West Wind above; that this is more than a bare Conjecture, the almost instantaneous Change of the Wind to the opposite Point, which is frequently found in passing the limits of the Trade-winds, seems to assure us; but that which above all confirms this Hypothesis is the Phænomenon of the Monsoons, by this means most easily solved, and without it hardly explicable.

Supposing therefore such a Circulation, as above, 'tis to be considered that to the Northward of the Indian Ocean there is every where Land within the usual limit of the Latitude of 30, viz. Arabia, Persia, India, &c. which for the same reason as the Mediterranean Parts of Africa, are subject to unsufferable Heats when the Sun is to the North, passing nearly Vertical; but yet are temperate enough when the Sun is removed towards the other Tropick; because of a ridge of Mountains at some distance within the Land, said to be frequently in Winter cover'd with Snow, over which the Air, as it passes, must needs be much chill'd. Hence it comes to pass, that the Air coming according to the general Rule, out of the N. E. in the Indian Seas, is sometimes hotter, sometimes colder, than that which by this Circulation is return'd out of the S. W. and by consequence, sometimes the under Current or Wind, is from the N. E. sometimes from the S. W.

That this has no other Cause, is clear from the times wherein these Winds set in, viz. in April, when the Sun begins to warm those Countries to the North, the S. W. Monsoon begins, and blows during the Heats till October; when the Sun being retir'd, and all things growing cooler Northward, and the Heat increasing to the South, the North-East Winds enter and blow all the Winter till April again. And it is undoubtedly from the same Principle that to the Southwards of the Æquator, in part of the Indian Ocean, the North-West Winds succeed to the South-East, when the Sun draws near the Tropick of Capricorn; but I must confess, that in this latter occurs a difficulty, not well to be accounted for, which is, why this Change of the Monsoons should be any more in this Ocean, than in the same Latitudes in the Æthopick, where there is nothing more certain than a S. E. Wind all the Year.

'Tis likewise very hard to conceive why the limits of the Trade-wind should be fixt, about the thirtieth Degree of Latitude all round the Globe; and that they should so seldom transgress or fall short of those bounds; as also that in the Indian Sea, only the Northern Part should be subject to the changeable Monsoons, and in the Southern there be a constant S. E.

These are Particulars that merit to be consider'd more at large, and furnish a sufficient Subject for a just Volume, which will be a very commendable Task for such, who being us'd to Philosophick Contemplation, shall have leisure to apply their serious Thoughts about it.

Plate 2 pag. 80

A new & Correct Sea chart of the whole World Shewing the Variations of y^e COMPASS as they were found Año 1700 with a View of the Generall and Coasting Trade Winds and Monsoons or shifting Trade Winds by the Direction of Cap^t. Edm. Halley.

A Discourse of the Rule of the Decrease of the height of the Mercury in the Barometer, according as Places are elevated above the Surface of the Earth; with an Attempt to discover the true Reason of the Rising and Falling of the Mercury, upon Change of Weather. By Edm. Halley.

THE Elastick Property of the Air has been long since made out, by Experiments before the Royal Society, and elsewhere; and the Resistance of its Spring is found to be nearly equal to the Weight or Force that compresses it; as also, that the Spaces the same Air occupies, under differing Pressures, are reciprocally as those Pressures: It has been shewn likewise by undoubted Experiment, that the specifick Gravity of the Air, near the Earth's Surface to that of Water, was once as 1 to 840; again as 1 to 852; and a third time, in a very large Vessel holding 10 Gallons, as 1 to 860; all which, considering the Difficulty of the Experiment, agree well enough, the Mercury standing at all those times about 29 Inches ¾: But by Reason 'twas Summer-weather, and consequently the Air rarified, when all these were tried, we may without sensible Error say in round numbers, that the Barometer standing at 30 Inches, and in a mean State of Heat and Cold, the specifick Gravity of the Air to Water, is as 1 to 800. By the like Trials the weight of Mercury to Water, is as 13½ to 1, or very near it; so that the weight of Mercury to Air, is as 10800 to 1; and a Cylinder of Air of 10800 Inches or 900 Feet, is equal to an Inch of Mercury; and were the Air of an equal density like Water, the whole Atmosphere would be no more than 5,1 Miles high, and in the Ascent of every 900 Feet the Barometer would sink an Inch. But the Expansion of the Air increasing in the same proportion as the incumbent weight of the Atmosphere decreases; that is, as the Mercury in the Barometer sinks; the upper Parts of the Air are much more rarified than the lower, and each Space answering to an Inch of Quicksilver, grows greater and greater; so that the Atmosphere must be extended to a much greater height. Now, upon these Principles, to determine the height of the Mercury at any assigned height in the Air; and è contra, having the height of the Mercury given, to find the height of the Place where the Barometer stands, are Problems not more difficult than curious; and which I thus resolve.

The Expansions of the Air being reciprocally as the heights of the Mercury, it is evident, that by the help of the Curve of the Hyperbola and its Asymptotes, the said Expansions may be expounded to any given height of the Mercury: For by the 65th Prop. lib. 2. Conic. Mydorgii, the Rectangles, ABCE, AKGE, ALDE, &c. (in Plate 1. Fig. 4.) are always equal, and consequently the sides, CB, GK, LD, &c. are reciprocally as the sides AB, AK, AL, &c. If then the Lines AB, AK, AL, be supposed equal to the heights of the Mercury, or the pressures of the Atmosphere, the Lines CB, GK, LD, answering thereto, will be as the Expansions of the Air under those Pressures, or the Bulks that the same quantity of Air will occupy; which Expansions being taken infinitely many, and infinitely little, (according to the Method of Indivisibles) their Summ will give the Spaces of Air between the several heights of the Barometer; that is to say, the Summ of all the Lines between CB and KG, or the Area CBKG, will be proportioned to the Distance or Space intercepted between the Levels of two Places in the Air, where the Mercury would stand at the heights represented by the Lines AB, AK; so then the Spaces of Air answering to equal Parts of Mercury in the Barometer, are as the Area's CBKG, GKLD, DLFM, &c. These Area's again are, by the Demonstration of Gregory of St. Vincent, proportionate to the Logarithms of the Numbers expressing the Rationes of AK to AB, of AL to AK, of AM to AL, &c. So then by the common Table of Logarithms, the height of any Place in the Atmosphere, having any assign'd height of the Mercury, may most easily be found: For the Line CB in the Hyperbola, whereof the Area's design the Tabular Logarithms, being 0,0144765; 'twill be, as 0,0144765, to the difference of the Logarithms of 30, or any other lesser Number, for 900 Feet, or the Space answering to an Inch of Mercury, if the Air were equally prest with 30 Inches of Mercury, and every where alike, to the height of the Barometer in the Air, where it will stand at that lesser number of Inches: And by the Converse of this Proportion may the height of the Mercury be found, having the Altitude of the Place given. From these Rules I deriv'd the following Tables.

