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- visibility: hidden;} - - p.cap09:first-letter, - p.cap13:first-letter - {padding-right: 0em; margin-left: 0em;} -} - -.transnote {background-color: #E6E6FA; color: black; font-size:smaller; padding:0.5em; margin-bottom:5em; font-family:sans-serif, serif; } - </style> - </head> -<body> - - -<pre> - -Project Gutenberg's A View of Sir Isaac Newton's Philosophy, by Anonymous - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - - - -Title: A View of Sir Isaac Newton's Philosophy - -Author: Anonymous - -Release Date: September 28, 2016 [EBook #53161] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK SIR ISAAC NEWTON'S PHILOSOPHY *** - - - - -Produced by Giovanni Fini, Markus Brenner, Irma Spehar and -the Online Distributed Proofreading Team at -http://www.pgdp.net (This file was produced from images -generously made available by The Internet Archive/Canadian -Libraries) - - - - - - -</pre> - -<div class="limit"> - -<div class="chapter"> -<div class="transnote p4"> -<p class="pc large">TRANSCRIBER’S NOTES:</p> -<p class="ptn">—Obvious print and punctuation errors were corrected.</p> -<p class="ptn">—The transcriber of this project created the book cover -image using the title page of the original book. The image -is placed in the public domain.</p> -</div> - -<hr class="chap" /> - -</div> - -<p><span class="pagenum"><a name="Page_i" id="Page_i">[i]</a></span></p> - -<div class="chapter"> - -<h1 class="p4"><span class="small">A</span><br /> -<span class="large"><em class="gesperrt">VIEW</em></span><br /> -<span class="small"><em class="gesperrt">OF</em></span><br /> -<span class="mid">Sir <em class="gesperrt"><i>ISAAC NEWTON</i></em>’s</span><br /> -<span class="large">PHILOSOPHY.</span></h1> - -<div class="figcenter"> - <img src="images/title.jpg" width="400" height="251" - alt="" - title="" /> -</div> - -<p class="pc large"><em class="gesperrt"><i>LONDON</i></em>:</p> - -<p class="pc mid">Printed by <span class="smcap"><em class="gesperrt">S. Palmer</em></span>, 1728.</p> - -</div> -<p><span class="pagenum"><a name="Page_ii" id="Page_ii">[ii]</a></span></p> -<p> </p> -<p><span class="pagenum"><a name="Page_iii" id="Page_iii">[iii]</a></span></p> - -<div class="chapter"> - -<div class="figcenter"> - <img src="images/ill-003.jpg" width="400" height="210" - alt="" - title="" /> -</div> - -<p class="pc"><span class="lmid">To the Noble and Right Honourable</span><br /> -<span class="mid"><span class="smcap">Sir</span> <i>ROBERT WALPOLE.</i></span></p> - -<p class="pi4 p1 mid"><i>SIR,</i></p> - -<div> - <img class="dcap1" src="images/di1.jpg" width="80" height="81" alt=""/> -</div> -<p class="cap09">I Take the liberty to send you -this view of Sir <em class="gesperrt"><span class="smcap">Isaac Newton’s</span></em> -philosophy, which, if -it were performed suitable to the -dignity of the subject, might -not be a present unworthy the -acceptance of the greatest person. For his philosophy<span class="pagenum"><a name="Page_iv" id="Page_iv">[iv]</a></span> -operations of nature, which for so many ages -had imployed the curiosity of mankind; though -no one before him was furnished with the -strength of mind necessary to go any depth in -this difficult search. However, I am encouraged -to hope, that this attempt, imperfect as it is, to -give our countrymen in general some conception -of the labours of a person, who shall always -be the boast of this nation, may be received -with indulgence by one, under whose -influence these kingdoms enjoy so much happiness. -Indeed my admiration at the surprizing -inventions of this great man, carries me to conceive -of him as a person, who not only must -raise the glory of the country, which gave him -birth; but that he has even done honour to human -nature, by having extended the greatest -and most noble of our faculties, reason, to subjects, -which, till he attempted them, appeared -to be wholly beyond the reach of our limited -capacities. And what can give us a<span class="pagenum"><a name="Page_v" id="Page_v">[v]</a></span> -more pleasing prospect of our own condition, -than to see so exalted a proof of the strength -of that faculty, whereon the conduct of our -lives, and our happiness depends; our passions -and all our motives to action being in such -manner guided by our opinions, that where -these are just, our whole behaviour will be -praise-worthy? But why do I presume to detain -you, <span class="smcap">Sir</span>, with such reflections as these, -who must have the fullest experience within -your own mind, of the effects of right reason? -For to what other source can be ascribed that -amiable frankness and unreserved condescension -among your friends, or that masculine perspicuity -and strength of argument, whereby you draw -the admiration of the publick, while you are -engaged in the most important of all causes, -the liberties of mankind?</p> - -<p class="p2">I humbly crave leave to make the only acknowledgement -within my power, for the benefits,<span class="pagenum"><a name="Page_vi" id="Page_vi">[vi]</a></span> -which I receive in common with the rest of my -countrymen from these high talents, by subscribing -my self</p> - -<p class="pi10 p2 mid"><em class="gesperrt"><i>SIR</i></em>,</p> -<p class="pi10 p1 mid"><i>Your most faithful</i>,</p> -<p class="pi12 p1 mid"><i>and</i></p> -<p class="pi10 p1 mid"><i>Most humble Servant</i>,</p> - -<p class="pi8 p1 large"><span class="smcap"><em class="gesperrt">Henry Pemberton</em>.</span></p> - -<hr class="chap" /> - -</div> - -<p><span class="pagenum"><a name="Page_vii" id="Page_vii">[vii]</a></span></p> - -<div class="chapter"> - -<h2 class="p4"><em class="gesperrt">PREFACE</em>.</h2> - - -<p class="drop-cap00">I <i>Drew up the following papers many years ago at the desire of -some friends, who, upon my taking care of the late edition of -Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton’s</span></em> <i>Principia, perswaded me to make them -publick. I laid hold of that opportunity, when my thoughts -were afresh employed on this subject, to revise what I had formerly -written. And I now send it abroad not without some hopes of answering -these two ends. My first intention was to convey to such, as are not -used to mathematical reasoning, some idea of the philosophy of a person, -who has acquired an universal reputation, and rendered our nation -famous for these speculations in the learned world. To which purpose -I have avoided using terms of art as much as possible, and taken -care to define such as I was obliged to use. Though this caution -was the less necessary at present, since many of them are become familiar -words to our language, from the great number of books wrote -in it upon philosophical subjects, and the courses of experiments, that -have of late years been given by several ingenious men. The other -view I had, was to encourage such young gentlemen as have a turn for -the mathematical sciences, to pursue those studies the more chearfully, -in order to understand in our author himself the demonstrations of the -things I here declare. And to facilitate their progress herein, I intend -to proceed still farther in the explanation of Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton’s</span></em> -<i>philosophy. For as I have received very much pleasure from -perusing his writings, I hope it is no illaudable ambition to endeavour -the rendering them more easily understood, that greater numbers may -enjoy the same satisfaction.</i></p> - -<p><i>It will perhaps be expected, that I should say something particular -of a person, to whom I must always acknowledge my self to be much -obliged. What I have to declare on this head will be but short; for -it was in the very last years of Sir</i> <em class="gesperrt"><span class="smcap">Isaac</span></em><i>’s life, that I had the honour<span class="pagenum"><a name="Page_viii" id="Page_viii">[viii]</a></span> -of his acquaintance. This happened on the following occasion. -Mr.</i> Polenus, <i>a Professor in the University of</i> Padua, <i>from a new experiment -of his, thought the common opinion about the force of moving -bodies was overturned, and the truth of Mr.</i> Libnitz<i>’s notion in that -matter fully proved. The contrary of what Polenus had asserted I -demonstrated in a paper, which Dr.</i> <em class="gesperrt"><span class="smcap">Mead</span></em>, <i>who takes all opportunities -of obliging his friends, was pleased to shew Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> -<i>This was so well approved of by him, that he did me the honour -to become a fellow-writer with me, by annexing to what I had -written, a demonstration of his own drawn from another consideration. -When I printed my discourse in the philosophical transactions, I -put what Sir</i> <em class="gesperrt"><span class="smcap">Isaac</span></em> <i>had written in a scholium by it self, that I -might not seem to usurp what did not belong to me. But I concealed -his name, not being then sufficiently acquainted with him to ask whether -he was willing I might make use of it or not. In a little time -after he engaged me to take care of the new edition he was about -making if his Principia. This obliged me to be very frequently with -him, and as he lived at some distance from me, a great number of -letters passed between us on this account. When I had the honour of -his conversation, I endeavoured to learn his thoughts upon mathematical -subjects, and something historical concerning his inventions, that I -had not been before acquainted with. I found, he had read fewer of the -modern mathematicians, than one could have expected; but his own -prodigious invention readily supplied him with what he might have an -occasion for in the pursuit of any subject he undertook. I have often heard -him censure the handling geometrical subjects by algebraic calculations; -and his book of Algebra he called by the name of Universal Arithmetic, -in opposition to the injudicious title of Geometry, which</i> Des Cartes <i>had -given to the treatise, wherein he shews, how the geometer may assist his -invention by such kind of computations. He frequently praised</i> Slusius, -Barrow <i>and</i> Huygens <i>for not being influenced by the false taste, which -then began to prevail. He used to commend the laudable attempt of</i> Hugo -de Omerique <i>to restore the ancient analysis, and very much esteemed Apollonius’s -book De sectione rationis for giving us a clearer notion of that -analysis than we had before. Dr.</i> Barrow <i>may be esteemed as having<span class="pagenum"><a name="Page_ix" id="Page_ix">[ix]</a></span> -shewn a compass of invention equal, if not superior to any of the -moderns, our author only excepted; but Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> <i>has -several times particularly recommended to me</i> Huygens<i>’s stile and -manner. He thought him the most elegant of any mathematical writer -of modern times, and the most just imitator of the antients. Of -their taste, and form of demonstration Sir</i> <em class="gesperrt"><span class="smcap">Isaac</span></em> <i>always professed -himself a great admirer: I have heard him even censure himself for -not following them yet more closely than he did; and speak with regret -of his mistake at the beginning of his mathematical studies, in -applying himself to the works of</i> Des Cartes <i>and other algebraic writers, -before he had considered the elements of</i> Euclide <i>with that attention, -which so excellent a writer deserves. As to the history of his -inventions, what relates to his discoveries of the methods of series and -fluxions, and of his theory of light and colours, the world has been sufficiently -informed of already. The first thoughts, which gave rise -to his Principia, he had, when he retired from</i> Cambridge <i>in 1666 on -account of the plague. As he sat alone in a garden, he fell into a -speculation on the power of gravity: that as this power is not found -sensibly diminished at the remotest distance from the center of the earth, -to which we can rise, neither at the tops of the loftiest buildings, nor -even on the summits of the highest mountains; it appeared to him -reasonable to conclude, that this power must extend much farther than -was usually thought; why not as high as the moon, said he to himself? -and if so, her motion must be influenced by it; perhaps she is retained -in her orbit thereby. However, though the power of gravity -is not sensibly weakened in the little change of distance, at which we -can place our selves from the center of the earth; yet it is very possible, -that so high as the moon this power may differ much in strength from -what it is here. To make an estimate, what might be the degree of -this diminution, he considered with himself, that if the moon be retained -in her orbit by the force of gravity, no doubt the primary planets -are carried round the sun by the like power. And by comparing the -periods of the several planets with their distances from the sun, he found, -that if any power like gravity held them in their courses, its strength must -decrease in the duplicate proportion of the increase of distance. This<span class="pagenum"><a name="Page_x" id="Page_x">[x]</a></span> -be concluded by supposing them to move in perfect circles concentrical -to the sun, from which the orbits of the greatest part of them do -not much differ. Supposing therefore the power of gravity, when -extended to the moon, to decrease in the same manner, he computed -whether that force would be sufficient to keep the moon in her orbit. -In this computation, being absent from books, he took the common estimate -in use among geographers and our seamen, before</i> Norwood <i>had measured -the earth, that 60 English miles were contained in one degree -of latitude on the surface of the earth. But as this is a very faulty -supposition, each degree containing about 69½ of our miles, his computation -did not answer expectation; whence he concluded, that some -other cause must at least join with the action of the power of gravity -on the moon. On this account he laid aside for that time any farther -thoughts upon this matter. But some years after, a letter which he -received from Dr.</i> Hook, <i>put him on inquiring what was the real -figure, in which a body let fall from any high place descends, taking -the motion of the earth round its axis into consideration. Such a body, -having the same motion, which by the revolution of the earth the -place has whence it falls, is to be considered as projected forward -and at the same time drawn down to the center of the earth. This -gave occasion to his resuming his former thoughts concerning the -moon; and</i> Picart <i>in</i> France <i>having lately measured the earth, by -using his measures the moon appeared to be kept in her orbit purely -by the power of gravity; and consequently, that this power decreases -as you recede from the center of the earth in the manner our author -had formerly conjectured. Upon this principle he found the line described -by a falling body to be an ellipsis, the center of the earth being -one focus. And the primary planets moving in such orbits round -the sun, he had the satisfaction to see, that this inquiry, which he -had undertaken merely out of curiosity, could be applied to the -greatest purposes. Hereupon he composed near a dozen propositions -relating to the motion of the primary planets about the sun. Several -years after this, some discourse he had with Dr.</i> Halley, <i>who at -Cambridge made him a visit, engaged Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> <i>to -resume again the consideration of this subject; and gave occasion<span class="pagenum"><a name="Page_xi" id="Page_xi">[xi]</a></span> -to his writing the treatise which he published under the title of mathematical -principles of natural philosophy. This treatise, full of -such a variety of profound inventions, was composed by him from -scarce any other materials than the few propositions before mentioned, -in the space of one year and an half.</i></p> - -<p><i>Though his memory was much decayed, I found he perfectly understood -his own writings, contrary to what I had frequently heard -in discourse from many persons. This opinion of theirs might arise -perhaps from his not being always ready at speaking on these subjects, -when it might be expected he should. But as to this, it may be -observed, that great genius’s are frequently liable to be absent, not only -in relation to common life, but with regard to some of the parts of science -they are the best informed of. Inventors seem to treasure up in their -minds, what they have found out, after another manner than those do -the same things, who have not this inventive faculty. The former, -when they have occasion to produce their knowledge, are in some measure -obliged immediately to investigate part of what they want. For -this they are not equally fit at all times: so it has often happened, -that such as retain things chiefly by means of a very strong memory, -have appeared off hand more expert than the discoverers themselves.</i></p> - -<p><i>As to the moral endowments of his mind, they were as much to be -admired as his other talents. But this is a field I leave others to -exspatiate in. I only touch upon what I experienced myself during the -few years I was happy in his friendship. But this I immediately -discovered in him, which at once both surprized and charmed me: -Neither his extreme great age, nor his universal reputation had -rendred him stiff in opinion, or in any degree elated. Of this -I had occasion to have almost daily experience. The Remarks I -continually sent him by letters on his Principia were received with -the utmost goodness. These were so far from being any ways displeasing -to him, that on the contrary it occasioned him to speak many kind -things of me to my friends, and to honour me with a publick testimony -of his good opinion. He also approved of the following treatise, a -great part of which we read together. As many alterations were<span class="pagenum"><a name="Page_xii" id="Page_xii">[xii]</a></span> -made in the late edition of his Principia, so there would have been -many more if there had been a sufficient time. But whatever of this -kind may be thought wanting, I shall endeavour to supply in my comment -on that book. I had reason to believe he expected such a thing -from me, and I intended to have published it in his life time, after I -had printed the following discourse, and a mathematical treatise Sir</i> -<em class="gesperrt"><span class="smcap">Isaac Newton</span></em> <i>had written a long while ago, containing the -first principles of fluxions, for I had prevailed on him to let that piece -go abroad. I had examined all the calculations, and prepared part -of the figures; but as the latter part of the treatise had never been -finished, he was about letting me have other papers, in order to -supply what was wanting. But his death put a stop to that design. -As to my comment on the Principia, I intend there to demonstrate -whatever Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> <i>has set down without -express proof, and to explain all such expressions in his book, as I shall -judge necessary. This comment I shall forthwith put to the press, -joined to an english translation of his Principia, which I have -had some time by me. A more particular account of my whole design -has already been published in the new memoirs of literature for -the month of march 1727.</i></p> - -<p><i>I have presented my readers with a copy of verses on Sir</i> <em class="gesperrt"><span class="smcap">Isaac -Newton</span></em>, <i>which I have just received from a young Gentleman, -whom I am proud to reckon among the number of my dearest friends. -If I had any apprehension that this piece of poetry stood in need of -an apology, I should be desirous the reader might know, that the -author is but sixteen years old, and was obliged to finish his composition -in a very short space of time. But I shall only take the liberty -to observe, that the boldness of the digressions will be best judged of -by those who are acquainted with</i> <em class="gesperrt"><span class="smcap">Pindar</span></em>.</p> - -<p><span class="pagenum"><a name="Page_xiii" id="Page_xiii">[xiii]</a></span></p> - -<hr class="d1" /> -<hr class="d2" /> - -<p class="pc4">A<br /> -<span class="xlarge"><em class="gesperrt">POEM</em></span><br /> -ON<br /> -<span class="large">Sir <em class="gesperrt"><i>ISAAC NEWTON</i></em>.</span><br /> -</p> - -<div class="pi6"> - -<p class="drop-cap04"><span class="smcap">To</span> <em class="gesperrt"><span class="smcap">Newton</span></em>’s genius, and immortal fame<br /> -Th’ advent’rous muse with trembling pinion soars.<br /> -Thou, heav’nly truth, from thy seraphick throne<br /> -Look favourable down, do thou assist<br /> -My lab’ring thought, do thou inspire my song.<br /> -<span class="smcap">Newton</span>, who first th’ almighty’s works display’d,<br /> -And smooth’d that mirror, in whose polish’d face<br /> -The great creator now conspicuous shines;<br /> -Who open’d nature’s adamantine gates,<br /> -And to our minds her secret powers expos’d;<br /> -<span class="smcap">Newton</span> demands the muse; his sacred hand<br /> -Shall guide her infant steps; his sacred hand<br /> -Shall raise her to the Heliconian height,<br /> -Where, on its lofty top inthron’d, her head<br /> -Shall mingle with the Stars. Hail nature, hail,<br /> -O Goddess, handmaid of th’ ethereal power,<br /> -Now lift thy head, and to th’ admiring world<br /> -Shew thy long hidden beauty. Thee the wise<br /> -Of ancient fame, immortal <em class="gesperrt"><span class="smcap">Plato</span></em>’s self,<br /> -<span class="pagenum"><a name="Page_xiv" id="Page_xiv">[xiv]</a></span>The Stagyrite, and Syracusian sage,<br /> -From black obscurity’s abyss to raise,<br /> -(Drooping and mourning o’er thy wondrous works)<br /> -With vain inquiry sought. Like meteors these<br /> -In their dark age bright sons of wisdom shone:<br /> -But at thy <em class="gesperrt"><span class="smcap">Newton</span></em> all their laurels fade,<br /> -They shrink from all the honours of their names.<br /> -So glimm’ring stars contract their feeble rays,<br /> -When the swift lustre of <em class="gesperrt"><span class="smcap">Aurora</span></em>’s face<br /> -Flows o’er the skies, and wraps the heav’ns in light.</p> - -<p class="p1"><span class="smcap">The</span> Deity’s omnipotence, the cause,<br /> -Th’ original of things long lay unknown.<br /> -Alone the beauties prominent to sight<br /> -(Of the celestial power the outward form)<br /> -Drew praise and wonder from the gazing world.<br /> -As when the deluge overspread the earth,<br /> -Whilst yet the mountains only rear’d their heads<br /> -Above the surface of the wild expanse,<br /> -Whelm’d deep below the great foundations lay,<br /> -Till some kind angel at heav’n’s high command<br /> -Roul’d back the rising tides, and haughty floods,<br /> -And to the ocean thunder’d out his voice:<br /> -Quick all the swelling and imperious waves,<br /> -The foaming billows and obscuring surge,<br /> -Back to their channels and their ancient seats<br /> -Recoil affrighted: from the darksome main<br /> -Earth raises smiling, as new-born, her head,<br /> -And with fresh charms her lovely face arrays.<br /> -So his extensive thought accomplish’d first<br /> -The mighty task to drive th’ obstructing mists<br /> -Of ignorance away, beneath whose gloom<br /> -Th’ inshrouded majesty of Nature lay.<br /> -He drew the veil and swell’d the spreading scene.<br /> -<span class="pagenum"><a name="Page_xv" id="Page_xv">[xv]</a></span>How had the moon around th’ ethereal void<br /> -Rang’d, and eluded lab’ring mortals care,<br /> -Till his invention trac’d her secret steps,<br /> -While she inconstant with unsteady rein<br /> -Through endless mazes and meanders guides<br /> -In its unequal course her changing carr:<br /> -Whether behind the sun’s superior light<br /> -She hides the beauties of her radiant face,<br /> -Or, when conspicuous, smiles upon mankind,<br /> -Unveiling all her night-rejoicing charms.<br /> -When thus the silver-tressed moon dispels<br /> -The frowning horrors from the brow of night,<br /> -And with her splendors chears the sullen gloom,<br /> -While sable-mantled darkness with his veil<br /> -The visage of the fair horizon shades,<br /> -And over nature spreads his raven wings;<br /> -Let me upon some unfrequented green<br /> -While sleep sits heavy on the drowsy world,<br /> -Seek out some solitary peaceful cell,<br /> -Where darksome woods around their gloomy brows<br /> -Bow low, and ev’ry hill’s protended shade<br /> -Obscures the dusky vale, there silent dwell,<br /> -Where contemplation holds its still abode,<br /> -There trace the wide and pathless void of heav’n,<br /> -And count the stars that sparkle on its robe.<br /> -Or else in fancy’s wild’ring mazes lost<br /> -Upon the verdure see the fairy elves<br /> -Dance o’er their magick circles, or behold,<br /> -In thought enraptur’d with the ancient bards,<br /> -Medea’s baleful incantations draw<br /> -Down from her orb the paly queen of night.<br /> -But chiefly <em class="gesperrt"><span class="smcap">Newton</span></em> let me soar with thee,<br /> -And while surveying all yon starry vault<br /> -With admiration I attentive gaze,<br /> -<span class="pagenum"><a name="Page_xvi" id="Page_xvi">[xvi]</a></span>Thou shalt descend from thy celestial seat,<br /> -And waft aloft my high-aspiring mind,<br /> -Shalt shew me there how nature has ordain’d<br /> -Her fundamental laws, shalt lead my thought<br /> -Through all the wand’rings of th’ uncertain moon,<br /> -And teach me all her operating powers.<br /> -She and the sun with influence conjoint<br /> -Wield the huge axle of the whirling earth,<br /> -And from their just direction turn the poles,<br /> -Slow urging on the progress of the years.<br /> -The constellations seem to leave their seats,<br /> -And o’er the skies with solemn pace to move.<br /> -You, splendid rulers of the day and night,<br /> -The seas obey, at your resistless sway<br /> -Now they contract their waters, and expose<br /> -The dreary desart of old ocean’s reign.<br /> -The craggy rocks their horrid sides disclose;<br /> -Trembling the sailor views the dreadful scene,<br /> -And cautiously the threat’ning ruin shuns.<br /> -But where the shallow waters hide the sands,<br /> -There ravenous destruction lurks conceal’d,<br /> -There the ill-guided vessel falls a prey,<br /> -And all her numbers gorge his greedy jaws.<br /> -But quick returning see th’ impetuous tides<br /> -Back to th’ abandon’d shores impell the main.<br /> -Again the foaming seas extend their waves,<br /> -Again the rouling floods embrace the shoars,<br /> -And veil the horrours of the empty deep.<br /> -Thus the obsequious seas your power confess,<br /> -While from the surface healthful vapours rise<br /> -Plenteous throughout the atmosphere diffus’d,<br /> -Or to supply the mountain’s heads with springs,<br /> -Or fill the hanging clouds with needful rains,<br /> -That friendly streams, and kind refreshing show’rs<br /> -<span class="pagenum"><a name="Page_xvii" id="Page_xvii">[xvii]</a></span>May gently lave the sun-burnt thirsty plains,<br /> -Or to replenish all the empty air<br /> -With wholsome moisture to increase the fruits<br /> -Of earth, and bless the labours of mankind.<br /> -O <em class="gesperrt"><span class="smcap">Newton</span></em>, whether flies thy mighty soul,<br /> -How shall the feeble muse pursue through all<br /> -The vast extent of thy unbounded thought,<br /> -That even seeks th’ unseen recesses dark<br /> -To penetrate of providence immense.<br /> -And thou the great dispenser of the world<br /> -Propitious, who with inspiration taught’st<br /> -Our greatest bard to send thy praises forth;<br /> -Thou, who gav’st <em class="gesperrt"><span class="smcap">Newton</span></em> thought; who smil’dst serene,<br /> -When to its bounds he stretch’d his swelling soul;<br /> -Who still benignant ever blest his toil,<br /> -And deign’d to his enlight’ned mind t’ appear<br /> -Confess’d around th’ interminated world:<br /> -To me O thy divine infusion grant<br /> -(O thou in all so infinitely good)<br /> -That I may sing thy everlasting works,<br /> -Thy inexhausted store of providence,<br /> -In thought effulgent and resounding verse.<br /> -O could I spread the wond’rous theme around,<br /> -Where the wind cools the oriental world,<br /> -To the calm breezes of the Zephir’s breath,<br /> -To where the frozen hyperborean blasts.<br /> -To where the boist’rous tempest-leading south<br /> -From their deep hollow caves send forth their storms.<br /> -Thou still indulgent parent of mankind,<br /> -Left humid emanations should no more<br /> -Flow from the ocean, but dissolve away<br /> -Through the long series of revolving time;<br /> -And left the vital principle decay,<br /> -By which the air supplies the springs of life;<br /> -<span class="pagenum"><a name="Page_xviii" id="Page_xviii">[xviii]</a></span>Thou hast the fiery visag’d comets form’d<br /> -With vivifying spirits all replete,<br /> -Which they abundant breathe about the void,<br /> -Renewing the prolifick soul of things.<br /> -No longer now on thee amaz’d we call,<br /> -No longer tremble at imagin’d ills,<br /> -When comets blaze tremendous from on high,<br /> -Or when extending wide their flaming trains<br /> -With hideous grasp the skies engirdle round,<br /> -And spread the terrors of their burning locks.<br /> -For these through orbits in the length’ning space<br /> -Of many tedious rouling years compleat<br /> -Around the sun move regularly on;<br /> -And with the planets in harmonious orbs,<br /> -And mystick periods their obeysance pay<br /> -To him majestick ruler of the skies<br /> -Upon his throne of circled glory fixt.<br /> -He or some god conspicuous to the view,<br /> -Or else the substitute of nature seems,<br /> -Guiding the courses of revolving worlds.<br /> -He taught great <em class="gesperrt"><span class="smcap">Newton</span></em> the all-potent laws<br /> -Of gravitation, by whose simple power<br /> -The universe exists. Nor here the sage<br /> -Big with invention still renewing staid.<br /> -But O bright angel of the lamp of day,<br /> -How shall the muse display his greatest toil?<br /> -Let her plunge deep in Aganippe’s waves,<br /> -Or in Castalia’s ever-flowing stream,<br /> -That re-inspired she may sing to thee,<br /> -How <em class="gesperrt"><span class="smcap">Newton</span></em> dar’d advent’rous to unbraid<br /> -The yellow tresses of thy shining hair.<br /> -Or didst thou gracious leave thy radiant sphere,<br /> -And to his hand thy lucid splendours give,<br /> -<span class="pagenum"><a name="Page_xix" id="Page_xix">[xix]</a></span>T’ unweave the light-diffusing wreath, and part<br /> -The blended glories of thy golden plumes?<br /> -He with laborious, and unerring care,<br /> -How different and imbodied colours form<br /> -Thy piercing light, with just distinction found.<br /> -He with quick sight pursu’d thy darting rays,<br /> -When penetrating to th’ obscure recess<br /> -Of solid matter, there perspicuous saw,<br /> -How in the texture of each body lay<br /> -The power that separates the different beams.<br /> -Hence over nature’s unadorned face<br /> -Thy bright diversifying rays dilate<br /> -Their various hues: and hence when vernal rains<br /> -Descending swift have burst the low’ring clouds,<br /> -Thy splendors through the dissipating mists<br /> -In its fair vesture of unnumber’d hues<br /> -Array the show’ry bow. At thy approach<br /> -The morning risen from her pearly couch<br /> -With rosy blushes decks her virgin cheek;<br /> -The ev’ning on the frontispiece of heav’n<br /> -His mantle spreads with many colours gay;<br /> -The mid-day skies in radiant azure clad,<br /> -The shining clouds, and silver vapours rob’d<br /> -In white transparent intermixt with gold,<br /> -With bright variety of splendor cloath<br /> -All the illuminated face above.<br /> -When hoary-headed winter back retires<br /> -To the chill’d pole, there solitary sits<br /> -Encompass’d round with winds and tempests bleak<br /> -In caverns of impenetrable ice,<br /> -And from behind the dissipated gloom<br /> -Like a new Venus from the parting surge<br /> -The gay-apparell’d spring advances on;<br /> -When thou in thy meridian brightness sitt’st,<br /> -<span class="pagenum"><a name="Page_xx" id="Page_xx">[xx]</a></span>And from thy throne pure emanations flow<br /> -Of glory bursting o’er the radiant skies:<br /> -Then let the muse Olympus’ top ascend,<br /> -And o’er Thessalia’s plain extend her view,<br /> -And count, O Tempe, all thy beauties o’er.<br /> -Mountains, whose summits grasp the pendant clouds,<br /> -Between their wood-invelop’d slopes embrace<br /> -The green-attired vallies. Every flow’r<br /> -Here in the pride of bounteous nature clad<br /> -Smiles on the bosom of th’ enamell’d meads.<br /> -Over the smiling lawn the silver floods<br /> -Of fair Peneus gently roul along,<br /> -While the reflected colours from the flow’rs,<br /> -And verdant borders pierce the lympid waves,<br /> -And paint with all their variegated hue<br /> -The yellow sands beneath. Smooth gliding on<br /> -The waters hasten to the neighbouring sea.<br /> -Still the pleas’d eye the floating plain pursues;<br /> -At length, in Neptune’s wide dominion lost,<br /> -Surveys the shining billows, that arise<br /> -Apparell’d each in Phœbus’ bright attire:<br /> -Or from a far some tall majestick ship,<br /> -Or the long hostile lines of threat’ning fleets,<br /> -Which o’er the bright uneven mirror sweep,<br /> -In dazling gold and waving purple deckt;<br /> -Such as of old, when haughty Athens power<br /> -Their hideous front, and terrible array<br /> -Against Pallene’s coast extended wide,<br /> -And with tremendous war and battel stern<br /> -The trembling walls of Potidæa shook.<br /> -Crested with pendants curling with the breeze<br /> -The upright masts high bristle in the air,<br /> -Aloft exalting proud their gilded heads.<br /> -The silver waves against the painted prows<br /> -<span class="pagenum"><a name="Page_xxi" id="Page_xxi">[xxi]</a></span>Raise their resplendent bosoms, and impearl<br /> -The fair vermillion with their glist’ring drops:<br /> -And from on board the iron-cloathed host<br /> -Around the main a gleaming horrour casts;<br /> -Each flaming buckler like the mid-day sun,<br /> -Each plumed helmet like the silver moon,<br /> -Each moving gauntlet like the light’ning’s blaze,<br /> -And like a star each brazen pointed spear.<br /> -But lo the sacred high-erected fanes,<br /> -Fair citadels, and marble-crowned towers,<br /> -And sumptuous palaces of stately towns<br /> -Magnificent arise, upon their heads<br /> -Bearing on high a wreath of silver light.<br /> -But see my muse the high Pierian hill,<br /> -Behold its shaggy locks and airy top,<br /> -Up to the skies th’ imperious mountain heaves<br /> -The shining verdure of the nodding woods.<br /> -See where the silver Hippocrene flows,<br /> -Behold each glitt’ring rivulet, and rill<br /> -Through mazes wander down the green descent,<br /> -And sparkle through the interwoven trees.<br /> -Here rest a while and humble homage pay,<br /> -Here, where the sacred genius, that inspir’d<br /> -Sublime <em class="gesperrt"><span class="smcap">Mæonides</span></em> and <em class="gesperrt"><span class="smcap">Pindar’s</span></em> breast,<br /> -His habitation once was fam’d to hold.<br /> -Here thou, O <em class="gesperrt"><span class="smcap">Homer</span></em>, offer’dst up thy vows,<br /> -Thee, the kind muse <em class="gesperrt"><span class="smcap">Calliopæa</span></em> heard,<br /> -And led thee to the empyrean feats,<br /> -There manifested to thy hallow’d eyes<br /> -The deeds of gods; thee wise <em class="gesperrt"><span class="smcap">Minerva</span></em> taught<br /> -The wondrous art of knowing human kind;<br /> -Harmonious <em class="gesperrt"><span class="smcap">Phœbus</span></em> tun’d thy heav’nly mind,<br /> -And swell’d to rapture each exalted sense;<br /> -Even <em class="gesperrt"><span class="smcap">Mars</span></em> the dreadful battle-ruling god,<br /> -<span class="pagenum"><a name="Page_xxii" id="Page_xxii">[xxii]</a></span><em class="gesperrt"><span class="smcap">Mars</span></em> taught thee war, and with his bloody hand<br /> -Instructed thine, when in thy sounding lines<br /> -We hear the rattling of Bellona’s carr,<br /> -The yell of discord, and the din of arms.<br /> -<em class="gesperrt"><span class="smcap">Pindar</span></em>, when mounted on his fiery steed,<br /> -Soars to the sun, opposing eagle like<br /> -His eyes undazled to the fiercest rays.<br /> -He firmly seated, not like <em class="gesperrt"><span class="smcap">Glaucus’</span></em> son,<br /> -Strides his swift-winged and fire-breathing horse,<br /> -And born aloft strikes with his ringing hoofs<br /> -The brazen vault of heav’n, superior there<br /> -Looks down upon the stars, whose radiant light<br /> -Illuminates innumerable worlds,<br /> -That through eternal orbits roul beneath.<br /> -But thou all hail immortalized son<br /> -Of harmony, all hail thou Thracian bard,<br /> -To whom <em class="gesperrt"><span class="smcap">Apollo</span></em> gave his tuneful lyre.<br /> -O might’st thou, <em class="gesperrt"><span class="smcap">Orpheus</span></em>, now again revive,<br /> -And <em class="gesperrt"><span class="smcap">Newton</span></em> should inform thy list’ning ear<br /> -How the soft notes, and soul-inchanting strains<br /> -Of thy own lyre were on the wind convey’d.<br /> -He taught the muse, how sound progressive floats<br /> -Upon the waving particles of air,<br /> -When harmony in ever-pleasing strains,<br /> -Melodious melting at each lulling fall,<br /> -With soft alluring penetration steals<br /> -Through the enraptur’d ear to inmost thought,<br /> -And folds the senses in its silken bands.<br /> -So the sweet musick, which from <em class="gesperrt"><span class="smcap">Orpheus</span></em>’ touch<br /> -And fam’d <em class="gesperrt"><span class="smcap">Amphion’s</span></em>, on the sounding string<br /> -Arose harmonious, gliding on the air,<br /> -Pierc’d the tough-bark’d and knotty-ribbed woods,<br /> -Into their saps soft inspiration breath’d<br /> -And taught attention to the stubborn oak.<br /> -<span class="pagenum"><a name="Page_xxiii" id="Page_xxiii">[xxiii]</a></span>Thus when great <em class="gesperrt"><span class="smcap">Henry</span></em>, and brave <em class="gesperrt"><span class="smcap">Marlb’rough</span></em> led<br /> -Th’ imbattled numbers of <em class="gesperrt"><span class="smcap">Britannia’s</span></em> sons,<br /> -The trump, that swells th’ expanded cheek of fame,<br /> -That adds new vigour to the gen’rous youth,<br /> -And rouzes sluggish cowardize it self,<br /> -The trumpet with its Mars-inciting voice,<br /> -The winds broad breast impetuous sweeping o’er<br /> -Fill’d the big note of war. Th’ inspired host<br /> -With new-born ardor press the trembling <em class="gesperrt"><span class="smcap">Gaul</span></em>;<br /> -Nor greater throngs had reach’d eternal night,<br /> -Not if the fields of Agencourt had yawn’d<br /> -Exposing horrible the gulf of fate;<br /> -Or roaring Danube spread his arms abroad,<br /> -And overwhelm’d their legions with his floods.<br /> -But let the wand’ring muse at length return;<br /> -Nor yet, angelick genius of the sun,<br /> -In worthy lays her high-attempting song<br /> -Has blazon’d forth thy venerated name.<br /> -Then let her sweep the loud-resounding lyre<br /> -Again, again o’er each melodious string<br /> -Teach harmony to tremble with thy praise.<br /> -And still thine ear O favourable grant,<br /> -And she shall tell thee, that whatever charms,<br /> -Whatever beauties bloom on nature’s face,<br /> -Proceed from thy all-influencing light.<br /> -That when arising with tempestuous rage,<br /> -The North impetuous rides upon the clouds<br /> -Dispersing round the heav’ns obstructive gloom,<br /> -And with his dreaded prohibition stays<br /> -The kind effusion of thy genial beams;<br /> -Pale are the rubies on <em class="gesperrt"><span class="smcap">Aurora’s</span></em> lips,<br /> -No more the roses blush upon her cheeks,<br /> -Black are Peneus’ streams and golden sands<br /> -In Tempe’s vale dull melancholy sits,<br /> -<span class="pagenum"><a name="Page_xxiv" id="Page_xxiv">[xxiv]</a></span>And every flower reclines its languid head.<br /> -By what high name shall I invoke thee, say,<br /> -Thou life-infusing deity, on thee<br /> -I call, and look propitious from on high,<br /> -While now to thee I offer up my prayer.<br /> -O had great <em class="gesperrt"><span class="smcap">Newton</span></em>, as he found the cause,<br /> -By which sound rouls thro’ th’ undulating air,<br /> -O had he, baffling times resistless power,<br /> -Discover’d what that subtle spirit is,<br /> -Or whatsoe’er diffusive else is spread<br /> -Over the wide-extended universe,<br /> -Which causes bodies to reflect the light,<br /> -And from their straight direction to divert<br /> -The rapid beams, that through their surface pierce.<br /> -But since embrac’d by th’ icy arms of age,<br /> -And his quick thought by times cold hand congeal’d,<br /> -Ev’n <em class="gesperrt"><span class="smcap">Newton</span></em> left unknown this hidden power;<br /> -Thou from the race of human kind select<br /> -Some other worthy of an angel’s care,<br /> -With inspiration animate his breast,<br /> -And him instruct in these thy secret laws.<br /> -O let not <em class="gesperrt"><span class="smcap">Newton</span></em>, to whose spacious view,<br /> -Now unobstructed, all th’ extensive scenes<br /> -Of the ethereal ruler’s works arise;<br /> -When he beholds this earth he late adorn’d,<br /> -Let him not see philosophy in tears,<br /> -Like a fond mother solitary sit,<br /> -Lamenting him her dear, and only child.<br /> -But as the wise <em class="gesperrt"><span class="smcap">Pythagoras</span></em>, and he,<br /> -Whose birth with pride the fam’d Abdera boasts,<br /> -With expectation having long survey’d<br /> -This spot their ancient seat, with joy beheld<br /> -Divine philosophy at length appear<br /> -In all her charms majestically fair,<br /> -<span class="pagenum"><a name="Page_xxv" id="Page_xxv">[xxv]</a></span>Conducted by immortal <em class="gesperrt"><span class="smcap">Newton’s</span></em> hand.<br /> -So may he see another sage arise,<br /> -That shall maintain her empire: then no more<br /> -Imperious ignorance with haughty sway<br /> -Shall stalk rapacious o’er the ravag’d globe:<br /> -Then thou, O <em class="gesperrt"><span class="smcap">Newton</span></em>, shalt protect these lines.<br /> -The humble tribute of the grateful muse;<br /> -Ne’er shall the sacrilegious hand despoil<br /> -Her laurel’d temples, whom his name preserves:<br /> -And were she equal to the mighty theme,<br /> -Futurity should wonder at her song;<br /> -Time should receive her with extended arms,<br /> -Seat her conspicuous in his rouling carr,<br /> -And bear her down to his extreamest bound.</p> - -<p class="p1"><span class="smcap"><em class="gesperrt">Fables</em></span> with wonder tell how Terra’s sons<br /> -With iron force unloos’d the stubborn nerves<br /> -Of hills, and on the cloud-inshrouded top<br /> -Of Pelion Ossa pil’d. But if the vast<br /> -Gigantick deeds of savage strength demand<br /> -Astonishment from men, what then shalt thou,<br /> -O what expressive rapture of the soul,<br /> -When thou before us, <em class="gesperrt"><span class="smcap">Newton</span></em>, dost display<br /> -The labours of thy great excelling mind;<br /> -When thou unveilest all the wondrous scene,<br /> -The vast idea of th’ eternal king,<br /> -Not dreadful bearing in his angry arm<br /> -The thunder hanging o’er our trembling heads;<br /> -But with th’ effulgency of love replete,<br /> -And clad with power, which form’d th’ extensive heavens.<br /> -O happy he, whose enterprizing hand<br /> -Unbars the golden and relucid gates<br /> -Of th’ empyrean dome, where thou enthron’d<br /> -Philosophy art seated. Thou sustain’d<br /> -<span class="pagenum"><a name="Page_xxvi" id="Page_xxvi">[xxvi]</a></span>By the firm hand of everlasting truth<br /> -Despisest all the injuries of time;<br /> -Thou never know’st decay when all around,<br /> -Antiquity obscures her head. Behold<br /> -Th’ Egyptian towers, the Babylonian walls,<br /> -And Thebes with all her hundred gates of brass,<br /> -Behold them scatter’d like the dust abroad.<br /> -Whatever now is flourishing and proud,<br /> -Whatever shall, must know devouring age.<br /> -Euphrates’ stream, and seven-mouthed Nile,<br /> -And Danube, thou that from Germania’s soil<br /> -To the black Euxine’s far remoted shore,<br /> -O’er the wide bounds of mighty nations sweep’st<br /> -In thunder loud thy rapid floods along.<br /> -Ev’n you shall feel inexorable time;<br /> -To you the fatal day shall come; no more<br /> -Your torrents then shall shake the trembling ground,<br /> -No longer then to inundations swol’n<br /> -Th’ imperious waves the fertile pastures drench,<br /> -But shrunk within a narrow channel glide;<br /> -Or through the year’s reiterated course<br /> -When time himself grows old, your wond’rous streams<br /> -Lost ev’n to memory shall lie unknown<br /> -Beneath obscurity, and Chaos whelm’d,<br /> -But still thou sun illuminatest all<br /> -The azure regions round, thou guidest still<br /> -The orbits of the planetary spheres;<br /> -The moon still wanders o’er her changing course,<br /> -And still, O <em class="gesperrt"><span class="smcap">Newton</span></em>, shall thy name survive:<br /> -As long as nature’s hand directs the world,<br /> -When ev’ry dark obstruction shall retire,<br /> -And ev’ry secret yield its hidden store,<br /> -Which thee dim-sighted age forbad to see<br /> -Age that alone could stay thy rising soul.<br /> -<span class="pagenum"><a name="Page_xxvii" id="Page_xxvii">[xxvii]</a></span>And could mankind among the fixed stars,<br /> -E’en to th’ extremest bounds of knowledge reach,<br /> -To those unknown innumerable suns,<br /> -Whose light but glimmers from those distant worlds,<br /> -Ev’n to those utmost boundaries, those bars<br /> -That shut the entrance of th’ illumin’d space<br /> -Where angels only tread the vast unknown,<br /> -Thou ever should’st be seen immortal there:<br /> -In each new sphere, each new-appearing sun,<br /> -In farthest regions at the very verge<br /> -Of the wide universe should’st thou be seen.<br /> -And lo, th’ all-potent goddess <em class="gesperrt"><span class="smcap">Nature</span></em> takes<br /> -With her own hand thy great, thy just reward<br /> -Of immortality; aloft in air<br /> -See she displays, and with eternal grasp<br /> -Uprears the trophies of great <em class="gesperrt"><span class="smcap">Newton</span></em>’s fame.</p> - -<p class="pr2 p1 large"><span class="smcap">R. Glover.</span></p> - -</div> - -</div> - -<p><span class="pagenum"><a name="Page_xxviii" id="Page_xxviii">[xxviii]</a></span></p> - -<div class="chapter"> - -<hr class="d1" /> -<hr class="d2" /> - -<h2 class="p4">THE<br /> -<span class="large"><em class="gesperrt">CONTENTS</em>.</span></h2> - -<p class="drop1">I<i>NTRODUCTION concerning Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton</span></em>’<i>s<br /> -method of reasoning in philosophy</i><span class="vh">————————</span>pag. 1</p> - -<p class="pc1 mid"><span class="smcap">Book I.</span><br /></p> - -<table id="toc1" summary="cont"> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c27">Chap. 1.</a></em></span> <i>Of the laws of motion</i></td> - </tr> - - <tr> - <td class="tdl2"><i>The first law of motion proved</i></td> - <td class="tdrl"><a href="#c29a">p. 29</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The second law of motion proved</i></td> - <td class="tdrl"><a href="#c29b">p. 29</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The third law of motion proved</i></td> - <td class="tdrl"><a href="#c31">p. 31</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c48">Chap. 2.</a></em></span> <i>Further proofs of the laws of motion</i></td> - </tr> - - <tr> - <td class="tdl2"><i>The effects of percussion</i></td> - <td class="tdrl"><a href="#c49">p. 49</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The perpendicular descent of bodies</i></td> - <td class="tdrl"><a href="#c55">p. 55</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The oblique descent of bodies in a straight line</i></td> - <td class="tdrl"><a href="#c57">p. 57</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The curvilinear descent of bodies</i></td> - <td class="tdrl"><a href="#c58a">p. 58</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The perpendicular ascent of bodies</i></td> - <td class="tdrl"><a href="#c58b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The oblique ascent of bodies</i></td> - <td class="tdrl"><a href="#c59">p. 59</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The power of gravity proportional to the quantity of matter in each body</i></td> - <td class="tdrl"><a href="#c60">p. 60</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The centre of gravity of bodies</i></td> - <td class="tdrl"><a href="#c62">p. 62</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The mechanical powers</i></td> - <td class="tdrl"><a href="#c69">p. 69</a></td> - </tr> - - <tr> - <td class="tdl3"><i>The lever</i></td> - <td class="tdrl"><a href="#c71">p. 71</a></td> - </tr> - - <tr> - <td class="tdl3"><i>The wheel and axis</i></td> - <td class="tdrl"><a href="#c77">p. 77</a></td> - </tr> - - <tr> - <td class="tdl3"><i>The pulley</i></td> - <td class="tdrl"><a href="#c80">p. 80</a></td> - </tr> - - <tr> - <td class="tdl3"><i>The wedge</i></td> - <td class="tdrl"><a href="#c83a">p. 83</a></td> - </tr> - - <tr> - <td class="tdl3"><i>The screw</i></td> - <td class="tdrl"><a href="#c83b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl3"><i>The inclined plain</i></td> - <td class="tdrl"><a href="#c84">p. 84</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The pendulum<span class="pagenum"><a name="Page_xxix" id="Page_xxix">[xxix]</a></span></i></td> - <td class="tdrl"><a href="#c86a">p. 86</a></td> - </tr> - - <tr> - <td class="tdl3"><i>Vibrating in a circle</i></td> - <td class="tdrl"><a href="#c86b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl3"><i>Vibrating in a cycloid</i></td> - <td class="tdrl"><a href="#c91">p. 91</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The line of swiftest descent</i></td> - <td class="tdrl"><a href="#c93">p. 93</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The centre of oscillation</i></td> - <td class="tdrl"><a href="#c94">p. 94</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Experiments upon the percussion of bodies made by pendulums</i></td> - <td class="tdrl"><a href="#c98">p. 98</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The centre of percussion</i></td> - <td class="tdrl"><a href="#c100">p. 100</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The motion of projectiles</i></td> - <td class="tdrl"><a href="#c102">p. 102</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The description of the conic sections</i></td> - <td class="tdrl"><a href="#c106">p. 106</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The difference between absolute and relative motion, -as also between absolute and relative time</i></td> - <td class="tdrl"><a href="#c112">p. 112</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c117">Chap. 3.</a></em></span> <i>Of centripetal forces</i></td> - <td class="tdrl"><a href="#c117">p. 117</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c143">Chap. 4.</a></em></span> <i>Of the resistance of fluids</i></td> - <td class="tdrl"><a href="#c143">p. 143</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Bodies are resisted in the duplicate proportion of their velocities</i></td> - <td class="tdrl"><a href="#c147">p. 147</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of elastic fluids and their resistance</i></td> - <td class="tdrl"><a href="#c149">p. 149</a></td> - </tr> - - <tr> - <td class="tdl2"><i>How fluids may be rendered elastic </i></td> - <td class="tdrl"><a href="#c150">p. 150</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The degree of resistance in regard to the proportion -between the density of the body and of the fluid</i></td> - </tr> - - <tr> - <td class="tdl3"><i>In rare and uncompressed fluids</i></td> - <td class="tdrl"><a href="#c153">p. 153</a></td> - </tr> - - <tr> - <td class="tdl3"><i>In compressed fluids</i></td> - <td class="tdrl"><a href="#c155a">p. 155</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The degree of resistance as it depends upon the figure of bodies</i></td> - </tr> - - <tr> - <td class="tdl3"><i>In rare and uncompressed fluids</i></td> - <td class="tdrl"><a href="#c155b">p. 155</a></td> - </tr> - - <tr> - <td class="tdl3"><i>In compressed fluids</i></td> - <td class="tdrl"><a href="#c158">p. 158</a></td> - </tr> - - -</table> - -<p class="pc1 mid"><span class="smcap">Book II.</span><br /></p> - -<table id="toc2" summary="cont2"> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c161">Chap. 1.</a></em></span> -<i>That the planets move in a space empty of sensible matter</i></td> - <td class="tdrl"><a href="#c161">p. 161</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The system of the world described</i></td> - <td class="tdrl"><a href="#c162">p. 162</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The planets suffer no sensible resistance in their motion</i></td> - <td class="tdrl"><a href="#c166">p. 166</a></td> - </tr> - - <tr> - <td class="tdl2"><i>They are not kept in motion by a fluid</i></td> - <td class="tdrl"><a href="#c168">p. 168</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That all space is not full of matter without vacancies</i></td> - <td class="tdrl"><a href="#c169">p. 169</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="pagenum"><a name="Page_xxx" id="Page_xxx">[xxx]</a></span><span class="smcap"><em class="gesperrt"><a href="#c171a">Chap. 2.</a></em></span> -<i>Concerning the cause that keeps in motion the primary planets</i></td> - <td class="tdrl"><a href="#c171a">p. 171</a></td> - </tr> - - <tr> - <td class="tdl2"><i>They are influenced by a centripetal power directed to the sun</i></td> - <td class="tdrl"><a href="#c171b">p. 171</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The strength of this power is reciprocally in the -duplicate proportion of the distance</i></td> - <td class="tdrl"><a href="#c171c">ibid.</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The cause of the irregularities in the motions of the planets</i></td> - <td class="tdrl"><a href="#c175">p. 175</a></td> - </tr> - - <tr> - <td class="tdl2"><i>A correction of their motions</i></td> - <td class="tdrl"><a href="#c178">p. 178</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That the frame of the world is not eternal</i></td> - <td class="tdrl"><a href="#c180">p. 180</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c181">Chap. 3.</a></em></span> <i>Of the motion of the moon and the other -secondary planets</i></td> - </tr> - - <tr> - <td class="tdl2"><i>That they are influenced by a centripetal force directed -toward their primary, as the primary are influenced by the sun</i></td> - <td class="tdrl"><a href="#c182">p. 182</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That the power usually called gravity extends to the moon</i></td> - <td class="tdrl"><a href="#c189">p. 189</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That the sun acts on the secondary planets</i></td> - <td class="tdrl"><a href="#c190">p. 190</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The variation of the moon</i></td> - <td class="tdrl"><a href="#c193">p. 193</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That the circuit of the moons orbit is increased by the -sun in the quarters, and diminished in the conjunction and opposition</i></td> - <td class="tdrl"><a href="#c198">p. 198</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The distance of the moon from the earth in the quarters -and in the conjunction and opposition is altered by the sun</i></td> - <td class="tdrl"><a href="#c200">p. 200</a></td> - </tr> - - <tr> - <td class="tdl2"><i>These irregularities in the moon’s motion varied by the -change of distance between the earth and sun</i></td> - <td class="tdrl"><a href="#c201a">p. 201</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The period of the moon round the earth and her distance -varied by the same means</i></td> - <td class="tdrl"><a href="#c201b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The motion of the nodes and the inclination of the -moons orbit</i></td> - <td class="tdrl"><a href="#c202">p. 202</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The motion of the apogeon and change of the -eccentricity</i></td> - <td class="tdrl"><a href="#c218">p. 218</a></td> - </tr> - - <tr> - <td class="tdl2"><span class="pagenum"><a name="Page_xxxi" id="Page_xxxi">[xxxi]</a></span><i>The inequalities of the other secondary planets deducible -from these of the moon</i></td> - <td class="tdrl"><a href="#c229">p. 229</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c230a">Chap. 4.</a></em></span> <i>Of comets</i></td> - </tr> - - <tr> - <td class="tdl2"><i>They are not meteors, nor placed totally without the -planetary system</i></td> - <td class="tdrl"><a href="#c230b">p. 230</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The sun acts on them in the same manner as on the -planets</i></td> - <td class="tdrl"><a href="#c231">p. 231</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Their orbits are near to parabola’s</i></td> - <td class="tdrl"><a href="#c233">p. 233</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The comet that appeared at the end of the year 1680, -probably performs its period in 575 years, and another -comet in 75 years</i></td> - <td class="tdrl"><a href="#c234">p. 234</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Why the comets move in planes more different from -one another than the planets</i></td> - <td class="tdrl"><a href="#c235">p. 235</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The tails of comets</i></td> - <td class="tdrl"><a href="#c238">p. 238</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The use of them</i></td> - <td class="tdrl"><a href="#c243">p. 243 244</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The possible use of the comet it self</i></td> - <td class="tdrl"><a href="#c245">p. 245 246</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c247">Chap. 5.</a></em></span> <i>Of the bodies of the sun and planets</i></td> - </tr> - - <tr> - <td class="tdl2"><i>That each of the heavenly bodies is endued with an -attractive power, and that the force of the same -body on others is proportional to the quantity of -matter in the body attracted</i></td> - <td class="tdrl"><a href="#c247">p. 247</a></td> - </tr> - - <tr> - <td class="tdl2"><i>This proved in the earth</i></td> - <td class="tdrl"><a href="#c248">p. 248</a></td> - </tr> - - <tr> - <td class="tdl3"><i>In the sun</i></td> - <td class="tdrl"><a href="#c250">p. 250</a></td> - </tr> - - <tr> - <td class="tdl3"><i>In the rest of the planets</i></td> - <td class="tdrl"><a href="#c251">p. 251</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That the attractive power is of the same nature in -the sun and in all the planets, and therefore is -the same with gravity</i></td> - <td class="tdrl"><a href="#c252a">p. 252</a></td> - </tr> - - <tr> - <td class="tdl2"><i>That the attractive power in each of these bodies is -proportional to the quantity of matter in the body attracting</i></td> - <td class="tdrl"><a href="#c252b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl2"><span class="pagenum"><a name="Page_xxxii" id="Page_xxxii">[xxxii]</a></span><i>That each particle of which the sun and planets are -composed is endued with an attracting power, the -strength of which is reciprocally in the duplicate -proportion of the distance</i></td> - <td class="tdrl"><a href="#c257">p. 257</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The power of gravity universally belongs to all matter</i></td> - <td class="tdrl"><a href="#c259">p. 259</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The different weight of the same body upon the surface -of the sun, the earth, Jupiter and Saturn; the respective -densities of these bodies, and the proportion -between their diameters</i></td> - <td class="tdrl"><a href="#c261">p. 261</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c263">Chap. 6.</a></em></span> <i>Of the fluid parts of the planets</i></td> - </tr> - - <tr> - <td class="tdl2"><i>The manner in which fluids press</i></td> - <td class="tdrl"><a href="#c264">p. 264</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The motion of waves on the surface of water</i></td> - <td class="tdrl"><a href="#c269">p. 269</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The motion of sound through the air</i></td> - <td class="tdrl"><a href="#c270">p. 270</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The velocity of sound</i></td> - <td class="tdrl"><a href="#c282">p. 282</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Concerning the tides</i></td> - <td class="tdrl"><a href="#c283">p. 283</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The figure of the earth</i></td> - <td class="tdrl"><a href="#c296">p. 296</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The effect of this figure upon the power of gravity</i></td> - <td class="tdrl"><a href="#c300">p. 300</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The effect it has upon pendulums</i></td> - <td class="tdrl"><a href="#c302">p. 302</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Bodies descend perpendicularly to the surface of the earth</i></td> - <td class="tdrl"><a href="#c304">p. 304</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The axis of the earth changes its direction twice a year, -and twice a month</i></td> - <td class="tdrl"><a href="#c313a">p. 313</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The figure of the secondary planets</i></td> - <td class="tdrl"><a href="#c313b">ibid.</a></td> - </tr> - -</table> - -<p class="pc1 mid"><span class="smcap">Book III.</span><br /></p> - -<table id="toc3" summary="cont3"> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c316">Chap. 1.</a></em></span> <i>Concerning the cause of colours inherent in the light</i></td> - </tr> - - - <tr> - <td class="tdl2"><i>The sun’s light is composed of rays of different colours</i></td> - <td class="tdrl"><a href="#c318">p. 318</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The refraction of light</i></td> - <td class="tdrl"><a href="#c319">p. 319<br />320</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Bodies appear of different colour by day-light, because -some reflect one kind of light more copiously than the -rest, and other bodies other kinds of light</i></td> - <td class="tdrl"><a href="#c329">p. 329</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The effect of mixing rays of different colours</i></td> - <td class="tdrl"><a href="#c334">p. 334</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="pagenum"><a name="Page_xxxiii" id="Page_xxxiii">[xxxiii]</a></span><span class="smcap"><em class="gesperrt"><a href="#c338">Chap. 2.</a></em></span> <i>Of the properties of bodies whereon their -colours depend.</i></td> - </tr> - - <tr> - <td class="tdl2"><i>Light is not reflected by impinging against the solid -parts of bodies</i></td> - <td class="tdrl"><a href="#c339">p. 339</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The particles which compose bodies are transparent</i></td> - <td class="tdrl"><a href="#c341">p. 341</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Cause of opacity</i></td> - <td class="tdrl"><a href="#c342">p. 342</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Why bodies in the open day-light have different colours</i></td> - <td class="tdrl"><a href="#c344">p. 344</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The great porosity of bodies considered</i></td> - <td class="tdrl"><a href="#c355">p. 355</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c356">Chap. 3.</a></em></span> <i>Of the refraction, reflection, and -inflection of light.</i></td> - </tr> - - <tr> - <td class="tdl2"><i>Rays of different colours are differently refracted</i></td> - <td class="tdrl"><a href="#c357">p. 357</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The sine of the angle of incidence in each kind of rays -bears a given proportion to the sine of refraction</i></td> - <td class="tdrl"><a href="#c361">p. 361</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The proportion between the refractive powers in different -bodies</i></td> - <td class="tdrl"><a href="#c366">p. 366</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Unctuous bodies refract most in proportion to their -density</i></td> - <td class="tdrl"><a href="#c368">p. 368</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The action between light and bodies is mutual</i></td> - <td class="tdrl"><a href="#c369">p. 369</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Light has alternate fits of easy transmission and -reflection</i></td> - <td class="tdrl"><a href="#c371">p. 371</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The fits found to return alternately many thousand -times</i></td> - <td class="tdrl"><a href="#c375a">p. 375</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Why bodies reflect part of the light incident upon them -and transmit another part</i></td> - <td class="tdrl"><a href="#c375b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Sir</i> <em class="gesperrt"><span class="smcap">Isaac Newton</span></em>’s <i>conjecture -concerning the cause of this alternate reflection and -transmission of light</i></td> - <td class="tdrl"><a href="#c376">p. 376</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The inflection of light</i></td> - <td class="tdrl"><a href="#c377a">p. 377</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c377b">Chap. 4.</a></em></span> <i>Of optic glasses.</i></td> - </tr> - - <tr> - <td class="tdl2"><i>How the rays of light are refracted by a spherical -surface of glass</i></td> - <td class="tdrl"><a href="#c378">p. 378</a></td> - </tr> - - <tr> - <td class="tdl2"><i>How they are refracted by two such surfaces</i></td> - <td class="tdrl"><a href="#c380">p. 380</a></td> - </tr> - - <tr> - <td class="tdl2"><i>How the image of objects is formed by a convex glass</i></td> - <td class="tdrl"><a href="#c381">p. 381</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Why convex glasses help the sight in old age, and concave -glasses assist short-sighted people</i></td> - <td class="tdrl"><a href="#c383">p. 383</a></td> - </tr> - - <tr> - <td class="tdl2"><i>The manner in which vision is performed by the eye</i></td> - <td class="tdrl"><a href="#c385">p. 385</a></td> - </tr> - - <tr> - <td class="tdl2"><i><span class="pagenum"><a name="Page_xxxiv" id="Page_xxxiv">[xxxiv]</a></span>Of telescopes with two convex glasses</i></td> - <td class="tdrl"><a href="#c386">p. 386</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of telescopes with four convex glasses</i></td> - <td class="tdrl"><a href="#c388a">p. 388</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of telescopes with one convex and one concave glass</i></td> - <td class="tdrl"><a href="#c388b">ibid.</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of microscopes</i></td> - <td class="tdrl"><a href="#c389">p. 389</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of the imperfection of telescopes arising from the -different refrangibility of the light</i></td> - <td class="tdrl"><a href="#c390">p. 390</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of the reflecting telescope</i></td> - <td class="tdrl"><a href="#c393">p. 393</a></td> - </tr> - - <tr> - <td class="tdl1"><span class="smcap"><em class="gesperrt"><a href="#c394a">Chap. 5.</a></em></span> <i>Of the rainbow</i></td> - </tr> - - <tr> - <td class="tdl2"><i>Of the inner rainbow</i></td> - <td class="tdrl"><a href="#c394b">p. 394<br />395 398 399</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of the outter bow</i></td> - <td class="tdrl"><a href="#c396">p. 396<br />397 400</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Of a particular appearance in the inner rainbow</i></td> - <td class="tdrl"><a href="#c401">p. 401</a></td> - </tr> - - <tr> - <td class="tdl2"><i>Conclusion</i></td> - <td class="tdrl"><a href="#c405">p. 405</a></td> - </tr> - -</table> - -<hr class="d3" /> - -<h2><em class="gesperrt">ERRATA.</em></h2> - -<div class="pbq"> - -<p class="drop-cap04">PAGE 25. line 4. read <i>In these Precepts.</i> p. 40. l. 24. for <i>I</i> read <i>K</i>. p. 53. l. penult. f. Æ. r. F. -p. 82. l. ult. f. 40. r. 41. p. 83 l. ult. f. 43. r. 45. p. 91. l. 3. f. 48. r. 50. ibid. l. 25. -for 49. r. 51. p. 92. l. 18. f. <i>A G F E.</i> r. <i>H G F C.</i> p. 96. l. 23. dele the comma after {⅓}. -p. 140. l. 12. dele <i>and.</i> p. 144. l. 15. f. <i>threefold.</i> r. <i>two-fold.</i> p. 162. l. 25. f. {⅓}. r. {⅞}. p. 193. -1. 2. r. <i>always.</i> p. 199. l. penult. and p. 200. l. 3. 5. f. F. r. C. p. 201. l. 8. f. <i>ascends.</i> r.<i> must -ascend.</i> ibid. l. 10. f. <i>it descends.</i> r. <i>descend.</i> p. 208. l. 14. f. <i>W T O.</i> r. <i>N T O.</i> In <i>fig.</i> 110. draw a line -from <i>I</i> through <i>T</i>, till it meets the circle <i>A D C B</i>, where place <i>W.</i> p. 216. l. penult. f. <i>action.</i> r. -<i>motion.</i> p. 221. l. 23. f. <i>A F.</i> r. <i>A H.</i> p. 232. l. 23. after <i>invention</i> put a full point. p. 253. l. penult. -delete the comma after <i>remarkable</i>. p. 255. l. ult. f. <i>D E.</i> r. <i>B E.</i> p. 278. l. 17. f. ξ τ. r. ξ π. -p. 299. l. 19 r. <i>the.</i> p. 361. l. 12. f. I. r. t. p. 369. l. 2, 3. r. <i>Pseudo-topaz.</i> p. 378. l. 12. f. <i>that.</i> -r. <i>than.</i> p. 379. l. 15. f. <i>converge.</i> r. <i>diverge.</i> p. 384. l. 7. f. <i>optic-glass.</i> r. <i>optic-nerve.</i> p. 391. -l. 18. r. <i>as 50 to 78.</i> p. 392. l. 18. after <i>telescope</i> add <i>be about 100 feet long and the.</i> in <i>fig. 161.</i> -f. δ put ε. p. 399. l. 8. r. A n, A x. &c. p. 400. 1. 19. r. A π, A ρ. A σ, A τ. A φ. p. 401. -l. 14. r. <i>fig. 163.</i> The pages 374, 375, 376 are erroneously numbered 375, 376, 377; and the -pages 382, 383 are numbered 381, 382.</p></div> - -</div> - -<p><span class="pagenum"><a name="Page_xxxv" id="Page_xxxv">[xxxv]</a></span></p> - -<div class="chapter"> - -<hr class="d1" /> -<hr class="d2" /> - -<h2 class="p4"><span class="reduct wn">A LIST of such of the</span><br /> -<span class="mid">SUBSCRIBERS NAMES</span><br /> -<span class="reduct wn">As are come to the <span class="smcap"><em class="gesperrt">Hand</em></span> of the</span><br /> -<span class="large">AUTHOR.</span></h2> - -<p class="pi4 p4">A</p> - -<p class="drop-cap04">M<i>Onseigneur</i> d’Aguesseau, <i>Chancelier de</i> France<br /> -<i>Reverend</i> Mr Abbot, <i>of</i> Emanuel Coll. Camb.<br /> -<i>Capt.</i> George Abell<br /> -<i>The Hon. Sir</i> John Anstruther, <i>Bar.</i><br /> -Thomas Abney, <i>Esq;</i><br /> -Mr. Nathan Abraham<br /> -<i>Sir</i> Arthur Acheson, Bart.<br /> -Mr William Adair<br /> -<i>Rev.</i> Mr John Adams, <i>Fellow of</i> Sidney Coll. Cambridge<br /> -Mr William Adams<br /> -Mr George Adams<br /> -Mr William Adamson, <i>Scholar of</i> Caius Coll. Camb.<br /> -Mr Samuel Adee, <i>Fell. of</i> Corp. Chr. Coll. Oxon<br /> -Mr Andrew Adlam<br /> -Mr John Adlam<br /> -Mr Stephen Ainsworth<br /> -Mrs Aiscot<br /> -Mr Robert Akenhead, <i>Bookseller at</i> Newcastle <i>upon</i> Tyne<br /> -S. B. Albinus, M. D. Anatom. <i>and</i> Chirurg <i>in</i> Acad. L. B. Prof.<br /> -George Aldridge, <i>M. D.</i><br /> -Mr George Algood<br /> -Mr Aliffe<br /> -Robert Allen, <i>Esq;</i><br /> -Mr Zach. Allen<br /> -<i>Rev.</i> Mr Allerton, <i>Fellow of</i> Sidney Coll. Cambridge<br /> -Mr St. Amand<br /> -Mr John Anns<br /> -Thomas Anson, <i>Esq;</i><br /> -<i>Rev. Dr.</i> Christopher Anstey<br /> -Mr Isaac Antrabus<br /> -Mr Joshua Appleby<br /> -John Arbuthnot, <i>M. D.</i><br /> -William Archer, <i>Esq;</i><br /> -Mr John Archer, <i>Merchant of</i> Amsterdam<br /> -Thomas Archer, <i>Esq;</i><br /> -<i>Coll.</i> John Armstrong, Surveyor-General <i>of</i> His Majesty’s Ordnance<br /> -Mr Armytage<br /> -Mr Street Arnold, <i>Surgeon</i><br /> -Mr Richard Arnold<br /> -Mr Ascough<br /> -Mr Charles Asgill<br /> -Richard Ash, <i>Esq; of</i> Antigua<br /> -Mr Ash, <i>Fellow-Commoner of</i> Jesus Coll. Cambridge<br /> -William Ashurst, <i>Esq; of</i> Castle Henningham, Essex<br /> -Mr Thomas Ashurst<br /> -Mr Samuel Ashurst<br /> -Mr John Askew, <i>Merchant</i><br /> -Mr Edward Athawes, <i>Merchant</i><br /> -Mr Abraham Atkins<br /> -Mr Edward Kensey Atkins<br /> -Mr Ayerst<br /> -Mr Jonathan Ayleworth, <i>Jun.</i><br /> -Rowland Aynsworth, <i>Esq;</i></p> - -<p class="pi4 p2">B</p> - -<p class="pn2"><i>His Grace the Duke of</i> Bedford<br /> -<i>Right Honourable the Marquis of</i> Bowmont<br /> -<i>Right Hon. the Earl of</i> Burlington<br /> -<i>Right Honourable Lord Viscount</i> Bateman<br /> -<i>Rt. Rev. Ld. Bp. of</i> Bath <i>and</i> Wells<br /> -<i>Rt. Rev. Lord Bishop of</i> Bristol<br /> -<i>Right Hon. Lord</i> Bathurst<br /> -Richard Backwell, <i>Esq;</i><br /> -Mr William Backshell, <i>Merch.</i><br /> -Edmund Backwell, <i>Gent.</i><br /> -<i>Sir</i> Edmund Bacon<br /> -Richard Bagshaw, <i>of</i> Oakes, <i>Esq;</i><br /> -Tho. Bagshaw, <i>of</i> Bakewell, <i>Esq;</i><br /> -<i>Rev.</i> Mr. Bagshaw<br /> -<i>Sir</i> Robert Baylis<br /> -<i>Honourable</i> George Baillie, <i>Esq;</i><br /> -Giles Bailly, <i>M. D. of</i> Bristol<br /> -Mr Serjeant Baines<br /> -<i>Rev.</i> Mr. Samuel Baker, <i>Residen. of St.</i> Paul’s.<br /> -Mr George Baker<br /> -Mr Francis Baker<br /> -Mr Robert Baker<br /> -Mr John Bakewell<br /> -Anthony Balam, <i>Esq;</i><br /> -<span class="pagenum"><a name="Page_xxxvi" id="Page_xxxvi">[xxxvi]</a></span>Charles Bale, <i>M. D.</i><br /> -Mr Atwell, <i>Fellow of</i> Exeter Coll. Oxon<br /> -Mr Savage Atwood<br /> -Mr John Atwood<br /> -Mr James Audley<br /> -<i>Sir</i> Robert Austen, <i>Bart.</i><br /> -<i>Sir</i> John Austen<br /> -Benjamin Avery, <i>L. L. D.</i><br /> -Mr Balgay<br /> -<i>Rev.</i> Mr Tho. Ball, <i>Prebendary of</i> Chichester<br /> -Mr Pappillon Ball, <i>Merchant</i><br /> -Mr Levy Ball<br /> -<i>Rev.</i> Mr Jacob Ball, <i>of</i> Andover<br /> -<i>Rev.</i> Mr Edward Ballad, <i>of</i> Trin. Coll. Cambridge<br /> -Mr Baller<br /> -John Bamber, <i>M. D.</i><br /> -<i>Rev.</i> Mr Banyer, <i>Fellow of</i> Emanuel Coll. Cambridge<br /> -Mr Henry Banyer, <i>of</i> Wisbech, <i>Surgeon</i><br /> -Mr John Barber, <i>Apothecary in</i> Coventry<br /> -Henry Steuart Barclay, <i>of</i> Colairny, <i>Esq;</i><br /> -<i>Rev.</i> Mr Barclay, <i>Canon of</i> Windsor<br /> -Mr David Barclay<br /> -Mr Benjamin Barker, <i>Bookseller in</i> London<br /> -—— Barker, <i>Esq;</i><br /> -Mr Francis Barkstead<br /> -<i>Rev.</i> Mr Barnard<br /> -Thomas Barrett, <i>Esq;</i><br /> -Mr Barrett<br /> -Richard Barret, <i>M. D.</i><br /> -Mr Barrow, <i>Apothecary</i><br /> -William Barrowby, <i>M. D.</i><br /> -Edward Barry, <i>M. D. of</i> Corke<br /> -Mr Humphrey Bartholomew, <i>of</i> University College, Oxon<br /> -Mr Benjamin Bartlett<br /> -Mr Henry Bartlett<br /> -Mr James Bartlett<br /> -Mr Newton Barton, <i>of</i> Trinity College, Cambridge<br /> -<i>Rev.</i> Mr. Barton<br /> -William Barnsley, <i>Esq;</i><br /> -Mr Samuel Bateman<br /> -Mr Thomas Bates<br /> -Peter Barhurst, <i>Esq;</i><br /> -Mark Barr, <i>Esq;</i><br /> -Thomas Bast, <i>Esq;</i><br /> -Mr Batley, <i>Bookseller in</i> London<br /> -Mr Christopher Batt, <i>jun.</i><br /> -Mr William Batt, <i>Apothecary</i><br /> -Rev. Mr Battely, <i>M. A. Student of</i> Christ Church, Oxon<br /> -Mr Edmund Baugh<br /> -<i>Rev.</i> Mr. Thomas Bayes<br /> -Edward Bayley, <i>M. D. of</i> Havant<br /> -John Bayley, <i>M. D. of</i> Chichester<br /> -Mr. Alexander Baynes, <i>Professor of Law in the University of</i> Edinburgh<br /> -Mr Benjamin Beach<br /> -Thomas Beacon, <i>Esq;</i><br /> -<i>Rev.</i> Mr Philip Bearcroft<br /> -Mr Thomas Bearcroft<br /> -Mr William Beachcroft<br /> -Richard Beard, <i>M. D. of</i> Worcester<br /> -Mr Joseph Beasley<br /> -<i>Rev.</i> Mr Beats, <i>M. A. Fellow of</i> Magdalen College, Cambridge<br /> -<i>Sir</i> George Beaumont<br /> -John Beaumont, <i>Esq; of</i> Clapham<br /> -William Beecher, <i>of</i> Howberry, <i>Esq;</i><br /> -Mr Michael Beecher<br /> -Mr Finney Beifield, <i>of the</i> Inner-Temple<br /> -Mr Benjamin Bell<br /> -Mr Humphrey Bell<br /> -Mr Phineas Bell<br /> -Leonard Belt, <i>Gent.</i><br /> -William Benbow, <i>Esq;</i><br /> -Mr Martin Bendall<br /> -Mr George Bennet, <i>of</i> Cork, <i>Bookseller</i><br /> -Rev. Mr Martin Benson, <i>Archdeacon of</i> Berks<br /> -Samuel Benson, <i>Esq;</i><br /> -William Benson, <i>Esq;</i><br /> -Rev. Richard Bently, <i>D. D. Master of</i> Trinity Coll. Cambridge<br /> -Thomas Bere, <i>Esq;</i><br /> -<i>The Hon.</i> John Berkley, <i>Esq;</i><br /> -Mr Maurice Berkley, sen. <i>Surgeon</i><br /> -John Bernard, <i>Esq;</i><br /> -Mr Charles Bernard<br /> -Hugh Bethell, <i>of</i> Rise <i>in</i> Yorkshire, <i>Esq;</i><br /> -Hugh Bethell, <i>of</i> Swindon <i>in</i> Yorkshire, <i>Esq;</i><br /> -Mr Silvanus Bevan, <i>Apothecary</i><br /> -Mr Calverly Bewick, jun.<br /> -Henry Bigg, <i>B. D.</i> Warden <i>of</i> New College, Oxon<br /> -<i>Sir</i> William Billers<br /> -—— Billers, <i>Esq;</i><br /> -Mr John Billingsley<br /> -Mr George Binckes<br /> -<i>Rev.</i> Mr Birchinsha, <i>of</i> Exeter College, Oxon<br /> -<i>Rev.</i> Mr Richard Biscoe<br /> -Mr Hawley Bishop, <i>Fellow of St.</i> John’s College, Oxon<br /> -<i>Dr</i> Bird, <i>of</i> Reading<br /> -Henry Blaake, <i>Esq;</i><br /> -Mr Henry Blaake<br /> -<i>Rev.</i> Mr George Black<br /> -Steward Blacker, <i>Esq;</i><br /> -William Blacker, <i>Esq;</i><br /> -Rowland Blackman, <i>Esq;</i><br /> -<i>Rev.</i> Mr Charles Blackmore, <i>of</i> Worcester<br /> -<i>Rev</i> Mr Blackwall, <i>of</i> Emanuel College, Cambridge<br /> -Jonathan Blackwel, <i>Esq;</i><br /> -James Blackwood, <i>Esq;</i><br /> -Mr Thomas Blandford<br /> -Arthur Blaney, <i>Esq;</i><br /> -Mr James Blew<br /> -Mr William Blizard<br /> -<i>Dr</i> Blomer<br /> -Mr Henry Blunt<br /> -Mr Elias Bocket<br /> -Mr Thomas Bocking<br /> -Mr Charles Boehm, <i>Merchant</i><br /> -Mr William Bogdani<br /> -Mr John Du Bois, <i>Merchant</i><br /> -Mr Samuel Du Bois<br /> -Mr Joseph Bolton, of Londonderry, <i>Esq;</i><br /> -Mr John Bond<br /> -John Bonithon, <i>M. A.</i><br /> -Mr James Bonwick, <i>Bookseller in</i> London<br /> -Thomas Boone, <i>Esq;</i><br /> -<i>Rev.</i> Mr Pennystone, <i>M. A.</i><br /> -Mrs Judith Booth<br /> -Thomas Bootle, <i>Esq;</i><br /> -Thomas Borret, <i>Esq;</i><br /> -Mr Benjamin Boss<br /> -<i>Dr</i> Bostock<br /> -Henry Bosville, <i>Esq;</i><br /> -Mr John Bosworth<br /> -<i>Dr</i> George Boulton<br /> -<i>Hon.</i> Bourn <i>M. D. of</i> Chesterfield<br /> -Mrs Catherine Bovey<br /> -Mr Humphrey Bowen<br /> -Mr Bower<br /> -John Bowes, <i>Esq;</i><br /> -William Bowles, <i>Esq;</i><br /> -Mr John Bowles<br /> -Mr Thomas Bowles<br /> -Mr Duvereux Bowly<br /> -<span class="pagenum"><a name="Page_xxxvii" id="Page_xxxvii">[xxxvii]</a></span>Duddington Bradeel, <i>Esq;</i><br /> -Rev. Mr James Bradley, <i>Professor of</i> Astronomy, <i>in</i> Oxford<br /> -Mr Job Bradley, <i>Bookseller in</i> Chesterfield<br /> -<i>Rev.</i> Mr John Bradley<br /> -<i>Rev.</i> Mr Bradshaw, <i>Fellow of</i> Jesus College, Cambridge<br /> -Mr Joseph Bradshaw<br /> -Mr Thomas Blackshaw<br /> -Mr Robert Bragge<br /> -Champion Bramfield, <i>Esq;</i><br /> -Joseph Brand, <i>Esq;</i><br /> -Mr Thomas Brancker<br /> -Mr Thomas Brand<br /> -Mr Braxton<br /> -<i>Capt.</i> David Braymer<br /> -<i>Rev</i> Mr Charles Brent, <i>of</i> Bristol<br /> -Mr William Brent<br /> -Mr Edmund Bret<br /> -John Brickdale, <i>Esq;</i><br /> -<i>Rev.</i> Mr John Bridgen <i>A. M.</i><br /> -Abraham Bridges, <i>Esq;</i><br /> -George Briggs, <i>Esq;</i><br /> -John Bridges, <i>Esq;</i><br /> -Brook Bridges, <i>Esq;</i><br /> -Orlando Bridgman, <i>Esq;</i><br /> -Mr Charles Bridgman<br /> -Mr William Bridgman, <i>of</i> Trinity College, Cambridge<br /> -<i>Sir</i> Humphrey Briggs, <i>Bart.</i><br /> -Robert Bristol, <i>Esq;</i><br /> -Mr Joseph Broad<br /> -Peter Brooke, <i>of</i> Meer, <i>Esq;</i><br /> -Mr Jacob Brook<br /> -Mr Brooke, <i>of</i> Oriel Coll. Oxon<br /> -Mr Thomas Brookes<br /> -Mr James Brooks<br /> -William Brooks, <i>Esq;</i><br /> -<i>Rev.</i> Mr William Brooks<br /> -Stamp Brooksbank, <i>Esq;</i><br /> -Mr Murdock Broomer<br /> -William Brown, <i>Esq;</i><br /> -Mr Richard Brown, <i>of</i> Norwich<br /> -Mr William Brown, <i>of</i> Hull<br /> -Mrs Sarah Brown<br /> -Mr John Browne<br /> -Mr John Browning, <i>of</i> Bristol<br /> -Mr John Browning<br /> -Noel Broxholme, <i>M. D.</i><br /> -William Bryan, <i>Esq;</i><br /> -<i>Rev.</i> Mr Brydam<br /> -Christopher Buckle, <i>Esq;</i><br /> -Samuel Buckley, <i>Esq;</i><br /> -Mr Budgen<br /> -<i>Sir</i> John Bull<br /> -Josiah Bullock, <i>of</i> Faulkbourn-Hall, Essex, <i>Esq;</i><br /> -<i>Rev.</i> Mr Richard Bullock<br /> -<i>Rev.</i> Mr Richard Bundy<br /> -Mr Alexander Bunyan<br /> -<i>Rev.</i> Mr D. Burges<br /> -Ebenezer Burgess, <i>Esq;</i><br /> -Robert Burleston, <i>M. B.</i><br /> -Gilbert Burnet, <i>Esq;</i><br /> -Thomas Burnet, <i>Esq;</i><br /> -<i>Rev.</i> Mr Gilbert Burnet<br /> -<i>His Excellency</i> Will. Burnet, <i>Esq;</i> Governour <i>of</i> New-York<br /> -Mr Trafford Burnston, <i>of</i> Trin. College, Cambridge<br /> -Peter Burrel <i>Esq;</i><br /> -John Burridge, <i>Esq;</i><br /> -James Burrough, <i>Esq;</i> Beadle <i>and Fellow of</i> Caius Coll. Cambr.<br /> -Mr Benjamin Burroughs<br /> -Jeremiah Burroughs, <i>Esq;</i><br /> -<i>Rev.</i> Mr Joseph Burroughs<br /> -Christopher Burrow, <i>Esq;</i><br /> -James Burrow, <i>Esq;</i><br /> -William Burrow, <i>A. M.</i><br /> -Francis Burton, <i>Esq;</i><br /> -John Burton, <i>Esq;</i><br /> -Samuel Burton, <i>of</i> Dublin, <i>Esq;</i><br /> -William Burton, <i>Esq;</i><br /> -Mr Burton.<br /> -Richard Burton, <i>Esq;</i><br /> -<i>Dr</i> Simon Burton<br /> -<i>Rev.</i> Mr Thomas Burton, <i>M.A. Fellow of</i> Caius College, Cambridge<br /> -John Bury, jun. <i>Esq;</i><br /> -<i>Rev.</i> Mr Samuel Bury<br /> -Mr William Bush<br /> -<i>Rev.</i> Mr Samuel Butler<br /> -Mr Joseph Button, <i>of</i> Newcastle <i>upon</i> Tyne<br /> -<i>Hon.</i> Edward Byam, <i>Governour of</i> Antigua<br /> -Mr Edward Byam, <i>Merchant</i><br /> -Mr John Byrom<br /> -Mr Duncumb Bristow, <i>Merch.</i><br /> -Mr William Bradgate</p> - -<p class="pi4 p2">C</p> - -<p class="pn2"><i>His Grace the</i> Archbishop <i>of</i> Canterbury<br /> -<i>Right Hon. the Lord</i> Chancellor<br /> -<i>His Grace the</i> Duke <i>of</i> Chandois<br /> -<i>The Right Hon. the Earl of</i> Carlisle<br /> -<i>Right Hon.</i> Earl Cowper<br /> -<i>Rt. Rev. Lord Bishop of</i> Carlisle<br /> -<i>Rt. Rev. Lord Bishop of</i> Chichester<br /> -<i>Rt. Rev. Lord Bish. of</i> Clousert <i>in</i> Ireland<br /> -<i>Rt. Rev, Lord Bishop of</i> Cloyne<br /> -<i>Rt. Hon. Lord</i> Clinton<br /> -<i>Rt. Hon. Lord</i> Chetwynd<br /> -<i>Rt. Hon. Lord</i> James Cavendish<br /> -<i>The Hon. Lord</i> Cardross<br /> -<i>Rt. Hon. Lord</i> Castlemain<br /> -<i>Right Hon. Lord St.</i> Clare<br /> -Cornelius Callaghan, <i>Esq;</i><br /> -Mr Charles Callaghan<br /> -Felix Calvert, <i>of</i> Allbury, <i>Esq;</i><br /> -Peter Calvert, <i>of</i> Hunsdown <i>in</i> Hertfordshire, <i>Esq;</i><br /> -Mr William Calvert <i>of</i> Emanuel College, Cambridge<br /> -<i>Reverend</i> Mr John Cambden<br /> -John Campbell, <i>of</i> Stackpole-Court, <i>in the County of</i> Pembroke, <i>Esq;</i><br /> -Mrs Campbell, <i>of</i> Stackpole-Court<br /> -Mrs. Elizabeth Caper<br /> -Mr Dellillers Carbonel<br /> -Mr John Carleton<br /> -Mr Richard Carlton, <i>of</i> Chesterfield<br /> -Mr Nathaniel Carpenter<br /> -Henry Carr, <i>Esq;</i><br /> -John Carr, <i>Esq;</i><br /> -John Carruthers, <i>Esq;</i><br /> -<i>Rev. Dr.</i> George Carter, <i>Provost of</i> Oriel College<br /> -Mr Samuel Carter<br /> -<i>Honourable</i> Edward Carteret, <i>Esq;</i><br /> -Robert Cartes, jun. <i>in</i> Virginia, <i>Esq;</i><br /> -Mr William Cartlich<br /> -James Maccartney, <i>Esq;</i><br /> -Mr Cartwright, <i>of</i> Ainho<br /> -Mr William Cartwright, <i>of</i> Trinity College, Cambridge<br /> -<i>Reverend</i> Mr William Cary, <i>of</i> Bristol<br /> -Mr Lyndford Caryl<br /> -Mr John Case<br /> -Mr John Castle<br /> -<i>Reverend</i> Mr Cattle<br /> -<i>Hon.</i> William Cayley, <i>Consul at</i> Cadiz, <i>Esq;</i><br /> -William Chambers, <i>Esq;</i><br /> -Mr Nehemiah Champion<br /> -Mr Richard Champion<br /> -Matthew Chandler, <i>Esq;</i><br /> -Mr George Channel<br /> -Mr Channing<br /> -Mr Joseph Chappell, <i>Attorney at</i> Bristol<br /> -<span class="pagenum"><a name="Page_xxxviii" id="Page_xxxviii">[xxxviii]</a></span>Mr Rice Charlton, <i>Apothecary at</i> Bristol<br /> -St. John Charelton, <i>Esq;</i><br /> -Mr Richard Charelton<br /> -Mr Thomas Chase, <i>of</i> Lisbon, <i>Merchant</i><br /> -Robert Chauncey, <i>M. D.</i><br /> -Mr Peter Chauvel<br /> -Patricius Chaworth, <i>of</i> Ansley, <i>Esq;</i><br /> -Pole Chaworth <i>of the</i> Inner Temple, <i>Esq;</i><br /> -Mr William Cheselden, <i>Surgeon to her Majesty</i><br /> -James Chetham, <i>Esq;</i><br /> -Mr James Chetham<br /> -Charles Child, A. B. <i>of</i> Clare-Hall, <i>in</i> Cambridge, <i>Esq;</i><br /> -Mr Cholmely, <i>Gentleman Commoner of</i> New-College, Oxon<br /> -Thomas Church, <i>Esq;</i><br /> -<i>Reverend</i> Mr St. Clair<br /> -<i>Reverend</i> Mr Matthew Clarke<br /> -Mr William Clark<br /> -Bartholomew Clarke, <i>Esq;</i><br /> -Charles Clarke, <i>of</i> Lincolns-Inn, <i>Esq;</i><br /> -George Clarke, <i>Esq;</i><br /> -Samuel Clarke, <i>of the</i> Inner-Temple, <i>Esq;</i><br /> -<i>Reverend</i> Mr Alured Clarke, <i>Prebendary of</i> Winchester<br /> -<i>Rev.</i> John Clarke, <i>D. D. Dean of</i> Sarum<br /> -Mr John Clark, <i>A. B. of</i> Trinity College, Cambridge<br /> -Matthew Clarke, <i>M. D.</i><br /> -<i>Rev.</i> Mr Renb. Clarke, <i>Rector of</i> Norton, Leicestershire<br /> -<i>Rev.</i> Mr Robert Clarke, <i>of</i> Bristol<br /> -<i>Rev.</i> Samuel Clarke, <i>D. D.</i><br /> -Mr Thomas Clarke, <i>Merchant</i><br /> -Mr Thomas Clarke<br /> -<i>Rev.</i> Mr Clarkson, <i>of</i> Peter-House, Cambridge<br /> -Mr Richard Clay<br /> -William Clayton, <i>of</i> Marden, <i>Esq;</i><br /> -Samuel Clayton, <i>Esq;</i><br /> -Mr William Clayton<br /> -Mr John Clayton<br /> -Mr Thomas Clegg<br /> -Mr Richard Clements, <i>of</i> Oxford, <i>Bookseller</i><br /> -Theophilus Clements, <i>Esq;</i><br /> -Mr George Clifford, <i>jun. of</i> Amsterdam<br /> -George Clitherow, <i>Esq;</i><br /> -George Clive, <i>Esq;</i><br /> -<i>Dr.</i> Clopton, <i>of</i> Bury<br /> -Stephen Clutterbuck, <i>Esq;</i><br /> -Henry Coape, <i>Esq;</i><br /> -Mr Nathaniel Coatsworth<br /> -<i>Rev.</i> Dr. Cobden, <i>Chaplain to the Bishop of</i> London<br /> -<i>Hon. Col.</i> John Codrington, <i>of</i> Wraxall, Somersetshire<br /> -<i>Right Hon.</i> Marmaduke Coghill, <i>Esq;</i><br /> -Francis Coghlan, <i>Esq;</i><br /> -Sir Thomas Coke<br /> -Mr Charles Colborn<br /> -Benjamin Cole, <i>Gent.</i><br /> -Dr Edward Cole<br /> -Mr Christian Colebrandt<br /> -James Colebrooke, <i>Esq;</i><br /> -Mr William Coleman, <i>Merchant</i><br /> -Mr Edward Collet<br /> -Mrs Henrietta Collet<br /> -Mr John Collet<br /> -Mrs Mary Collett<br /> -Mr Samuel Collet<br /> -Mr Nathaniel Collier<br /> -Anthony Collins, <i>Esq;</i><br /> -Thomas Collins, <i>of</i> Greenwich, <i>M. D.</i><br /> -Mr Peter Collinson<br /> -Edward Colmore, <i>Fellow of</i> Magdalen College, Oxon<br /> -<i>Rev.</i> Mr John Colson<br /> -Mrs Margaret Colstock, <i>of</i> Chichester<br /> -<i>Capt.</i> John Colvil<br /> -Renè de la Combe, <i>Esq;</i><br /> -<i>Rev.</i> Mr John Condor<br /> -John Conduit, <i>Esq;</i><br /> -John Coningham, <i>M. D.</i><br /> -<i>His Excellency</i> William Conolly, <i>one of the Lords Justices of</i> Ireland<br /> -Mr Edward Constable, <i>of</i> Reading<br /> -<i>Rev.</i> Mr Conybeare, <i>M. A.</i><br /> -<i>Rev.</i> Mr James Cook<br /> -Mr John Cooke<br /> -Mr Benjamin Cook<br /> -William Cook, <i>B L. of St.</i> John’s College, Oxon<br /> -James Cooke, <i>Esq;</i><br /> -John Cooke, <i>Esq;</i><br /> -Mr Thomas Cooke<br /> -Mr William Cooke, <i>Fellow of St.</i> John’s College, Oxon<br /> -<i>Rev.</i> Mr Cooper, <i>of</i> North-Hall<br /> -Charles Cope, <i>Esq;</i><br /> -<i>Rev.</i> Mr Barclay Cope<br /> -Mr John Copeland<br /> -John Copland, <i>M. B.</i><br /> -Godfrey Copley, <i>Esq;</i><br /> -Sir Richard Corbet, <i>Bar.</i><br /> -<i>Rev.