Produced by Deaurider, Chris Pinfield and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive) 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. Gesperrt font has been condensed. Small capitals have been replaced by full capitals. Brackets extending over several columns have been replaced by columns of standard brackets. Words that are stacked one over the other are rendered thus: {upper|lower}. Italicised text is indicated by _underscores_. Where an italicised sentence or paragraph includes a word in ordimary font this is also indicated by _underscores_. Mathematical variables are usually italicised. In order to avoid an excessive number of underscores, and where it is possible without ambiguity, complete mathematical expressions have instead been encased in underscores. These usually extend over mathematical operators (such as "+"), or Greek characters, that are not italicised. The more complex mathematical expressions have been separated out from the surrounding text. Fifth roots and nth roots are indicated by [âµâ] and [â¿â] respectively. The decimal point may be indicated by a "." or "," while illustrations are referred to as a "Plate" or a "Tab." The Table of Discourses has been amended to include one omitted title and to correct erroneous page numbers. [Illustration, probably of Charles II: _M: VáµÊ³ Gucht Sculp:_] _Miscellanea Curiosa._ CONTAINING A COLLECTION Of some of the Principal _PHÃNOMENA_ 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 TABLE OF THE _Discourses_ contain'd in this _Volume_. _An Estimate of the Quantity of _Vapours_ raised out of the Sea, as derived from Experiment: Together with an Account of the _Circulation_ of the wat'ry Vapours of the Sea, and of the Cause of _Springs_. Presented to the Royal Society by Mr. _E. Halley_, F. R. S._ Pag. 1 _The True Theory of the _Tides_, extracted from that admired Treatise of Mr. _Isaac Newton_, Intituled _PhilosophiÃ¦ Naturalis Principia Mathematica_; being a Discourse presented with that Book to the late King _James_, by Mr. _E. Halley_._ 13 _A Theory of the _Variation_ of the _Magnetical Compass_, by Mr. _E. Halley_._ 27 _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 presented to the Royal Society in one of their late Meetings, by Mr. _E. Halley_._ 43 _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. _E. Halley_._ 61 _A Discourse of the Rule of the Decrease of the Heighth 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 Mr. _E. Halley_._ 81 _A Letter from Mr. _Isaac Newton_, while Professor of the Mathematicks in the University of _Cambridge_; containing his new _Theory_ about _Light_ and _Colours_: Sent from _Cambridge, Feb. 6. 1671/72._ in order to be communicated to the Royal Society._ 97 _A farther Explanation of the same _Theory_._ 114 _A Demonstration concerning the _Motion of Light_, communicated from _Paris_._ 118 _An Introductory Essay to the Doctrine of _Sounds_, containing some Proposals for the Improvement of _Acousticks_; as it was presented to the _Dublin_ Society, by the Right Reverend Father in God _Narcissus_, Lord Bishop of _Ferns_ and _Leighlin_._ 121 _A Discourse concerning the Modern _Theory_ of _Generation_, by Dr. _Geo. Garden_, of _Aberdeen_, being part of a Letter to Dr. _William Musgrave_, L. L. D. _Reg. Soc. S._ and by him communicated to the Royal Society._ 142 _A short Discourse concerning _Concoction_ Read at a Meeting of the _Royal Society_, by _Clopton Havers_, M. D. Fellow of the Royal Society._ 153 _A Discourse concerning some Influence of _Respiration_ on the Motion of the _Heart_ hitherto unobserved. By _J. Drake_, M. D. F. R. S._ 171 _Some Thoughts and Experiments concerning _Vegetation_. By _John Woodward_, M. D. of the College of Physicians and Royal Society, and Professor of Physick in _Gresham-College_._ 203 _An Account of the Measure of _Gold_ upon Gilt Wire; together with a Demonstration of the exceeding Minuteness of the _Atoms_, or constituent Parts of _Gold_; as it was read before the _Royal Society_, by Mr. _E. Halley_._ 243 _An Account of the several Species of _Infinite Quantity_, and of the Proportions they bear one to the other; as it was read before the _Royal Society_, by _E. Halley_._ 246 _An Account of Dr. _Robert Hook's_ Invention of the _Marine Barometer_, with it's Description and Uses. Published by Order of the Royal Society by Mr. _E. Halley_._ 250 _A Discourse concerning the _Proportional Heat_ of the Sun in all _Latitudes_; with the Method of collecting the same, as it was read before the _Royal Society_ in one of their late Meetings, by Mr. _E. Halley_._ 256 _Concerning the Distance of the _Fixed Stars_, by the Honourable _Fran. Roberts_, Esq; F. R. S._ 265 _Mr. _Isaac Newton's_ Theory of the _Moon_._ 268 _An estimate of the Degrees of the Mortality of _Mankind_, drawn from Curious Tables of _Births_ and _Funerals_ at the City of _Breslaw_; with an Attempt to ascertain the _Price of Annuities_ upon Lives, by Mr. _E. Halley_._ 280 _A Discourse concerning _Gravity_, and its Properties, wherein the Descent of _Heavy Bodies_, and the Motion of _Projects_ is briefly, but fully handled: Together with the Solution of a Problem of great Use in _Gunnery_, by Mr. _E. Halley_._ 302 _A Proposition of General Use in the Art of _Gunnery_, shewing the Rule of laying a _Mortar_ to pass, in order to strike any Object above or below the Horizon, by Mr. _E. Halley_._ 326 _A Discourse concerning the Measure of the Air's Resistance to Bodies moved in it. By the Learned _John Wallis_, S. T. D. and F. R. S._ 332 _An Instance of the Excellency of the Modern _Algebra_, in the Resolution of the Problem of finding the _Foci_ of Optick Glasses universally. By Mr. _E. Halley_, S. R. S._ 348 APPENDIX. _An Analytical Resolution of certain Equations of the 3d, 5th, 7th, 9th Powers, and so on _ad Infinitum_, in finite Terms, after the manner of _Cardan's_ Rules for Cubicks. By Mr. _A. Moivre_, F. R. S._ 365 _A Discourse concerning the Action of the Sun and Moon on Animal Bodies; and the Influence which this may have in many Diseases. By _Richard Mead_, M. D. F. R. S._ 371 _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 AbscissÃ¦; 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 CÅlestial 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 CÅlestial 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 _FÃ¦cundity_, 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 PhÃ¦nomenon, 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. 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 253â  grains, or Â½ ounce 13â  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 7-9/10 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 â  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 â  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 â  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 _PhÃ¦nomenon_: 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 LunÃ¦_, 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 CÅlestial 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,
{'title': 'Miscellanea Curiosa, Vol. 1 by M. de Fontenelle et al.', 'source': 'Project Gutenberg', 'lang': 'en'}