UPON these Suppositions it appears, that at the height of 41 Miles the Air is so rarified, as to take up 3000 times the Space it occupies here, and at 53 Miles high it would be expanded above 30000 times; but it's probable that the utmost Power of its Spring cannot exert it self, to so great an Extension, and that no part of the Atmosphere reaches above 45 Miles from the Surface of the Earth.

This seems confirm'd from the Observations of the Crepusculum, which is observ'd commonly to begin and end when the Sun is about 18 Degrees below the Horizon; for supposing the Air to reflect light from its most rarified Parts, and that as long as the Sun illuminates any of its Atoms, they are visible to an Eye not intercepted by the Curvity of the Earth, it will follow from Fig. 5. Plate 1. that the proportion of the height of the whole Air, to the Semi-diameter of the Earth, is much about, as 1 to 90, or as the excess of the Secant of about 8½ Degrees to the Radius. For if E be the Eye of the Observer, S a Place where the Sun sets at the end of Twilight in E, and the Arch ECS, or TCA, be found 18 Degrees, the excess of the Secant of half thereof ECH, would be the height of the Air, viz. GH: But the Beam of the Sun ASH, and the Visual Ray EH, do each of them suffer a Refraction of about 32 or 33 Minutes, whereby being bent inwards from H towards G, the height of the Air need not be so great as if they went streight; and having from the Angle ECS taken the double Refraction of the Horizontal Ray, the half of the Remainder will be 8½ Degrees circiter, whose Secant being 10,111, it follows, that as 10000 to 111, so the Semi-diameter of the Earth supposed 4000 Miles, to 44,4 Miles; which will be the height of the whole Air, if the Places E, S, whose visible Portions of the Atmosphere ERZH, and SHKB, just touch one the other, be 18 Degrees asunder.

At this height the Air is expanded into above 3000 times the space it occupies here, and we have seen the Experience of condensing it into the 60th part of the same Space, so that it should seem, that the Air is a Substance capable of being compressed into the 180000th part of the Space it would naturally take up, when free from pressure. Now what Texture or Composition of Parts shall be capable of this great Expansion and Contraction, seems a very hard Question; and which, I suppose, is scarce sufficiently accounted for, by comparing it to Wool, Cotten, and the like springy Bodies.

Hitherto I have only consider'd the Air and Atmosphere, as one unalter'd Body, as having constantly at the Earth's Surface the 800th part of the weight of Water, and being capable of Rarifaction and Condensation in infinitum; neither of which Hypotheses are rigidly true: For here in England it is notoriously known, that the weight of the whole Atmosphere is various, being counterpoised sometimes by 28½ Inches of Mercury, and at other times by no less than 30½; so that the under parts being pressed by about a 15th part, less weight, the specifick Gravity of the Air upon that score will sometimes be a 15th part lighter than another; besides Heat and Cold, does very considerably dilate and contract the Air, and consequently alter its Gravity; to which add the mixture of Effluvia, or steams arising from almost all Bodies, which assimulating into the Form of Air, are kept suspended therein, as Salts dissolv'd in Liquors, or Metals in corroding Menstrua; which Bodies being all of them very much heavier than Air, their Particles by their Admixture must needs encrease the weight of that Air they lie incorporated withal, after the same manner as melted Salts do augment the specifick Gravity of Water. The other Consideration is, that the Rarifaction and Condensation of the Air is not precisely according to the proportion here laid down; for the Experiment very nearly agrees thereto, as may be seen in the 58th Chapter of Mr. Hook's Micrography; yet are the Condensations not possible beyond certain degrees: For being compressed into an 800th part of the Space it takes up here, its consistence would be equally dense with that of Water; which yields not to any force whatsoever, as hath been found by several Experiments tried here, and at Florence, by the Academia del Cimento. Nor can the Rarifaction proceed in infinitum; for supposing the Spring whereby it dilates it self, occasion'd by what Texture of Parts you please, yet must there be a determinate Magnitude of the natural State of each Particle, as we see it is in Wool, and the like, whose Bodies being compressable into a very small Space, have yet a determinate bulk which they cannot exceed, when free'd from all manner of Pressure.

These Objections being true, do disturb the Geometrical Accuracy of these Conclusions, drawn from the specifick Gravity of the Air observ'd at any time; but the Method here shewn will compute by a like Calculation, the heights of the Quick-silver, and the Rarifactions of the Air from any assign'd height of the Barometer at the Earth's Surface, and any specifick Gravity given. As to the Condensation and Rarifaction by Heat and Cold, and the various mixture of Aqueous and other Vapours, these two Objections seem generally to compensate each other; for when the Air is rarified by Heat, they are raised most copiously; so that though the Air properly so call'd, be expanded, and consequently lighter, yet the Interstices thereof being crouded full of Vapours of much heavier Matters, bulk for bulk, the weight of the Compositum may continue much the same, at least a most curious Experiment made by the Ingenious Mr. John Caswell, of Oxford, upon the top of Snowdon Hill, in Carnarvanshire, seems to prove, that the first Inches of Mercury have their Portions of Air near enough to what I now determine: For the height of the Hill being 1240 Yards, or very near it, he found the Mercury to have subsided to 25,6 Inches, or 4 inches below the mean Altitude thereof at the Level of the Sea, (which is a greater difference than has been found in any of our former Experiments,) and the Space answering to 4 Inches, by my Calculation, should be 1288 Yards; and it agrees as well with the Observations in the Appendix to Mr. Pascall's Book, del Equilibre des Liqueurs, made on the high Hill in Auvergne, call'd le puy de Domme. So that the Rarifaction and Vapours seem not to have alter'd considerably, the Gravity of the under Parts of the Air; and much above the height where these Experiments were made, do few Vapours ascend, and the Cold is such that the Snow lies continually, so that for the more elevated Parts of the Sphere of Air, there is much less Reason to doubt.