</i> Mr Francis Corbett<br /> -Mr Paul Corbett<br /> -Mr Thomas Corbet<br /> -Henry Cornelisen, <i>Esq;</i><br /> -<i>Rev.</i> Mr John Cornish<br /> -Mrs Elizabeth Cornwall<br /> -Library <i>of</i> Corpus Christi College, Cambridge<br /> -Mr William Cossley, <i>of</i> Bristol, <i>Bookseller</i><br /> -Mr Solomon du Costa<br /> -<i>Dr.</i> Henry Costard<br /> -<i>Dr.</i> Cotes, <i>of</i> Pomfret<br /> -Caleb Cotesworth, <i>M. D.</i><br /> -Peter Cottingham, <i>Esq;</i><br /> -Mr John Cottington<br /> -<i>Sir</i> John Hinde Cotton<br /> -Mr James Coulter<br /> -George Courthop, <i>of</i> Whiligh <i>in</i> Sussex, <i>Esq;</i><br /> -Mr Peter Courthope<br /> -Mr John Coussmaker, <i>jun.</i><br /> -Mr Henry Coward, <i>Merchant</i><br /> -Anthony Ashley Cowper, <i>Esq;</i><br /> -<i>The Hon.</i> Spencer Cowper, <i>Esq; One of the Justices of the Court of</i> Common Pleas<br /> -Mr Edward Cowper<br /> -<i>Rev.</i> Mr John Cowper<br /> -<i>Sir</i> Charles Cox<br /> -Samuel Cox, <i>Esq;</i><br /> -Mr Cox, <i>of</i> New Coll. Oxon<br /> -Mr Thomas Cox<br /> -Mr Thomas Cradock, <i>M. A.</i><br /> -<i>Rev.</i> Mr John Craig<br /> -<i>Rev.</i> Mr John Cranston, <i>Archdeacon of</i> Cloghor<br /> -John Crafter, <i>Esq;</i><br /> -Mr John Creech<br /> -James Creed, <i>Esq;</i><br /> -<i>Rev.</i> Mr William Crery<br /> -John Crew, <i>of</i> Crew Hall, <i>in</i> Cheshire, <i>Esq;</i><br /> -Thomas Crisp, <i>Esq;</i><br /> -Mr Richard Crispe<br /> -<i>Rev.</i> Mr Samuel Cuswick<br /> -Tobias Croft, <i>of</i> Trinity College, Cambridge<br /> -Mr John Crook<br /> -<i>Rev.</i> Dr Crosse, <i>Master of</i> Katherine Hall<br /> -Christopher Crowe, <i>Esq;</i><br /> -George Crowl, <i>Esq;</i><br /> -<i>Hon.</i> Nathaniel Crump, <i>Esq; of</i> Antigua<br /> -Mrs Mary Cudworth<br /> -<span class="pagenum"><a name="Page_xxxix" id="Page_xxxix">[xxxix]</a></span>Alexander Cunningham, <i>Esq;</i><br /> -Henry Cunningham, <i>Esq;</i><br /> -Mr Cunningham<br /> -Dr Curtis <i>of</i> Sevenoak<br /> -Mr William Curtis<br /> -Henry Curwen, <i>Esq;</i><br /> -Mr John Caswall, <i>of</i> London, <i>Merchant</i><br /> -<i>Dr</i> Jacob de Castro Sarmento</p> - -<p class="pi4 p2">D</p> - -<p class="pn2"><i>His Grace the Duke of</i> Devonshire<br /> -<i>His Grace the Duke of</i> Dorset<br /> -<i>Right Rev. Ld. Bishop of</i> Durham<br /> -<i>Right Rev. Ld. Bishop of St.</i> David<br /> -<i>Right Hon. Lord</i> Delaware<br /> -<i>Right Hon. Lord</i> Digby<br /> -<i>Right Rev. Lord Bishop of</i> Derry<br /> -<i>Right Rev. Lord Bishop of</i> Donne<br /> -<i>Rt. Rev. Lord Bishop of</i> Dromore<br /> -<i>Right Hon.</i> Dalhn, <i>Lord Chief Baron of</i> Ireland<br /> -Mr Thomas Dade<br /> -<i>Capt.</i> John Dagge<br /> -Mr Timothy Dallowe<br /> -Mr James Danzey, <i>Surgeon</i><br /> -<i>Rev. Dr</i> Richard Daniel, <i>Dean of</i> Armagh<br /> -Mr Danvers<br /> -<i>Sir</i> Coniers Darcy, <i>Knight of the</i> Bath<br /> -Mr Serjeant Darnel<br /> -Mr Joseph Dash<br /> -Peter Davall, <i>Esq;</i><br /> -Henry Davenant, <i>Esq;</i><br /> -Davies Davenport, <i>of the</i> Inner-Temple, <i>Esq;</i><br /> -<i>Sir</i> Jermyn Davers, <i>Bart.</i><br /> -<i>Capt.</i> Thomas Davers<br /> -Alexander Davie, <i>Esq;</i><br /> -<i>Rev. Dr.</i> Davies, <i>Master of</i> Queen’s College, Cambridge<br /> -Mr John Davies, <i>of</i> Christ-Church, Oxon<br /> -Mr Davies, <i>Attorney at Law</i><br /> -Mr William Dawkins, <i>Merch.</i><br /> -Rowland Dawkin, <i>of</i> Glamorganshire, <i>Esq;</i><br /> -Mr John Dawson<br /> -Edward Dawson, <i>Esq;</i><br /> -Mr Richard Dawson<br /> -William Dawsonne, <i>Esq;</i><br /> -Thomas Day, <i>Esq;</i><br /> -Mr John Day<br /> -Mr Nathaniel Day<br /> -Mr Deacon<br /> -Mr William Deane<br /> -Mr James Dearden, <i>of</i> Trinity College, Cambridge<br /> -Sir Matthew Deckers, <i>Bart.</i><br /> -Edward Deering, <i>Esq;</i><br /> -Simon Degge, <i>Esq;</i><br /> -Mr Staunton Degge, <i>A. B. of</i> Trinity Col. Cambridge<br /> -<i>Rev. Dr</i> Patrick Delaney<br /> -Mr Delhammon<br /> -<i>Rev.</i> Mr Denne<br /> -Mr William Denne<br /> -<i>Capt.</i> Jonathan Dennis<br /> -Daniel Dering, <i>Esq;</i><br /> -Jacob Desboverie, <i>Esq;</i><br /> -Mr James Deverell, <i>Surgeon in</i> Bristol<br /> -<i>Rev.</i> Mr John Diaper<br /> -Mr Rivers Dickenson<br /> -<i>Dr.</i> George Dickens, <i>of</i> Liverpool<br /> -<i>Hon.</i> Edward Digby, <i>Esq;</i><br /> -Mr Dillingham<br /> -Mr Thomas Dinely<br /> -Mr Samuel Disney, <i>of</i> Bennet College, Cambridge<br /> -Robert Dixon, <i>Esq;</i><br /> -Pierce Dodd, <i>M. D.</i><br /> -<i>Right Hon.</i> Geo. Doddinton, <i>Esq;</i><br /> -<i>Rev. Sir</i> John Dolben, <i>of</i> Findon, <i>Bart.</i><br /> -Nehemiah Donellan, <i>Esq;</i><br /> -Paul Doranda, <i>Esq;</i><br /> -James Douglas, <i>M. D.</i><br /> -Mr Richard Dovey, <i>A. B. of</i> Wadham College, Oxon<br /> -John Dowdal, <i>Esq;</i><br /> -William Mac Dowell, <i>Esq;</i><br /> -Mr Peter Downer<br /> -Mr James Downes<br /> -<i>Sir</i> Francis Henry Drake, <i>Knt.</i><br /> -William Drake, <i>of</i> Barnoldswick-Cotes, <i>Esq;</i><br /> -Mr Rich. Drewett, <i>of</i> Fareham<br /> -Mr Christopher Drisfield, <i>of</i> Christ-Church, Oxon<br /> -Edmund Dris, <i>A. M. Fellow of</i> Trinity Coll. Cambridge<br /> -George Drummond, <i>Esq; Lord Provost of</i> Edenburgh<br /> -Mr Colin Drummond, <i>Professor of Philosophy in the University of</i> Edinburgh<br /> -Henry Dry, <i>Esq;</i><br /> -Richard Ducane <i>Esq;</i><br /> -<i>Rev. Dr</i> Paschal Ducasse, <i>Dean of</i> Ferns<br /> -George Ducket, <i>Esq;</i><br /> -Mr Daniel Dufresnay<br /> -Mr Thomas Dugdale<br /> -Mr Humphry Duncalfe, <i>Merchant</i><br /> -Mr James Duncan<br /> -John Duncombe, <i>Esq;</i><br /> -Mr William Duncombe<br /> -John Dundass, <i>jun. of</i> Duddinstown, <i>Esq;</i><br /> -William Dunstar, <i>Esq;</i><br /> -James Dupont, <i>of</i> Trinity Coll. Cambridge</p> - -<p class="pi4 p2">E</p> - -<p class="pn2"><i>Right Rev. and Right Hon. Lord</i> Erskine<br /> -Theophilus, <i>Lord Bishop of</i> Elphin<br /> -Mr Thomas Eames<br /> -<i>Rev.</i> Mr. Jabez Earle<br /> -Mr William East<br /> -<i>Sir</i> Peter Eaton<br /> -Mr John Eccleston<br /> -James Eckerfall, <i>Esq;</i><br /> -—— Edgecumbe, <i>Esq;</i><br /> -<i>Rev.</i> Mr Edgley<br /> -<i>Rev. Dr</i> Edmundson, <i>President of</i> St. John’s Coll. Cambridge<br /> -Arthur Edwards, <i>Esq;</i><br /> -Thomas Edwards, <i>Esq;</i><br /> -Vigerus Edwards, <i>Esq;</i><br /> -<i>Capt.</i> Arthur Edwards<br /> -Mr Edwards<br /> -Mr William Elderton<br /> -Mrs Elizabeth Elgar<br /> -<i>Sir</i> Gilbert Eliot, <i>of</i> Minto, <i>Bart. one of the Lords of</i> Session<br /> -Mr John Elliot, <i>Merchant</i><br /> -George Ellis, <i>of</i> Barbadoes, <i>Esq;</i><br /> -Mr John Ellison, <i>of</i> Sheffield<br /> -<i>Sir</i> Richard Ellys, <i>Bart.</i><br /> -Library <i>of</i> Emanuel College, Cambridge<br /> -Francis Emerson, <i>Gent.</i><br /> -Thomas Emmerson, <i>Esq;</i><br /> -Mr Henry Emmet<br /> -Mr John Emmet<br /> -Thomas Empson, <i>of the</i> Middle-Temple, <i>Esq;</i><br /> -Mr Thomas Engeir<br /> -Mr Robert England<br /> -Mr Nathaniel English<br /> -<i>Rev.</i> Mr Ensly, <i>Minister of the</i> Scotch Church <i>in</i> Rotterdam<br /> -<span class="pagenum"><a name="Page_xl" id="Page_xl">[xl]</a></span>John Essington, <i>Esq;<br /> -Rev.</i> Mr Charles Este, <i>of</i> Christ-Church, Oxon<br /> -Mr Hugh Ethersey, <i>Apothecary</i><br /> -Henry Evans, <i>of</i> Surry, <i>Esq;</i><br /> -Isaac Ewer, <i>Esq;</i><br /> -Mr Charles Ewer<br /> -<i>Rev.</i> Mr Richard Exton<br /> -<i>Sir</i> John Eyles, <i>Bar.</i><br /> -<i>Sir</i> Joseph Eyles<br /> -<i>Right Hon. Sir</i> Robert Eyre, <i>Lord Chief Justice of the Common Pleas.</i><br /> -Edward Eyre, <i>Esq;</i><br /> -Henry Samuel Eyre, <i>Esq;</i><br /> -Kingsmill Eyre, <i>Esq;</i><br /> -Mr Eyre</p> - -<p class="pi4 p2">F</p> - -<p class="pn2"><i>Right Rev.</i> Josiah, <i>Lord Bishop of</i> Fernes <i>and</i> Loghlin<br /> -Den Heer Fagel<br /> -Mr Thomas Fairchild<br /> -Thomas Fairfax, <i>of the</i> Middle Temple, <i>Esq;</i><br /> -Mr John Falconer, <i>Merchant</i><br /> -Daniel Falkiner, <i>Esq;</i><br /> -Charles Farewell, <i>Esq;</i><br /> -Mr Thomas Farnaby, <i>of</i> Merton College, Oxon<br /> -Mr William Farrel<br /> -James Farrel, <i>Esq;</i><br /> -Thomas Farrer, <i>Esq;</i><br /> -Dennis Farrer, <i>Esq;</i><br /> -John Farrington, <i>Esq;</i><br /> -Mr Faukener<br /> -Mr Edward Faulkner<br /> -Francis Fauquiere, <i>Esq;</i><br /> -Charles De la Fay, <i>Esq;</i><br /> -Thomas De lay Fay, <i>Esq;</i><br /> -<i>Capt.</i> Lewis De la Fay<br /> -Nicholas Fazakerly, <i>Esq;</i><br /> -<i>Governour</i> Feake<br /> -Mr John Fell, <i>of</i> Attercliffe<br /> -Martyn Fellowes, <i>Esq;</i><br /> -Coston Fellows, <i>Esq;</i><br /> -Mr Thomas Fellows<br /> -Mr Francis Fennell<br /> -Mr Michael Fenwick<br /> -John Ferdinand, <i>of the</i> Inner-Temple, <i>Esq;</i><br /> -Mr James Ferne, <i>Surgeon</i><br /> -Mr John Ferrand, <i>of</i> Trinity College, Cambridge<br /> -Mr Daniel Mussaphia Fidalgo<br /> -Mr Fidler<br /> -<i>Hon.</i> Mrs Celia Fiennes<br /> -<i>Hon. and Rev.</i> Mr. Finch, <i>Dean of</i> York<br /> -<i>Hon.</i> Edward Finch, <i>Esq;</i><br /> -Mr John Finch<br /> -Philip Fincher <i>Esq;</i><br /> -Mr Michael Fitch, <i>of</i> Trinity College, Cambridge<br /> -Hon. John Fitz-Morris, <i>Esq;</i><br /> -Mr Fletcher<br /> -Martin Folkes, <i>Esq;</i><br /> -<i>Dr</i> Foot<br /> -Mr Francis Forester<br /> -John Forester, <i>Esq;</i><br /> -Mrs Alice Forth<br /> -Mr John Forthe<br /> -Mr Joseph Foskett<br /> -Mr Edward Foster<br /> -Mr Peter Foster<br /> -Peter Foulkes, <i>D. D. Canon of</i> Christ-Church, Oxon<br /> -<i>Rev. Dr.</i> Robert Foulkes<br /> -<i>Rev. Mr</i> Robert Foulks, <i>M. A. Fellow of</i> Magdalen College, Cambridge<br /> -Mr Abel Founereau, <i>Merchant</i><br /> -Mr Christopher Fowler<br /> -Mr John Fowler, <i>of</i> Northamp.<br /> -Mr Joseph Fowler<br /> -<i>Hon. Sir</i> William Fownes, <i>Bar.</i><br /> -George Fox, <i>Esq;</i><br /> -Edward Foy, <i>Esq;</i><br /> -<i>Rev. 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Lord Bishop of</i> Landaff<br /> -<i>Right Honourable Lord</i> Lyn<br /> -John Lade, <i>Esq;</i><br /> -Mr Hugh Langharne<br /> -Mr John Langford<br /> -Mr William Larkman<br /> -Mr William Lambe, <i>of</i> Exeter College, Oxon<br /> -Richard Langley, <i>Esq;</i><br /> -Mr Robert Lacy<br /> -James Lamb, <i>Esq;</i><br /> -<i>Rev.</i> Mr Thomas Lambert, <i>M. A. Vicar of</i> Ledburgh, Yorkshire<br /> -Mr Daniel Lambert<br /> -Mr John Lampe<br /> -Dr. Lane, <i>of</i> Hitchin <i>in</i> Hertfordshire<br /> -Mr Timothy Lane<br /> -<i>Rev.</i> Dr. Laney, <i>Master of</i> Pembroke Hall, Cambr. 2 Books<br /> -Mr Peter de Langley<br /> -<i>Rev.</i> Mr Nathaniel Lardner<br /> -Mr Larnoul<br /> -Mr Henry Lascelles, <i>of</i> Barbadoes, <i>Merchant</i><br /> -<i>Rev.</i> Mr John Laurence, <i>Rector of</i> Bishop’s Waremouth<br /> -Mr Roger Laurence, <i>M. A.</i><br /> -Mr Lavington<br /> -Mr William Law, <i>Professor of</i> Moral Philosophy <i>in the University of</i> Edinburgh<br /> -Mr John Lawton, <i>of the</i> Excise-Office<br /> -Mr Godfrey Laycock, <i>of</i> Hallifax<br /> -Mr Charles Leadbetter, <i>Teacher of the</i> Mathematicks<br /> -Mr James Leake, <i>Bookseller in</i> Bath<br /> -Stephen Martin Leak, <i>Esq;</i><br /> -<i>Rev.</i> Mr Lechmere<br /> -William Lee, <i>Esq;</i><br /> -Mr Lee, <i>of</i> Christ Church, Oxon<br /> -<i>Rev.</i> Mr John Lee<br /> -Mr William Leek<br /> -<i>Rev.</i> Mr Leeson<br /> -<span class="pagenum"><a name="Page_xliv" id="Page_xliv">[xliv]</a></span>Peter Legh, <i>of</i> Lyme <i>in</i> Cheshire, <i>Esq;</i><br /> -Robert Leguarre, <i>of</i> Gray’s-Inn, <i>Esq</i>;<br /> -Mr Lehunt<br /> -Mr John Lehunt, <i>of</i> Canterbury<br /> -Francis Leigh, <i>Esq</i>;<br /> -Mr John Leigh<br /> -Mr Percival Lewis<br /> -Mr Thomas Lewis<br /> -New College Library<br /> -<i>Sir</i> Henry Liddell, <i>Bar. of St.</i> Peter’s College, Cambridge<br /> -Henry Liddell, <i>Esq</i>;<br /> -Mr William Limbery<br /> -Robert Lindsay, <i>Esq</i>;<br /> -<i>Countess of</i> Lippe<br /> -<i>Rev. Dr.</i> James Lisle<br /> -<i>Rev. Mr</i> Lister<br /> -Mr George Livingstone, <i>One of the Clerks of</i> Session<br /> -Salisbury Lloyd, <i>Esq</i>;<br /> -<i>Rev.</i> Mr John Lloyd, <i>A. B. of</i> Jesus College<br /> -Mr Nathaniel Lloyd, <i>Merchant</i><br /> -Mr Samuel Lobb, <i>Bookseller at</i> Chelmsford<br /> -William Lock, <i>Esq</i>;<br /> -Mr James Lock, 2 Books<br /> -Mr Joshua Locke<br /> -Charles Lockier, <i>Esq</i>;<br /> -Richard Lockwood, <i>Esq</i>;<br /> -Mr Bartholom. Loftus, 9 Books<br /> -William Logan, <i>M. D.</i><br /> -Mr Moses Loman, <i>jun.</i><br /> -Mr Longley<br /> -Mr Benjamin Longuet<br /> -Mr Grey Longueville<br /> -Mr Robert Lord<br /> -Mrs Mary Lord<br /> -Mr Benjamin Lorkin<br /> -Mr William Loup<br /> -Richard Love, <i>of</i> Basing <i>in</i> Hants, <i>Esq</i>;<br /> -Mrs Love, <i>in</i> Laurence-Lane<br /> -Mr Joshua Lover, <i>of</i> Chichester<br /> -William Lowndes, <i>Esq</i>;<br /> -Charles Lowndes, <i>Esq</i>;<br /> -Mr Cornelius Lloyd<br /> -Robert Lucas, <i>Esq</i>;<br /> -<i>Coll.</i> Richard Lucas<br /> -<i>Sir</i> Bartlet Lucy<br /> -Edward Luckin, <i>Esq</i>;<br /> -Mr John Ludbey<br /> -Mr Luders, <i>Merchant</i><br /> -Lambert Ludlow, <i>Esq</i>;<br /> -William Ludlow, <i>Esq</i>;<br /> -Peter Ludlow, <i>Esq</i>;<br /> -John Lupton, <i>Esq</i>;<br /> -Nicholas Luke, <i>Esq</i>;<br /> -Lyonel Lyde, <i>Esq</i>;<br /> -<i>Dr.</i> George Lynch<br /> -Mr Joshua Lyons</p> - -<p class="pi4 p2">M.</p> - -<p class="pn2"><i>His Grace the Duke of</i> Montague<br /> -<i>His Grace the Duke of</i> Montrosse<br /> -<i>His Grace the Duke of</i> Manchester<br /> -<i>The Rt. Hon. Lord Viscount</i> Molesworth<br /> -<i>The Rt. Hon. Lord</i> Mansel<br /> -<i>The Rt. Hon. Ld.</i> Micklethwait<br /> -<i>The Rt. Rev. Ld. Bishop of</i> Meath<br /> -Mr Mace<br /> -Mr Joseph Macham, <i>Merchant</i><br /> -Mr John Machin, <i>Professor of</i> Astronomy <i>in</i> Gresham College<br /> -Mr Mackay<br /> -Mr Mackelcan<br /> -William Mackinen, <i>of</i> Antigua, <i>Esq</i>;<br /> -Mr Colin Mac Laurin, <i>Professor of the</i> Mathematicks <i>in the University of</i> Edinburgh<br /> -Galatius Macmahon, <i>Esq</i>;<br /> -Mr Madox, <i>Apothecary</i><br /> -<i>Rev.</i> Mr Isaac Madox, <i>Prebendary of</i> Chichester<br /> -Henry Mainwaring, <i>of</i> Over-Peover <i>in</i> Cheshire, <i>Esq</i>;<br /> -Mr Robert Mainwaring, <i>of</i> London, <i>Merchant</i><br /> -<i>Capt.</i> John Maitland<br /> -Mr Cecil Malcher<br /> -Sydenham Mallhust, <i>Esq</i>;<br /> -Richard Malone, <i>Esq</i>;<br /> -Mr Thomas Malyn<br /> -Mr John Mann<br /> -Mr William Man<br /> -<i>Dr.</i> Manaton<br /> -Mr John Mande<br /> -<i>Dr.</i> Bernard Mandeville<br /> -Mr James Mandy<br /> -<i>Rev.</i> Mr Bellingham Manleveror, <i>M. A. Rector of</i> Mahera<br /> -Isaac Manley, <i>Esq</i>;<br /> -Thomas Manley, <i>of the</i> Inner-Temple, <i>Esq</i>;<br /> -Mr John Manley<br /> -Mr William Manley<br /> -Mr Benjamin Manning<br /> -Rawleigh Mansel, <i>Esq</i>;<br /> -Henry March, <i>Esq</i>;<br /> -Mr John Marke<br /> -<i>Sir</i> George Markham<br /> -Mr John Markham, <i>Apothecary</i><br /> -Mr William Markes<br /> -Mr James Markwick<br /> -<i>Hon.</i> Thomas Marley, <i>Esq; one of his Majesty’s Sollicitors general of</i> Ireland<br /> -<i>Rev.</i> Mr George Marley<br /> -Mr Benjamin Marriot, <i>of the Exchequer</i><br /> -John Marsh, <i>Esq</i>;<br /> -Mr Samuel Marsh<br /> -Robert Marshall, <i>Esq; Recorder of</i> Clonmell<br /> -<i>Rev.</i> Mr Henry Marshall<br /> -<i>Rev.</i> Nathaniel Marshall, <i>D. D. 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Dr.</i> Peter Maturin, <i>Dean of</i> Killala<br /> -William Maubry, <i>Esq</i>;<br /> -Mr Gamaliel Maud<br /> -<i>Rev.</i> Mr Peter Maurice, <i>Treasurer of the Ch. of</i> Bangor<br /> -Henry Maxwell, <i>Esq</i>;<br /> -John Maxwell, <i>jun. of</i> Pollock, <i>Esq</i>;<br /> -<i>Rev.</i> Dr. Robert Maxwell, <i>of</i> Fellow’s Hall, Ireland<br /> -Mr May<br /> -Mr Thomas Mayleigh<br /> -Thomas Maylin, <i>jun. Esq</i>;<br /> -<i>Hon.</i> Charles Maynard, <i>Esq</i>;<br /> -Thomas Maynard, <i>Esq</i>;<br /> -<i>Dr.</i> Richard Mayo<br /> -Mr Samuel Mayo<br /> -Samuel Mead, <i>Esq</i>;<br /> -Richard Mead, <i>M. D.</i><br /> -<i>Rev.</i> Mr Meadowcourt<br /> -<i>Rev.</i> Mr Richard Meadowcourt, <i>Fellow of</i> Merton Coll. Oxon<br /> -<span class="pagenum"><a name="Page_xlv" id="Page_xlv">[xlv]</a></span>Mr Mearson<br /> -Mr George Medcalfe<br /> -Mr David Medley, 3 Books<br /> -Charles Medlycott, <i>Esq;</i><br /> -<i>Sir</i> Robert Menzies, <i>of</i> Weem, <i>Bart.</i><br /> -Mr Thomas Mercer, <i>Merchant</i><br /> -John Merrill, <i>Esq;</i><br /> -Mr Francis Merrit<br /> -<i>Dr.</i> Mertins<br /> -Mr John Henry Mertins<br /> -<i>Library of</i> Merton College<br /> -Mr William Messe, Apothecary<br /> -Mr Metcalf<br /> -Mr Thomas Metcalf, <i>of</i> Trinity Coll. Cambridge<br /> -Mr Abraham Meure, <i>of</i> Leatherhead in Surrey<br /> -Mr John Mac Farlane<br /> -<i>Dr.</i> John Michel<br /> -<i>Dr.</i> Robert Michel, <i>of</i> Blandford<br /> -Mr Robert Michell<br /> -Nathaniel Micklethwait, <i>Esq;</i><br /> -Mr Jonathan Micklethwait, <i>Merchant</i><br /> -Mr John Midford, <i>Merchant</i><br /> -Mr Midgley<br /> -<i>Rev.</i> Mr Miller, 2 Books<br /> -<i>Rev.</i> Mr Milling, <i>of</i> the Hague<br /> -<i>Rev.</i> Mr Benjamin Mills<br /> -<i>Rev.</i> Mr Henry Mills, <i>Rector of</i> Meastham, <i>Head-Master of</i> Croyden-School<br /> -Thomas Milner, <i>Esq;</i><br /> -Charles Milner, <i>M. D.</i><br /> -Mr William Mingay<br /> -John Misaubin, <i>M. D.</i><br /> -Mrs Frances Mitchel<br /> -David Mitchell, <i>Esq;</i><br /> -Mr John Mitton<br /> -Mr Abraham de Moivre<br /> -John Monchton, <i>Esq;</i><br /> -Mr John Monk, <i>Apothecary</i><br /> -J. Monro, <i>M. D.</i><br /> -<i>Sir</i> William Monson, <i>Bart.</i><br /> -Edward Montagu, <i>Esq;</i><br /> -Colonel John Montagu<br /> -<i>Rev.</i> John Montague, <i>Dean of</i> Durham, <i>D. D.</i><br /> -Mr Francis Moor<br /> -Mr Jarvis Moore<br /> -Mr Richard Moore, <i>of</i> Hull, 3 Books<br /> -Mr William Moore<br /> -<i>Sir</i> Charles Mordaunt, <i>of</i> Walton, <i>in</i> Warwickshire<br /> -Mr Mordant, <i>Gentleman Commoner of</i> New College, Oxon<br /> -Charles Morgan, <i>Esq;</i><br /> -Francis Morgan, <i>Esq;</i><br /> -Morgan Morgan, <i>Esq;</i><br /> -<i>Rev.</i> Mr William Morland, <i>Fell. of</i> Trin. Coll. Cambr. 2 Books<br /> -Thomas Morgan, <i>M. D.</i><br /> -Mr John Morgan, <i>of</i> Bristol<br /> -Mr Benjamin Morgan, <i>High-Master of</i> St. Paul’s-School<br /> -<i>Hon. Coll.</i> Val. Morris, <i>of</i> Antigua<br /> -Mr Gael Morris<br /> -Mr John Morse, <i>of</i> Bristol<br /> -Hon. Ducey Morton, <i>Esq;</i><br /> -Mr Motte<br /> -Mr William Mount<br /> -<i>Coll.</i> Moyser<br /> -<i>Dr.</i> Edward Mullins<br /> -Mr Joseph Murden<br /> -Mr Mustapha<br /> -Robert Myddleton, <i>Esq;</i><br /> -Robert Myhil, <i>Esq;</i></p> - -<p class="pi4 p2">N</p> - -<p class="pn2"><i>His Grace the Duke of</i> Newcastle<br /> -<i>Rt. Rev. Ld. Bishop of</i> Norwich<br /> -Stephen Napleton, <i>M. D.</i><br /> -Mr Robert Nash, <i>M. A. Fellow of</i> Wadham College, Oxon<br /> -Mr Theophilus Firmin Nash<br /> -<i>Dr.</i> David Natto<br /> -Mr Anthony Neal<br /> -Mr Henry Neal, <i>of</i> Bristol<br /> -Hampson Nedham, <i>Esq; Gentleman Commoner of</i> Christ Church Oxon<br /> -<i>Rev. Dr.</i> Newcome, <i>Senior-Fellow of St.</i> John’s College, Cambridge, 6 Books<br /> -<i>Rev.</i> Mr Richard Newcome<br /> -Mr Henry Newcome<br /> -Mr Newland<br /> -<i>Rev.</i> Mr John Newey, <i>Dean of</i> Chichester<br /> -Mr Benjamin Newington, <i>M. A.</i><br /> -John Newington, <i>M. B. of</i> Greenwich in Kent<br /> -Mr Samuel Newman<br /> -Mrs Anne Newnham<br /> -Mr Nathaniel Newnham, <i>sen.</i><br /> -Mr Nathaniel Newnham, <i>jun.</i><br /> -Mr Thomas Newnham<br /> -Mrs Catherine Newnham<br /> -<i>Sir</i> Isaac Newton, 12 Books<br /> -<i>Sir</i> Michael Newton<br /> -Mr Newton<br /> -William Nicholas, <i>Esq;</i><br /> -John Nicholas, <i>Esq;</i><br /> -John Niccol, <i>Esq;</i><br /> -<i>General</i> Nicholson<br /> -Mr Samuel Nicholson<br /> -John Nicholson, <i>M. A. Rector of</i> Donaghmore<br /> -Mr Josias Nicholson, 3 Books<br /> -Mr James Nimmo, <i>Merchant of</i> Edinburgh<br /> -David Nixon, <i>Esq;</i><br /> -Mr George Noble<br /> -Stephen Noquiez, <i>Esq;</i><br /> -Mr Thomas Norman, <i>Bookseller at</i> Lewes<br /> -Mr Anthony Norris<br /> -Mr Henry Norris<br /> -<i>Rev.</i> Mr Edward Norton<br /> -Richard Nutley, <i>Esq;</i><br /> -Mr John Nutt, <i>Merchant</i></p> - -<p class="pi4 p2">O</p> - -<p class="pn2"><i>Right Hon. 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Countess of</i> Pembroke, 10 Books<br /> -<i>Right Hon. Lord</i> Paisley<br /> -<span class="pagenum"><a name="Page_xlvi" id="Page_xlvi">[xlvi]</a></span><i>Right Hon. Lady</i> Paisley<br /> -<i>The Right Hon. Lord</i> Parker<br /> -Christopher Pack, <i>M. D.</i><br /> -Mr Samuel Parker, <i>Merchant at</i> Bristol<br /> -Mr Thomas Page, <i>Surgeon at</i> Bristol<br /> -<i>Sir</i> Gregory Page, <i>Bar.</i><br /> -William Palgrave, <i>M. D, Fellow of</i> Caius Coll. Cambridge<br /> -William Pallister, <i>Esq;</i><br /> -Thomas Palmer, <i>Esq;</i><br /> -Samuel Palmer, <i>Esq;</i><br /> -Henry Palmer, <i>Merchant</i><br /> -Mr John Palmer, <i>of</i> Coventry<br /> -Mr Samuel Palmer, <i>Surgeon</i><br /> -William Parker, <i>Esq;</i><br /> -Edmund Parker, <i>Gent.</i><br /> -<i>Rev.</i> Mr Henry Parker, <i>M. 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D.</i><br /> -Robert Paul, <i>of</i> Gray’s-Inn, <i>Esq;</i><br /> -Mr Josiah Paul, <i>Surgeon</i><br /> -Mr Paulin<br /> -Robert Paunceforte, <i>Esq;</i><br /> -Edward Pawlet, <i>of</i> Hinton St. George, <i>Esq;</i><br /> -Mr Henry Pawson, <i>of</i> York, <i>Merchant</i><br /> -Mr Payne<br /> -Mr Samuel Peach<br /> -Mr Marmaduke Peacock, <i>Merchant in</i> Rotterdam<br /> -Flavell Peake, <i>Esq;</i><br /> -<i>Capt.</i> Edward Pearce<br /> -<i>Rev.</i> Zachary Pearce, <i>D. D.</i><br /> -James Pearse, <i>Esq;</i><br /> -Thomas Pearson, <i>Esq;</i><br /> -John Peers, <i>Esq;</i><br /> -Mr Samuel Pegg, <i>of St.</i> John’s College, Cambridge<br /> -Mr Peirce, <i>Surgeon at</i> Bath<br /> -Mr Adam Peirce<br /> -Harry Pelham, <i>Esq;</i><br /> -James Pelham, <i>Esq;</i><br /> -Jeremy Pemberton, <i>of the</i> Inner-Temple, <i>Esq;</i><br /> -<i>Library of</i> Pembroke-Hall, Camb.<br /> -Mr Thomas Penn<br /> -Philip Pendock, <i>Esq;</i><br /> -Edward Pennant, <i>Esq;</i><br /> -<i>Capt.</i> Philip Pennington<br /> -Mr Thomas Penny<br /> -Mr Henry Penton<br /> -Mr Francis Penwarne, <i>at</i> Liskead <i>in</i> Cornwall<br /> -<i>Rev.</i> Mr Thomas Penwarne<br /> -Mr John Percevall<br /> -<i>Rev.</i> Mr Edward Percevall<br /> -Mr Joseph Percevall<br /> -<i>Rev. 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D.</i><br /> -Mr Thomas Phipps, <i>of</i> Trinity College, Cambridge<br /> -<i>The</i> Physiological <i>Library in the College of</i> Edinburgh<br /> -Mr Pichard<br /> -Mr William Pickard<br /> -Mr John Pickering<br /> -Robert Pigott, <i>of</i> Chesterton, <i>Esq;</i><br /> -Mr Richard Pike<br /> -Henry Pinfield, <i>of</i> Hampstead, <i>Esq;</i><br /> -Charles Pinfold, <i>L. L. D.</i><br /> -<i>Rev.</i> Mr. Pit, <i>of</i> Exeter College, Oxon<br /> -Mr Andrew Pitt<br /> -Mr Francis Place<br /> -Thomas Player, <i>Esq;</i><br /> -<i>Rev.</i> Mr Plimly<br /> -Mr William Plomer<br /> -William Plummer, <i>Esq;</i><br /> -Mr Richard Plumpton<br /> -John Plumptre, <i>Esq;</i><br /> -Fitz-Williams Plumptre, <i>M. D.</i><br /> -Henry Plumptre, <i>M. D.</i><br /> -John Pollen, <i>Esq;</i><br /> -Mr Joshua Pocock<br /> -Francis Pole, <i>of</i> Park-Hall, <i>Esq;</i><br /> -Mr Isaac Polock<br /> -Mr Benjamin Pomfret<br /> -Mr Thomas Pool, <i>Apothecary</i><br /> -Alexander Pope, <i>Esq;</i><br /> -Mr Arthur Pond<br /> -Mr Thomas Port<br /> -Mr John Porter<br /> -Mr Joseph Porter<br /> -Mr Thomas Potter, <i>of St.</i> John’s College, Oxon<br /> -Mr John Powel<br /> -—— Powis, <i>Esq;</i><br /> -Mr Daniel Powle<br /> -John Prat, <i>Esq;</i><br /> -Mr James Pratt<br /> -Mr Joseph Pratt<br /> -Mr Samuel Pratt<br /> -Mr Preston, <i>City-Remembrancer</i><br /> -Capt. John Price<br /> -<i>Rev.</i> Mr Samuel Price<br /> -Mr Nathaniel Primat<br /> -Dr. John Pringle<br /> -Thomas Prior, <i>Esq;</i><br /> -Mr Henry Proctor, <i>Apothecary</i><br /> -<i>Sir</i> John Pryse, <i>of</i> Newton Hill <i>in</i> Montgomeryshire<br /> -Mr Thomas Purcas<br /> -Mr Robert Purse<br /> -Mr John Putland<br /> -George Pye, <i>M. D.</i><br /> -Samuel Pye, <i>M. D.</i><br /> -Mr Samuel Pye, <i>Surgeon at</i> Bristol<br /> -Mr Edmund Pyle, <i>of</i> Lynn<br /> -Mr John Pine, <i>Engraver</i></p> - -<p class="pi4 p2">Q.</p> - -<p class="pn2"><i>His Grace the Duke of</i> Queenborough<br /> -<i>Rev.</i> Mr. Question, <i>M. A. of</i> Exeter College, Oxon<br /> -Jeremiah Quare, <i>Merchant</i></p> - -<p class="pi4 p2">R.</p> - -<p class="pn2"><i>His Grace the Duke of</i> Richmond<br /> -<i>The Rt. Rev. Ld. Bishop of</i> Raphoe<br /> -<i>The Rt. Hon. Lord</i> John Russel<br /> -<i>Rev.</i> Mr Walter Rainstorp, <i>of</i> Bristol<br /> -<span class="pagenum"><a name="Page_xlvii" id="Page_xlvii">[xlvii]</a></span>Mr John Ranby, <i>Surgeon</i><br /> -<i>Rev.</i> Mr Rand<br /> -Mr Richard Randall<br /> -<i>Rev.</i> Mr Herbert Randolph, <i>M.A.</i><br /> -Moses Raper, <i>Esq;</i><br /> -Matthew Raper, <i>Esq;</i><br /> -Mr William Rastrick, <i>of</i> Lynne<br /> -Mr Ratcliffe, <i>M. A. of</i> Pembroke College, Oxon<br /> -<i>Rev.</i> Mr John Ratcliffe<br /> -Anthony Ravell, <i>Esq;</i><br /> -Mr Richard Rawlins<br /> -Mr Robert Rawlinson <i>A. B. of</i> Trinity College, Cambr.<br /> -Mr Walter Ray<br /> -<i>Coll.</i> Hugh Raymond<br /> -<i>Rt. Hon. Sir</i> Robert Raymond, <i>Lord Chief Justice of the</i> King’s-Bench<br /> -Mr Alexander Raymond<br /> -Samuel Read, <i>Esq;</i><br /> -<i>Rev.</i> Mr James Read<br /> -Mr John Read, <i>Merchant</i><br /> -Mr William Read, <i>Merchant</i><br /> -Mr Samuel Read<br /> -Mrs Mary Reade<br /> -Mr Thomas Reddall<br /> -Mr Andrew Reid<br /> -Felix Renolds, <i>Esq;</i><br /> -John Renton, <i>of</i> Christ-Church, <i>Esq;</i><br /> -Leonard Reresby, <i>Esq;</i><br /> -Thomas Reve, <i>Esq;</i><br /> -Mr Gabriel Reve<br /> -William Reeves, <i>Merch. of</i> Bristol<br /> -Mr Richard Reynell, <i>Apothecary</i><br /> -Mr John Reynolds<br /> -Mr Richard Ricards<br /> -John Rich, <i>of</i> Bristol, <i>Esq;</i><br /> -Francis Richards, <i>M. B.</i><br /> -<i>Rev.</i> Mr Escourt Richards, <i>Prebend. of</i> Wells<br /> -<i>Rev.</i> Mr Richards, <i>Rector of</i> Llanvyllin, <i>in</i> Montgomeryshire<br /> -William Richardson, <i>of</i> Smally <i>in</i> Derbyshire, <i>Esq;</i><br /> -Mr Richard Richardson<br /> -Mr Thomas Richardson, <i>Apothecary</i><br /> -Edward Richier, <i>Esq;</i><br /> -Dudley Rider, <i>Esq;</i><br /> -Richard Rigby, <i>M. D.</i><br /> -Edward Riggs, <i>Esq;</i><br /> -Thomas Ripley, <i>Esq. Comptroller of his Majesty’s Works</i><br /> -<i>Sir</i> Thomas Roberts, <i>Bart.</i><br /> -Richard Roberts, <i>Esq;</i><br /> -<i>Capt.</i> John Roberts<br /> -Thomas Robinson, <i>Esq;</i><br /> -Matthew Robinson, <i>Esq;</i><br /> -Tancred Robinson, <i>M. D.</i><br /> -Nicholas Robinson, <i>M. D.</i><br /> -Christopher Robinson, <i>of</i> Sheffield, <i>A. M.</i><br /> -Mr Henry Robinson<br /> -Mr William Robinson<br /> -Mrs Elizabeth Robinson<br /> -John Rochfort, <i>Esq;</i><br /> -Mr Rodrigues<br /> -Mr Rocke<br /> -<i>Sir</i> John Rodes, <i>Bart.</i><br /> -Mr Francis Rogers<br /> -<i>Rev.</i> Mr Sam. Rogers, <i>of</i> Bristol<br /> -John Rogerson, <i>Esq; his Majesty’s General of</i> Ireland<br /> -Edmund Rolfe, <i>Esq;</i><br /> -Henry Roll, <i>Esq; Gent. Comm. of</i> New College, Oxon<br /> -<i>Rev.</i> Mr Samuel Rolleston, <i>Fell. of</i> Merton College, Oxon<br /> -Lancelot Rolleston, <i>of</i> Wattnal, <i>Esq;</i><br /> -Philip Ronayne, <i>Esq;</i><br /> -<i>Rev.</i> Mr de la Roque<br /> -Mr Benjamin Rosewell, <i>jun.</i><br /> -Joseph Rothery, <i>M. A. Arch-Deacon of</i> Derry<br /> -Guy Roussignac, <i>M. D.</i><br /> -Mr James Round<br /> -Mr William Roundell, <i>of</i> Christ Church, Oxon<br /> -Mr Rouse, <i>Merchant</i><br /> -Cuthbert Routh, <i>Esq;</i><br /> -John Rowe, <i>Esq;</i><br /> -Mr John Rowe<br /> -<i>Dr.</i> Rowel, <i>of</i> Amsterdam<br /> -John Rudge, <i>Esq;</i><br /> -Mr James Ruck<br /> -<i>Rev. Dr.</i> Rundle, <i>Prebendary of</i> Durham<br /> -Mr John Rust<br /> -John Rustatt, <i>Gent.</i><br /> -Mr Zachias Ruth<br /> -William Rutty, <i>M. D. Secretary of the Royal Society</i><br /> -Maltis Ryall, <i>Esq;</i></p> - -<p class="pi4 p2">S</p> - -<p class="pn2"><i>His Grace the Duke of St.</i> Albans<br /> -<i>Rt. Hon. Earl of</i> Sunderland<br /> -<i>Rt. Hon. Earl of</i> Scarborough<br /> -<i>Rt. Rev. Ld. Bp. of</i> Salisbury<br /> -<i>Rt. Rev. Lord Bishop of St.</i> Asaph<br /> -<i>Rt. Hon.</i> Thomas <i>Lord</i> Southwell<br /> -<i>Rt. Hon. Lord</i> Sidney<br /> -<i>Rt. Hon. Lord</i> Shaftsbury<br /> -<i>The Rt. Hon. Lord</i> Shelburn<br /> -<i>His Excellency Baron</i> Sollenthal, <i>Envoy extraordinary from the King of</i> Denmark<br /> -Mrs Margarita Sabine<br /> -Mr Edward Sadler, 2 Books<br /> -Thomas Sadler, <i>of the</i> Pell-Office, <i>Esq;</i><br /> -<i>Rev.</i> Mr Joseph Sager, <i>Canon of the Church of</i> Salisbury<br /> -Mr William Salkeld<br /> -Mr Robert Salter<br /> -<i>Lady</i> Vanaker Sambrooke<br /> -Jer. Sambrooke, <i>Esq;</i><br /> -John Sampson, <i>Esq;</i><br /> -<i>Dr.</i> Samuda<br /> -Mr John Samwaies<br /> -Alexander Sanderland, <i>M. D.</i><br /> -Samuel Sanders, <i>Esq;</i><br /> -William Sanders, <i>Esq;</i><br /> -<i>Rev.</i> Mr Daniel Sanxey<br /> -John Sargent, <i>Esq;</i><br /> -Mr Saunderson<br /> -Mr Charles Savage, <i>jun.</i><br /> -Mr John Savage<br /> -Mrs Mary Savage<br /> -<i>Rev.</i> Mr Samuel Savage<br /> -Mr William Savage<br /> -Jacob Sawbridge, <i>Esq;</i><br /> -John Sawbridge, <i>Esq;</i><br /> -Mr William Sawrey<br /> -Humphrey Sayer, <i>Esq;</i><br /> -Exton Sayer, <i>L. L. D. Chanceller of</i> Durham<br /> -<i>Rev.</i> Mr George Sayer, <i>Prebendary of</i> Durham<br /> -Mr Thomas Sayer<br /> -Herm. Osterdyk Schacht, <i>M. D.</i> & <i>M. Theor. & Pratt, in Acad.</i> Lug. Bat. Prof.<br /> -Meyer Schamberg, <i>M. D.</i><br /> -Mrs Schepers, <i>of</i> Rotterdam<br /> -<i>Dr.</i> Scheutcher<br /> -Mr Thomas Scholes<br /> -Mr Edward Score, <i>of</i> Exeter, <i>Bookseller</i><br /> -Thomas Scot, of Essex, <i>Esq;</i><br /> -Daniel Scott, <i>L. L. D.</i><br /> -<i>Rev.</i> Mr Scott, <i>Fellow of</i> Winton College<br /> -Mr Richard Scrafton, <i>Surgeon</i><br /> -Mr Flight Scurry, <i>Surgeon</i><br /> -<i>Rev.</i> Mr Thomas Seeker<br /> -<i>Rev</i> Mr Sedgwick<br /> -Mr Selwin<br /> -Mr Peter Serjeant<br /> -Mr John Serocol, <i>Merchant</i><br /> -<span class="pagenum"><a name="Page_xlviii" id="Page_xlviii">[xlviii]</a></span><i>Rev.</i> Mr Seward, <i>of</i> Hereford<br /> -Mr Joseph Sewel<br /> -Mr Thomas Sewell<br /> -Mr Lancelot Shadwell<br /> -Mr Arthur Shallet<br /> -Mr Edmund Shallet, <i>Consul at</i> Barcelona<br /> -Mr <i>Archdeacon</i> Sharp<br /> -James Sharp, <i>jun. Surgeon</i><br /> -<i>Rev.</i> Mr Thomas Sharp, <i>Arch-Deacon of</i> Northumberland<br /> -Mr John Shaw, <i>jun.</i><br /> -Mr Joseph Shaw<br /> -Mr Sheafe<br /> -Mr Edw. Sheldon, <i>of</i> Winstonly<br /> -Mr Shell<br /> -Mr Richard Shephard<br /> -Mr Shepherd <i>of</i> Trinity Coll. Oxon<br /> -Mrs Mary Shepherd<br /> -Mr William Sheppard<br /> -<i>Rev.</i> Mr William Sherlock, <i>M. A.</i><br /> -William Sherrard, <i>L. L. D.</i><br /> -John Sherwin, <i>Esq;</i><br /> -Mr Thomas Sherwood<br /> -Mr Thomas Shewell<br /> -Mr John Shipton, <i>Surgeon</i><br /> -Mr John Shipton, <i>sen.</i><br /> -Mr John Shipton, <i>jun.</i><br /> -Francis Shipwith, <i>Esq, Fellow Comm. of</i> Trinity Coll. Camb.<br /> -John Shish, <i>of</i> Greenwich <i>in</i> Kent, <i>Esq;</i><br /> -Mr Abraham Shreighly<br /> -John Shore, <i>Esq;</i><br /> -<i>Rev.</i> Mr Shove<br /> -Bartholomew Shower, <i>Esq;</i><br /> -Mr Thomas Sibley, <i>jun.</i><br /> -Mr Jacob Silver, <i>Bookseller in</i> Sandwich<br /> -Robert Simpson, <i>Esq; Beadle and Fellow of</i> Caius Coll. Cambr.<br /> -Mr Robert Simpson <i>Professor of the</i> Mathematicks <i>in the University of</i> Glascow<br /> -Henry Singleton, <i>Esq; Prime Sergeant of</i> Ireland<br /> -<i>Rev.</i> Mr John Singleton<br /> -<i>Rev.</i> Mr Rowland Singleton<br /> -Mr Singleton, <i>Surgeon</i><br /> -Mr Jonathan Sisson<br /> -Francis Sitwell, <i>of</i> Renishaw, <i>Esq;</i><br /> -Ralph Skerret, <i>D. D.</i><br /> -Thomas Skinner, <i>Esq;</i><br /> -Mr John Skinner<br /> -Mr Samuel Skinner, <i>jun.</i><br /> -Mr John Skrimpshaw<br /> -Frederic Slare, <i>M. D.</i><br /> -Adam Slater, <i>of</i> Chesterfield, <i>Surgeon</i><br /> -<i>Sir</i> Hans Sloane, <i>Bar.</i><br /> -William Sloane, <i>Esq;</i><br /> -William Sloper, <i>Esq;</i><br /> -William Sloper, <i>Esq, Fellow Commoner of</i> Trin. Coll. Cambr.<br /> -<i>Dr.</i> Sloper, <i>Chancellor of the Diocese of</i> Bristol<br /> -Mr Smart<br /> -Mr John Smibart<br /> -Robert Smith, <i>L. L. D. Professor of</i> Astronomy <i>in the University of</i> Cambridge, 22 Books<br /> -Robert Smith, <i>of</i> Bristol, <i>Esq;</i><br /> -William Smith, <i>of the</i> Middle-Temple, <i>Esq;</i><br /> -James Smith, <i>Esq;</i><br /> -Morgan Smith, <i>Esq;</i><br /> -<i>Rev.</i> Mr Smith, <i>of</i> Stone <i>in the County of</i> Bucks<br /> -John Smith, <i>Esq;</i><br /> -Mr John Smith<br /> -Mr John Smith, <i>Surgeon in</i> Coventry, 2 Books<br /> -Mr John Smith, <i>Surgeon in</i> Chichester<br /> -Mr Allyn Smith<br /> -Mr Joshua Smith<br /> -Mr Joseph Smith<br /> -<i>Rev.</i> Mr Elisha Smith, <i>of</i> Tid <i>St. Gyles’s, in the Isle of</i> Ely<br /> -Mr Ward Smith<br /> -Mr Skinner Smith<br /> -<i>Rev.</i> Mr George Smyth<br /> -Mr Snablin<br /> -<i>Dr.</i> Snell, <i>of</i> Norwich<br /> -Mr Samuel Snell<br /> -Mr William Snell<br /> -William Snelling, <i>Esq;</i><br /> -William Sneyd, <i>Esq;</i><br /> -Mr Ralph Snow<br /> -Mr Thomas Snow<br /> -Stephen Soame, <i>Esq; Fellow Commoner of</i> Sidney Coll. Cambr.<br /> -Cockin Sole, <i>Esq;</i><br /> -Joseph Somers, <i>Esq;</i><br /> -Mr Edwin Sommers, <i>Merchant</i><br /> -Mr Adam Soresby<br /> -Thomas Southby, <i>Esq;</i><br /> -Sontley South, <i>Esq;</i><br /> -Mr Sparrow<br /> -Mr Speke, <i>of</i> Wadham Coll. Ox.<br /> -<i>Rev.</i> Mr Joseph Spence<br /> -Mr Abraham Spooner<br /> -<i>Sir</i> Conrad Joachim Springel<br /> -Mr William Stammers<br /> -Mr Charles Stanhope<br /> -Mr Thomas Stanhope<br /> -<i>Sir</i> John Stanley<br /> -George Stanley, <i>Esq;</i><br /> -<i>Rev.</i> Dr. Stanley, <i>Dean of St.</i> Asaph<br /> -Mr John Stanly<br /> -Eaton Stannard, <i>Esq;</i><br /> -Thomas Stansal, <i>Esq;</i><br /> -Mr Samuel Stanton<br /> -Temple Stanyan, <i>Esq;</i><br /> -Mrs Mary Stanyforth<br /> -<i>Rev.</i> Mr Thomas Starges, <i>Rector of</i> Hadstock, Essex<br /> -Mr Benjamin Steel<br /> -Mr John Stebbing, <i>of St.</i> John’s College, Cambridge<br /> -Mr John Martis Stehelin, <i>Merch.</i><br /> -<i>Dr.</i> Steigerthal<br /> -Mr Stephens, <i>of</i> Gloucester<br /> -Mr Joseph Stephens<br /> -<i>Sir</i> James Steuart <i>of</i> Gutters, <i>Bar.</i><br /> -Mr Robert Steuart, <i>Professor of</i> Natural Philosophy, <i>in the University of</i> Edinburgh<br /> -<i>Rev.</i> Mr Stevens, <i>Fellow of</i> Corp. Chr. Coll. Cambridge<br /> -Mr John Stevens, <i>of</i> Trinity College, Oxon<br /> -<i>Rev.</i> Mr Bennet Stevenson<br /> -<i>Hon.</i> Richard Stewart, <i>Esq;</i><br /> -<i>Major</i> James Stewart<br /> -<i>Capt</i> Bartholomew Stibbs<br /> -Mr Denham Stiles<br /> -Mr Thomas Stiles, <i>sen.</i><br /> -Mr Thomas Stiles, <i>jun.</i><br /> -<i>Rev.</i> Mr Stillingfleet<br /> -Mr Edward Stillingfleet<br /> -Mr John Stillingfleet<br /> -Mr William Stith<br /> -Mr Stock, <i>of</i> Rochdall <i>in</i> Lancashire<br /> -Mr Stocton, <i>Watch-Maker</i><br /> -Mr Robert Stogdon<br /> -<i>Rev.</i> Mr Richard Stonehewer<br /> -Thomas Stoner, <i>Esq;</i><br /> -Mr George Story, <i>of</i> Trinity College, Cambridge<br /> -Mr Thomas Story<br /> -William Strahan, <i>L. L. D.</i><br /> -Mr Thomas Stratfield<br /> -<i>Rev. Dr.</i> Stratford, <i>Canon of</i> Christ Church, Oxford<br /> -<i>Capt.</i> William Stratton<br /> -<i>Rev.</i> Mr Streat<br /> -Samuel Strode, <i>Esq;</i><br /> -Mr George Strode<br /> -<span class="pagenum"><a name="Page_xlix" id="Page_xlix">[xlix]</a></span><i>Rev.</i> Mr John Strong<br /> -<i>Hon. Commodore</i> Stuart<br /> -Alexander Stuart, <i>M. D.</i><br /> -Charles Stuart, <i>M. D.</i><br /> -Lewis Stucly<br /> -Mr John Sturges, <i>of</i> Bloomsbury<br /> -Mr Sturgeon, <i>Surgeon in</i> Bury<br /> -<i>Hon. Lady</i> Suasso<br /> -Mr Gerrard Suffield<br /> -Mr William Sumner, <i>of</i> Windsor<br /> -<i>Sir</i> Robert Sutton, <i>Kt. of the</i> Bath<br /> -<i>Rev.</i> Mr John Sutton<br /> -Mr Gerrard Swartz<br /> -Mr Thomas Swayne<br /> -William Swinburn, <i>Esq;</i><br /> -<i>Rev.</i> Mr. John Swinton, <i>M. A.</i><br /> -Mr Joshua Symmonds, <i>Surgeon</i><br /> -<i>Rev.</i> Mr Edward Synge</p> - -<p class="pi4 p2">T.</p> - -<p class="pn2"><i>His Grace the Archbishop of</i> Tuam<br /> -<i>Right Hon. Earl of</i> Tankerville<br /> -<i>Rt. Hon. Ld. Viscount</i> Townshend, <i>One of His Majesty’s Principal Secretaries of State</i><br /> -<i>Right Honourable Lady Viscountess</i> Townshend<br /> -<i>Right Hon Ld Viscount</i> Tyrconnel<br /> -<i>The Honourable Lord</i> Trevor Charles Talbot, <i>Esq; Solicitor-General.</i><br /> -Francis Talbot, <i>Esq;</i><br /> -John Ivory Talbot, <i>Esq;</i><br /> -Mr George Talbot, <i>M. A.</i><br /> -Mr Talbot<br /> -Thomas Tanner, <i>D. D. Chancellor of</i> Norwich<br /> -Mr Thomas Tanner<br /> -Mr Tateham <i>of</i> Clapham<br /> -Mr Henry Tatham<br /> -Mr John Tatnall<br /> -Mr Arthur Tayldeur<br /> -Mr John Tayleur<br /> -Arthur Taylor, <i>Esq;</i><br /> -Joseph Taylor, <i>Esq;</i><br /> -Simon Taylor, <i>Esq;</i><br /> -<i>Rev.</i> Mr Abraham Taylor<br /> -Brook Taylor, <i>L. L. D.</i><br /> -William Tempest, <i>Esq;</i><br /> -William Tenison, <i>Esq;</i><br /> -<i>Dr.</i> Tenison<br /> -<i>Rev. Dr.</i> Terry, <i>Canon of</i> Christ Church, Oxon<br /> -Mr Theed, <i>Attorney</i><br /> -Mr Lewis Theobald<br /> -James Theobalds, <i>Esq;</i><br /> -Robert Thistlethwayte, <i>D. D. Warden of</i> Wadham Coll. Oxon<br /> -<i>Rev.</i> Mr Thomlinson<br /> -Richard Thompson Coley, <i>Esq;</i><br /> -<i>Rev.</i> Mr William Thompson<br /> -Mr William Thompson, <i>A. B. of</i> Trinity Coll. Cambridge<br /> -Mr Thoncas<br /> -Mr Thornbury, <i>Vicar of</i> Thame<br /> -<i>Sir</i> James Thornhill, 3 Books<br /> -Mr Thornhill<br /> -William Thornton, <i>Esq;</i><br /> -Mr Catlyn Thorowgood<br /> -Mr John Thorpe<br /> -William Thorseby, <i>Esq;</i><br /> -Mr William Thurlbourn, <i>Bookseller in</i> Cambridge<br /> -Mark Thurston, <i>Esq; Master in</i> Chancery<br /> -<i>Rev.</i> Mr William Tiffin, <i>of</i> Lynn<br /> -Edmund Tigh, <i>Esq;</i><br /> -<i>Right Hon.</i> Richard Tighe, <i>Esq;</i><br /> -Mr Abraham Tilghman<br /> -Mr George Tilson<br /> -<i>Rev</i> Mr Tilson<br /> -Mr William Tims<br /> -<i>Rev.</i> Mr John Tisser<br /> -<i>Capt.</i> Joseph Tolson<br /> -Mr Tomkins<br /> -Mr William Tomlinson<br /> -Richard Topham, <i>Esq;</i><br /> -<i>Dr.</i> Torey<br /> -George Torriano, <i>of</i> West-Ham, <i>Esq;</i><br /> -Mr John Torriano<br /> -Mr James le Touch<br /> -<i>Rev.</i> Mr Charles Tough<br /> -Mr John Towers<br /> -<i>Rev.</i> Mr Nehemiah Towgood<br /> -Mr Edward Town<br /> -Joseph Townsend, <i>Esq;</i><br /> -Charles Townshend, <i>of</i> Lincoln’s Inn, <i>Esq;</i><br /> -<i>Hon.</i> Thomas Townshend, <i>Esq;</i><br /> -Mr Townson<br /> -John Tracey, <i>of</i> Stanway <i>in</i> Gloucester, <i>Esq;</i><br /> -Capt. 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Lord</i> Viscount Vane<br /> -<i>Rev.</i> Mr Thomas Valentine<br /> -Mr Vallack, <i>of</i> Plymouth<br /> -Mr John Vanderbank<br /> -Mr Daniel Vandewall<br /> -Mr John Vandewall, <i>Merchant</i><br /> -Mr Edward Vaus<br /> -<i>Hon.</i> John Verney, <i>Esq;</i><br /> -William Vesey, <i>Esq;</i><br /> -<i>Rev.</i> Mr John Vesey<br /> -William Vigor, <i>of</i> Westbury College <i>near</i> Bristol<br /> -Mr George Virgoe<br /> -Mr Frederick Voguel, <i>Merchant</i><br /> -Mr Thomas Vickers<br /> -Robert Viner, <i>Esq;</i></p> - -<p class="pi4 p2">W</p> - -<p class="pn2"><i>Rt. Hon. the Earl of</i> Winchelsea<br /> -<i>Rt. Rev. Lord Bishop of</i> Winchester<br /> -<i>Rev.</i> Mr Wade<br /> -<i>Sir</i> Charles Wager<br /> -<i>Rev.</i> Mr Wagstaffe<br /> -<i>Rev. Dr.</i> Edward Wake<br /> -Mr Jasper Wakefield<br /> -Mr Samuel Walbank<br /> -Mr Walbridge<br /> -Mr Waldron<br /> -Edmund Waldrond. <i>M. A.</i><br /> -Mr Walford, <i>of</i> Wadham Coll. 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D.</i></p> - -</div> - -<p><span class="pagenum"><a name="Page_1" id="Page_1">[1]</a></span></p> - -<div class="chapter"> - -<div class="figcenter"> - <img src="images/ill-051.jpg" width="400" height="221" - alt="" - title="" /> -</div> - -<h2 class="p4">INTRODUCTION.</h2> - -<div> - <img class="dcap1" src="images/dt1.jpg" width="80" height="79" alt=""/> -</div> -<p class="cap13">THE manner, in which Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> -has published his philosophical discoveries, -occasions them to lie very much -concealed from all, who have not made -the mathematics particularly their study. -He once, indeed, intended to deliver, -in a more familiar way, that part -of his inventions, which relates to the system of the world; -but upon farther consideration he altered his design. For as -the nature of those discoveries made it impossible to prove -them upon any other than geometrical principles; he apprehended, -that those, who should not fully perceive the force -of his arguments, would hardly be prevailed on to exchange -their former sentiments for new opinions, so very different from<span class="pagenum"><a name="Page_2" id="Page_2">[2]</a></span> -what were commonly received<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a>. He therefore chose rather -to explain himself only to mathematical readers; and declined -the attempting to instruct such in any of his principles, who, -by not comprehending his method of reasoning, could not, at -the first appearance of his discoveries, have been persuaded of -their truth. But now, since Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em>’s doctrine -has been fully established by the unanimous approbation of all, -who are qualified to understand the same; it is without doubt -to be wished, that the whole of his improvements in philosophy -might be universally known. For this purpose therefore -I drew up the following papers, to give a general notion of our -great philosopher’s inventions to such, as are not prepared to -read his own works, and yet might desire to be informed of -the progress, he has made in natural knowledge; not doubting -but there were many, besides those, whose turn of mind had -led them into a course of mathematical studies, that would take -great pleasure in tasting of this delightful fountain of science.</p> - -<p>2. <span class="smcap gesperrt">It</span> is a just remark, which has been made upon the human -mind, that nothing is more suitable to it, than the contemplation -of truth; and that all men are moved with a strong -desire after knowledge; esteeming it honourable to excel -therein; and holding it, on the contrary, disgraceful to mistake, -err, or be in any way deceived. And this sentiment -is by nothing more fully illustrated, than by the inclination -of men to gain an acquaintance with the operations of nature; -which disposition to enquire after the causes of things is<span class="pagenum"><a name="Page_3" id="Page_3">[3]</a></span> -so general, that all men of letters, I believe, find themselves -influenced by it. Nor is it difficult to assign a reason for this, -if we consider only, that our desire after knowledge is an effect -of that taste for the sublime and the beautiful in things, -which chiefly constitutes the difference between the human -life, and the life of brutes. These inferior animals partake -with us of the pleasures, that immediately flow from the bodily -senses and appetites; but our minds are furnished with a -superior sense, by which we are capable of receiving various -degrees of delight, where the creatures below us perceive no -difference. Hence arises that pursuit of grace and elegance in -our thoughts and actions, and in all things belonging to us, -which principally creates imployment for the active mind of -man. The thoughts of the human mind are too extensive -to be confined only to the providing and enjoying of what is -necessary for the support of our being. It is this taste, which -has given rise to poetry, oratory, and every branch of literature -and science. From hence we feel great pleasure in conceiving -strongly, and in apprehending clearly, even where -the passions are not concerned. Perspicuous reasoning appears -not only beautiful; but, when set forth in its full -strength and dignity, it partakes of the sublime, and not -only pleases, but warms and elevates the soul. This is the -source of our strong desire of knowledge; and the same -taste for the sublime and the beautiful directs us to chuse -particularly the productions of nature for the subject of our -contemplation: our creator having so adapted our minds to -the condition, wherein he has placed us, that all his visible<span class="pagenum"><a name="Page_4" id="Page_4">[4]</a></span> -works, before we inquire into their make, strike us with -the most lively ideas of beauty and magnificence.</p> - -<p>3. <span class="smcap gesperrt">But</span> if there be so strong a passion in contemplative -minds for natural philosophy; all such must certainly receive a -particular pleasure in being informed of Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em>’s -discoveries, who alone has been able to make any great -advancements in the true course leading to natural knowledge: -whereas this important subject had before been usually -attempted with that negligence, as cannot be reflected -on without surprize. Excepting a very few, who, by -pursuing a more rational method, had gained a little true -knowledge in some particular parts of nature; the writers in -this science had generally treated of it after such a manner, as -if they thought, that no degree of certainty was ever to be hoped -for. The custom was to frame conjectures; and if upon -comparing them with things, there appeared some kind of agreement, -though very imperfect, it was held sufficient. Yet -at the same time nothing less was undertaken than intire systems, -and fathoming at once the greatest depths of nature; -as if the secret causes of natural effects, contrived and framed -by infinite wisdom, could be searched out by the slightest -endeavours of our weak understandings. Whereas the only -method, that can afford us any prospect of success in this -difficult work, is to make our enquiries with the utmost -caution, and by very slow degrees. And after our most diligent -labour, the greatest part of nature will, no doubt, for ever -remain beyond our reach.</p> - -<p><span class="pagenum"><a name="Page_5" id="Page_5">[5]</a></span></p> - -<p>4. <span class="smcap gesperrt">This</span> neglect of the proper means to enlarge our -knowledge, joined with the presumption to attempt, what -was quite out of the power of our limited faculties, the Lord -<span class="smcap">Bacon</span> judiciously observes to be the great obstruction to the -progress of science<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a>. Indeed that excellent person was the first, -who expresly writ against this way of philosophizing; and he -has laid open at large the absurdity of it in his admirable treatise, -intitled <span class="smcap">Novum organon scientiarum</span>; and has there -likewise described the true method, which ought to be followed.</p> - -<p>5. <span class="smcap gesperrt">There</span> are, saith he, but two methods, that can be -taken in the pursuit of natural knowledge. One is to make -a hasty transition from our first and slight observations on -things to general axioms, and then to proceed upon those -axioms, as certain and uncontestable principles, without farther -examination. The other method; (which he observes -to be the only true one, but to his time unattempted;) is to -proceed cautiously, to advance step by step, reserving the -most general principles for the last result of our inquiries<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a>. -Concerning the first of these two methods; where objections, -which happen to appear against any such axioms taken up in -haste, are evaded by some frivolous distinction, when the axiom -it self ought rather to be corrected<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a>; he affirms, that -the united endeavours of all ages cannot make it successful; -because this original error in the first digestion of the mind -(as he expresses himself) cannot afterwards be remedied<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a>: -whereby he would signify to us, that if we set out in a<span class="pagenum"><a name="Page_6" id="Page_6">[6]</a></span> -wrong way; no diligence or art, we can use, while we -follow so erroneous a course, will ever bring us to our designed -end. And doubtless it cannot prove otherwise; for -in this spacious field of nature, if once we forsake the true -path, we shall immediately lose our selves, and must for -ever wander with uncertainty.</p> - -<p>6. <span class="smcap gesperrt">The</span> impossibility of succeeding in so faulty a method -of philosophizing his Lordship endeavours to prove from the -many false notions and prejudices, to which the mind of man -is exposed<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a>. And since this judicious writer apprehends, that -men are so exceeding liable to fall into these wrong tracts of -thinking, as to incur great danger of being misled by them, -even while they enter on the true course in pursuit of nature<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a>; -I trust, I shall be excused, if, by insisting a little particularly -upon this argument, I endeavour to remove whatever -prejudice of this kind, might possibly entangle the mind -of any of my readers.</p> - -<p>7. <span class="smcap gesperrt">His</span> Lordship has reduced these prejudices and false -modes of conception under four distinct heads<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a>.</p> - -<p>8. <span class="smcap gesperrt">The</span> first head contains such, as we are subject to from -the very condition of humanity, through the weakness both -of our senses, and of the faculties of the mind<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a>; seeing, as -this author well observes, the subtilty of nature far exceeds -the greatest subtilty of our senses or acutest reasonings<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a>. One<span class="pagenum"><a name="Page_7" id="Page_7">[7]</a></span> -of the false modes of conception, which he mentions under -this head, is the forming to our selves a fanciful simplicity -and regularity in natural things. This he illustrates -by the following instances; the conceiving the planets to -move in perfect circles; the adding an orb of fire to the other -three elements, and the supposing each of these to exceed -the other in rarity, just in a decuple proportion<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a>. -And of the same nature is the assertion of <span class="smcap"><em class="gesperrt">Des Cartes</em></span>, -without any proof, that all things are made up of three -kinds of matter only<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a>. As also this opinion of another -philosopher; that light, in passing through different mediums, -was refracted, so as to proceed by that way, through -which it would move more speedily, than through any other<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a>. -The second erroneous turn of mind, taken notice of -by his Lordship under this head, is, that all men are in some -degree prone to a fondness for any notions, which they have -once imbibed; whereby they often wrest things to reconcile -them to those notions, and neglect the consideration of whatever -will not be brought to an agreement with them; just as -those do, who are addicted to judicial astrology, to the observation -of dreams, and to such-like superstitions; who carefully -preserve the memory of every incident, which serves to -confirm their prejudices, and let slip out of their minds all instances, -that make against them<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a>. There is also a farther impediment -to true knowledge, mentioned under the same head by -this noble writer, which is; that whereas, through the weakness -and imperfection of our senses, many things are concealed.<span class="pagenum"><a name="Page_8" id="Page_8">[8]</a></span> -from us, which have the greatest effect in producing natural -appearances; our minds are ordinarily most affected by -that, which makes the strongest impression on our organs -of sense; whereby we are apt to judge of the real importance -of things in nature by a wrong measure<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a>. So, because -the figuration and the motion of bodies strike our senses more -immediately than most of their other properties, <span class="smcap">Des Cartes</span> -and his followers will not allow any other explication of natural -appearances, than from the figure and motion of the parts -of matter. By which example we see how justly his Lordship -observes this cause of error to be the greatest of any<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a>; -since it has given rise to a fundamental principle in a system -of philosophy, that not long ago obtained almost an universal -reputation.</p> - -<p>9. <span class="smcap gesperrt">These</span> are the chief branches of those obstructions to -knowledge, which this author has reduced under his first -head of false conceptions. The second head contains the -errors, to which particular persons are more especially obnoxious<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a>. -One of these is the consequence of a preceding observation: -that as we are exposed to be captivated by any opinions, -which have once taken possession of our minds; so in -particular, natural knowledge has been much corrupted by -the strong attachment of men to some one part of science, -of which they reputed themselves the inventers, or about -which they have spent much of their time; and hence have -been apt to conceive it to be of greater use in the study of natural<span class="pagenum"><a name="Page_9" id="Page_9">[9]</a></span> -philosophy than it was: like <span class="smcap">Aristotle</span>, who reduced -his physics to logical disputations; and the chymists, who -thought, that nature could be laid open only by the force -of their fires<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a>. Some again are wholly carried away by an -excessive veneration for antiquity; others, by too great fondness -for the moderns; few having their minds so well balanced, -as neither to depreciate the merit of the ancients, nor yet to -despise the real improvements of later times<a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a>. To this is -added by his Lordship a difference in the genius of men, -that some are most fitted to observe the similitude, there is in -things, while others are more qualified to discern the particulars, -wherein they disagree; both which dispositions of -mind are useful: but to the prejudice of philosophy men are -apt to run into excess in each; while one sort of genius dwells -too much upon the gross and sum of things, and the other -upon trifling minutenesses and shadowy distinctions<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a>.</p> - -<p>10. <span class="smcap gesperrt">Under</span> the third head of prejudices and false notions -this writer considers such, as follow from the lax and indefinite -use of words in ordinary discourse; which occasions great -ambiguities and uncertainties in philosophical debates (as another -eminent philosopher has since shewn more at large<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a>;) insomuch -that this our author thinks a strict defining of terms to -be scarce an infallible remedy against this inconvenience<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a>. And -perhaps he has no small reason on his side: for the common -inaccurate sense of words, notwithstanding the limitations -given them by definitions, will offer it self so constantly to<span class="pagenum"><a name="Page_10" id="Page_10">[10]</a></span> -the mind, as to require great caution and circumspection -for us not to be deceived thereby. Of this we have a very -eminent instance in the great disputes, that have been raised -about the use of the word attraction in philosophy; of which -we shall be obliged hereafter to make particular mention<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a>. -Words thus to be guarded against are of two kinds. Some -are names of things, that are only imaginary<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a>; such words -are wholly to be rejected. But there are other terms, that allude -to what is real, though their signification is confused<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a>. -And these latter must of necessity be continued in use; but -their sense cleared up, and freed, as much as possible, from -obscurity.</p> - -<p>11. <span class="smcap gesperrt">The</span> last general head of these errors comprehends -such, as follow from the various sects of false philosophies; -which this author divides into three sorts, the sophistical, empirical, -and superstitious<a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a>. By the first of these he means -a philosophy built upon speculations only without experiments<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a>; -by the second, where experiments are blindly adhered -to, without proper reasoning upon them<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a>; and by -the third, wrong opinions of nature fixed in mens minds either -through false religions, or from misunderstanding the -declarations of the true<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a>.</p> - -<p>12. <span class="smcap gesperrt">These</span> are the four principal canals, by which this judicious -author thinks, that philosophical errors have flowed in -upon us. And he rightly observes, that the faulty method of<span class="pagenum"><a name="Page_11" id="Page_11">[11]</a></span> -proceeding in philosophy, against which he writes<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a>, is so far -from assisting us towards overcoming these prejudices; that -he apprehends it rather suited to rivet them more firmly to the -mind<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a>. How great reason then has his Lordship to call this -way of philosophizing the parent of error, and the bane of -all knowledge<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a>? For, indeed, what else but mistakes can so -bold and presumptuous a treatment of nature produce? have -we the wisdom necessary to frame a world, that we should -think so easily, and with so slight a search to enter into the most -secret springs of nature, and discover the original causes of -things? what chimeras, what monsters has not this preposterous -method brought forth? what schemes, or what hypothesis’s -of the subtilest wits has not a stricter enquiry into nature not -only overthrown, but manifested to be ridiculous and absurd? -Every new improvement, which we make in this science, lets -us see more and more the weakness of our guesses. Dr. <span class="smcap gesperrt">Harvey</span>, -by that one discovery of the circulation of the blood, has -dissipated all the speculations and reasonings of many ages upon -the animal oeconomy. <span class="smcap gesperrt">Asellius</span>, by detecting the lacteal -veins, shewed how little ground all physicians and philosophers -had in conjecturing, that the nutritive part of the -aliment was absorbed by the mouths of the veins spread upon -the bowels: and then <span class="smcap">Pecquet</span>, by finding out the thoracic -duct, as evidently proved the vanity of the opinion, which -was persisted in after the lacteal vessels were known, that the -alimental juice was conveyed immediately to the liver, and -there converted into blood.</p> - -<p><span class="pagenum"><a name="Page_12" id="Page_12">[12]</a></span></p> - -<p>13. <span class="smcap gesperrt">As</span> these things set forth the great absurdity of proceeding -in philosophy on conjectures, by informing us how far -the operations of nature are above our low conceptions; so -on the other hand, such instances of success from a more -judicious method shew us, that our bountiful maker has -not left us wholly without means of delighting our selves in -the contemplation of his wisdom. That by a just way of -inquiry into nature, we could not fail of arriving at discoveries -very remote from our apprehensions; the Lord <span class="smcap"><em class="gesperrt">Bacon</em></span> himself -argues from the experience of mankind. If, says he, the -force of guns should be described to any one ignorant of -them, by their effects only, he might reasonably suppose, that -those engines of destruction were only a more artificial composition, -than he knew, of wheels and other mechanical -powers: but it could never enter his thoughts, that their -immense force should be owing to a peculiar substance, -which would enkindle into so violent an explosion, as we -experience in gunpowder: since he would no where see -the least example of any such operation; except perhaps in -earthquakes and thunder, which he would doubtless look -upon as exalted powers of nature, greatly surpassing any art of -man to imitate. In the same manner, if a stranger to the original -of silk were shewn a garment made of it, he would be -very far from imagining so strong a substance to be spun out -of the bowels of a small worm; but must certainly believe -it either a vegetable substance, like flax or cotton; or the natural -covering of some animal, as wool is of sheep. Or had -we been told, before the invention of the magnetic needle -among us, that another people was in possession of a certain<span class="pagenum"><a name="Page_13" id="Page_13">[13]</a></span> -contrivance, by which they were inabled to discover the position -of the heavens, with vastly more ease, than we could -do; what could have been imagined more, than that they -were provided with some fitter astronomical instrument for -this purpose than we? That any stone should have so amazing -a property, as we find in the magnet, must have been -the remotest from our thoughts<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a>.</p> - -<p>14. <span class="smcap gesperrt">But</span> what surprizing advancements in the knowledge -of nature may be made by pursuing the true course in philosophical -inquiries; when those searches are conducted by a -genius equal to so divine a work, will be best understood by -considering Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> discoveries. That my’s -reader may apprehend as just a notion of these, as can be conveyed -to him, by the brief account, which I intend to lay before -him; I have set apart this introduction for explaining, in -the fullest manner I am able, the principles, whereon Sir -<em class="gesperrt"><span class="smcap">Isaac Newton</span></em> proceeds. For without a clear conception -of these, it is impossible to form any true idea of the -singular excellence of the inventions of this great philosopher.</p> - -<p>15. <span class="smcap gesperrt">The</span> principles then of this philosophy are; upon no consideration -to indulge conjectures concerning the powers and -laws of nature, but to make it our endeavour with all diligence -to search out the real and true laws, by which the constitution -of things is regulated. The philosopher’s first care must be -to distinguish, what he sees to be within his power, from what<span class="pagenum"><a name="Page_14" id="Page_14">[14]</a></span> -is beyond his reach; to assume no greater degree of knowledge, -than what he finds himself possessed of; but to advance -by slow and cautious steps; to search gradually into natural causes; -to secure to himself the knowledge of the most immediate -cause of each appearance, before he extends his views farther -to causes more remote. This is the method, in which philosophy -ought to be cultivated; which does not pretend to so great -things, as the more airy speculations; but will perform abundantly -more: we shall not perhaps seem to the unskilful to -know so much, but our real knowledge will be greater. And -certainly it is no objection against this method, that some others -promise, what is nearer to the extent of our wishes: since -this, if it will not teach us all we could desire to be informed -of, will however give us some true light into nature; which no -other can do. Nor has the philosopher any reason to think -his labour lost, when he finds himself stopt at the cause first -discovered by him, or at any other more remote cause, short -of the original: for if he has but sufficiently proved any one -cause, he has entered so far into the real constitution of things, -has laid a safe foundation for others to work upon, and -has facilitated their endeavours in the search after yet more -distant causes; and besides, in the mean time he may apply -the knowledge of these intermediate causes to many useful -purposes. Indeed the being able to make practical deductions -from natural causes, constitutes the great distinction -between the true philosophy and the false. Causes assumed -upon conjecture, must be so loose and undefined, -that nothing particular can be collected from them. But those -causes, which are brought to light by a strict examination<span class="pagenum"><a name="Page_15" id="Page_15">[15]</a></span> -of things, will be more distinct. Hence it appears to have -been no unuseful discovery, that the ascent of water in pumps -is owing to the pressure of the air by its weight or spring; -though the causes, which make the air gravitate, and render -it elastic, be unknown: for notwithstanding we are ignorant -of the original, whence these powers of the air are derived; -yet we may receive much advantage from the bare -knowledge of these powers. If we are but certain of the degree -of force, wherewith they act, we shall know the extent of -what is to be expected from them; we shall know the greatest -height, to which it is possible by pumps to raise water; and -shall thereby be prevented from making any useless efforts -towards improving these instruments beyond the limits prescribed -to them by nature; whereas without so much knowledge -as this, we might probably have wasted in attempts of -this kind much time and labour. How long did philosophers -busy themselves to no purpose in endeavouring to perfect -telescopes, by forming the glasses into some new figure; till -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> demonstrated, that the effects of telescopes -were limited from another cause, than was supposed; -which no alteration in the figure of the glasses could remedy? -What method Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> himself has found for -the improvement of telescopes shall be explained hereafter<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a>. -But at present I shall proceed to illustrate, by some farther instances, -this distinguishing character of the true philosophy, which -we have now under consideration. It was no trifling discovery, -that the contraction of the muscles of animals puts their -limbs in motion, though the original cause of that contraction<span class="pagenum"><a name="Page_16" id="Page_16">[16]</a></span> -remains a secret, and perhaps may always do so; for the -knowledge of thus much only has given rise to many speculations -upon the force and artificial disposition of the muscles, -and has opened no narrow prospect into the animal fabrick. -The finding out, that the nerves are great agents in this action, -leads us yet nearer to the original cause, and yields us a -wider view of the subject. And each of these steps affords us -assistance towards restoring this animal motion, when impaired -in our selves, by pointing out the seats of the injuries, to -which it is obnoxious. To neglect all this, because we can -hitherto advance no farther, is plainly ridiculous. It is -confessed by all, that <span class="smcap"><em class="gesperrt">Galileo</em></span> greatly improved philosophy, -by shewing, as we shall relate hereafter, that the power -in bodies, which we call gravity, occasions them to move -downwards with a velocity equably accelerated<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a>; and that -when any body is thrown forwards, the same power obliges it -to describe in its motion that line, which is called by geometers -a parabola<a name="FNanchor_36_36" id="FNanchor_36_36"></a><a href="#Footnote_36_36" class="fnanchor">[36]</a>: yet we are ignorant of the cause, which makes -bodies gravitate. But although we are unacquainted with -the spring, whence this power in nature is derived, nevertheless -we can estimate its effects. When a body falls perpendicularly, -it is known, how long time it takes in descending from -any height whatever: and if it be thrown forwards, we know -the real path, which it describes; we can determine in what -direction, and with what degree of swiftness it must be projected, -in order to its striking against any object desired; and -we can also ascertain the very force, wherewith it will strike.<span class="pagenum"><a name="Page_17" id="Page_17">[17]</a></span> -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> has farther taught, that this power of -gravitation extends up to the moon, and causes that planet to -gravitate as much towards the earth, as any of the bodies, which -are familiar to us, would, if placed at the same distance<a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a>: -he has proved likewise, that all the planets gravitate towards -the sun, and towards one another; and that their respective -motions follow from this gravitation. All this he has demonstrated -upon indisputable geometrical principles, which cannot -be rendered precarious for want of knowing what it is, which -causes these bodies thus mutually to gravitate: any more than -we can doubt of the propensity in all the bodies about us, to -descend towards the earth; or can call in question the forementioned -propositions of <span class="smcap"><em class="gesperrt">Galileo</em></span>, which are built upon -that principle. And as <span class="smcap"><em class="gesperrt">Galileo</em></span> has shewn more fully, -than was known before, what effects were produced in the -motion of bodies by their gravitation towards the earth; so -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span>, by this his invention, has much advanced -our knowledge in the celestial motions. By discovering -that the moon gravitates towards the sun, as well as towards -the earth; he has laid open those intricacies in the moon’s -motion, which no astronomer, from observations only, could -ever find out<a name="FNanchor_38_38" id="FNanchor_38_38"></a><a href="#Footnote_38_38" class="fnanchor">[38]</a>: and one kind of heavenly bodies, the comets, -have their motion now clearly ascertained; whereof we had -before no true knowledge at all<a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a>.</p> - -<p>16. <span class="smcap gesperrt">Doubtless</span> it might be expected, that such surprizing -success should have silenced, at once, every cavil. But we<span class="pagenum"><a name="Page_18" id="Page_18">[18]</a></span> -have seen the contrary. For because this philosophy professes -modestly to keep within the extent of our faculties, and is -ready to confess its imperfections, rather than to make any -fruitless attempts to conceal them, by seeking to cover the defects -in our knowledge with the vain ostentation of rash and -groundless conjectures; hence has been taken an occasion to -insinuate that we are led to miraculous causes, and the occult -qualities of the schools.</p> - -<p>17. <span class="smcap gesperrt">But</span> the first of these accusations is very extraordinary. -If by calling these causes miraculous nothing more is -meant than only, that they often appear to us wonderful and -surprizing, it is not easy to see what difficulty can be raised -from thence; for the works of nature discover every where -such proofs of the unbounded power, and the consummate -wisdom of their author, that the more they are known, the -more they will excite our admiration: and it is too manifest -to be insisted on, that the common sense of the word miraculous -can have no place here, when it implies what is above -the ordinary course of things. The other imputation, that -these causes are occult upon the account of our not perceiving -what produces them, contains in it great ambiguity. That -something relating to them lies hid, the followers of this -philosophy are ready to acknowledge, nay desire it should -be carefully remarked, as pointing out proper subjects for future -inquiry. But this is very different from the proceeding -of the schoolmen in the causes called by them occult. For -as their occult qualities were understood to operate in a manner -occult, and not apprehended by us; so they were obtruded<span class="pagenum"><a name="Page_19" id="Page_19">[19]</a></span> -upon us for such original and essential properties in bodies, -as made it vain to seek any farther cause; and a greater -power was attributed to them, than any natural appearances -authorized. For instance, the rise of water in pumps was ascribed -to a certain abhorrence of a vacuum, which they thought -fit to assign to nature. And this was so far a true observation, -that the water does move, contrary to its usual course, into -the space, which otherwise would be left void of any sensible -matter; and, that the procuring such a vacuity was the apparent -cause of the water’s ascent. But while we were not in -the least informed how this power, called an abhorrence of a -vacuum, produced the visible effects; instead of making any -advancement in the knowledge of nature, we only gave -an artificial name to one of her operations: and when the -speculation was pushed so beyond what any appearances required, -as to have it concluded, that this abhorrence of a vacuum -was a power inherent in all matter, and so unlimited as -to render it impossible for a vacuum to exist at all; it then -became a much greater absurdity, in being made the foundation -of a most ridiculous manner of reasoning; as at length -evidently appeared, when it came to be discovered, that this -rise of the water followed only from the pressure of the air, -and extended it self no farther, than the power of that cause. -The scholastic stile in discoursing of these occult qualities, -as if they were essential differences in the very substances, -of which bodies consisted, was certainly very absurd; by -reason it tended to discourage all farther inquiry. But no -such ill consequences can follow from the considering of -any natural causes, which confessedly are not traced up to<span class="pagenum"><a name="Page_20" id="Page_20">[20]</a></span> -their first original. How shall we ever come to the knowledge -of the several original causes of things, otherwise than -by storing up all intermediate causes which we can discover? -Are all the original and essential properties of matter so very -obvious, that none of them can escape our first view? This is -not probable. It is much more likely, that, if some of the -essential properties are discovered by our first observations, a -stricter examination should bring more to light.</p> - - -<p>18. <span class="smcap gesperrt">But</span> in order to clear up this point concerning the -essential properties of matter, let us consider the subject a little -distinctly. We are to conceive, that the matter, out of -which the universe of things is formed, is furnished with certain -qualities and powers, whereby it is rendered fit to answer -the purposes, for which it was created. But every property, -of which any particle of this matter is in it self possessed, and -which is not barely the consequence of the union of this particle -with other portions of matter, we may call an essential property: -whereas all other qualities or attributes belonging to -bodies, which depend on their particular frame and composition, -are not essential to the matter, whereof such bodies are -made; because the matter of these bodies will be deprived -of those qualities, only by the dissolution of the body, without -working any change in the original constitution of one -single particle of this mass of matter. Extension we apprehend -to be one of these essential properties, and impenetrability -another. These two belong universally to all matter; and -are the principal ingredients in the idea, which this word -matter usually excites in the mind. Yet as the idea, marked<span class="pagenum"><a name="Page_21" id="Page_21">[21]</a></span> -by this name, is not purely the creature of our own understandings, -but is taken for the representation of a certain -substance without us; if we should discover, that every part -of the substance, in which we find these two properties, -should likewise be endowed universally with any other essential -qualities; all these, from the time they come to our notice, -must be united under our general idea of matter. How -many such properties there are actually in all matter we know -not; those, of which we are at present apprized, have been -found out only by our observations on things; how many -more a farther search may bring to light, no one can say; -nor are we certain, that we are provided with sufficient methods -of perception to discern them all. Therefore, since we -have no other way of making discoveries in nature, but by -gradual inquiries into the properties of bodies; our first step -must be to admit without distinction all the properties, which -we observe; and afterwards we must endeavour, as far as we -are able, to distinguish between the qualities, wherewith the -very substances themselves are indued, and those appearances, -which result from the structure only of compound bodies. -Some of the properties, which we observe in things, are the -attributes of particular bodies only; others universally belong -to all, that fall under our notice. Whether some of the -qualities and powers of particular bodies, be derived from different -kinds of matter entring their composition, cannot, in -the present imperfect state of our knowledge, absolutely be -decided; though we have not yet any reason to conclude, -but that all the bodies, with which we converse, are framed -out of the very same kind of matter, and that their distinct<span class="pagenum"><a name="Page_22" id="Page_22">[22]</a></span> -qualities are occasioned only by their structure; through the variety -whereof the general powers of matter are caused to produce -different effects. On the other hand, we should not hastily -conclude, that whatever is found to appertain to all matter, -which falls under our examination, must for that reason -only be an essential property thereof, and not be derived from -some unseen disposition in the frame of nature. Sir <span class="smcap"><em class="gesperrt">Isaac -Newton</em></span> has found reason to conclude, that gravity is a property -universally belonging to all the perceptible bodies in the -universe, and to every particle of matter, whereof they are -composed. But yet he no where asserts this property to be -essential to matter. And he was so far from having any design -of establishing it as such, that, on the contrary, he has -given some hints worthy of himself at a cause for it<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a>; and expresly -says, that he proposed those hints to shew, that he had -no such intention<a name="FNanchor_41_41" id="FNanchor_41_41"></a><a href="#Footnote_41_41" class="fnanchor">[41]</a>.</p> - -<p>19. <span class="smcap gesperrt">It</span> appears from hence, that it is not easy to determine, -what properties of bodies are essentially inherent in the -matter, out of which they are made, and what depend upon -their frame and composition. But certainly whatever properties -are found to belong either to any particular systems of -matter, or universally to all, must be considered in philosophy; -because philosophy will be otherwise imperfect. Whether -those properties can be deduced from some other appertaining -to matter, either among those, which are already known, -or among such as can be discovered by us, is afterwards to be -sought for the farther improvement of our knowledge. But this<span class="pagenum"><a name="Page_23" id="Page_23">[23]</a></span> -inquiry cannot properly have place in the deliberation about admitting -any property of matter or bodies into philosophy; for -that purpose it is only to be considered, whether the existence -of such a property has been justly proved or not. Therefore -to decide what causes of things are rightly received into natural -philosophy, requires only a distinct and clear conception -of what kind of reasoning is to be allowed of as convincing, -when we argue upon the works of nature.</p> - -<p>20. <span class="smcap gesperrt">The</span> proofs in natural philosophy cannot be so absolutely -conclusive, as in the mathematics. For the subjects of -that science are purely the ideas of our own minds. They -may be represented to our senses by material objects, but they -are themselves the arbitrary productions of our own thoughts; -so that as the mind can have a full and adequate knowledge -of its own ideas, the reasoning in geometry can be rendered -perfect. But in natural knowledge the subject of our contemplation -is without us, and not so compleatly to be known: -therefore our method of arguing must fall a little short of absolute -perfection. It is only here required to steer a just course -between the conjectural method of proceeding, against which -I have so largely spoke; and demanding so rigorous a proof, as -will reduce all philosophy to mere scepticism, and exclude all -prospect of making any progress in the knowledge of nature.</p> - -<p>21. <span class="smcap gesperrt">The</span> concessions, which are to be allowed in this science, -are by Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> included under a very -few simple precepts.</p> - -<p><span class="pagenum"><a name="Page_24" id="Page_24">[24]</a></span></p> - -<p>22. <span class="smcap gesperrt">The</span> first is, that more causes are not to be received -into philosophy, than are sufficient to explain the appearances -of nature. That this rule is approved of unanimously, is evident -from those expressions so frequent among all philosophers, -that nature does nothing in vain; and that a variety -of means, where fewer would suffice, is needless. And -certainly there is the highest reason for complying with this -rule. For should we indulge the liberty of multiplying, -without necessity, the causes of things, it would reduce -all philosophy to mere uncertainty; since the only proof, -which we can have, of the existence of a cause, is the necessity -of it for producing known effects. Therefore where -one cause is sufficient, if there really should in nature be -two, which is in the last degree improbable, we can have no -possible means of knowing it, and consequently ought not to -take the liberty of imagining, that there are more than one.</p> - -<p>23. <span class="smcap gesperrt">The</span> second precept is the direct consequence of the -first, that to like effects are to be ascribed the same causes. -For instance, that respiration in men and in brutes is brought -about by the same means; that bodies descend to the earth -here in <span class="smcap">Europe</span>, and in <span class="smcap">America</span> from the same principle; -that the light of a culinary fire, and of the sun have the same -manner of production; that the reflection of light is effected in -the earth, and in the planets by the same power; and the like.</p> - -<p>24. <span class="smcap gesperrt">The</span> third of these precepts has equally evident reason -for it. It is only, that those qualities, which in the same -body can neither be lessened nor increased, and which belong<span class="pagenum"><a name="Page_25" id="Page_25">[25]</a></span> -to all bodies that are in our power to make trial upon, ought -to be accounted the universal properties of all bodies whatever.</p> - -<p>25. <span class="smcap gesperrt">In</span> this precept is founded that method of arguing by -induction, without which no progress could be made in natural -philosophy. For as the qualities of bodies become -known to us by experiments only; we have no other way of -finding the properties of such bodies, as are out of our reach -to experiment upon, but by drawing conclusions from those -which fall under our examination. The only caution here -required is, that the observations and experiments, we argue -upon, be numerous enough, and that due regard be paid to -all objections, that occur, as the Lord <span class="smcap">Bacon</span> very judiciously -directs<a name="FNanchor_42_42" id="FNanchor_42_42"></a><a href="#Footnote_42_42" class="fnanchor">[42]</a>. And this admonition is sufficiently complied -with, when by virtue of this rule we ascribe impenetrability -and extension to all bodies, though we have no sensible -experiment, that affords a direct proof of any of the celestial -bodies being impenetrable; nor that the fixed stars -are so much as extended. For the more perfect our instruments -are, whereby we attempt to find their visible magnitude, -the less they appear; insomuch that all the sensible -magnitude, which we observe in them, seems only to be an -optical deception by the scattering of their light. However, -I suppose no one will imagine they are without any magnitude, -though their immense distance makes it undiscernable -by us. After the same manner, if it can be proved, that all<span class="pagenum"><a name="Page_26" id="Page_26">[26]</a></span> -bodies here gravitate towards the earth, in proportion to the -quantity of solid matter in each; and that the moon gravitates -to the earth likewise, in proportion to the quantity of matter -in it; and that the sea gravitates towards the moon, and all -the planets towards each other; and that the very comets have -the same gravitating faculty; we shall have as great reason to -conclude by this rule, that all bodies gravitate towards each -other. For indeed this rule will more strongly hold in this -case, than in that of the impenetrability of bodies; because -there will more instances be had of bodies gravitating, than -of their being impenetrable.</p> - -<p>25. <span class="smcap gesperrt">This</span> is that method of induction, whereon all philosophy -is founded; which our author farther inforces by -this additional precept, that whatever is collected from this -induction, ought to be received, notwithstanding any conjectural -hypothesis to the contrary, till such times as it shall be -contradicted or limited by farther observations on nature.</p> - -<div class="figcenter"> - <img src="images/ill-076.jpg" width="300" height="229" - alt="" - title="" /> -</div> - -</div> - -<p><span class="pagenum"><a name="Page_27" id="Page_27">[27]</a></span></p> - -<div class="chapter"> - -<div class="figcenter"> - <img src="images/ill-077.jpg" width="400" height="209" - alt="" - title="" /> -</div> - -<p class="pc xlarge"><em class="gesperrt">BOOK I</em>.</p> -<p class="pc reduct"><span class="smcap">Concerning the</span></p> -<p class="pc large">MOTION of BODIES</p> -<p class="pc">IN GENERAL.</p> - -<hr class="d3" /> - -<h2><a name="c27" id="c27"><span class="smcap">Chap. I.</span></a><br /> -Of the LAWS of MOTION.</h2> - -<div> - <img class="dcap1" src="images/dh1.jpg" width="80" height="79" alt=""/> -</div> -<p class="cap13">HAVING thus explained Sir <em class="gesperrt"><span class="smcap">Isaac -Newton</span>’s</em> method of reasoning in -philosophy, I shall now proceed to -my intended account of his discoveries. -These are contained in two treatises. -In one of them, the <span class="smcap">Mathematical -principles of natural philosophy</span>, -his chief design is to shew by what laws the heavenly<span class="pagenum"><a name="Page_28" id="Page_28">[28]</a></span> -motions are regulated; in the other, his <span class="smcap">Optics</span>, he discourses -of the nature of light and colours, and of the action between -light and bodies. This second treatise is wholly confined to -the subject of light: except some conjectures proposed at the -end concerning other parts of nature, which lie hitherto more -concealed. In the other treatise our author was obliged to -smooth the way to his principal intention, by explaining many -things of a more general nature: for even some of the most -simple properties of matter were scarce well established at that -time. We may therefore reduce Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span>’s doctrine -under three general heads; and I shall accordingly divide -my account into three books. In the first I shall speak -of what he has delivered concerning the motion of bodies, -without regard to any particular system of matter; in the second -I shall treat of the heavenly motions; and the third -shall be employed upon light.</p> - -<p>2. <span class="smcap gesperrt">In</span> the first part of my design, we must begin with an -account of the general laws of motion.</p> - -<p>3. <span class="smcap gesperrt">These</span> laws are some universal affections and properties -of matter drawn from experience, which are made use -of as axioms and evident principles in all our arguings upon the -motion of bodies. For as it is the custom of geometers to -assume in their demonstrations some propositions, without -exhibiting the proof of them; so in philosophy, all our reasoning -must be built upon some properties of matter, first admitted -as principles whereon to argue. In geometry these axioms -are thus assumed, on account of their being so evident<span class="pagenum"><a name="Page_29" id="Page_29">[29]</a></span> -as to make any proof in form needless. But in philosophy -no properties of bodies can be in this manner received for self-evident; -since it has been observed above, that we can conclude -nothing concerning matter by any reasonings upon its -nature and essence, but that we owe all the knowledge, we -have thereof, to experience. Yet when our observations on -matter have inform’d us of some of its properties, we may securely -reason upon them in our farther inquiries into nature. -And these laws of motion, of which I am here to speak, are -found so universally to belong to bodies, that there is no motion -known, which is not regulated by them. These are by -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> reduced to three<a name="FNanchor_43_43" id="FNanchor_43_43"></a><a href="#Footnote_43_43" class="fnanchor">[43]</a>.</p> - -<p><a name="c29a" id="c29a">4.</a> <span class="smcap gesperrt">The</span> first law is, that all bodies have such an indifference -to rest, or motion, that if once at rest they remain so, till disturbed -by some power acting upon them: but if once put -in motion, they persist in it; continuing to move right forwards -perpetually, after the power, which gave the motion, -is removed; and also preserving the same degree of velocity -or quickness, as was first communicated, not stopping or remitting -their course, till interrupted or otherwise disturbed by -some new power impressed.</p> - -<p><a name="c29b" id="c29b">5.</a> <span class="smcap gesperrt">The</span> second law of motion is, that the alteration of the -state of any body, whether from rest to motion, or from motion -to rest, or from one degree of motion to another, is always -proportional to the force impressed. A body at rest, when<span class="pagenum"><a name="Page_30" id="Page_30">[30]</a></span> -acted upon by any power, yields to that power, moving in -the same line, in which the power applied is directed; and -moves with a less or greater degree of velocity, according to -the degree of the power; so that twice the power shall communicate -a double velocity, and three times the power a -threefold velocity. If the body be moving, and the power -impressed act upon the body in the direction of its motion, -the body shall receive an addition to its motion, as great as -the motion, into which that power would have put it from a -state of rest; but if the power impressed upon a moving body -act directly opposite to its former motion, that power shall -then take away from the body’s motion, as much as in the other -case it would have added to it. Lastly, if the power be -impressed obliquely, there will arise an oblique motion differing -more or less from the former direction, according as -the new impression is greater or less. For example, if the body -A (in fig. 1.) be moving in the direction A B, and when it is -at the point A, a power be impressed upon it in the direction -A C, the body shall from henceforth neither move in its first -direction A B, nor in the direction of the adventitious power, -but shall take a course as A D between them: and if the -power last impressed be just equal to that, which first gave -to the body its motion; the line A D shall pass in the middle -between A B and A C, dividing the angle under B A C into -two equal parts; but if the power last impressed be greater -than the first, the line A D shall incline most to A C; whereas -if the last impression be less than the first, the line A D shall -incline most to A B. To be more particular, the situation of<span class="pagenum"><a name="Page_31" id="Page_31">[31]</a></span> -the line A D is always to be determined after this manner. -Let A E be the space, which the body would have moved -through in the line A B during any certain portion of time; -provided that body, when at A, had received no second impulse. -Suppose likewise, that A F is the part of the line A C, -through which the body would have moved during an equal -portion of time, if it had been at rest in A, when it received -the impulse in the direction A C: then if from E be drawn -a line parallel to, or equidistant from A C, and from F another -line parallel to A B, those two lines will meet in the -line A D.</p> - -<p><a name="c31" id="c31">6.</a> <span class="smcap gesperrt">The</span> third and last of these laws of motion is, that -when any body acts upon another, the action of that body -upon the other is equalled by the contrary reaction of that -other body upon the first.</p> - -<p>7. <span class="smcap gesperrt">These</span> laws of motion are abundantly confirmed by -this, that all the deductions made from them, in relation to -the motion of bodies, how complicated soever, are found to -agree perfectly with observation. This shall be shewn more -at large in the next chapter. But before we proceed to so -diffusive a proof; I chuse here to point out those appearances -of bodies, whereby the laws of motion are first suggested -to us.</p> - -<p>8. <span class="smcap gesperrt">Daily</span> observation makes it appear to us, that any -body, which we once see at rest, never puts it self into fresh<span class="pagenum"><a name="Page_32" id="Page_32">[32]</a></span> -motion; but continues always in the same place, till removed -by some power applied to it.</p> - -<p>9. <span class="smcap gesperrt">Again</span>, whenever a body is once in motion, it continues -in that motion some time after the moving power has quitted -it, and it is left to it self. Now if the body continue to move -but a single moment, after the moving power has left it, there -can no reason be assigned, why it should ever stop without -some external force. For it is plain, that this continuance of -the motion is caused only by the body’s having already moved, -the sole operation of the power upon the body being the -putting it in motion; therefore that motion continued will equally -be the cause of its farther motion, and so on without -end. The only doubt that can remain, is, whether this motion -communicated continues intire, after the power, that caused -it, ceases to act; or whether it does not gradually languish and -decrease. And this suspicion cannot be removed by a transient -and slight observation on bodies, but will be fully cleared -up by those more accurate proofs of the laws of motion, -which are to be considered in the next chapter.</p> - -<p>10. <span class="smcap gesperrt">Lastly</span>, bodies in motion appear to affect a straight -course without any deviation, unless when disturbed by some -adventitious power acting upon them. If a body be thrown -perpendicularly upwards or downwards, it appears to continue -in the same straight line during the whole time of its motion. -If a body be thrown in any other direction, it is found to deviate -from the line, in which it began to move, more and<span class="pagenum"><a name="Page_33" id="Page_33">[33]</a></span> -more continually towards the earth, whither it is directed -by its weight: but since, when the weight of a body does -not alter the direction of its motion, it always moves in -a straight line, without doubt in this other case the body’s, -declining from its first course is no more, than what is caused -by its weight alone. As this appears at first sight to be -unquestionable, so we shall have a very distinct proof thereof -in the next chapter, where the oblique motion of bodies will -be particularly considered.</p> - -<p>11. <span class="smcap gesperrt">Thus</span> we see how the first of the laws of motion -agrees with what appears to us in moving bodies. But -here occurs this farther consideration, that the real and absolute -motion of any body is not visible to us: for we -are our selves also in constant motion along with the -earth whereon we dwell; insomuch that we perceive bodies -to move so far only, as their motion is different from -our own. When a body appears to us to lie at rest, in -reality it only continues the motion, it has received, without -putting forth any power to change that motion. If we -throw a body in the course or direction, wherein we are -carried our selves; so much motion as we seem to have -given to the body, so much we have truly added to the -motion, it had, while it appeared to us to be at rest. But -if we impel a body the contrary way, although the body -appears to us to have received by such an impulse as much -motion, as when impelled the other way; yet in this case we -have taken from the body so much real motion, as we seem -to have given it. Thus the motion, which we see in bodies,<span class="pagenum"><a name="Page_34" id="Page_34">[34]</a></span> -is not their real motion, but only relative with respect to us; -and the forementioned observations only shew us, that this -first law of motion has place in this relative or apparent -motion. However, though we cannot make any observation -immediately on the absolute motion of bodies, yet by -reasoning upon what we observe in visible motion, we can -discover the properties and effects of real motion.</p> - -<p>12. <span class="smcap gesperrt">With</span> regard to this first law of motion, which is -now under consideration, we may from the foregoing observations -most truly collect, that bodies are disposed to continue -in the absolute motion, which they have once received, -without increasing or diminishing their velocity. When a -body appears to us to lie at rest, it really preserves without -change the motion, which it has in common with our selves: -and when we put it into visible motion, and we see it continue -that motion; this proves, that the body retains that degree -of its absolute motion, into which it is put by our acting -upon it: if we give it such an apparent motion, which adds -to its real motion, it preserves that addition; and if our acting -on the body takes off from its real motion, it continues -afterwards to move with no more real motion, than we have -left it.</p> - -<p>13. <span class="smcap gesperrt">Again</span>, we do not observe in bodies any disposition or -power within themselves to change the direction of their motion; -and if they had any such power, it would easily be discovered. -For suppose a body by the structure or disposition -of its parts, or by any other circumstance in its make, was indued<span class="pagenum"><a name="Page_35" id="Page_35">[35]</a></span> -with a power of moving it self; this self-moving principle, -which should be thus inherent in the body, and not -depend on any thing external, must change the direction -wherein it would act, as often as the position of the body -was changed: so that for instance, if a body was lying before -me in such a position, that the direction, wherein this -principle disposes the body to move, was pointed directly from -me; if I then gradually turned the body about, the direction -of this self-moving principle would no longer be pointed directly -from me, but would turn about along with the body. -Now if any body, which appears to us at rest, were furnished -with any such self-moving principle; from the body’s appearing -without motion we must conclude, that this self-moving -principle lies directed the same way as the earth is carrying -the body; and such a body might immediately be put -into visible motion only by turning it about in any degree, -that this self-moving principle might receive a different direction.</p> - -<p>14. <span class="smcap gesperrt">From</span> these considerations it very plainly follows, -that if a body were once absolutely at rest; not being furnished -with any principle, whereby it could put it self into -motion, it must for ever continue in the same place, till acted -upon by something external: and also that when a body is put -into motion, it has no power within it self to make any -change in the direction of that motion; and consequently -that the body must move on straight forward without declining -any way whatever. But it has before been shewn, that -bodies do not appear to have in themselves any power to<span class="pagenum"><a name="Page_36" id="Page_36">[36]</a></span> -change the velocity of their motion: therefore this first law -of motion has been illustrated and confirmed, as much as can -be from the transient observations, which have here been discoursed -upon; and in the next chapter all this will be farther -established by more correct observations.</p> - -<p>15. <span class="smcap gesperrt">But</span> I shall now pass to the second law of motion; -wherein, when it is asserted, that the velocity, with which -any body is moved by the action of a power upon it, is proportional -to that power; the degree of power is supposed to -be measured by the greatness of the body, which it can move -with a given celerity. So that the sense of this law is, that -if any body were put into motion with that degree of swiftness, -as to pass in one hour the length of a thousand yards; -the power, which would give the same degree of velocity to -a body twice as great, would give this lesser body twice the -velocity, causing it to describe in the same space of an hour -two thousand yards. But by a body twice as great as another, -I do not here mean simply of twice the bulk, but one that -contains a double quantity of solid matter.</p> - -<p>16. <span class="smcap gesperrt">Why</span> the power, which can move a body twice as great -as another with the same degree of velocity, should be called -twice as great as the power, which can give the lesser body -the same velocity, is evident. For if we should suppose the -greater body to be divided into two equal parts, each equal -to the lesser body, each of these halves will require the same -degree of power to move them with the velocity of the lesser -body, as the lesser body it self requires; and therefore both<span class="pagenum"><a name="Page_37" id="Page_37">[37]</a></span> -those halves, or the whole greater body, will require the -moving power to be doubled.</p> - -<p>17. <span class="smcap gesperrt">That</span> the moving power being in this sense doubled, -should just double likewise the velocity of the same body, -seems near as evident, if we consider, that the effect of the -power applied must needs be the same, whether that power -be applied to the body at once, or in parts. Suppose then the -double power not applied to the body at once, but half of it -first, and afterwards the other half; it is not conceivable for -what reason the half last applied should come to have a different -effect upon the body, from that which is applied first; -as it must have, if the velocity of the body was not just doubled -by the application of it. So far as experience can determine, -we see nothing to favour such a supposition. We cannot -indeed (by reason of the constant motion of the earth) -make trial upon any body perfectly at rest, whereby to see -whether a power applied in that case would have a different -effect, from what it has, when the body is already moving; -but we find no alteration in the effect of the same power on -account of any difference there may be in the motion of the -body, when the power is applied. The earth does not always -carry bodies with the same degree of velocity; yet we -find the visible effects of any power applied to the same body -to be, at all times the very same: and a bale of goods, or -other moveable body lying in a ship is as easily removed -from place to place, while the ship is under sail, if its motion -be steady, as when it is fixed at anchor.</p> - -<p><span class="pagenum"><a name="Page_38" id="Page_38">[38]</a></span></p> - -<p>18. <span class="smcap gesperrt">Now</span> this experience is alone sufficient to shew to us -the whole of this law of motion.</p> - -<p>19. <span class="smcap gesperrt">Since</span> we find, that the same power will always produce -the same change in the motion of any body, whether -that body were before moving with a swifter or slower motion; -the change wrought in the motion of a body depends -only on the power applied to it, without any regard to the -body’s former motion: and therefore the degree of motion, -which the body already possesses, having no influence on the -power applied to disturb its operation, the effects of the -same power will not only be the same in all degrees of motion -of the body; but we have likewise no reason to doubt, -but that a body perfectly at rest would receive from any power -as much motion, as would be equivalent to the effect of the -same power applied to that body already in motion.</p> - -<p>20. <span class="smcap gesperrt">Again</span>, suppose a body being at rest, any number of -equal powers should be successively applied to it; pushing it -forward from time to time in the same course or direction. -Upon the application of the first power the body would begin -to move; when the second power was applied, it appears from -what has been said, that the motion of the body would become -double; the third power would treble the motion of the -body; and so on, till after the operation of the last power the -motion of the body would be as many times the motion, -which the first power gave it, as there are powers in number. -and the effect of this number of powers will be always the<span class="pagenum"><a name="Page_39" id="Page_39">[39]</a></span> -same, without any regard to the space of time taken up in -applying them: so that greater or lesser intervals between -the application of each of these powers will produce no difference -at all in their effects. Since therefore the distance of -time between the action of each power is of no consequence; -without doubt the effect will still be the same, though the -powers should all be applied at the very same instant; or although -a single power should be applied equal in strength to -the collective force of all these powers. Hence it plainly follows, -that the degree of motion, into which any body will -be put out of a state of rest by any power, will be proportional -to that power. A double power will give twice the velocity, -a treble power three times the velocity, and so on. The -foregoing reasoning will equally take place, though the body -were not supposed to be at rest, when the powers began to -be applied to it; provided the direction, in which the powers -were applied, either conspired with the action of the body, or -was directly opposite to it. Therefore if any power be applied -to a moving body, and act upon the body either in -the direction wherewith the body moves, so as to accelerate -the body; or if it act directly opposite to the motion of the -body, so as to retard it: in both these cases the change of -motion will be proportional to the power applied; nay, the -augmentation of the motion in one case, and the diminution -thereof in the other, will be equal to that degree of -motion, into which the same power would put the body, had -it been at rest, when the power was applied.</p> - -<p><span class="pagenum"><a name="Page_40" id="Page_40">[40]</a></span></p> - -<p>21. <span class="smcap gesperrt">Farther</span>, a power may be so applied to a moving -body, as to act obliquely to the motion of the body. And -the effects of such an oblique motion may be deduced from -this observation; that as all bodies are continually moving along -with the earth, we see that the visible effects of the same -power are always the same, in whatever direction the power -acts: and therefore the visible effects of any power upon a -body, which seems only to be at rest, is always to appearance -the same as the real effect would be upon a body truly at rest. -Now suppose a body were moving along the line A B (in -fig. 2.) and the eye accompanied it with an equal motion in -the line C D equidistant from A B; so that when the body is -at A, the eye shall be at C, and when the body is advanced to -E in the line A B, the eye shall be advanced to F in the line -C D, the distances A E and C F being equal. It is evident, -that here the body will appear to the eye to be at rest; and -the line F E G drawn from the eye through the body shall seem -to the eye to be immoveable; though as the body and eye -move forward together, this line shall really also move; so -that when the body shall be advanced to H and the eye to K, -the line F E G shall be transferred into the situation K H L, -this line K H L being equidistant from F E G. Now if the body -when at E were to receive an impulse in the direction of -the line F E G; while the eye is moving on from F to K and -carrying along with it the line F E G, the body will appear to -the eye to move along this line F E G: for this is what has just -now been said; that while bodies are moving along with the -earth, and the spectator’s eye partakes of the same motion, -the effect of any power upon the body will appear to be what<span class="pagenum"><a name="Page_41" id="Page_41">[41]</a></span> -it would really have been, had the body been truly at rest, -when the power was applied. From hence it follows, that -when the eye is advanced to K, the body will appear somewhere -in the line K H L. Suppose it appear in M; then it is -manifest, from what has been premised at the beginning of -this paragraph, that the distance H M is equal to what the -body would have run upon the line E G, during the time, -wherein the eye has passed from F to K, provided that the body -had been at rest, when acted upon in E. If it be farther -asked, after what manner the body has moved from E to M? -I answer, through a straight line; for it has been shewn above -in the explication of the first law of motion, that a moving -body, from the time it is left to it self, will proceed on in -one continued straight line.</p> - -<p>22. <span class="smcap gesperrt">If</span> E N be taken equal to H M and N M be drawn; -since H M is equidistant from E N, N M will be equidistant -from E H. Therefore the effect of any power upon a moving -body, when that power acts obliquely to the motion of the -body, is to be determined in this manner. Suppose the body -is moving along the straight line A E B, if when the body is -come to E, a power gives it an impulse in the direction of the -line E G, to find what course the body will afterwards take -we must proceed thus. Take in E B any length E H, and in -E G take such a length E N, that if the body had been at rest -in E, the power applied to it would have caused it to move -over E N in the same space of time, as it would have employed -in passing over E H, if the power had not acted at all upon it. -Then draw H L equidistant from E G, and N M equidistant<span class="pagenum"><a name="Page_42" id="Page_42">[42]</a></span> -from E B. After this, if a line be drawn from E to the -point M, where these two lines meet, the line E M will be the -course into which the body will be put by the action of the -power upon it at E.</p> - -<p>23. <span class="smcap gesperrt">A mathematical</span> reader would here expect in -some particulars more regular demonstrations; but as I do -not at present address my self to such, so I hope, what I have -now written will render my meaning evident enough to those, -who are unacquainted with that kind of reasoning.</p> - -<p>24. <span class="smcap gesperrt">Now</span> as we have been shewing, that some actual -force is necessary either to put bodies out of a state of rest into -motion, or to change the motion, which they have once -received; it is proper here to observe, that this quality in bodies, -whereby they preserve their present state, with regard -to motion or rest, till some active force disturb them, is called -the <span class="smcap"><em class="gesperrt">vis inertiae</em></span> of matter: and by this property, matter, -sluggish and unactive of it self, retains all the power impressed -upon it, and cannot be made to cease from action, but -by the opposition of as great a power, as that which first moved -it. By the degree of this <span class="smcap"><em class="gesperrt">vis inertiae</em></span>, or power of inactivity, -as we shall henceforth call it, we primarily judge of -the quantity of solid matter in each body; for as this quality is -inherent in all the bodies, upon which we can make any trial, -we conclude it to be a property essential to all matter; and -as we yet know no reason to suppose, that bodies are composed -of different kinds of matter, we rather presume, that -the matter of all bodies is the same; and that the degree of<span class="pagenum"><a name="Page_43" id="Page_43">[43]</a></span> -this power of inactivity is in every body proportional to the -quantity of the solid matter in it. But although we have no -absolute proof, that all the matter in the universe is uniform, -and possesses this power of inactivity in the same degree; yet -we can with certainty compare together the different degrees -of this power of inactivity in different bodies. Particularly -this power is proportional to the weight of bodies, as Sir <em class="gesperrt"><span class="smcap">Isaac -Newton</span></em> has demonstrated<a name="FNanchor_44_44" id="FNanchor_44_44"></a><a href="#Footnote_44_44" class="fnanchor">[44]</a>. However, notwithstanding -that this power of inactivity in any body can be more certainly -known, than the quantity of solid matter in it; yet since -there is no reason to suspect that one is not proportional to the -other, we shall hereafter speak without hesitation of the quantity -of matter in bodies, as the measure of the degree of their -power of inactivity.</p> - -<p>25. <span class="smcap gesperrt">This</span> being established, we may now compare the -effects of the same power upon different bodies, as hitherto -we have shewn the effects of different powers upon the -same body. And here if we limit the word motion to the -peculiar sense given to it in philosophy, we may comprehend -all that is to be said upon this head under one short precept; -that the same power, to whatever body it is applied, will always -produce the same degree of motion. But here motion -does not signify the degree of celerity or velocity with which -a body moves, in which sense only we have hitherto used it; -but it is made use of particularly in philosophy to signify the -force with which a body moves: as if two bodies A and B being<span class="pagenum"><a name="Page_44" id="Page_44">[44]</a></span> -in motion, twice the force would be required to stop A as -to stop B, the motion of A would be esteemed double the -motion of B. In moving bodies, these two things are carefully -to be distinguished; their velocity or celerity, which is -measured by the space they pass through during any determinate -portion of time; and the quantity of their motion, or -the force, with which they will press against any resistance. -Which force, when different bodies move with the same velocity, -is proportional to the quantity of solid matter in the -bodies; but if the bodies are equal, this force is proportional -to their respective velocities, and in other cases it is proportional -both to the quantity of solid matter in the body, and -also to its velocity. To instance in two bodies A and B: if A be -twice as great as B, and they have both the same velocity, the -motion of A shall be double the motion of B; and if the bodies -be equal, and the velocity of A be twice that of B, the -motion of A shall likewise be double that of B; but if A be -twice as large as B, and move twice as swift, the motion of A -will be four times the motion of B; and lastly, if A be twice -as large as B, and move but half as fast, the degree of their -motion shall be the same.</p> - -<p>26. <span class="smcap gesperrt">This</span> is the particular sense given to the word motion -by philosophers, and in this sense of the word the same power -always produces the same quantity or degree of motion. If -the same power act upon two bodies A and B, the velocities, -it shall give to each of them, shall be so adjusted to the respective -bodies, that the same degree of motion shall be produced -in each. If A be twice as great as B, its velocity shall be half<span class="pagenum"><a name="Page_45" id="Page_45">[45]</a></span> -that of B; if A has three times as much solid matter as B, the -velocity of A shall be one third of the velocity of B; and generally -the velocity given to A shall bear the same proportion -to the velocity given to B, as the quantity of solid matter contained -in the body B bears to the quantity of solid matter contained -in A.</p> - -<p>27. <span class="smcap gesperrt">The</span> reason of all this is evident from what has gone -before. If a power were applied to B, which should bear -the same proportion to the power applied to A, as the body B -bears to A, the bodies B and A would both receive the same -velocity; and the velocity, which B will receive from this -power, will bear the same proportion to the velocity, which -it would receive from the action of the power applied to A, -as the former of these powers bears to the latter: that is, -the velocity, which A receives from the power applied to it, -will bear to the velocity, which B would receive from -the same power, the same proportion as the body B bears -to A.</p> - -<p>28. <span class="smcap gesperrt">From</span> hence we may now pass to the third law of -motion, where this distinction between the velocity of a body -and its whole motion is farther necessary to be regarded, as -shall immediately be shewn; after having first illustrated the -meaning of this law by a familiar instance. If a stone or other -load be drawn by a horse; the load re-acts upon the horse, -as much as the horse acts upon the load; for the harness, -which is strained between them, presses against the horse as -much as against the load; and the progressive motion of the<span class="pagenum"><a name="Page_46" id="Page_46">[46]</a></span> -horse forward is hindred as much by the load, as the motion -of the load is promoted by the endeavour of the horse: that -is, if the horse put forth the same strength, when loosened -from the load, he would move himself forwards with greater -swiftness in proportion to the difference between the weight -of his own body and the weight of himself and load together.</p> - -<p>29. <span class="smcap gesperrt">This</span> instance will afford some general notion of the -meaning of this law. But to proceed to a more philosophical -explication: if a body in motion strike against another at -rest, let the body striking be ever so small, yet shall it communicate -some degree of motion to the body it strikes against, -though the less that body be in comparison of that it impinges -upon, and the less the velocity is, with which it moves, -the smaller will be the motion communicated. But whatever -degree of motion it gives to the resting body, the same it -shall lose it self. This is the necessary consequence of the -forementioned power of inactivity in matter. For suppose -the two bodies equal, it is evident from the time they meet, -both the bodies are to be moved by the single motion of the -first; therefore the body in motion by means of its power of -inactivity retaining the motion first given it, strikes upon the -other with the same force, wherewith it was acted upon it -self: but now both the bodies being to be moved by that -force, which before moved one only, the ensuing velocity -will be the same, as if the power, which was applied to one -of the bodies, and put it into motion, had been applied to -both; whence it appears, that they will proceed forwards,<span class="pagenum"><a name="Page_47" id="Page_47">[47]</a></span> -with half the velocity, which the body first in motion had: -that is, the body first moved will have lost half its motion, -and the other will have gained exactly as much. This rule -is just, provided the bodies keep contiguous after meeting; as -they would always do, if it were not for a certain cause that -often intervenes, and which must now be explained. Bodies -upon striking against each other, suffer an alteration in their -figure, having their parts pressed inwards by the stroke, which -for the most part recoil again afterwards, the bodies endeavouring -to recover their former shape. This power, whereby -bodies are inabled to regain their first figure, is usually called -their elasticity, and when it acts, it forces the bodies from -each other, and causes them to separate. Now the effect of -this elasticity in the present case is such, that if the bodies are -perfectly elastic, so as to recoil with as great a force as they -are bent with, that they recover their figure in the same space -of time, as has been taken up in the alteration made in it by -their compression together; then this power will separate the -bodies as swiftly, as they before approached, and acting upon -both equally, upon the body first in motion contrary to -the direction in which it moves, and upon the other as much -in the direction of its motion, it will take from the first, and -add to the other equal degrees of velocity: so that the power -being strong enough to separate them with as great a velocity, -as they approached with, the first will be quite stopt, and -that which was at rest, will receive all the motion of the -other. If the bodies are elastic in a less degree, the first will -not lose all its motion, nor will the other acquire the motion -of the first, but fall as much short of it, as the other retains.<span class="pagenum"><a name="Page_48" id="Page_48">[48]</a></span> -For this rule is never deviated from, that though the degree -of elasticity determines how much more than half its velocity -the body first in motion shall lose; yet in every case the -loss in the motion of this body shall be transferred to the other, -that other body always receiving by the stroke as much motion, -as is taken from the first.</p> - -<p>30. This is the case of a body striking directly against an -equal body at rest, and the reasoning here used is fully confirmed -by experience. There are many other cases of bodies -impinging against one another: but the mention of these -shall be reserved to the next chapter, where we intend to be -more particular and diffusive in the proof of these laws of motion, -than we have been here.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c48" id="c48"><span class="smcap">Chap. II.</span></a><br /> -Farther proofs of the <span class="smcap">Laws of Motion</span>.</h2> - -<p class="drop-cap06"><span class="gesperrt">HAVING</span> in the preceding chapter deduced the three -laws of motion, delivered by our great philosopher, -from the most obvious observations, that suggest them to us; -I now intend to give more particular proofs of them, by recounting -some of the discoveries which have been made in -philosophy before Sir Isaac Newton. For as they were -all collected by reasoning upon those laws; so the conformity -of these discoveries to experience makes them so many proofs -of the truth of the principles, from which they were derived.</p> - -<p><span class="pagenum"><a name="Page_49" id="Page_49">[49]</a></span></p> - -<p><a name="c49" id="c49"></a>2. <span class="smcap gesperrt">Let</span> us begin with the subject, which concluded the -last chapter. Although the body in motion be not equal to -the body at rest, on which it strikes; yet the motion after -the stroke is to be estimated in the same manner as above. -Let A (in fig. 3.) be a body in motion towards another body -B lying at rest. When A is arrived at B, it cannot proceed -farther without putting B into motion; and what motion it -gives to B, it must lose it self, that the whole degree of motion -of A and B together, if neither of the bodies be elastic, -shall be equal, after the meeting of the bodies, to the single -motion of A before the stroke. Therefore, from what has -been said above, it is manifest, that as soon as the two bodies -are met, they will move on together with a velocity, which -will bear the same proportion to the original velocity of A, as -the body A bears to the sum of both the bodies.</p> - -<p>3. <span class="smcap gesperrt">If</span> the bodies are elastic, so that they shall separate after -the stroke, A must lose a greater part of its motion, and -the subsequent motion of B will be augmented by this elasticity, -as much as the motion of A is diminished by it. The -elasticity acting equally between both the bodies, it will communicate -to each the same degree of motion; that is, it will -separate the bodies by taking from the body A and adding to -the body B different degrees of velocity, so proportioned to -their respective quantities of matter, that the degree of motion, -wherewith A separates from B, shall be equal to the degree -of motion, wherewith B separates from A. It follows -therefore, that the velocity taken from A by the elasticity -bears to the velocity, which the same elasticity adds to B, the<span class="pagenum"><a name="Page_50" id="Page_50">[50]</a></span> -same proportion, as B bears to A: consequently the velocity, -which the elasticity takes from A, will bear the same proportion -to the whole velocity, wherewith this elasticity causes the -two bodies to separate from each other, as the body B bears to -the sum of the two bodies A and B; and the velocity, which -is added to B by the elasticity, bears to the velocity, wherewith -the bodies separate, the same proportion, as the body A -bears to the sum of the two bodies A and B. Thus is found, -how much the elasticity takes from the velocity of A, and -adds to the velocity of B; provided the degree of elasticity be -known, whereby to determine the whole velocity wherewith -the bodies separate from each other after the stroke<a name="FNanchor_45_45" id="FNanchor_45_45"></a><a href="#Footnote_45_45" class="fnanchor">[45]</a>.</p> - -<p>4. <span class="smcap gesperrt">After</span> this manner is determined in every case the result -of a body in motion striking against another at rest. The -same principles will also determine the effects, when both -bodies are in motion.</p> - -<p>5. <span class="smcap gesperrt">Let</span> two equal bodies move against each other with equal -swiftness. Then the force, with which each of them -presses forwards, being equal when they strike; each pressing -in its own direction with the same energy, neither shall -surmount the other, but both be stopt, if they be not elastic: -for if they be elastic, they shall from thence recover new motion, -and recede from each other, as swiftly as they met, if -they be perfectly elastic; but more slowly, if less so. In the -same manner, if two bodies of unequal bigness strike against -each other, and their velocities be so related, that the velocity<span class="pagenum"><a name="Page_51" id="Page_51">[51]</a></span> -of the lesser body shall exceed the velocity of the greater in -the same proportion, as the greater body exceeds the lesser (for -instance, if one body contains twice the solid matter as the other, -and moves but half as fast) two such bodies will entirely -suppress each other’s motion, and remain from the time of -their meeting fixed; if, as before, they are not elastic: but, -if they are so in the highest degree, they shall recede again, -each with the same velocity, wherewith they met. For this -elastic power, as in the preceding case, shall renew their motion, -and pressing equally upon both, shall give the same motion -to both; that is, shall cause the velocity, which the lesser -body receives, to bear the same proportion to the velocity, -which the greater receives, as the greater body bears to the -lesser: so that the velocities shall bear the same proportion to -each other after the stroke, as before. Therefore if the bodies, -by being perfectly elastic, have the sum of their velocities -after the stroke equal to the sum of their velocities before the -stroke, each body after the stroke will receive its first velocity. -And the same proportion will hold likewise between the -velocities, wherewith they go off, though they are elastic but -in a less degree; only then the velocity of each will be less in -proportion to the defect of elasticity.</p> - -<p>6. <span class="smcap gesperrt">If</span> the velocities, wherewith the bodies meet, are not -in the proportion here supposed; but if one of the bodies, as -A, has a swifter velocity in comparison to the velocity of the -other; then the effect of this excess of velocity in the body A -must be joined to the effect now mentioned, after the manner -of this following example. Let A be twice as great as B, and<span class="pagenum"><a name="Page_52" id="Page_52">[52]</a></span> -move with the same swiftness as B. Here A moves with twice -that degree of swiftness, which would answer to the forementioned -proportion. For A being double to B, if it moved -but with half the swiftness, wherewith B advances, it has been -just now shewn, that the two bodies upon meeting would -stop, if they were not elastic; and if they were elastic, that -they would each recoil, so as to cause A to return with half -the velocity, wherewith B would return. But it is evident -from hence, that B by encountring A will annul half its velocity, -if the bodies be not elastic; and the future motion of the -bodies will be the same, as if A had advanced against B at -rest with half the velocity here assigned to it. If the bodies -be elastic, the velocity of A and B after the stroke may be thus -discovered. As the two bodies advance against each other, -the velocity, with which they meet, is made up of the velocities -of both bodies added together. After the stroke their -elasticity will separate them again. The degree of elasticity -will determine what proportion the velocity, wherewith they -separate, must bear to that, wherewith they meet. Divide -this velocity, with which the bodies separate into two parts, -that one of the parts bear to the other the same proportion, as -the body A bears to B; and ascribe the lesser part to the greater -body A, and the greater part of the velocity to the lesser -body B. Then take the part ascribed to A from the common -velocity, which A and B would have had after the stroke, if -they had not been elastic; and add the part ascribed to B to -the same common velocity. By this means the true velocities -of A and B after the stroke will be made known.</p> - -<p><span class="pagenum"><a name="Page_53" id="Page_53">[53]</a></span></p> - -<p>7. <span class="smcap gesperrt">If</span> the bodies are perfectly elastic, the great <span class="smcap"><em class="gesperrt">Huygens</em></span> -has laid down this rule for finding their motion after concourse<a name="FNanchor_46_46" id="FNanchor_46_46"></a><a href="#Footnote_46_46" class="fnanchor">[46]</a>. -Any straight line C D (in fig. 4, 5.) being drawn, -let it be divided in E, that C E bear the same proportion to -E D, as the swiftness of A bore to the swiftness of B before the -stroke. Let the same line C D be also divided in F, that C F -bear the same proportion to F D, as the body B bears to the -body A. Then F G being taken equal to F E, if the point G -falls within the line C D, both the bodies shall recoil after the -stroke, and the velocity, wherewith the body A shall return, -will bear the same proportion to the velocity, wherewith B -shall return, as G C bears to G D; but if the point G falls without -the line C D, then the bodies after their concourse shall -both proceed to move the same way, and the velocity of A -shall bear to the velocity of B the same proportion, that G C -bears to G D, as before.</p> - -<p>8. <span class="smcap gesperrt">If</span> the body B had stood still, and received the impulse -of the other body A upon it; the effect has been already explained -in the case, when the bodies are not elastic. And -when they are elastic, the result of their collision is found by -combining the effect of the elasticity with the other effect, in -the same manner as in the last case.</p> - -<p>9. <span class="smcap gesperrt">When</span> the bodies are perfectly elastic, the rule of -<span class="smcap"><em class="gesperrt">Huygens</em></span><a name="FNanchor_47_47" id="FNanchor_47_47"></a><a href="#Footnote_47_47" class="fnanchor">[47]</a> here is to divide the line C D (fig. 6.) in E as -before, and to take E G equal to E D. And by these points<span class="pagenum"><a name="Page_54" id="Page_54">[54]</a></span> -thus found, the motion of each body after the stroke is determined, -as before.</p> - -<p>10. <span class="smcap gesperrt">In</span> the next place, suppose the bodies A and B were -both moving the same way, but A with a swifter motion, so -as to overtake B, and strike against it. The effect of the percussion -or stroke, when the bodies are not elastic, is discovered -by finding the common motion, which the two bodies -would have after the stroke, if B were at rest, and A were to -advance against it with a velocity equal to the excess of the -present velocity of A above the velocity of B; and by adding -to this common velocity thus found the velocity of B.</p> - -<p>11. <span class="smcap gesperrt">If</span> the bodies are elastic, the effect of the elasticity is -to be united with this other, as in the former cases.</p> - -<p>12. <span class="smcap gesperrt">When</span> the bodies are perfectly elastic, the rule of -<span class="smcap">Huygens</span><a name="FNanchor_48_48" id="FNanchor_48_48"></a><a href="#Footnote_48_48" class="fnanchor">[48]</a> in this case is to prolong C D (fig. 7.) and to -take in it thus prolonged C E in the same proportion to E D, -as the greater velocity of A bears to the lesser velocity of B; -after which F G being taken equal to F E, the velocities of the -two bodies after the stroke will be determined, as in the two -preceding cases.</p> - -<p>13. <span class="smcap gesperrt">Thus</span> I have given the sum of what has been written -concerning the effects of percussion, when two bodies -freely in motion strike directly against each other; and the -results here set down, as the consequence of our reasoning<span class="pagenum"><a name="Page_55" id="Page_55">[55]</a></span> -from the laws of motion, answer most exactly to experience. -A particular set of experiments has been invented to make -trial of these effects of percussion with the greatest exactness. -But I must defer these experiments, till I have explained the -nature of pendulums<a name="FNanchor_49_49" id="FNanchor_49_49"></a><a href="#Footnote_49_49" class="fnanchor">[49]</a>. I shall therefore now proceed to describe -some of the appearances, which are caused in bodies -from the influence of the power of gravity united with the -general laws of motion; among which the motion of the -pendulum will be included.</p> - -<p><a name="c55" id="c55">14.</a> <span class="smcap gesperrt">The</span> most simple of these appearances is, when bodies -fall down merely by their weight. In this case the body -increases continually its velocity, during the whole time of its -fall, and that in the very same proportion as the time increases. -For the power of gravity acts constantly on the body with -the same degree of strength: and it has been observed above -in the first law of motion, that a body being once in motion -will perpetually preserve that motion without the continuance -of any external influence upon it: therefore, after a body has -been once put in motion by the force of gravity, the body -would continue that motion, though the power of gravity -should cease to act any farther upon it; but, if the power of -gravity continues still to draw the body down, fresh degrees -of motion must continually be added to the body; and the -power of gravity acting at all times with the same strength, -equal degrees of motion will constantly be added in equal -portions of time.</p> - -<p><span class="pagenum"><a name="Page_56" id="Page_56">[56]</a></span></p> - -<p>15. <span class="smcap gesperrt">This</span> conclusion is not indeed absolutely true: for we -shall find hereafter<a name="FNanchor_50_50" id="FNanchor_50_50"></a><a href="#Footnote_50_50" class="fnanchor">[50]</a>, that the power of gravity is not of the -same strength at all distances from the center of the earth. But -nothing of this is in the least sensible in any distance, to which -we can convey bodies. The weight of bodies is the very same -to sense upon the highest towers or mountains, as upon the -level ground; so that in all the observations we can make, -the forementioned proportion between the velocity of a falling -body and the time, in which it has been descending, obtains -without any the least perceptible difference.</p> - -<p>16. <span class="smcap gesperrt">From</span> hence it follows, that the space, through which -a body falls, is not proportional to the time of the fall; for -since the body increases its velocity, a greater space will be -passed over in the same portion of time at the latter part of the -fall, than at the beginning. Suppose a body let fall from the -point A (in fig. 8.) were to descend from A to B in any portion -of time; then if in an equal portion of time it were to -proceed from B to C; I say, the space B C is greater than A B; -so that the time of the fall from A to C being double the time -of the fall from A to B, A C shall be more than double of A B.</p> - -<p>17. <span class="smcap gesperrt">The</span> geometers have proved, that the spaces, through -which bodies fall thus by their weight, are just in a duplicate -or two-fold proportion of the times, in which the body has -been falling. That is, if we were to take the line D E in the -same proportion to A B, as the time, which the body has imployed -in falling from A to C, bears to the time of the fall<span class="pagenum"><a name="Page_57" id="Page_57">[57]</a></span> -from A to B; then A C will be to D E in the same proportion. -In particular, if the time of the fall through A C be twice the -time of the fall through A B; then D E will be twice A B, and -A C twice D E; or A C four times A B. But if the time of the -fall through A C had been thrice the time of the fall through -A B; D E would have been treble of A B, and A C treble of -D E; that is, A C would have been equal to nine times A B.</p> - -<p><a name="c57" id="c57">18.</a> <span class="smcap gesperrt">If</span> a body fall obliquely, it will approach the ground -by slower degrees, than when it falls perpendicularly. Suppose -two lines A B, A C (in fig. 9.) were drawn, one perpendicular, -and the other oblique to the ground D E: then if a -body were to descend in the slanting line A C; because the -power of gravity draws the body directly downwards, if the -line A C supports the body from falling in that manner, it -must take off part of the effect of the power of gravity; so -that in the time, which would have been sufficient for the -body to have fallen through the whole perpendicular line A B, -the body shall not have passed in the line A C a length equal -to A B; consequently the line A C being longer than A B, -the body shall most certainly take up more time in passing -through A C, than it would have done in falling perpendicularly -down through A B.</p> - -<p>19. <span class="smcap gesperrt">The</span> geometers demonstrate, that the time, in which -the body will descend through the oblique straight line A C, -bears the same proportion to the time of its descent through -the perpendicular A B, as the line it self A C bears to A B. -And in respect to the velocity, which the body will have acquired<span class="pagenum"><a name="Page_58" id="Page_58">[58]</a></span> -in the point C, they likewise prove, that the length of -the time imployed in the descent through A C so compensates -the diminution of the influence of gravity from the obliquity -of this line, that though the force of the power of gravity on -the body is opposed by the obliquity of the line A C, yet the -time of the body’s descent shall be so much prolonged, that -the body shall acquire the very same velocity in the point C, -as it would have got at the point B by falling perpendicularly -down.</p> - -<p><a name="c58a" id="c58a">20.</a> <span class="smcap gesperrt">If</span> a body were to descend in a crooked line, the time -of its descent cannot be determined in so simple a manner; -but the same property, in relation to the velocity, is demonstrated -to take place in all cases: that is, in whatever line the -body descends, the velocity will always be answerable to the -perpendicular height, from which the body has fell. For instance, -suppose the body A (in fig. 10.) were hung by a -string to the pin B. If this body were let fall, till it came to -the point C perpendicularly under B, it will have moved from -A to C in the arch of a circle. Then the horizontal line A D -being drawn, the velocity of the body in C will be the same, -as if it had fallen from the point D directly down to C.</p> - -<p><a name="c58b" id="c58b">21.</a> <span class="smcap gesperrt">If</span> a body be thrown perpendicularly upward with any -force, the velocity, wherewith the body ascends, shall -continually diminish, till at length it be wholly taken away; -and from that time the body will begin to fall down again, -and pass over a second time in its descent the line, wherein it -ascended; falling through this line with an increasing velocity -in such a manner, that in every point thereof, through<span class="pagenum"><a name="Page_59" id="Page_59">[59]</a></span> -which it falls, it shall have the very same velocity, as it had in -the same place, when it ascended; and consequently shall come -down into the place, whence it first ascended, with the velocity -which was at first given to it. Thus if a body were thrown -perpendicularly up in the line A B (in fig. II.) with such a -force, as that it should stop at the point B, and there begin -to fall again; when it shall have arrived in its descent to any -point as C in this line, it shall there have the same velocity, -as that wherewith it passed by this point C in its ascent; and -at the point A it shall have gained as great a velocity, as -that wherewith it was first thrown upwards. As this is demonstrated -by the geometrical writers; so, I think, it will -appear evident, by considering only, that while the body descends, -the power of gravity must act over again, in an inverted -order, all the influence it had on the body in its ascent; -so as to give again to the body the same degrees of velocity, -which it had taken away before.</p> - -<p>22. <span class="smcap gesperrt">After</span> the same manner, if the body were thrown -upwards in the oblique straight line C A (in fig. 9.) from the -point C, with such a degree of velocity as just to reach the -point A; it shall by its own weight return again through the -line A C by the same degrees, as it ascended.</p> - -<p><a name="c59" id="c59">23.</a> <span class="smcap gesperrt">And</span> lastly, if a body were thrown with any velocity -in a line continually incurvated upwards, the like effect will -be produced upon its return to the point, whence it was -thrown. Suppose for instance, the body A (in fig. 12.) were -hung by a string A B. Then if this body be impelled any<span class="pagenum"><a name="Page_60" id="Page_60">[60]</a></span> -way, it must move in the arch of a circle. Let it receive such -an impulse, as shall cause it to move in the arch A C; and let -this impulse be of such strength, that the body may be carried -from A as far as D, before its motion is overcome by its -weight: I say here, that the body forthwith returning from -D, shall come again into the point A with the same velocity, -as that wherewith it began to move.</p> - -<p><a name="c60" id="c60">24.</a> <span class="smcap gesperrt">It</span> will be proper in this place to observe concerning -the power of gravity, that its force upon any body does not -at all depend upon the shape of the body; but that it continues -constantly the same without any variation in the same -body, whatever change be made in the figure of the body: and -if the body be divided into any number of pieces, all those -pieces shall weigh just the same, as they did, when united -together in one body: and if the body be of a uniform contexture, -the weight of each piece will be proportional to its -bulk. This has given reason to conclude, that the power of -gravity acts upon bodies in proportion to the quantity of matter -in them. Whence it should follow, that all bodies must -fall from equal heights in the same space of time. And as -we evidently see the contrary in feathers and such like substances, -which fall very slowly in comparison of more solid -bodies; it is reasonable to suppose, that some other cause concurs -to make so manifest a difference. This cause has been -found by particular experiments to be the air. The experiments -for this purpose are made thus. They set up a very -tall hollow glass; within which near the top they lodge a feather -and some very ponderous body, usually a piece of gold,<span class="pagenum"><a name="Page_61" id="Page_61">[61]</a></span> -this metal being the most weighty of any body known to us. -This glass they empty of the air contained within it, and by -moving a wire, which passes through the top of the glass, they -let the feather and the heavy body fall together; and it is always -found, that as the two bodies begin to descend at the -same time, so they accompany each other in the fall, and -come to the bottom at the very same instant, as near as the eye -can judge. Thus, as far as this experiment can be depended -on, it is certain, that the effect of the power of gravity upon -each body is proportional to the quantity of solid matter, or to -the power of inactivity in each body. For in the limited -sense, which we have given above to the word motion, it has -been shown, that the same force gives to all bodies the same -degree of motion, and different forces communicate different -degrees of motion proportional to the respective powers<a name="FNanchor_51_51" id="FNanchor_51_51"></a><a href="#Footnote_51_51" class="fnanchor">[51]</a>. In -this case, if the power of gravity were to act equally upon the -feather, and upon the more solid body, the solid body would -descend so much slower than the feather, as to have no greater -degree of motion than the feather: but as both bodies descend -with equal swiftness, the degree of motion in the solid -body is greater than in the feather, bearing the same proportion -to it, as the quantity of matter in the solid body to the -quantity of matter in the feather. Therefore the effect of -gravity on the solid body is greater than on the feather, in proportion -to the greater degree of motion communicated; that -is, the effect of the power of gravity on the solid body bears -the same proportion to its effect on the feather, as the quantity<span class="pagenum"><a name="Page_62" id="Page_62">[62]</a></span> -of matter in the solid body bears to the quantity of matter -in the feather. Thus it is the proper deduction from this experiment, -that the power of gravity acts not on the surface of bodies -only, but penetrates the bodies themselves most intimately, -and operates alike on every particle of matter in them. But -as the great quickness, with which the bodies fall, leaves it -something uncertain, whether they do descend absolutely in -the same time, or only so nearly together, that the difference -in their swift motion is not discernable to the eye; this property -of the power of gravity, which has here been deduced -from this experiment, is farther confirmed by pendulums, -whose motion is such, that a very minute difference would -become sufficiently sensible. This will be farther discoursed -on in another place<a name="FNanchor_52_52" id="FNanchor_52_52"></a><a href="#Footnote_52_52" class="fnanchor">[52]</a>; but here I shall make use of the principle -now laid down to explain the nature of what is called -the center of gravity in bodies.</p> - -<p><a name="c62" id="c62">25.</a> <span class="smcap gesperrt">The</span> center of gravity is that point, by which if a -body be suspended, it shall hang at rest in any situation. In -a globe of a uniform texture the center of gravity is the same -with the center of the globe; for as the parts of the globe on -every side of its center are similarly disposed, and the power -of gravity acts alike on every part; it is evident, that the parts -of the globe on each side of the center are drawn with equal -force, and therefore neither side can yield to the other; but -the globe, if supported at its center, must of necessity hang -at rest. In like manner, if two equal bodies A and B (in<span class="pagenum"><a name="Page_63" id="Page_63">[63]</a></span> -fig. 13.) be hung at the extremities of an inflexible rod C D, -which should have no weight; these bodies, if the rod be -supported at its middle E, shall equiponderate; and the rod -remain without motion. For the bodies being equal and at -the same distance from the point of support E, the power of -gravity will act upon each with equal strength, and in all respects -under the same circumstances; therefore the weight of -one cannot overcome the weight of the other. The weight -of A can no more surmount the weight of B, than the weight -of B can surmount the weight of A. Again, suppose a body -as A B (in fig. 14.) of a uniform texture in the form of a -roller, or as it is more usually called a cylinder, lying horizontally. -If a straight line be drawn between C and D, the -centers of the extreme circles of this cylinder; and if this -straight line, commonly called the axis of the cylinder, be -divided into two equal parts in E: this point E will be the -center of gravity of the cylinder. The cylinder being a uniform -figure, the parts on each side of the point E are equal, and -situated in a perfectly similar manner; therefore this cylinder, -if supported at the point E, must hang at rest, for the -same reason as the inflexible rod above-mentioned will remain -without motion, when suspended at its middle point. And -it is evident, that the force applied to the point E, which -would uphold the cylinder, must be equal to the cylinder’s -weight. Now suppose two cylinders of equal thickness A B -and C D to be joined together at C B, so that the two axis’s -E F, and F G lie in one straight line. Let the axis E F be divided -into two equal parts at H, and the axis F G into two<span class="pagenum"><a name="Page_64" id="Page_64">[64]</a></span> -equal parts at I. Then because the cylinder A B would be -upheld at rest by a power applied in H equal to the weight of -this cylinder, and the cylinder C D would likewise be upheld -by a power applied in I equal to the weight of this cylinder; -the whole cylinder A D will be supported by these two powers: -but the whole cylinder may likewise be supported by a power -applied to K, the middle point of the whole axis E G, provided -that power be equal to the weight of the whole cylinder. It -is evident therefore, that this power applied in K will produce -the same effect, as the two other powers applied in H and I. It -is farther to be observed, that H K is equal to half F G, and -K I equal to half E F; for E K being equal to half E G, and E H -equal to half E F, the remainder H K must be equal to half -the remainder F G; so likewise G K being equal to half G E, -and G I equal to half G F, the remainder I K must be equal to -half the remainder E F. It follows therefore, that H K bears -the same proportion to K I, as F G bears to E F. Besides, I -believe, my readers will perceive, and it is demonstrated in -form by the geometers, that the whole body of the cylinder -C D bears the same proportion to the whole body of the cylinder -A B, as the axis F G bears to the axis E F<a name="FNanchor_53_53" id="FNanchor_53_53"></a><a href="#Footnote_53_53" class="fnanchor">[53]</a>. But hence -it follows, that in the two powers applied at H and I, the -power applied at H bears the same proportion to the power -applied at I, as K I bears to K H. Now suppose two strings -H L and I M extended upwards, one from the point H and the -other from I, and to be laid hold on by two powers, one -strong enough to hold up the cylinder A B, and the other of<span class="pagenum"><a name="Page_65" id="Page_65">[65]</a></span> -strength sufficient to support the cylinder C D. Here as these -two powers uphold the whole cylinder, and therefore produce -an effect, equal to what would have been produced by -a power applied to the point K of sufficient force to sustain the -whole cylinder: it is manifest, that if the cylinder be taken -away, the axis only being left, and from the point K a string, -as K N, be extended, which shall be drawn down by a power -equivalent to the weight of the cylinder, this power shall act -against the other two powers, as much as the cylinder acted -against them; and consequently these three powers shall be -upon a balance, and hold the axis H I fixed between them. -But if these three powers preserve a mutual balance, the -two powers applied to the strings H L and I M are a balance -to each other; the power applied to the string H L bearing -the same proportion to the power applied to the string I M, -as the distance I K bears to the distance K H. Hence it farther -appears, that if an inflexible rod A B (in fig. 15.) be -suspended by any point C not in the middle thereof; and if -at A the end of the shorter arm be hung a weight, and at B -the end of the longer arm be also hung a weight less than -the other, and that the greater of these weights bears to the -lesser the same proportion, as the longer arm of the rod bears -to the shorter; then these two weights will equiponderate: -for a power applied at C equal to both these weights will support -without motion the rod thus charged; since here nothing -is changed from the preceding case but the situation -of the powers, which are now placed on the contrary -sides of the line, to which they are fixed. Also for the<span class="pagenum"><a name="Page_66" id="Page_66">[66]</a></span> -same reason, if two weights A and B (in fig. 16.) were connected -together by an inflexible rod C D, drawn from C the -center of gravity of A to D the center of gravity of B; and -if the rod C D were to be so divided in E, that the part D E -bear the same proportion to the other part C E, as the weight -A bears to the weight B: then this rod being supported at E -will uphold the weights, and keep them at rest without motion. -This point E, by which the two bodies A and B will be -supported, is called their common center of gravity. And if -a greater number of bodies were joined together, the point, by -which they could all be supported, is called the common center -of gravity of them all. Suppose (in fig. 17.) there were three -bodies A, B, C, whose respective centers of gravity were joined -by the three lines D E, D F, E F: the line D E being so divided -in G, that D G bear the same proportion to G E, as B bears to -A; G is the center of gravity common to the two bodies A -and B; that is, a power equal to the weight of both the bodies -applied to G would support them, and the point G is -pressed as much by the two weights A and B, as it would be, -if they were both hung together at that point. Therefore, -if a line be drawn from G to F, and divided in H, so that G H -bear the same proportion to H F, as the weight C bears to -both the weights A and B, the point H will be the common -center of gravity of all the three weights; for H would be -their common center of gravity, if both the weights A and B -were hung together at G, and the point G is pressed as much -by them in their present situation, as it would be in that case. -In the same manner from the common center of these three<span class="pagenum"><a name="Page_67" id="Page_67">[67]</a></span> -weights, you might proceed to find the common center, if a -fourth weight were added, and by a gradual progress might -find the common center of gravity belonging to any number -of weights whatever.</p> - -<p>26. <span class="smcap gesperrt">As</span> all this is the obvious consequence of the proposition -laid down for assigning the common center of gravity of -any two weights, by the same proposition the center of gravity -of all figures is found. In a triangle, as A B C (in -fig. 18.) the center of gravity lies in the line drawn from the -middle point of any one of the sides to the opposite angle, -as the line B D is drawn from D the middle of the line A C to -the opposite angle B<a name="FNanchor_54_54" id="FNanchor_54_54"></a><a href="#Footnote_54_54" class="fnanchor">[54]</a>; so that if from the middle of either -of the other sides, as from the point E in the side A B, a line -be drawn, as E C, to the opposite angle; the point F, where -this line crosses the other line B D, will be the center of gravity -of the triangle<a name="FNanchor_55_55" id="FNanchor_55_55"></a><a href="#Footnote_55_55" class="fnanchor">[55]</a>. Likewise D F is equal to half F B, and -E F equal to half F C<a name="FNanchor_56_56" id="FNanchor_56_56"></a><a href="#Footnote_56_56" class="fnanchor">[56]</a>. In a hemisphere, as A B C (fig. 19.) -if from D the center of the base the line D B be erected perpendicular -to that base, and this line be so divided in E, that -D E be equal to three fifths of B E, the point E is the center of -gravity of the hemisphere<a name="FNanchor_57_57" id="FNanchor_57_57"></a><a href="#Footnote_57_57" class="fnanchor">[57]</a>.</p> - -<p>27. <span class="smcap gesperrt">It</span> will be of use to observe concerning the center of -gravity of bodies; that since a power applied to this center -alone can support a body against the power of gravity, and<span class="pagenum"><a name="Page_68" id="Page_68">[68]</a></span> -hold it fixed at rest; the effect of the power of gravity on a -body is the same, as if that whole power were to exert itself -on the center of gravity only. Whence it follows, that, when -the power of gravity acts on a body suspended by any point, -if the body is so suspended, that the center of gravity of the -body can descend; the power of gravity will give motion to -that body, otherwise not: or if a number of bodies are so -connected together, that, when any one is put into motion, -the rest shall, by the manner of their being joined, receive -such motion, as shall keep their common center of gravity at -rest; then the power of gravity shall not be able to produce -any motion in these bodies, but in all other cases it will. -Thus, if the body A B (in fig. 20, 21.) whose center of gravity -is C, be hung on the point A, and the center C be perpendicularly -under A (as in fig. 20.) the weight of the body -will hold it still without motion, because the center C -cannot descend any lower. But if the body be removed into -any other situation, where the center C is not perpendicularly -under A (as in fig. 21.) the body by its weight will -be put into motion towards the perpendicular situation of its -center of gravity. Also if two bodies A, B (in fig. 22.) be -joined together by the rod C D lying in an horizontal situation, -and be supported at the point E; if this point be the -center of gravity common to the two bodies, their weight -will not put them into motion; but if this point E is not their -common center of gravity, the bodies will move; that part -of the rod C D descending, in which the common center of -gravity is found. So in like manner, if these two bodies were -connected together by any more complex contrivance; yet<span class="pagenum"><a name="Page_69" id="Page_69">[69]</a></span> -if one of the bodies cannot move without so moving the -other, that their common center of gravity shall rest, the -weight of the bodies will not put them in motion, otherwise -it will.</p> - -<p><a name="c69" id="c69">28.</a> <span class="smcap gesperrt">I shall</span> proceed in the next place to speak of the mechanical -powers. These are certain instruments or machines, -contrived for the moving great weights with small force; and -their effects are all deducible from the observation we have -just been making. They are usually reckoned in number -five; the lever, the wheel and axis, the pulley, the wedge, -and the screw; to which some add the inclined plane. As -these instruments have been of very ancient use, so the celebrated -<em class="gesperrt"><span class="smcap">Archimedes</span></em> seems to have been the first, who discovered -the true reason of their effects. This, I think, may be -collected from what is related of him, that some expressions, -which he used to denote the unlimited force of these instruments, -were received as very extraordinary paradoxes: -whereas to those, who had understood the cause of their -great force, no expressions of that kind could have appeared -surprizing.</p> - -<p>29. <span class="smcap gesperrt">All</span> the effects of these powers may be judged of by -this one rule, that, when two weights are applied to any of -these instruments, the weights will equiponderate, if, when -put into motion, their velocities will be reciprocally proportional -to their respective weights. And what is said of weights, -must of necessity be equally understood of any other forces<span class="pagenum"><a name="Page_70" id="Page_70">[70]</a></span> -equivalent to weights, such as the force of a man’s arm, a -stream of water, or the like.</p> - -<p>30. <span class="smcap gesperrt">But</span> to comprehend the meaning of this rule, the -reader must know, what is to be understood by reciprocal -proportion; which I shall now endeavour to explain, as distinctly -as I can; for I shall be obliged very frequently to -make use of this term. When any two things are so related, -that one increases in the same proportion as the other, they are -directly proportional. So if any number of men can perform -in a determined space of time a certain quantity of any work, -suppose drain a fish-pond, or the like; and twice the number -of men can perform twice the quantity of the same work, -in the same time; and three times the number of men can -perform as soon thrice the work; here the number of men -and the quantity of the work are directly proportional. On -the other hand, when two things are so related, that one decreases -in the same proportion, as the other increases, they -are said to be reciprocally proportional. Thus if twice the -number of men can perform the same work in half the time, -and three times the number of men can finish the same in a -third part of the time; then the number of men and the -time are reciprocally proportional. We shewed above<a name="FNanchor_58_58" id="FNanchor_58_58"></a><a href="#Footnote_58_58" class="fnanchor">[58]</a> how -to find the common center of gravity of two bodies, there -the distances of that common center from the centers of gravity -of the two bodies are reciprocally proportional to the respective -bodies. For C E in fig. 16. being in the same proportion<span class="pagenum"><a name="Page_71" id="Page_71">[71]</a></span> -to E D, as B bears to A; C E is so much greater in -proportion than E D, as A is less in proportion than B.</p> - -<p>31. <span class="smcap gesperrt">Now</span> this being understood, the reason of the rule -here stated will easily appear. For if these two bodies were -put in motion, while the point E rested, the velocity, wherewith -A would move, would bear the same proportion to the -velocity, wherewith B would move, as E C bears to E D. The -velocity therefore of each body, when the common center -of gravity rests, is reciprocally proportional to the body. But -we have shewn above<a name="FNanchor_59_59" id="FNanchor_59_59"></a><a href="#Footnote_59_59" class="fnanchor">[59]</a>, that if two bodies are so connected together, -that the putting them in motion will not move their -common center of gravity; the weight of those bodies will -not produce in them any motion. Therefore in any of these -mechanical engines, if, when the bodies are put into motion, -their velocities are reciprocally proportional to their respective -weights, whereby the common center of gravity would remain -at rest; the bodies will not receive any motion from their -weight, that is, they will equiponderate. But this perhaps -will be yet more clearly conceived by the particular description -of each mechanical power.</p> - -<p><a name="c71" id="c71">32.</a> <span class="smcap gesperrt">The</span> lever was first named above. This is a bar made -use of to sustain and move great weights. The bar is applied -in one part to some strong support; as the bar A B (in -fig. 23, 24.) is applied at the point C to the support D. In -some other part of the bar, as E, is applied the weight to be -sustained or moved; and in a third place, as F, is applied another -weight or equivalent force, which is to sustain or move<span class="pagenum"><a name="Page_72" id="Page_72">[72]</a></span> -the weight at E. Now here, if, when the level should be -put in motion, and turned upon the point C, the velocity, -wherewith the point F would move, bears the same proportion -to the velocity, wherewith the point E would move, as -the weight at E bears to the weight or force at F; then the -lever thus charged will have no propensity to move either -way. If the weight or other force at F be not so great as to -bear this proportion, the weight at E will not be sustained; -but if the force at F be greater than this, the weight at E will -be surmounted. This is evident from what has been said -above<a name="FNanchor_60_60" id="FNanchor_60_60"></a><a href="#Footnote_60_60" class="fnanchor">[60]</a>, when the forces at E and F are placed (as in fig. 23.) -on different sides of the support D. It will appear also equally -manifest in the other case, by continuing the bar B C in -fig. 24. on the other side of the support D, till C G be equal -to C F, and by hanging at G a weight equivalent to the power -at F; for then, if the power at F were removed, the two -weights at G and E would counterpoize each other, as in -the former case: and it is evident, that the point F will -be lifted up by the weight at G with the same degree of -force, as by the other power applied to F; since, if the -weight at E were removed, a weight hung at F equal to -that at G would balance the lever, the distances C G and -C F being equal.</p> - -<p>33. <span class="smcap gesperrt">If</span> the two weights, or other powers, applied to the -lever do not counterbalance each other; a third power may -be applied in any place proposed of the lever, which shall<span class="pagenum"><a name="Page_73" id="Page_73">[73]</a></span> -hold the whole in a just counterpoize. Suppose (in fig. 25.) -the two powers at E and F did not equiponderate, and it were -required to apply a third power to the point G, that might be -sufficient to balance the lever. Find what power in F would -just counterbalance the power in E; then if the difference -between this power and that, which is actually applied at F, -bear the same proportion to the third power to be applied at -G, as the distance C G bears to C F; the lever will be counterpoized -by the help of this third power, if it be so applied -as to act the same way with the power in F, when that power -is too small to counterbalance the power in E; but otherwise -the power in G must be so applied, as to act against the -power in F. In like manner, if a lever were charged with three, -or any greater number of weights or other powers, which did -not counterpoize each other, another power might be applied -in any place proposed, which should bring the whole to a -just balance. And what is here said concerning a plurality of -powers, may be equally applied to all the following cases.</p> - -<p>34. <span class="smcap gesperrt">If</span> the lever should consist of two arms making an -angle at the point C (as in fig. 26.) yet if the forces are applied -perpendicularly to each arm, the same proportion will -hold between the forces applied, and the distances of the center, -whereon the lever rests, from the points to which they -are applied. That is, the weight at E will be to the force in -F in the same proportion, as C F bears to C E.</p> - -<p>35. <span class="smcap gesperrt">But</span> whenever the forces applied to the lever act obliquely -to the arm, to which they are applied (as in fig. 27.)<span class="pagenum"><a name="Page_74" id="Page_74">[74]</a></span> -then the strength of the forces is to be estimated by lines let -fall from the center of the lever to the directions, wherein the -forces act. To balance the levers in fig. 27, the weight or -other force at F will bear the same proportion to the weight -at E, as the distance C E bears to C G the perpendicular let fall -from the point C upon the line, which denotes the direction -wherein the force applied to F acts: for here, if the lever be -put into motion, the power applied to F will begin to move in -the direction of the line F G; and therefore its first motion will -be the same, as the motion of the point G.</p> - -<p>36. <span class="smcap gesperrt">When</span> two weights hang upon a lever, and the point, -by which the lever is supported, is placed in the middle between -the two weights, that the arms of the lever are both -of equal length; then this lever is particularly called a balance; -and equal weights equiponderate as in common scales. -When the point of support is not equally distant from both -weights, it constitutes that instrument for weighing, which -is called a steelyard. Though both in common scales, and the -steelyard, the point, on which the beam is hung, is not usually -placed just in the same straight line with the points, that -hold the weights, but rather a little above (as in fig. 28.) -where the lines drawn from the point C, whereon the beam -is suspended, to the points E and F, on which the weights are -hung, do not make absolutely one continued line. If the -three points E, C, and F were in one straight line, those weights, -which equiponderated, when the beam hung horizontally, -would also equiponderate in any other situation.</p> - -<div class="figcenter"> - <img src="images/ill-125.jpg" width="400" height="513" - alt="" - title="" /> -</div> - -<p>But we see in these instruments, when they are charged with weights, -<span class="pagenum"><a name="Page_75" id="Page_75">[75]</a></span>which equiponderate with the beam hanging horizontally; -that, if the beam be inclined either way, the weight most -elevated surmounts the other, and descends, causing the beam -to swing, till by degrees it recovers its horizontal position. -This effect arises from the forementioned structure: for by -this structure these instruments are levers composed of two -arms, which make an angle at the point of support (as in -fig. 29, 30.) the first of which represents the case of the -common balance, the second the case of the steelyard. In -the first, where C E and C F are equal, equal weights hung -at E and F will equiponderate, when the points E and F are -in an horizontal situation. Suppose the lines E G and F H to -be perpendicular to the horizon, then they will denote the directions, -wherein the forces applied to E and F act. Therefore -the proportion between the weights at E and F, which -shall equiponderate, are to be judged of by perpendiculars, -as C I, C K, let fall from C upon E G and F H: so that the -weights being equal, the lines C I, C K, must be equal also, -when the weights equiponderate. But I believe my readers -will easily see, that since C E and C F are equal, the lines -C I and C K will be equal, when the points E and F are horizontally -situated.</p> - -<p>37. <span class="smcap gesperrt">If</span> this lever be set into any other position (as in -fig. 31.) then the weight, which is raised highest, will outweigh -the other. Here, if the point F be raised higher than -E, the perpendicular C K will be longer than C I: and therefore -the weights would equiponderate, if the weight at F<span class="pagenum"><a name="Page_76" id="Page_76">[76]</a></span> -were less than the weight at E. But the weight at F is equal -to that at E; therefore is greater, than is necessary to counterbalance -the weight at E, and consequently will outweigh it, -and draw the beam of the lever down.</p> - -<p>38. <span class="smcap gesperrt">In</span> like manner in the case of the steelyard (fig. 32.) -if the weights at E and F are so proportioned, as to equiponderate, -when the points E and F are horizontally situated; -then in any other situation of this lever the weight, which is -raised highest, will preponderate. That is, if in the horizontal -situation of the points E and F the weight at F bears -the same proportion to the weight at E, as C I bears to C K; -then, if the point F be raised higher than E (as in fig. 32.) -the weight at F shall bear a greater proportion to the weight -at E, than C I bears to C K.</p> - -<p>39. <span class="smcap gesperrt">Farther</span> a lever may be hung upon an axis, and -then the two arms of the lever need not be continuous, but -fixed to different parts of this axis; as in fig. 33, where -the axis A B is supported by its two extremities A and B. To -this axis one arm of the lever is fixed at the point C, the other -at the point D. Now here, if a weight be hung at E, the -extremity of that arm, which is fixed to the axis at the point -C; and another weight be hung at F, the extremity of the -arm, which is fixed on the axis at D; then these weights -will equiponderate, when the weight at E bears the same -proportion to the weight at F, as the arm D F bears to -C E.</p> - -<p><span class="pagenum"><a name="Page_77" id="Page_77">[77]</a></span></p> - -<p>40. <span class="smcap gesperrt">This</span> is the case, if both the arms are perpendicular -to the axis, and lie (as the geometers express themselves) -in the same plane; or, in other words, if the arms are so fixed -perpendicularly upon the axis, that, when one of them -lies horizontally, the other shall also be horizontal. If either -arm stand not perpendicular to the axis; then, in determining -the proportion between the weights, instead of the -length of that arm, you must use the perpendicular let fall -upon the axis from the extremity of that arm. If the arms -are not so fixed as to become horizontal, at the same time; -the method of assigning the proportion between the weights -is analogous to that made use of above in levers, which make -an angle at the point, whereon they are supported.</p> - -<p><a name="c77" id="c77">41.</a> <span class="smcap gesperrt">From</span> this case of the lever hung on an axis, it is easy -to make a transition to another mechanical power, the -wheel and axis.</p> - -<p>42. <span class="smcap gesperrt">This</span> instrument is a wheel fixed on a roller, the -roller being supported at each extremity so as to turn -round freely with the wheel, in the manner represented in -fig. 34, where A B is the wheel, C D the roller, and E F its -two supports. Now suppose a weight G hung by a cord -wound round the roller, and another weight H hung by a -cord wound about the wheel the contrary way: that these -weights may support each other, the weight H must bear the -same proportion to the weight G, as the thickness of the roller -bears to the diameter of the wheel.</p> - -<p><span class="pagenum"><a name="Page_78" id="Page_78">[78]</a></span></p> - -<p>43. <span class="smcap gesperrt">Suppose</span> the line <i>k l</i> to be drawn through the middle -of the roller; and from the place of the roller, where -the cord, on which the weight G hangs, begins to leave the -roller, as at <i>m</i>, let the line<i> m n</i> be drawn perpendicularly to -<i>k l</i>; and from the point, where the cord holding the weight -H begins to leave the wheel, as at <i>o</i>, let the line <i>o p</i> be drawn -perpendicular to <i>k l</i>. This being done, the two lines <i>o p</i> -and <i>m n</i> represent two arms of a lever fixed on the axis <i>k l</i>; -consequently the weight H will bear to the weight G the same -proportion, as <i>m n</i> bears to <i>o p</i>. But <i>m n</i> bears the same proportion -to <i>o p</i>, as the thickness of the roller bears to the diameter -of the wheel; for <i>m n</i> is half the thickness of the roller, -and <i>o p</i> half the diameter of the wheel.