But now we have had occasion to mention the difference there is between the height of the Mercury at one time, from the height thereof at another, it may not be unacceptable to offer at some Reasons for the said difference; which, at least to my self, seem to have some appearance of Truth. First, Then it's undoubtedly demonstrable, that the height of the Cylinder of Mercury is equal to the weight of the whole incumbent Air, and consequently that that whole is sometimes a fifteenth more than at other times; which cannot otherwise be, but by the access of new Matter when 'tis heavy, and its diminution when 'tis light; that Hypothesis therefore that shews how the Air shall be encreased or diminished, in any particular place, will give a Reason for the greater and lesser height of the Mercury in the Baroscope: But to direct us in the choice of the several Causes, which may be assign'd for the Increase and Decrease of the Air, 'twill not be unnecessary to enumerate some of the principal Observations made upon the Barometer, most whereof are sufficiently known already to all those that are curious in these Matters.

The First is, That in calm Weather, when the Air is inclin'd to Rain, the Mercury is commonly low.

2. That in serene good settled Weather, the Mercury is generally high.

3. That upon very great Winds, though they be not accompanied with Rain, the Mercury sinks lowest of all, with relation to the Point of the Compass the Wind blows upon.

4. That cæteris paribus the greatest heights of the Mercury are found upon Easterly and North-Easterly Winds.

5. That in calm frosty Weather the Mercury generally stands high.

6. That after very great Storms of Wind, when the Quicksilver has been low, it generally rises again very fast.

7. That the more Northerly places have greater Alterations of the Baroscope, than the more Southerly.

8. That within the Tropicks and near them, those Accounts I have had from others, and my own Observation at St. Helena, make very little or no Variation of the height of the Mercury in all Weathers.

Now that Theory that can well account for all these appearances, will, in all probability, approach nearer the true cause of the Barometers Variations, than any thing hitherto afforded; and such an one I am bound to believe, is that which I here lay down with submission to better Judgments.

I conceive that the principal Cause of the rise and fall of the Mercury, is from the variable Winds, which are found in the Temperate Zones, and whose great unconstancy here in England is most notorious. I shall not at present inquire into the Cause of its uncertainty, but the Matter of Fact being most undoubted, the Legitimate Consequences thereof must be allow'd me, let it proceed from what it will.

A second Cause is the uncertain Exhalation and Præcipitation of the Vapours lodging in the Air, whereby it comes to be at one time much more crowded than at another, and consequently heavier; but this latter in a great measure depends upon the former. Now from these Principles I shall endeavour to explicate the several Phænomena of the Barometer, taking them in the same order I laid them down.

1. Why in calm Weather the Air being inclin'd to Rain, the Mercury is commonly low? I Answer, That the Mercury's being low, inclines it to Rain; for the Air being light, the Vapours are no longer supported thereby, being become specifically heavier than the Medium wherein they floated; so that they descend towards the Earth, and in their fall meeting with other aqueous Particles, they incorporate together, and form little drops of Rain; but the Mercury's being at one time lower than another, is the effect of two contrary Winds blowing from the place whence the Barometer stands; whereby the Air of that place is carried both ways from it, and consequently the incumbent Cylinder of Air is diminished, and accordingly the Mercury sinks; as for Instance, if in the German Ocean it should blow a Gale of Westerly Wind, and at the same time an Easterly Wind in the Irish Sea; or if in France it should blow a Southerly Wind, and in Scotland a Northern; it must be granted me, that That part of the Atmosphere impendent over England, would thereby be exhausted and attenuated, and the Mercury would subside, and the Vapours which before floated in those parts of the Air of equal Gravity with themselves, would sink to the Earth.

2. Why in serene good settled weather the Mercury is generally high? To this I Answer, That the greater height of the Barometer, is occasion'd by two contrary Winds blowing towards the place of Observation, whereby the Air of other places is brought thither and accumulated; so that the incumbent Cylinder of Air being encreas'd both in height and weight, the Mercury press'd thereby must needs rise and stand high, as long as the Winds continue so to blow; and then the Air being specifically heavier, the Vapours are better kept suspended, so that they have no inclination to Præcipitate and fall down in Drops, which is the reason of the serene good Weather, which attends the greater heights of the Mercury.

3. Why upon very great Winds or Storms, tho' accompanied with no Rain, the Mercury sinks lowest of all, with relation to the Point of the Compass upon which the Wind blows? This is caus'd by the very rapid Motion of the Air in these Storms; for the Tract or Region of the Earths Surface, wherein these Winds rage, not extending all round the Globe, that stagnant Air which is left behind, as likewise that on the sides, cannot come in so fast as to supply the Evacuation made by so swift a Current; so that the Air must necessarily be attenuated, when and where the said Winds continue to blow, and that more or less, according to their Violence; add to which, that the Horizontal Motion of the Air being so quick as it is, may in all probability take off some part of the perpendicular pressure thereof; and the great Agitation of its Particles, is the Reason why the Vapours are dissipated, and do not condense into Drops, so as to form Rain, otherwise the natural Consequence of the Airs Rarifaction.