</p> - -<p>44. <span class="smcap gesperrt">If</span> the wheel be put into motion, and turned once -round, that the cord, on which the weight G hangs, be -wound once more round the axis; then at the same time the -cord, whereon the weight H hangs, will be wound off from -the wheel one circuit. Therefore the velocity of the weight -G will bear the same proportion to the velocity of the weight -H, as the circumference of the roller to the circumference of -the wheel. But the circumference of the roller bears the same -proportion to the circumference of the wheel, as the thickness -of the roller bears to the diameter of the wheel, consequently -the velocity of the weight G bears to the velocity -of the weight H the same proportion, as the thickness of -the roller bears to the diameter of the wheel, which is the -proportion that the weight H bears to the weight G. Therefore -as before in the lever, so here also the general rule laid<span class="pagenum"><a name="Page_79" id="Page_79">[79]</a></span> -down above is verified, that the weights equiponderate, when -their velocities would be reciprocally proportional to their -respective weights.</p> - -<p>45. <span class="smcap gesperrt">In</span> like manner, if on the same axis two wheels of different -sizes are fixed (as in fig. 35.) and a weight hung on -each; the weights will equiponderate, if the weight hung on -the greater wheel bear the same proportion to the weight hung -on the lesser, as the diameter of the lesser wheel bears to the -diameter of the greater.</p> - -<p>46. <span class="smcap gesperrt">It</span> is usual to join many wheels together in the same -frame, which by the means of certain teeth, formed in the circumference -of each wheel, shall communicate motion to each -other. A machine of this nature is represented in fig. 36. Here -A B C is a winch, upon which is fixed a small wheel D indented -with teeth, which move in the like teeth of a larger wheel -E F fixed on the axis G H. Let this axis carry another wheel -I, which shall move in like manner a greater wheel K L fixed -on the axis M N. Let this axis carry another small wheel O, -which after the same manner shall turn about a larger wheel -P Q fixed on the roller R S, on which a cord shall be wound, -that holds a weight, as T. Now the proportion required between -the weight T and a power applied to the winch at A -sufficient to support the weight, will most easily be estimated, -by computing the proportion, which the velocity of the point -A would bear to the velocity of the weight. If the winch be -turned round, the point A will describe a circle as A V. Suppose -the wheel E F to have ten times the number of teeth, as<span class="pagenum"><a name="Page_80" id="Page_80">[80]</a></span> -the wheel D; then the winch must turn round ten times to -carry the wheel E F once round. If wheel K L has also ten -times the number of teeth, as I, the wheel I must turn round -ten times to carry the wheel K L once round; and consequently -the winch A B C must turn round an hundred times -to turn the wheel K L once round. Lastly, if the wheel P Q -has ten times the number of teeth, as the wheel O, the winch -must turn about one thousand times in order to turn the wheel -P Q, or the roller R S once round. Therefore here the point -A must have gone over the circle A V a thousand times, in order -to lift the weight T through a space equal to the circumference -of the roller R S: whence it follows, that the power -applied at A will balance the weight T, if it bear the same -proportion to it, as the circumference of the roller to one -thousand times the circle A V; or the same proportion as half -the thickness of the roller bears to one thousand times A B.</p> - -<p><a name="c80" id="c80">47.</a> <span class="smcap gesperrt">I shall</span> now explain the effect of the pulley. Let -a weight hang by a pulley, as in fig. 37. Here it is evident, -that the power A, by which the weight B is supported, -must be equal to the weight; for the cord C D is equally -strained between them; and if the weight B move, the power -A must move with equal velocity. The pulley E has no other -effect, than to permit the power A to act in another direction, -than it must have done, if it had been directly applied to support -the weight without the intervention of any such instrument.</p> - -<p>48. <span class="smcap gesperrt">Again</span>, let a weight be supported, as in fig. 38; -where the weight A is fixed to the pulley B, and the cord, by<span class="pagenum"><a name="Page_81" id="Page_81">[81]</a></span> -which the weight is upheld, is annexed by one extremity to a -hook C, and at the other end is held by the power D. Here -the weight is supported by a cord doubled; insomuch that -although the cord were not strong enough to hold the weight -single, yet being thus doubled it might support it. If the -end of the cord held by the power D were hung on the hook -C, as well as the other end; then, when both ends of the cord -were tied to the hook, it is evident, that the hook would -bear the whole weight; and each end of the string would -bear against the hook with the force of half the weight only, -seeing both ends together bear with the force of the whole. -Hence it is evident, that, when the power D holds one end of -the weight, the force, which it must exert to support the -weight, must be equal to just half the weight. And the same -proportion between the weight and power might be collected -from comparing the respective velocities, with which they -would move; for it is evident, that the power must move -through a space equal to twice the distance of the pulley from -the hook, in order to lift the pulley up to the hook.</p> - -<p>49. <span class="smcap gesperrt">It</span> is equally easy to estimate the effect, when many -pulleys are combined together, as in fig. 39, 40; in the first -of which the under set of pulleys, and consequently the -weight is held by six strings; and in the latter figure by five: -therefore in the first of these figures the power to support the -weight, must be one sixth part only of the weight, and in -the latter figure the power must be one fifth part.</p> - -<p><span class="pagenum"><a name="Page_82" id="Page_82">[82]</a></span></p> - -<p>50. <span class="smcap gesperrt">There</span> are two other ways of supporting a weight -by pulleys, which I shall particularly consider.</p> - -<p>51. <span class="smcap gesperrt">One</span> of these ways is represented in fig. 41. Here the -weight being connected to the pulley B, a power equal to -half the weight A would support the pulley C, if applied immediately -to it. Therefore the pulley C is drawn down -with a force equal to half the weight A. But if the pulley D -were to be immediately supported by half the force, with -which the pulley C is drawn down, this pulley D will uphold -the pulley C; so that if the pulley D be upheld with a force -equal to one fourth part of the weight A, that force will support -the weight. But, for the same reason as before, if the -power in E be equal to half the force necessary to uphold the -pulley D; this pulley, and consequently the weight A, will -be upheld: therefore, if the power in E be one eighth part -of the weight A, it will support the weight.</p> - -<p>52. <span class="smcap gesperrt">Another</span> way of applying pulleys to a weight is -represented in fig. 42. To explain the effect of pulleys thus -applied, it will be proper to consider different weights hanging, -as in fig. 43. Here, if the power and weights balance each -other, the power A is equal to the weight B; the weight C is -equal to twice the power A, or the weight B; and for the same -reason the weight D is equal to twice the weight C, or equal -to four times the power A. It is evident therefore, that all -the three weights B, C, D together are equal to seven times the -power A. But if these three weights were joined in one, they -would produce the case of fig. 40: so that in that figure the<span class="pagenum"><a name="Page_83" id="Page_83">[83]</a></span> -weight A, where there are three pulleys, is seven times the -power B. If there had been but two pulleys, the weight would -have been three times the power; and if there had been four -pulleys, the weight would have been fifteen times the power.</p> - -<p><a name="c83a" id="c83a">53.</a> <span class="smcap gesperrt">The</span> wedge is next to be considered. The form of -this instrument is sufficiently known. When it is put under -any weight (as in fig. 44.) the force, with which the wedge -will lift the weight, when drove under it by a blow upon the -end A B, will bear the same proportion to the force, wherewith -the blow would act on the weight, if directly applied to -it; as the velocity, which the wedge receives from the blow, -bears to the velocity, wherewith the weight is lifted by the -wedge.</p> - -<p><a name="c83b" id="c83b">54.</a> <span class="smcap gesperrt">The</span> screw is the fifth mechanical power. There are -two ways of applying this instrument. Sometimes it is screwed -into a hole, as in fig. 45, where the screw A B is screwed -through the plank C D. Sometimes the screw is applied to -the teeth of a wheel, as in fig. 46, where the thread of the -screw A B turns in the teeth of a wheel C D. In both these -cases, if a bar, as A E, be fixed to the end A of the screw; the -force, wherewith the end B of the screw in fig. 45 is -forced down, and the force, wherewith the teeth of the -wheel C D in fig. 44 are held, bears the same proportion -to the power applied to the end E of the bar; as the velocity, -wherewith the end E will move, when the screw is turned, -bears to the velocity, wherewith the end B of the screw in fig. -43, or the teeth of the wheel C D in fig. 46, will be moved.</p> - -<p><span class="pagenum"><a name="Page_84" id="Page_84">[84]</a></span></p> - -<p><a name="c84" id="c84">55.</a> <span class="smcap gesperrt">The</span> inclined plane affords also a means of raising -a weight with less force, than what is equal to the weight it -self. Suppose it were required to raise the globe A (in fig. -47.) from the ground B C up to the point, whose perpendicular -height from the ground is E D. If this globe be drawn -along the slant D F, less force will be required to raise it, than -if it were lifted directly up. Here if the force applied to the -globe bear the same proportion only to its weight, as E D bears -to F D, it will be sufficient to hold up the globe; and therefore -any addition to that force will put it in motion, and draw -it up; unless the globe, by pressing against the plane, whereon -it lies, adhere in some degree to the plane. This indeed -it must always do more or less, since no plane can be made so -absolutely smooth as to have no inequalities at all; nor yet so -infinitely hard, as not to yield in the least to the pressure of the -weight. Therefore the globe cannot be laid on such a plane, -whereon it will slide with perfect freedom, but they must in -some measure rub against each other; and this friction will -make it necessary to imploy a certain degree of force more, -than what is necessary to support the globe, in order to give -it any motion. But as all the mechanical powers are subject -in some degree or other to the like impediment from friction; -I shall here only shew what force would be necessary to sustain -the globe, if it could lie upon the plane without causing -any friction at all. And I say, that if the globe were -drawn by the cord G H, lying parallel to the plane D F; and -the force, wherewith the cord is pulled, bear the same -proportion to the weight of the globe, as E D bears to D F;<span class="pagenum"><a name="Page_85" id="Page_85">[85]</a></span> -this force will sustain the globe. In order to the making -proof of this, let the cord G H be continued on, and turned -over the pulley I, and let the weight K be hung to it. -Now I say, if this weight bears the same proportion to -the globe A, as D E bears to D F, the weight will support -the globe. I think it is very manifest, that the center of the -globe A will lie in one continued line with the cord H G. Let -L be the center of the globe, and M the center of gravity of -the weight K. In the first place let the weight hang so, that -a line drawn from L to M shall lie horizontally; and I say, -if the globe be moved either up or down the plane D F, the -weight will so move along with it, that the center of gravity -common to both the weights shall continue in this line L M, -and therefore shall in no case descend. To prove this more -fully, I shall depart a little from the method of this treatise, -and make use of a mathematical proportion or two: but they -are such, as any person, who has read <span class="smcap"><em class="gesperrt">Euclid’s Elements</em></span>, -will fully comprehend; and are in themselves so evident, that, -I believe, my readers, who are wholly strangers to geometrical -writings, will make no difficulty of admitting them. This -being premised, let the globe be moved up, till its center be -at G, then will M the center of gravity of the weight K be -sunk to N; so that M N shall be equal to G L. Draw N G -crossing the line M L in O; then I say, that O is the common -center of gravity of the two weights in this their new situation. -Let G P be drawn perpendicular to M L; then G L will -bear the same proportion to G P, as D F bears to D E; and -M N being equal to G L, M N will bear the same proportion<span class="pagenum"><a name="Page_86" id="Page_86">[86]</a></span> -to G P, as D F bears to D E. But N O bears the same proportion -to O G, as M N bears to G P; consequently N O will bear -the same proportion to O G, as D F bears to D E. In the last -place, the weight of the globe A bears the same proportion to -the other weight K, as D F bears to D E; therefore N O bears -the same proportion to O G, as the weight of the globe A bears -to the weight K. Whence it follows, that, when the center -of the globe A is in G, and the center of gravity of the weight -K is in N, O will be the center of gravity common to both -the weights. After the same manner, if the globe had been -caused to descend, the common center of gravity would have -been found in this line M L. Since therefore no motion of -the globe either way will make the common center of gravity -descend, it is manifest, from what has been said above, that -the weights A and K counterpoize each other.</p> - -<p><a name="c86a" id="c86a">56.</a> <span class="smcap gesperrt">I shall</span> now consider the case of pendulums. A -pendulum is made by hanging a weight to a line, so that it -may swing backwards and forwards. This motion the geometers -have very carefully considered, because it is the most -commodious instrument of any for the exact measurement of -time.</p> - -<p><a name="c86b" id="c86b">57.</a> <span class="smcap gesperrt">I have</span> observed already<a name="FNanchor_61_61" id="FNanchor_61_61"></a><a href="#Footnote_61_61" class="fnanchor">[61]</a>, that if a body hanging -perpendicularly by a string, as the body A (in fig. 48.) hangs -by the string A B, be put so into motion, as to be made to ascend -up the circular arch A C; then as soon as it has arrived<span class="pagenum"><a name="Page_87" id="Page_87">[87]</a></span> -at the highest point, to which the motion, that the body has -received, will carry it; it will immediately begin to descend, -and at A will receive again as great a degree of motion, as it -had at first. This motion therefore will carry the body up -the arch A D, as high as it ascended before in the arch A C. -Consequently in its return through the arch D A it will acquire -again at A its original velocity, and advance a second time up -the arch A C as high as at first; by this means continuing without -end its reciprocal motion. It is true indeed, that in fact -every pendulum, which we can put in motion, will gradually -lessen its swing, and at length stop, unless there be some -power constantly applied to it, whereby its motion shall be -renewed; but this arises from the resistance, which the body -meets with both from the air, and the string by which it is -hung: for as the air will give some obstruction to the progress -of the body moving through it; so also the string, whereon -the body hangs, will be a farther impediment; for this string -must either slide on the pin, whereon it hangs, or it must bend -to the motion of the weight; in the first there must be some -degree of friction, and in the latter the string will make some -resistance to its inflection. However, if all resistance could -be removed, the motion of a pendulum would be perpetual.</p> - -<p>58. <span class="smcap gesperrt">But</span> to proceed, the first property, I shall take notice -of in this motion, is, that the greater arch the pendulous -body moves through, the greater time it takes up: though -the length of time does not increase in so great a proportion -as the arch. Thus if C D be a greater arch, and E F a lesser, -where C A is equal to A D, and E A equal to A F; the body,<span class="pagenum"><a name="Page_88" id="Page_88">[88]</a></span> -when it swings through the greater arch C D, shall take up in -its swing from C to D a longer time than in swinging from E -to F, when it moves only in that lesser arch; or the time in -which the body let fall from C will descend through the arch -C A is greater than the time, in which it will descend through -the arch E A, when let fall from E. But the first of these -times will not hold the same proportion to the latter, as the -first arch C A bears to the other arch E A; which will appear -thus. Let C G and E H be two horizontal lines. It has been -remarked above<a name="FNanchor_62_62" id="FNanchor_62_62"></a><a href="#Footnote_62_62" class="fnanchor">[62]</a>, that the body in falling through the arch -C A will acquire as great a velocity at the point A, as it would -have gained by falling directly down through G A; and in -falling through the arch E A it will acquire in the point A only -that velocity, which it would have got in falling through -H A. Therefore, when the body descends through the greater -arch C A, it shall gain a greater velocity, than when it passes -only through the lesser; so that this greater velocity will in -some degree compensate the greater length of the arch.</p> - -<p>59. <span class="smcap gesperrt">The</span> increase of velocity, which the body acquires -in falling from a greater height, has such an effect, that, if -straight lines be drawn from A to C and E, the body would -fall through the longer straight line C A just in the same time, -as through the shorter straight line E A. This is demonstrated -by the geometers, who prove, that if any circle, as A B C D -(fig. 49.) be placed in a perpendicular situation; a body -shall fall obliquely through every line, as A B drawn from the -lowest point A in the circle to any other point in the circumference<span class="pagenum"><a name="Page_89" id="Page_89">[89]</a></span> -just in the same time, as would be imployed by the -body in falling perpendicularly down through the diameter -C A. But the time in which the body will descend through -the arch, is different from the time, which it would take up -in falling through the line A B.</p> - -<p>60. <span class="smcap gesperrt">It</span> has been thought by some, that because in very -small arches this correspondent straight line differs but little -from the arch itself; therefore the descent through this -straight line would be performed in such small arches nearly -in the same time as through the arches themselves: so that -if a pendulum were to swing in small arches, half the time -of a single swing would be nearly equal to the time, in which -a body would fall perpendicularly through twice the length -of the pendulum. That is, the whole time of the swing, according -to this opinion, will be four fold the time required -for the body to fall through half the length of the pendulum; -because the time of the body’s falling down twice the -length of the pendulum is half the time required for the fall -through one quarter of this space, that is through half the -pendulum’s length. However there is here a mistake; for -the whole time of the swing, when the pendulum moves -through small arches, bears to the time required for a body -to fall down through half the length of the pendulum very -nearly the same proportion, as the circumference of a circle -bears to its diameter; that is very nearly the proportion of -355 to 113, or little more than the proportion of 3 to 1. -If the pendulum takes so great a swing, as to pass over an arch -equal to one sixth part of the whole circumference of the<span class="pagenum"><a name="Page_90" id="Page_90">[90]</a></span> -circle, it will swing 115 times, while it ought according to -this proportion to have swung 117 times; so that, when it -swings in so large an arch, it loses something less than two -swings in an hundred. If it swing through 1/10 only of the -circle, it shall not lose above one vibration in 160. If it -swing in 1/20 of the circle, it shall lose about one vibration in -690. If its swing be confined to 1/40 of the whole circle, it -shall lose very little more than one swing in 2600. And -if it take no greater a swing than through 1/60 of the whole circle, -it shall not lose one swing in 5800.</p> - -<p>61. <span class="smcap gesperrt">Now</span> it follows from hence, that, when pendulums -swing in small arches, there is very nearly a constant proportion -observed between the time of their swing, and the time, -in which a body would fall perpendicularly down through -half their length. And we have declared above, that the -spaces, through which bodies fall, are in a two fold proportion -of the times, which they take up in falling<a name="FNanchor_63_63" id="FNanchor_63_63"></a><a href="#Footnote_63_63" class="fnanchor">[63]</a>. Therefore -in pendulums of different lengths, swinging through small -arches, the lengths of the pendulums are in a two fold or -duplicate proportion of the times, they take in swinging; -so that a pendulum of four times the length of another shall -take up twice the time in each swing, one of nine times the -length will make one swing only for three swings of the -shorter, and so on.</p> - -<p>62. <span class="smcap gesperrt">This</span> proportion in the swings of different pendulums -not only holds in small arches; but in large ones also,<span class="pagenum"><a name="Page_91" id="Page_91">[91]</a></span> -provided they be such, as the geometers call similar; that -is, if the arches bear the same proportion to the whole circumferences -of their respective circles. Suppose (in fig. 48.) -A B, C D to be two pendulums. Let the arch E F be described -by the motion of the pendulum A B, and the arch G H -be described by the pendulum C D; and let the arch E F bear -the same proportion to the whole circumference, which -would be formed by turning the pendulum A B quite round -about the point A, as the arch G H bears to the whole circumference, -that would be formed by turning the pendulum -C D quite round the point C. Then I say, the proportion, -which the length of the pendulum A B bears to the -length of the pendulum C D, will be two fold of the proportion, -which the time taken up in the description of the arch -E F bears to the time employed in the description of the arch -G H.</p> - -<p><a name="c91" id="c91">63.</a> <span class="smcap gesperrt">Thus</span> pendulums, which swing in very small arches, -are nearly an equal measure of time. But as they are not such -an equal measure to geometrical exactness; the mathematicians -have found out a method of causing a pendulum so to swing, -that, if its motion were not obstructed by any resistance, it -would always perform each swing in the same time, whether -it moved through a greater, or a lesser space. This was first -discovered by the great <span class="smcap"><em class="gesperrt">Huygens</em></span>, and is as follows. Upon -the straight line A B (in fig. 49.) let the circle C D E be so -placed, as to touch the straight line in the point C. Then let -this circle roll along upon the straight line A B, as a coach-wheel -rolls along upon the ground. It is evident, that, as<span class="pagenum"><a name="Page_92" id="Page_92">[92]</a></span> -soon as ever the circle begins to move, the point C in the circle -will be lifted off from the straight line A B; and in the -motion of the circle will describe a crooked course, which is -represented by the line C F G H. Here the part C H of the -straight line included between the two extremities C and H -of the line C F G H will be equal to the whole circumference -of the circle C D E; and if C H be divided into two equal -parts at the point I, and the straight line I K be drawn perpendicular -to C H, this line I K will be equal to the diameter -of the circle C D E. Now in this line if a body were to be -let fall from the point H, and were to be carried by its weight -down the line H G K, as far as the point K, which is the lowest -point of the line C F G H; and if from any other point G a -body were to be let fall in the same manner; this body, -which falls from G, will take just the same time in coming to -K, as the body takes up, which falls from H. Therefore if -a pendulum can be so hung, that the ball shall move in the -line A G F E, all its swings, whether long or short, will be performed -in the same time; for the time, in which the ball -will descend to the point K, is always half the time of the -whole swing. But the ball of a pendulum will be made to -swing in this line by the following means. Let K I (in fig. -52.) be prolonged upwards to L, till I L is equal to I K. -Then let the line L M H equal and like to K H be applied, as -in the figure between the points L and H, so that the point -which in this line L M H answers to the point H in the line -K H shall be applied to the point L, and the point answering -to the point K shall be applied to the point H. Also let such -another line L N C be applied between L and C in the same<span class="pagenum"><a name="Page_93" id="Page_93">[93]</a></span> -manner. This preparation being made; if a pendulum be -hung at the point L of such a length, that the ball thereof -shall reach to K; and if the string shall continually bend against -the lines H M L and L N C, as the pendulum swings -to and fro; by this means the ball shall constantly keep in -the line C K H.</p> - -<p><a name="c93" id="c93">64.</a> <span class="smcap gesperrt">Now</span> in this pendulum, as all the swings, whether -long or short, will be performed in the same time; so the time -of each will exactly bear the same proportion to the time required -for a body to fall perpendicularly down, through half -the length of the pendulum, that is from I to K, as the circumference -of a circle bears to its diameter.</p> - -<p>65. <span class="smcap gesperrt">It</span> may from hence be understood in some measure, -why, when pendulums swing in circular arches, the times of -their swings are nearly equal, if the arches are small, though -those arches be of very unequal lengths; for if with the semidiameter -L K the circular arch O K P be described, this arch -in the lower part of it will differ very little from the line -C K H.</p> - -<p>66. <span class="smcap gesperrt">It</span> may not be amiss here to remark, that a body -will fall in this line C K H (fig. 53.) from C to any other -point, as Q or R in a shorter space of time, than if it moved -through the straight line drawn from C to the other point; -or through any other line whatever, that can be drawn between -these two points.</p> - -<p><span class="pagenum"><a name="Page_94" id="Page_94">[94]</a></span></p> - -<p>67. <span class="smcap gesperrt">But</span> as I have observed, that the time, which a pendulum -takes in swinging, depends upon its length; I shall -now say something concerning the way, in which this length -of the pendulum is to be estimated. If the whole ball of the -pendulum could be crouded into one point, this length, by -which the motion of the pendulum is to be computed, would -be the length of the string or rod. But the ball of the pendulum -must have a sensible magnitude, and the several parts -of this ball will not move with the same degree of swiftness; -for those parts, which are farthest from the point, whereon -the pendulum is suspended, must move with the greatest velocity. -Therefore to know the time in which the pendulum -swings, it is necessary to find that point of the ball, which -moves with the same degree of velocity, as if the whole ball -were to be contracted into that point.</p> - -<p><a name="c94" id="c94">68.</a> <span class="smcap gesperrt">This</span> point is not the center of gravity, as I shall now -endeavour to shew. Suppose the pendulum A B (in fig. 54.) -composed of an inflexible rod A C and ball C B, to be fixed -on the point A, and lifted up into an horizontal situation. -Here if the rod were not fixed to the point A, the body C B -would descend directly with the whole force of its weight; -and each part of the body would move down with the same -degree of swiftness. But when the rod is fixed at the point -A, the body must fall after another manner; for the parts -of the body must move with different degrees of velocity, -the parts more remote from A descending with a swifter motion, -than the parts nearer to A; so that the body will receive -a kind of rolling motion while it descends. But it has -been observed above, that the effect of gravity upon any body -is the same, as if the whole force were exerted on the body’s -center of gravity<a name="FNanchor_64_64" id="FNanchor_64_64"></a><a href="#Footnote_64_64" class="fnanchor">[64]</a>.</p> - -<div class="figcenter"> - <img src="images/ill-147.jpg" width="400" height="499" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_95" id="Page_95">[95]</a></span></p> - -<p>Since therefore the power of gravity -in drawing down the body must also communicate to it the -rolling motion just described; it seems evident, that the center -of gravity of the body cannot be drawn down as swiftly, -as when the power of gravity has no other effect to produce -on the body, than merely to draw it downward. If therefore -the whole matter of the body C B could be crouded into -its center of gravity, so that being united into one point, this -rolling motion here mentioned might give no hindrance to -its descent; this center would descend faster, than it can now -do. And the point, which now descends as fast, as if the -whole matter or the body C B were crouded into it, will be -farther removed from the point A, than the center of gravity -of the body C B.</p> - -<p>69. <span class="smcap gesperrt">Again</span>, suppose the pendulum A B (in fig. 55.) to -hang obliquely. Here the power of gravity will operate less -upon the ball of the pendulum, than before: but the line D E -being drawn so, as to stand perpendicular to the rod A C of -the pendulum; the force of gravity upon the body C B, -now it is in this situation, will produce the same effect, as -if the body were to glide down an inclined plane in the position -of D E. But here the motion of the body, when the -rod is fixed to the point A, will not be equal to the uninterrupted -descent of the body down this plane; for the body<span class="pagenum"><a name="Page_96" id="Page_96">[96]</a></span> -will here also receive the same kind of rotation in its motion, -as before; so that the motion of the center of gravity will in -like manner be retarded; and the point, which here descends -with that degree of swiftness, which the body would -have, if not hindered by being fixed to the point A; that is, -the point, which descends as fast, as if the whole body were -crouded into it, will be as far removed from the point A, as -before.</p> - -<p>70. <span class="smcap gesperrt">This</span> point, by which the length of the pendulum is -to be estimated, is called the center of oscillation. And the -mathematicians have laid down general directions, whereby -to find this center in all bodies. If the globe A B (in fig. 56.) -be hung by the string C D, whose weight need not be regarded, -the center of oscillation is found thus. Let the -straight line drawn from C to D be continued through the -globe to F. That it will pass through the center of the globe -is evident. Suppose E to be this center of the globe; and -take the line G of such a length, that it shall bear the same -proportion to E D, as E D bears to E C. Then E H being -made equal to ⅖ of G, the point H shall be the center of oscillation<a name="FNanchor_65_65" id="FNanchor_65_65"></a><a href="#Footnote_65_65" class="fnanchor">[65]</a>. -If the weight of the rod C D is too considerable -to be neglected, divide C D (fig. 57) in I, that D I be equal -to ⅓, part of C D; and take K in the same proportion to C I, as -the weight of the globe A B to the weight of the rod C D. -Then having found H, the center of oscillation of the globe, as -before, divide I K in I, so that I L shall bear the same proportion<span class="pagenum"><a name="Page_97" id="Page_97">[97]</a></span> -to L H, as the line C H bears to K; and L shall be -the center of oscillation of the whole pendulum.</p> - -<p>71. <span class="smcap gesperrt">This</span> computation is made upon supposition, that the -center of oscillation of the rod C D, if that were to swing alone -without any other weight annexed, would be the point I. -And this point would be the true center of oscillation, so far -as the thickness of the rod is not to be regarded. If any one -chuses to take into consideration the thickness of the rod, he -must place the center of oscillation thereof so much below -the point I, that eight times the distance of the center from -the point I shall bear the same proportion to the thickness of -the rod, as the thickness of the rod bears to its length C D<a name="FNanchor_66_66" id="FNanchor_66_66"></a><a href="#Footnote_66_66" class="fnanchor">[66]</a>.</p> - -<p>72. <span class="smcap gesperrt">It</span> has been observed above, that when a pendulum -swings in an arch of a circle, as here in fig. 58, the pendulum -A B swings in the circular arch C D; if you draw an horizontal -line, as E F, from the place whence the pendulum is -let fall, to the line A G, which is perpendicular to the horizon: -then the velocity, which the pendulum will acquire in coming -to the point G, will be the same, as any body would acquire -in falling directly down from F to G. Now this is to be -understood of the circular arch, which is described by the center -of oscillation of the pendulum. I shall here farther observe, -that if the straight line E G be drawn from the point, -whence the pendulum falls, to the lowest point of the arch; -in the same or in equal pendulums the velocity, which the<span class="pagenum"><a name="Page_98" id="Page_98">[98]</a></span> -pendulum acquires in G, is proportional to this line: that is, if -the pendulum, after it has descended from E to G, be taken -back to H, and let fall from thence, and the line H G be -drawn; the velocity, which the pendulum shall acquire in -G by its descent from H, shall bear the same proportion to -the velocity, which it acquires in falling from E to G, as the -straight line H G bears to the straight line E G.</p> - -<p><a name="c98" id="c98">73.</a> <span class="smcap gesperrt">We</span> may now proceed to those experiments upon the -percussion of bodies, which I observed above might be -made with pendulums. This expedient for examining the -effects of percussion was first proposed by our late great -architect Sir <span class="smcap"><em class="gesperrt">Christopher Wren</em></span>. And it is as follows. -Two balls, as A and B (in fig. 59.) either equal or unequal, -are hung by two strings from two points C and D, so -that, when the balls hang down without motion, they shall -just touch each other, and the strings be parallel. Here if -one of these balls be removed to any distance from its perpendicular -situation, and then let fall to descend and strike against -the other; by the last preceding paragraph it will be -known, with what velocity this ball shall return into its first -perpendicular situation, and consequently with what force it -shall strike against the other ball; and by the height to which -this other ball ascends after the stroke, the velocity communicated -to this ball will be discovered. For instance, let the -ball A be taken up to E, and from thence be let fall to strike -against B, passing over in its descent the circular arch E F. -By this impulse let B fly up to G, moving through the circular -arch H G. Then E I and G K being drawn horizontally,<span class="pagenum"><a name="Page_99" id="Page_99">[99]</a></span> -the ball A will strike against B with the velocity, which it -would acquire in falling directly down from I; and the ball -B has received a velocity, wherewith, if it had been thrown -directly upward, it would have ascended up to K. Likewise -if straight lines be drawn from E to F and from H to G, the -velocity of A, wherewith it strikes, will bear the same proportion -to the velocity, which B has received by the blow, as -the straight line E F bears to the straight line H G. In the -same manner by noting the place to which A ascends after the -stroke, its remaining velocity may be compared with that, -wherewith it struck against B. Thus may be experimented -the effects of the body A striking against B at rest. If both -the bodies are lifted up, and so let fall as to meet and impinge -against each other just upon the coming of both into their -perpendicular situation; by observing the places into which -they move after the stroke, the effects of their percussion in -all these cases may be found in the same manner as before.</p> - -<p>74. <span class="smcap gesperrt">Sir <em class="gesperrt">Isaac Newton</em></span> has described these experiments; -and has shewn how to improve them to a greater exactness by -making allowance for the resistance, which the air gives to -the motion of the balls<a name="FNanchor_67_67" id="FNanchor_67_67"></a><a href="#Footnote_67_67" class="fnanchor">[67]</a>. But as this resistance is exceeding -small, and the manner of allowing for it is delivered by himself -in very plain terms, I need not enlarge upon it here. I -shall rather speak to a discovery, which he made by these experiments -upon the elasticity of bodies. It has been explained -above<a name="FNanchor_68_68" id="FNanchor_68_68"></a><a href="#Footnote_68_68" class="fnanchor">[68]</a>, that when two bodies strike, if they be not elastic,<span class="pagenum"><a name="Page_100" id="Page_100">[100]</a></span> -they remain contiguous after the stroke; but that if they are -elastic, they separate, and that the degree of their elasticity -determines the proportion between the celerity wherewith -they separate, and the celerity wherewith they meet. Now -our author found, that the degree of elasticity appeared in -the same bodies always the same, with whatever degree of -force they struck; that is, the celerity wherewith they separated, -always bore the same proportion to the celerity -wherewith they met: so that the elastic power in all the bodies, -he made trial upon, exerted it self in one constant proportion -to the compressing force. Our author made trial -with balls of wool bound up very compact, and found the -celerity with which they receded, to bear about the proportion -of 5 to 9 to the celerity wherewith they met; and in -steel he found nearly the same proportion; in cork the elasticity -was something less; but in glass much greater; for the -celerity, wherewith balls of that material separated after percussion, -he found to bear the proportion of 15 to 16 to the -celerity wherewith they met<a name="FNanchor_69_69" id="FNanchor_69_69"></a><a href="#Footnote_69_69" class="fnanchor">[69]</a>.</p> - -<p><a name="c100" id="c100">75.</a> <span class="smcap gesperrt">I shall</span> finish my discourse on pendulums, with -this farther observation only, that the center of oscillation is -also the center of another force. If a body be fixed to any -point, and being put in motion turns round it; the body, if -uninterrupted by the power of gravity or any other means, -will continue perpetually to move about with the same equable -motion. Now the force, with which such a body<span class="pagenum"><a name="Page_101" id="Page_101">[101]</a></span> -moves, is all united in the point, which in relation to the -power of gravity is called the center of oscillation. Let the -cylinder A B C D (in fig. 60.) whose axis is E F, be fixed to -the point E. And supposing the point E to be that on which -the cylinder is suspended, let the center of oscillation be -found in the axis E F, as has been explained above<a name="FNanchor_70_70" id="FNanchor_70_70"></a><a href="#Footnote_70_70" class="fnanchor">[70]</a>. Let G -be that center: then I say, that the force, wherewith this cylinder -turns round the point E, is so united in the point G, that -a sufficient force applied in that point shall stop the motion of -the cylinder, in such a manner, that the cylinder should immediately -remain without motion, though it were to be loosened -from the point E at the same instant, that the impediment -was applied to G: whereas, if this impediment had been -applied to any other point of the axis, the cylinder would -turn upon the point, where the impediment was applied. If -the impediment had been applied between E and G, the cylinder -would so turn on the point, where the impediment -was applied, that the end B C would continue to move on -the same way it moved before along with the whole cylinder; -but if the impediment were applied to the axis farther off from -E than G, the end A D of the cylinder would start out of its -present place that way in which the cylinder moved. From -this property of the center of oscillation, it is also called the -center of percussion. That excellent mathematician, Dr. <span class="smcap">Brook -Taylor</span>, has farther improved this doctrine concerning the -center of percussion, by shewing, that if through this point -G a line, as G H I, be drawn perpendicular to E F, and lying<span class="pagenum"><a name="Page_102" id="Page_102">[102]</a></span> -in the course of the body’s motion; a sufficient power applied -to any point of this line will have the same effect, as the -like power applied to G<a name="FNanchor_71_71" id="FNanchor_71_71"></a><a href="#Footnote_71_71" class="fnanchor">[71]</a>: so that as we before shewed the -center of percussion within the body on its axis; by this means -we may find this center on the surface of the body also, for -it will be where this line H I crosses that surface.</p> - -<p><a name="c102" id="c102">76.</a> <span class="smcap gesperrt">I shall</span> now proceed to the last kind of motion, to -be treated on in this place, and shew what line the power of -gravity will cause a body to describe, when it is thrown forwards -by any force. This was first discovered by the great -<span class="smcap"><em class="gesperrt">Galileo</em></span>, and is the principle, upon which engineers -should direct the shot of great guns. But as in this case bodies -describe in their motion one of those lines, which in geometry -are called conic sections; it is necessary here to premise -a description of those lines. In which I shall be the -more particular, because the knowledge of them is not only -necessary for the present purpose, but will be also required -hereafter in some of the principal parts of this treatise.</p> - -<p>77. <span class="smcap gesperrt">The</span> first lines considered by the ancient geometers -were the straight line and the circle. Of these they composed -various figures, of which they demonstrated many properties, -and resolved divers problems concerning them. These -problems they attempted always to resolve by the describing -straight lines and circles. For instance, let a square A B C D -(fig. 61.) be proposed, and let it be required to make another<span class="pagenum"><a name="Page_103" id="Page_103">[103]</a></span> -square in any assigned proportion to this. Prolong one -side, as D A, of this square to E, till A E bear the same proportion -to A D, as the new square is to bear to the square A C. -If the opposite side B C of the square A C be also prolonged -to F, till B F be equal to A E, and E F be afterwards drawn, -I suppose my readers will easily conceive, that the figure A B F E -will bear to the square A B C D the same proportion, as the line -A E bears to the line A D. Therefore the figure A B F E will -be equal to the new square, which is to be found, but is not -it self a square, because the side A E is not of the same length -with the side E F. But to find a square equal to the figure -A B F E you must proceed thus. Divide the line D E into two -equal parts in the point G, and to the center G with the interval -G D describe the circle D H E I; then prolong the line A B, -till it meets the circle in K; and make the square A K L M, which -square will be equal to the figure A B F E, and bear to the square -A B C D the same proportion, as the line A E bears to A D.</p> - -<p>78. <span class="smcap gesperrt">I shall</span> not proceed to the proof of this, having -only here set it down as a specimen of the method of resolving -geometrical problems by the description of straight lines -and circles. But there are some problems, which cannot be -resolved by drawing straight lines or circles upon a plane. For -the management therefore of these they took into consideration -solid figures, and of the solid figures they found that, -which is called a cone, to be the most useful.</p> - -<p><span class="pagenum"><a name="Page_104" id="Page_104">[104]</a></span></p> - -<p>79. <span class="smcap gesperrt">A cone</span> is thus defined by <span class="smcap">Euclide</span> in his elements -of geometry<a name="FNanchor_72_72" id="FNanchor_72_72"></a><a href="#Footnote_72_72" class="fnanchor">[72]</a>. If to the straight line A B (in fig. 62.) -another straight line, as A C, be drawn perpendicular, and the -two extremities B and C be joined by a third straight line -composing the triangle A C B (for so every figure is called, -which is included under three straight lines) then the two -points A and B being held fixed, as two centers, and the triangle -A C B being turned round upon the line A B, as on an axis; -the line A C will describe a circle, and the figure A C B will -describe a cone, of the form represented by the figure B C D E F -(fig. 63.) in which the circle C D E F is usually called the -base of the cone, and B the vertex.</p> - -<p>80. <span class="smcap gesperrt">Now</span> by this figure may several problems be resolved, -which cannot by the simple description of straight lines and -circles upon a plane. Suppose for instance, it were required -to make a cube, which should bear any assigned proportion -to some other cube named. I need not here inform my readers, -that a cube is the figure of a dye. This problem was -much celebrated among the ancients, and was once inforced -by the command of an oracle. This problem may be performed -by a cone thus. First make a cone from a triangle, -whose side A C shall be half the length of the side B C -Then on the plane A B C D (fig. 64.) let the line E F be -exhibited equal in length to the side of the cube proposed; -and let the line F G be drawn perpendicular to E F, and of -such a length, that it bear the same proportion to E F, as the<span class="pagenum"><a name="Page_105" id="Page_105">[105]</a></span> -cube to be sought is required to bear to the cube proposed. -Through the points E, F, and G let the circle F H I be described. -Then let the line E F be prolonged beyond F to K, that F K -be equal to F E, and let the triangle F K L, having all its sides -F K, K L, L F equal to each other, be hung down perpendicularly -from the plane A B C D. After this, let another plane -M N O P be extended through the point L, so as to be equidistant -from the former plane A B C D, and in this plane let -the line Q L R be drawn so, as to be equidistant from the line -E F K. All this being thus prepared, let such a cone, as was -above directed to be made, be so applied to the plane M N O P, -that it touch this plane upon the line Q R, and that the vertex -of the cone be applied to the point L. This cone, by cutting -through the first plane A B C D, will cross the circle F H I before -described. And if from the point S, where the surface -of this cone intersects the circle, the line S T be drawn so, as -to be equidistant from the line E F; the line F T will be equal -to the side of the cube sought: that is, if there be two cubes -or dyes formed, the side of one being equal to E F, and the -side of the other equal to F T; the former of these cubes shall -bear the same proportion to the latter, as the line E F bears -to F G.</p> - -<p>81. <span class="smcap gesperrt">Indeed</span> this placing a cone to cut through a plane is -not a practicable method of resolving problems. But when -the geometers had discovered this use of the cone, they applied -themselves to consider the nature of the lines, which -will be produced by the intersection of the surface of a cone<span class="pagenum"><a name="Page_106" id="Page_106">[106]</a></span> -and a plane; whereby they might be enabled both to reduce -these kinds of solutions to practice, and also to render their -demonstrations concise and elegant.</p> - -<p><a name="c106" id="c106">82.</a> <span class="smcap gesperrt">Whenever</span> the plane, which cuts the cone, is equidistant -from another plane, that touches the cone on the side; -(which is the case of the present figure;) the line, wherein -the plane cuts the surface of the cone, is called a parabola. -But if the plane, which cuts the cone, be so inclined to this -other, that it will pass quite through the cone (as in fig. 65.) -such a plane by cutting the cone produces the figure called -an ellipsis, in which we shall hereafter shew the earth and -other planets to move round the sun. If the plane, which -cuts the cone, recline the other way (as in fig. 66.) so as not -to be parallel to any plane, whereon the cone can lie, nor yet -to cut quite through the cone; such a plane shall produce in -the cone a third kind of line, which is called an hyperbola. -But it is the first of these lines named the parabola, wherein -bodies, that are thrown obliquely, will be carried by the force -of gravity; as I shall here proceed to shew, after having first -directed my readers how to describe this sort of line upon a -plane, by which the form of it may be seen.</p> - -<p>83. <span class="smcap gesperrt">To</span> any straight line A B (fig. 67.) let a straight ruler -C D be so applied, as to stand against it perpendicularly. Upon -the edge of this ruler let another ruler E F be so placed, as to -move along upon the edge of the first ruler C D, and keep always -perpendicular to it. This being so disposed, let any -point, as G, be taken in the line A B, and let a string equal<span class="pagenum"><a name="Page_107" id="Page_107">[107]</a></span> -in length to the ruler E F be fastened by one end to the point -G, and by the other to the extremity F of the ruler E F. Then -if the string be held down to the ruler E F by a pin H, as is -represented in the figure; the point of this pin, while the -ruler E F moves on the ruler C D, shall describe the line I K L, -which will be one part of the curve line, whose description -we were here to teach: and by applying the rulers in the like -manner on the other side of the line A B, we may describe -the other part I M of this line. If the distance C G be equal -to half the line E F in fig. 64, the line M I L will be that very -line, wherein the plane A B C D in that figure cuts the cone.</p> - -<p>84. <span class="smcap gesperrt">The</span> line A I is called the axis of the parabola M I L, -and the point G is called the focus.</p> - -<p>85. <span class="smcap gesperrt">Now</span> by comparing the effects of gravity upon falling -bodies, with what is demonstrated of this figure by the geometers, -it is proved, that every body thrown obliquely is -carried forward in one of these lines, the axis whereof is perpendicular to the horizon.</p> - -<p>86. <span class="smcap gesperrt">The</span> geometers demonstrate, that if a line be drawn to -touch a parabola in any point, as the line A B (in fig. 68.) touches -the parabola C D, whose axis is Y Z, in the point E; and several -lines F G, H I, K L be drawn parallel to the axis of the parabola: -then the line F G will be to H I in the duplicate proportion of -E F to E H, and F G to K L in the duplicate proportion of E F -to E K; likewise H I to K L in the duplicate proportion of E H -to E K. What is to be understood by duplicate or two-fold<span class="pagenum"><a name="Page_108" id="Page_108">[108]</a></span> -proportion, has been already explained<a name="FNanchor_73_73" id="FNanchor_73_73"></a><a href="#Footnote_73_73" class="fnanchor">[73]</a>. Accordingly I -mean here, that if the line M be taken to bear the same proportion -to E H, as E H bears to E F, H I will bear the same -proportion to F G, as M bears to E F; and if the line N bears -the same proportion to E K, as E K bears to E F, K L will bear -the same proportion to F G, as N bears to E F; or if the line -O bear the same proportion to E K, as E K bears to E H, K L -will bear the same proportion to H I, as O bears to E H.</p> - -<p>87. <span class="smcap gesperrt">This</span> property is essential to the parabola, being -so connected with the nature of the figure, that every line -possessing this property is to be called by this name.</p> - -<p>88. <span class="smcap gesperrt">Now</span> suppose a body to be thrown from the point A -(in fig. 69.) towards B in the direction of the line A B. This -body, if left to it self, would move on with a uniform motion -through this line A B. Suppose the eye of a spectator to -be placed at the point C just under the point A; and let us -imagine the earth to be so put into motion along with the -body, as to carry the spectator’s eye along the line C D parallel -to A B; and that the eye would move on with the same velocity, -wherewith the body would proceed in the line A B, if -it were to be left to move without any disturbance from its -gravitation towards the earth. In this case if the body moved -on without being drawn towards the earth, it would appear -to the spectator to be at rest. But if the power of gravity -exerted it self on the body, it would appear to the spectator<span class="pagenum"><a name="Page_109" id="Page_109">[109]</a></span> -to fall directly down. Suppose at the distance of time, -wherein the body by its own progressive motion would have -moved from A to E, it should appear to the spectator to -have fallen through a length equal to E F: then the body at -the end of this time will actually have arrived at the point F. -If in the space of time, wherein the body would have moved -by its progressive motion from A to G, it would have appeared -to the spectator to have fallen down the space G H: -then the body at the end of this greater interval of time -will be arrived at the point H. Now if the line A F H I be -that, through which the body actually passes; from what -has here been said, it will follow, that this line is one of those, -which I have been describing under the name of the parabola. -For the distances E F, G H, through which the body is -seen to fall, will increase in the duplicate proportion of the -times<a name="FNanchor_74_74" id="FNanchor_74_74"></a><a href="#Footnote_74_74" class="fnanchor">[74]</a>; but the lines A E, A G will be proportional to the -times wherein they would have been described by the single -progressive motion of the body: therefore the lines E F, G H -will be in the duplicate proportion of the lines A F, A G; and -the line A F H I possesses the property of the parabola.</p> - -<p>89. <span class="smcap gesperrt">If</span> the earth be not supposed to move along with the -body, the case will be a little different. For the body being -constantly drawn directly towards the center of the earth, -the body in its motion will be drawn in a direction a little oblique -to that, wherein it would be drawn by the earth in motion, -as before supposed. But the distance to the center of the<span class="pagenum"><a name="Page_110" id="Page_110">[110]</a></span> -earth bears so vast a proportion to the greatest length, to which -we can throw bodies, that this obliquity does not merit any -regard. From the sequel of this discourse it may indeed be -collected, what line the body being thrown thus would be -found to describe, allowance being made for this obliquity of -the earth’s action<a name="FNanchor_75_75" id="FNanchor_75_75"></a><a href="#Footnote_75_75" class="fnanchor">[75]</a>. This is the discovery of Sir <span class="smcap">Is. Newton</span>; -but has no use in this place. Here it is abundantly sufficient -to consider the body as moving in a parabola.</p> - -<p>90. <span class="smcap gesperrt">The</span> line, which a projected body describes, being -thus known, practical methods have been deduced from -hence for directing the shot of great guns to strike any object -desired. This work was first attempted by <span class="smcap"><em class="gesperrt">Galileo</em></span>, -and soon after farther improved by his scholar <span class="smcap"><em class="gesperrt">Torricelli</em></span>; -but has lately been rendred more complete by the great -Mr. <span class="smcap"><em class="gesperrt">Cotes</em></span>, whose immature death is an unspeakable loss to -mathematical learning. If it be required to throw a body -from the point A (in fig. 70.) so as to strike the point B; -through the points A, B draw the straight line C D, and erect -the line A E perpendicular to the horizon, and of four times -the height, from which a body must fall to acquire the velocity, -wherewith the body is intended to be thrown. Through -the points A and E describe a circle, that shall touch the line -C D in the point A. Then from the point B draw the line -B F perpendicular to the horizon, intersecting the circle in the -points G and H. This being done, if the body be projected -directly towards either of these points G or H, it shall fall upon -the point B; but with this difference, that, if it be thrown<span class="pagenum"><a name="Page_111" id="Page_111">[111]</a></span> -in the direction A G, it shall sooner arrive at B, than if it were -projected in the direction A H. When the body is projected -in the direction A G; the time, it will take up in arriving at -B, will bear the same proportion to the time, wherein it would -fall down through one fourth part of A E, as A G bears to -half A E. But when the body is thrown in the direction of -A H, the time of its passing to B will bear the same proportion -to the time, wherein it would fall through one fourth part -of A E, as A H bears to half A E.</p> - -<p>91. <span class="smcap gesperrt">If</span> the line A I be drawn so as to divide the angle under -E A D in the middle, and the line I K be drawn perpendicular -to the horizon; this line will touch the circle in the -point I, and if the body be thrown in the direction A I, it -will fall upon the point K: and this point K is the farthest -point in the line A D, which the body can be made to strike, -without increasing its velocity.</p> - -<p>92. <span class="smcap gesperrt">The</span> velocity, wherewith the body every where -moves, may be found thus. Suppose the body to move in -the parabola A B (fig. 71.) Erect A C perpendicular to the -horizon, and equal to the height, from which a body must -fall to acquire the velocity, wherewith the body sets out from -A. If you take any points as D and E in the parabola, and -draw D F and E G parallel to the horizon; the velocity of the -body in D will be equal to what a body will acquire in falling -down by its own weight through C F, and in E the velocity -will be the same, as would be acquired in falling through -C G. Thus the body moves slowest at the highest point H -of the parabola; and at equal distances from this point will<span class="pagenum"><a name="Page_112" id="Page_112">[112]</a></span> -move with equal swiftness, and descend from that highest -point through the line H B altogether like to the line A H in -which it ascended; abating only the resistance of the air, -which is not here considered. If the line H I be drawn from -the highest point H parallel to the horizon, A I will be equal -to ¼ of B G in fig. 70, when the body is projected in the direction -A G, and equal to ¼ of B H, when the body is thrown in -the direction A H provided A D be drawn horizontally.</p> - -<p><a name="c112" id="c112">93.</a> <span class="smcap gesperrt">Thus</span> I have recounted the principal discoveries, -which had been made concerning the motion of bodies by -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em>’s</span> predecessors; all these discoveries, by -being found to agree with experience, contributing to establish -the laws of motion, from whence they were deduced. -I shall therefore here finish what I had to say upon those -laws; and conclude this chapter with a few words concerning -the distinction which ought to be made between absolute -and relative motion. For some have thought fit to confound -them together; because they observe the laws of motion to -take place here on the earth, which is in motion, after the same -manner as if it were at rest. But Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> has -been careful to distinguish between the relative and absolute -consideration both of motion and time<a name="FNanchor_76_76" id="FNanchor_76_76"></a><a href="#Footnote_76_76" class="fnanchor">[76]</a>. The astronomers -anciently found it necessary to make this distinction in time. -Time considered in it self passes on equably without relation to -any thing external, being the proper measure of the continuance -and duration of all things. But it is most frequently conceived -of by us under a relative view to some succession in<span class="pagenum"><a name="Page_113" id="Page_113">[113]</a></span> -sensible things, of which we take cognizance. The succession -of the thoughts in our own minds is that, from whence -we receive our first idea of time, but is a very uncertain measure -thereof; for the thoughts of some men flow on much -more swiftly, than the thoughts of others; nor does the same -person think equally quick at all times. The motions of the -heavenly bodies are more regular; and the eminent division -of time into night and day, made by the sun, leads us to -measure our time by the motion of that luminary: nor do we -in the affairs of life concern our selves with any inequality, -which there may be in that motion; but the space of time -which comprehends a day and night is rather supposed to be -always the same. However astronomers anciently found -these spaces of time not to be always of the same length, and -have taught how to compute their differences. Now the -time, when so equated as to be rendered perfectly equal, is -the true measure of duration, the other not. And therefore -this latter, which is absolutely true time, differs from the -other, which is only apparent. And as we ordinarily make -no distinction between apparent time, as measured by the -sun, and the true; so we often do not distinguish in our usual -discourse between the real, and the apparent or relative -motion of bodies; but use the same words for one, as we -should for the other. Though all things about us are really -in motion with the earth; as this motion is not visible, we -speak of the motion of every thing we see, as if our selves -and the earth stood still. And even in other cases, where we -discern the motion of bodies, we often speak of them not in -relation to the whole motion we see, but with regard to other<span class="pagenum"><a name="Page_114" id="Page_114">[114]</a></span> -bodies, to which they are contiguous. If any body were lying -on a table; when that table shall be carried along, we -say the body rests upon the table, or perhaps absolutely, that -the body is at rest. However philosophers must not reject all -distinction between true and apparent motions, any more than -astronomers do the distinction between true and vulgar time; -for there is as real a difference between them, as will appear -by the following consideration. Suppose all the bodies of -the universe to have their courses stopped, and reduced to -perfect rest. Then suppose their present motions to be again -restored; this cannot be done without an actual impression -made upon some of them at least. If any of them be -left untouched, they will retain their former state, that is, -still remain at rest; but the other bodies, which are -wrought upon, will have changed their former state of rest, -for the contrary state of motion. Let us now suppose the -bodies left at rest to be annihilated, this will make no alteration -in the state of the moving bodies; but the effect -of the impression, which was made upon them, will still -subsist. This shews the motion they received to be an absolute -thing, and to have no necessary dependence upon -the relation which the body said to be in motion has to any -other body<a name="FNanchor_77_77" id="FNanchor_77_77"></a><a href="#Footnote_77_77" class="fnanchor">[77]</a>.</p> - -<p>94. <span class="smcap gesperrt">Besides</span> absolute and relative motion are distinguishable -by their Effects. One effect of motion is, that bodies, -when moved round any center or axis, acquire a certain<span class="pagenum"><a name="Page_115" id="Page_115">[115]</a></span> -power, by which they forcibly press themselves from that center -or axis of motion. As when a body is whirled about in a -sling, the body presses against the sling, and is ready to fly -out as soon as liberty is given it. And this power is proportional -to the true, not relative motion of the body round such -a center or axis. Of this Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> gives the following -instance<a name="FNanchor_78_78" id="FNanchor_78_78"></a><a href="#Footnote_78_78" class="fnanchor">[78]</a>. If a pail or such like vessel near full of water -be suspended by a string of sufficient length, and be turned -about till the string be hard twisted. If then as soon as the -vessel and water in it are become still and at rest, the vessel be -nimbly turned about the contrary way the string was twisted, -the vessel by the strings untwisting it self shall continue its motion -a long time. And when the vessel first begins to turn, the -water in it shall receive little or nothing of the motion of the -vessel, but by degrees shall receive a communication of motion, -till at last it shall move round as swiftly as the vessel it -self. Now the definition of motion, which <span class="smcap"><em class="gesperrt">Des Cartes</em></span> has -given us upon this principle of making all motion meerly relative, -is this: that motion, is a removal of any body from its -vicinity to other bodies, which were in immediate contact -with it, and are considered as at rest<a name="FNanchor_79_79" id="FNanchor_79_79"></a><a href="#Footnote_79_79" class="fnanchor">[79]</a>. And if this be compared -with what he soon after says, that there is nothing real -or positive in the body moved, for the sake of which we -ascribe motion to it, which is not to be found as well in the -contiguous bodies, which are considered as at rest<a name="FNanchor_80_80" id="FNanchor_80_80"></a><a href="#Footnote_80_80" class="fnanchor">[80]</a>; it will -follow from thence, that we may consider the vessel as at rest<span class="pagenum"><a name="Page_116" id="Page_116">[116]</a></span> -and the water as moving in it: and the water in respect of -the vessel has the greatest motion, when the vessel first begins -to turn, and loses this relative motion more and more, till at -length it quite ceases. But now, when the vessel first begins -to turn, the surface of the water remains smooth and flat, as -before the vessel began to move; but as the motion of the -vessel communicates by degrees motion to the water, the surface -of the water will be observed to change, the water subsiding -in the middle and rising at the edges: which elevation -of the water is caused by the parts of it pressing from the axis, -they move about; and therefore this force of receding from -the axis of motion depends not upon the relative motion of -the water within the vessel, but on its absolute motion; for -it is least, when that relative motion is greatest, and greatest, -when that relative motion is least, or none at all.</p> - -<p>95. <span class="smcap gesperrt">Thus</span> the true cause of what appears in the surface -of this water cannot be assigned, without considering the -water’s motion within the vessel. So also in the system of the -world, in order to find out the cause of the planetary motions, -we must know more of the real motions, which belong -to each planet, than is absolutely necessary for the uses -of astronomy. If the astronomer should suppose the earth to -stand still, he could ascribe such motions to the celestial bodies, -as should answer all the appearances; though he would -not account for them in so simple a manner, as by attributing -motion to the earth. But the motion of the earth must of -necessity be considered, before the real causes, which actuate -the planetary system, can be discovered.</p> - -<hr class="chap" /> - -</div> - -<p><span class="pagenum"><a name="Page_117" id="Page_117">[117]</a></span></p> - -<div class="chapter"> - -<h2 class="p4"><a name="c117" id="c117"><span class="smcap"><span class="gesperrt">Chap</span>. III.</span></a><br /> -Of CENTRIPETAL FORCES.</h2> - -<p class="drop-cap04"><span class="gesperrt">WE</span> have just been describing in the preceding chapter -the effects produced on a body in motion, from its -being continually acted upon by a power always equal in -strength, and operating in parallel directions<a name="FNanchor_81_81" id="FNanchor_81_81"></a><a href="#Footnote_81_81" class="fnanchor">[81]</a>. But bodies -may be acted upon by powers, which in different places shall -have different degrees of force, and whose several directions -shall be variously inclined to each other. The most simple -of these in respect to direction is, when the power is -pointed constantly to one center. This is truly the case of -that power, whose effects we described in the foregoing chapter; -though the center of that power is so far removed, that -the subject then before us is most conveniently to be considered -in the light, wherein we have placed it: But Sir <span class="smcap">Isaac -Newton</span> has considered very particularly this other case of -powers, which are constantly directed to the same center. It -is upon this foundation, that all his discoveries in the system -of the world are raised. And therefore, as this subject bears -so very great a share in the philosophy, of which I am discoursing, -I think it proper in this place to take a short view -of some of the general effects of these powers, before we -come to apply them particularly to the system of the world.</p> - -<p><span class="pagenum"><a name="Page_118" id="Page_118">[118]</a></span></p> - -<p>2. <span class="smcap gesperrt">These</span> powers or forces are by Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> -called centripetal; and their first effect is to cause the body, on -which they act, to quit the straight course, wherein it would -proceed if undisturbed, and to describe an incurvated line, -which shall always be bent towards the center of the force. -It is not necessary, that such a power should cause the body -to approach that center. The body may continue to recede -from the center of the power, notwithstanding its being drawn -by the power; but this property must always belong to its -motion, that the line, in which it moves, will continually be -concave towards the center, to which the power is directed. -Suppose A (in fig. 72.) to be the center of a force. Let a -body in B be moving in the direction of the straight line B C, -in which line it would continue to move, if undisturbed; but -being attracted by the centripetal force towards A, the body -must necessarily depart from this line B C, and being drawn -into the curve line B D, must pass between the lines A B and -B C. It is evident therefore, that the body in B being gradually -turned off from the straight line B C, it will at first be -convex toward the line B C, and consequently concave towards -the point A: for these centripetal powers are supposed -to be in strength proportional to the power of gravity, and, -like that, not to be able after the manner of an impulse to turn -the body sensibly out of its course into a different one in an instant, -but to take up some space of time in producing a visible -effect. That the curve will always continue to have its -concavity towards A may thus appear. In the line B C near -to B take any point as E, from which the line E F G may be so<span class="pagenum"><a name="Page_119" id="Page_119">[119]</a></span> -drawn, as to touch the curve line B D in some point as F. Now -when the body is come to F, if the centripetal power were immediately -to be suspended, the body would no longer continue -to move in a curve line, but being left to it self would -forthwith reassume a straight course; and that straight course -would be in the line F G: for that line is in the direction of -the body’s motion at the point F. But the centripetal force -continuing its energy, the body will be gradually drawn from -this line F G so as to keep in the line F D, and make that line -near the point F to be convex toward F G, and concave toward -A. After the same manner the body may be followed on in -its course through the line B D, and every part of that line be -shewn to be concave toward the point A.</p> - -<p>3. <span class="smcap gesperrt">This</span> then is the constant character belonging to those -motions, which are carried on by centripetal forces; that the -line, wherein the body moves, is throughout concave towards -the center of the force. In respect to the successive distances -of the body from the center there is no general rule to be laid -down; for the distance of the body from the center may either -increase, or decrease, or even keep always the same. The -point A (in fig. 73.) being the center of a centripetal force, -let a body at B set out in the direction of the straight line B C -perpendicular to the line A B drawn from A to B. It will be -easily conceived, that there is no other point in the line B C so -near to A, as the point B; that A B is the shortest of all the -lines, which can be drawn from A to any part of the line B C; -all other lines, as A D, or A E, drawn from A to the line B C -being longer than A B. Hence it follows, that the body setting<span class="pagenum"><a name="Page_120" id="Page_120">[120]</a></span> -out from B, if it moved in the line B C, it would recede -more and more from the point A. Now as the operation of -a centripetal force is to draw a body towards the center of -the force: if such a force act upon a resting body, it must -necessarily put that body so into motion, as to cause it to -move towards the center of the force: if the body were of -it self moving towards that center, the centripetal force -would accelerate that motion, and cause it to move faster -down: but if the body were in such a motion, as being left -to itself it would recede from this center, it is not necessary, -that the action of a centripetal power upon it should -immediately compel the body to approach the center, from -which it would otherwise have receded; the centripetal -power is not without effect, if it cause the body to recede -more slowly from that center, than otherwise it would have -done. Thus in the case before us, the smallest centripetal -power, if it act on the body, will force it out of the line B C, -and cause it to pass in a bent line between B C and the point -A, as has been before explained. When the body, for instance, -has advanced to the line A D, the effect of the centripetal -force discovers it self by having removed the body out -of the line B C, and brought it to cross the line A D somewhere -between A and D: suppose at F. Now A D being -longer than A B, A F may also be longer than A B. The centripetal -power may indeed be so strong, that A F shall be -shorter than A B; or it may be so evenly balanced with the -progressive motion of the body, that A F and A B shall be just -equal: and in this last case, when the centripetal force is of -that strength, as constantly to draw the body as much toward<span class="pagenum"><a name="Page_121" id="Page_121">[121]</a></span> -the center, as the progressive motion would carry it off, the -body will describe a circle about the center A, this center of -the force being also the center of the circle.</p> - -<p>4. <span class="smcap gesperrt">If</span> the body, instead of setting out in the line B C perpendicular -to A B, had set out in another line B G more inclined -towards the line A B, moving in the curve line B H; -then as the body, if it were to continue its motion in the line -B G, would for some time approach the center A; the centripetal -force would cause it to make greater advances toward -that center. But if the body were to set out in the line B I reclined -the other way from the perpendicular B C, and were to -be drawn by the centripetal force into the curve line B K; the -body, notwithstanding any centripetal force, would for some -time recede from the center; since some part at least of the -curve line B K lies between the line B I and the perpendicular B C.</p> - -<p>5. <span class="smcap gesperrt">Thus</span> far we have explained such effects, as attend -every centripetal force. But as these forces may be very different -in regard to the different degrees of strength, wherewith -they act upon bodies in different places; I shall now proceed -to make mention in general of some of the differences -attending these centripetal motions.</p> - -<p>6. <span class="smcap gesperrt">To</span> reassume the consideration of the last mentioned -case. Suppose a centripetal power directed toward the point -A (in fig. 74.) to act on a body in B, which is moving in -the direction of the straight line B C, the line B C reclining -off from A B. If from A the straight lines A D, A E, A F are<span class="pagenum"><a name="Page_122" id="Page_122">[122]</a></span> -drawn at pleasure to the line C B; the line C B being prolonged -beyond B to G, it appears that A D is inclined to the line -G C more obliquely, than A B is inclined to it, A E is inclined -more obliquely than A D, and A F more than A E. To -speak more correctly, the angle under A D G is less than that -under A B G, the angle under A E G less than that under -A D G, and the angle under A F G less than that under A E G. -Now suppose the body to move in the curve line B H I K. -Then it is here likewise evident, that the line B H I K being -concave towards A, and convex towards the line B C, -it is more and more turned off from the line B C; so -that in the point H the line A H will be less obliquely inclined -to the curve line B H I K, than the same line A H D is inclined -to B C at the point D; at the point I the inclination of the -line A I to the curve line will be more different from the inclination -of the same line A I E to the line B C, at the point E; -and in the points K and F the difference of inclination will be -still greater; and in both the inclination at the curve will be -less oblique, than at the straight line B C. But the straight -line A B is less obliquely inclined to B G, than A D is inclined -towards D G: therefore although the line A H be less obliquely -inclined towards the curve H B, than the same line A H D is -inclined towards D G; yet it is possible, that the inclination -at H may be more oblique, than the inclination at B. The inclination -at H may indeed be less oblique than the other, or -they may be both the same. This depends upon the degree -of strength, wherewith the centripetal force exerts it self, -during the passage of the body from B to H. After the same -manner the inclinations at I and K depend entirely on the degree<span class="pagenum"><a name="Page_123" id="Page_123">[123]</a></span> -of strength, wherewith the centripetal force acts on the -body in its passage from H to K: if the centripetal force be -weak enough, the lines A H and A I drawn from the center A -to the body at H and at I shall be more obliquely inclined to -the curve, than the line A B is inclined towards B G. The centripetal -force may be of that strength as to render all these inclinations -equal, or if stronger, the inclinations at I and K -will be less oblique than at B. Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> has particularly -shewn, that if the centripetal power decreases after -a certain manner with the increase of distance, a body may -describe such a curve line, that all the lines drawn from the -center to the body shall be equally inclined to that curve line.<a name="FNanchor_82_82" id="FNanchor_82_82"></a><a href="#Footnote_82_82" class="fnanchor">[82]</a> -But I do not here enter into any particulars, my present intention -being only to shew, that it is possible for a body to be -acted upon by a force continually drawing it down towards a -center, and yet that the body shall continue to recede from -that center; for here as long as the lines A H, A I, &c drawn -from the center A to the body do not become less oblique to -the curve, in which the body moves; so long shall those lines -perpetually increase, and consequently the body shall more -and more recede from the center.</p> - -<p>7. <span class="smcap gesperrt">But</span> we may observe farther, that if the centripetal -power, while the body increases its distance from the center, -retain sufficient strength to make the lines drawn from the -center to the body to become at length less oblique to the -curve; then if this diminution of the obliquity continue, till<span class="pagenum"><a name="Page_124" id="Page_124">[124]</a></span> -at last the line drawn from the center to the body shall cease -to be obliquely inclined to the curve, and shall become perpendicular -thereto; from this instant the body shall no longer -recede from the center, but in its following motion it shall -again descend, and shall describe a curve line in all respects -like to that, which it has described already; provided the -centripetal power, every where at the same distance from the -center, acts with the same strength. So we observed in the -preceding chapter, that, when the motion of a projectile became -parallel to the horizon, the projectile no longer ascended, -but forthwith directed its course downwards, descending -in a line altogether like that, wherein it had before ascended<a name="FNanchor_83_83" id="FNanchor_83_83"></a><a href="#Footnote_83_83" class="fnanchor">[83]</a>.</p> - -<p>8. <span class="smcap gesperrt">This</span> return of the body may be proved by the following -proposition: that if the body in any place, suppose at -I, were to be stopt, and be thrown directly backward with the -velocity, wherewith it was moving forward in that point I; -then the body, by the action of the centripetal force upon it, -would move back again over the path I H B, in which it had -before advanced forward, and would arrive again at the point -B in the same space of time, as was taken up in its passage -from B to I; the velocity of the body at its return to the point -B being the same, as that wherewith it first set out from that -point. To give a full demonstration of this proposition, -would require that use of mathematics, which I here purpose -to avoid; but, I believe, it will appear in great measure -evident from the following considerations.</p> - -<p><span class="pagenum"><a name="Page_125" id="Page_125">[125]</a></span></p> - -<p>9. <span class="smcap gesperrt">Suppose</span> (in fig. 75.) that a body were carried after -the following manner through the bent figure A B C D E F, -composed of the straight lines A B, B C, C D, D E, E F. First -let it be moving in the line A B, from A towards B, with any -uniform velocity. At B let the body receive an impulse directed -toward some point, as G, taken within the concavity -of the figure. Now whereas this body, when once moving -in the straight line A B, will continue to move on in this line, -so long as it shall be left to it self; but being disturbed at the -point B in its motion by the impulse, which there acts upon -it, it will be turned out of this line A B into some other straight -line, wherein it will afterwards continue to move, as long as it -shall be left to itself. Therefore let this impulse have strength -sufficient to turn the body into the line B C. Then let the -body move on undisturbed from B to C, but at C let it receive -another impulse pointed toward the same point G, and of sufficient -strength to turn the body into the line C D. At D let -a third impulse, directed like the rest to the point G, turn the -body into the line D E. And at E let another impulse, directed -likewise to the point G, turn the body into the line E F. -Now, I say, if the body while moving in the line E F -be stopt, and turned back again in this line with the same -velocity, as that wherewith it was moving forward in this line; -then by the repetition of the former impulse at E the body will -be turned into the line E D, and move in it from E to D with -the same velocity as before it moved with from D to E; by -the repetition of the impulse at D, when the body shall -have returned to that point, it will be turned into the line -D C; and by the repetition of the other impulses at C and B<span class="pagenum"><a name="Page_126" id="Page_126">[126]</a></span> -the body will be brought back again into the line B A, with -the velocity, wherewith it first moved in that line.</p> - -<p>10. <span class="smcap gesperrt">This</span> I prove as follows. Let D E and F E be continued -beyond E. In D E thus continued take at pleasure the -length E H, and let H I be so drawn, as to be equidistant from -the line G E. Then, by what has been written upon the second -law of motion<a name="FNanchor_84_84" id="FNanchor_84_84"></a><a href="#Footnote_84_84" class="fnanchor">[84]</a>, it follows, that after the impulse on -the body in E it will move through E I in the same time, as -it would have imployed in moving from E to H, with the velocity -which it had in the line D E. In F E prolonged take -E K equal to E I, and draw K L equidistant from G E. Then, -because the body is thrown back in the line F E with the same -velocity as that wherewith it went forward in that line; if, -when the body was returned to E, it were permitted to go -straight on, it would pass through E K in the same time, as it -took up in passing through E I, when it went forward in the -line E F. But, if at the body’s return to the point E, such an -impulse directed toward the point D were to be given it, whereby -it should be turned into the line D E; I say, that the -impulse necessary to produce this effect must be equal to -that, which turned the body out of the line D E into E F; -and that the velocity, with which the body will return into -the line E D, is the same, as that wherewith it before moved -through this line from D to E. Because E K is equal to E I, and -K L and H I, being each equidistant from G E, are by consequence -equidistant from each other; it follows, that the two<span class="pagenum"><a name="Page_127" id="Page_127">[127]</a></span> -triangular figures I E H and K E L are altogether like and equal -to each other. If I were writing to mathematicians, I might -refer them to some proportions in the elements of <span class="smcap">Euclid</span> -for the proof of this<a name="FNanchor_85_85" id="FNanchor_85_85"></a><a href="#Footnote_85_85" class="fnanchor">[85]</a> but as I do not here address my self to -such, so I think this assertion will be evident enough without -a proof in form; at least I must desire my readers to receive -it as a proposition true in geometry. But these two triangular -figures being altogether like each other and equal; as E K -is equal to E I, so E L is equal to E H, and K L equal to H I. -Now the body after its return to E being turned out of the line -F E into E D by an impulse acting upon it in E, after the manner -above expressed; the body will receive such a velocity by -this impulse, as will carry it through E L in the same time, as it -would have imployed in passing through E K, if it had gone -on in that line undisturbed. And it has already been observed, -that the time, in which the body would pass over E K -with the velocity wherewith it returns, is equal to the time -it took up in going forward from E to I; that is, equal to the -time, in which it would have gone through E H with the velocity, -wherewith it moved from D to E. Therefore the time, -in which the body will pass through E L after its return into -the line E D, is the same, as would have been taken up by -the body in passing through E H with the velocity, wherewith -the body first moved in the line D E. Since therefore -E L and E H are equal, the body returns into the line D E with -the velocity, which it had before in that line. Again I say, -the second impulse in E is equal to the first. By what has<span class="pagenum"><a name="Page_128" id="Page_128">[128]</a></span> -been said on the second law of motion concerning the effect of -oblique impulses<a name="FNanchor_86_86" id="FNanchor_86_86"></a><a href="#Footnote_86_86" class="fnanchor">[86]</a>, it will be understood, that the impulse in E, -whereby the body was turned out of the line D E into the line -E F, is of such strength, that if the body had been at rest, -when this impulse had acted upon it, this impulse would have -communicated so much motion to the body, as would have -carried it through a length equal to H I, in the time wherein -the body would have passed from E to H, or in the time -wherein it passed from E to I. In the same manner, on the return -of the body, the impulse in E, whereby the body is turned -out of the line F E into E D, is of such strength, that if it -had acted on the body at rest, it would have caused the body -to move through a length equal to K L, in the same time, as -the body would imploy in passing through E K with the velocity, -wherewith it returns in the line F E. Therefore the second -impulse, had it acted on the body at rest, would have -caused it to move through a length equal to K L in the same -space of time, as would be taken up by the body in passing -through a length equal to H I, were the first impulse to act on -the body when at rest. That is, the effects of the first and -second impulse on the body when at rest would be the same; -for K L and H I are equal: consequently the second impulse -is equal to the first.