4. Why cæteris paribus the Mercury stands highest upon an Easterly or North-Easterly Wind? This happens because that in the great Atlantick Ocean, on this side the thirty fifth Degree of North Latitude, the Westerly and South-Westerly Trade-Winds blow almost always; so that whenever here the Wind comes up at East and North-East, 'tis sure to be checked by a contrary Gale, as soon as it reaches the Ocean; wherefore, according to what is made out in our second Remark, the Air must needs be heaped over this Island; and consequently the Mercury must stand high, as often as these Winds blow. This holds true in this Country, but is not a general Rule for others, where the Winds are under different Circumstances; and I have sometimes seen the Mercury here as low as twenty nine Inches, upon an Easterly Wind, but then it blows exceeding hard, and so comes to be accounted for by what was observ'd upon the third Remark.

5. Why in calm Weather the Mercury generally stands high? The cause hereof is, as I conceive, that it seldom freezes but when the Winds come out of the Northern and North-Eastern Quarters, or at least unless those Winds blow at no great distance off; for the Northern Parts of Germany, Denmark, Sweden, Norway, and all that Tract from whence North-Eastern Winds come, are subject to almost continual Frost all the Winter; and thereby the lower Air is very much condens'd, and in that State is brought hitherwards by these Winds, and being accumulated by the opposition of the Westerly Wind blowing in the Ocean, the Mercury must needs be prest to a more than ordinary height, and as a concurring Cause, the shrinking of the lower parts of the Air into lesser room by cold, must needs cause a descent of the upper parts of the Atmosphere, to reduce the Cavity made by this contraction to an Æquilibrium.

6. Why after very great Storms of Wind, when the Mercury has been very low, it generally rises again very fast? This I have frequently observed, and once found it risen an Inch and a half in less than six Hours, after a long continu'd Storm of South-West Wind. This seems to be occasion'd by the sudden Accession of new Air to supply the great Evacuation which such continu'd Storms make thereof, in those places whence they happen (as in the third Remark) and by the Recoile of the Air, after the force ceases that impelled it; and the Reason why the Mercury rises so fast, is because the Air being very much rarify'd beyond its mean density, the Neighbouring Air runs in the more swiftly to bring it to an Æquilibration, as we see Water runs the faster for having a great declivity.

7. Why in more Northerly places the Variations of the Baroscope are greater than in the Southerly? The truth of the Matter of Fact is prov'd from Observations made at Clermont and Paris, compar'd with others, made at Stockholm, as may be seen in the Appendix to Mr. Pascal's Book before-cited. The Reason I conjecture to be, that the more Northerly Parts have usually greater Storms of Wind than the more Southerly, whereby the Mercury should sink lower in that Extream; and then the Northerly Winds bringing the condens'd and ponderous Air from the Neighbourhood of the Pole, and that again being check'd by a Southerly Wind, at no great distance, and so heaped, must of necessity make the Mercury in such case stand higher in the other Extream.

8. And Lastly, Why near the Æquinoctial, as at Barbadoes and St. Helena, there is very little or no Variation of the height of the Barometer? This Remark, above all others, confirms the Hypothesis of the variable Winds, being the cause of these Variations of the height of the Mercury; for in the Places above-named, there is always an easie Gale of Wind blowing nearly upon the same Point, viz. E. N. E. at Barbadoes, and E. S. E. at St. Helena; so that there being no contrary Currents of the Air, to exhaust or accumulate it, the Atmosphere continues much in the same State. However, upon Hurricanes, the most violent of Storms, the Mercury has been observ'd very low, but this is but for once in two or three Years, and it soon recovers its settled state of about 29½ Inches. I doubt not but the same thing is in the East Coast of Africa, and in India, where the Monsoons or Trade-Winds are for half the Year one way, and half the Year another; only it's probable, that there may something worth noting happen, about the times of the change or shifting of the Winds, which might be obtain'd, if any Body had the Curiosity to keep the Barometer at our Factories in India.

I doubt not but this Doctrine will find some Opposers, and that one principal Objection will be, that I suppose the Air sometimes to move from those Parts where it is already evacuated below the Æquilibrium, and sometimes again towards those parts, where it is condens'd and crouded above the mean State, which may be thought contradictory to the Laws of Staticks and the Rules of the Æquilibrium of Fluids. But those that shall consider how, when once an impetus is given to a Fluid Body, it is capable of mounting above its Level, and checking others that have a contrary tendency to descent by their own Gravity, will no longer regard this as a material Obstacle, but will rather conclude, that the great Analogy there is between the rising and falling of the Water upon the Flux and Reflux of the Sea, and this of the accumulating and extenuating the Air, is a great Argument for the Truth of this Hypothesis: For as the Sea over against the Coast of Essex, rises and swells by the meeting of the two contrary Tides of Flood, (whereof the one comes from the S. W. along the Channel of England, and the other from the North); and on the contrary sinks below its Level upon the retreat of the Water both ways in the Tide of Ebb; so it is very probable that the Air may Ebb and Flow, after the same manner; but by reason of the diversity of Causes, whereby the Air may be set in moving, the times of these Fluxes and Refluxes thereof, are purely Casual, and not reducible to any Rule, as are the Motions of the Sea, depending wholly upon the regular Course of the Moon.

Plate 1. pag. 97

A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; containing his New Theory about Light and Colours: Sent by the Author to the Publisher from Cambridge, Feb. 6. 1671/2; in order to be communicated to the Royal Society.

SIR,

TO perform my late promise to you, I shall without further Ceremony acquaint you, That in the beginning of the Year 1666 (at which time I apply'd my self to the grinding of Optick-glasses of other Figures than Spherical,) I procur'd me a Triangular Glass-Prism, to try therewith the celebrated Phænomena of Colours. And in order thereto, having darken'd my Chamber, and made a small hole in my Window-shuts, to let in a convenient quantity of the Sun's Light, I plac'd my Prism at his entrance, that it might be thereby refracted to the opposite Wall. It was at first a very pleasing Divertisement, to view the vivid and intense Colours produced thereby; but after a while applying my self to consider them more circumspectly, I became surpriz'd to see them in an oblong Form; which, according to the received Laws of Rarefraction, I expected should have been Circular.

They were terminated at the sides with streight Lines, but at the ends, the decay of Light was so gradual, that it was difficult to determine justly, what was their Figure; yet they seem'd Semicircular.

Comparing the length of this colour'd Spectrum with its breadth, I found it about five times greater; a disproportion so extravagant, that it excited me to a more than ordinary Curiosity of examining, from whence it might proceed. I could scarce think, that the various thickness of the Glass, or the termination with shadow or darkness, could have any Influence on Light to produce such an effect; yet I thought it not amiss, first to examine those Circumstances, and so try'd what would happen by transmitting Light through parts of the Glass of divers thicknesses, or through holes in the Window of divers bignesses, or by setting the Prism without, so that the Light might pass through it, and be refracted before it was terminated by the hole: But I found none of those Circumstances material. The fashion of the Colours was, in all these Cases, the same.

Then I suspected, whether by any unevenness in the Glass, or other contingent Irregularity, these Colours might be thus dilated. And to try this, I took another Prism like the former, and so plac'd it, that the Light passing through them both, might be refracted contrary ways, and so by the latter return'd into that Course, from which the former had diverted it. For, by this means, I thought the regular effects of the first Prism would be destroy'd by the second Prism, but the irregular ones more augmented by the multiplicity of Refractions. The Event was, that the Light, which by the first Prism was diffused into an oblong Form, was, by the second, reduc'd into an orbicular one, with as much regularity, as when it did not at all pass through them. So that whatever was the cause of that length, 'twas not any contingent Irregularity.

I then proceeded to examine more critically, what might be effected by the difference of the incidence of Rays coming from divers parts of the Sun; and to that end, measur'd the several Lines and Angles belonging to the Image. Its distance from the Hole or Prism was twenty two Foot; its utmost length 13¼ Inches; its breadth 2⅝; the Diameter of the Hole ¼ of an Inch; the Angle, with the Rays, tending towards the middle of the Image, made with those Lines, in which they would have proceeded without Refraction, was 44° 56'. And the Vertical Angle of the Prism, 63° 12'. Also the Refractions on both sides the Prism, that is, of the Incident, and Emergent Rays, were as near, as I could make them, equal, and consequently about 54° 4'. And the Rays fell perpendicularly upon the Wall. Now subducting the Diameter of the Hole from the length and breadth of the Image, there remains 13 Inches the length, and 2⅜ the breadth, comprehended by those Rays, which passed thro' the Center of the said Hole, and consequently the Angle of the Hole, which that breadth subtended, was about 31', answerable to the Sun's Diameter; but the Angle, which its length subtended, was more than five such Diameters, namely 2° 49'.

Having made these Observations, I first computed from them the refractive Power of that Glass, and found it measur'd by the ratio of the Sines, twenty to thirty one. And then, by that ratio, I computed the Refractions of two Rays flowing from opposite parts of the Sun's discus, so as to differ 31' in their obliquity of Incidence, and found that the emergent Rays should have comprehended an Angle of about 31', as they did, before they were incident.

But because this Computation was founded on the Hypothesis of the proportionality of the Sines of Incidence and Refraction, which, tho' by my own Experience I could not imagine to be so erroneous as to make that Angle but 31', which in reality was 2° 49'; yet my Curiosity caus'd me again to take my Prism. And having plac'd it at my Window, as before, I observ'd, that by turning it a little about its Axis to and fro, so as to vary its obliquity to the light, more than an Angle of four or five Degrees, the Colours were not thereby sensibly translated from their place on the Wall, and consequently by that Variation of Incidence, the quantity of Refraction was not sensibly varied. By this Experiment therefore, as well as by the former Computation, it was evident, that the difference of the Incidence of Rays, flowing from divers parts of the Sun could not make them, after decussation, diverge at a sensibly greater Angle, than that at which they before converged; which being, at most, but about thirty one or thirty two Minutes, there still remain'd some other cause to be found out, from whence it could be two Deg. 49 Min.

Then I began to suspect, whether the Rays, after their Trajection through the Prism, did not move in curve Lines, and according to their more or less Curvity, tend to divers parts of the Wall. And it increas'd my suspicion, when I remember'd that I had often seen a Tennis-Ball, struck with an oblique Racket, describe such a curve Line. For a Circular as well as a Progressive Motion being communicated to it by that stroak, its parts on that side, where the Motions conspire, must press and beat the contiguous Air more violently than on the other, and there excite a Reluctancy and Reaction of the Air proportionably greater. And for the same Reason, if the Rays of Light should possibly be globular Bodies, and by their oblique Passage out of one Medium into another, acquire a circulating Motion, they ought to feel the greater resistance from the ambient Æther, on that side, where this Motion conspires, and thence be continually bowed to the other. But notwithstanding this plausible ground of suspicion, when I came to examine it, I could observe no such Curvity in them. And besides (which was enough for my purpose) I observ'd, that the difference 'twixt the length of the Image, and Diameter of the Hole, through which the Light was transmitted, was proportionable to their distance.

The gradual removal of these suspicions, at length led me to the Experimentum Crucis, which was this; I took two Boards, and plac'd one of them close behind the Prism at the Window, so that the light might pass through a small hole, made in it for the purpose, and fall on the other Board, which I plac'd at about twelve Feet distance, having first made a small hole in it also, for some of that incident Light to pass through. Then I plac'd another Prism behind this second Board, so that the Light, trajected through both the Boards, might pass thro' that also, and be again refracted before it arrived at the Wall. This done, I took the first Prism in my Hand, and turn'd it to and fro slowly about its Axis, so much as to make the several parts of the Image, cast on the second Board, successively pass through the hole in it, that I might observe to what places on the Wall the second Prism would refract them. And I saw by the Variation of those places, that the Light, tending to that end of the Image, towards which the Refraction of the first Prism was made, did, in the second Prism, suffer a Refraction considerably greater than the Light tending to the other end. And so the true cause of the length of that Image was detected to be no other, than that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of Refrangibility, transmitted towards divers parts of the Wall.