</p> - -<p>11. <span class="smcap gesperrt">Thus</span> if the body be returned through F E with the -velocity, wherewith it moved forward; we have shewn how -by the repetition of the impulse, which acted on it at E, the<span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span> -body will return again into the line D E with the velocity, -which it had before in that line. By the same process of reasoning -it may be proved, that, when the body is returned -back to D, the impulse, which before acted on the body at -that point, will throw the body into the line D C with the velocity, -which it first had in that line; and the other impulses -being successively repeated, the body will at length be brought -back again into the line B A with the velocity, wherewith it -set out in that line.</p> - -<p>12. <span class="smcap gesperrt">Thus</span> these impulses, by acting over again in an inverted -order all their operation on the body, bring it back again -through the path, in which it had proceeded forward. And -this obtains equally, whatever be the number of the straight -lines, whereof this curve figure is composed. Now by a method -of reasoning, which Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> makes great -use of, and which he introduced into geometry, thereby -greatly inriching that science<a name="FNanchor_87_87" id="FNanchor_87_87"></a><a href="#Footnote_87_87" class="fnanchor">[87]</a>; we might make a transition -from this figure composed of a number of straight lines to a -figure of one continued curvature, and from a number of separate -impulses repeated at distinct intervals to a continual -centripetal force, and shew, that, because what has been -here advanced holds universally true, whatever be the number -of straight lines, whereof the curve figure A C F is composed, -and howsoever frequently the impulses at the angles of -this figure are repeated; therefore the same will still remain -true, although this figure should be converted into one of a -continued curvature, and these distinct impulses should be<span class="pagenum"><a name="Page_130" id="Page_130">[130]</a></span> -changed into a continual centripetal force. But as the explaining -this method of reasoning is foreign to my present design; -so I hope my readers, after what has been said, will find no -difficulty in receiving the proposition laid down above: that, if -the body, which has moved through the curve line B H I (in fig. -74.) from B to I, when it is come to I, be thrown directly back -with the same velocity as that, wherewith it proceeded forward, -the centripetal force, by acting over again all its operation on -the body, shall bring the body back again in the line I H B: -and as the motion of the body in its course from B to I was every -where in such a manner oblique to the line drawn from the -center to the body, that the centripetal power acted in some -degree against the body’s motion, and gradually diminished it; -so in the return of the body, the centripetal power will every -where draw the body forward, and accelerate its motion by -the same degrees, as before it retarded it.</p> - -<p>13. <span class="smcap gesperrt">This</span> being agreed, suppose the body in K to have the -line A K no longer obliquely inclined to its motion. In this case, -if the body be turned back, in the manner we have been considering, -it must be directed back perpendicularly to A K. -But if it had proceeded forward, it would likewise have moved -in a direction perpendicular to A K; consequently, whether -it move from this point K backward or forward, it must -describe the same kind of course. Therefore since by being -turned back it will go over again the line K I H B; if it be permitted -to go forward, the line K L, which it shall describe, -will be altogether similar to the line K H B.</p> - -<p><span class="pagenum"><a name="Page_131" id="Page_131">[131]</a></span></p> - -<p>14. <span class="smcap gesperrt">In</span> like manner we may determine the nature of the -motion, if the line, wherein the body sets out, be inclined (as -in fig. 76.) down toward the line B A drawn between the -body and the center. If the centripetal power so much increases -in strength, as the body approaches, that it can bend -the path, in which the body moves, to that degree, as to cause -all the lines as A H, A I, A K to remain no less oblique to the -motion of the body, than A B is oblique to B C; the body -shall continually more and more approach the center. But -if the centripetal power increases in so much less a degree, as -to permit the line drawn from the center to the body, as it accompanies -the body in its motion, at length to become more -and more erect to the curve wherein the body moves, and in -the end, suppose at K, to become perpendicular thereto; from -that time the body shall rise again. This is evident from what -has been said above; because for the very same reason here also -the body shall proceed from the point K to describe a line altogether -similar to the line, in which it has moved from B to K. -Thus, as it was observed of the pendulum in the preceding chapter<a name="FNanchor_88_88" id="FNanchor_88_88"></a><a href="#Footnote_88_88" class="fnanchor">[88]</a>, -that all the time it approaches towards being perpendicular -to the horizon, it more and more descends; but, as soon as it -is come into that perpendicular situation, it immediately rises -again by the same degrees, as it descended by before: so here -the body more and more approaches the center all the time it -is moving from B to K; but thence forward it rises from the -center again by the same degrees, as it approached by before.</p> - -<p><span class="pagenum"><a name="Page_132" id="Page_132">[132]</a></span></p> - -<p>15. <span class="smcap gesperrt">If</span> (in fig. 77.) the line B C be perpendicular to A B; then -it has been observed above<a name="FNanchor_89_89" id="FNanchor_89_89"></a><a href="#Footnote_89_89" class="fnanchor">[89]</a>, that the centripetal power may -be so balanced with the progressive motion of the body, that -the body may keep moving round the center A constantly at -the same distance; as a body does, when whirled about any -point, to which it is tyed by a string. If the centripetal power -be too weak to produce this effect, the motion of the body -will presently become oblique to the line drawn from itself to -the center, after the manner of the first of the two cases, -which we have been considering. If the centripetal power -be stronger, than what is required to carry the body in a circle, -the motion of the body will presently fall in with the second -of the cases, we have been considering.</p> - -<p>16. <span class="smcap gesperrt">If</span> the centripetal power so change with the change of -distance, that the body, after its motion has become oblique -to the line drawn from itself to the center, shall again become -perpendicular thereto; which we have shewn to be possible -in both the cases treated of above; then the body shall in its -subsequent motion return again to the distance of A B, and -from that distance take a course similar to the former: and -thus, if the body move in a space free from all resistance, -which has been here all along supposed; it shall continue in -a perpetual motion about the center, descending and ascending -alternately therefrom. If the body setting out from B (in -fig. 78.) in the line B C perpendicular to A B, describe the line -B D E, which in D shall be oblique to the line A D, but in E -shall again become erect to A E drawn from the body in E to the -center A; then from this point E the body shall describe the -line E F G altogether like to the line B D E, and at G shall be -at the same distance from A, as it was at B. But likewise the -line A G shall be erect to the body’s motion. Therefore the -body shall proceed to describe from G the line G H I altogether -similar to the line G F E, and at I have the same distance -from the center, as it had at E; and also have the line A I erect -to its motion: so that its following motion must be in the line -I K L similar to I H G, and the distance A L equal to A G. Thus -the body will go on in a perpetual round without ceasing, alternately -inlarging and contracting its distance from the center.</p> - -<div class="figcenter"> - <img src="images/ill-187.jpg" width="400" height="512" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_133" id="Page_133">[133]</a></span></p> - -<p>17. <span class="smcap gesperrt">If</span> it so happen, that the point E fall upon the line B A -continued beyond A; then the point G will fall on B, I on E, -and L also on B; so that the body will describe in this case a -simple curve line round the center A, like the line B D E F in -fig. 79, in which it will continually revolve from B to E -and from E to B without end.</p> - -<p>18. <span class="smcap gesperrt">If</span> A E in fig. 78 should happen to be perpendicular -to A B, in this case also a simple line will be described; for the -point G will fall on the line B A prolonged beyond A, the -point I on the line A E prolonged beyond A, and the point L -on B: so that the body will describe a line like the curve line -B E G I in fig. 80, in which the opposite points B and G -are equally distant from A, and the opposite points E and I -are also equally distant from the same point A.</p> - -<p><span class="pagenum"><a name="Page_134" id="Page_134">[134]</a></span></p> - -<p>19. <span class="smcap gesperrt">In</span> other cases the line described will have a more -complex figure.</p> - -<p>20. <span class="smcap gesperrt">Thus</span> we have endeavoured to shew how a body, -while it is constantly attracted towards a center, may notwithstanding -by its progressive motion keep it self from falling -down to that center; but describe about it an endless circuit, -sometimes approaching toward that center, and at other -times as much receding from the same.</p> - -<p>21. <span class="smcap gesperrt">But</span> here we have supposed, that the centripetal power -is of equal strength every where at the same distance from the -center. And this is the case of that centripetal power, which -will hereafter be shewn to be the cause, that keeps the planets -in their courses. But a body may be kept on in a perpetual -circuit round a center, although the centripetal power have -not this property. Indeed a body may by a centripetal force -be kept moving in any curve line whatever, that shall have its -concavity turned every where towards the center of the force.</p> - -<p>22. <span class="smcap gesperrt">To</span> make this evident I shall first propose the case of a -body moving through the incurvated figure A B C D E (in fig. 81.) -which is composed of the straight lines A B, B C, C D, D E, and -E A; the motion being carried on in the following manner. -Let the body first move in the line A B with any uniform velocity. -When it is arrived at the point B, let it receive an impulse -directed toward any point F taken within the figure; -and let the impulse be of that strength as to turn the body out<span class="pagenum"><a name="Page_135" id="Page_135">[135]</a></span> -of the line A B into the line B C. The body after this impulse, -while left to itself, will continue moving in the line B C. -At C let the body receive another impulse directed towards -the same point F, of such strength, as to turn the body from -the line B C into the line C D. At D let the body by another -impulse, directed likewise to the point F, be turned out of the -line C D into D E. And at E let another impulse, directed toward -the point F, turn the body from the line D E into E A. -Thus we see how a body may be carried through the figure -A B C D E by certain impulses directed always toward the same -center, only by their acting on the body at proper intervals, -and with due degrees of strength.</p> - -<p>23. <span class="smcap gesperrt">But</span> farther, when the body is come to the point A, if -it there receive another impulse directed like the rest toward the -point F, and of such a degree of strength as to turn the body -into the line A B, wherein it first moved; I say that the body -shall return into this line with the same velocity, as it had at first.</p> - -<p>24. <span class="smcap gesperrt">Let</span> A B be prolonged beyond B at pleasure, suppose to -G; and from G let G H be drawn, which if produced should -always continue equidistant from B F, or, according to the -more usual phrase, let G H be drawn parallel to B F. Then -it appears, from what has been said upon the second law of -motion<a name="FNanchor_90_90" id="FNanchor_90_90"></a><a href="#Footnote_90_90" class="fnanchor">[90]</a>, that in the time, wherein the body would have moved -from B to G, had it not received a new impulse in B, by the -means of that impulse it will have acquired a velocity, which -will carry it from B to H. After the same manner, if C I be<span class="pagenum"><a name="Page_136" id="Page_136">[136]</a></span> -taken equal to B H, and I K be drawn equidistant from or parallel -to C F; the body will have moved from C to K with the -velocity, which it has in the line C D, in the same time, as it -would have employed in moving from C to I with the velocity, -it had in the line B C. Therefore since C I and B H are equal, -the body will move through C K in the same time, as it would -have taken up in moving from B to G with the original velocity, -wherewith it moved through the line A B. Again, D L -being taken equal to C K and L M drawn parallel to D F; for -the same reason as before the body will move through D M with -the velocity, which it has in the line D E, in the same time, -as it would imploy in moving through B G with its original velocity. -In the last place, if E N be taken equal to D M, and -N O be drawn parallel to E F; likewise if A P be taken equal -to E O, and P Q be drawn parallel to A F: then the body with -the velocity, wherewith it returns into the line A B, will pass -through A Q in the same time, as it would have imployed in -passing through B G with its original velocity. Now as all -this follows directly from what has above been delivered, concerning -the effect of oblique impulses impressed upon bodies -in motion; so we must here observe farther, that it can be -proved by geometry, that A Q will always be equal to E G. -The proof of this I am obliged, from the nature of my present -design, to omit; but this geometrical proportion being -granted, it follows, that the body has returned into the line -A B with the velocity, which it had, when it first moved in -that line; for the velocity, with which it returns into the line -A B, will carry it over the line A Q in the same time, as would<span class="pagenum"><a name="Page_137" id="Page_137">[137]</a></span> -have been taken up in its passing over an equal line B G with -the original velocity.</p> - -<p>25. <span class="smcap gesperrt">Thus</span> we have found, how a body may be carried round -the figure A B C D E by the action of certain impulses upon it -which should all be pointed toward one center. And we likewise -see, that when the body is brought back again to the -point, whence it first set out; if it there meet with an impulse -sufficient to turn it again into the line, wherein it moved -at first, its original velocity will be again restored; and by -the repetition of the same impulses, the body will be carried -again in the same round. Therefore if these impulses, which -act on the body at the points B, C, D, E, and A, continue always -the same, the body will make round this figure innumerable -revolutions.</p> - -<p>26. <span class="smcap gesperrt">The</span> proof, which we have here made use of, holds the -same in any number of straight lines, whereof the figure A B D -should be composed; and therefore by the method of reasoning -referred to above<a name="FNanchor_91_91" id="FNanchor_91_91"></a><a href="#Footnote_91_91" class="fnanchor">[91]</a> we are to conclude, that what has here -been said upon this rectilinear figure, will remain true, if this -figure were changed into one of a continued curvature, and -instead of distinct impulses acting by intervals at the angles of -this figure, we had a continual centripetal force. We have -therefore shewn, that a body may be carried round in any -curve figure A B C ( fig. 82.) which shall every where be -concave towards any one point as D, by the continual action<span class="pagenum"><a name="Page_138" id="Page_138">[138]</a></span> -of a centripetal power directed to that point, and when it is -returned to the point, from whence it set out, it shall recover -again the velocity, with which it departed from that point. -It is not indeed always necessary, that it should return again -into its first course; for the curve line may have some such -figure as the line A B C D B E in fig. 83. In this curve line, -if the body set out from B in the direction B F, and moved -through the line B C D, till it returned to B; here the body -would not enter again into the line B C D, because the two -parts B D and B C of the curve line make an angle at the point -B: so that the centripetal power, which at the point B could -turn the body from the line B F into the curve, will not be -able to turn the body into the line B C from the direction, in -which it returns to the point B; a forceable impulse must be -given the body in the point B to produce that effect.</p> - -<p>27. <span class="smcap gesperrt">If</span> at the point B, whence the body sets out, the curve -line return into it self (as in fig. 82;) then the body, upon -its arrival again at B, may return into its former course, -and thus make an endless circuit about the center of the centripetal -power.</p> - -<p>28. <span class="smcap gesperrt">What</span> has here been said, I hope, will in some measure -enable my readers to form a just idea of the nature of -these centripetal motions.</p> - -<p>29. <span class="smcap gesperrt">I have</span> not attempted to shew, how to find particularly, -what kind of centripetal force is necessary to carry a body in -any curve line proposed. This is to be deduced from the degree<span class="pagenum"><a name="Page_139" id="Page_139">[139]</a></span> -of curvature, which the figure has in each point of it, -and requires a long and complex mathematical reasoning. -However I shall speak a little to the first proportion, which -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> lays down for this purpose. By this -proposition, when a body is found moving in a curve line, it -may be known, whether the body be kept in its course by a -power always pointed toward the same center; and if it be so, -where that center is placed. The proposition is this: that if -a line be drawn from some fixed point to the body, and remaining -by one extream united to that point, it be carried -round along with the body; then, if the power, whereby -the body is kept in its course, be always pointed to this fixed -point as a center, this line will move over equal spaces in equal -portions of time. Suppose a body were moving through the -curve line A B C D (in fig. 84.) and passed over the arches A B, -B C, C D in equal portions of time; then if a point, as E, can -be found, from whence the line E A being drawn to the body -in A, and accompanying the body in its motion, it shall make -the spaces E A B, E B C, and E C D equal, over which it passes, -while the body describes the arches A B, B C, and C D: -and if this hold the same in all other arches, both great and -small, of the curve line A B C D, that these spaces are always -equal, where the times are equal; then is the body kept in -this line by a power always pointed to E as a center.</p> - -<p>30. <span class="smcap gesperrt">The</span> principle, upon which Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> has -demonstrated this, requires but small skill in geometry to comprehend. -I shall therefore take the liberty to close the present<span class="pagenum"><a name="Page_140" id="Page_140">[140]</a></span> -chapter with an explication of it; because such an example -will give the clearest notion of our author’s method of applying -mathematical reasoning to these philosophical subjects.</p> - -<p>31. <span class="smcap gesperrt">He</span> reasons thus. Suppose a body set out from the point -A (in fig. 85.) to move in the straight line A B; and after it -had moved for some time in that line, it were to receive an -impulse directed to some point as C. Let it receive that impulse -at D; and thereby be turned into the line D E; and let -the body after this impulse take the same length of time in -passing from D to E, as it imployed in the passing from A to -D. Then the straight lines C A, C D, and C E being drawn, -Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> proves, that the and triangular spaces -C A D and C D E are equal. This he does in the following -manner.</p> - -<p>32. <span class="smcap gesperrt">Let</span> E F be drawn parallel to C D. Then, from what has -been said upon the second law of motion<a name="FNanchor_92_92" id="FNanchor_92_92"></a><a href="#Footnote_92_92" class="fnanchor">[92]</a>, it is evident, that -since the body was moving in the line A B, when it received -the impulse in the direction D C; it will have moved after -that impulse through the line D E in the same time, as it would -have taken up in moving through D F, provided it had received -no disturbance in D. But the time of the body’s moving -from D to E is supposed to be equal to the time of its moving -through A D; therefore the time, which the body would -have imployed in moving through D F, had it not been disturbed -in D, is equal to the time, wherein it moved through -A D: consequently D F is equal in length to A D; for if the<span class="pagenum"><a name="Page_141" id="Page_141">[141]</a></span> -body had gone on to move through the line A B without interruption, -it would have moved through all parts thereof -with the same velocity, and have passed over equal parts of -that line in equal portions of time. Now C F being drawn, -since A D and D F are equal, the triangular space C D F is equal -to the triangular space C A D. Farther, the line E F being -parallel to C D, it is proved by <span class="smcap">Euclid</span>, that the triangle -C E D is equal to the triangle C F D<a name="FNanchor_93_93" id="FNanchor_93_93"></a><a href="#Footnote_93_93" class="fnanchor">[93]</a>: therefore the triangle -C E D is equal to the triangle C A D.</p> - -<p>33. <span class="smcap gesperrt">After</span> the same manner, if the body receive at E another -impulse directed toward the point C, and be turned by -that impulse into the line E G; if it move afterwards from E to -G in the same space of time, as was taken up by its motion from -D to E, or from A to D; then C G being drawn, the triangle -C E G is equal to C D E. A third impulse at G directed as the -two former to C, whereby the body shall be turned into the -line G H, will have also the like effect with the rest. If the -body move over G H in the same time, as it took up in moving -over E G, the triangle C G H will be equal to the triangle -C E G. Lastly, if the body at H be turned by a fresh impulse -directed toward C into the line H I, and at I by another impulse -directed also to C be turned into the line I K; and if the -body move over each of the lines H I, and I K in the same -time, as it imployed in moving over each of the preceding -lines A D, D E, E G, and G H: then each of the triangles -C H I, and C I K will be equal to each of the preceding. Likewise<span class="pagenum"><a name="Page_142" id="Page_142">[142]</a></span> -as the time, in which the body moves over A D E, is -equal to the time of its moving over E G H, and to the time -of its moving over H I K; the space C A D E will be equal to -the space C E G H, and to the space C H I K. In the same -manner as the time, in which the body moved over A D E G -is equal to the time of its moving over G H I K, so the space -C A D E G will be equal to the space C G H I K.</p> - -<p>34. <span class="smcap gesperrt">From</span> this principle Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> demonstrates -the proposition mentioned above, by that method of arguing -introduced by him into geometry, whereof we have before -taken notice<a name="FNanchor_94_94" id="FNanchor_94_94"></a><a href="#Footnote_94_94" class="fnanchor">[94]</a>, by making according to the principles of that -method a transition from this incurvated figure composed of -straight lines, to a figure of continued curvature; and by -shewing, that since equal spaces are described in equal times -in this present figure composed of straight lines, the same relation -between the spaces described and the times of their description -will also have place in a figure of one continued -curvature. He also deduces from this proposition the reverse -of it; and proves, that whenever equal spaces are continually -described; the body is acted upon by a centripetal force -directed to the center, at which the spaces terminate.</p> - -<hr class="chap" /> - -</div> - -<p><span class="pagenum"><a name="Page_143" id="Page_143">[143]</a></span></p> - -<div class="chapter"> - -<h2 class="p4"><a name="c143" id="c143"><span class="smcap">Chap. IV.</span></a><br /> -Of the RESISTANCE of FLUIDS.</h2> - -<p class="drop-cap06"><span class="gesperrt">BEFORE</span> the cause can be discovered, which keeps the -planets in motion, it is necessary first to know, whether -the space, wherein they move, is empty and void, or filled -with any quantity of matter. It has been a prevailing -opinion, that all space contains in it matter of some kind or -other; so that where no sensible matter is found, there was -yet a subtle fluid substance by which the space was filled up; -even so as to make an absolute plenitude. In order to examine -this opinion, Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> has largely considered -the effects of fluids upon bodies moving in them.</p> - -<p>2. <span class="smcap gesperrt">These</span> effects he has reduced under these three heads. -In the first place he shews how to determine in what manner -the resistance, which bodies suffer, when moving in a fluid, -gradually increases in proportion to the space, they describe -in any fluid; to the velocity, with which they describe it; -and to the time they have been in motion. Under the second -head he considers what degree of resistance different -bodies moving in the same fluid undergo, according to the -different proportion between the density of the fluid and the -density of the body. The densities of bodies, whether fluid -or solid, are measured by the quantity of matter, which is -comprehended under the same magnitude; that body being<span class="pagenum"><a name="Page_144" id="Page_144">[144]</a></span> -the most dense or compact, which under the same bulk contains -the greatest quantity of solid matter, or which weighs -most, the weight of every body being observed above to be -proportional to the quantity of matter in it<a name="FNanchor_95_95" id="FNanchor_95_95"></a><a href="#Footnote_95_95" class="fnanchor">[95]</a>. Thus water is -more dense than cork or wood, iron more dense than water, -and gold than iron. The third particular Sir <span class="smcap"><em class="gesperrt">Is. Newton</em></span> -considers concerning the resistance of fluids is the influence, -which the diversity of figure in the resisted body has upon its -resistance.</p> - -<p>3. <span class="smcap gesperrt">For</span> the more perfect illustration of the first of these -heads, he distinctly shews the relation between all the particulars -specified upon three different suppositions. The first -is, that the same body be resisted more or less in the simple -proportion to its velocity; so that if its velocity be doubled, -its resistance shall become threefold. The second is of the -resistance increasing in the duplicate proportion of the velocity; -so that, if the velocity of a body be doubled, its resistance -shall be rendered four times; and if the velocity be -trebled, nine times as great as at first. But what is to be understood -by duplicate proportion has been already explained<a name="FNanchor_96_96" id="FNanchor_96_96"></a><a href="#Footnote_96_96" class="fnanchor">[96]</a>. -The third supposition is, that the resistance increases -partly in the single proportion of the velocity, and partly in -the duplicate proportion thereof.</p> - -<p>4. <span class="smcap gesperrt">In</span> all these suppositions, bodies are considered under -two respects, either as moving, and opposing themselves<span class="pagenum"><a name="Page_145" id="Page_145">[145]</a></span> -against the fluid by that power alone, which is essential to -them, of resisting to the change of their state from rest to -motion, or from motion to rest, which we have above called -their power of inactivity; or else, as descending or ascending, -and so having the power of gravity combined with -that other power. Thus our author has shewn in all those -three suppositions, in what manner bodies are resisted in an -uniform fluid, when they move with the aforesaid progressive -motion<a name="FNanchor_97_97" id="FNanchor_97_97"></a><a href="#Footnote_97_97" class="fnanchor">[97]</a>; and what the resistance is, when they ascend or -descend perpendicularly<a name="FNanchor_98_98" id="FNanchor_98_98"></a><a href="#Footnote_98_98" class="fnanchor">[98]</a>. And if a body ascend or descend -obliquely, and the resistance be singly proportional to the velocity, -it is shewn how the body is resisted in a fluid of an uniform -density, and what line it will describe<a name="FNanchor_99_99" id="FNanchor_99_99"></a><a href="#Footnote_99_99" class="fnanchor">[99]</a>, which is determined -by the measurement of the hyperbola, and appears -to be no other than that line, first considered in particular -by Dr. <span class="smcap gesperrt"><em class="gesperrt">Barrow</em></span><a name="FNanchor_100_100" id="FNanchor_100_100"></a><a href="#Footnote_100_100" class="fnanchor">[100]</a>, which is now commonly known -by the name of the logarithmical curve. In the supposition -that the resistance increases in the duplicate proportion -of the velocity, our author has not given us the line -which would be described in an uniform fluid; but has instead -thereof discussed a problem, which is in some sort the -reverse; to find the density of the fluid at all altitudes, by -which any given curve line may be described; which problem -is so treated by him, as to be applicable to any kind of -resistance whatever<a name="FNanchor_101_101" id="FNanchor_101_101"></a><a href="#Footnote_101_101" class="fnanchor">[101]</a>. But here not unmindful of practice, -he shews that a body in a fluid of uniform density, like the<span class="pagenum"><a name="Page_146" id="Page_146">[146]</a></span> -air, will describe a line, which approaches towards an hyperbola; -that is, its motion will be nearer to that curve line -than to the parabola. And consequent upon this remark, he -shews how to determine this hyperbola by experiment, and -briefly resolves the chief of those problems relating to projectiles, -which are in use in the art of gunnery, in this curve<a name="FNanchor_102_102" id="FNanchor_102_102"></a><a href="#Footnote_102_102" class="fnanchor">[102]</a>; -as <span class="smcap"><em class="gesperrt">Torricelli</em></span> and others have done in the parabola<a name="FNanchor_103_103" id="FNanchor_103_103"></a><a href="#Footnote_103_103" class="fnanchor">[103]</a>, -whose inventions have been explained at large above<a name="FNanchor_104_104" id="FNanchor_104_104"></a><a href="#Footnote_104_104" class="fnanchor">[104]</a>.</p> - -<p>5. <span class="smcap gesperrt">Our</span> author has also handled distinctly that particular -sort of motion, which is described by pendulums<a name="FNanchor_105_105" id="FNanchor_105_105"></a><a href="#Footnote_105_105" class="fnanchor">[105]</a>; and -has likewise considered some few cases of bodies moving in -resisting fluids round a center, to which they are impelled by -a centripetal force, in order to give an idea of those kinds of -motions<a name="FNanchor_106_106" id="FNanchor_106_106"></a><a href="#Footnote_106_106" class="fnanchor">[106]</a>.</p> - -<p>6. <span class="smcap gesperrt">The</span> treating of the resistance of pendulums has given -him an opportunity of inserting into another part of -his work some speculations upon the motions of them without -resistance, which have a very peculiar elegance; where -in he treats of them as moved by a gravitation acting in -the law, which he shews to belong to the earth below its -surface<a name="FNanchor_107_107" id="FNanchor_107_107"></a><a href="#Footnote_107_107" class="fnanchor">[107]</a>; performing in this kind of gravitation, where the -force is proportional to the distance from the center, all that -<span class="smcap">Huygens</span> had before done in the common supposition of -its being uniform, and acting in parallel lines<a name="FNanchor_108_108" id="FNanchor_108_108"></a><a href="#Footnote_108_108" class="fnanchor">[108]</a>.</p> - -<p><span class="pagenum"><a name="Page_147" id="Page_147">[147]</a></span></p> - -<p>7. <span class="smcap gesperrt">Huygens</span> at the end of his treatise of the cause of -gravity<a name="FNanchor_109_109" id="FNanchor_109_109"></a><a href="#Footnote_109_109" class="fnanchor">[109]</a> informs us, that he likewise had carried his speculations -on the first of these suppositions, of the resistance in -fluids being proportional to the velocity of the body, as far as -our author. But finding by experiment that the second was -more conformable to nature, he afterwards made some progress -in that, till he was stopt, by not being able to execute to his -wish what related to the perpendicular descent of bodies; not -observing that the measurement of the curve line, he made -use of to explain it by, depended on the hyperbola. Which -oversight may well be pardoned in that great man, considering -that our author had not been pleased at that time to -communicate to the publick his admirable discourse of the -<span class="smcap">quadrature</span> or <span class="smcap">measurement of curve lines</span>, with which he -has since obliged the world: for without the use of that -treatise, it is I think no injury even to our author’s unparalleled -abilities to believe, it would not have been easy for -himself to have succeeded so happily in this and many other -parts of his writings.</p> - -<p><a name="c147" id="c147">8.</a> <span class="smcap gesperrt">What Huygens</span> found by experiment, that bodies -were in reality resisted in the duplicate proportion of their velocity, -agrees with the reasoning of our author<a name="FNanchor_110_110" id="FNanchor_110_110"></a><a href="#Footnote_110_110" class="fnanchor">[110]</a>, who distinguishes -the resistance, which fluids give to bodies by the tenacity -of their parts, and the friction between them and the body, -from that, which arises from the power of inactivity, with -which the constituent particles of fluids are endued like all<span class="pagenum"><a name="Page_148" id="Page_148">[148]</a></span> -other portions of matter, by which power the particles of fluids -like other bodies make resistance against being put into motion.</p> - -<p>9. <span class="smcap gesperrt">The</span> resistance, which arises from the friction of the -body against the parts of the fluid, must be very inconsiderable; -and the resistance, which follows from the tenacity of -the parts of fluids, is not usually very great, and does not -depend much upon the velocity of the body in the fluid; -for as the parts of the fluid adhere together with a certain -degree of force, the resistance, which the body receives from -thence, cannot much depend upon the velocity, with which -the body moves; but like the power of gravity, its effect must -be proportional to the time of its acting. This the reader -may find farther explained by Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> himself -in the postscript to a discourse published by me in <span class="smcap">the philosophical -transactions</span>, N<sup>o</sup> 371. The principal resistance, -which most fluids give to bodies, arises from the power of -inactivity in the parts of the fluids, and this depends upon the -velocity, with which the body moves, on a double account. -In the first place, the quantity of the fluid moved out of -place by the moving body in any determinate space of time -is proportional to the velocity, wherewith the body moves; -and in the next place, the velocity with which each particle of -the fluid is moved, will also be proportional to the velocity of -the body: therefore since the resistance, which any body makes -against being put into motion, is proportional both to the quantity -of matter moved and the velocity it is moved with; the -resistance, which a fluid gives on this account, will be doubly increased -with the increase of the velocity in the moving body;<span class="pagenum"><a name="Page_149" id="Page_149">[149]</a></span> -that is, the resistance will be in a two-fold or duplicate proportion -of the velocity, wherewith the body moves through the -fluid.</p> - -<p>10. <span class="smcap gesperrt">Farther</span> it is most manifest, that this latter kind -of resistance increasing with the increase of velocity, even -in a greater degree than the velocity it self increases, the -swifter the body moves, the less proportion the other species -of resistance will bear to this: nay that this part of the resistance -may be so much augmented by a due increase of velocity, -till the former resistances shall bear a less proportion to -this, than any that might be assigned. And indeed experience -shews, that no other resistance, than what arises from -the power of inactivity in the parts of the fluid, is of moment, -when the body moves with any considerable swiftness.</p> - -<p><a name="c149" id="c149">11.</a> <span class="smcap gesperrt">There</span> is besides these yet another species of resistance, -found only in such fluids, as, like our air, are elastic. -Elasticity belongs to no fluid known to us beside the air. By -this property any quantity of air may be contracted into a -less space by a forcible pressure, and as soon as the compressing -power is removed, it will spring out again to its -former dimensions. The air we breath is held to its present -density by the weight of the air above us. And as this incumbent -weight, by the motion of the winds, or other causes, -is frequently varied (which appears by the barometer;) -so when this weight is greatest, we breath a more dense air -than at other times. To what degree the air would expand -it self by its spring, if all pressure were removed, is not<span class="pagenum"><a name="Page_150" id="Page_150">[150]</a></span> -known, nor yet into how narrow a compass it is capable -of being compressed. Mr. <span class="smcap">Boyle</span> found it by experiment -capable both of expansion and compression to such a degree, -that he could cause a quantity of air to expand it self over a -space some hundred thousand times greater, than the space to -which he could confine the same quantity<a name="FNanchor_111_111" id="FNanchor_111_111"></a><a href="#Footnote_111_111" class="fnanchor">[111]</a>. But I shall -treat more fully of this spring in the air hereafter<a name="FNanchor_112_112" id="FNanchor_112_112"></a><a href="#Footnote_112_112" class="fnanchor">[112]</a>. I am -now only to consider what resistance to the motion of bodies -arises from it.</p> - -<p><a name="c150" id="c150">12.</a> <span class="smcap gesperrt">But</span> before our author shews in what manner this -cause of resistance operates, he proposes a method, by which -fluids may be rendered elastic, demonstrating that if their -particles be provided with a power of repelling each other, -which shall exert it self with degrees of strength reciprocally -proportional to the distances between the centers of -the particles; that then such fluids will observe the same -rule in being compressed, as our air does, which is this, that -the space, into which it yields upon compression, is reciprocally -proportional to the compressing weight<a name="FNanchor_113_113" id="FNanchor_113_113"></a><a href="#Footnote_113_113" class="fnanchor">[113]</a>. The term -reciprocally proportional has been explained above<a name="FNanchor_114_114" id="FNanchor_114_114"></a><a href="#Footnote_114_114" class="fnanchor">[114]</a>. And if -the centrifugal force of the particles acted by other laws, such -fluids would yield in a different manner to compression<a name="FNanchor_115_115" id="FNanchor_115_115"></a><a href="#Footnote_115_115" class="fnanchor">[115]</a>.</p> - -<p>13. <span class="smcap gesperrt">Whether</span> the particles of the air be endued with -such a power, by which they can act upon each other out -of contact, our author does not determine, but leaves that<span class="pagenum"><a name="Page_151" id="Page_151">[151]</a></span> -to future examination, and to be discussed by philosophers. -Only he takes occasion from hence to consider the resistance -in elastic fluids, under this notion; making remarks, as -he passes along, upon the differences, which will arise, if their -elasticity be derived from any other fountain<a name="FNanchor_116_116" id="FNanchor_116_116"></a><a href="#Footnote_116_116" class="fnanchor">[116]</a>. And this, I -think, must be confessed to be done by him with great judgment; -for this is far the most reasonable account, which has -been given of this surprizing power, as must without doubt be -freely acknowledged by any one, who in the least considers -the insufficiency of all the other conjectures, which have -been framed; and also how little reason there is to deny to -bodies other powers, by which they may act upon each other -at a distance, as well as that of gravity; which we shall hereafter -shew to be a property universally belonging to all the -bodies of the universe, and to all their parts<a name="FNanchor_117_117" id="FNanchor_117_117"></a><a href="#Footnote_117_117" class="fnanchor">[117]</a>. Nay we actually -find in the loadstone a very apparent repelling, as well as -an attractive power. But of this more in the conclusion of -this discourse.</p> - -<p>14. <span class="smcap gesperrt">By</span> these steps our author leads the way to explain -the resistance, which the air and such like fluids will give -to bodies by their elasticity; which resistance he explains -thus. If the elastic power of the fluid were to be varied -so, as to be always in the duplicate proportion of the -velocity of the resisted body, it is shewn that then the -resistance derived from the elasticity, would increase in the -duplicate proportion of the velocity; in so much that the<span class="pagenum"><a name="Page_152" id="Page_152">[152]</a></span> -whole resistance would be in that proportion, excepting only -that small part, which arises from the friction between the -body and the parts of the fluid. From whence it follows, -that because the elastic power of the same fluid does in -truth continue the same, if the velocity of the moving body be -diminished, the resistance from the elasticity, and therefore -the whole resistance, will decrease in a less proportion, than the -duplicate of the velocity; and if the velocity be increased, the -resistance from the elasticity will increase in a less proportion, -than the duplicate of the velocity, that is in a less proportion, -than the resistance made by the power of inactivity of the -parts of the fluid. And from this foundation is raised the proof -of a property of this resistance, given by the elasticity in common -with the others from the tenacity and friction of the -parts of the fluid; that the velocity may be increased, till this -resistance from the fluid’s elasticity shall bear no considerable -proportion to that, which is produced by the power of inactivity -thereof<a name="FNanchor_118_118" id="FNanchor_118_118"></a><a href="#Footnote_118_118" class="fnanchor">[118]</a>. From whence our author draws this conclusion; -that the resistance of a body, which moves very swiftly -in an elastic fluid, is near the same, as if the fluid were -not elastic; provided the elasticity arises from the centrifugal -power of the parts of the medium, as before explained, especially -if the velocity be so great, that this centrifugal power -shall want time to exert it self<a name="FNanchor_119_119" id="FNanchor_119_119"></a><a href="#Footnote_119_119" class="fnanchor">[119]</a>. But it is to be observed, -that in the proof of all this our author proceeds upon the supposition -of this centrifugal power in the parts of the fluid; but -if the elasticity be caused by the expansion of the parts in the<span class="pagenum"><a name="Page_153" id="Page_153">[153]</a></span> -manner of wool compressed, and such like bodies, by which -the parts of the fluid will be in some measure entangled -together, and their motion be obstructed, the fluid will -be in a manner tenacious, and give a resistance upon that account -over and above what depends upon its elasticity only<a name="FNanchor_120_120" id="FNanchor_120_120"></a><a href="#Footnote_120_120" class="fnanchor">[120]</a>; -and the resistance derived from that cause is to be -judged of in the manner before set down.</p> - -<p>15. <span class="smcap gesperrt">It</span> is now time to pass to the second part of this theory; -which is to assign the measure of resistance, according -to the proportion between the density of the body and the -density of the fluid. What is here to be understood by the -word density has been explained above<a name="FNanchor_121_121" id="FNanchor_121_121"></a><a href="#Footnote_121_121" class="fnanchor">[121]</a>. For this purpose -as our author before considered two distinct cases of bodies -moving in mediums; one when they opposed themselves to -the fluid by their power of inactivity only, and another -when by ascending or descending their weight was combined -with that other power: so likewise, the fluids themselves -are to be regarded under a double capacity; either -as having their parts at rest, and disposed freely without restraint, -or as being compressed together by their own -weight, or any other cause.</p> - -<p><a name="c153" id="c153">16.</a> <span class="smcap gesperrt">In</span> the first case, if the parts of the fluid be wholly -disingaged from one another, so that each particle is at liberty -to move all ways without any impediment, it is shewn, -that if a globe move in such a fluid, and the globe and particles<span class="pagenum"><a name="Page_154" id="Page_154">[154]</a></span> -of the fluid are endued with perfect elasticity; so that -as the globe impinges upon the particles of it, they shall -bound off and separate themselves from the globe, with the -same velocity, with which the globe strikes upon them; then -the resistance, which the globe moving with any known velocity -suffers, is to be thus determined. From the velocity -of the globe, the time, wherein it would move over two -third parts of its own diameter with that velocity, will be -known. And such proportion as the density of the fluid bears -to the density of the globe, the same the resistance given to -the globe will bear to the force, which acting, like the power -of gravity, on the globe without intermission during the space -of time now mentioned, would generate in the globe the -same degree of motion, as that wherewith it moves in the -fluid<a name="FNanchor_122_122" id="FNanchor_122_122"></a><a href="#Footnote_122_122" class="fnanchor">[122]</a>. But if neither the globe nor the particles of the -fluid be elastic, so that the particles, when the globe -strikes against them, do not rebound from it, then the -resistance will be but half so much<a name="FNanchor_123_123" id="FNanchor_123_123"></a><a href="#Footnote_123_123" class="fnanchor">[123]</a>. Again, if the particles -of the fluid and the globe are imperfectly elastic, so -that the particles will spring from the globe with part only -of that velocity wherewith the globe impinges upon them; -then the resistance will be a mean between the two preceding -cases, approaching nearer to the first or second, according -as the elasticity is more or less<a name="FNanchor_124_124" id="FNanchor_124_124"></a><a href="#Footnote_124_124" class="fnanchor">[124]</a>.</p> - -<p>17. <span class="smcap gesperrt">The</span> elasticity, which is here ascribed to the particles -of the fluid, is not that power of repelling one another,<span class="pagenum"><a name="Page_155" id="Page_155">[155]</a></span> -when out of contact, by which, as has before been mentioned, -the whole fluid may be rendred elastic; but such -an elasticity only, as many solid bodies have of recovering -their figure, whenever any forcible change is made in it, by -the impulse of another body or otherwise. Which elasticity -has been explained above at large<a name="FNanchor_125_125" id="FNanchor_125_125"></a><a href="#Footnote_125_125" class="fnanchor">[125]</a>.</p> - -<p><a name="c155a" id="c155a">18.</a> <span class="smcap gesperrt">This</span> is the case of discontinued fluids, where the body, -by pressing against their particles, drives them before -itself, while the space behind the body is left empty. But -in fluids which are compressed, so that the parts of them removed -out of place by the body resisted immediately retire -behind the body, and fill that space, which in the other case -is left vacant, the resistance is still less; for a globe in such a -fluid which shall be free from all elasticity, will be resisted -but half as much as the least resistance in the former case<a name="FNanchor_126_126" id="FNanchor_126_126"></a><a href="#Footnote_126_126" class="fnanchor">[126]</a>. -But by elasticity I now mean that power, which renders the -whole fluid so; of which if the compressed fluid be possessed, -in the manner of the air, then the resistance will be greater -than by the foregoing rule; for the fluid being capable in some -degree of condensation, it will resemble so far the case of uncompressed -fluids<a name="FNanchor_127_127" id="FNanchor_127_127"></a><a href="#Footnote_127_127" class="fnanchor">[127]</a>. But, as has been before related, this difference -is most considerable in slow motions.</p> - -<p><a name="c155b" id="c155b">19.</a> <span class="smcap gesperrt">In</span> the next place our author is particular in determining -the degrees of resistance accompanying bodies of -different figures; which is the last of the three heads, we<span class="pagenum"><a name="Page_156" id="Page_156">[156]</a></span> -divided the whole discourse of resistance into. And in this -disquisition he finds a very surprizing and unthought of difference, -between free and compressed fluids. He proves, -that in the former kind, a globe suffers but half the resistance, -which the cylinder, that circumscribes the globe, will -do, if it move in the direction of its axis<a name="FNanchor_128_128" id="FNanchor_128_128"></a><a href="#Footnote_128_128" class="fnanchor">[128]</a>. But in the latter -he proves, that the globe and cylinder are resisted alike<a name="FNanchor_129_129" id="FNanchor_129_129"></a><a href="#Footnote_129_129" class="fnanchor">[129]</a>. -And in general, that let the shape of bodies be -ever so different, yet if the greatest sections of the bodies -perpendicular to the axis of their motion be equal, the -bodies will be resisted equally<a name="FNanchor_130_130" id="FNanchor_130_130"></a><a href="#Footnote_130_130" class="fnanchor">[130]</a>.</p> - -<p>20. <span class="smcap gesperrt">Pursuant</span> to the difference found between the resistance -of the globe and cylinder in rare and uncompressed -fluids, our author gives us the result of some other inquiries -of the same nature. Thus of all the frustums of a cone, -that can be described upon the same base and with the same -altitude, he shews how to find that, which of all others -will be the least resisted, when moving in the direction of -its axis<a name="FNanchor_131_131" id="FNanchor_131_131"></a><a href="#Footnote_131_131" class="fnanchor">[131]</a>. And from hence he draws an easy method of altering -the figure of any spheroidical solid, so that its capacity -may be enlarged, and yet the resistance of it diminished<a name="FNanchor_132_132" id="FNanchor_132_132"></a><a href="#Footnote_132_132" class="fnanchor">[132]</a>: -a note which he thinks may not be useless to ship-wrights. -He concludes with determining the solid, which -will be resisted the least that is possible, in these discontinued -fluids<a name="FNanchor_133_133" id="FNanchor_133_133"></a><a href="#Footnote_133_133" class="fnanchor">[133]</a>.</p> - -<p><span class="pagenum"><a name="Page_157" id="Page_157">[157]</a></span></p> - -<p>21. <span class="smcap gesperrt">That</span> I may here be understood by readers unacquainted -with mathematical terms, I shall explain what I -mean by a frustum of a cone, and a spheroidical solid. A -cone has been defined above. A frustum is what remains, -when part of the cone next the vertex is cut away by a section -parallel to the base of the cone, as in fig. 86. A spheroid -is produced from an ellipsis, as a sphere or globe is made -from a circle. If a circle turn round on its diameter, it describes -by its motion a sphere; so if an ellipsis (which figure -has been defined above, and will be more fully explained -hereafter<a name="FNanchor_134_134" id="FNanchor_134_134"></a><a href="#Footnote_134_134" class="fnanchor">[134]</a>) be turned round either upon the longest or -shortest line, that can be drawn through the middle of it, -there will be described a kind of oblong or flat sphere, as -in fig. 87. Both these figures are called spheroids, and any -solid resembling these I here call spheroidical.</p> - -<p>22. <span class="smcap gesperrt">If</span> it should be asked, how the method of altering -spheroidical bodies, here mentioned, can contribute to the -facilitating a ship’s motion, when I just above affirmed, -that the figure of bodies, which move in a compressed -fluid not elastic, has no relation to the augmentation or diminution -of the resistance; the reply is, that what was -there spoken relates to bodies deep immerged into such fluids, -but not of those, which swim upon the surface of them; -for in this latter case the fluid, by the appulse of the anterior -parts of the body, is raised above the level of the -surface, and behind the body is sunk somewhat below; so<span class="pagenum"><a name="Page_158" id="Page_158">[158]</a></span> -that by this inequality in the superficies of the fluid, that -part of it, which at the head of the body is higher than -the fluid behind, will resist in some measure after the -manner of discontinued fluids<a name="FNanchor_135_135" id="FNanchor_135_135"></a><a href="#Footnote_135_135" class="fnanchor">[135]</a>, analogous to what was before -observed to happen in the air through its elasticity, -though the body be surrounded on every side by it<a name="FNanchor_136_136" id="FNanchor_136_136"></a><a href="#Footnote_136_136" class="fnanchor">[136]</a>. And -as far as the power of these causes extends, the figure of the -moving body affects its resistance; for it is evident, that the -figure, which presses least directly against the parts of the fluid, -and so raises least the surface of a fluid not elastic, and least -compresses one that is elastic, will be least resisted.</p> - -<p>23. <span class="smcap gesperrt">The</span> way of collecting the difference of the resistance -in rare fluids, which arises from the diversity of figure, is -by considering the different effect of the particles of the fluid -upon the body moving against them, according to the different -obliquity of the several parts of the body upon which -they respectively strike; as it is known, that any body impinging -against a plane obliquely, strikes with a less force, -than if it fell upon it perpendicularly; and the greater the -obliquity is, the weaker is the force. And it is the same -thing, if the body be at rest, and the plane move against it<a name="FNanchor_137_137" id="FNanchor_137_137"></a><a href="#Footnote_137_137" class="fnanchor">[137]</a>.</p> - -<p><a name="c158" id="c158">24.</a> <span class="smcap gesperrt">That</span> there is no connexion between the figure -of a body and its resistance in compressed fluids, is proved -thus. Suppose A B C D (in fig. 88.) to be a canal, having such a -fluid, water for instance, running through it with an equable<span class="pagenum"><a name="Page_159" id="Page_159">[159]</a></span> -velocity; and let any body E, by being placed in the axis -of the canal, hinder the passage of the water. It is evident, -that the figure of the fore part of this body will -have little influence in obstructing the water’s motion, but -the whole impediment will arise from the space taken up -by the body, by which it diminishes the bore of the canal, -and straightens the passage of the water<a name="FNanchor_138_138" id="FNanchor_138_138"></a><a href="#Footnote_138_138" class="fnanchor">[138]</a>. But proportional -to the obstruction of the water’s motion, will be -the force of the water upon the body E<a name="FNanchor_139_139" id="FNanchor_139_139"></a><a href="#Footnote_139_139" class="fnanchor">[139]</a>. Now suppose -both orifices of the canal to be closed, and the water in it -to remain at rest; the body E to move, so that the parts -of the water may pass by it with the same degree of velocity, -as they did before; it is beyond contradiction, that the pressure -of the water upon the body, that is, the resistance -it gives to its motion, will remain the same; and therefore -will have little connexion with the figure of the body<a name="FNanchor_140_140" id="FNanchor_140_140"></a><a href="#Footnote_140_140" class="fnanchor">[140]</a>.</p> - -<p>25. <span class="smcap gesperrt">By</span> a method of reasoning drawn from the same fountain -is determined the measure of resistance these compressed -fluids give to bodies, in reference to the proportion between -the density of the body and that of the fluid. This shall be -explained particularly in my comment on Sir <span class="smcap"><em class="gesperrt">Is. Newton</em></span>’s -mathematical principles of natural philosophy; but is not a -proper subject to be insisted on farther in this place.</p> - -<p>26. <span class="smcap gesperrt">We</span> have now gone through all the parts of this -theory. There remains nothing more, but in few words to -mention the experiments, which our author has made, both<span class="pagenum"><a name="Page_160" id="Page_160">[160]</a></span> -with bodies falling perpendicularly through water, and the -air<a name="FNanchor_141_141" id="FNanchor_141_141"></a><a href="#Footnote_141_141" class="fnanchor">[141]</a>, and with pendulums<a name="FNanchor_142_142" id="FNanchor_142_142"></a><a href="#Footnote_142_142" class="fnanchor">[142]</a>: all which agree with the theory. -In the case of falling bodies, the times of their fall determined -by the theory come out the same, as by observation, to a -surprizing exactness; in the pendulums, the rod, by which -the ball of the pendulum hangs, suffers resistance as well as -the ball, and the motion of the ball being reciprocal, it communicates -such a motion to the fluid, as increases the resistance, -but the deviation from the theory is no more, than -what may reasonably follow from these causes.</p> - -<p>27. <span class="smcap gesperrt">By</span> this theory of the resistance of fluids, and these experiments, -our author decides the question so long agitated -among natural philosophers, whether all space is absolutely -full of matter. The Aristotelians and Cartesians both assert -this plenitude; the Atomists have maintained the contrary. -Our author has chose to determine this question by his theory -of resistance, as shall be explained in the following chapter.</p> - -<div class="figcenter"> - <img src="images/ill-216.jpg" width="300" height="170" - alt="" - title="" /> -</div> - -</div> - -<p><span class="pagenum"><a name="Page_161" id="Page_161">[161]</a></span></p> - -<div class="chapter"> - -<div class="figcenter"> - <img src="images/ill-217.jpg" width="400" height="207" - alt="" - title="" /> -</div> - -<p class="pc xlarge"><em class="gesperrt">BOOK II</em>.</p> -<p class="pc reduct"><span class="smcap">Concerning the</span></p> -<p class="pc large">SYSTEM of the WORLD.</p> - -<hr class="d3" /> - -<h2><a name="c161" id="c161"><span class="smcap">Chap. I.</span></a><br /> -That the Planets move in a space empty of -all sensible matter.</h2> - -<div> - <img class="dcap1" src="images/di2.jpg" width="80" height="81" alt=""/> -</div> -<p class="cap09">I HAVE now gone through the -first part of my design, and have explained, -as far as the nature of my -undertaking would permit, what -Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> has delivered -in general concerning the motion -of bodies. It follows now to speak -of the discoveries, he has made in the system of the world;<span class="pagenum"><a name="Page_162" id="Page_162">[162]</a></span> -and to shew from him what cause keeps the heavenly bodies -in their courses. But it will be necessary for the use of -such, as are not skilled in astronomy, to premise a brief description -of the planetary system.</p> - -<p><a name="c162" id="c162">2.</a> <span class="smcap gesperrt">This</span> system is disposed in the following manner. In -the middle is placed the sun. About him six globes continually -roll. These are the primary planets; that which -is nearest to the sun is called Mercury, the next Venus, -next to this is our earth, the next beyond is Mars, after -him Jupiter, and the outermost of all Saturn. Besides these -there are discovered in this system ten other bodies, which -move about some of these primary planets in the same -manner, as they move round the sun. These are called -secondary planets. The most conspicuous of them is the -moon, which moves round our earth; four bodies move in -like manner round Jupiter; and five round Saturn. Those -which move about Jupiter and Saturn, are usually called -satellites; and cannot any of them be seen without a telescope. -It is not impossible, but there may be more secondary -planets, beside these; though our instruments -have not yet discovered any other. This disposition of -the planetary or solar system is represented in fig. 89.</p> - -<p>3. <span class="smcap gesperrt">The</span> same planet is not always equally distant from -the sun. But the middle distance of Mercury is between -⅕ and ⅖ of the distance of the earth from the sun; Venus -is distant from the sun almost ¾ of the distance of the -earth; the middle distance of Mars is something more than -half as much again, as the distance of the earth; Jupiter’s -middle distance exceeds five times the distance of the -earth, by between ⅕ and 1/6 part of this distance; Saturn’s -middle distance is scarce more than 9½ times the distance -between the earth and sun; but the middle distance between -the earth and sun is about 217⅛ times the sun’s semidiameter.</p> - -<div class="figcenter"> - <img src="images/ill-219.jpg" width="400" height="510" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_163" id="Page_163">[163]</a></span></p> - -<p>4. <span class="smcap gesperrt">All</span> these planets move one way, from west to -east; and of the primary planets the most remote is longest -in finishing its course round the sun. The period -of Saturn falls short only sixteen days of 29 years and -a half. The period of Jupiter is twelve years wanting about -50 days. The period of Mars falls short of two years -by about 43 days. The revolution of the earth constitutes -the year. Venus performs her period in about 224½ days, -and Mercury in about 88 days.</p> - -<p>5. <span class="smcap gesperrt">The</span> course of each planet lies throughout in one -plane or flat surface, in which the sun is placed; but they do -not all move in the same plane, though the different planes, -in which they move, cross each other in very small angles. -They all cross each other in lines, which pass through the -sun; because the sun lies in the plane of each orbit. This -inclination of the several orbits to each other is represented in -fig. 90. The line, in which the plane of any orbit crosses -the plane of the earth’s motion, is called the line of the nodes -of that orbit.</p> - -<p><span class="pagenum"><a name="Page_164" id="Page_164">[164]</a></span></p> - -<p>6. <span class="smcap gesperrt">Each</span> planet moves round the sun in the line, which -we have mentioned above<a name="FNanchor_143_143" id="FNanchor_143_143"></a><a href="#Footnote_143_143" class="fnanchor">[143]</a> under the name of ellipsis; which -I shall here shew more particularly how to describe. I have -there said how it is produced in the cone. I shall now shew -how to form it upon a plane. Fix upon any plane two pins, -as at A and B in fig. 91. To these tye a string A C B of any -length. Then apply a third pin D so to the string, as to hold -it strained; and in that manner carrying this pin about, the -point of it will describe an ellipsis. If through the points A, -B the straight line E A B F be drawn, to be terminated at -the ellipsis in the points E and F, this is the longest line -of any, that can be drawn within the figure, and is called -the greater axis of the ellipsis. The line G H, drawn -perpendicular to this axis E F, so as to pass through the -middle of it, is called the lesser axis. The two points A -and B are called focus’s. Now each planet moves round -the sun in a line of this kind, so that the sun is found in -one focus. Suppose A to be the place of the sun. Then E -is the point, wherein the planet will be nearest of all to the -sun, and at F it will be most remote. The point E is called -the perihelion of the planet, and F the aphelion. In G -and H the planet is said to be in its middle or mean distance; -because the distance A G or A H is truly the middle between -A E the least, and A F the greatest distance. In fig. 92. -is represented how the greater axis of each orbit is situated in -respect of the rest. The proportion between the greatest and -least distances of the planet from the sun is very different -in the different planets.</p> - -<div class="figcenter"> - <img src="images/ill-223.jpg" width="400" height="499" - alt="" - title="" /> -</div> - -<p>In Saturn the proportion of the -<span class="pagenum"><a name="Page_165" id="Page_165">[165]</a></span>greatest distance to the least is something less, than the proportion -of 9 to 8, but much nearer to this, than to the proportion -of 10 to 9. In Jupiter this proportion is a little greater, -than that of 11 to 10. In Mars it exceeds the proportion of -6 to 5. In the earth it is about the proportion of 30 to 29. -In Venus it is near to that of 70 to 69. And in Mercury it -comes not a great deal short of the proportion of 3 to 2.</p> - -<div class="floatright"> - <img src="images/ill-225.jpg" width="100" height="167" - alt="" - title="" /> -</div> - -<p>7. <span class="smcap gesperrt">Each</span> of these planets so moves through its ellipsis, that -the line drawn from the sun to the planet, by accompanying -the planet in its motion, will describe about the sun equal spaces -in equal times, after the manner spoke of in the chapter of -centripetal forces<a name="FNanchor_144_144" id="FNanchor_144_144"></a><a href="#Footnote_144_144" class="fnanchor">[144]</a>. There is also a certain relation between -the greater axis’s of these ellipsis’s, and the times, in which -the planets perform their revolutions through them. Which -relation may be expressed thus. Let the period -of one planet be denoted by the letter A, the -greater axis of its orbit by D; let the period -of another planet be denoted by B, and the -greater axis of this planet’s orbit by E. Then -if C be taken to bear the same proportion to B, -as B bears to A; likewise if F be taken to bear the same proportion -to E, as E bears to D; and G taken to bear the same -proportion likewise to F, as E bears to D; then A shall bear -the same proportion to C, as D bears to G.</p> - -<p>8. <span class="smcap gesperrt">The</span> secondary planets move round their respective -primary, much in the same manner as the primary do round<span class="pagenum"><a name="Page_166" id="Page_166">[166]</a></span> -the sun. But the motions of these shall be more fully explained -hereafter<a name="FNanchor_145_145" id="FNanchor_145_145"></a><a href="#Footnote_145_145" class="fnanchor">[145]</a>. And there is, besides the planets, another -sort of bodies, which in all probability move round the sun; -I mean the comets. The farther description of which bodies -I also leave to the place, where they are to be particularly -treated on<a name="FNanchor_146_146" id="FNanchor_146_146"></a><a href="#Footnote_146_146" class="fnanchor">[146]</a>.</p> - -<p>9. <span class="smcap gesperrt">Far</span> without this system the fixed stars are placed. -These are all so remote from us, that we seem almost incapable -of contriving any means to estimate their distance. Their -number is exceeding great. Besides two or three thousand, -which we see with the naked eye, telescopes open to our view -vast numbers; and the farther improved these instruments -are, we still discover more and more. Without doubt these -are luminous globes, like our sun, and ranged through the -wide extent of space; each of which, it is to be supposed, -perform the same office, as our sun, affording light and heat -to certain planets moving about them. But these conjectures -are not to be pursued in this place.</p> - -<p>10. <span class="smcap gesperrt">I shall</span> therefore now proceed to the particular design -of this chapter, and shew, that there is no sensible matter -lodged in the space where the planets move.</p> - -<p><a name="c166" id="c166">11.</a> <span class="smcap gesperrt">That</span> they suffer no sensible resistance from any -such matter, is evident from the agreement between the observations -of astronomers in different ages, with regard to the -time, in which the planets have been found to perform their<span class="pagenum"><a name="Page_167" id="Page_167">[167]</a></span> -periods. But it was the opinion of <span class="smcap">Des Cartes</span><a name="FNanchor_147_147" id="FNanchor_147_147"></a><a href="#Footnote_147_147" class="fnanchor">[147]</a>, that the -planets might be kept in their courses by the means of a fluid -matter, which continually circulating round should carry -the planets along with it. There is one appearance that -may seem to favour this opinion; which is, that the sun turns -round its own axis the same way, as the planets move. The -earth also turns round its axis the same way, as the moon -moves round the earth. And the planet Jupiter turns upon -its axis the same way, as his satellites revolve round him. It -might therefore be supposed, that if the whole planetary region -were filled with a fluid matter, the sun, by turning round on -its own axis, might communicate motion first to that part of -the fluid, which was contiguous, and by degrees propagate -the like motion to the parts more remote. After the same -manner the earth might communicate motion to this fluid, to -a distance sufficient to carry round the moon, and Jupiter communicate -the like to the distance of its satellites. Sir <span class="smcap"><em class="gesperrt">Isaac -Newton</em></span> has particularly examined what might be the result -of such a motion as this<a name="FNanchor_148_148" id="FNanchor_148_148"></a><a href="#Footnote_148_148" class="fnanchor">[148]</a>; and he finds, that the velocities, -with which the parts of this fluid will move in different distances -from the center of the motion, will not agree with the -motion observed in different planets: for instance, that the -time of one intire circulation of the fluid, wherein Jupiter -should swim, would bear a greater proportion to the time of -one intire circulation of the fluid, where the earth is; than the -period of Jupiter bears to the period of the earth. But he -also proves<a name="FNanchor_149_149" id="FNanchor_149_149"></a><a href="#Footnote_149_149" class="fnanchor">[149]</a>, that the planet cannot circulate in such a fluid,<span class="pagenum"><a name="Page_168" id="Page_168">[168]</a></span> -so as to keep long in the same course, unless the planet and -the contiguous fluid are of the same density, and the planet -be carried along with the same degree of motion, as the fluid. -There is also another remark made upon this motion by our -author; which is, that some vivifying force will be continually -necessary at the center of the motion<a name="FNanchor_150_150" id="FNanchor_150_150"></a><a href="#Footnote_150_150" class="fnanchor">[150]</a>. The sun in particular, -by communicating motion to the ambient fluid, will -lose from it self as much motion, as it imparts to the fluid; -unless some acting principle reside in the sun to renew its -motion continually. If the fluid be infinite, this gradual loss -of motion would continue till the whole should stop<a name="FNanchor_151_151" id="FNanchor_151_151"></a><a href="#Footnote_151_151" class="fnanchor">[151]</a>; and -if the fluid were limited, this loss of motion would continue, -till there would remain no swifter a revolution in the sun, -than in the utmost part of the fluid; so that the whole -would turn together about the axis of the sun, like one solid -globe<a name="FNanchor_152_152" id="FNanchor_152_152"></a><a href="#Footnote_152_152" class="fnanchor">[152]</a>.</p> - -<p><a name="c168" id="c168">12.</a> <span class="smcap gesperrt">It</span> is farther to be observed, that as the planets do not -move in perfect circles round the sun; there is a greater distance -between their orbits in some places, than in others. For -instance, the distance between the orbit of Mars and Venus is -near half as great again in one part of their orbits, as in the -opposite place. Now here the fluid, in which the earth -should swim, must move with a less rapid motion, where -there is this greater interval between the contiguous orbits; but -on the contrary, where the space is straitest, the earth moves -more slowly, than where it is widest<a name="FNanchor_153_153" id="FNanchor_153_153"></a><a href="#Footnote_153_153" class="fnanchor">[153]</a>.</p> - -<p><span class="pagenum"><a name="Page_169" id="Page_169">[169]</a></span></p> - -<p>13. <span class="smcap gesperrt">Farther</span>, if this our globe of earth swam in a fluid -of equal density with the earth it self, that is, in a fluid more -dense than water; all bodies put in motion here upon the -earth’s surface must suffer a great resistance from it; where -as, by Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span>’s experiments mentioned in the -preceding chapter, bodies, that fell perpendicularly down -through the air, felt about 1/860 part only of the resistance, -which bodies suffered that fell in like manner through water.</p> - -<p><a name="c169" id="c169">14.</a> Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> applies these experiments yet -farther, and examines by them the general question concerning -the absolute plenitude of space. According to the Aristotelians, -all space was full without any the least vacuities whatever. -<span class="smcap">DesCartes</span> embraced the same opinion, and therefore -supposed a subtile fluid matter, which should pervade all bodies, -and adequately fill up their pores. The Atomical philosophers, -who suppose all bodies both fluid and solid to be composed -of very minute but solid atoms, assert that no fluid, how -subtile soever the particles or atoms whereof it is composed -should be, can ever cause an absolute plenitude; because it -is impossible that any body can pass through the fluid without -putting the particles of it into such a motion, as to separate -them, at least in part, from one another, and so perpetually -to cause small vacuities; by which these Atomists endeavour -to prove, that a vacuum, or some space empty of all -matter, is absolutely necessary to be in nature. Sir <span class="smcap"><em class="gesperrt">Isaac -Newton</em></span> objects against the filling of space with such a subtile -fluid, that all bodies in motion must be unmeasurably resisted<span class="pagenum"><a name="Page_170" id="Page_170">[170]</a></span> -by a fluid so dense, as absolutely to fill up all the space, -through which it is spread. And lest it should be thought, -that this objection might be evaded by ascribing to this fluid -such very minute and smooth parts, as might remove all adhesion -or friction between them, whereby all resistance -would be lost, which this fluid might otherwise give to bodies -moving in it; Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> proves, in the -manner above related, that fluids resist from the power of -inactivity of their particles; and that water and the air resist -almost entirely on this account: so that in this subtile -fluid, however minute and lubricated the particles, which -compose it, might be; yet if the whole fluid was as dense as -water, it would resist very near as much as water does; and -whereas such a fluid, whose parts are absolutely close together -without any intervening spaces, must be a great deal -more dense than water, it must resist more than water in -proportion to its greater density; unless we will suppose the -matter, of which this fluid is composed, not to be endued -with the same degree of inactivity as other matter. But if -you deprive any substance of the property so universally belonging -to all other matter, without impropriety of speech -it can scarce be called by this name.</p> - -<p>15. Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> made also an experiment to try in -particular, whether the internal parts of bodies suffered any resistance. -And the result did indeed appear to favour some small -degree of resistance; but so very little, as to leave it doubtful, -whether the effect did not arise from some other latent cause<a name="FNanchor_154_154" id="FNanchor_154_154"></a><a href="#Footnote_154_154" class="fnanchor">[154]</a>.</p> - -<hr class="chap" /> - -</div> - -<p><span class="pagenum"><a name="Page_171" id="Page_171">[171]</a></span></p> - -<div class="chapter"> - -<h2 class="p4"><a name="c171a" id="c171a"><span class="smcap">Chap. II.</span></a><br /> -Concerning the cause, which keeps in motion -the primary planets.</h2> - -<p class="drop-cap08"><a name="c171b" id="c171b">SINCE</a> the planets move in a void space and are free -from resistance; they, like all other bodies, when -once in motion, would move on in a straight line without -end, if left to themselves. And it is now to be explained -what kind of action upon them carries them round the sun. -Here I shall treat of the primary planets only, and discourse -of the secondary apart in the next chapter. It has been -just now declared, that these primary planets move so about -the sun, that a line extended from the sun to the planet, will, -by accompanying the planet in its motion, pass over equal spaces -in equal portions of time<a name="FNanchor_155_155" id="FNanchor_155_155"></a><a href="#Footnote_155_155" class="fnanchor">[155]</a>. And this one property in the -motion of the planets proves, that they are continually acted -on by a power directed perpetually to the sun as a center. This -therefore is one property of the cause, which keeps the -planets in their courses, that it is a centripetal power, whose -center is the sun.</p> - -<p><a name="c171c" id="c171c">2.</a> <span class="smcap gesperrt">Again</span>, in the chapter upon centripetal forces<a name="FNanchor_156_156" id="FNanchor_156_156"></a><a href="#Footnote_156_156" class="fnanchor">[156]</a> it -was observ’d, that if the strength of the centripetal power -was suitably accommodated every where to the motion of -any body round a center, the body might be carried in<span class="pagenum"><a name="Page_172" id="Page_172">[172]</a></span> -any bent line whatever, whose concavity should be every -where turned towards the center of the force. It was farther -remarked, that the strength of the centripetal force, -in each place, was to be collected from the nature of the -line, wherein the body moved<a name="FNanchor_157_157" id="FNanchor_157_157"></a><a href="#Footnote_157_157" class="fnanchor">[157]</a>. Now since each planet -moves in an ellipsis, and the sun is placed in one focus; -Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> deduces from hence, that the strength -of this power is reciprocally in the duplicate proportion of the -distance from the sun. This is deduced from the properties, -which the geometers have discovered in the ellipsis. The process -of the reasoning is not proper to be enlarged upon here; -but I shall endeavour to explain what is meant by the reciprocal -duplicate proportion. Each of the terms reciprocal proportion, -and duplicate proportion, has been already defined<a name="FNanchor_158_158" id="FNanchor_158_158"></a><a href="#Footnote_158_158" class="fnanchor">[158]</a>. -Their sense when thus united is as follows. Suppose the planet -moved in the orbit A B C (in fig. 93.) about the sun in S. -Then, when it is said, that the centripetal power, which acts on -the planet in A, bears to the power acting on it in B a proportion, -which is the reciprocal of the duplicate proportion of the -distance S A to the distance S B; it is meant that the power -in A bears to the power in B the duplicate of the proportion -of the distance S B to the distance S A. The reciprocal duplicate -proportion may be explained also by numbers as follows. -Suppose several distances to bear to each other proportions -expressed by the numbers 1, 2, 3, 4, 5; that is, let the -second distance be double the first, the third be three times, -the fourth four times, and the fifth five times as great as the<span class="pagenum"><a name="Page_173" id="Page_173">[173]</a></span> -first. Multiply each of these numbers by it self, and 1 multiplied -by 1 produces still 1, 2 multiplied by 2 produces 4, 3 -by 3 makes 9, 4 by 4 makes 16, and 5 by 5 gives 25. This -being done, the fractions ¼, 1/9, 1/16, 1/25, will respectively express -the proportion, which the centripetal power in each of the -following distances bears to the power at the first distance: for -in the second distance, which is double the first, the centripetal -power will be one fourth part only of the power at the -first distance; at the third distance the power will be one -ninth part only of the first power; at the fourth distance, -the power will be but one sixteenth part of the first; and at -the fifth distance, one twenty fifth part of the first power.</p> - -<p>3. <span class="smcap gesperrt">Thus</span> is found the proportion, in which this centripetal -power decreases, as the distance from the sun increases, within -the compass of one planet’s motion. How it comes to pass, -that the planet can be carried about the sun by this centripetal -power in a continual round, sometimes rising from the sun, -then descending again as low, and from thence be carried -up again as far remote as before, alternately rising and falling -without end; appears from what has been written above concerning -centripetal forces: for the orbits of the planets resemble -in shape the curve line proposed in § 17 of the chapter -on these forces<a name="FNanchor_159_159" id="FNanchor_159_159"></a><a href="#Footnote_159_159" class="fnanchor">[159]</a>.</p> - -<p>4. <span class="smcap gesperrt">But</span> farther, in order to know whether this centripetal -force extends in the same proportion throughout, and consequently -whether all the planets are influenced by the very same<span class="pagenum"><a name="Page_174" id="Page_174">[174]</a></span> -power, our author proceeds thus. He inquires what relation -there ought to be between the periods of the different planets, -provided they were acted upon by the same power decreasing -throughout in the forementioned proportion; and he finds, -that the period of each in this case would have that very relation -to the greater axis of its orbit, as I have declared above<a name="FNanchor_160_160" id="FNanchor_160_160"></a><a href="#Footnote_160_160" class="fnanchor">[160]</a> -to be found in the planets by the observations of astronomers. -And this puts it beyond question, that the different planets are -pressed towards the sun, in the same proportion to their distances, -as one planet is in its several distances. And thence -in the last place it is justly concluded, that there is such a -power acting towards the sun in the foresaid proportion at all -distances from it.</p> - -<p>5. <span class="smcap gesperrt">This</span> power, when referred to the planets, our author -calls centripetal, when to the sun attractive; he gives it likewise -the name of gravity, because he finds it to be of the same -nature with that power of gravity, which is observed in our -earth, as will appear hereafter<a name="FNanchor_161_161" id="FNanchor_161_161"></a><a href="#Footnote_161_161" class="fnanchor">[161]</a>. By all these names he designs -only to signify a power endued with the properties before -mentioned; but by no means would he have it understood, as -if these names referred any way to the cause of it. In particular -in one place where he uses the name of attraction, he cautions -us expressly against implying any thing but a power directing -a body to a center without any reference to the cause -of it, whether residing in that center, or arising from any -external impulse<a name="FNanchor_162_162" id="FNanchor_162_162"></a><a href="#Footnote_162_162" class="fnanchor">[162]</a>.</p> - -<p><span class="pagenum"><a name="Page_175" id="Page_175">[175]</a></span></p> - -<p><a name="c175" id="c175">6.</a> <span class="smcap gesperrt">But</span> now, in these demonstrations some very minute inequalities -in the motion of the planets are neglected; which is -done with a great deal of judgment; for whatever be their -cause, the effects are very inconsiderable, they being so exceeding -small, that some astronomers have thought fit wholly to pass -them by<a name="FNanchor_163_163" id="FNanchor_163_163"></a><a href="#Footnote_163_163" class="fnanchor">[163]</a>. However the excellency of this philosophy, when -in the hands of so great a geometer as our author, is such, that -it is able to trace the least variations of things up to their causes. -The only inequalities, which have been observed common to -all the planets, are the motion of the aphelion and the nodes. -The transverse axis of each orbit does not always remain fixed, -but moves about the sun with a very slow progressive -motion: nor do the planets keep constantly the same plane, -but change them, and the lines in which those planes intersect -each other by insensible degrees. The first of these -inequalities, which is the motion of the aphelion, may be accounted -for, by supposing the gravitation of the planets towards -the sun to differ a little from the forementioned reciprocal -duplicate proportion of the distances; but the second, -which is the motion of the nodes, cannot be accounted -for by any power directed towards the sun; for no such -can give the planet any lateral impulse to divert it from the -plane of its motion into any new plane, but of necessity must -be derived from some other center. Where that power is -lodged, remains to be discovered. Now it is proved, as -shall be explained in the following chapter, that the three -primary planets Saturn, Jupiter, and the earth, which have -satellites revolving about them, are endued with a power of<span class="pagenum"><a name="Page_176" id="Page_176">[176]</a></span> -causing bodies, in particular those satellites, to gravitate towards -them with a force, which is reciprocally in the duplicate -proportion of their distances; and the planets are in all respects, -in which they come under our examination, so similar -and alike, that there is no reason to question, but they have -all the same property. Though it be sufficient for the present -purpose to have it proved of Jupiter and Saturn only; for -these planets contain much greater quantities of matter than -the rest, and proportionally exceed the others in power<a name="FNanchor_164_164" id="FNanchor_164_164"></a><a href="#Footnote_164_164" class="fnanchor">[164]</a>. But -the influence of these two planets being allowed, it is evident -how the planets come to shift continually their planes: -for each of the planets moving in a different plane, the -action of Jupiter and Saturn upon the rest will be oblique to -the planes of their motion; and therefore will gradually draw -them into new ones. The same action of these two planets upon -the rest will cause likewise a progressive motion of the -aphelion; so that there will be no necessity of having recourse -to the other cause for this motion, which was before hinted -at<a name="FNanchor_165_165" id="FNanchor_165_165"></a><a href="#Footnote_165_165" class="fnanchor">[165]</a>; viz, the gravitation of the planets towards the sun differing -from the exact reciprocal duplicate proportion of the distances. -And in the last place, the action of Jupiter and Saturn -upon each other will produce in their motions the same inequalities, -as their joint action produces in the rest. All this -is effected in the same manner, as the sun produces the same -kind of inequalities and many others in the motion of the -moon and the other secondary planets; and therefore will be -best apprehended by what shall be said in the next chapter.