When I understood this, I left off my aforesaid Glass Works; for I saw, that the perfection of Telescopes was hitherto limited, not so much for want of Glasses truly figur'd, according to the prescriptions of Optick Authors (which all Men have hitherto imagin'd), as because that Light it self is a Heterogeneous mixture of differently refrangible Rays. So that, were a Glass so exactly figur'd, so as to collect any one sort of Rays into one Point, it could not collect those also into the same Point, which having the same Incidence upon the same Medium, are apt to suffer a different Refraction. Nay, I wonder'd, that seeing the difference of Refrangibility was so great, as I found it, Telescopes should arrive to that perfection they are now at. For, measuring the Refractions in one of my Prisms, I found, that, supposing the common Sine of Incidence upon one of its plains, was forty four Parts, the Sine of Refraction of the utmost Rays on the red end of the Colours, made out of the Glass into the Air, would be sixty eight parts, and the Sine of Refraction of the utmost Rays on the other end, sixty nine parts; so that the difference is about a twenty fourth or twenty fifth part of the whole Refraction. And consequently the Object glass of any Telescope cannot collect all the Rays, which come from one point of an Object, so as to make them convene at its Focus in less room than in a Circular space, whose Diameter is the fiftieth part of the Diameter of its Aperture; which is an irregularity, some hundred of times greater, than a circularly figur'd Lens, of so small a section as the Object-glasses of long Telescopes are, would cause by the unfitness of its Figure, were Light uniform.

This made me take Reflections into Consideration, and finding them regular, so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation, Optick Instruments might be brought to any degree of Perfection imaginable, provided a Reflecting Substance could be found, which would polish as finely as Glass, and reflect as much Light as Glass transmits; and the art of communicating to it a Parabolick Figure be also attain'd. But there seem'd very great Difficulties, and I have almost thought them insuperable, when I further consider'd, that every Irregularity in a reflecting Superficies makes the Rays stray five or six times more out of their due course, than the like Irregularities in a refracting one; So that a much greater Curiosity would be here requisite, than in Figuring Glasses for Refraction.

Amidst these Thoughts I was forc'd from Cambridge by the Intervening Plague, and it was more than two Years before I proceeded further. But then having thought on a tender way of polishing, proper for Metal, whereby, as I imagin'd, the Figure also would be corrected to the last; I began to try what might be effected in this kind, and by degrees so far perfected an Instrument (in the essential parts of it like that I sent to London,) by which I could discern Jupiter's four Concomitants, and shew'd them divers times to two others of my Acquaintance. I could also discern the Moon-like Phase of Venus, but not very distinctly, nor without some niceness in disposing the Instrument.

From that time I was interrupted, till this last Autumn, when I made the other. And as that was sensibly better than the first (especially for Day-Objects,) so I doubt not but they will be still brought to a much greater perfection by their Endeavours, who, as you inform me, are taking care about it at London.

I have sometimes thought to make a Microscope, which in like manner should have, instead of an Object-glass, a reflecting piece of Metal. And this I hope they will also take into Consideration: For those Instruments seem as capable of improvement as Telescopes, and perhaps more, because but one reflective piece of Metal is requisite in them, as you may perceive in Plate 3. Fig. 1. where AB representeth the Object Metal, CD the Eye-glass, F their common Focus, and O the other Focus of the Metal, in which the Object is placed.

But to return from this digression, I told you, that Light is not similar, or homogeneal, but consists of difform Rays, some of which are more refrangible than others: So that of those, which are alike incident on the same Medium, some shall be more refracted than others, and that not by any virtue of the Glass, or other external Cause, but from a predisposition, which every particular Ray hath to suffer a particular degree of Refraction.

I shall now proceed to acquaint you with another more notable deformity in its Rays, wherein the Origin of Colours is unfolded: Concerning which I shall lay down the Doctrine first, and then, for its Examination, give you an Instance or two of the Experiments, as a Specimen of the rest.

The Doctrine you will find comprehended and illustrated in the following Propositions.

1. As the Rays of Light differ in degrees of Refrangibility, so they also differ in their disposition to exhibit this or that particular Colour. Colours are not Qualifications of Light, derived from Refractions, or Reflections of natural Bodies, (as 'tis generally believed) but Original and connate Properties, which in divers Rays are divers. Some Rays are disposed to exhibit a red Colour and no other; some a yellow and no other, some a green and no other, and so of the rest. Nor are there only Rays proper and particular to the more eminent Colours, but even to all their intermediate Gradations.

2. To the same degree of Refrangibility ever belongs the same Colour, and to the same Colour ever belongs the same degree of Refrangibility. The least Refrangible Rays are all disposed to exhibit a Red Colour, and contrarily those Rays, which are disposed to exhibit a Red Colour, are all the least Refrangible: So the most Refrangible Rays are all disposed to exhibit a deep Violet Colour, and contrarily those which are apt to exhibit such a Violet Colour, are all the most Refrangible. And so to all the intermediate Colours in a continued Series belong intermediate degrees of Refrangibility. And this Analogy 'twixt Colours, and Refrangibility, is very precise and strict; the Rays always either exactly agreeing in both, or proportionally disagreeing in both.

3. The Species of Colour, and Degree of Refrangibility proper to any particular sort of Rays, is not mutable by Refraction, nor by Reflection from Natural Bodies, nor by any other Cause, that I could yet observe. When any one sort of Rays hath been well parted from those of other kinds, it hath afterwards obstinately retain'd its Colour, notwithstanding my utmost Endeavours to change it. I have refracted it with Prisms, and reflected it with Bodies, which in Day-light were of other Colours; I have intercepted it with the colour'd Film of Air interceding two compressed Plates of Glass; transmitted it through colour'd Mediums, and through Mediums irradiated with other sorts of Rays, and diversly terminated it, and yet could never produce any new Colour out of it. It would by contracting and dilating become more brisk, or faint, and by the loss of many Rays in some Cases very obscure and dark; but I could never see it chang'd in specie.

4. Yet seeming Transmutations of Colours may be made, where there is any mixture of divers sorts of Rays. For in such mixtures, the component Colours appear not, but by their mutual allaying each other, constitute a midling Colour. And therefore, if by Refraction, or any other of the aforesaid Causes, the difform Rays, latent in such a mixture, be separated, there shall emerge Colours different from the colour of the Composition. Which Colours are not new generated, but only made apparent by being parted; for if they be again intirely mix'd and blended together, they will again compose that Colour, which they did before separation. And for the same reason, Transmutations made by the convening of divers Colours are not real; for when the difform Rays are again severed, they will exhibit the very same Colours, which they did before they entered the Composition; as you see, Blue and Yellow Powders, when finely mixed, appear to the naked Eye Green, and yet the Colours of the component Corpuscles are not thereby really transmuted, but only blended. For, when viewed with a good Microscope, they still appear Blue and Yellow interspersedly.

5. There are therefore two sorts of Colours. The one Original and Simple, the other compounded of these. The Original or Primary Colours are, Red, Yellow, Green, Blue, and a Violet-purple, together with Orange, Indico, and an indefinite variety of intermediate Gradations.

6. The same Colours in Specie with these primary Ones, may be also produced by Composition: For, a mixture of Yellow and Blue makes Green; of Red and Yellow, makes Orange; of Orange and Yellowish Green, makes Yellow. And in general, if any two Colours be mix'd, which in the Series of those, generated by the Prism, are not too far distant one from another, they by their mutual Alloy compound that Colour, which in the said Series appeareth in the mid-way between them. But those, which are situated at too great a distance, do not so. Orange and Indico produce not the intermediate Green, nor Scarlet and Green the intermediate Yellow.

7. But the most surprizing and wonderful Composition was that of Whiteness. There is no one sort of Rays which alone can exhibit this. 'Tis ever compounded, and to its Composition are requisite all the aforesaid primary Colours, mix'd in a due proportion. I have often with admiration beheld, that all the Colours of the Prism being made to converge, and thereby to be again mixed as they were in the light before it was incident upon the Prism, reproduced light, intirely and perfectly white, and not at all sensibly differing from a direct light of the Sun, unless when the Glasses, I used, were not sufficiently clear; for then they would a little incline it to their Colour.

8. Hence therefore it comes to pass, that Whiteness is the usual Colour of Light; for Light is a confused aggregate of Rays, indued with all sorts of Colours, as they are promiscuously darted from the various parts of luminous Bodies. And of such a confused aggregate, as I said, is generated Whiteness, if there be a due proportion of the Ingredients; but if any one predominate, the Light must incline to that Colour; as it happens in the blue Flame of Brimstone, the yellow Flame of a Candle, and the various Colours of the fixed Stars.

9. These things consider'd, the manner, how Colours are produced by the Prism, is evident. For, of the Rays, constituting the incident Light, since those which differ in Colour proportionally differ in Refrangibility, they by their unequal Refractions must be severed and dispersed into an oblong Form, in an orderly succession, from the least refracted Scarlet to the most refracted Violet. And for the same reason it is, that Objects, when look'd upon through a Prism, appear coloured. For the difform Rays, by their unequal Refractions, are made to diverge towards several parts of the Retina, and there express the Images of things coloured, as in the former case they did the Sun's Image upon a Wall. And by this inequality of Refractions, they become not only coloured, but also very confused and indistinct.

10. Why the Colours of the Rainbow appear in falling drops of Rain, is also from hence evident. For those drops, which refract the Rays, disposed to appear Purple, in greatest quantity to the Spectator's Eye, refract the Rays of other sorts so much less, as to make them pass beside it; and such are the drops on the inside of the Primary Bow, and on the outside of the Secondary or Exteriour one. So those drops, which refract in greatest plenty the Rays, apt to appear red, toward the Spectator's Eye, refract those of other sorts so much more, as to make them pass beside it; and such are the drops on the Exteriour part of the Primary, and Interiour part of the Secondary Bow.

11. The odd Phænomena of an infusion of Lignum Nephriticum, Leaf-gold, Fragments of colour'd Glass, and some other transparently coloured Bodies, appearing in one Position of one Colour, and of another in another, are on these grounds no longer Riddles. For those are Substances apt to reflect one sort of Light, and transmit another; as may be seen in a dark Room, by illuminating them with similar or uncompounded Light. For then they appear of that Colour only, with which they are illuminated; but yet in one Position more vivid and luminous than in another, accordingly as they are disposed more or less to reflect or transmit the incident Colour.

12. From hence also is manifest the reason of an unexpected Experiment, which Mr. Hook, somewhere in his Micrography, relates to have made with two wedge-like transparent Vessels fill'd, the one with a red, the other with a blue Liquor; namely, that though they were severally transparent enough, yet both together became opake: For, if one transmitted only red, and the other only blue, no Rays could pass through both.

13. I might add more Instances of this Nature; but I shall conclude with this general one, that the Colours of all natural Bodies have no other Origin than this, that they are variously qualified to reflect one sort of Light in greater plenty than another. And this I have experimented in a dark Room, by illuminating those Bodies with uncompounded Light of divers Colours. For by that means any body may be made to appear of any Colour. They have there no appropriate Colour, but ever appear of the Colour of the Light cast upon them; but yet with this difference, that they are most brisk and vivid in the Light of their own day-light-colour. Minium appeareth there of any Colour indifferently, with which 'tis illustrated, but yet most luminous in red; and so Bise appeareth indifferently of any Colour with which 'tis illustrated, but yet most luminous in blue. And therefore Minium reflecteth Rays of any Colour, but most copiously those endu'd with red, and consequently when illustrated with day-light, that is, with all sorts of Rays promiscuously blended, those qualified with red, shall abound most in the reflected Light, and by their prevalence cause it to appear of that Colour. And for the same reason Bise, reflecting blue most copiously, shall appear blue by the excess of those Rays in its reflected Light; and the like of other Bodies. And that this is the intire and adequate cause of their Colours, is manifest, because they have no power to change or alter the Colours of any sort of Rays incident apart, but put on all Colours indifferently, with which they are enlightned.