<span class="pagenum"><a name="Page_177" id="Page_177">[177]</a></span> -Those other irregularities in the motion of the secondary -planets have place likewise here; but are too minute to be -observable: because they are produced and rectified alternately, -for the most part in the time of a single revolution; -whereas the motion of the aphelion and nodes, which continually -increase, become sensible in a long series of years. Yet -some of these other inequalities are discernible in Jupiter and -Saturn, in Saturn chiefly; for when Jupiter, who moves faster -than Saturn, approaches near to a conjunction with him, his -action upon Saturn will a little retard the motion of that planet, -and by the reciprocal action of Saturn he will himself be -accelerated. After conjunction, Jupiter will again accelerate -Saturn, and be likewise retarded in the same degree, as before -the first was retarded and the latter accelerated. Whatever -inequalities besides are produced in the motion of Saturn by -the action of Jupiter upon that planet, will be sufficiently rectified, -by placing the focus of Saturn’s ellipsis, which should -otherwise be in the sun, in the common center of gravity of -the sun and Jupiter. And all the inequalities in the motion -of Jupiter, caused by Saturn’s action upon him, are much -less considerable than the irregularities of Saturn’s motion<a name="FNanchor_166_166" id="FNanchor_166_166"></a><a href="#Footnote_166_166" class="fnanchor">[166]</a>.</p> - -<p>7. <span class="smcap gesperrt">This</span> one principle therefore of the planets having a -power, as well as the sun, to cause bodies to gravitate towards -them, which is proved by the motion of the secondary planets -to obtain in fact, explains all the irregularities relating to -the planets ever observed by astronomers.</p> - -<p><span class="pagenum"><a name="Page_178" id="Page_178">[178]</a></span></p> - -<p><a name="c178" id="c178">8.</a> Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> after this proceeds to make an -improvement in astronomy by applying this theory to the farther -correction of their motions. For as we have here observed -the planets to possess a principle of gravitation, as well as -the sun; so it will be explained at large hereafter, that the -third law of motion, which makes action and reaction equal, -is to be applied in this case<a name="FNanchor_167_167" id="FNanchor_167_167"></a><a href="#Footnote_167_167" class="fnanchor">[167]</a>; and that the sun does not only -attract each planet, but is it self also attracted by them; the -force, wherewith the planet is acted on, bearing to the force, -wherewith the sun it self is acted on at the same time, the -proportion, which the quantity of matter in the sun bears to -the quantity of matter in the planet. From the action between -the sun and planet being thus mutual Sir <span class="smcap">Isaac -Newton</span> proves that the sun and planet will describe about -their common center of gravity similar ellipsis’s; and then that -the transverse axis of the ellipsis described thus about the moveable -sun, will bear to the transverse axis of the ellipsis, which -would be described about the sun at rest in the same time, the -same proportion as the quantity of solid matter in the sun and -planet together bears to the first of two mean proportionals between -this quantity and the quantity of matter in the sun only<a name="FNanchor_168_168" id="FNanchor_168_168"></a><a href="#Footnote_168_168" class="fnanchor">[168]</a>.</p> - -<p>9. <span class="smcap gesperrt">Above</span>, where I shewed how to find a cube, that -should bear any proportion to another cube<a name="FNanchor_169_169" id="FNanchor_169_169"></a><a href="#Footnote_169_169" class="fnanchor">[169]</a>, the lines F T -and T S are two mean proportionals between E F and F G; -and counting from E F, F T is called the first, and F S the second -of those means. In numbers these mean proportionals<span class="pagenum"><a name="Page_179" id="Page_179">[179]</a></span> -are thus found.</p> - -<div class="floatright"> - <img src="images/ill-239.jpg" width="100" height="114" - alt="" - title="" /> -</div> - -<p>Suppose A and B two numbers, and it be -required to find C the first, and D the second of -the two mean proportionals between them. First -multiply A by it self, and the product multiply -by B; then C will be the number which in arithmetic -is called the cubic root of this last product; that is, -the number C being multiplied by it self, and the product -again multiplied by the same number C, will produce the -product above mentioned. In like manner D is the cubic -root of the product of B multiplied by it self, and the produce -of that multiplication multiplied again by A.</p> - -<p>10. <span class="smcap gesperrt">It</span> will be asked, perhaps, how this correction can be -admitted, when the cause of the motions of the planets was -before found by supposing the sun the center of the power, -which acted upon them: for according to the present correction -this power appears rather to be directed to their common -center of gravity. But whereas the sun was at first concluded -to be the center, to which the power acting on the planets -was directed, because the spaces described round the sun in -equal times were found to be equal; so Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> -proves, that if the sun and planet move round their common -center of gravity, yet to an eye placed in the planet, the spaces, -which will appear to be described about the sun, will have -the same relation to the times of their description, as the real -spaces would have, if the sun were at rest<a name="FNanchor_170_170" id="FNanchor_170_170"></a><a href="#Footnote_170_170" class="fnanchor">[170]</a>. I farther asserted, -that, supposing the planets to move round the sun at rest,<span class="pagenum"><a name="Page_180" id="Page_180">[180]</a></span> -and to be attracted by a power, which every where should -act with degrees of strength reciprocally in the duplicate -proportion of the distances; then the periods of the planets -must observe the same relation to their distances, as astronomers -find them to do. But here it must not be supposed, that -the observations of astronomers absolutely agree without any -the least difference; and the present correction will not cause -a deviation from any one astronomer’s observations, so much -as they differ from one another. For in Jupiter, where this -correction is greatest, it hardly amounts to the 3000<sup>th</sup> part -of the whole axis.</p> - -<p><a name="c180" id="c180">11.</a> <span class="smcap gesperrt">Upon</span> this head I think it not improper to mention -a reflection made by our excellent author upon these small inequalities -in the planets motions; which contains under it a -very strong philosophical argument against the eternity of the -world. It is this, that these inequalities must continually increase -by slow degrees, till they render at length the present -frame of nature unfit for the purposes, it now serves<a name="FNanchor_171_171" id="FNanchor_171_171"></a><a href="#Footnote_171_171" class="fnanchor">[171]</a>. And -a more convincing proof cannot be desired against the present -constitution’s having existed from eternity than this, -that a certain period of years will bring it to an end. I am -aware this thought of our author has been represented even -as impious, and as no less than casting a reflection upon -the wisdom of the author of nature, for framing a perishable -work. But I think so bold an assertion ought to have -been made with singular caution. For if this remark -upon the increasing irregularities of the heavenly motions<span class="pagenum"><a name="Page_181" id="Page_181">[181]</a></span> -be true in fact, as it really is, the imputation must return -upon the asserter, that this does detract from the divine -wisdom. Certainly we cannot pretend to know all the -omniscient Creator’s purposes in making this world, and -therefore cannot undertake to determine how long he designed -it should last. And it is sufficient, if it endure -the time intended by the author. The body of every animal -shews the unlimited wisdom of its author no less, nay -in many respects more, than the larger frame of nature; -and yet we see, they are all designed to last but a small -space of time.</p> - -<p>12. <span class="smcap gesperrt">There</span> need nothing more be said of the primary planets; -the motions of the secondary shall be next considered.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c181" id="c181"><span class="smcap">Chap. III.</span></a><br /> -Of the motion of the MOON and the other -SECONDARY PLANETS.</h2> - -<p class="drop-cap04">THE excellency of this philosophy sufficiently appears -from its extending in the manner, which has been related, -to the minutest circumstances of the primary planets -motions; which nevertheless bears no proportion to the vast -success of it in the motions of the secondary; for it not only -accounts for all the irregularities, by which their motions were -known to be disturbed, but has discovered others so complicated, -that astronomers were never able to distinguish them, and -reduce them under proper heads; but these were only to be<span class="pagenum"><a name="Page_182" id="Page_182">[182]</a></span> -found out from their causes, which this philosophy has brought -to light, and has shewn the dependence of these inequalities -upon such causes in so perfect a manner, that we not only learn -from thence in general, what those inequalities are, but are -able to compute the degree of them. Of this Sir <span class="smcap"><em class="gesperrt">Is. Newton</em></span> -has given several specimens, and has moreover found means -to reduce the moon’s motion so completely to rule, that he -has framed a theory, from which the place of that planet -may at all times be computed, very nearly or altogether as exactly, -as the places of the primary planets themselves, which is -much beyond what the greatest astronomers could ever effect.</p> - -<p><a name="c182" id="c182">2.</a> <span class="smcap gesperrt">The</span> first thing demonstrated of these secondary planets -is, that they are drawn towards their respective primary in the -same manner as the primary planets are attracted by the sun. -That each secondary planet is kept in its orbit by a power -pointed towards the center of the primary planet, about -which the secondary revolves; and that the power, by which -the secondaries of the same primary are influenced, bears the -same relation to the distance from the primary, as the power, -by which the primary planets are guided, does in regard to -the distance from the sun<a name="FNanchor_172_172" id="FNanchor_172_172"></a><a href="#Footnote_172_172" class="fnanchor">[172]</a>. This is proved in the satellites of -Jupiter and Saturn, because they move in circles, as far as we -can observe, about their respective primary with an equable -course, the respective primary being the center of each orbit: -and by comparing the times, in which the different satellites -of the same primary perform their periods, they are<span class="pagenum"><a name="Page_183" id="Page_183">[183]</a></span> -found to observe the same relation to the distances from their -primary, as the primary planets observe in respect of their -mean distances from the sun<a name="FNanchor_173_173" id="FNanchor_173_173"></a><a href="#Footnote_173_173" class="fnanchor">[173]</a>. Here these bodies moving in -circles with an equable motion, each satellite passes over equal -parts of its orbit in equal portions of time; consequently -the line drawn from the center of the orbit, that is, from -the primary planet, to the satellite, will pass over equal spaces -along with the satellite in equal portions of time; which -proves the power, by which each satellite is held in its orbit, -to be pointed towards the primary as a center<a name="FNanchor_174_174" id="FNanchor_174_174"></a><a href="#Footnote_174_174" class="fnanchor">[174]</a>. It is also manifest -that the centripetal power, which carries a body in a -circle concentrical with the power, acts upon the body at all -times with the same strength. But Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> demonstrates -that, when bodies are carried in different circles by -centripetal powers directed to the centers of those circles, then, -the degrees of strength of those powers are to be compared by -considering the relation between the times, in which the bodies -perform their periods through those circles<a name="FNanchor_175_175" id="FNanchor_175_175"></a><a href="#Footnote_175_175" class="fnanchor">[175]</a>; and in particular -he shews, that if the periodical times bear that relation, -which I have just now asserted the satellites of the same primary -to observe; then the centripetal powers are reciprocally -in the duplicate proportion of the semidiameters of the circles, -or in that proportion to the distances of the bodies from the -centers<a name="FNanchor_176_176" id="FNanchor_176_176"></a><a href="#Footnote_176_176" class="fnanchor">[176]</a>. Hence it follows that in the planets Jupiter and -Saturn, the centripetal power in each decreases with the increase -of distance, in the same proportion as the centripetal<span class="pagenum"><a name="Page_184" id="Page_184">[184]</a></span> -power appertaining to the sun decreases with the increase of -distance. I do not here mean that this proportion of the centripetal -powers holds between the power of Jupiter at any distance -compared with the power of Saturn at any other distance; -but only in the change of strength of the power belonging -to the same planet at different distances from him. -Moreover what is here discovered of the planets Jupiter and -Saturn by means of the different satellites, which revolve -round each of them, appears in the earth by the moon alone; -because she is found to move round the earth in an ellipsis after -the same manner as the primary planets do about the sun; -excepting only some small irregularities in her motion, the -cause of which will be particularly explained in what follows, -whereby it will appear, that they are no objection against -the earth’s acting on the moon in the same manner as the sun -acts on the primary planets; that is, as the other primary -planets Jupiter and Saturn act upon their satellites. Certainly -since these irregularities can be otherwise accounted for, we -ought not to depart from that rule of induction so necessary -in philosophy, that to like bodies like properties are to be attributed, -where no reason to the contrary appears. We cannot -therefore but ascribe to the earth the same kind of action -upon the moon, as the other primary planets Jupiter and Saturn -have upon their satellites; which is known to be very -exactly in the proportion assigned by the method of comparing -the periodical times and distances of all the satellites which -move about the same planet; this abundantly compensating -our not being near enough to observe the exact figure of -their orbits. For if the little deviation of the moon’s orbit<span class="pagenum"><a name="Page_185" id="Page_185">[185]</a></span> -orbit from a true permanent ellipsis arose from the action of the -earth upon the moon not being in the exact reciprocal duplicate -proportion of the distance, were another moon to revolve -about the earth, the proportion between the periodical times of -this new moon, and the present, would discover the deviation -from the mentioned proportion much more manifestly.</p> - -<p>3. <span class="smcap gesperrt">By</span> the number of satellites, which move round Jupiter -and Saturn, the power of each of these planets is measured in -a great diversity of distance; for the distance of the outermost -satellite in each of these planets exceeds several times the distance -of the innermost. In Jupiter the astronomers have usually -placed the innermost satellite at a distance from the center of -that planet equal to about 5⅔ of the semidiameters of Jupiter’s -body, and this satellite performs its revolution in about 1 day -18½ hours. The next satellite, which revolves round Jupiter in -about 3 days 13⅕ hours, they place at the distance from Jupiter -of about 9 of that planet’s semidiameters. To the third satellite, -which performs its period nearly in 7 days 3¾ hours, -they assign the distance of about 14⅖ semidiameters. But -the outermost satellite they remove to 25⅓ semidiameters, and -this satellite makes its period in about 16 days 16½ hours<a name="FNanchor_177_177" id="FNanchor_177_177"></a><a href="#Footnote_177_177" class="fnanchor">[177]</a>. -In Saturn there is still a greater diversity in the distance of the -several satellites. By the observations of the late <span class="smcap"><em class="gesperrt">Cassini</em></span>, a -celebrated astronomer in France, who first discovered all these -satellites, except one known before, the innermost is distant -about 4½ of Saturn’s semidiameters from his center, and revolves<span class="pagenum"><a name="Page_186" id="Page_186">[186]</a></span> -round in about 1 day 21⅓ hours. The next satellite -is distant about 5¾ semidiameters, and makes its period in about -2 days 17⅔ hours. The third is removed to the distance -of about 8 semidiameters, and performs its revolution in -near 4 days 12½ hours. The fourth satellite discovered first -by the great <span class="smcap">Huygens</span>, is near 18⅔ semidiameters, and -moves round Saturn in about 15 days 22⅔ hours. The outermost -is distant 56 semidiameters, and makes its revolution -in about 79 days 7⅘ hours<a name="FNanchor_178_178" id="FNanchor_178_178"></a><a href="#Footnote_178_178" class="fnanchor">[178]</a>. Besides these satellites, there -belongs to the planet Saturn another body of a very singular -kind. This is a shining, broad, and flat ring, which encompasses -the planet round. The diameter of the outermost -verge of this ring is more than double the diameter of Saturn. -<span class="smcap"><em class="gesperrt">Huygens</em></span>, who first described this ring, makes the whole -diameter thereof to bear to the diameter of Saturn the proportion -of 9 to 4. The late reverend Mr. <span class="smcap">Pound</span> makes the -proportion something greater, viz. that of 7 to 3. The distances -of the satellites of this planet Saturn are compared by -<span class="smcap"><em class="gesperrt">Cassini</em></span> to the diameter of the ring. His numbers I have -reduced to those above, according to Mr. <span class="smcap">Pound</span>’s proportion -between the diameters of Saturn and of his ring. As -this ring appears to adhere no where to Saturn, so the distance -of Saturn from the inner edge of the ring seems rather -greater than the breadth of the ring. The distances, which -have here been given, of the several satellites, both for Jupiter -and Saturn, may be more depended on in relation to the -proportion, which those belonging to the same primary planet<span class="pagenum"><a name="Page_187" id="Page_187">[187]</a></span> -bear one to another, than in respect to the very numbers, that -have been here set down, by reason of the difficulty there is -in measuring to the greatest exactness the diameters of the primary -planets; as will be explained hereafter, when we come -to treat of telescopes<a name="FNanchor_179_179" id="FNanchor_179_179"></a><a href="#Footnote_179_179" class="fnanchor">[179]</a>. By the observations of the forementioned -Mr. <span class="smcap">Pound</span>, in Jupiter the distance of the innermost -satellite should rather be about 6 semidiameters, of the second -9-½, of the third 15, and of the outermost 26⅔<a name="FNanchor_180_180" id="FNanchor_180_180"></a><a href="#Footnote_180_180" class="fnanchor">[180]</a>; and in Saturn -the distance of the innermost satellite 4 semidiameters, -of the next 6¼, of the third 8¾, of the fourth 20⅓, and of the -fifth 59<a name="FNanchor_181_181" id="FNanchor_181_181"></a><a href="#Footnote_181_181" class="fnanchor">[181]</a>. However the proportion between the distances -of the satellites in the same primary is the only thing necessary -to the point we are here upon.</p> - -<p>4. <span class="smcap gesperrt">But</span> moreover the force, wherewith the earth acts in -different distances, is confirmed from the following consideration, -yet more expresly than by the preceding analogical -reasoning. It will appear, that if the power of the earth, by -which it retains the moon in her orbit, be supposed to act at all -distances between the earth and moon, according to the forementioned -rule; this power will be sufficient to produce upon -bodies, near the surface of the earth, all the effects ascribed -to the principle of gravity. This is discovered by the following -method. Let A (in fig. 94.) represent the earth, -B the moon, B C D the moon’s orbit, which differs little from -a circle, of which A is the center. If the moon in B were -left to it self to move with the velocity, it has in the point B, it<span class="pagenum"><a name="Page_188" id="Page_188">[188]</a></span> -would leave the orbit, and proceed right forward in the line -B E, which touches the orbit in B. Suppose the moon would -upon this condition move from B to E in the space of one minute -of time. By the action of the earth upon the moon, whereby -it is retained in its orbit, the moon will really be found at the -end of this minute in the point F, from whence a straight line -drawn to A shall make the space B F A in the circle equal to the -triangular space B E A; so that the moon in the time wherein -it would have moved from B to E, if left to it self, has been -impelled towards the earth from E to F. And when the time -of the moon’s passing from B to F is small, as here it is only -one minute, the distance between E and F scarce differs from -the space, through which the moon would descend in the -same time, if it were to fall directly down from B toward A -without any other motion. A B the distance of the earth and -moon is about 60 of the earth’s semidiameters, and the moon -completes her revolution round the earth in about 27 days -7 hours and 43 minutes: therefore the space E F will here be -found by computation to be about 16⅛ feet. Consequently, -if the power, by which the moon is retained in its orbit, be -near the surface of the earth greater, than at the distance of -the moon in the duplicate proportion of that distance; the -number of feet, a body would descend near the surface of the -earth by the action of this power upon it in one minute of -time, would be equal to 16⅛ multiplied twice into the number -60, that is, equal to 58050. But how fast bodies fall near -the surface of the earth may be known by the pendulum<a name="FNanchor_182_182" id="FNanchor_182_182"></a><a href="#Footnote_182_182" class="fnanchor">[182]</a>; and<span class="pagenum"><a name="Page_189" id="Page_189">[189]</a></span> -by the exactest experiments they are found to descend the space -of 16⅛ feet in a second of time; and the spaces described by -falling bodies being in the duplicate proportion of the times -of their fall<a name="FNanchor_183_183" id="FNanchor_183_183"></a><a href="#Footnote_183_183" class="fnanchor">[183]</a>, the number of feet, a body would describe in its -fall near the surface of the earth in one minute of time, will -be equal to 16⅛ twice multiplied by 60, the same as would -be caused by the power which acts upon the moon.</p> - -<p>5. <span class="smcap gesperrt">In</span> this computation the earth is supposed to be at -rest, whereas it would have been more exact to have supposed -it to move, as well as the moon, about their common -center of gravity; as will easily be understood, by what -has been said in the preceding chapter, where it was shewn, -that the sun is subjected to the like motion about the common -center of gravity of it self and the planets. The action -of the sun upon the moon, which is to be explain’d -in what follows, is likewise here neglected: and Sir <span class="smcap">Isaac -Newton</span> shews, if you take in both these considerations, -the present computation will best agree to a somewhat greater -distance of the moon and earth, viz. to 60½ semidiameters -of the earth, which distance is more conformable to -astronomical observations.</p> - -<p><a name="c189" id="c189">6.</a> <span class="smcap gesperrt">These</span> computations afford an additional proof, that -the action of the earth observes the same proportion to the -distance, which is here contended for. Before I said, it -was reasonable to conclude so by induction from the planets<span class="pagenum"><a name="Page_190" id="Page_190">[190]</a></span> -Jupiter and Saturn; because they act in that manner. -But now the same thing will be evident by drawing no other -consequence from what is seen in those planets, than that the -power, by which the primary planets act on their secondary, -is extended from the primary through the whole interval between, -so that it would act in every part of the intermediate -space. In Jupiter and Saturn this power is so far from being -confined to a small extent of distance, that it not only reaches -to several satellites at very different distances, but also from -one planet to the other, nay even through the whole planetary -system<a name="FNanchor_184_184" id="FNanchor_184_184"></a><a href="#Footnote_184_184" class="fnanchor">[184]</a>. Consequently there is no appearance of reason, -why this power should not act at all distances, even at the -very surfaces of these planets as well as farther off. But from -hence it follows, that the power, which retains the moon -in her orbit, is the same, as causes bodies near the surface of -the earth to gravitate. For since the power, by which the -earth acts on the moon, will cause bodies near the surface -of the earth to descend with all the velocity they are found -to do, it is certain no other power can act upon them -besides; because if it did, they must of necessity descend -swifter. Now from all this it is at length very evident, -that the power in the earth, which we call gravity, extends -up to the moon, and decreases in the duplicate proportion -of the increase of the distance from the earth.</p> - -<p><a name="c190" id="c190">7.</a> <span class="smcap gesperrt">This</span> finishes the discoveries made in the action of -the primary planets upon their secondary. The next thing<span class="pagenum"><a name="Page_191" id="Page_191">[191]</a></span> -to be shewn is, that the sun acts upon them likewise: for -this purpose it is to be observed, that if to the motion of the -satellite, whereby it would be carried round its primary at -rest, be superadded the same motion both in regard to -velocity and direction, as the primary it self has, it will -describe about the primary the same orbit, with as great -regularity, as if the primary was indeed at rest. The -cause of this is that law of motion, which makes a -body near the surface of the earth, when let fall, to -descend perpendicularly, though the earth be in so swift -a motion, that if the falling body did not partake of it, -its descent would be remarkably oblique; and that a body -projected describes in the most regular manner the same -parabola, whether projected in the direction, in which the -earth moves, or in the opposite direction, if the projecting -force be the same<a name="FNanchor_185_185" id="FNanchor_185_185"></a><a href="#Footnote_185_185" class="fnanchor">[185]</a>. From this we learn, that -if the satellite moved about its primary with perfect regularity, -besides its motion about the primary, it would -participate of all the motion of its primary; have the -same progressive velocity, with which the primary is carried -about the sun; and be impelled with the same velocity -as the primary towards the sun, in a direction parallel -to that impulse of its primary. And on the contrary, the -want of either of these, in particular of the impulse towards -the sun, will occasion great inequalities in the motion -of the secondary planet. The inequalities, which would -arise from the absence of this impulse towards the sun are<span class="pagenum"><a name="Page_192" id="Page_192">[192]</a></span> -so great, that by the regularity, which appears in the motion -of the secondary planets, it is proved, that the sun communicates, -the same velocity to them by its action, as it gives -to their primary at the same distance. For Sir <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> -informs us, that upon examination he found, that if -any of the satellites of Jupiter were attracted by the sun -more or less, than Jupiter himself at the same distance, the -orbit of that satellite, instead of being concentrical to Jupiter, -must have its center at a greater or less distance, than -the center of Jupiter from the sun, nearly in the subduplicate -proportion of the difference between the sun’s action upon -the satellite, and upon Jupiter; and therefore if any satellite -were attracted by the sun but 1/1000 part more or less, -than Jupiter is at the same distance, the center of the -orbit of that satellite would be distant from the center of -Jupiter no less than a fifth part of the distance of the outermost -satellite from Jupiter<a name="FNanchor_186_186" id="FNanchor_186_186"></a><a href="#Footnote_186_186" class="fnanchor">[186]</a>; which is almost the whole -distance of the innermost satellite. By the like argument -the satellites of Saturn gravitate towards the sun, as much -as Saturn it self at the same distance; and the moon as -much as the earth.</p> - -<p>8. <span class="smcap gesperrt">Thus</span> is proved, that the sun acts upon the secondary -planets, as much as upon the primary at the same -distance: but it was found in the last chapter, that the -action of the sun upon bodies is reciprocally in the duplicate -proportion of the distance; therefore the secondary<span class="pagenum"><a name="Page_193" id="Page_193">[193]</a></span> -planets being sometimes nearer to the sun than the primary, -and sometimes more remote, they are not alway -acted upon in the same degree with their primary, but -when nearer to the sun, are attracted more, and when farther -distant, are attracted less. Hence arise various inequalities -in the motion of the secondary planets<a name="FNanchor_187_187" id="FNanchor_187_187"></a><a href="#Footnote_187_187" class="fnanchor">[187]</a>.</p> - -<p><a name="c193" id="c193">9.</a> <span class="smcap gesperrt">Some</span> of these inequalities would take place, though -the moon, if undisturbed by the sun, would have moved in -a circle concentrical to the earth, and in the plane of the earth’s -motion; others depend on the elliptical figure, and the oblique -situation of the moon’s orbit. One of the first kind is, -that the moon is caused so to move, as not to describe equal -spaces in equal times, but is continually accelerated, as she -passes from the quarter to the new or full, and is retarded -again by the like degrees in returning from the new and full -to the next quarter. Here we consider not so much the absolute, -as the apparent motion of the moon in respect to us.</p> - -<p>10. <span class="smcap gesperrt">The</span> principles of astronomy teach how to distinguish -these two motions. Let S (in fig. 95.) represent the -sun, A the earth moving in its orbit B C, D E F G the moon’s -orbit, the place of the moon H. Suppose the earth to have -moved from A to I. Because it has been shewn, that the -moon partakes of all the progressive motion of the earth; and -likewise that the sun attracts both the earth and moon equally, -when they are at the same distance from it, or that the -mean action of the sun upon the moon is equal to its action<span class="pagenum"><a name="Page_194" id="Page_194">[194]</a></span> -upon the earth: we must therefore consider the earth as carrying -about with it the moon’s orbit; so that when the -earth is removed from A to I, the moon’s orbit shall likewise -be removed from its former situation into that denoted -by K L M N. But now the earth being in I, if the moon -were found in O, so that O I should be parallel to H A, -though the moon would really have moved from H to O, yet -it would not have appeared to a spectator upon the earth to -have moved at all, because the earth has moved as much it -self; so that the moon would still appear in the same place -with respect to the fixed stars. But if the moon be observed -in P, it will then appear to have moved, its apparent motion -being measured by the angle under O I P. And if the angle -under P I S be less than the angle under H A S, the moon -will have approached nearer to its conjunction with the sun.</p> - -<p>11. <span class="smcap gesperrt">To</span> come now to the explication of the mentioned -inequality in the moon’s motion: let S (in fig. 96.) represent -the sun, A the earth, B C D E the moon’s orbit, C the place of the -moon, when in the latter quarter. Here it will be nearly at the -same distance from the sun, as the earth is. In this case therefore -they will both be equally attracted, the earth in the direction -A S, and the moon in the direction C S. Whence as the -earth in moving round the sun is continually descending toward -it, so the moon in this situation must in any equal portion -of time descend as much; and therefore the position of -the line A C in respect of A S, and the change, which the -moon’s motion produces in the angle under C A S, will not be -altered by the sun.</p> - -<p><span class="pagenum"><a name="Page_195" id="Page_195">[195]</a></span></p> - -<p>12. <span class="smcap gesperrt">But</span> now as soon as ever the moon is advanced from -the quarter toward the new or conjunction, suppose to G, -the action of the sun upon it will have a different effect. Here, -were the sun’s action upon the moon to be applied in the direction -G H parallel to A S, if its action on the moon were -equal to its action on the earth, no change would be wrought -by the sun on the apparent motion of the moon round the -earth. But the moon receiving a greater impulse in G than -the earth receives in A, were the sun to act in the direction -G H, yet it would accelerate the description of the space -D A G, and cause the angle under G A D to decrease faster, -than otherwise it would. The sun’s action will have this effect -upon account of the obliquity of its direction to that, in -which the earth attracts the moon. For the moon by this -means is drawn by two forces oblique to each other, one -drawing from G toward A, the other from G toward H, -therefore the moon must necessarily be impelled toward D. -Again, because the sun does not act in the direction G H parallel -to S A, but in the direction G S oblique to it, the sun’s -action on the moon will by reason of this obliquity farther contribute -to the moon’s acceleration. Suppose the earth in any -short space of time would have moved from A to I, if not -attracted by the sun; the point I being in the straight line C E, -which touches the earth’s orbit in A. Suppose the moon in -the same time would have moved in her orbit from G to K, -and besides have partook of all the progressive motion of the -earth. Then if K L be drawn parallel to A I, and taken equal -to it, the moon, if not attracted by the sun, would be found<span class="pagenum"><a name="Page_196" id="Page_196">[196]</a></span> -in L. But the earth by the sun’s action is removed from I. Suppose -it were moved down to M in the line I M N parallel -to S A, and if the moon were attracted but as much, and in -the same direction, as the earth is here supposed to be attracted, -so as to have descended during the same time in the line L O, -parallel also to A S, down as far as P, till L P were equal -to I M; the angle under P M N would be equal to that -under L I N, that is, the moon will appear advanced no farther -forward, than if neither it nor the earth had been subject -to the sun’s action. But this is upon the supposition, that the -action of the sun upon the moon and earth were equal; -whereas the moon being acted upon more than the earth, did -the sun’s action draw the moon in the line L O parallel to A S, -it would draw it down so far as to make L P greater than -I M; whereby the angle under P M N will be rendred less, -than that under L I N. But moreover, as the sun draws the -earth in a direction oblique to I N, the earth will be found -in its orbit somewhat short of the point M; however the -moon is attracted by the sun still more out of the line L O, -than the earth is out of the line I N; therefore this obliquity -of the sun’s action will yet farther diminish the angle -under P M N.</p> - -<p>13. <span class="smcap gesperrt">Thus</span> the moon at the point G receives an impulse -from the sun, whereby her motion is accelerated. And the -sun producing this effect in every place between the quarter -and the conjunction, the moon will move from the quarter -with a motion continually more and more accelerated; and -therefore by acquiring from time to time additional degrees<span class="pagenum"><a name="Page_197" id="Page_197">[197]</a></span> -of velocity in its orbit, the spaces, which are described in -equal times by the line drawn from the earth to the moon, will -not be every where equal, but those toward the conjunction -will be greater, than those toward the quarter. But now in -the moon’s passage from the conjunction D to the next quarter -the sun’s action will again retard the moon, till at the next -quarter in E it be restored to the first velocity, which it had -in C.</p> - -<p>14. <span class="smcap gesperrt">Again</span> as the moon moves from E to the full or opposition -to the sun in B, it is again accelerated, the deficiency -of the sun’s action upon the moon, from what it has upon the -earth, producing here the same effect as before the excess of its -action. Consider the moon in Q, moving from E towards B. -Here if the moon were attracted by the sun in a direction -parallel to A S, yet being acted on less than the earth, as -the earth descends toward the sun, the moon will in some -measure be left behind. Therefore Q F being drawn parallel -to S B, a spectator on the earth would see the moon -move, as if attracted from the point Q in the direction -Q F with a degree of force equal to that, whereby the sun’s -action on the moon falls short of its action on the earth. But -the obliquity of the sun’s action has also here an effect. In -the time the earth would have moved from A to I without the -influence of the sun, let the moon have moved in its orbit from -Q to R. Drawing therefore R T parallel to A I, and equal to the -same, for the like reason as before, the moon by the motion of -its orbit, if not at all attracted by the sun, must be found in T; -and therefore, if attracted in a direction parallel to S A, would<span class="pagenum"><a name="Page_198" id="Page_198">[198]</a></span> -be in the line T V parallel to A S; suppose in W. But the -moon in Q being farther off the sun than the earth, it will be -less attracted, that is, T W will be less than I M, and if the -line S M be prolonged toward X, the angle under X M W -will be less than that under X I T. Thus by the sun’s action -the moon’s passage from the quarter to the full would be accelerated, -if the sun were to act on the earth and moon in a -direction parallel to A S: and the obliquity of the sun’s action -will still more increase this acceleration. For the action -of the sun on the moon is oblique to the line S A the whole -time of the moon’s passage from Q to T, and will carry -the moon out of the line T V toward the earth. Here I suppose -the time of the moon’s passage from Q to T so short, that -it shall not pass beyond the line S A. The earth also will come -a little short of the line I N, as was said before. From these -causes the angle under X M W will be still farther lessened.</p> - -<p><a name="c198" id="c198">15.</a> <span class="smcap gesperrt">The</span> moon in passing from the opposition B to the -next quarter will be retarded again by the same degrees, as -it is accelerated before its appulse to the opposition. Because -this action of the sun, which in the moon’s passage from the -quarter to the opposition causes it to be extraordinarily accelerated, -and diminishes the angle, which measures its distance -from the opposition; will make the moon slacken its pace afterwards, -and retard the augmentation of the same angle in -its passage from the opposition to the following quarter; that -is, will prevent that angle from increasing so fast, as otherwise -it would. And thus the moon, by the sun’s action upon it, is -twice accelerated and twice restored to its first velocity, every<span class="pagenum"><a name="Page_199" id="Page_199">[199]</a></span> -circuit it makes round the earth. This inequality of the moon’s -motion about the earth is called by astronomers its variation.</p> - -<p>16. <span class="smcap gesperrt">The</span> next effect of the sun upon the moon is, that it -gives the orbit of the moon in the quarters a greater degree -of curvature, than it would receive from the action of -the earth alone; and on the contrary in the conjunction and -opposition the orbit is less inflected.</p> - -<p>17. <span class="smcap gesperrt">When</span> the moon is in conjunction with the sun in -the point D, the sun attracting the moon more forcibly than -it does the earth, the moon by that means is impelled less toward -the earth, than otherwise it would be, and so the orbit -is less incurvated; for the power, by which the moon is impelled -toward the earth, being that, by which it is inflected -from a rectilinear course, the less that power is, the less it -will be inflected. Again, when the moon is in the opposition -in B, farther removed from the sun than the earth is; -it follows then, though the earth and moon are both continually -descending to the sun, that is, are drawn by the sun -toward it self out of the place they would otherwise move -into, yet the moon descends with less velocity than the -earth; insomuch that the moon in any given space of -time from its passing the point of opposition will have -less approached the earth, than otherwise it would have -done, that is, its orbit in respect of the earth will approach -nearer to a straight line. In the last place, when -the moon is in the quarter in F, and equally distant -from the sun as the earth, we observed before, that<span class="pagenum"><a name="Page_200" id="Page_200">[200]</a></span> -the earth and moon would descend with equal pace toward -the sun, so as to make no change by that descent -in the angle under F A S; but the length of the line F A must -of necessity be shortned. Therefore the moon in moving from -F toward the conjunction with the sun will be impelled more -toward the earth by the sun’s action, than it would have been -by the earth alone, if neither the earth nor moon had been -acted on by the sun; so that by this additional impulse the -orbit is rendred more curve, than it would otherwise be. -The same effect will also be produced in the other quarter.</p> - -<p><a name="c200" id="c200">18.</a> <span class="smcap gesperrt">Another</span> effect of the sun’s action, consequent upon -this we have now explained, is, that though the moon undisturbed -by the sun might move in a circle having the earth -for its center; by the sun’s action, if the earth were to be -in the very middle or center of the moon’s orbit, yet the -moon would be nearer the earth at the new and full, than -in the quarters. In this probably will at first appear some -difficulty, that the moon should come nearest to the earth, -where it is least attracted to it, and be farthest off when most -attracted. Which yet will appear evidently to follow from -that very cause, by considering what was last shewn, that the -orbit of the moon in the conjunction and opposition is rendred -less curve; for the less curve the orbit of the moon is, -the less will the moon have descended from the place -it would move into, without the action of the earth. Now -if the moon were to move from any place without farther -disturbance from that action, since it would proceed in -the line, which would touch its orbit in that place, it would<span class="pagenum"><a name="Page_201" id="Page_201">[201]</a></span> -recede continually from the earth; and therefore if the power -of the earth upon the moon, be sufficient to retain it at -the same distance, this diminution of that power will cause -the distance to increase, though in a less degree. But on the -other hand in the quarters, the moon, being pressed more towards -the earth than by the earth’s single action, will be -made to approach it; so that in passing from the conjunction -or opposition to the quarters the moon ascends from the -earth, and in passing from the quarters to the conjunction -and opposition it descends again, becoming nearer in these -last mentioned places than in the other.</p> - -<p><a name="c201a" id="c201a">19.</a> <span class="smcap gesperrt">All</span> these forementioned inequalities are of different -degrees, according as the sun is more or less distant from the -earth; greater when the earth is nearest the sun, and less -when it is farthest off. For in the quarters, the nearer the -moon is to the sun, the greater is the addition to the earth’s -action upon it by the power of the sun; and in the conjunction -and opposition, the difference between the sun’s action -upon the earth and upon the moon is likewise so much the -greater.</p> - -<p><a name="c201b" id="c201b">20.</a> This difference in the distance between the earth -and the sun produces a farther effect upon the moon’s motion; -causing the orbit to dilate when less remote from the -sun, and become greater, than when at a farther distance. -For it is proved by Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em>, that the action of -the sun, by which it diminishes the earth’s power over the -moon, in the conjunction or opposition, is about twice as<span class="pagenum"><a name="Page_202" id="Page_202">[202]</a></span> -great, as the addition to the earth’s action by the sun in the -quarters<a name="FNanchor_188_188" id="FNanchor_188_188"></a><a href="#Footnote_188_188" class="fnanchor">[188]</a>; so that upon the whole, the power of the earth -upon the moon is diminished by the sun, and therefore is -most diminished, when the action of the sun is strongest: but -as the earth by its approach to the sun has its influence lessened, -the moon being less attracted will gradually recede from -the earth; and as the earth in its recess from the sun recovers -by degrees its former power, the orbit of the moon must again -contract. Two consequences follow from hence: the -moon will be most remote from the earth, when the earth is -nearest the sun; and also will take up a longer time in performing -its revolution through the dilated orbit, than through -the more contracted.</p> - -<p><a name="c202" id="c202">21.</a> <span class="smcap gesperrt">These</span> irregularities the sun would produce in the -moon, if the moon, without being acted on unequally by the -sun, would describe a perfect circle about the earth, and in -the plane of the earth’s motion; but though neither of these -suppositions obtain in the motion of the moon, yet the forementioned -inequalities will take place, only with some difference -in respect to the degree of them; but the moon by not -moving in this manner is subject to some other inequalities also. -For as the moon describes, instead of a circle concentrical -to the earth, an ellipsis, with the earth in one focus, that -ellipsis will be subjected to various changes. It can neither -preserve constantly the same position, nor yet the same figure; -and because the plane of this ellipsis is not the same<span class="pagenum"><a name="Page_203" id="Page_203">[203]</a></span> -with that of the earth’s orbit, the situation of the plane, wherein -the moon moves, will continually change; neither the line -in which it intersects the plane of the earth’s orbit, nor the -inclination of the planes to each other, will remain for any -time the same. All these alterations offer themselves now to -be explained.</p> - -<p>22. <span class="smcap gesperrt">I shall</span> first consider the changes which are made -in the plane of the moon’s orbit. The moon not moving -in the same plane with the earth, the sun is seldom in the -plane of the moon’s orbit, viz. only when the line made by -the common intersection of the two planes, if produced, -will pass through the sun, as is represented in fig. 97. where -S denotes the sun; T the earth; A T B the earth’s orbit described -upon the plane of this scheme; C D E F the moon’s -orbit, the part C D E being raised above, and the part C F E -depressed under the plane of this scheme. Here the line C E, -in which the plane of this scheme, that is, the plane of the -earth’s orbit and the plane of the moon’s orbit intersect each -other, being continued passes through the sun in S. When -this happens, the action of the sun is directed in the plane -of the moon’s orbit, and cannot draw the moon out of this -plane, as will evidently appear to any one that shall consider -the present scheme: for suppose the moon in G, and let a -straight line be drawn from G to S, the sun draws the moon -in the direction of this line from G toward S: but this line lies -in the plane of the orbit; and if it be prolonged from S beyond -G, the continuation of it will lie on the plane C D E; for the -plane itself, if sufficiently extended, will pass through the sun.<span class="pagenum"><a name="Page_204" id="Page_204">[204]</a></span> -But in other cases the obliquity of the sun’s action to the plane -of the orbit will cause this plane continually to change.</p> - -<p>23. <span class="smcap gesperrt">Suppose</span> in the first place, the line, in which the two -planes intersect each other, to be perpendicular to the line -which joins the earth and sun. Let T (in fig. 98, 99, 100, 101.) -represent the earth; S the sun; the plane of this scheme the -plane of the earth’s motion, in which both the sun and earth -are placed. Let A C be perpendicular to S T, which joins the -earth and sun; and let the line A C be that, in which the plane -of the moon’s orbit intersects the plane of the earth’s motion. -To the center T describe in the plane of the earth’s motion -the circle A B C D. And in the plane of the moon’s orbit -describe the circle A E C F, one half of which A E C will -be elevated above the plane of this scheme, the other half -A F C as much depressed below it.</p> - -<p>24. <span class="smcap gesperrt">Now</span> suppose the moon to set forth from the point A -(in fig. 98.) in the direction of the plane A E C. Here she -will be continually drawn out of this plane by the action of -the sun: for this plane A E C, if extended, will not pass through -the sun, but above it; so that the sun, by drawing the moon -directly toward it self, will force it continually more and more -from that plane towards the plane of the earth’s motion, in -which it self is; causing it to describe the line A K G H I, which -will be convex to the plane A E C, and concave to the plane -of the earth’s motion. But here this power of the sun, which -is said to draw the moon toward the plane of the earth’s -motion, must be understood principally of so much only of -the sun’s action upon the moon, as it exceeds the action of the -same upon the earth. For suppose the preceding figure to be -viewed by the eye, placed in the plane of that scheme, and in -the line C T A on the side of A, the plane A B C D will appear as -the straight line D T B, (in fig. 102.) and the plane A E C F as another -straight line F E; and the curve line A K G H I under the -form of the line T K G H I.</p> - -<div class="figcenter"> - <img src="images/ill-265.jpg" width="400" height="494" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_205" id="Page_205">[205]</a></span></p> - -<p>Now it is plain, that the earth and -moon being both attracted by the sun, if the sun’s action upon -both was equally strong, the earth T, and with it the plane -A E C F or line F T E in this scheme, would be carried toward -the sun with as great a pace as the moon, and therefore the -moon not drawn out of it by the sun’s action, excepting -only from the small obliquity of the direction of this action -upon the moon to that of the sun’s action upon the earth, -which arises from the moon’s being out of the plane of the -earth’s motion, and is not very considerable; but the action -of the sun upon the moon being greater than upon the earth, -all the time the moon is nearer to the sun than the earth is, -it will be drawn from the plane A E C or the line T E by -that excess, and made to describe the curve line A G I or -T G I. But it is the custom of astronomers, instead of considering -the moon as moving in such a curve line, to refer -its motion continually to the plane, which touches the true -line wherein it moves, at the point where at any time the -moon is. Thus when the moon is in the point A, its motion -is considered as being in the plane A E C, in whose direction it -then essaies to move; and when in the point K (in fig. 99.) -its motion is referred to the plane, which passes through the -earth, and touches the line A K G H I in the point K. Thus<span class="pagenum"><a name="Page_206" id="Page_206">[206]</a></span> -the moon in passing from A to I will continually change the -plane of her motion. In what manner this change proceeds, -I shall now particularly explain.</p> - -<p>25. <span class="smcap gesperrt">Let</span> the plane, which touches the line A K I in the point -K (in fig. 99.) intersect the plane of the earth’s orbit in the line -L T M. Then, because the line A K I is concave to the plane -A B C, it falls wholly between that plane, and the plane which -touches it in K; so that the plane M K L will cut the plane A E C, -before it meets with the plane of the earth’s motion; suppose -in the line Y T, and the point A will fall between K and L. -With a semidiameter equal to T Y or T L describe the semicircle -L Y M. Now to a spectator on the earth the moon, when -in A, will appear to move in the circle A E C F, and, when in -K, will appear to be moving in the semicircle L Y M. The -earth’s motion is performed in the plane of this scheme, and -to a spectator on the earth the sun will appear always moving -in that plane. We may therefore refer the apparent motion -of the sun to the circle A B C D, described in this plane about -the earth. But the points where this circle, in which the -sun seems to move, intersects the circle in which the moon -is seen at any time to move, are called the nodes of the moon’s -orbit at that time. When the moon is seen moving in the circle -A E C D, the points A and C are the nodes of the orbit; -when she appears in the semicircle L Y M, then L and M are -the nodes. Now here it appears, from what has been said, -that while the moon has moved from A to K, one of the -nodes has been carried from A to L, and the other as much -from C to M. But the motion from A to L, and from C to<span class="pagenum"><a name="Page_207" id="Page_207">[207]</a></span> -M, is backward in regard to the motion of the moon, which -is the other way from A to K, and from thence toward C.</p> - -<p>26. <span class="smcap gesperrt">Farther</span> the angle, which the plane, wherein the -moon at any time appears, makes with the plane of the earth’s -motion, is called the inclination of the moon’s orbit at that -time. And I shall now proceed to shew, that this inclination -of the orbit, when the moon is in K, is less than when -she was in A; or, that the plane L Y M, which touches the -line of the moon’s motion in K, makes a less angle with the -plane of the earth’s motion or with the circle A B C D, than -the plane A E C makes with the same. The semicircle L Y M -intersects the semicircle A E C in Y; and the arch A Y is less -than L Y, and both together less than half a circle. But it is demonstrated -by the writers on that part of astronomy, which is -called the doctrine of the sphere, that when a triangle is made, -as here, by three arches of circles A L, A Y, and Y L, the angle -under Y A B without the triangle is greater than the angle under -Y L A within, if the two arches A Y, Y L taken together do -not amount to a semicircle; if the two arches make a complete -semicircle, the two angles will be equal; but if the two -arches taken together exceed a semicircle, the inner angle under -Y L A is greater than the other<a name="FNanchor_189_189" id="FNanchor_189_189"></a><a href="#Footnote_189_189" class="fnanchor">[189]</a>. Here therefore the two -arches A Y and L Y together being less than a semicircle, the -angle under A L Y is less, than the angle under B A E. But -from the doctrine of the sphere it is also evident, that the angle -under A L Y is equal to that, in which the plane of the<span class="pagenum"><a name="Page_208" id="Page_208">[208]</a></span> -circle L Y K M, that is, the plane which touches the line A K G H I -in K, is inclined to the plane of the earth’s motion A B C; -and the angle under B A E is equal to that, in which the plane -A E C is inclined to the same plane. Therefore the inclination -of the former plane is less than the inclination of the latter.</p> - -<p>27. <span class="smcap gesperrt">Suppose</span> now the moon to be advanced to the point -G (in fig. 100.) and in this point to be distant from its node -a quarter part of the whole circle; or in other words, to be -in the midway between its two nodes. And in this case the -nodes will have receded yet more, and the inclination of the -orbit be still more diminished: for suppose the line A K G H I -to be touched in the point G by a plane passing through the -earth T: let the intersection of this plane with the plane of -the earth’s motion be the line W T O, and the line T P its intersection -with the plane L K M. In this plane let the circle -N G O be described with the semidiameter T P or N T cutting -the other circle L K M in P. Now the line A K G I is convex -to the plane L K M, which touches it in K; and therefore the -plane N G O, which touches it in G, will intersect the other -touching plane between G and K; that is, the point P will fall -between those two points, and the plane continued to the -plane of the earth’s motion will pass beyond L; so that the -points N and O, or the places of the nodes, when the moon -is in G, will be farther from A and C than L and M, that is, -will have moved farther backward. Besides, the inclination -of the plane N G O to the plane of the earth’s motion A B C -is less, than the inclination of the plane L K M to the same; for -here also the two arches L P and N P taken together are less<span class="pagenum"><a name="Page_209" id="Page_209">[209]</a></span> -than a semicircle, each of these arches being less than a quarter -of a circle; as appears, because G N, the distance of the -moon in G from its node N, is here supposed to be a quarter -part of a circle.</p> - -<p>28. <span class="smcap gesperrt">After</span> the moon is passed beyond G, the case is altered; -for then these arches will be greater than quarters of the circle, -by which means the inclination will be again increased, tho’ -the nodes still go on to move the same way. Suppose the -moon in H, (in fig. 101.) and that the plane, which touches -the line A K G I in H, intersects the plane of the earth’s motion -in the line Q T R, and the plane N G O in the line T V, -and besides that the circle Q H R be described in that plane; -then, for the same reason as before, the point V will fall between -H and G, and the plane R V Q will pass beyond the -last plane O V N, causing the points Q and R to fall farther -from A and C than N and O. But the arches N V, V Q are -each greater than a quarter of a circle, N V the least of them -being greater than G N, which is a quarter of a circle; and -therefore the two arches N V and V Q together exceed a semicircle; -consequently the angle under B Q V will be greater, -than that under B N V.</p> - -<p>29. <span class="smcap gesperrt">In</span> the last place, when the moon is by this attraction -of the sun, drawn at length into the plane of the earth’s -motion, the node will have receded yet more, and the inclination -be so much increased, as to become somewhat more -than at first: for the line A K G H I being convex to all the -planes, which touch it, the part H I will wholly fall between<span class="pagenum"><a name="Page_210" id="Page_210">[210]</a></span> -the plane Q V R and the plane A B C; so that the point I will fall -between B and R; and drawing I T W, the point W will be farther -remov’d from A than Q. But it is evident, that the plane, -which passes through the earth T, and touches the line A G I -in the point I, will cut the plane of the earth’s motion A B C D -in the line I T W, and be inclined to the same in the angle under -H I B; so that the node, which was first in A, after having -passed into L, N and Q, comes at last into the point W; as the -node which was at first in C has passed successively from thence -through the points M, O and R to I: but the angle under H I B, -which is now the inclination of the orbit to the plane of the -ecliptic, is manifestly not less than the angle under E C B or -E A B, but rather something greater.</p> - -<p>30. <span class="smcap gesperrt">Thus</span> the moon in the case before us, while it passes -from the plane of the earth’s motion in the quarter, till it -comes again into the same plane, has the nodes of its orbit -continually moved backward, and the inclination of its orbit -is at first diminished, viz. till it comes to G in fig. 100, which is -near to its conjunction with the sun, but afterwards is increased -again almost by the same degrees, till upon the moon’s -arrival again to the plane of the earth’s motion, the inclination -of the orbit is restored to something more than its first -magnitude, though the difference is not very great, because -the points I and C are not far distant from each other<a name="FNanchor_190_190" id="FNanchor_190_190"></a><a href="#Footnote_190_190" class="fnanchor">[190]</a>.</p> - -<p><span class="pagenum"><a name="Page_211" id="Page_211">[211]</a></span></p> - -<p>31. <span class="smcap gesperrt">After</span> the same manner, if the moon had departed -from the quarter in C, it should have described the curve -line C X W (in fig. 98.) between the planes A F C and A D C, -which would be convex to the former of those planes, and -concave to the latter; so that, here also, the nodes should -continually recede, and the inclination of the orbit gradually -diminish more and more, till the moon arrived near its opposition -to the sun in X; but from that time the inclination -should again increase, till it became a little greater than at first. -This will easily appear, by considering, that as the action of -the sun upon the moon, by exceeding its action upon the earth, -drew it out of the plane A E C towards the sun, while the moon -passed from A to I; so, during its passage from C to W, the -moon being all that time farther from the sun than the earth, -it will be attracted less; and the earth, together with the -plane A E C F, will as it were be drawn from the moon, in -such sort, that the path the moon describes shall appear from -the earth, as it did in the former case by the moon’s being -drawn away.</p> - -<p>32. <span class="smcap gesperrt">These</span> are the changes, which the nodes and the inclination -of the moon’s orbit undergo, when the nodes are in -the quarters; but when the nodes by their motion, and the -motion of the sun together, come to be situated between the -quarter and conjunction or opposition, their motion and the -change made in the inclination of the orbit are somewhat different.</p> - -<p><span class="pagenum"><a name="Page_212" id="Page_212">[212]</a></span></p> - -<p>33. <span class="smcap gesperrt">Let</span> A G C H (in fig. 103.) be a circle described in the -plane of the earth’s motion, having the earth in T for its center. -Let the point opposite to the sun be A, and the point G a fourth -part of the circle distant from A. Let the nodes of the moon’s -orbit be situated in the line B T D, and B the node, falling between -A, the place where the moon would be in the full, -and G the place where the moon would be in the quarter. -Suppose B E D F to be the plane, in which the moon essays to -move, when it proceeds from the point B. Because the moon -in B is more distant from the sun than the earth, it shall be -less attracted by the sun, and shall not descend towards the -sun so fast as the earth: consequently it shall quit the plane -B E D F, which we suppose to accompany the earth, and describe -the line B I K convex thereto, till such time as it comes -to the point K, where it will be in the quarter: but from -thenceforth being more attracted than the earth, the moon -shall change its course, and the following part of the path -it describes shall be concave to the plane B E D or B G D, -and shall continue concave to the plane B G D, till it crosses -that plane in L, just as in the preceding case. Now I say, -while the moon is passing from B to K, the nodes, contrary -to what was found in the foregoing case, will proceed forward, -or move the same way with the moon<a name="FNanchor_191_191" id="FNanchor_191_191"></a><a href="#Footnote_191_191" class="fnanchor">[191]</a>; and at the -same time the inclination of the orbit will increase<a name="FNanchor_192_192" id="FNanchor_192_192"></a><a href="#Footnote_192_192" class="fnanchor">[192]</a>.</p> - -<div class="figcenter"> - <img src="images/ill-275.jpg" width="400" height="506" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_213" id="Page_213">[213]</a></span></p> - -<p>34. <span class="smcap gesperrt">When</span> the moon is in the point I, let the plane -M I N pass through the earth T, and touch the path of the -moon in I, cutting the plane of the earth’s motion, in the line -M T N, and the plane B E D in the line T O. Because the line -B I K is convex to the plane B E D, which touches it in B, the -plane N I M must cross the plane D E B, before it meets the -plane C G B; and therefore the point M will fall from B towards -G, and the node of the moon’s orbit being translated -from B to M is moved forward.</p> - -<p>35. <span class="smcap gesperrt">I say</span> farther, the angle under O M G, which the -plane M O N makes with the plane B G C, is greater than the -angle under O B G, which the plane B O D makes with the -same. This appears from what has been already explained; -because the arches B O, O M are each less than the quarter of -a circle, and therefore taken both together are less than a semicircle.</p> - -<p>36. <span class="smcap gesperrt">Again</span>, when the moon is come to the point K in -its quarter, the nodes will be advanced yet farther forward, -and the inclination of the orbit also more augmented. Hitherto -the moon’s motion has been referred to the plane, -which passing through the earth touches the path of the -moon in the point, where the moon is, according to what -was asserted at the beginning of this discourse upon the -nodes, that it is the custom of astronomers so to do. But -here in the point K no such plane can be found; on the contrary, -seeing the line of the moon’s motion on one side the point -K is convex to the plane B E D, and on the other side concave -to the same, no plane can pass through the points T and -K but will cut the line B K L in that point. Therefore instead<span class="pagenum"><a name="Page_214" id="Page_214">[214]</a></span> -of such a touching plane, we must here make use of what is -equivalent, the plane P K Q, with which the line B K L shall -make a less angle than with any other plane; for this plane -does as it were touch the line B K in the point K, since it so -cuts it, that no other plane can be drawn so, as to pass between -the line B K and the plane P K Q. But now it is evident, -that the point P, or the node, is removed from M towards -G, that is, has moved yet farther forward; and it is -likewise as manifest, that the angle under K P G, or the inclination -of the moon’s orbit in the point K, is greater than -the angle under I M G, for the reason so often assigned.</p> - -<p>37. <span class="smcap gesperrt">After</span> the moon has passed the quarter, the path of -the moon being concave to the plane A G C H, the nodes, as -in the preceding case, shall recede, till the moon arrives at -the point L; which shews, that considering the whole time -of the moon’s passing from B to L, at the end of that time the -nodes shall be found to have receded, or to be placed backwarder, -when the moon is in L, than when it was in B. For -the moon takes a longer time in passing from K to L, than -in passing from B to K; and therefore the nodes continue to -recede a longer time, than they moved forwards; so that their -recess must surmount their advance.</p> - -<p>38. <span class="smcap gesperrt">In</span> the same manner, while the moon is in its passage -from K to L, the inclination of the orbit shall diminish, till -the moon comes to the point, in which it is one quarter -part of a circle distant from its node; suppose in the point -R; and from that time the inclination shall again increase.<span class="pagenum"><a name="Page_215" id="Page_215">[215]</a></span> -Since therefore the inclination of the orbit increases, while -the moon is passing from B to K, and diminishes itself again -only, while the moon is passing from K to R, and then -augments again, till the moon arrive in L; while the moon is -passing from B to L, the inclination of the orbit is much more -increased than diminished, and will be distinguishably greater, -when the moon is come to L, than when it set out from B.</p> - -<p>39. <span class="smcap gesperrt">In</span> like manner, while the moon is passing from L on -the other side the plane A G C H, the node shall advance forward, -as long as the moon is between the point L and the next -quarter; but afterwards it shall recede, till the moon come -to pass the plane A G C H again in the point V, between B and -A: and because the time between the moon’s passing from -L to the next quarter is less, than the time between that quarter -and the moon’s coming to the point V, the node shall -have more receded than advanced; so that the point V will -be nearer to A, than L is to C. So also the inclination of the -orbit, when the moon is in V, will be greater, than when the -moon was at L; for this inclination increases all the time the -moon is between L and the next quarter; it decreases only -while the moon is passing from this quarter to the mid way -between the two nodes, and from thence increases again during -the whole passage through the other half of the way to -the next node.</p> - -<p>40. <span class="smcap gesperrt">Thus</span> we have traced the moon from her node in -the quarter, and shewn, that at every period of the moon the -nodes will have receded, and thereby will have approached<span class="pagenum"><a name="Page_216" id="Page_216">[216]</a></span> -toward a conjunction with the sun. But this conjunction will -be much forwarded by the visible motion of the sun itself. -In the last scheme the sun will appear to move from S toward -W. Suppose it appeared to have moved from S to W, -while the moon’s node has receded from B to V, then drawing -the line W T X, the arch V X will represent the distance of the -line drawn between the nodes from the sun, when the moon -is in V; whereas the arch B A represented that distance, when -the moon was in B. This visible motion of the sun is much -greater, than that of the node; for the sun appears to revolve -quite round each year, and the node is near 19 years in making -one revolution. We have also seen, that when the node -was in the quadrature, the inclination of the moon’s orbit decreased, -till the moon came to the conjunction, or opposition, -according to which node it set out from; but that afterwards -it again increased, till it became at the next node rather -greater than at the former. When the node is once removed -from the quarter nearer to a conjunction with the sun, -the inclination of the moon’s orbit, when the moon comes -into the node, is more sensibly greater, than it was in the node -preceding; the inclination of the orbit by this means more -and more increasing till the node comes into conjunction with -the sun; at which time it has been shewn above, that the sun -has no power to change the plane of the moon’s motion; and -consequently has no effect either on the nodes, or on the inclination -of the orbit.</p> - -<p>41. <span class="smcap gesperrt">As</span> soon as the nodes, by the action of the sun, are -got out of conjunction toward the other quarters, they begin<span class="pagenum"><a name="Page_217" id="Page_217">[217]</a></span> -again to recede as before; but the inclination of the orbit in -the appulse of the moon to each succeeding node is less than -at the preceding, till the nodes come again into the quarters. -This will appear as follows. Let A (in fig. 104.) represent -one of the moon’s nodes placed between the point -of opposition B and the quarter C. Let the plane A D E pass -through the earth T, and touch the path of the moon in A. -Let the line A F G H be the path of the moon in her passage -from A to H, where she crosses again the plane of the earth’s -motion. This line will be convex toward the plane A D E, till -the moon comes to G, where she is in the quarter; and after -this, between G and H, the same line will be concave toward -this plane. All the time this line is convex toward the plane -A D E, the nodes will recede; and on the contrary proceed, -while it is concave to that plane. All this will easily be conceived -from what has been before so largely explained. But -the moon is longer in passing from A to G, than from G to H; -therefore the nodes recede a longer time, than they proceed; -consequently upon the whole, when the moon is arrived at -H, the nodes will have receded, that is, the point H will fall -between B and E. The inclination of the orbit will decrease, -till the moon is arrived to the point F, in the middle between -A and H. Through the passage between F and G the inclination -will increase, but decrease again in the remaining part -of the passage from G to H, and consequently at H must be -less than at A. The like effects, both in respect to the nodes -and inclination of the orbit, will take place in the following -passage of the moon on the other side of the plane A B E C, -from H, till it comes over that plane again in I.</p> - -<p><span class="pagenum"><a name="Page_218" id="Page_218">[218]</a></span></p> - -<p>42. <span class="smcap gesperrt">Thus</span> the inclination of the orbit is greatest, when -the line drawn between the moon’s nodes will pass through -the sun; and least, when this line lies in the quarters, especially -if the moon at the same time be in conjunction with the -sun, or in the opposition. In the first of these cases the nodes -have no motion, in all others, the nodes will each month -have receded: and this regressive motion will be greatest, -when the nodes are in the quarters; for in that case the nodes -have no progressive motion during the whole month, but in -all other cases the nodes do at some times proceed forward, -viz. whenever the moon is between either quarter, and the -node which is less distant from that quarter than a fourth -part of a circle.</p> - -<p><a name="c218" id="c218">43.</a> <span class="smcap gesperrt">It</span> now remains only to explain the irregularities in -the moon’s motion, which follow from the elliptical figure -of the orbit. By what has been said at the beginning of this -chapter it appears, that the power of the earth on the moon -acts in the reciprocal duplicate proportion of the distance: -therefore the moon, if undisturbed by the sun, would move -round the earth in a true ellipsis, and the line drawn from -the earth to the moon would pass over equal spaces in equal -portions of time. That this description of the spaces is -altered by the sun, has been already declared. It has also -been shown, that the figure of the orbit is changed each -month; that the moon is nearer the earth at the new and -full, and more remote in the quarters, than it would be without -the sun. Now we must pass by these monthly changes, -and consider the effect, which the sun will have in the different<span class="pagenum"><a name="Page_219" id="Page_219">[219]</a></span> -situations of the axis of the orbit in respect of that luminary.</p> - -<p>44. <span class="smcap gesperrt">The</span> action of the sun varies the force, wherewith -the moon is drawn toward the earth; in the quarters the -force of the earth is directly increased by the sun; at the -new and full the same is diminished; and in the intermediate -places the influence of the earth is sometimes aided, and -sometimes lessened by the sun. In these intermediate places -between the quarters and the conjunction or opposition, -the sun’s action is so oblique to the action of the earth on -the moon, as to produce that alternate acceleration and retardment -of the moon’s motion, which I observed above -to be stiled the variation. But besides this effect, the power, -by which the earth attracts the moon toward itself, will not -be at full liberty to act with the same force, as if the sun -acted not at all on the moon. And this effect of the sun’s -action, whereby it corroborates or weakens the action of the -earth, is here only to be considered. And by this influence -of the sun it comes to pass, that the power, by which the -moon is impelled toward the earth, is not perfectly in the reciprocal -duplicate proportion of the distance. Consequently -the moon will not describe a perfect ellipsis. One particular, -wherein the moon’s orbit will differ from an ellipsis, consists -in the places, where the motion of the moon is perpendicular -to the line drawn from itself to the earth. In an -ellipsis, after the moon should have set out in the direction -perpendicular to this line drawn from itself to the earth, -and at its greatest distance from the earth, its motion would<span class="pagenum"><a name="Page_220" id="Page_220">[220]</a></span> -again become perpendicular to this line drawn between itself -and the earth, and the moon be at its nearest distance -from the earth, when it should have performed half its period; -after performing the other half of its period its motion -would again become perpendicular to the forementioned -line, and the moon return into the place whence it set out, -and have recovered again its greatest distance. But the moon -in its real motion, after setting out as before, sometimes makes -more than half a revolution, before its motion comes again -to be perpendicular to the line drawn from itself to the earth, -and the moon is at its nearest distance; and then performs -more than another half of an intire revolution before its motion -can a second time recover its perpendicular direction to -the line drawn from the moon to the earth, and the moon -arrive again to its greatest distance from the earth. At other -times the moon will descend to its nearest distance, before it -has made half a revolution, and recover again its greatest distance, -before it has made an intire revolution. The place, -where the moon is at its greatest distance from the earth, is called -the moon’s apogeon, and the place of the least distance -the perigeon. This change of the place, where the moon -successively comes to its greatest distance from the earth, is -called the motion of the apogeon. In what manner the sun -causes the apogeon to move, I shall now endeavour to explain.</p> - -<p>45. <span class="smcap gesperrt">Our</span> author shews, that if the moon were attracted -toward the earth by a composition of two powers, one -of which were reciprocally in the duplicate proportion of -the distance from the earth, and the other reciprocally<span class="pagenum"><a name="Page_221" id="Page_221">[221]</a></span> -in the triplicate proportion of the same distance; then, -though the line described by the moon would not be in -reality an ellipsis, yet the moon’s motion might be perfectly -explained by an ellipsis, whose axis should be made to move -round the earth; this motion being in consequence, as astronomers -express themselves, that is, the same way as the moon -itself moves, if the moon be attracted by the sum of the two -powers; but the axis must move in antecedence, or the contrary -way, if the moon be acted on by the difference of these -powers. What is meant by duplicate proportion has been -often explained; namely, that if three magnitudes, as A, B, -and C, are so related, that the second B bears the same proportion -to the third C, as the first A bears to the second -B, then the proportion of the first A to the third C, is the -duplicate of the proportion of the first A to the second B. -Now if a fourth magnitude, as D, be assumed, to which C -shall bear the same proportion as A bears to B, and B to C, -then the proportion of A to D is the triplicate of the proportion -of A to B.</p> - -<p>46. <span class="smcap gesperrt">The</span> way of representing the moon’s motion in -this case is thus. T denoting the earth (in fig. 105, 106.) -suppose the moon in the point A, its apogeon, or greatest -distance from the earth, moving in the direction A F perpendicular -to A B, and acted upon from the earth by two -such forces as have been named. By that power alone, -which is reciprocally in the duplicate proportion of the -distance, if the moon let out from the point A with a -proper degree of velocity, the ellipsis A M B may be described.<span class="pagenum"><a name="Page_222" id="Page_222">[222]</a></span> -But if the moon be acted upon by the sum of the -forementioned powers, and the velocity of the moon in the -point A be augmented in a certain proportion<a name="FNanchor_193_193" id="FNanchor_193_193"></a><a href="#Footnote_193_193" class="fnanchor">[193]</a>; or if that -velocity be diminished in a certain proportion, and the moon -be acted upon by the difference of those powers; in both -these cases the line A E, which shall be described by the -moon, is thus to be determined. Let the point M be that, -into which the moon would have arrived in any given space -of time, had it moved in the ellipsis A M B. Draw M T, -and likewise C T D in such sort, that the angle under A T M -shall bear the same proportion to the angle under A T C, as -the velocity, with which the ellipsis A M B must have been described, -bears to the difference between this velocity, and the -velocity, with which the moon must set out from the point A -in order to describe the path A E. Let the angle A T C be taken -toward the moon (as in fig. 105.) if the moon be attracted -by the sum of the powers; but the contrary way (as in -fig. 106.) if by their difference. Then let the line A B be -moved into the position C D, and the ellipsis A M B into the -situation C N D, so that the point M be translated to L: then -the point L shall fall upon the path of the moon A E.</p> - -<p>47. <span class="smcap gesperrt">The</span> angular motion of the line A T, wereby it is -removed into the situation C T, represents the motion of the -apogeon; by the means of which the motion of the moon -might be fully explicated by the ellipsis A M B, if the action of -the sun upon it was directed to the center of the earth, and<span class="pagenum"><a name="Page_223" id="Page_223">[223]</a></span> -reciprocally in the triplicate proportion of the moon’s distance -from it. But that not being so, the apogeon will not move in -the regular manner now described. However, it is to be observed -here, that in the first of the two preceding cases, where -the apogeon moves forward, the whole centripetal power -increases faster, with the decrease of distance, than if the -intire power were reciprocally in the duplicate proportion of -the distance; because one part only is in that proportion, -and the other part, which is added to this to make up the -whole power, increases faster with the decrease of distance. -On the other hand, when the centripetal power is the difference -between these two, it increases less with the decrease of -the distance, than if it were simply in the reciprocal duplicate -proportion of the distance. Therefore if we chuse to explain -the moon’s motion by an ellipsis (as is most convenient -for astronomical uses to be done, and by reason of the small -effect of the sun’s power, the doing so will not be attended -with any sensible error;) we may collect in general, that -when the power, by which the moon is attracted to the earth, -by varying the distance, increases in a greater than in the duplicate -proportion of the distance diminished, a motion in consequence -must be ascribed to the apogeon; but that when the -attraction increases in a less proportion than that named, the -apogeon must have given to it a motion in antecedence<a name="FNanchor_194_194" id="FNanchor_194_194"></a><a href="#Footnote_194_194" class="fnanchor">[194]</a>. It is -then observed by Sir <span class="smcap">Is. Newton</span>, that the first of these cases -obtains, when the moon is in the conjunction and opposition; -and the latter, when the moon is in the quarters: so that -in the first the apogeon moves according to the order of the<span class="pagenum"><a name="Page_224" id="Page_224">[224]</a></span> -signs; in the other, the contrary way<a name="FNanchor_195_195" id="FNanchor_195_195"></a><a href="#Footnote_195_195" class="fnanchor">[195]</a>. But, as was said before, -the disturbance given to the action of the earth by the sun in -the conjunction and opposition being near twice as great as -in the quarters<a name="FNanchor_196_196" id="FNanchor_196_196"></a><a href="#Footnote_196_196" class="fnanchor">[196]</a>, the apogeon will advance with a greater -velocity than recede, and in the compass of a whole revolution -of the moon will be carried in consequence<a name="FNanchor_197_197" id="FNanchor_197_197"></a><a href="#Footnote_197_197" class="fnanchor">[197]</a>.</p> - -<p>48. <span class="smcap gesperrt">It</span> is shewn in the next place by our author, that -when the line A B coincides with that, which joins the earth -and the sun, the progressive motion of the apogeon, when -the moon is in the conjunction or opposition, exceeds the -regressive in the quadratures more than in any other situation -of the line A B<a name="FNanchor_198_198" id="FNanchor_198_198"></a><a href="#Footnote_198_198" class="fnanchor">[198]</a>. On the contrary, when the line A B -makes right angles with that, which joins the earth and sun, -the retrograde motion will be more considerable<a name="FNanchor_199_199" id="FNanchor_199_199"></a><a href="#Footnote_199_199" class="fnanchor">[199]</a>, nay is -found so great as to exceed the progressive; so that in this -case the apogeon in the compass of an intire revolution of -the moon is carried in antecedence. Yet from the considerations -in the last paragraph the progressive motion exceeds -the other; so that in the whole the mean motion of -the apogeon is in consequence, according as astronomers -find. Moreover, the line A B changes its situation with that, -which joins the earth and sun, by such slow degrees, that the -inequalities in the motion of the apogeon arising from this -last consideration, are much greater than what arises from -the other<a name="FNanchor_200_200" id="FNanchor_200_200"></a><a href="#Footnote_200_200" class="fnanchor">[200]</a>.