These things being so, it can be no longer disputed, whether there be Colours in the dark, nor whether they be the Qualities of the Objects we see, no nor perhaps, whether Light be a Body. For, since Colours are the Qualities of Light, having its Rays for their intire and immediate Subject, how can we think those Rays Qualities also, unless one Quality may be the Subject of and sustain another; which in effect is to call it Substance? We should not know Bodies for Substances, were it not for their sensible Qualities; and the principal of those being now found due to something else, we have as good reason to believe that to be a Substance also.

Besides, whoever thought any Quality to be a heterogeneous Aggregate, such as Light is discovered to be? But to determine more absolutely, what Light is, after what manner refracted, and by what Modes or Actions it produceth in our Minds the Phantasms of Colours, is not so easie. And I shall not mingle Conjectures with Certainties.

Reviewing what I have written, I see the Discourse it self will lead to divers Experiments sufficient for its Examination; and therefore I shall not trouble you farther, than to describe one of those, which I have already insinuated.

In a darkned Room, make a hole in the shut of a Window, whose Diameter may conveniently be about a third part of an Inch, to admit a convenient quantity of the Sun's Light. And there place a clear and colourless Prism, to refract the entring Light towards the farther part of the Room; which, as I said, will thereby be diffused into an oblong coloured Image. Then place a Lens of about three Foot Radius (suppose a broad Object-glass of a three Foot Telescope,) at the distance of about four or five Foot from thence, through which all those Colours may at once be transmitted, and made by its Refraction to convene at a farther distance of about ten or twelve Feet. If at that distance you intercept this Light with a Sheet of white Paper, you will see the Colours converted into whiteness again by being mingled. But it is requisite, that the Prism and Lens be placed steady, and that the Paper, on which the Colours are cast, be moved to and fro; for, by such motion, you will not only find at what distance the whiteness is most perfect, but also see how the Colours gradually convene, and vanish into whiteness; and afterwards, having crossed one another in that place where they compound whiteness, are again dissipated and severed, and in an inverted order retain the same Colours, which they had before they entred the Composition. You may also see, that, if any of the Colours at the Lens be intercepted, the whiteness will be changed into the other Colours. And therefore, that the Composition of whiteness be perfect, care must be taken that none of the Colours fall besides the Lens.

In the annexed Design, Tab. 3. Fig. 2. of this Experiment, ABC expresseth the Prism set end-wise to sight, close by the hole F of the Window EG. Its vertical Angle ABC may conveniently be about 60 Degrees: MN designeth the Lens. Its breadth 2½ or 3 Inches. SF one of the streight Lines, in which difform Rays may be conceived to flow successively from the Sun. FP, and FR two of those Rays unequally refracted, which the Lens makes to converge towards Q, and after decussation to diverge again. And HI the Paper, at divers distances, on which the Colours are projected, which in Q constitute Whiteness, but are Red and Yellow in R, r, and ρ, and Blue and Purple in P, p, and π.

If you proceed further to try the impossibility of changing any uncompounded Colour (which I have asserted in the third and thirteenth Propositions,) 'tis requisite that the Room may be very dark, lest any scattering light, mixing with the Colour, disturb and allay it, and render it compound, contrary to the design of the Experiment. 'Tis also requisite, that there be a perfecter separation of the Colours, than, after the manner above described, can be made by the Refraction of one single Prism; and how to make such farther separations, will scarce be difficult to them, that consider the discovered Laws of Refractions. But if trial shall be made with Colours not throughly separated, there must be allowed changes proportionable to the mixture. Thus if compound Yellow Light fall upon blue Bise, the Bise will not appear perfectly yellow, but rather green, because there are in the yellow mixture many Rays indued with green, and green being less remote from the usual blue Colour of Bise than yellow, is the more copiously reflected by it.

In like manner, if any one of the Prismatick Colours, suppose red, be intercepted, on design to try the asserted impossibility of reproducing that Colour out of the others which are pretermitted; 'tis necessary, either that the Colours be very well parted before the red be intercepted; or that, together with the red, the neighbouring Colours, into which any red is secretly dispersed, (that is, the yellow, and perhaps green too) be intercepted; or else, that allowance be made for the emerging of so much red out of the yellow green, as may possibly have been diffused, and scatteringly blended in those Colours. And if these things be observed, the new Production of red, or any intercepted Colour, will be found impossible.

This, I conceive, is enough for an Introduction to Experiments of this kind; which if any of the Royal Society shall be so curious as to prosecute, I should be very glad to be informed with what success: That, if any thing seem to be defective, or to thwart this Relation, I may have an opportunity of giving farther Direction about it, or of acknowledging my Errors, if I have committed any.

Since the Publication of this Theory, some Misunderstandings happening between a French Philosopher at Paris and Mr. Newton, he has endeavour'd to explain himself a little further in these Things, according to the following Method.

A farther Explanation of the same Theory.

DEFINITIONS.

1. I call that Light Homogeneal, Similar, or Uniform, whose Rays are equally refrangible.

2. And that Heterogeneal, whose Rays are unequally refrangible.

Note, There are but three Affections of Light in which I have observ'd its Rays to differ; viz. Refrangibility, Reflexibility, and Colour; and those Rays which agree in Refrangibility, agree also in the other two, and therefore may well be defined Homogeneal; especially since Men usually call those things Homogeneal, which are so in all Qualities that come under their Knowledge, tho' in other Qualities, that their Knowledge extends not to, there may possibly be some Heterogeneity.

3. Those Colours I call Simple or Homogeneal, which are exhibited by Homogeneal Light.

4. And those Compound or Heterogeneal, which are exhibited by Heterogeneal Light.

5. Different Colours, I call, not only the more eminent Species, Red, Yellow, Green, Blue, Purple, but all other the minutest Gradations; much after the same manner, that not only the more eminent Degrees in Musick, but all the lead Gradations, are esteem'd different Sounds.