</p> - -<p><span class="pagenum"><a name="Page_225" id="Page_225">[225]</a></span></p> - -<p>49. <span class="smcap gesperrt">Farther</span>, this unsteady motion in the apogeon is attended -with another inequality in the motion of the moon, that -it cannot be explained at all times by the same ellipsis. The -ellipsis in general is called by astronomers an eccentric orbit. -The point, in which the two axis’s cross, is called the center of -the figure; because all lines drawn through this point within -the ellipsis, from side to side, are divided in the middle by -this point. But the center, about which the heavenly bodies -revolve, lying out of this center of the figure in one focus, -these orbits are said to be eccentric; and where the distance of -the focus from this center bears the greatest proportion to the -whole axis, that orbit is called the most eccentric: and in -such an orbit the distance from the focus to the remoter extremity -of the axis bears the greatest proportion to the distance -of the nearer extremity. Now whenever the apogeon -of the moon moves in consequence, the moon’s motion -must be referred to an orbit more eccentric, than what the -moon would describe, if the whole power, by which the -moon was acted on in its passing from the apogeon, changed -according to the reciprocal duplicate proportion of the distance -from the earth, and by that means the moon did describe -an immoveable ellipsis; and when the apogeon moves -in antecedence, the moon’s motion must be referred to an -orbit less eccentric. In the first of the two figures last referred -to, the true place of the moon L falls without the orbit -A M B, to which its motion is referred: whence the orbit A L E, -truly described by the moon, is less incurvated in the point A, -than is the orbit A M B; therefore the orbit A M B is more oblong, -and differs farther from a circle, than the ellipsis would,<span class="pagenum"><a name="Page_226" id="Page_226">[226]</a></span> -whose curvature in A were equal to that of the line A L B, -that is, the proportion of the distance of the earth T from -the center of the ellipsis to its axis will be greater in the ellipsis -A M B, than in the other; but that other is the ellipsis, -which the moon would describe, if the power acting upon it -in the point A were altered in the reciprocal duplicate proportion -of the distance. In the second figure, when the -apogeon recedes, the place of the moon L falls within the -orbit A M B, and therefore that orbit is less eccentric, than -the immoveable orbit which the moon should describe. The -truth of this is evident; for, when the apogeon moves forward, -the power, by which the moon is influenced in its descent -from the apogeon, increases faster with the decrease of -distance, than in the duplicate proportion of the distance; -and consequently the moon being drawn more forcibly toward -the earth, it will descend nearer to it. On the other -hand, when the apogeon recedes, the power acting on the -moon increases with the decrease of distance in less than the -duplicate proportion of the distance; and therefore the moon -is less impelled toward the earth, and will not descend so low.</p> - -<p>50. <span class="smcap gesperrt">Now</span> suppose in the first of these figures, that the -apogeon A is in the situation, where it is approaching toward -the conjunction or opposition of the sun. In this case the progressive -motion of the apogeon is more and more accelerated. -Here suppose that the moon, after having descended from A -through the orbit A E as far as F, where it is come to its nearest -distance from the earth, ascends again up the line F G. Because -the motion of the apogeon is here continually more and<span class="pagenum"><a name="Page_227" id="Page_227">[227]</a></span> -more accelerating, the cause of its motion is constantly upon -the increase; that is, the power, whereby the moon is -drawn to the earth, will decrease with the increase of distance, -in the moon’s ascent from F, in a greater proportion than that -wherewith it increased with the decrease of distance in the -moon’s descent to F. Consequently the moon will ascend higher -than to the distance A T, from whence it descended; therefore -the proportion of the greatest distance of the moon to -the least is increased. And when the moon descends again, the -power will yet more increase with the decrease of distance, -than in the last ascent it decreased with the augmentation -of distance; the moon therefore must descend nearer to the -earth than it did before, and the proportion of the greatest -distance to the least yet be more increased. Thus as long -as the apogeon is advancing toward the conjunction or opposition, -the proportion of the greatest distance of the moon -from the earth to the least will continually increase; and -the elliptical orbit, to which the moon’s motion is referred, -will be rendered more and more eccentric.</p> - -<p>51. <span class="smcap gesperrt">As</span> soon as the apogeon is passed the conjunction -with the sun or the opposition, the progressive motion thereof -abates, and with it the proportion of the greatest distance of -the moon from the earth to the least distance will also diminish; -and when the apogeon becomes regressive, the diminution -of this proportion will be still farther continued on, till -the apogeon comes into the quarter; from thence this proportion, -and the eccentricity of the orbit will increase again. -Thus the orbit of the moon is most eccentric, when the apogeon<span class="pagenum"><a name="Page_228" id="Page_228">[228]</a></span> -is in conjunction with the sun, or in opposition to it, -and least of all when the apogeon is in the quarters.</p> - -<p>52. <span class="smcap gesperrt">These</span> changes in the nodes, in the inclination of -the orbit to the plane of the earth’s motion, in the apogeon, -and in the eccentricity, are varied like the other inequalities -in the motion of the moon, by the different distance of the -earth from the sun; being greatest, when their cause is greatest, -that is, when the earth is nearest to the sun.</p> - -<p>53. <span class="smcap gesperrt">I said</span> at the beginning of this chapter, that Sir <span class="smcap">Isaac -Newton</span> has computed the very quantity of many of the -moon’s inequalities. That acceleration of the moon’s motion, -which is called the variation, when greatest, removes -the moon out of the place, in which it would otherwise be -found, something more than half a degree<a name="FNanchor_201_201" id="FNanchor_201_201"></a><a href="#Footnote_201_201" class="fnanchor">[201]</a>. In the phrase -of astronomers, a degree is 1/360 part of the whole circuit of -the moon or any planet. If the moon, without disturbance -from the sun, would have described a circle concentrical to -the earth, the sun will cause the moon to approach nearer -to the earth in the conjunction and opposition, than in the -quarters, nearly in the proportion of 69 to 70<a name="FNanchor_202_202" id="FNanchor_202_202"></a><a href="#Footnote_202_202" class="fnanchor">[202]</a>. We had -occasion to mention above, that the nodes perform their period -in almost 19 years. This the astronomers found by -observation; and our author’s computations assign to them -the same period<a name="FNanchor_203_203" id="FNanchor_203_203"></a><a href="#Footnote_203_203" class="fnanchor">[203]</a>. The inclination of the moon’s orbit when -least, is an angle about 1/18 part of that angle, which constitutes<span class="pagenum"><a name="Page_229" id="Page_229">[229]</a></span> -a perpendicular; and the difference between the greatest and -least inclination of the orbit is determined by our author’s -computation to be about 1/18 of the least inclination<a name="FNanchor_204_204" id="FNanchor_204_204"></a><a href="#Footnote_204_204" class="fnanchor">[204]</a>. And -this also is agreeable to the observations of astronomers. The -motion of the apogeon, and the changes in the eccentricity, -Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> has not computed. The apogeon -performs its revolution in about eight years and ten months. -When the moon’s orbit is most eccentric, the greatest distance -of the moon from the earth bears to the least distance -nearly the proportion of 8 to 7; when the orbit is -least eccentric, this proportion is hardly so great as that of -12 to 11.</p> - -<p><a name="c229" id="c229">54.</a> <span class="smcap gesperrt">Sir</span> <span class="smcap"><em class="gesperrt">Isaac Newton</em></span> shews farther, how, by comparing -the periods of the motion of the satellites, which revolve -round Jupiter and Saturn, with the period of our -moon round the earth, and the periods of those planets -round the sun with the period of our earth’s motion, the -inequalities in the motion of those satellites may be derived -from the inequalities in the moon’s motion; excepting only -in regard to that motion of the axis of the orbit, which -in the moon makes the motion of the apogeon; for the -orbits of those satellites, as far as can be discerned by us at -this distance, appearing little or nothing eccentric, this -motion, as deduced from the moon, must be diminished.</p> - -</div> - -<p><span class="pagenum"><a name="Page_230" id="Page_230">[230]</a></span></p> - -<div class="chapter"> - -<h2 class="p4"><a name="c230a" id="c230a"><span class="smcap"><em class="gesperrt">Chap. IV</em>.</span></a><br /> -Of <em class="gesperrt">Comets</em>.</h2> - -<p class="drop-cap04">IN the former of the two preceding chapters the powers -have been explained, which keep in motion those celestial -bodies, whose courses had been well determined by the -astronomers. In the last chapter we have shewn, how those -powers have been applied by our author to the making a -more perfect discovery of the motion of those bodies, the -courses of which were but imperfectly understood; for -some of the inequalities, which we have been describing -in the moon’s motion, were unknown to the astronomers. -In this chapter we are to treat of a third species of the heavenly -bodies, the true motion of which was not at all apprehended -before our author writ; in so much, that here -Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> has not only explained the causes of -the motion of these bodies, but has performed also the part -of an astronomer, by discovering what their motions are.</p> - -<p><a name="c230b" id="c230b">2.</a> <span class="smcap gesperrt">That</span> these bodies are not meteors in our air, is -manifest; because they rise and set in the same manner, -as the sun and stars. The astronomers had gone so far in -their inquiries concerning them, as to prove by their observations, -that they moved in the etherial spaces far beyond -the moon; but they had no true notion at all of the path, -which they described. The most prevailing opinion before<span class="pagenum"><a name="Page_231" id="Page_231">[231]</a></span> -our author was, that they moved in straight lines; but in -what part of the heavens was not determined. <span class="smcap">DesCartes</span><a name="FNanchor_205_205" id="FNanchor_205_205"></a><a href="#Footnote_205_205" class="fnanchor">[205]</a> -removed them far beyond the sphere of Saturn, as -finding the straight motion attributed to them, inconsistent -with the vortical fluid, by which he explains the motions -of the planets, as we have above related<a name="FNanchor_206_206" id="FNanchor_206_206"></a><a href="#Footnote_206_206" class="fnanchor">[206]</a>. But Sir <span class="smcap">Isaac -Newton</span> distinctly proves from astronomical observation, -that the comets pass through the region of the planets, and -are mostly invisible at a less distance, than that of Jupiter<a name="FNanchor_207_207" id="FNanchor_207_207"></a><a href="#Footnote_207_207" class="fnanchor">[207]</a>.</p> - -<p><a name="c231" id="c231">3.</a> <span class="smcap gesperrt">And</span> from hence finding the comets to be evidently -within the sphere of the sun’s action, he concludes they -must, necessarily move about the sun, as the planets do<a name="FNanchor_208_208" id="FNanchor_208_208"></a><a href="#Footnote_208_208" class="fnanchor">[208]</a>. -The planets move in ellipsis’s; but it is not necessary that -every body, which is influenced by the sun, should move -in that particular kind of line. However our author proves, -that the power of the sun being reciprocally in the duplicate -proportion of the distance, every body acted on by the sun -must either fall directly down, or move in some conic section; -of which lines I have above observed, that there are -three species, the ellipsis, parabola, and hyperbola<a name="FNanchor_209_209" id="FNanchor_209_209"></a><a href="#Footnote_209_209" class="fnanchor">[209]</a>. If a -body, which descends toward the sun as low as the orbit -of any planet, move with a swifter motion than the planet -does, that body will describe an orbit of a more oblong -figure, than that of the planet, and have a longer axis at -least. The velocity of the body may be so great, that it<span class="pagenum"><a name="Page_232" id="Page_232">[232]</a></span> -shall move in a parabola, and having once passed about -the sun, shall ascend for ever without returning any more: -but the sun will be placed in the focus of this parabola. -With a velocity still greater the body will move in an -hyperbola. But it is most probable, that the comets move -in elliptical orbits, though of a very oblong, or in the -phrase of astronomers, of a very eccentric form, such as -is represented in fig. 107, where S is the sun, C the comet, -and A B D E its orbit, wherein the distance of S -and D far exceeds that of S and A. Whence it is, that -they sometimes are found at a moderate distance from the -sun, and appear within the planetary regions; at other -times they ascend to vast distances, far beyond the very orbit -of Saturn, and so become invisible. That the comets -do move in this manner is proved by our author, from computations -built upon the observations, which astronomers had -made on many comets. These computations were performed -by Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> himself upon the comet, which -appeared toward the latter end of the year 1680, and at -the beginning of the year following<a name="FNanchor_210_210" id="FNanchor_210_210"></a><a href="#Footnote_210_210" class="fnanchor">[210]</a>; but the learned -Dr. <span class="smcap">Halley</span> prosecuted the like computations more at large -in this, and also in many other comets<a name="FNanchor_211_211" id="FNanchor_211_211"></a><a href="#Footnote_211_211" class="fnanchor">[211]</a>. Which computations -are made upon propositions highly worthy of our author’s unparallel’d -genius, such as could scarce have been discovered -by any one not possessed of the utmost force of invention;</p> - -<p><span class="pagenum"><a name="Page_233" id="Page_233">[233]</a></span></p> - -<p><a name="c233" id="c233">4.</a> <span class="smcap gesperrt">Those</span> computations depend upon this principle, -that the eccentricity of the orbits of the comets is so -great, that if they are really elliptical, yet they approach -so near to parabolas in that part of them, where they -come under our view, that they may be taken for such -without sensible error<a name="FNanchor_212_212" id="FNanchor_212_212"></a><a href="#Footnote_212_212" class="fnanchor">[212]</a>: as in the preceding figure the -parabola F A G differs in the lower part of it about A very -little from the ellipsis D E A B. Upon which ground -our great author teaches a method of finding by three observations -made upon any comet the parabola, which -nearest agrees with its orbit<a name="FNanchor_213_213" id="FNanchor_213_213"></a><a href="#Footnote_213_213" class="fnanchor">[213]</a>.</p> - -<p>5. <span class="smcap gesperrt">Now</span> what confirms this whole theory beyond the -least room for doubt is, that the places of the comets computed -in the orbits, which the method here mentioned -assigns them, agree to the observations of astronomers with -the same degree of exactness, as the computations of the -primary planets places usually do; and this in comets, -whose motions are very extraordinary<a name="FNanchor_214_214" id="FNanchor_214_214"></a><a href="#Footnote_214_214" class="fnanchor">[214]</a>.</p> - -<p>6. <span class="smcap gesperrt">Our</span> author afterwards shews how to make use of -any small deviation from the parabola, that shall be observed, -to determine whether the orbits of the comets are -elliptical or not, and so to discover if the same comet returns -at certain periods<a name="FNanchor_215_215" id="FNanchor_215_215"></a><a href="#Footnote_215_215" class="fnanchor">[215]</a>. And upon examining the comet -in 1680, by the rule laid down for this purpose, he -finds its orbit to agree more exactly to an ellipsis than<span class="pagenum"><a name="Page_234" id="Page_234">[234]</a></span> -to a parabola, though the ellipsis be so very eccentric, -that the comet cannot perform its period through it in the -space of 500 years<a name="FNanchor_216_216" id="FNanchor_216_216"></a><a href="#Footnote_216_216" class="fnanchor">[216]</a>. Upon this Dr. <span class="smcap">Halley</span> observed, -that mention is made in history of a comet, with the -like eminent tail as this, having appeared three several -times before; the first of which appearances was at the -death of <span class="smcap">Julius Cesar</span>, and each appearance was at the -distance of 575 years from the next preceding. He therefore -computed the motion of this comet in such an elliptic -orbit, as would require this number of years for the -body to revolve through it; and these computations agree -yet more perfectly with the observations made on this comet, -than any parabolical orbit will do<a name="FNanchor_217_217" id="FNanchor_217_217"></a><a href="#Footnote_217_217" class="fnanchor">[217]</a>.</p> - -<p><a name="c234" id="c234">7.</a> <span class="smcap gesperrt">The</span> comparing together different appearances of the -same comet, is the only way to discover certainly the true -form of the orbit: for it is impossible to determine with exactness -the figure of an orbit so exceedingly eccentric, from -single observations taken in one part of it; and therefore -Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em><a name="FNanchor_218_218" id="FNanchor_218_218"></a><a href="#Footnote_218_218" class="fnanchor">[218]</a> proposes to compare the orbits, -upon the supposition that they are parabolical, of such -comets as appear at different times; for if the same orbit -be found to be described by a comet at different times, -in all probability it will be the same comet which describes -it. And here he remarks from Dr. <span class="smcap">Halley</span>, that -the same orbit very nearly agrees to two appearances of -a comet about the space of 75 years distance<a name="FNanchor_219_219" id="FNanchor_219_219"></a><a href="#Footnote_219_219" class="fnanchor">[219]</a>; so that<span class="pagenum"><a name="Page_235" id="Page_235">[235]</a></span> -if those two appearances were really of the same comet, -the transverse axis of the orbit of the comet would be near -18 times the axis of the earth’s orbit; and the comet, -when at its greatest distance from the sun, will be removed -not less than 35 times as far as the middle distance -of the earth.</p> - -<p><a name="c235" id="c235">8.</a> <span class="smcap gesperrt">And</span> this seems to be the shortest period of any of -the comets. But it will be farther confirmed, if the same -comet should return a third time after another period of -75 years. However it is not to be expected, that comets -should preserve the same regularity in their periods, as -the planets; because the great eccentricity of their orbits -makes them liable to suffer very considerable alterations -from the action of the planets, and other comets, upon them.</p> - -<p>9. <span class="smcap gesperrt">It</span> is therefore to prevent too great disturbances -in their motions from these causes, as our author observes, -that while the planets revolve all of them nearly in the -same plane, the comets are disposed in very different ones; -and distributed over all parts of the heavens; that, -when in their greatest distance from the sun, and moving -slowest, they might be removed as far as possible out of the -reach of each other’s action<a name="FNanchor_220_220" id="FNanchor_220_220"></a><a href="#Footnote_220_220" class="fnanchor">[220]</a>. The same end is likewise -farther answered in those comets, which by moving slowest -in the aphelion, or remotest distance from the sun, descend -nearest to it, by placing the aphelion of these at the -greatest height from the sun<a name="FNanchor_221_221" id="FNanchor_221_221"></a><a href="#Footnote_221_221" class="fnanchor">[221]</a>.</p> - -<p><span class="pagenum"><a name="Page_236" id="Page_236">[236]</a></span></p> - -<p>10. <span class="smcap gesperrt">Our</span> philosopher being led by his principles to explain -the motions of the comets, in the manner now related, -takes occasion from thence to give us his thoughts -upon their nature and use. For which end he proves in -the first place, that they must necessarily be solid and compact -bodies, and by no means any sort of vapour or light -substance exhaled from the planets or stars: because at -the near distance, to which some comets approach the sun, -it could not be, but the immense heat, to which they are -exposed, should instantaneously disperse and scatter any -such light volatile substance<a name="FNanchor_222_222" id="FNanchor_222_222"></a><a href="#Footnote_222_222" class="fnanchor">[222]</a>. In particular the forementioned -comet of 1680 descended so near the sun, as to -come within a sixth part of the sun’s diameter from the -surface of it. In which situation it must have been exposed, -as appears by computation, to a degree of heat -exceeding the heat of the sun upon our earth no less than -28000 times; and therefore might have contracted a degree -of heat 2000 times greater, than that of red hot -iron<a name="FNanchor_223_223" id="FNanchor_223_223"></a><a href="#Footnote_223_223" class="fnanchor">[223]</a>. Now a substance, which could endure so intense -a heat, without being dispersed in vapor, must needs be -firm and solid.</p> - -<p>11. <span class="smcap gesperrt">It</span> is shewn likewise, that the comets are opake -substances, shining by a reflected light, borrowed from -the sun<a name="FNanchor_224_224" id="FNanchor_224_224"></a><a href="#Footnote_224_224" class="fnanchor">[224]</a>. This is proved from the observation, that comets, -though they are approaching the earth, yet diminish -in lustre, if at the same time they recede from<span class="pagenum"><a name="Page_237" id="Page_237">[237]</a></span> -the sun; and on the contrary, are found to encrease -daily in brightness, when they advance towards the sun, -though at the same time they move from the earth<a name="FNanchor_225_225" id="FNanchor_225_225"></a><a href="#Footnote_225_225" class="fnanchor">[225]</a>.</p> - -<p>12. <span class="smcap gesperrt">The</span> comets therefore in these respects resemble the -planets; that both are durable opake bodies, and both revolve -about the sun in conic sections. But farther the -comets, like our earth, are surrounded by an atmosphere. -The air we breath is called the earth’s atmosphere; -and it is most probable, that all the other planets -are invested with the like fluid. Indeed here a difference -is found between the planets and comets. The atmospheres -of the planets are of so fine and subtile a substance, as -hardly to be discerned at any distance, by reason of the -small quantity of light which they reflect, except only in -the planet Mars. In him there is some little appearance -of such a substance surrounding him, as stars which have -been covered by him are said to look somewhat dim a -small space before his body comes under them, as if their -light, when he is near, were obstructed by his atmosphere. -But the atmospheres which surround the comets are so -gross and thick, as to reflect light very copiously. They -are also much greater in proportion to the body they surround, -than those of the planets, if we may judge of -the rest from our air; for it has been observed of comets, -that the bright light appearing in the middle of them, which<span class="pagenum"><a name="Page_238" id="Page_238">[238]</a></span> -is reflected from the solid body, is scarce a ninth or tenth -part of the whole comet,</p> - -<p><a name="c238" id="c238">13.</a> <span class="smcap gesperrt">I speak</span> only of the heads of the comets, the most -lucid part of which is surrounded by a fainter light, the -most lucid part being usually not above a ninth or tenth -part of the whole in breadth<a name="FNanchor_226_226" id="FNanchor_226_226"></a><a href="#Footnote_226_226" class="fnanchor">[226]</a>. Their tails are an appearance -very peculiar, nothing of the same nature appertaining -in the least degree to any other of the celestial bodies. -Of that appearance there are several opinions; our -author reduces them to three<a name="FNanchor_227_227" id="FNanchor_227_227"></a><a href="#Footnote_227_227" class="fnanchor">[227]</a>. The two first, which he -proposes, are rejected by him; but the third he approves. -The first is, that they arise from a beam of light transmitted -through the head of the comet, in like manner as -a stream of light is discerned, when the sun shines into a -darkened room through a small hole. This opinion, as -Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> observes, implies the authors of it -wholly unskilled in the principles of optics; for that stream -of light, seen in a darkened room, arises from the reflection -of the sun beams by the dust and motes floating in -the air: for the rays of light themselves are not seen, but -by their being reflected to the eye from some substance, -upon which they fall<a name="FNanchor_228_228" id="FNanchor_228_228"></a><a href="#Footnote_228_228" class="fnanchor">[228]</a>. The next opinion examined by -our author is that of the celebrated <span class="smcap">DesCartes</span>, who -imagins these tails to be the light of the comet refracted -in its passage to us, and thence affording an oblong representation; -as the light of the sun does, when refracted<span class="pagenum"><a name="Page_239" id="Page_239">[239]</a></span> -by the prism in that noted experiment, which will have a -great share in the third book of this discourse<a name="FNanchor_229_229" id="FNanchor_229_229"></a><a href="#Footnote_229_229" class="fnanchor">[229]</a>. But this -opinion is at once overturned from this consideration only, -that the planets could be no more free from this refraction -than the comets; nay ought to have larger or -brighter tails, than they, because the light of the planets is -strongest. However our author has thought proper to add -some farther objections against this opinion: for instance, -that these tails are not variegated with colours, as is the -image produced by the prism, and which is inseparable -from that unequal refraction, which produces that disproportioned -length of the image. And besides, when the -light in its passage from different comets to the earth describes -the same path through the heavens, the refraction -of it should of necessity be in all respects the same. But -this is contrary to observation; for the comet in 1680, -the 28th day of December, and a former comet in the -year 1577, the 29th day of December, appear’d in the -same place of the heavens, that is, were seen adjacent to -the same fixed stars, the earth likewise being in the same -place at both times; yet the tail of the latter comet deviated -from the opposition to the sun a little to the northward, -and the tail of the former comet declined from the -opposition of the sun five times as much southward<a name="FNanchor_230_230" id="FNanchor_230_230"></a><a href="#Footnote_230_230" class="fnanchor">[230]</a>.</p> - -<p>14. <span class="smcap gesperrt">There</span> are some other false opinions, though less -regarded than these, which have been advanced upon this<span class="pagenum"><a name="Page_240" id="Page_240">[240]</a></span> -argument. These our excellent author passes over, hastening -to explain, what he takes to be the true cause of this -appearance. He thinks it is certainly owing to steams and -vapours exhaled from the body, and gross atmosphere of -the comets, by the heat of the sun; because all the appearances -agree perfectly to this sentiment. The tails are -but small, while the comet is descending to the sun, but -enlarge themselves to an immense degree, as soon as ever -the comet has passed its perihelion; which shews the tail -to depend upon the degree of heat, which the comet receives -from the sun. And that the intense heat to which -comets, when nearest the sun, are exposed, should exhale -from them a very copious vapour, is a most reasonable supposition; -especially if we consider, that in those free and -empty regions steams will more easily ascend, than here -upon the surface of the earth, where they are suppressed -and hindered from rising by the weight of the incumbent -air: as we find by experiments made in vessels exhausted -of the air, where upon removal of the air several substances -will fume and discharge steams plentifully, which -emit none in the open air. The tails of comets, like such -a vapour, are always in the plane of the comet’s orbit, and -opposite to the sun, except that the upper part thereof -inclines towards the parts, which the comet has left by its -motion; resembling perfectly the smoak of a burning coal, -which, if the coal remain fixed, ascends from it perpendicularly; -but, if the coal be in motion, ascends obliquely, -inclining from the motion of the coal. And besides, the -tails of comets may be compared to this smoak in another<span class="pagenum"><a name="Page_241" id="Page_241">[241]</a></span> -respect, that both of them are denser and more compact -on the convex side, than on the concave. The different -appearance of the head of the comet, after it has past its -perihelion, from what it had before, confirms greatly this -opinion of their tails: for smoke raised by a strong heat is -blacker and grosser, than when raised by a less; and accordingly -the heads of comets, at the same distance from -the sun, are observed less bright and shining after the perihelion, -than before, as if obscured by such a gross smoke.</p> - -<p>15. <span class="smcap gesperrt">The</span> observations of <span class="smcap">Hevelius</span> upon the atmospheres -of comets still farther illustrate the same; who relates, -that the atmospheres, especially that part of them next -the sun, are remarkably contracted when near the sun, and -dilated again afterwards.</p> - -<p>16. <span class="smcap gesperrt">To</span> give a more full idea of these tails, a rule is -laid down by our author, whereby to determine at any -time, when the vapour in the extremity of the tail first -rose from the head of the comet. By this rule it is found, -that the tail does not consist of a fleeting vapour, dissipated -soon after it is raised, but is of long continuance; -that almost all the vapour, which rose about the time of -the perihelion from the comet of 1680, continued to accompany -it, ascending by degrees, being succeeded constantly -by fresh matter, which rendered the tail contiguous -to the comet. From this computation the tails are -found to participate of another property of ascending vapours, -that, when they ascend with the greatest velocity, -they are least incurvated.</p> - -<p><span class="pagenum"><a name="Page_242" id="Page_242">[242]</a></span></p> - -<p>17. <span class="smcap gesperrt">The</span> only objection that can be made against this -opinion is the difficulty of explaining, how a sufficient -quantity of vapour can be raised from the atmosphere of a -comet to fill those vast spaces, through which their tails -are sometimes extended. This our author removes by the -following computation: our air being an elastic fluid, as -has been said before<a name="FNanchor_231_231" id="FNanchor_231_231"></a><a href="#Footnote_231_231" class="fnanchor">[231]</a>, is more dense here near the surface -of the earth, where it is pressed upon by the whole air -above; than it is at a distance from the earth, where it has -a less weight incumbent. I have observed, that the density -of the air is reciprocally proportional to the compressing -weight. From hence our author computes to what degree -of rarity the air must be expanded, according to this rule, at -an height equal to a semidiameter of the earth: and he finds, -that a globe of such air, as we breath here on the surface of -the earth, which shall be one inch only in diameter, if it were -expanded to the degree of rarity, which the air must have -at the height now mentioned, would fill all the planetary -regions even to the very sphere of Saturn, and far beyond. -Now since the air at a greater height will be still immensly -more rarified, and the surface of the atmospheres -of comets is usually about ten times the distance from the -center of the comet, as the surface of the comet it self, and -the tails are yet vastly farther removed from the center of -the comet; the vapour, which composes those tails, may very -well be allowed to be so expanded, as that a moderate -quantity of matter may fill all that space, they are seen to -take up. Though indeed the atmospheres of comets being<span class="pagenum"><a name="Page_243" id="Page_243">[243]</a></span> -very gross, they will hardly be rarified in their tails to so great -a degree, as our air under the same circumstances; especially -since they may be something condensed, as well by their gravitation -to the sun, as that the parts will gravitate to one another; -which will hereafter be shewn to be the universal property -of all matter<a name="FNanchor_232_232" id="FNanchor_232_232"></a><a href="#Footnote_232_232" class="fnanchor">[232]</a>. The only scruple left is, how so much -light can be reflected from a vapour so rare, as this computation -implies. For the removal of which our author observes, -that the most refulgent of these tails hardly appear brighter, -than a beam of the sun’s light transmitted into a darkened -room through a hole of a single inch diameter; and that -the smallest fixed stars are visible through them without any -sensible diminution of their lustre.</p> - -<p><a name="c243" id="c243">18.</a> <span class="smcap gesperrt">All</span> these considerations put it beyond doubt, what -is the true nature of the tails of comets. There has indeed -nothing been said, which will account for the irregular -figures, in which those tails are sometimes reported to have -appeared; but since none of those appearances have ever been -recorded by astronomers, who on the contrary ascribe the -same likeness to the tails of all comets, our author with great -judgment refers all those to accidental refractions by intervening -clouds, or to parts of the milky way contiguous to the -comets<a name="FNanchor_233_233" id="FNanchor_233_233"></a><a href="#Footnote_233_233" class="fnanchor">[233]</a>.</p> - -<p>19. <span class="smcap gesperrt">The</span> discussion of this appearance in comets has -led Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> into some speculations relating -to their use, which I cannot but extreamly admire, as<span class="pagenum"><a name="Page_244" id="Page_244">[244]</a></span> -representing in the strongest light imaginable the extensive -providence of the great author of nature, who, -besides the furnishing this globe of earth, and without -doubt the rest of the planets, so abundantly with every -thing necessary for the support and continuance of the -numerous races of plants and animals, they are stocked -with, has over and above provided a numerous train of -comets, far exceeding the number of the planets, to rectify -continually, and restore their gradual decay, which -is our author’s opinion concerning them<a name="FNanchor_234_234" id="FNanchor_234_234"></a><a href="#Footnote_234_234" class="fnanchor">[234]</a>. For since the -comets are subject to such unequal degrees of heat, being -sometimes burnt with the most intense degree of it, at -other times scarce receiving any sensible influence from the -sun; it can hardly be supposed, they are designed for any -such constant use, as the planets. Now the tails, which they -emit, like all other kinds of vapour, dilate themselves as -they ascend, and by consequence are gradually dispersed and -scattered through all the planetary regions, and thence cannot -but be gathered up by the planets, as they pass through -their orbs: for the planets having a power to cause all bodies -to gravitate towards them, as will in the sequel of this -discourse be shewn<a name="FNanchor_235_235" id="FNanchor_235_235"></a><a href="#Footnote_235_235" class="fnanchor">[235]</a>; these vapours will be drawn in process -of time into this or the other planet, which happens to -act strongest upon them. And by entering the atmospheres -of the earth and other planets, they may well be supposed to -contribute to the renovation of the face of things, in particular -to supply the diminution caused in the humid parts<span class="pagenum"><a name="Page_245" id="Page_245">[245]</a></span> -by vegetation and putrefaction. For vegetables are nourished -by moisture, and by putrefaction are turned in great -part into dry earth; and an earthy substance always subsides -in fermenting liquors; by which means the dry parts -of the planets must continually increase, and the fluids diminish, -nay in a sufficient length of time be exhausted, -if not supplied by some such means. It is farther our great -author’s opinion, that the most subtile and active parts of -our air, upon which the life of things chiefly depends, is -derived to us, and supplied by the comets. So far are -they from portending any hurt or mischief to us, which -the natural fears of men are so apt to suggest from the appearance -of any thing uncommon and astonishing.</p> - -<p><a name="c245" id="c245">20.</a> <span class="smcap gesperrt">That</span> the tails of comets have some such important -use seems reasonable, if we consider, that those bodies -do not send out those fumes merely by their near approach -to the sun; but are framed of a texture, which disposes -them in a particular manner to fume in that sort: for the -earth, without emitting any such steam, is more than half -the year at a less distance from the sun, than the comet -of 1664 and 1665 approached it, when nearest; likewise -the comets of 1682 and 1683 never approached the sun -much above a seventh part nearer than Venus, and were -more than half as far again from the sun as Mercury; yet -all these emitted tails.</p> - -<p>21. <span class="smcap gesperrt">From</span> the very near approach of the comet of -1680 our author draws another speculation; for if the<span class="pagenum"><a name="Page_246" id="Page_246">[246]</a></span> -sun have an atmosphere about it, the comet mentioned -seems to have descended near enough to the sun to enter -within it. If so, it must have been something retarded by -the resistance it would meet with, and consequently in its -next descent to the sun will fall nearer than now; by -which means it will meet with a greater resistance, and -be again more retarded. The event of which must be, that -at length it will impinge upon the sun’s surface, and thereby -supply any decrease, which may have happened by so long -an emission of light, or otherwise. And something like this -our author conjectures may be the case of those fixed stars -which by an additional increase of their lustre have for a -certain time become visible to us, though usually they are -out of sight. There is indeed a kind of fixed stars, which -appear and disappear at regular and equal intervals: here -some more steady cause must be sought for; perhaps these -stars turn round their own axis’s, as our sun does<a name="FNanchor_236_236" id="FNanchor_236_236"></a><a href="#Footnote_236_236" class="fnanchor">[236]</a>, and have -some part of their body more luminous than the other, -whereby they are seen, when the most lucid part is next to -us, and when the darker part is turned toward us, they -vanish out of sight.</p> - - -<p>22. <span class="smcap gesperrt">Whether</span> the sun does really diminish, as has been -here suggested, is difficult to prove; yet that it either does -so, or that the earth increases, if not both, is rendered probable -from Dr. <span class="smcap">Halley</span>’s observation<a name="FNanchor_237_237" id="FNanchor_237_237"></a><a href="#Footnote_237_237" class="fnanchor">[237]</a>, that by comparing<span class="pagenum"><a name="Page_247" id="Page_247">[247]</a></span> -the proportion, which the periodical time of the moon bore -to that of the sun in former times, with the proportion between -them at present, the moon is found to be something -accelerated in respect of the sun. But if the sun diminish, -the periods of the primary planets will be lengthened; and -if the earth be encreased, the period of the moon will be -shortened: as will appear by the next chapter, wherein -it shall be shewn, that the power of the sun and earth is -the result of the same power being lodg’d in all their parts, -and that this principle of producing gravitation in other bodies -is proportional to the solid matter in each body.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c247" id="c247"><span class="smcap"><em class="gesperrt">Chap.</em> V.</span></a><br /> -Of the BODIES of the SUN and PLANETS.</h2> - -<p class="drop-cap08">OUR author, after having discovered that the celestial -motions are performed by a force extended from the -sun and primary planets, follows this power into the deepest -recesses of those bodies themselves, and proves the same -to accompany the smallest particle, of which they are composed.</p> - -<p>2. <span class="smcap gesperrt">Preparative</span> hereto he shews first, that each of the -heavenly bodies attracts the rest, and all bodies, with such -different degrees of force, as that the force of the same attracting<span class="pagenum"><a name="Page_248" id="Page_248">[248]</a></span> -body is exerted on others exactly in proportion to -the quantity of matter in the body attracted<a name="FNanchor_238_238" id="FNanchor_238_238"></a><a href="#Footnote_238_238" class="fnanchor">[238]</a>.</p> - -<p><a name="c248" id="c248">3.</a> <span class="smcap gesperrt">Of</span> this the first proof he brings is from experiments -made here upon the earth. The power by which the moon -is influenced was above shewn to be the same, with that -power here on the surface of the earth, which we call gravity<a name="FNanchor_239_239" id="FNanchor_239_239"></a><a href="#Footnote_239_239" class="fnanchor">[239]</a>. -Now one of the effects of the principle of gravity -is, that all bodies descend by this force from the same height -in equal times. Which has been long taken notice of; -particular methods having been invented to shew that the -only cause, why some bodies were observed to fall from the -same height sooner than others, was the resistance of the -air. This we have above related<a name="FNanchor_240_240" id="FNanchor_240_240"></a><a href="#Footnote_240_240" class="fnanchor">[240]</a>; and proved from hence, -that since bodies resist to any change of their state from rest -to motion, or from motion to rest, in proportion to the -quantity of matter contained in them; the power that can -move different quantities of matter equally, must be proportional -to the quantity. The only objection here is, that -it can hardly be made certain, whether this proportion in -the effect of gravity on different bodies holds perfectly exact -or not from these experiments; by reason that the -great swiftness, with which bodies fall, prevents our being -able to determine the times of their descent with all the -exactness requisite. Therefore to remedy this inconvenience, -our author substitutes another more certain experiment -in the room of these made upon falling bodies. Pendulums<span class="pagenum"><a name="Page_249" id="Page_249">[249]</a></span> -are caused to vibrate by the same principle, as makes -bodies descend; the power of gravity putting them in motion, -as well as the other. But if the ball of any pendulum, -of the same length with another, were more or less -attracted in proportion to the quantity of solid matter in -the ball, that pendulum must accordingly move faster or -slower than the other. Now the vibrations of pendulums -continue for a great length of time, and the number of -vibrations they make may easily be determined without -suspicion of error; so that this experiment may be -extended to what exactness one pleases: and our author -assures us, that he examined in this way several -substances, as gold, silver, lead, glass, sand, common salt, -wood, water, and wheat; in all which he found not the -least deviation from the proportion mentioned, though he -made the experiment in such a manner, that in bodies of -the same weight a difference in the quantity of their matter -less than a thousandth part of the whole would have -discovered it self<a name="FNanchor_241_241" id="FNanchor_241_241"></a><a href="#Footnote_241_241" class="fnanchor">[241]</a>. It appears therefore, that all bodies are -made to descend by the power of gravity here, near the surface -of the earth, with the same degree of swiftness. We -have above observed this descent to be after the rate of 16⅛ -feet in the first second of time from the beginning of their -fall. Moreover it was also observed, that if any body, which -fell here at the surface of the earth after this rate, were -to be conveyed up to the height of the moon, it would<span class="pagenum"><a name="Page_250" id="Page_250">[250]</a></span> -descend from thence just with the same degree of velocity, -as that with which the moon is attracted toward the -earth; and therefore the power of the earth upon the moon -bears the same proportion to the power it would have upon -those bodies at the same distance, as the quantity of matter -in the moon bears to the quantity in those bodies.</p> - -<p><a name="c250" id="c250">4.</a> <span class="smcap gesperrt">Thus</span> the assertion laid down is proved in the earth, -that the power of the earth on every body it attracts is, at -the same distance from the earth, proportional to the quantity -of solid matter in the body acted on. As to the sun, it -has been shewn, that the power of the sun’s action upon -the same primary planet is reciprocally in the duplicate proportion -of the distance; and that the power of the sun -decreases throughout in the same proportion, the motion of -comets traversing the whole planetary region testifies. This -proves, that if any planet were removed from the sun to -any other distance whatever, the degree of its acceleration -toward the sun would yet remain reciprocally in the duplicate -proportion of its distance. But it has likewise been -shewn, that the degree of acceleration, which the sun gives -to every one of the planets, is reciprocally in the duplicate -proportion of their respective distances. All which compared -together puts it out of doubt, that the power of -the sun upon any planet, removed into the place of any -ether, would give it the same velocity of descent, as it -gives that other; and consequently, that the sun’s action -upon different planets at the same distance would be proportional -to the quantity of matter in each. It has farther<span class="pagenum"><a name="Page_251" id="Page_251">[251]</a></span> -been shewn, that the sun attracts the primary planets, and -their respective secondary, when at the same distance, so -as to communicate to both the same degree of velocity; -and therefore the force, wherewith the sun acts on the secondary -planet, bears the same proportion to the force, -wherewith at the same distance it attracts the primary, as -the quantity of solid matter in the secondary planet bears to -the quantity of matter in the primary.</p> - -<p><a name="c251" id="c251">5.</a> <span class="smcap gesperrt">This</span> property therefore is proved of both kinds of -planets, in respect of the sun. Therefore the sun possesses the -quality found in the earth, of acting on bodies with a degree -of force proportional to the quantity of matter in the -body, which receives the influence.</p> - -<p>6. <span class="smcap gesperrt">That</span> the power of attraction, with which the other -planets are endued, should differ from that of the earth, can -hardly be supposed, if we consider the similitude between -those bodies; and that it does not in this respect, is farther -proved from the satellites of Saturn and Jupiter, which are attracted -by their respective primary according to the same law, -that is, in the same proportion to their distances, as the primary -are attracted by the sun: so that what has been concluded -of the sun in relation to the primary planets, may be justly -concluded of these primary in respect of their secondary, and -in consequence of that, in regard likewise to all other bodies, -viz. that they will attract every body in proportion to the -quantity of solid matter it contains.</p> - -<p><span class="pagenum"><a name="Page_252" id="Page_252">[252]</a></span></p> - -<p>7. <span class="smcap gesperrt">Hence</span> it follows, that this attraction extends itself -to every particle of matter in the attracted body: and that -no portion of matter whatever is exempted from the influence -of those bodies, to which we have proved this attractive -power to belong.</p> - -<p><a name="c252a" id="c252a">8.</a> <span class="smcap gesperrt">Before</span> we proceed farther, we may here remark, -that this attractive power both of the sun and planets now -appears to be quite of the same nature in all; for it acts in -each in the same proportion to the distance, and in the same -manner acts alike upon every particle of matter. This -power therefore in the sun and other planets is not of a different -nature from this power in the earth; which has been already -shewn to be the same with that, which we call gravity<a name="FNanchor_242_242" id="FNanchor_242_242"></a><a href="#Footnote_242_242" class="fnanchor">[242]</a>.</p> - -<p><a name="c252b" id="c252b">9.</a> <span class="smcap gesperrt">And</span> this lays open the way to prove, that the attracting -power lodged in the sun and planets, belongs likewise -to every part of them: and that their respective powers -upon the same body are proportional to the quantity of matter, -of which they are composed; for instance, that the force -with which the earth attracts the moon, is to the force, with -which the sun would attract it at the same distance, as the -quantity of solid matter contained in the earth, to the quantity -contained in the sun<a name="FNanchor_243_243" id="FNanchor_243_243"></a><a href="#Footnote_243_243" class="fnanchor">[243]</a>.</p> - -<p>10. <span class="smcap gesperrt">The</span> first of these assertions is a very evident consequence -from the latter. And before we proceed to the proof,<span class="pagenum"><a name="Page_253" id="Page_253">[253]</a></span> -it must first be shewn, that the third law of motion, which -makes action and reaction equal, holds in these attractive -powers. The most remarkable attractive force, next to the -power of gravity, is that, by which the loadstone attracts iron. -Now if a loadstone were laid upon water, and supported by -some proper substance, as wood or cork, so that it might -swim; and if a piece of iron were caused to swim upon the -water in like manner: as soon as the loadstone begins to -attract the iron, the iron shall move toward the stone, and -the stone shall also move toward the iron; when they meet, -they shall stop each other, and remain fixed together without -any motion. This shews, that the velocities, wherewith -they meet, are reciprocally proportional to the quantities -of solid matter in each; and that by the stone’s attracting -the iron, the stone itself receives as much motion, -in the strict philosophic sense of that word<a name="FNanchor_244_244" id="FNanchor_244_244"></a><a href="#Footnote_244_244" class="fnanchor">[244]</a>, as it communicates -to the iron: for it has been declared above to be an -effect of the percussion of two bodies, that if they meet -with velocities reciprocally proportional to the respective -bodies, they shall be stopped by the concourse, unless their -elasticity put them into fresh motion; but if they meet -with any other velocities, they shall retain some motion -after meeting<a name="FNanchor_245_245" id="FNanchor_245_245"></a><a href="#Footnote_245_245" class="fnanchor">[245]</a>. Amber, glass, sealing-wax, and many other -substances acquire by rubbing a power, which from its -having been remarkable, particularly in amber, is called -electrical. By this power they will for some time after<span class="pagenum"><a name="Page_254" id="Page_254">[254]</a></span> -rubbing attract light bodies, that shall be brought within -the sphere of their activity. On the other hand Mr. <span class="smcap">Boyle</span> -found, that if a piece of amber be hung in a perpendicular -position by a string, it shall be drawn itself toward the body -whereon it was rubbed, if that body be brought near -it. Both in the loadstone and in electrical bodies we usually -ascribe the power to the particular body, whose presence -we find necessary for producing the effect. The loadstone -and any piece of iron will draw each other, but in -two pieces of iron no such effect is ordinarily observed; therefore -we call this attractive power the power of the loadstone: -though near a loadstone two pieces of iron will also -draw each other. In like manner the rubbing of amber, -glass, or any such body, till it is grown warm, being -necessary to cause any action between those bodies and other -substances, we ascribe the electrical power to those bodies. -But in all these cases if we would speak more correctly, -and not extend the sense of our expressions beyond what -we see; we can only say that the neighbourhood of a loadstone -and a piece of iron is attended with a power, whereby -the loadstone and the iron are drawn toward each other; -and the rubbing of electrical bodies gives rise to a power, -whereby those bodies and other substances are mutually attracted. -Thus we must also understand in the power of -gravity, that the two bodies are mutually made to approach -by the action of that power. When the sun draws any -planet, that planet also draws the sun; and the motion, -which the planet receives from the sun, bears the same proportion -to the motion, which the sun it self receives, as<span class="pagenum"><a name="Page_255" id="Page_255">[255]</a></span> -the quantity of solid matter in the sun bears to the quantity -of solid matter in the planet. Hitherto, for brevity -sake in speaking of these forces, we have generally ascribed -them to the body, which is least moved; as when we -called the power, which exerts itself between the sun and -any planet, the attractive power of the sun; but to speak -more correctly, we should rather call this power in any -case the force, which acts between the sun and earth, between -the sun and Jupiter, between the earth and moon, -&c. for both the bodies are moved by the power acting between -them, in the same manner, as when two bodies are -tied together by a rope, if that rope shrink by being wet, -or otherwise, and thereby cause the bodies to approach, by -drawing both, it will communicate to both the same degree -of motion, and cause them to approach with velocities -reciprocally proportional to the respective bodies. From -this mutual action between the sun and planet it follows, -as has been observed above<a name="FNanchor_246_246" id="FNanchor_246_246"></a><a href="#Footnote_246_246" class="fnanchor">[246]</a>, that the sun and planet -do each move about their common center of gravity. -Let A (in fig. 108.) represent the sun, B a planet, C their -common center of gravity. If these bodies were once at -rest, by their mutual attraction they would directly approach -each other with such velocities, that their common -center of gravity would remain at rest, and the two bodies -would at length meet in that point. If the planet B were -to receive an impulse, as in the direction of the line D E, -this would prevent the two bodies from falling together;<span class="pagenum"><a name="Page_256" id="Page_256">[256]</a></span> -but their common center of gravity would be put into motion -in the direction of the line C F equidistant from B E. -In this case Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> proves<a name="FNanchor_247_247" id="FNanchor_247_247"></a><a href="#Footnote_247_247" class="fnanchor">[247]</a>, that the sun and -planet would describe round their common center of gravity -similar orbits, while that center would proceed with an -uniform motion in the line C F; and so the system of the -two bodies would move on with the center of gravity without -end. In order to keep the system in the same place, -it is necessary, that when the planet received its impulse in -the direction B E, the sun should also receive such an impulse -the contrary way, as might keep the center of gravity -C without motion; for if these began once to move -without giving any motion to their common center of gravity, -that center would always remain fixed.</p> - -<p>11. <span class="smcap gesperrt">By</span> this may be understood in what manner the action -between the sun and planets is mutual. But farther, -we have shewn above<a name="FNanchor_248_248" id="FNanchor_248_248"></a><a href="#Footnote_248_248" class="fnanchor">[248]</a>, that the power, which acts between -the sun and primary planets, is altogether of the same nature -with that, which acts between the earth and the bodies -at its surface, or between the earth and its parts, and -with that which acts between the primary planets and their -secondary; therefore all these actions must be ascribed to -the same cause<a name="FNanchor_249_249" id="FNanchor_249_249"></a><a href="#Footnote_249_249" class="fnanchor">[249]</a>. Again, it has been already proved, that -in different planets the force of the sun’s action upon each at -the same distance would be proportional to the quantity of solid -matter in the planet<a name="FNanchor_250_250" id="FNanchor_250_250"></a><a href="#Footnote_250_250" class="fnanchor">[250]</a>; therefore the reaction of each planet -on the sun at the same distance, or the motion, which the sun -would receive from each planet, would also be proportional -to the quantity of matter in the planet; that is, these planets -at the same distance would act on the same body with -degrees of strength proportional to the quantity of solid matter -in each.</p> - -<div class="figcenter"> - <img src="images/ill-321.jpg" width="400" height="517" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_257" id="Page_257">[257]</a></span></p> - -<p><a name="c257" id="c257">12.</a> <span class="smcap gesperrt">In</span> the next place, from what has been now proved, -our great author has deduced this farther consequence, -no less surprizing than elegant; that each of the particles, -out of which the bodies of the sun and planets are framed, -exert their power of gravitation by the same law, and in -the same proportion to the distance, as the great bodies -which they compose. For this purpose he first demonstrates, -that if a globe were compounded of particles, which -will attract the particles of any other body reciprocally -in the duplicate proportion of their distances, the whole -globe will attract the same in the reciprocal duplicate proportion -of their distances from the center of the globe; -provided the globe be of uniform density throughout<a name="FNanchor_251_251" id="FNanchor_251_251"></a><a href="#Footnote_251_251" class="fnanchor">[251]</a>. And -from this our author deduces the reverse, that if a globe acts -upon distant bodies by the law just now specified, and the -power of the globe is derived from its being composed of attractive -particles; each of those particles will attract after the -same proportion<a name="FNanchor_252_252" id="FNanchor_252_252"></a><a href="#Footnote_252_252" class="fnanchor">[252]</a>. The manner of deducing this is not set -down at large by our author, but is as follows. The globe is<span class="pagenum"><a name="Page_258" id="Page_258">[258]</a></span> -supposed to act upon the particles of a body without it constantly -in the reciprocal duplicate proportion of their distances -from its center; and therefore at the same distance from -the globe, on which side soever the body be placed, the -globe will act equally upon it. Now because, if the particles, -of which the globe is composed, acted upon those without -in the reciprocal duplicate proportion of their distances, -the whole globe would act upon them in the same manner as -it does; therefore, if the particles of the globe have not all -of them that property, some must act stronger than in that -proportion, while others act weaker: and if this be the condition -of the globe, it is plain, that when the body attracted -is in such a situation in respect of the globe, that the greater -number of the strongest particles are nearest to it, the body -will be more forcibly attracted; than when by turning the -globe about, the greater quantity of weak particles should -be nearest, though the distance of the body should remain -the same from the center of the globe. Which is contrary -to what was at first remarked, that the globe on all sides of -it acts with the same strength at the same distance. Whence it -appears, that no other constitution of the globe can agree to it.</p> - -<p>13. <span class="smcap gesperrt">From</span> these propositions it is farther collected, that -if all the particles of one globe attract all the particles of another -in the proportion so often mentioned, the attracting -globe will act upon the other in the same proportion to the -distance between the center of the globe which attracts, and -the center of that which is attracted<a name="FNanchor_253_253" id="FNanchor_253_253"></a><a href="#Footnote_253_253" class="fnanchor">[253]</a>: and farther, that this<span class="pagenum"><a name="Page_259" id="Page_259">[259]</a></span> -proportion holds true, though either or both the globes be -composed of dissimilar parts, some rarer and some more -dense; provided only, that all the parts in the same globe -equally distant from the center be homogeneous<a name="FNanchor_254_254" id="FNanchor_254_254"></a><a href="#Footnote_254_254" class="fnanchor">[254]</a>. And -also, if both the globes attract each other<a name="FNanchor_255_255" id="FNanchor_255_255"></a><a href="#Footnote_255_255" class="fnanchor">[255]</a>. All which place -it beyond contradiction, that this proportion obtains with as -much exactness near and contiguous to the surface of attracting -globes, as at greater distances from them.</p> - -<p><a name="c259" id="c259">14.</a> <span class="smcap gesperrt">Thus</span> our author, without the pompous pretence of -explaining the cause of gravity, has made one very important -step toward it, by shewing that this power in the great bodies -of the universe, is derived from the same power being lodged -in every particle of the matter which composes them: and -consequently, that this property is no less than universal to -all matter whatever, though the power be too minute to produce -any visible effects on the small bodies, wherewith we -converse, by their action on each other<a name="FNanchor_256_256" id="FNanchor_256_256"></a><a href="#Footnote_256_256" class="fnanchor">[256]</a>. In the fixed stars -indeed we have no particular proof that they have this power; -for we find no apperance to demonstrate that they either -act, or are acted upon by it. But since this power -is found to belong to all bodies, whereon we can make -observation; and we see that it is not to be altered by any -change in the form of bodies, but always accompanies them -in every shape without diminution, remaining ever proportional -to the quantity of solid matter in each; such a -power must without doubt belong universally to all matter.</p> - -<p><span class="pagenum"><a name="Page_260" id="Page_260">[260]</a></span></p> - -<p>15. <span class="smcap gesperrt">This</span> therefore is the universal law of matter; which -recommends it self no less for its great plainness and simplicity, -than for the surprizing discoveries it leads us to. By -this principle we learn the different weight, which the same -body will have upon the surfaces of the sun and of diverse -planets; and by the same we can judge of the composition -of those celestial bodies, and know the density of -each; which is formed of the most compact, and which of -the most rare substance. Let the adversaries of this philosophy -reflect here, whether loading this principle with the -appellation of an occult quality, or perpetual miracle, or -any other reproachful name, be sufficient to dissuade us from -cultivating it; since this quality, which they call occult, leads -to the knowledge of such things, that it would have been reputed -no less than madness for any one, before they had been -discovered, even to have conjectured that our faculties should -ever have reached so far.</p> - -<p>16. <span class="smcap gesperrt">See</span> how all this naturally follows from the foregoing -principles in those planets, which have satellites moving -about them. By the times, in which these satellites -perform their revolutions, compared with their distances -from their respective primary, the proportion between the -power, with which one primary attracts his satellites, and -the force with which any other attracts his will be known; -and the proportion of the power with which any planet -attracts its secondary, to the power with which it attracts a -body at its surface is found, by comparing the distance of -the secondary planet from the center of the primary, to<span class="pagenum"><a name="Page_261" id="Page_261">[261]</a></span> -the distance of the primary planet’s surface from the same: -and from hence is deduced the proportion between the power -of gravity upon the surface of one planet, to the gravity upon -the surface of another. By the like method of comparing -the periodical time of a primary planet about the sun, with -the revolution of a satellite about its primary, may be found -the proportion of gravity, or of the weight of any body upon -the surface of the sun, to the gravity, or to the weight of -the same body upon the surface of the planet, which carries -about the satellite.</p> - -<p><a name="c261" id="c261">17.</a> <span class="smcap gesperrt">By</span> these kinds of computation it is found, that the -weight of the same body upon the surface of the sun will -be about 23 times as great, as here upon the surface of the -earth; about 10⅗ times as great, as upon the surface of Jupiter; -and near 19 times as great, as upon the surface of Saturn<a name="FNanchor_257_257" id="FNanchor_257_257"></a><a href="#Footnote_257_257" class="fnanchor">[257]</a>.</p> - -<p>18. <span class="smcap gesperrt">The</span> quantity of matter, which composes each of -these bodies, is proportional to the power it has upon a -body at a given distance. By this means it is found, that the -sun contains 1067 times as much matter as Jupiter; Jupiter -158⅔ times as much as the earth, and 2-5/6 times as much -as Saturn<a name="FNanchor_258_258" id="FNanchor_258_258"></a><a href="#Footnote_258_258" class="fnanchor">[258]</a>. The diameter of the sun is about 92 times, -that of Jupiter about 9 times, and that of Saturn about -7 times the diameter of the earth.</p> - -<p><span class="pagenum"><a name="Page_262" id="Page_262">[262]</a></span></p> - -<p>19. <span class="smcap gesperrt">By</span> making a comparison between the quantity of -matter in these bodies and their magnitudes, to be found -from their diameters, their respective densities are readily -deduced; the density of every body being measured by the -quantity of matter contained under the same bulk, as has -been above remarked<a name="FNanchor_259_259" id="FNanchor_259_259"></a><a href="#Footnote_259_259" class="fnanchor">[259]</a>. Thus the earth is found 4¼ times -more dense than Jupiter; Saturn has between ⅔ and ¾ of the -density of Jupiter; but the sun has one fourth part only of -the density of the earth<a name="FNanchor_260_260" id="FNanchor_260_260"></a><a href="#Footnote_260_260" class="fnanchor">[260]</a>. From which this observation is drawn -by our author; that the sun is rarified by its great heat, and that -of the three planets named, the more dense is nearer the sun -than the more rare; as was highly reasonable to expect, the -densest bodies requiring the greatest heat to agitate and put -their parts in motion; as on the contrary, the planets which -are more rare, would be rendered unfit for their office, by -the intense heat to which the denser are exposed. Thus the -waters of our seas, if removed to the distance of Saturn from -the sun, would remain perpetually frozen; and if as near -the sun as Mercury, would constantly boil<a name="FNanchor_261_261" id="FNanchor_261_261"></a><a href="#Footnote_261_261" class="fnanchor">[261]</a>.</p> - -<p>20. <span class="smcap gesperrt">The</span> densities of the three planets Mercury, Venus, -and Mars, which have no satellites, cannot be expresly assigned; -but from what is found in the others, it is very probable, -that they also are of such different degrees of density, -that universally the planet which is nearest to the sun, is -formed of the most compact substance.</p> - -</div> - -<p><span class="pagenum"><a name="Page_263" id="Page_263">[263]</a></span></p> - -<div class="chapter"> - -<h2 class="p4"><a name="c263" id="c263"><span class="smcap"><em class="gesperrt">Chap</em>. VI.</span></a><br /> -Of the FLUID PARTS of the PLANETS.</h2> - -<p class="drop-cap04">THIS globe, that we inhabit, is composed of two parts; -the solid earth, which affords us a foundation to dwell -upon; and the seas and other waters, that furnish rains and -vapours necessary to render the earth fruitful, and productive -of what is requisite for the support of life. And that the -moon, though but a secondary planet, is composed in like -manner, is generally thought, from the different degrees of -light which appear on its surface; the parts of that planet, -which reflect a dim light, being supposed to be fluid, and to -imbibe the sun’s rays, while the solid parts reflect them more -copiously. Some indeed do not allow this to be a conclusive -argument: but whether we can distinguish the fluid part of -the moon’s surface from the rest or not; yet it is most probable -that there are two such different parts, and with still greater -reason we may ascribe the like to the other primary planets, -which yet more nearly resemble our earth. The earth is also -encompassed by another fluid the air, and we have before remarked, -that probably the rest of the planets are surrounded -by the like. These fluid parts in particular engage our author’s -attention, both by reason of some remarkable appearances -peculiar to them, and likewise of some effects they -have upon the whole bodies to which they belong.</p> - -<p><span class="pagenum"><a name="Page_264" id="Page_264">[264]</a></span></p> - -<p><a name="c264" id="c264">2.</a> <span class="smcap gesperrt">Fluids</span> have been already treated of in general, with -respect to the effect they have upon solid bodies moving in -them<a name="FNanchor_262_262" id="FNanchor_262_262"></a><a href="#Footnote_262_262" class="fnanchor">[262]</a>; now we must consider them in reference to the operation -of the power of gravity upon them. By this power -they are rendered weighty, like all other bodies, in proportion -to the quantity of matter, which is contained in them. And -in any quantity of a fluid the upper parts press upon the lower -as much, as any solid body would press on another, whereon -it should lie. But there is an effect of the pressure of fluids on -the bottom of the vessel, wherein they are contained, which I -shall particularly explain. The force supported by the bottom -of such a vessel is not simply the weight of the quantity -of the fluid in the vessel, but is equal to the weight of that -quantity of the fluid, which would be contained in a vessel of -the same bottom and of equal width throughout, when this -vessel is filled up to the same height, as that to which the vessel -proposed is filled. Suppose water were contained in the -vessel A B C D (in fig. 109.) filled up to E F. Here it is evident, -that if a part of the bottom, as G H, which is directly under -any part of the space E F, be considered separately; it will appear -at once, that this part sustains the weight of as much of -the fluid, as stands perpendicularly over it up to the height of -E F; that is, the two perpendiculars G I and H K being drawn, -the part G H of the bottom will sustain the whole weight of -the fluid included between these two perpendiculars. Again, -I say, every other part of the bottom equally broad with this, -will sustain as great a pressure. Let the part L M be of the<span class="pagenum"><a name="Page_265" id="Page_265">[265]</a></span> -same breadth with G H. Here the perpendiculars L O and -M N being drawn, the quantity of water contained between -these perpendiculars is not so great, as that contained between -the perpendiculars G I and H K; yet, I say, the pressure on L M -will be equal to that on G H. This will appear by the following -considerations. It is evident, that if the part of the -vessel between O and N were removed, the water would immediately -flow out, and the surface E F would subside; for -all parts of the water being equally heavy, it must soon form -itself to a level surface, if the form of the vessel, which contains -it, does not prevent. Therefore since the water is prevented -from rising by the side N O of the vessel, it is manifest, -that it must press against N O with some degree of force. -In other words, the water between the perpendiculars L O and -M N endeavours to extend itself with a certain degree of force; -or more correctly, the ambient water presses upon this, and -endeavours to force this pillar or column of water into a greater -length. But since this column of water is sustained between -N O and L M, each of these parts of the vessel will be -equally pressed against by the power, wherewith this column -endeavours to extend. Consequently L M bears this force -over and above the weight of the column of water between -L O and M N. To know what this expansive force is, let the -part O N of the vessel be removed, and the perpendiculars L O -and M N be prolonged; then by means of some pipe fixed -over N O let water be filled between these perpendiculars up to -P Q an equal height with E F. Here the water between the perpendiculars -L P and M Q is of an equal height with the highest -part of the water in the vessel; therefore the water in the<span class="pagenum"><a name="Page_266" id="Page_266">[266]</a></span> -vessel cannot by its pressure force it up higher, nor can the -water in this column subside; because, if it should, it would -raise the water in the vessel to a greater height than itself. -But it follows from hence, that the weight of water contained -between P O and Q N is a just balance to the force, wherewith -the column between L O and M N endeavours to extend. So -the part L M of the bottom, which sustains both this force -and the weight of the water between L O and M N, is pressed -upon by a force equal to the united weight of the water -between L O and M N, and the weight of the water between -P O and Q N; that is, it is pressed on by a force equal to the -weight of all the water contained between L P and M Q. And -this weight is equal to that of the water contained between -G I and H K, which is the weight sustained by the part G H -of the bottom. Now this being true of every part of the -bottom B C, it is evident, that if another vessel R S T V be -formed with a bottom R V equal to the bottom B C, and be -throughout its whole height of one and the same breadth; -when this vessel is filled with water to the same height, as the -vessel A B C D is filled, the bottoms of these two vessels shall -be pressed upon with equal force. If the vessel be broader -at the top than at the bottom, it is evident, that the bottom -will bear the pressure of so much of the fluid, as is perpendicularly -over it, and the sides of the vessel will support the -rest. This property of fluids is a corollary from a proposition -of our author<a name="FNanchor_263_263" id="FNanchor_263_263"></a><a href="#Footnote_263_263" class="fnanchor">[263]</a>; from whence also he deduces the effects -of the pressure of fluids on bodies resting in them.<span class="pagenum"><a name="Page_267" id="Page_267">[267]</a></span> -These are, that any body heavier than a fluid will sink to -the bottom of the vessel, wherein the fluid is contained, -and in the fluid will weigh as much as its own weight exceeds -the weight of an equal quantity of the fluid; any body -uncompressible of the same density with the fluid, will rest -any where in the fluid without suffering the least change either -in its place or figure from the pressure of such a fluid, -but will remain as undisturbed as the parts of the fluid themselves; -but every body of less density than the fluid will -swim on its surface, a part only being received within the -fluid. Which part will be equal in bulk to a quantity of the -fluid, whose weight is equal to the weight of the whole body; -for by this means the parts of the fluid under the body -will suffer as great a pressure as any other parts of the -fluid as much below the surface as these.</p> - -<p>3. <span class="smcap gesperrt">In</span> the next place, in relation to the air, we have above -made mention, that the air surrounding the earth being -an elastic fluid, the power of gravity will have this effect -on it, to make the lower parts near the surface of the earth -more compact and compressed together by the weight of -the air incumbent, than the higher parts, which are pressed -upon by a less quantity of the air, and therefore sustain -a less weight<a name="FNanchor_264_264" id="FNanchor_264_264"></a><a href="#Footnote_264_264" class="fnanchor">[264]</a>. It has been also observed, that our author -has laid down a rule for computing the exact degree -of density in the air at all heights from the earth<a name="FNanchor_265_265" id="FNanchor_265_265"></a><a href="#Footnote_265_265" class="fnanchor">[265]</a>. But -there is a farther effect from the air’s being compressed by<span class="pagenum"><a name="Page_268" id="Page_268">[268]</a></span> -the power of gravity, which he has distinctly considered. -The air being elastic and in a state of compression, any tremulous -body will propagate its motion to the air, and excite -therein vibrations, which will spread from the body that -occasions them to a great distance. This is the efficient cause -of sound: for that sensation is produced by the air, which, -as it vibrates, strikes against the organ of hearing. As this -subject was extremely difficult, so our great author’s success -is surprizing.</p> - -<p>4. <span class="smcap gesperrt">Our</span> author’s doctrine upon this head I shall endeavour -to explain somewhat at large. But preliminary thereto -must be shewn, what he has delivered in general of pressure -propagated through fluids; and also what he has set -down relating to that wave-like motion, which appears upon -the surface of water, when agitated by throwing any thing -into it, or by the reciprocal motion of the finger, &c.</p> - -<p>5. <span class="smcap gesperrt">Concerning</span> the first, it is proved, that pressure is -spread through fluids, not only right forward in a streight -line, but also laterally, with almost the same ease and force. -Of which a very obvious exemplification by experiment is -proposed: that is, to agitate the surface of water by the reciprocal -motion of the finger forwards and backwards only; -for though the finger have no circular motion given it, yet the -waves excited in the water will diffuse themselves on each -hand of the direction of the motion, and soon surround the -finger. Nor is what we observe in sounds unlike to this, which -do not proceed in straight lines only, but are heard though a<span class="pagenum"><a name="Page_269" id="Page_269">[269]</a></span> -mountain intervene, and when they enter a room in any -part of it, they spread themselves into every corner; not by -reflection from the walls, as some have imagined, but as -far as the sense can judge, directly from the place where they -enter.</p> - -<p><a name="c269" id="c269">6.</a> <span class="smcap gesperrt">How</span> the waves are excited in the surface of stagnant -water, may be thus conceived. Suppose in any place, the -water raised above the rest in form of a small hillock; that -water will immediately subside, and raise the circumambient -water above the level of the parts more remote, to which the -motion cannot be communicated under longer time. And -again, the water in subsiding will acquire, like all falling bodies, -a force, which will carry it below the level surface, till -at length the pressure of the ambient water prevailing, it will -rise again, and even with a force like to that wherewith it descended, -which will carry it again above the level. But in -the mean time the ambient water before raised will subside, -as this did, sinking below the level; and in so doing, will -not only raise the water, which first subsided, but also the water -next without itself. So that now beside the first hillock, -we shall have a ring investing it, at some distance raised above -the plain surface likewise; and between them the water will -be sunk below the rest of the surface. After this, the first hillock, -and the new made annular rising, will descend; raising -the water between them, which was before depressed, and likewise -the adjacent part of the surface without. Thus will these -annular waves be successively spread more and more. For, -as the hillock subsiding produces one ring, and that ring subsiding<span class="pagenum"><a name="Page_270" id="Page_270">[270]</a></span> -raises again the hillock, and a second ring; so the hillock -and second ring subsiding together raise the first ring, -and a third; then this first and third ring subsiding together -raise the first hillock, the second ring, and a fourth; and so -on continually, till the motion by degrees ceases. Now it is demonstrated, -that these rings ascend and descend in the manner -of a pendulum; descending with a motion continually accelerated, -till they become even with the plain surface of the fluid, -which is half the space they descend; and then being retarded -again by the same degrees as those, whereby they were -accelerated, till they are depressed below the plain surface, as -much as they were before raised above it: and that this augmentation -and diminution of their velocity proceeds by the same -degrees, as that of a pendulum vibrating in a cycloid, and -whose length should be a fourth part of the distance between -any two adjacent waves: and farther, that a new ring is -produced every time a pendulum, whose length is four times -the former, that is, equal to the interval between the summits -of two waves, makes one oscillation or swing<a name="FNanchor_266_266" id="FNanchor_266_266"></a><a href="#Footnote_266_266" class="fnanchor">[266]</a>.</p> - -<p><a name="c270" id="c270">7.</a> <span class="smcap gesperrt">This</span> now opens the way for understanding the motion -consequent upon the tremors of the air, excited by -the vibrations of sonorous bodies: which we must conceive -to be performed in the following manner.</p> - -<p>8. <span class="smcap gesperrt">Let</span> A, B, C, D, E, F, G, H (in fig. 110.) represent a series -of the particles of the air, at equal distances from each -other. I K L a musical chord, which I shall use for the tremulous<span class="pagenum"><a name="Page_271" id="Page_271">[271]</a></span> -and sonorous body, to make the conception as simple -as may be. Suppose this chord stretched upon the points -I and L, and forcibly drawn into the situation I K L, so that -it become contiguous to the particle A in its middle point K: -and let the chord from this situation begin to recoil, pressing -against the particle A, which will thereby be put into motion -towards B: but the particles A, B, C being equidistant, the -elastic power, by which B avoids A, is equal to, and balanced -by the power, by which it avoids C; therefore the elastic -force, by which B is repelled from A, will not put B into any -degree of motion, till A is by the motion of the chord brought -nearer to B, than B is to C: but as soon as that is done, the -particle B will be moved towards C; and being made to approach -C, will in the next place move that; which will upon -that advance, put D likewise into motion, and so on: -therefore the particle A being moved by the chord, the following -particles of the air B, C, D, &c. will successively be -moved. Farther, if the point K of the chord moves forward -with an accelerated velocity, so that the particle A shall -move against B with an advancing pace, and gain ground of -it, approaching nearer and nearer continually; A by approaching -will press more upon B, and give it a greater velocity -likewise, by reason that as the distance between the particles -diminishes, the elastic power, by which they fly each other, -increases. Hence the particle B, as well as A, will have its -motion gradually accelerated, and by that means will more -and more approach to C. And from the same cause C will -more and more approach D; and so of the rest. Suppose -now, since the agitation of these particles has been shewn to<span class="pagenum"><a name="Page_272" id="Page_272">[272]</a></span> -be successive, and to follow one another, that E be the remotest -particle moved, while the chord is moving from its -curve situation I K L into that of a streight line, as I k L; and -F the first which remains unaffected, though just upon the -point of being put into motion. Then shall the particles -A, B, C, D, E, F, G, when the point K is moved into k, have -acquired the rangement represented by the adjacent points -<i>a, b, c, d, e, f, g</i>: in which <i>a</i> is nearer to <i>b</i> than <i>b</i> to <i>c</i>, and -<i>b</i> nearer to <i>c</i> than <i>c</i> to <i>d</i>, and <i>c</i> nearer to <i>d</i> than <i>d</i> to <i>e</i> and -<i>d</i> nearer to <i>e</i> than <i>e</i> to <i>f</i>, and lastly <i>e</i> nearer to <i>f</i> than <i>f</i> to <i>g</i>.</p> - -<p>9. <span class="smcap gesperrt">But</span> now the chord having recovered its rectilinear situation -I k L, the following motion will be changed, for the -point K, which before advanced with a motion more and -more accelerated, though by the force it has acquired it will -go on to move the same way as before, till it has advanced -near as far forwards, as it was at first drawn backwards; yet -the motion of it will henceforth be gradually lessened. The -effect of which upon the particles <i>a, b, c, d, e, f, g</i> will be, -that by the time the chord has made its utmost advance, and -is upon the return, these particles will be put into a contrary -rangement; so that <i>f</i> shall be nearer to <i>g</i>, than <i>e</i> to <i>f</i>, and -<i>e</i> nearer to <i>f</i> than <i>d</i> to <i>e</i>; and the like of the rest, till you -come to the first particles <i>a</i>, <i>b</i>, whose distance will then be -nearly or quite what it was at first. All which will appear -as follows. The present distance between <i>a</i> and <i>b</i> is such, -that the elastic power, by which <i>a</i> repels <i>b</i>, is strong enough to -maintain that distance, though a advance with the velocity, -with which the string resumes its rectilinear figure; and the<span class="pagenum"><a name="Page_273" id="Page_273">[273]</a></span> -motion of the particle <i>a</i> being afterwards slower, the -present elasticity between <i>a</i> and <i>b</i> will be more than -sufficient to preserve the distance between them. Therefore -while it accelerates <i>b</i> it will retard <i>a</i>. The distance -<i>b c</i> will still diminish, till <i>b</i> come about as near -to <i>c</i>, as it is from a at present; for after the distances -<i>a b</i> and <i>b c</i> are become equal, the particle <i>b</i> will continue -its velocity superior to that of <i>c</i> by its own power of inactivity, -till such time as the increase of elasticity between -<i>b</i> and <i>c</i> more than shall be between <i>a</i> and <i>b</i> shall suppress -its motion: for as the power of inactivity in <i>b</i> made a -greater elasticity necessary on the side of a than on the side -of <i>c</i> to push <i>b</i> forward, so what motion <i>b</i> has acquired it will -retain by the same power of inactivity, till it be suppressed -by a greater elasticity on the side of <i>c</i>, than on the side of <i>a</i>. -But as soon as <i>b</i> begins to slacken its pace the distance of <i>b</i> -from c will widen as the distance <i>a b</i> has already done. Now -as <i>a</i> acts on <i>b</i>, so will <i>b</i> on <i>c</i>, <i>c</i> on <i>d</i>, &c. so that the distances -between all the particles <i>b, c, d, e, f, g</i> will be successively -contracted into the distance of <i>a</i> from <i>b</i>, and then dilated -again. Now because the time, in which the chord describes -this present half of its vibration, is about equal to that it took -up in describing the former; the particles <i>a</i>, <i>b</i> will be as long -in dilating their distance, as before in contracting it, and -will return nearly to their original distance. And farther, -the particles <i>b</i>, <i>c</i>, which did not begin to approach so soon -as <i>a</i>, <i>b</i>, are now about as much longer, before they begin to -recede; and likewise the particles <i>c</i>, <i>d</i>, which began to approach -after <i>b</i>, <i>c</i>, begin to separate later. Whence it appears -that the particles, whose distance began to be lessened, when<span class="pagenum"><a name="Page_274" id="Page_274">[274]</a></span> -that of <i>a</i>, <i>b</i> was first enlarged, viz. the particles <i>f</i>, <i>g,</i> should -be about their nearest distance, when <i>a</i> and <i>b</i> have recovered -their prime interval. Thus will the particles <i>a, b, c, d, -e, f, g</i> have changed their situation in the manner asserted. -But farther, as the particles <i>f</i>, <i>g</i> or F, G gradually approach -each other, they will move by degrees the succeeding particles -to as great a length, as the particles A, B did by a like -approach. So that, when the chord has made its greatest advance, -being arrived into the situation I ϰ L, the particles moved -by it will have the rangement noted by the points α, β, γ, -δ, ε, ζ, η, θ, λ, μ, ν, χ. Where α, β are at the original distance of -the particles in the line A H; ζ, η are the nearest of all, and -the distance ν χ is equal to that between α and β.</p> - -<p>10. <span class="smcap gesperrt">By</span> this time the chord I ϰ L begins to return, and the -distance between the particles α and β being enlarged to its -original magnitude, α has lost all that force it had acquired -by its motion, being now at rest; and therefore will -return with the chord, making the distance between α and -β greater than the natural; for β will not return so soon, -because its motion forward is not yet quite suppressed, the -distance β γ not being already enlarged to its prime dimension: -but the recess of α, by diminishing the pressure upon -β by its elasticity, will occasion the motion of β to be -stopt in a little time by the action of γ, and then shall -β begin to return: at which time the distance between γ -and δ shall by the superior action of δ above β be enlarged -to the dimension of the distance β γ, and therefore -soon after to that of α β. Thus it appears, that each of -these particles goes on to move forward, till its distance from<span class="pagenum"><a name="Page_275" id="Page_275">[275]</a></span> -the preceding one be equal to its original distance; the -whole chain α, β, γ, δ, ε, ζ, η, having an undulating motion -forward, which is stopt gradually by the excess of the expansive -power of the preceding parts above that of the -hinder. Thus are these parts successively stopt, as before -they were moved; so that when the chord has regained its -rectilinear situation, the expansion of the parts of the air -will have advanced so far, that the interval between ζ η, -which at present is most contracted, will then be restored -to its natural size: the distances between η and θ, θ and λ, λ -and μ, μ and ν, ν and χ, being successively contracted into -the present distance of ζ from η, and again enlarged; so -that the same effect shall be produced upon the parts beyond -ζ η, by the enlargement of the distance between those two -particles, as was occasioned upon the particles α, β, γ, δ, ε, -ζ, η, θ, λ, μ, ν, χ, by the enlargement of the distance α β to -its natural extent. And therefore the motion in the air -will be extended half as much farther as at present, and -the distance between ν and χ contracted into that, which -is at present between ζ and η, all the particles of the air -in motion taking the rangement expressed in figure -111. by the points α, β, γ, δ, ε, ζ, η, θ, λ, μ, ν, χ, ϰ, ρ, σ, τ, φ -wherein the particles from α to χ have their distances from -each other gradually diminished, the distances between the -particles ν, χ being contracted the most from the natural distance -between those particles, and the distance between α, β as -much augmented, and the distance between the middle particles -ζ, η becoming equal to the natural. The particles π, ρ, ω<br /> -<span class="pagenum"><a name="Page_276" id="Page_276">[276]</a></span>τ, φ which follow χ, have their distances gradually greater -and greater, the particles ν, χ, π, ρ, σ, τ, φ being ranged like -the particles <i>a, b, c, d, e, f, g</i>, or like the particles ζ, η, θ, λ, -μ, ν, χ in the former figure. Here it will be understood, by what -has been before explained, that the particles ζ, η being at -their natural distance from each other, the particle ζ is at -rest, the particles ε, δ, λ, β, ϰ between them and the string -being in motion backward, and the rest of the particles -η, θ, λ, μ, ν, χ, π, ρ, σ, τ in motion forward: each of the particles -between η and χ moving faster than that, which immediately -follows it; but of the particles from χ to φ, on -the contrary, those behind moving on faster than those, -which precede.</p> - -<p>11. <span class="smcap gesperrt">But</span> now the string having recovered its rectilinear -figure, though it shall go on recoiling, till it return near to its -first situation I K L, yet there will be a change in its motion; so -that whereas it returned from the situation I ϰ L with an accelerated -motion, its motion shall from hence be retarded -again by the same degrees, as accelerated before. The effect -of which change upon the particles of the air will be -this. As by the accelerated motion of the chord α contiguous -to it moved faster than β, γ, so as to make the interval -α β greater than the interval β γ, and from thence β -was made likewise to move faster than γ, and the distance between -β and γ rendered greater than the distance between γ -and δ, and so of the rest; now the motion of α being diminished, -β shall overtake it, and the distance between α -and β be reduced into that, which is at present between β and -γ, the interval between β and γ being inlarged into the present<span class="pagenum"><a name="Page_277" id="Page_277">[277]</a></span> -distance between α and β; but when the interval β γ -is increased to that, which is at present between α and β γ -the distance between γ and δ shall be enlarged to the present -distance between γ and β, and the distance between δ -and ι inlarged into the present distance between γ and δ; -and the same of the rest. But the chord more and more -slackening its pace, the distance between α and β shall be -more and more diminished; and in consequence of that the -distance between β and γ shall be again contracted, first into -its present dimension, and afterwards into a narrower -space; while the interval γ δ shall dilate into that at present -between α and β, and as soon as it is so much enlarged, it shall -contract again. Thus by the reciprocal expansion and contraction -of the air between α and ζ, by that time the chord -is got into the situation I K L, the interval ζ η shall be expanded -into the present distance between α and β; and by -that time likewise the present distance of α from β will be -contracted into their natural interval: for this distance will -be about the same time in contracting it self, as has been -taken up in its dilatation; seeing the string will be as long -in returning from its rectilinear figure, as it has been in recovering -it from its situation I ϰ L. This is the change -which will be made in the particles between α and ζ. As -for those between ζ and χ, because each preceding particle -advances faster than that, which immediately follows it, -their distances will successively be dilated into that, which -is at present between ζ and η. And as soon as any two -particles are arrived at their natural distance, the hindermost -of them shall be stopt, and immediately after return,<span class="pagenum"><a name="Page_278" id="Page_278">[278]</a></span> -the distances between the returning particles being greater -than the natural. And this dilatation of these distances shall -extend so far, by that time the chord is returned into its first -situation I K L, that the particles ι χ shall be removed to their -natural distance. But the dilatation of ν χ shall contract -the interval τ φ into that at present between ν and χ, and the -contraction of the distance between those two particles τ -and φ will agitate a part of the air beyond; so that when -the chord is returned into the situation I K L, having made -an intire vibration, the moved particles of the air will take -the rangement expressed by the points, <i>l, m, n, o, p, q, r, s, -t, u, w, x, y, z</i>, 1, 2, 3, 4, 5, 6, 7, 8: in which <i>l m</i>, are at -the natural distance of the particles, the distance <i>m n</i> greater -than <i>l m</i> and <i>n o</i> greater than <i>m n</i>, and so on, till you come -to <i>q r</i>, the widest of all: and then the distances gradually -diminish not only to the natural distance, as <i>w x</i>, but till -they are contracted as much as χ τ was before; which falls -out in the points 2, 3, from whence the distances augment -again, till you come to the part of the air untouched.</p> - -<p>12. <span class="smcap gesperrt">This</span> is the motion, into which the air is put, while -the chord makes one vibration, and the whole length of air -thus agitated in the time of one vibration of the chord our -author calls the length of one pulse. When the chord goes -on to make another vibration, it will not only continue to -agitate the air at present in motion, but spread the pulsation -of the air as much farther, and by the same degrees, as before. -For when the chord returns into its rectilinear situation -I <i>k</i> L, <i>l m</i> shall be brought into its most contracted<span class="pagenum"><a name="Page_279" id="Page_279">[279]</a></span> -state, <i>q r</i> now in the state of greatest dilatation shall be reduced -to its natural distance, the points <i>w</i>, <i>x</i> now at their -natural distance shall be at their greatest distance, the points -2, 3 now most contracted enlarged to their natural distance, -and the points 7, 8 reduced to their most contracted state: -and the contraction of them will carry the agitation of the -air as far beyond them, as that motion was carried from the -chord, when it first moved out of the situation I K L into -its rectilinear figure. When the chord is got into the situation -I ϰ L, <i>l m</i> shall recover its natural dimensions, <i>q r</i> be -reduced to its state of greatest contraction, <i>w x</i> brought to -its natural dimension, the distance 2 3 enlarged to the utmost, -and the points 7, 8 shall have recovered their natural -distance; and by thus recovering themselves they shall -agitate the air to as great a length beyond them, as it was -moved beyond the chord, when it first came into the situation -I ϰ L. When the chord is returned back again into -its rectilinear situation, <i>l m</i> shall be in its utmost dilatation, -<i>q r</i> restored again to its natural distance, <i>w x</i> reduced into -its state of greatest contraction, 2 3 shall recover its natural -dimension, and 7 8 be in its state of greatest dilatation. -By which means the air shall be moved as far beyond the points -7, 8, as it was moved beyond the chord, when it before made -its return back to its rectilinear situation; for the particles -7, 8 have been changed from their state of rest and their -natural distance into a state of contraction, and then have -proceeded to the recovery of their natural distance, and after -that to a dilatation of it, in the same manner as the -particles contiguous to the chord were agitated before. In<span class="pagenum"><a name="Page_280" id="Page_280">[280]</a></span> -the last place, when the chord is returned into the situation -I K L, the particles of air from <i>l</i> to δ shall acquire their present -rangement, and the motion of the air be extended as -much farther. And the like will happen after every compleat -vibration of the string.</p> - -<p>13. <span class="smcap gesperrt">Concerning</span> this motion of sound, our author -shews how to compute the velocity thereof, or in what time -it will reach to any proposed distance from the sonorous -body. For this he requires to know the height of air, having -the same density with the parts here at the surface of -the earth, which we breath, that would be equivalent in -weight to the whole incumbent atmosphere. This is to -be found by the barometer, or common weatherglass. In -that instrument quicksilver is included in a hollow glass -cane firmly closed at the top. The bottom is open, but -immerged into quicksilver contained in a vessel open to the -air. Care is taken when the lower end of the cane is immerged, -that the whole cane be full of quicksilver, and that no air -insinuate itself. When the instrument is thus fixed, the quicksilver -in the cane being higher than that in the vessel, if -the top of the cane were open, the fluid would soon sink -out of the glass cane, till it came to a level with that in -the vessel. But the top of the cane being closed up, so -that the air, which has free liberty to press on the quicksilver -in the vessel, cannot bear at all on that, which is within -the cane, the quicksilver in the cane will be suspended -to such a height, as to balance the pressure of the air on -the quicksilver in the vessel. Here it is evident, that the<span class="pagenum"><a name="Page_281" id="Page_281">[281]</a></span> -weight of the quicksilver in the glass cane is equivalent to -the pressure of so much of the air, as is perpendicularly over -the hollow of the cane; for if the cane be opened that the -air may enter, there will be no farther use of the quicksilver -to sustain the pressure of the air without; for the quicksilver -in the cane, as has already been observed, will then subside -to a level with that without. Hence therefore if the proportion -between the density of quicksilver and of the air we -breath be known, we may know what height of such air would -form a column equal in weight to the column of quicksilver -within the glass cane. When the quicksilver is sustained -in the barometer at the height of 30 inches, the height -of such a column of air will be about 29725 feet; for in -this case the air has about 1/870 of the density of water, and -the density of quicksilver exceeds that of water about -13⅔ times, so that the density of quicksilver exceeds that -of the air about 11890 times; and so many times 30 inches -make 29725 feet. Now Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> determines, -that while a pendulum of the length of this column -should make one vibration or swing, the space, which any -sound will have moved, shall bear to this length the same -proportion, as the circumference of a circle bears to the diameter -thereof; that is, about the proportion of 355 to -113<a name="FNanchor_267_267" id="FNanchor_267_267"></a><a href="#Footnote_267_267" class="fnanchor">[267]</a>. Only our author here considers singly the gradual -progress of sound in the air from particle to particle in the -manner we have explained, without taking into consideration -the magnitude of those particles. And though there -requires time for the motion to be propagated from one particle<span class="pagenum"><a name="Page_282" id="Page_282">[282]</a></span> -to another, yet it is communicated to the whole of -the same particle in an instant: therefore whatever proportion -the thickness of these particles bears to their distance -from each other, in the same proportion will the motion -of sound be swifter. Again the air we breath is not simply -composed of the elastic part, by which sound is conveyed, -but partly of vapours, which are of a different nature; -and in the computation of the motion of sound we -ought to find the height of a column of this pure air only, -whose weight should be equal to the weight of the quicksilver -in the cane of the barometer, and this pure air being a -part only of that we breath, the column of this pure air will -be higher than 29725 feet. On both these accounts the -motion of sound is found to be about 1142 feet in one second -of time, or near 13 miles in a minute, whereas by the -computation proposed above, it should move but 979 feet -in one second.</p> - -<p><a name="c282" id="c282">14.</a> <span class="smcap gesperrt">We</span> may observe here, that from these demonstrations -of our author it follows, that all sounds whether acute -or grave move equally swift, and that sound is swiftest, -when the quicksilver stands highest in the barometer.</p> - -<p>15. <span class="smcap gesperrt">Thus</span> much of the appearances, which are caused in -these fluids from their gravitation toward the earth. They -also gravitate toward the moon; for in the last chapter it -has been proved, that the gravitation between the earth and -moon is mutual, and that this gravitation of the whole bodies -arises from that power acting in all their parts; so that<span class="pagenum"><a name="Page_283" id="Page_283">[283]</a></span> -every particle of the moon gravitates toward the earth, -and every particle of the earth toward the moon. But -this gravitation of these fluids toward the moon produces -no sensible effect, except only in the sea, where it causes -the tides.</p> - -<p><a name="c283" id="c283">16.</a> <span class="smcap gesperrt">That</span> the tides depend upon the influence of the -moon has been the receiv’d opinion of all antiquity; nor is -there indeed the least shadow of reason to suppose otherwise, -considering how steadily they accompany the moon’s course. -Though how the moon caused them, and by what principle -it was enabled to produce so distinguish’d an appearance, -was a secret left for this philosophy to unfold: which teaches, -that the moon is not here alone concerned, but that the -sun likewise has a considerable share in their production; -though they have been generally ascribed to the other luminary, -because its effect is greatest, and by that means -the tides more immediately suit themselves to its motion; -the sun discovering its influence more by enlarging or restraining -the moon’s power, than by any distinct effects. -Our author finds the power of the moon to bear to the -power of the sun about the proportion of 4½ to 1. This -he deduces from the observations made at the mouth of -the river Avon, three miles from Bristol, by Captain <span class="smcap">Sturmey</span>, -and at Plymouth by Mr. <span class="smcap">Colepresse</span>, of the height -to which the water is raised in the conjunction and opposition -of the luminaries, compared with the elevation of it, -when the moon is in either quarter; the first being caused<span class="pagenum"><a name="Page_284" id="Page_284">[284]</a></span> -by the united actions of the sun and moon, and the other -by the difference of them, as shall hereafter be shewn.</p> - -<p>17. <span class="smcap gesperrt">That</span> the sun should have a like effect on the sea, -as the moon, is very manifest; since the sun likewise attracts -every single particle, of which this earth is composed. And -in both luminaries since the power of gravity is reciprocally -in the duplicate proportion of the distance, they will not -draw all the parts of the waters in the same manner; but -must act upon the nearest parts stronger, than upon the remotest, -producing by this inequality an irregular motion. -We shall now attempt to shew how the actions of the sun -and moon on the waters, by being combined together, produce -all the appearances observed in the tides.</p> - -<p>18. <span class="smcap gesperrt">To</span> begin therefore, the reader will remember what -has been said above, that if the moon without the sun would -have described an orbit concentrical to the earth, the action -of the sun would make the orbit oval, and bring the moon -nearer to the earth at the new and full, than at the quarters<a name="FNanchor_268_268" id="FNanchor_268_268"></a><a href="#Footnote_268_268" class="fnanchor">[268]</a>. -Now our excellent author observes, that if instead of one moon, -we suppose a ring of moons, contiguous and occupying the -whole orbit of the moon, his demonstration would still take -place, and prove that the parts of this ring in passing from the -quarter to the conjunction or opposition would be accelerated, -and be retarded again in passing from the conjunction or opposition -to the next quarter. And as this effect does not depend<span class="pagenum"><a name="Page_285" id="Page_285">[285]</a></span> -on the magnitude of the bodies, whereof the ring is -composed, the same would hold, though the magnitude of -these moons were so far to be diminished, and their number -increased, till they should form a fluid<a name="FNanchor_269_269" id="FNanchor_269_269"></a><a href="#Footnote_269_269" class="fnanchor">[269]</a>. Now the -earth turns round continually upon its own center, causing -thereby the alternate change of day and night, while -by this revolution each part of the earth is successively -brought toward the sun, and carried off again in the space -of 24 hours. And as the sea revolves round along with the -earth itself in this diurnal motion, it will represent in some -sort such a fluid ring.</p> - -<p>19. <span class="smcap gesperrt">But</span> as the water of the sea does not move round -with so much swiftness, as would carry it about the center -of the earth in the circle it now describes, without being -supported by the body of the earth; it will be necessary to -consider the water under three distinct cases. The first case -shall suppose the water to move with the degree of swiftness, -required to carry a body round the center of the earth disingaged -from it in a circle at the distance of the earth’s -semidiameter, like another moon. The second case is, that -the waters make but one turn about the axis of the earth -in the space of a month, keeping pace with the moon; -so that all parts of the water should preserve continually -the same situation in respect of the moon. The third -case shall be the real one of the waters moving with a velocity -between these two, neither so swift as the first case -requires, nor so slow as the second.</p> - -<p><span class="pagenum"><a name="Page_286" id="Page_286">[286]</a></span></p> - -<p>20. <span class="smcap gesperrt">In</span> the first case the waters, like the body which -they equalled in velocity, by the action of the moon would -be brought nearer the center under and opposite to the moon, -than in the parts in the middle between these eastward or -westward. That such a body would so alter its distance by -the moon’s action upon it, is clear from what has been -mentioned of the like changes in the moon’s motion caused -by the sun<a name="FNanchor_270_270" id="FNanchor_270_270"></a><a href="#Footnote_270_270" class="fnanchor">[270]</a>. And computation shews, that the difference -between the greatest and least distance of such a body -would not be much above 4½ feet. But in the second -case, where all the parts of the water preserve the same situation -continually in respect of the moon, the weight of those -parts under and opposite to the moon will be diminished -by the moon’s action, and the parts in the middle between -these will have their weight increased: this being effected -just in the same manner, as the sun diminishes the attraction -of the moon towards the earth in the conjunction and -opposition, but increases that attraction in the quarters. -For as the first of these consequences from the sun’s action -on the moon is occasioned by the moon’s being attracted -by the sun in the conjunction more than the earth, -and in the opposition less than it, and therefore in the -common motion of the earth and moon, the moon is -made to advance toward the sun in one case too fast, and -in the other is left as it were behind; so the earth will -not have its middle parts drawn towards the moon so strongly -as the nearer parts, and yet more forcibly than the remotest: -and therefore since the earth and moon move each<span class="pagenum"><a name="Page_287" id="Page_287">[287]</a></span> -month round their common center of gravity<a name="FNanchor_271_271" id="FNanchor_271_271"></a><a href="#Footnote_271_271" class="fnanchor">[271]</a>, while -the earth moves round this center, the same effect will be -produced, on the parts of the water nearest to that center -or to the moon, as the moon feels from the sun when -in conjunction, and the water on the contrary side of the -earth will be affected by the moon, as the moon is by the -sun, when in opposition<a name="FNanchor_272_272" id="FNanchor_272_272"></a><a href="#Footnote_272_272" class="fnanchor">[272]</a>; that is, in both cases the weight -of the water, or its propensity towards the center of the -earth, will be diminished. The parts in the middle between -these will have their weight increased, by being pressed -towards the center of the earth through the obliquity of -the moon’s action upon them to its action upon the earth’s -center, just as the sun increases the gravitation of the moon -in the quarters from the same cause<a name="FNanchor_273_273" id="FNanchor_273_273"></a><a href="#Footnote_273_273" class="fnanchor">[273]</a>. But now it is manifest, -that where the weight of the same quantity of water -is least, there it will be accumulated; while the parts, which -have the greatest weight, will subside. Therefore in this -case there would be no tide or alternate rising and falling -of the water, but the water would form it self into an -oblong figure, whose axis prolonged would pass through -the moon. By Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em>’s computation the -excess of this axis above the diameters perpendicular to it, -that is, the height of the waters under and opposite to the -moon above their height in the middle between these places -eastward or westward caused by the moon, is about -8⅔ feet.</p> - -<p><span class="pagenum"><a name="Page_288" id="Page_288">[288]</a></span></p> - -<p>21. <span class="smcap gesperrt">Thus</span> the difference of height in this latter supposition -is little short of twice that difference in the preceding. -But the case of the sea is a middle between these -two: for a body, which should revolve round the center -of the earth at the distance of a semidiameter without pressing -on the earth’s surface, must perform its period in less than -an hour and half, whereas the earth turns round but once -in a day; and in the case of the waters keeping pace with -the moon it should turn round but once in a month: so -that the real motion of the water is between the motions required -in these two cases. Again, if the waters moved round -as swiftly as the first case required, their weight would be -wholly taken off by their motion; for this case supposes -the body to move so, as to be kept revolving in a circle -round the earth by the power of gravity without pressing -on the earth at all, so that its motion just supports its weight. -But if the power of gravity had been only 1/289 part of -what it is, the body could have moved thus without pressing -on the earth, and have been as long in moving round, -as the earth it self is. Consequently the motion of the -earth takes off from the weight of the water in the middle -between the poles, where its motion is swiftest, 1/289 part -of its weight and no more. Since therefore in the first -case the weight of the waters must be intirely taken off by -their motion, and by the real motion of the earth they lose -only 1/289 part thereof, the motion of the water will so little -diminish their weight, that their figure will much nearer resemble -the case of their keeping pace with the moon than the -other. Upon the whole, if the waters moved with the<span class="pagenum"><a name="Page_289" id="Page_289">[289]</a></span> -velocity necessary to carry a body round the center of the -earth at the distance of the earth’s semidiameter without -bearing on its surface, the water would be lowest under -the moon, and rise gradually as it moved on with the earth -eastward, till it came half way toward the place opposite -to the moon; from thence it would subside again, till it -came to the opposition, where it would become as low as -at first; afterwards it would rise again, till it came half -way to the place under the moon; and from hence it -would subside, till it came a second time under the moon. -But in case the water kept pace with the moon, it -would be highest where in the other case it is lowest, -and lowest where in the other it is highest; therefore the -diurnal motion of the earth being between the motions of -these two cases, it will cause the highest place of the water to -fall between the places of the greatest height in these two -cases. The water as it passes from under the moon shall -for some time rise, but descend again before it arrives half -way to the opposite place, and shall come to its least -height before it becomes opposite to the moon; then it shall -rise again, continuing so to do till it has passed the place -opposite to the moon, but subside before it comes to the -middle between the places opposite to and under the moon; -and lastly it shall come to its lowest, before it comes a second -time under the moon. If A (in fig. 112, 113, 114.) -represent the moon, B the center of the earth, the oval C D E F -in fig. 112. will represent the situation of the water in the -first case; but if the water kept pace with the moon, -the line C D E F in fig. 113. would represent the situation<span class="pagenum"><a name="Page_290" id="Page_290">[290]</a></span> -of the water; but the line C D E F in fig. 114. will represent -the same in the real motion of the water, as it -accompanies the earth in its diurnal rotation: in all these -figures C and E being the places where the water is lowest, -and D and F the places where it is highest. Pursuant -to this determination it is found, that on the shores, -which lie exposed to the open sea, the high water usually -falls out about three hours after the moon has passed the -meridian of each place.</p> - -<p>22. <span class="smcap gesperrt">Let</span> this suffice in general for explaining the manner, -in which the moon acts upon the seas. It is farther -to be noted, that these effects are greatest, when the moon -is over the earth’s equator<a name="FNanchor_274_274" id="FNanchor_274_274"></a><a href="#Footnote_274_274" class="fnanchor">[274]</a>, that is, when it shines perpendicularly -upon the parts of the earth in the middle between -the poles. For if the moon were placed over either of the -poles, it could have no effect upon the water to make it ascend -and descend. So that when the moon declines from the equator -toward either pole, it’s action must be something -diminished, and that the more, the farther it declines. The -tides likewise will be greatest, when the moon is -nearest to the earth, it’s action being then the strongest.</p> - -<p>23. <span class="smcap gesperrt">Thus</span> much of the action of the moon. That -the sun should produce the very same effects, though in -a less degree, is too obvious to require a particular explanation: -but as was remarked before, this action of the<span class="pagenum"><a name="Page_291" id="Page_291">[291]</a></span> -sun being weaker than that of the moon, will cause the -tides to follow more nearly the moon’s course, and principally -shew it self by heightening or diminishing the effects -of the other luminary. Which is the occasion, that -the highest tides are found about the conjunction and opposition -of the luminaries, being then produced by their united -action, and the weakest tides about the quarters of -the moon; because the moon in this case raising the water -where the sun depresses it, and depressing it where the -sun raises it, the stronger action of the moon is in part -retunded and weakened by that of the sun. Our author -computes that the sun will add near two feet to the height -of the water in the first case, and in the other take from -it as much. However the tides in both comply with the -same hour of the moon. But at other times, between -the conjunction or opposition and quarters, the time deviates -from that forementioned, towards the hour in which -the sun would make high water, though still it keeps much -nearer to the moon’s hour than to the sun’s.</p> - -<p>24. <span class="smcap gesperrt">Again</span> the tides have some farther varieties from -the situation of the places where they happen northward -or southward. Let <i>p</i> P (in fig. 115.) represent the axis, on -which the earth daily revolves, let <i>h</i> <i>p</i> H P represent the -figure of the water, and let <i>n</i> B N D be a globe inscribed -within this figure. Suppose the moon to be advanced -from the equator toward the north pole, so that <i>h</i> H the -axis of the figure of the water <i>p</i> A H P E <i>h</i> shall decline -towards the north pole N; take any place G nearer to<span class="pagenum"><a name="Page_292" id="Page_292">[292]</a></span> -the north pole than to the south, and from the center -of the earth C draw C G F; then will G F denote the altitude -to which the water is raised by the tide, when the moon is -above the horizon: in the space of twelve hours, the earth -having turned half round its axis, the place G will be removed -to <i>g</i>; but the axis <i>h</i> H will have kept its place preserving its -situation in respect of the moon, at least will have moved no -more than the moon has done in that time, which it is not -necessary here to take into consideration. Now in this case -the height of the water will be equal to <i>g</i> <i>f</i>, which is -not so great as G F. But whereas G F is the altitude at -high water, when the moon is above the horizon, <i>g</i> <i>f</i> will -be the altitude of the same, when the moon is under the -horizon. The contrary happens toward the south pole, for -K L is less than <i>k</i> <i>l</i>. Hence is proved, that when the moon -declines from the equator, in those places, which are on -the same side of the equator as the moon, the tides are -greater, when the moon is above the horizon, than when -under it; and the contrary happens on the other side of -the equator.</p> - -<p>25. <span class="smcap gesperrt">Now</span> from these principles may be explained all -the known appearances in the tides; only by the assistance -of this additional remark, that the fluctuating motion, -which the water has in flowing and ebbing, is of a -durable nature, and would continue for some time, though -the action of the luminaries should cease; for this prevents -the difference between the tide when the moon is above<span class="pagenum"><a name="Page_293" id="Page_293">[293]</a></span> -the horizon, and the tide when the moon is below it from -being so great, as the rule laid down requires. This likewise -makes the greatest tides not exactly upon the new and full -moon, but to be a tide or two after; as at Bristol and Plymouth -they are found the third after.</p> - -<p>26. <span class="smcap gesperrt">This</span> doctrine farther shews us, why not only the -spring tides fall out about the new and full moon, and the -neap tides about the quarters; but likewise how it comes -to pass, that the greatest spring tides happen about the equinoxes; -because the luminaries are then one of them over the -equator, and the other not far from it. It appears too, why -the neap tides, which accompany these, are the least of all, -for the sun still continuing over the equator continues to have -the greatest power of lessening the moon’s action, and the -moon in the quarters being far removed toward one of the -poles, has its power thereby weakned.</p> - -<p>27. <span class="smcap gesperrt">Moreover</span> the action of the moon being stronger, -when near the earth, than when more remote; if the moon, -when new suppose, be at its nearest distance from the earth, -it shall when at the full be farthest off; whence it is, that -two of the very largest spring tides do never immediately -succeed each other.</p> - -<p>28. <span class="smcap gesperrt">Because</span> the sun in its passage from the winter -solstice to the summer recedes from the earth, and passing -from the summer solstice to the winter approaches it, and -is therefore nearer the earth before the vernal equinox than<span class="pagenum"><a name="Page_294" id="Page_294">[294]</a></span> -after, but nearer after the autumnal equinox than before; -the greatest tides oftner precede the vernal equinox than -follow it, and in the autumnal equinox on the contrary -they oftner follow it than come before it.</p> - -<p>29. <span class="smcap gesperrt">The</span> altitude, to which the water is raised in the -open ocean, corresponds very well to the forementioned calculations; -for as it was shewn, that the water in spring tides -should rise to the height of 10 or 11 feet, and the neap -tides to 6 or 7; accordingly in the Pacific, Atlantic and -Ethiopic oceans in the parts without the tropics, the -water is observed to rise about 6, 9, 12 or 15 feet. In the -Pacific ocean this elevation is said to be greater than in the -other, as it ought to be by reason of the wide extent of -that sea. For the same reason in the Ethiopic ocean between -the tropics the ascent of the water is less than without, -by reason of the narrowness of the sea between the -coasts of Africa and the southern parts of America. -And islands in such narrow seas, if far from shore, have -less tides than the coasts. But now in those ports where -the water flows in with great violence upon fords and shoals, -the force it acquires by that means will carry it to a much -greater height, so as to make it ascend and descend to 30, -40 or even 50 feet and more; instances of which we have -at Plymouth, and in the Severn near Chepstow; at -St. Michael’s and Auranches in Normandy; at Cambay and -Pegu in the East Indies.</p> - -<p>30. <span class="smcap gesperrt">Again</span> the tides take a considerable time in passing -through long straits, and shallow places. Thus the tide,<span class="pagenum"><a name="Page_295" id="Page_295">[295]</a></span> -which is made on the west coast of Ireland and on the -coast of Spain at the third hour after the moon’s coming -to the meridian, in the ports eastward toward the British -channel falls out later, and as the flood passes up that channel -still later and later, so that the tide takes up full twelve -hours in coming up to London bridge.</p> - -<p>31. <span class="smcap gesperrt">In</span> the last place tides may come to the same port -from different seas, and as they may interfere with each -other, they will produce particular effects. Suppose the -tide from one sea come to a port at the third hour after -the moon’s passing the meridian of the place, but from -another sea to take up six hours more in its passage. Here -one tide will make high water, when by the other it should -be lowest; so that when the moon is over the equator, and -the two tides are equal, there will be no rising and falling -of the water at all; for as much as the water is carried off -by one tide, it will be supplied by the other. But when the -moon declines from the equator, the same way as the port -is situated, we have shewn that of the two tides of the -ocean, which are made each day, that tide, which is made -when the moon is above the horizon, is greater than the -other. Therefore in this case, as four tides come to this -port each day the two greatest will come on the third, and -on the ninth hour after the moon’s passing the meridian, -and the two least at the fifteenth and at the twenty first -hour. Thus from the third to the ninth hour more water -will be in this port by the two greatest tides than from -the ninth to the fifteenth, or from the twenty first to the<span class="pagenum"><a name="Page_296" id="Page_296">[296]</a></span> -following third hour, where the water is brought by one -great and one small tide; but yet there will be more -water brought by these tides, than what will be found between -the two least tides, that is, between the fifteenth and -twenty first hour. Therefore in the middle between the -third and ninth hour, or about the moon’s setting, the water -will be at its greatest height; in the middle between the -ninth and fifteenth, as also between the twenty first and -following third hour it will have its mean height; and be -lowest in the middle between the fifteenth and twenty first -hour, that is, at the moon’s rising. Thus here the water -will have but one flood and one ebb each day. When the -moon is on the other side of the equator, the flood will be -turned into ebb, and the ebb into flood; the high water falling -out at the rising of the moon, and the low water at -the setting. Now this is the case of the port of Batsham -in the kingdom of Tunquin in the East Indies; to which -port there are two inlets, one between the continent and the -islands which are called the Manillas, and the other between -the continent and Borneo.</p> - -<p><a name="c296" id="c296">32.</a> <span class="smcap gesperrt">The</span> next thing to be considered is the effect, which -these fluids of the planets have upon the solid part of the -bodies to which they belong. And in the first place I -shall shew, that it was necessary upon account of these fluid -parts to form the bodies of the planets into a figure something -different from that of a perfect globe. Because the -diurnal rotation, which our earth performs about its axis, -and the like motion we see in some of the other planets,<span class="pagenum"><a name="Page_297" id="Page_297">[297]</a></span> -(which is an ample conviction that they all do the like) will -diminish the force, with which bodies are attracted upon -all the parts of their surfaces, except at the very poles, -upon which they turn. Thus a stone or other weighty -substance resting upon the surface of the earth, by the -force which it receives from the motion communicated to -it by the earth, if its weight prevented not, would continue -that motion in a straight line from the point where -it received it, and according to the direction, in which it -was given, that is, in a line which touches the surface at -that point; insomuch that it would move off from the -earth in the same manner, as a weight fasten’d to a string -and whirled about endeavours continually to recede from -the center of motion, and would forthwith remove it self -to a greater distance from it, if loosed from the string which -retains it. And farther, as the centrifugal force, with which -such a weight presses from the center of its motion, is -greater, by how much greater the velocity is, with which -it moves; so such a body, as I have been supposing to lie -on the earth, would recede from it with the greater force, -the greater the velocity is, with which the part of the -earth’s surface it rests upon is moved, that is, the farther -distant it is from the poles. But now the power of gravity -is great enough to prevent bodies in any part of the earth -from being carried off from it by this means; however it is -plain that bodies having an effort contrary to that of gravity, -though much weaker than it, their weight, that is, the degree -of force, with which they are pressed to the earth, -will be diminished thereby, and be the more diminished,<span class="pagenum"><a name="Page_298" id="Page_298">[298]</a></span> -the greater this contrary effort is; or in other words, the -same body will weigh heavier at either of the poles, than -upon any other part of the earth; and if any body be -removed from the pole towards the equator, it will lose -of its weight more and more, and be lightest of all at -the equator, that is, in the middle between the poles.</p> - -<p>33. <span class="smcap gesperrt">This</span> now is easily applied to the waters of the seas, -and shews that the water under the poles will press more forcibly -to the earth, than at or near the equator: and consequently -that which presses least, must give place, till by ascending -it makes room for receiving a greater quantity, which by -its additional weight may place the whole upon a ballance. -To illustrate this more particularly I shall make use of fig. 116 -In which let A C B D be a circle, by whose revolution about -the diameter A B a globe should be formed, representing a -globe of solid earth. Suppose this globe covered on all sides -with water to the same height, suppose that of E A or B F, -at which distance the circle E G F H surrounds the circle -A C B D; then it is evident, if the globe of earth be at rest, -the water which surrounds it will rest in that situation. -But if the globe be turned incessantly about its axis A B, -and the water have likewise the same motion, it is also -evident, from what has been explained, that the water between -the circles E H F G and A D B C will remain no longer -in the present situation, the parts of it between H and D, and -between G and C being by this rotation become lighter, than -the parts between E and A and between B and F; so that the -water over the poles A and B must of necessity subside, and the<span class="pagenum"><a name="Page_299" id="Page_299">[299]</a></span> -water be accumulated over D and C, till the greater quantity -in these latter places supply the defect of its weight. -This would be the case, were the globe all covered with -water. And the same figure of the surface would also be -preserved, if some part of the water adjoining to the globe -in any part of it were turned into solid earth, as is too -evident to need any proof; because the parts of the water -remaining at rest, it is the same thing, whether they continue -in the state of being easily separable, which denominates -them fluid, or were to be consolidated together, so -as to make a hard body: and this, though the water should -in some places be thus consolidated, even to the surface of it. -Which shews that the form of the solid part of the earth makes -no alteration in the figure the water will take: and by -consequence in order to the preventing some parts of the -earth from being entirely overflowed, and other parts -quite deserted, the solid parts of the earth must have given -them much the same figure, as if the whole earth were -covered on all sides with water.</p> - -<p>34. <span class="smcap gesperrt">Farther</span>, I say, this figure of the earth is the -same, as it would receive, were it entirely a globe of water, -provided that water were of the same density as the substance -of the globe. For suppose the globe A C B D to be -liquified, and that the globe E H F G, now entirely water, -by its rotation about its axis should receive such a figure -as we have been describing, and then the globe A C B D -should be consolidated again, the figure of the water -would plainly not be altered, by such a consolidation.</p> - -<p><span class="pagenum"><a name="Page_300" id="Page_300">[300]</a></span></p> - -<p>35. <span class="smcap gesperrt">But</span> from this last observation our author is enabled -to determine the proportion between the axis of the -earth drawn from pole to pole, and the diameter of the equator, -upon the supposition that all the parts of the earth are -of equal density; which he does by computing in the first -place the proportion of the centrifugal force of the parts under -the equator to the power of gravity; and then by considering -the earth as a spheroid, made by the revolution -of an ellipsis about its lesser axis, that is, supposing the -line M I L K to be an exact ellipsis, from which it can differ -but little, by reason that the difference between the -lesser axis M L and the greater I K is but very small. From -this supposition, and what was proved before, that all the -particles which compose the earth have the attracting power -explained in the preceding chapter, he finds at what distance -the parts under the equator ought to be removed from -the center, that the force, with which they shall be attracted -to the center, diminished by their centrifugal force, shall -be sufficient to keep those parts in a ballance with those which -lie under the poles. And upon the supposition of all the -parts of the earth having the same degree of density, the -earth’s surface at the equator must be above 17 miles more -distant from the center, than at the poles<a name="FNanchor_275_275" id="FNanchor_275_275"></a><a href="#Footnote_275_275" class="fnanchor">[275]</a>.</p> - -<p><a name="c300" id="c300">36.</a> <span class="smcap gesperrt">After</span> this it is shewn, from the proportion of the -equatorial diameter of the earth to its axis, how the same -may be determined of any other planet, whose density in<span class="pagenum"><a name="Page_301" id="Page_301">[301]</a></span> -comparison of the density of the earth, and the time of its -revolution about its axis, are known. And by the rule delivered -for this, it is found, that the diameter of the equator -in Jupiter should bear to its axis about the proportion -of 10 to 9<a name="FNanchor_276_276" id="FNanchor_276_276"></a><a href="#Footnote_276_276" class="fnanchor">[276]</a>, and accordingly this planet appears of an oval -form to the astronomers. The most considerable effects -of this spheroidical figure our author takes likewise -into consideration; one of which is that bodies are not equally -heavy in all distances from the poles; but near the equator, -where the distance from the center is greatest, they are -lighter than towards the poles: and nearly in this proportion, -that the actual power, by which they are drawn to the center, -resulting from the difference between their absolute gravity -and centrifugal force, is reciprocally as the distance from -the center. That this may not appear to contradict what -has before been said of the alteration of the power of gravity, -in proportion to the change of the distance from the center, -it is proper carefully to remark, that our author has -demonstrated three things relating hereto: the first is, that -decrease of the power of gravity as we recede from the -center, which has been fully explained in the last chapter, -upon supposition that the earth and planets are perfect -spheres, from which their difference is by many degrees too -little to require notice for the purposes there intended: the -next is, that whether they be perfect spheres, or exactly such -spheroids as have now been mentioned, the power of gravity, -as we descend in the same line to the center, is at all -distances as the distance from the center, the parts of the<span class="pagenum"><a name="Page_302" id="Page_302">[302]</a></span> -earth above the body by drawing the body towards them -lessening its gravitation towards the center<a name="FNanchor_277_277" id="FNanchor_277_277"></a><a href="#Footnote_277_277" class="fnanchor">[277]</a>; and both -these assertions relate to gravity alone: the third is what -we mentioned in this place, that the actual force on different -parts of the surface, with which bodies are drawn to the -center, is in the proportion here assigned<a name="FNanchor_278_278" id="FNanchor_278_278"></a><a href="#Footnote_278_278" class="fnanchor">[278]</a>.</p> - -<p><a name="c302" id="c302">38.</a> <span class="smcap gesperrt">The</span> next effect of this figure of the earth is an -obvious consequence of the former: that pendulums of -the same length do not in different distances from the pole -make their vibrations in the same time; but towards the poles, -where the gravity is strongest, they move quicker than near -the equator, where they are less impelled to the center; and -accordingly pendulums, that measure the same time by their -vibrations, must be shorter near the poles than at a greater -distance. Both which deductions are found true in fact; of -which our author has recounted particularly several experiments, -in which it was found, that clocks exactly adjusted to -the true measure of time at Paris, when transported nearer to -the equator, became erroneous and moved too slow, but were -reduced to their true motion by contracting their pendulums. -Our author is particular in remarking, how much they lost of -their motion, while the pendulums remained unaltered; and -what length the observers are said to have shortened them, to -bring them to time. And the experiments, which appear -to be most carefully made, shew the earth to be raised in -the middle between the poles, as much as our author found -it by his computation<a name="FNanchor_279_279" id="FNanchor_279_279"></a><a href="#Footnote_279_279" class="fnanchor">[279]</a>.</p> - -<p><span class="pagenum"><a name="Page_303" id="Page_303">[303]</a></span></p> - -<p>39. <span class="smcap gesperrt">These</span> experiments on the pendulum our author -has been very exact in examining, inquiring particularly -how much the extension of the rod of the pendulum by -the great heats in the torrid zone might make it necessary -to shorten it. For by an experiment made by <span class="smcap">Picart</span>, and -another made by <span class="smcap">De la Hire</span>, heat, though not very intense, -was found to increase the length of rods of iron. The experiment -of <span class="smcap">Picart</span> was made with a rod one foot long, -which in winter, at the time of frost, was found to increase -in length by being heated at the fire. In the experiment -of <span class="smcap">De la Hire</span> a rod of six foot in length was found, -when heated by the summer sun only, to grow to a greater -length, than it had in the aforesaid cold season. From which -observations a doubt has been raised, whether the rod of the -pendulums in the aforementioned experiments was not -extended by the heat of those warm climates to all that -excess of length, the observers found themselves obliged -to lessen them by. But the experiments now mentioned -shew the contrary. For in the first of them the rod of a -foot long was lengthened no more than 1/9 part of what the -pendulum under the equator must be diminished; and therefore -a rod of the length of the pendulum would not have been -extended above ⅓ of that length. In the experiment -of <span class="smcap">De la Hire</span>, where the heat was less, the rod of six foot -long was extended no more than 3/10 of what the pendulum -must be shortened; so that a rod of the length of the pendulum -would not have gained above 3/20 or 1/7 of that length. -And the heat in this latter experiment, though less than in the -former, was yet greater than the rod of a pendulum can ordinarily<span class="pagenum"><a name="Page_304" id="Page_304">[304]</a></span> -contract in the hottest country; for metals receive a -great heat when exposed to the open sun, certainly much -greater than that of a human body. But pendulums are not -usually so exposed, and without doubt in these experiments -were kept cool enough to appear so to the touch; which they -would do in the hottest place, if lodged in the shade. Our -author therefore thinks it enough to allow about 1/10 of the -difference observed upon account of the greater warmth of -the pendulum.</p> - -<p><a name="c304" id="c304">40.</a> <span class="smcap gesperrt">There</span> is a third effect, which the water has on the -earth by changing its figure, that is taken notice of by -our author; for the explaining of which we shall first prove, -that bodies descend perpendicularly to the surface of the -earth in all places. The manner of collecting this from observation, -is as follows. The surfaces of all fluids rest parallel -to that part of the surface of the sea, which is in the same -place with them, to the figure of which, as has been particularly -shewn, the figure of the whole earth is formed. For -if any hollow vessel, open at the bottom, be immersed into -the sea; it is evident, that the surface of the sea within the -vessel will retain the same figure it had, before the vessel -inclosed it; since its communication with the external water -is not cut off by the vessel. But all the parts of the water -being at rest, it is as clear, that if the bottom of the vessel -were closed, the figure of the water could receive no change -thereby, even though the vessel were raised out of the -sea; any more than from the insensible alteration of the -power of gravity, consequent upon the augmentation of<span class="pagenum"><a name="Page_305" id="Page_305">[305]</a></span> -the distance from the center. But now it is clear, that bodies -descend in lines perpendicular to the surfaces of quiescent fluids; -for if the power of gravity did not act perpendicularly -to the surface of fluids, bodies which swim on them -could not rest, as they are seen to do; because, if the power -of gravity drew such bodies in a direction oblique to the -surface whereon they lay, they would certainly be put in -motion, and be carried to the side of the vessel, in which -the fluid was contained, that way the action of gravity inclined.</p> - -<p>41. <span class="smcap gesperrt">Hence</span> it follows, that as we stand, our bodies are -perpendicular to the surface of the earth. Therefore in -going from north to south our bodies do not keep in a -parallel direction. Now in all distances from the pole the -same length gone on the earth will not make the same -change in the position of our bodies, but the nearer we -are to the poles, we must go greater length to cause the -same variation herein. Let M I L K (in fig. 117) represent -the figure of the earth, M, L the poles, I, K two opposite -points in the middle between these poles. Let T V -and P O be two arches, T V being most remote from the pole -L; draw T W, V X, P Q, O R, each perpendicular to the -surface of the earth, and let T W, V X meet in Y, and -P Q, O R in S. Here it is evident, that in passing from V to -T the position of a man’s body would be changed by the -angle under T Y V, for at V he would stand in the line Y V -continued upward, and at T in the line Y T; but in passing -from O to P the position of his body would be changed by<span class="pagenum"><a name="Page_306" id="Page_306">[306]</a></span> -the angle under O S P. Now I say, if these two angles are -equal the arch O P is longer than T V: for the figure M I L K -being oblong, and I K longer than M L, the figure will be -more incurvated toward I than toward L; so that the lines -T W and V X will meet in Y before they are drawn out to -so great a length as the lines P Q and O R must be continued -to, before they will meet in S. Since therefore Y T and -Y V are shorter than P S and S V, T V must be less than O P. -If these angles under T Y V and O S P are each 1/90 part of -the angle made by a perpendicular line, they are said each -to contain one degree. And the unequal length of these -arches O P and V T gives occasion to the assertion, that in -passing from north to south the degrees on the earth’s surface -are not of an equal length, but those near the pole -longer than those toward the equator. For the length of -the arch on the earth lying between the two perpendiculars, -which make an angle of a degree with each other, is -called the length of a degree on the earth’s surface.</p> - -<p>42. <span class="smcap gesperrt">This</span> figure of the earth has some effect on eclipses. -It has been observed above, that sometimes the nodes of the -moon’s orbit lie in a straight line drawn from the sun to -the earth; in which case the moon will cross the plane of -the earth’s motion at the new and full. But whenever the -moon passes near the plane at the full, some part of the -earth will intercept the sun’s light, and the moon shining -only with light borrow’d from the sun, when that light is -prevented from falling on any part of the moon, so much -of her body will be darkened. Also when the moon at the<span class="pagenum"><a name="Page_307" id="Page_307">[307]</a></span> -new is near the plane of the earth’s motion, the inhabitants -on some part of the earth will see the moon come under -the sun, and the sun thereby be covered from them either -wholly or in part. Now the figure, which we have shewn -to belong to the earth, will occasion the shadow of the -earth on the moon not to be perfectly round, but cause the -diameter from east to west to be somewhat longer than the -diameter from north to south. In eclipse of the sun this -figure of the earth will make some little difference in the -place, where the sun shall appear wholly or in any given -part covered. Let A B C D (in fig. 118.) represent the earth, -A C the axis whereon it turns daily, E the center. Let F A G C -represent a perfect globe inscribed within the earth. Let H I -be a line drawn through the centers of the sun and moon, crossing -the surface of the earth in K, and the surface of the -globe inscribed in L. Draw E L, which will be perpendicular -to the surface of the globe in L: and draw likewise K M, -so that it shall be perpendicular to the surface of the earth -in K. Now whereas the eclipse would appear central at L, -if the earth were the globe A G C F, and does really appear -so at K; I say, the latitude of the place K on the real earth -is different from the latitude of the place L on the globe -F A G C. What is called the latitude of any place is determined -by the angle which the line perpendicular to the surface of -the earth at that place makes with the axis; the difference -between this angle, and that made by a perpendicular line or -square being called the latitude of each place. But it might -here be proved, that the angle which K M makes with M C -is less, than the angle made between L E and E C: consequently<span class="pagenum"><a name="Page_308" id="Page_308">[308]</a></span> -the latitude of the place K is greater, than the latitude, -which the place L would have.</p> - -<p>43. <span class="smcap gesperrt">The</span> next effect, which follows from this figure of -the earth, is that gradual change in the distance of the fixed -stars from the equinoctial points, which astronomers observe. -But before this can be explained, it is necessary to -say something more particular, than has yet been done, -concerning the manner of the earth’s motion round the sun.</p> - -<p>44. <span class="smcap gesperrt">It</span> has already been said, that the earth turns round -each day on its own axis, while its whole body is carried -round the sun once in a year. How these two motions -are joined together may be conceived in some degree by -the motion of a bowl on the ground, where the bowl in -rouling on continually turns upon its axis, and at the same -time the whole body thereof is carried straight on. But -to be more express let A (in fig. 119) represent the sun -B C D E four different situations of the earth in its orbit -moving about the sun. In all these let F G represent the -axis, about which the earth daily turns. The points F, G -are called the poles of the earth; and this axis is supposed -to keep always parallel to it self in every situation of -the earth; at least that it would do so, were it not for a -minute deviation, the cause whereof will be explained in -what follows. When the earth is in B, the half H I K will -be illuminated by the sun, and the other half H L K will -be in darkness. Now if on the globe any point be taken<span class="pagenum"><a name="Page_309" id="Page_309">[309]</a></span> -in the middle between the poles, this point shall describe -by the motion of the globe the circle M N, half of which -is in the enlightened part of the globe, and half in the -dark part. But the earth is supposed to move round its axis -with an equable motion; therefore on this point of the -globe the sun will be seen just half the day, and be invisible -the other half. And the same will happen to every -point of this circle, in all situations of the earth during its -whole revolution round the sun. This circle M N is called -the equator, of which we have before made mention.</p> - -<p>45. <span class="smcap gesperrt">Now</span> suppose any other point taken on the surface -of the globe toward the pole F, which in the diurnal revolution -of the globe shall describe the circle O P. Here -it appears that more than half this circle is enlightned by -the sun, and consequently that in any particular point of -this circle the sun will be longer seen than lie hid, that is -the day will be longer than the night. Again if we consider -the same circle O P on the globe situated in D the opposite -part of the orbit from B, we shall see, that here in -any place of this circle the night will be as much longer -than the day.</p> - -<p>46. <span class="smcap gesperrt">In</span> these situations of the globe of earth a line -drawn from the sun to the center of the earth will be -obliquely inclined toward the axis F G. Now suppose, that -such a line drawn from the sun to the center of the earth, -when in C or E, would be perpendicular to the axis F G;<span class="pagenum"><a name="Page_310" id="Page_310">[310]</a></span> -in which cases the sun will shine perpendicularly upon the -equator, and consequently the line drawn from the center -of the earth to the sun will cross the equator, as it passes -through the surface of the earth; whereas in all other situations -of the globe this line will pass through the surface -of the globe at a distance from the equator either northward -or southward. Now in both these cases half the circle -O P will be in the light, and half in the dark; and therefore -to every place in this circle the day will be equal -to the night. Thus it appears, that in these two opposite -situations of the earth the day is equal to the night in all -parts of the globe; but in all other situations this equality -will only be found in places situated in the very middle -between the poles, that is, on the equator.</p> - -<p>47. <span class="smcap gesperrt">The</span> times, wherein this universal equality between -the day and night happens, are called the equinoxes. Now -it has been long observed by astronomers, that after the -earth hath set out from either equinox, suppose from E -(which will be the spring equinox, if F be the north pole) -the same equinox shall again return a little before the earth -has made a compleat revolution round the sun. This return -of the equinox preceding the intire revolution of the -earth is called the precession of the equinox, and is caused -by the protuberant figure of the earth.</p> - -<p>49. <span class="smcap gesperrt">Since</span> the sun shines perpendicularly upon the equator, -when the line drawn from the sun to the center -of the earth is perpendicular to the earth’s axis, in this case<span class="pagenum"><a name="Page_311" id="Page_311">[311]</a></span> -the plane, which should cut through the earth at the equator, -may be extended to pass through the sun; but it -will not do so in any other position of the earth. Now -let us consider the prominent part of the earth about the -equator, as a solid ring moving with the earth round the -sun. At the time of the equinoxes, this ring will have -the same kind of situation in respect of the sun, as the -orbit of the moon has, when the line of the nodes is directed -to the sun; and at all other times will resemble the -moon’s orbit in other situations. Consequently this ring, -which otherwise would keep throughout its motion parallel -to it self, will receive some change in its position from -the action of the sun upon it, except only at the time of -the equinox. The manner of this change may be understood -as follows. Let A B C D (in fig. 120) represent this ring, -E the center of the earth, S the sun, A F C G a circle described -in the plane of the earth’s motion to the center E. -Here A and C are the two points, in which the earth’s equator -crosses the plane of the earth’s motion; and the time -of the equinox falls out, when the straight line A C continued -would pass through the sun. Now let us recollect -what was said above concerning the moon, when her orbit -was in the same situation with this ring. From thence -it will be understood, if a body were supposed to be moving -in any part of this circle A B C D, what effect the action -of the sun on the body would have toward changing -the position of the line A C. In particular H I being drawn -perpendicular to S E, if the body be in any part of this -circle between A and H, or between C and I, the line A C<span class="pagenum"><a name="Page_312" id="Page_312">[312]</a></span> -would be so turned, that the point A shall move toward B, -and the point C toward D; but if it were in any other part -of the circle, either between H and C, or between I and A, -the line A C would be turned the contrary way. Hence -it follows, that as this solid ring turns round the center -of the earth, the parts of this ring between A and H, and -between C and I, are so influenced by the sun, that they -will endeavour, so to change the situation of the line A C -as to cause the point A to move toward B, and the point -C to move toward D; but all the parts of the ring between -H and C, and between I and A, will have the opposite -tendency, and dispose the line A C to move the contrary -way. And since these last named parts are larger than -the other, they will prevail over the other, so that by the -action of the sun upon this ring, the line A C will be so -turned, that A shall continually be more and more moving -toward D, and C toward B. Thus no sooner shall the -sun in its visible motion have departed from A, but the motion -of the line A C shall hasten its meeting with C, and -from thence the motion of this line shall again hasten the -sun’s second conjunction with A; for as this line so turns, -that A is continually moving toward D, so the sun’s visible -motion is the same way as from S toward T.</p> - -<p>49. <span class="smcap gesperrt">The</span> moon will have on this ring the like effect as -the sun, and operate on it more strongly, in the same proportion -as its force on the sea exceeded that of the sun on the -same. But the effect of the action of both luminaries will -be greatly diminished by reason of this ring’s being connected<span class="pagenum"><a name="Page_313" id="Page_313">[313]</a></span> -to the rest of the earth; for by this means the sun and -moon have not only this ring to move, but likewise the -whole globe of the earth, upon whose spherical part they have -no immediate influence. Beside the effect is also rendred -less, by reason that the prominent part of the earth is not -collected all under the equator, but spreads gradually from -thence toward both poles. Upon the whole, though the -sun alone carries the nodes of the moon through an intire -revolution in about 19 years, the united force of both luminaries -on the prominent parts of the earth will hardly -carry round the equinox in a less space of time than 26000 -years.</p> - -<p><a name="c313a" id="c313a">50.</a> <span class="smcap gesperrt">To</span> this motion of the equinox we must add another -consequence of this action of the sun and moon upon -the elevated parts of the earth, that this annular part of the -earth about the equator, and consequently the earth’s axis, -will twice a year and twice a month change its inclination -to the plane of the earth’s motion, and be again restored, -just as the inclination of the moon’s orbit by the action of -the sun is annually twice diminished, and as often recovers its -original magnitude. But this change is very insensible.</p> - -<p><a name="c313b" id="c313b">51.</a> <span class="smcap gesperrt">I shall</span> now finish the present chapter with our great -author’s inquiry into the figure of the secondary planets, particularly -of our moon, upon the figure of which its fluid -parts will have an influence. The moon turns always the -same side towards the earth, and consequently revolves -but once round its axis in the space of an entire month;<span class="pagenum"><a name="Page_314" id="Page_314">[314]</a></span> -for a spectator placed without the circle, in which the moon -moves, would in that time observe all the parts of the moon -successively to pass once before his view and no more, that -is, that the whole globe of the moon has turned once round. -Now the great slowness of this motion will render the centrifugal -force of the parts of the waters very weak, so that -the figure of the moon cannot, as in the earth, be much affected -by this revolution upon its axis: but the figure of those -waters are made different from spherical by another cause, -viz. the action of the earth upon them; by which they will -be reduced to an oblong oval form, whose axis prolonged -would pass through the earth; for the same reason, as we -have above observed, that the waters of the earth would -take the like figure, if they had moved so slowly, as to keep -pace with the moon. And the solid part of the moon must -correspond with this figure of the fluid part: but this elevation -of the parts of the moon is nothing near so great as -is the protuberance of the earth at the equator, for it will not -exceed 93 english feet.</p> - -<p>52. The waters of the moon will have no tide, except -what will arise from the motion of the moon round the -earth. For the conversion of the moon about her axis is equable, -whereby the inequality in the motion round the -earth discovers to us at some times small parts of the moon’s -surface towards the east or west, which at other times lie -hid; and as the axis, whereon the moon turns, is oblique to -her motion round the earth, sometimes small parts of her<span class="pagenum"><a name="Page_315" id="Page_315">[315]</a></span> -surface toward the north, and sometimes the like toward -the south are visible, which at other times are out of sight. -These appearances make what is called the libration of the -moon, discovered by <span class="smcap">Hevelius</span>. But now as the axis of -the oval figure of the waters will he pointed towards the -earth, there must arise from hence some fluctuation in them; -and beside, by the change of the moon’s distance from the -earth, they will not always have the very same height.</p> - -<div class="figcenter"> - <img src="images/ill-381.jpg" width="300" height="184" - alt="" - title="" /> -</div> - -</div> - -<p><span class="pagenum"><a name="Page_316" id="Page_316">[316]</a></span></p> - -<div class="chapter"> - -<div class="figcenter"> - <img src="images/ill-382.jpg" width="400" height="208" - alt="" - title="" /> -</div> - -<p class="pc xlarge"><em class="gesperrt">BOOK III</em>.</p> - -<hr class="d3" /> - -<h2><a name="c316" id="c316"><span class="smcap"><em class="gesperrt">Chap</em> I.</span></a><br /> -Concerning the cause of COLOURS inherent in the LIGHT.</h2> - -<div> - <img class="dcap1" src="images/da1.jpg" width="80" height="81" alt=""/> -</div> -<p class="cap13">AFTER this view which has been taken -of Sir <span class="smcap">Isaac Newton’s</span> mathematical -principles of philosophy, and the -use he has made of them, in explaining -the system of the world, &c. the -course of my design directs us to turn -our eyes to that other philosophical -work, his treatise of Optics, in which we shall find our great -author’s inimitable genius discovering it self no less, than in<span class="pagenum"><a name="Page_317" id="Page_317">[317]</a></span> -the former; nay perhaps even more, since this work gives -as many instances of his singular force of reasoning, and -of his unbounded invention, though unassisted in great -measure by those rules and general precepts, which facilitate -the invention of mathematical theorems. Nor yet is -this work inferior to the other in usefulness; for as that -has made known to us one great principle in nature, by -which the celestial motions are continued, and by which -the frame of each globe is preserved; so does this point out -to us another principle no less universal, upon which depends -all those operations in the smaller parts of matter, -for whose sake the greater frame of the universe is erected; -all those immense globes, with which the whole heavens are -filled, being without doubt only design’d as so many convenient -apartments for carrying on the more noble operations -of nature in vegetation and animal life. Which single -consideration gives abundant proof of the excellency of -our author’s choice, in applying himself carefully to examine -the action between light and bodies, so necessary -in all the varieties of these productions, that none of them -can be successfully promoted without the concurrence of -heat in a greater or less degree.</p> - -<p>2. <span class="smcap gesperrt">’Tis</span> true, our author has not made so full a discovery -of the principle, by which this mutual action between light -and bodies is caused; as he has in relation to the power, by -which the planets are kept in their courses: yet he has led -us to the very entrance upon it, and pointed out the path -so plainly which must be followed to reach it; that one may<span class="pagenum"><a name="Page_318" id="Page_318">[318]</a></span> -be bold to say, whenever mankind shall be blessed with this -improvement of their knowledge, it will be derived so directly -from the principles laid down by our author in this -book, that the greatest share of the praise due to the discovery -will belong to him.</p> - -<p><a name="c318" id="c318">3.</a> <span class="smcap gesperrt">In</span> speaking of the progress our author has made, -I shall distinctly pursue three things, the two first relating -to the colours of natural bodies: for in the first head shall -be shewn, how those colours are derived from the properties -of the light itself; and in the second upon what -properties of the bodies they depend: but the third head -of my discourse shall treat of the action of bodies upon -light in refracting, reflecting, and inflecting it.</p> - -<p>4. <span class="smcap gesperrt">The</span> first of these, which shall be the business of -the present chapter, is contained in this one proposition: that -the sun’s direct light is not uniform in respect of colour, not -being disposed in every part of it to excite the idea of whiteness, -which the whole raises; but on the contrary is a composition -of different kinds of rays, one sort of which if alone -would give the sense of red, another of orange, a -third of yellow, a fourth of green, a fifth of light blue, -a sixth of indigo, and a seventh of a violet purple; that -all these rays together by the mixture of their sensations -impress upon the organ of sight the sense of whiteness, -though each ray always imprints there its own colour; and -all the difference between the colours of bodies when viewed -in open day light arises from this, that coloured bodies<span class="pagenum"><a name="Page_319" id="Page_319">[319]</a></span> -do not reflect all the sorts of rays falling upon them in equal -plenty, but some sorts much more copiously than others; -the body appearing of that colour, of which the -light coming from it is most composed.</p> - -<p><a name="c319" id="c319">5.</a> <span class="smcap gesperrt">That</span> the light of the sun is compounded, as has been -said, is proved by refracting it with a prism. By a prism I here -mean a glass or other body of a triangular form, such as is represented -in fig. 121. But before we proceed to the illustration -of the proposition we have just now laid down, it will be necessary -to spend a few words in explaining what is meant by -the refraction of light; as the design of our present labour is -to give some notion of the subject, we are engaged in, to -such as are not versed in the mathematics.</p> - -<p>6. <span class="smcap gesperrt">It</span> is well known, that when a ray of light passing -through the air falls obliquely upon the surface of any transparent -body, suppose water or glass, and enters it, the ray -will not pass on in that body in the same line it described -through the air, but be turned off from the surface, so -as to be less inclined to it after passing it, than before. Let -A B C D (in fig. 122.) represent a portion of water, or glass, -A B the surface of it, upon which the ray of light E F falls -obliquely; this ray shall not go right on in the course delineated -by the line F G, but be turned off from the surface -A B into the line F H, less inclined to the surface A B -than the line E F is, in which the ray is incident upon that -surface.</p> - -<p><span class="pagenum"><a name="Page_320" id="Page_320">[320]</a></span></p> - -<p>7. <span class="smcap gesperrt">On</span> the other hand, when the light passes out of any -such body into the air, it is inflected the contrary way, -being after its emergence rendred more oblique to the surface -it passes through, than before. Thus the ray F H, when -it goes out of the surface C D, will be turned up towards -that surface, going out into the air in the line H I.</p> - -<p>8. <span class="smcap gesperrt">This</span> turning of the light out of its way, as it passes -from one transparent body into another is called its refraction. -Both these cases may be tried by an easy experiment with -a bason and water. For the first case set an empty bason -in the sunshine or near a candle, making a mark upon -the bottom at the extremity of the shadow cast by the brim -of the bason, then by pouring water into the bason you -will observe the shadow to shrink, and leave the bottom -of the bason enlightned to a good distance from the mark. -Let A B C (in fig. 123.) denote the empty bason, E A D the -light shining over the brim of it, so that all the part A B D -be shaded. Then a mark being made at D, if water be -poured into the bason (as in fig. 124.) to F G, you shall observe -the light, which before went on to D, now to come -much short of the mark D, falling on the bottom in the -point H, and leaving the mark D a good way within the -enlightened part; which shews that the ray E A, when it -enters the water at I, goes no longer straight forwards, but -is at that place incurvated, and made to go nearer the -perpendicular. The other case may be tryed by putting -any small body into an empty bason, placed lower than your -eye, and then receding from the bason, till you can but just<span class="pagenum"><a name="Page_321" id="Page_321">[321]</a></span> -see the body over the brim. After which, if the bason be -filled with water, you shall presently observe the body to be -visible, though you go farther off from the bason. Let -A B C (in fig. 125.) denote the bason as before, D the body -in it, E the place of your eye, when the body is seen just -over the edge A, while the bason is empty. If it be then -filled with water, you will observe the body still to be visible, -though you take your eye farther off. Suppose you see -the body in this case just over the brim A, when your eye -is at F, it is plain that the rays of light, which come from -the body to your eye have not come straight on, but are -bent at A, being turned downwards, and more inclined to -the surface of the water, between A and your eye at F, -than they are between A and the body D.</p> - -<p>9. <span class="smcap gesperrt">This</span> we hope is sufficient to make all our readers -apprehend, what the writers of optics mean, when they -mention the refraction of the light, or speak of the rays of -light being refracted. We shall therefore now go on to prove -the assertion advanced in the forementioned proposition, in -relation to the different kinds of colours, that the direct light -of the sun exhibits to our sense: which may be done in -the following manner.</p> - -<p>10. <span class="smcap gesperrt">If</span> a room be darkened, and the sun permitted to -shine into it through a small hole in the window shutter, and -be made immediately to fall upon a glass prism, the beam of -light shall in passing through such a prism be parted into rays, -which exhibit all the forementioned colours. In this manner<span class="pagenum"><a name="Page_322" id="Page_322">[322]</a></span> -if A B (in fig. 126) represent the window shutter; C the -hole in it; D E F the prism; Z Y a beam of light coming -from the sun, which passes through the hole, and falls upon -the prism at Y, and if the prism were removed would -go on to X, but in entring the surface B F of the glass it -shall be turned off, as has been explained, into the course Y W -falling upon the second surface of the prism D F in W, -going out of which into the air it shall be again farther inflected. -Let the light now, after it has passed the prism, be -received upon a sheet of paper held at a proper distance, -and it shall paint upon the paper the picture, image, or spectrum -L M of an oblong figure, whose length shall much exceed -its breadth; though the figure shall not be oval, the -ends L and M being semicircular and the sides straight. -But now this figure will be variegated with colours in this -manner. From the extremity M to some length, suppose -to the line <i>n o</i>, it shall be of an intense red; from <i>n o</i> to -<i>p q</i> it shall be an orange; from <i>p q</i> to <i>r s</i> it shall be yellow; -from thence to <i>t u</i> it shall be green; from thence to -<i>w x</i> blue; from thence to <i>y z</i> indigo; and from thence -to the end violet.</p> - -<p>11. <span class="smcap gesperrt">Thus</span> it appears that the sun’s white light by its passage -through the prism, is so changed as now to be divided -into rays, which exhibit all these several colours. The -question is, whether the rays while in the sun’s beam before -this refraction possessed these properties distinctly; so -that some part of that beam would without the rest have -given a red colour, and another part alone have given an..orange, &c. That this is possible to be the case, appears from -hence; that if a convex glass be placed between the paper -and the prism, which may collect all the rays proceeding -out of the prism into its focus, as a burning glass does the -sun’s direct rays; and if that focus fall upon the paper, the -spot formed by such a glass upon the paper shall appear -white, just like the sun’s direct light.</p> - -<div class="figcenter"> - <img src="images/ill-389.jpg" width="400" height="513" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_323" id="Page_323">[323]</a></span></p> - -<p>The rest remaining -as before, let P Q. (in fig. 127.) be the convex glass, causing -the rays to meet upon the paper H G I K in the point -N, I say that point or rather spot of light shall appear white, -without the least tincture of any colour. But it is evident -that into this spot are now gathered all those rays, which before -when separate gave all those different colours; which -shews that whiteness may be made by mixing those colours: -especially if we consider, it can be proved that the glass -P Q does not alter the colour of the rays which pass -through it. Which is done thus: if the paper be made -to approach the glass P Q, the colours will manifest themselves -as far as the magnitude of the spectrum, which the -paper receives, will permit. Suppose it in the situation <i>h g i k</i>, -and that it then receive the spectrum <i>l m</i>, this spectrum -shall be much smaller, than if the glass P Q were removed, -and therefore the colours cannot be so much separated; but -yet the extremity <i>m</i> shall manifestly appear red, and -the other extremity <i>l</i> shall be blue; and these colours as -well as the intermediate ones shall discover themselves more -perfectly, the farther the paper is removed from N, that -is, the larger the spectrum is: the same thing happens, if -the paper be removed farther off from P Q than N. Suppose<span class="pagenum"><a name="Page_324" id="Page_324">[324]</a></span> -into the position θ γ η ϰ, the spectrum λ μ painted upon it -shall again discover its colours, and that more distinctly, the -farther the paper is removed, but only in an inverted order: -for as before, when the paper was nearer the convex -glass, than at N, the upper part of the image was -blue, and the under red; now the upper part shall be red, -and the under blue: because the rays cross at N.</p> - -<p>12. <span class="smcap gesperrt">Nay</span> farther that the whiteness at the focus N, is made -by the union of the colours may be proved without removing -the paper out of the focus, by intercepting with -any opake body part of the light near the glass; for if the -under part, that is the red, or more properly the red-making -rays, as they are styled by our author, are intercepted, the -spot shall take a bluish hue; and if more of the inferior -rays are cut off, so that neither the red-making nor orange-making -rays, and if you please the yellow-making rays likewise, -shall fall upon the spot; then shall the spot incline more -and more to the remaining colours. In like manner if you -cut off the upper part of the rays, that is the violet coloured -or indigo-making rays, the spot shall turn reddish, and become, -more so, the more of those opposite colours are intercepted.</p> - -<p>13. <span class="smcap gesperrt">This</span> I think abundantly proves that whiteness may -be produced by a mixture of all the colours of the spectrum. -At least there is but one way of evading the present -arguments, which is, by asserting that the rays of light -after passing the prism have no different properties to exhibit -this or the other colour, but are in that respect perfectly<span class="pagenum"><a name="Page_325" id="Page_325">[325]</a></span> -homogeneal, so that the rays which pass to the under -and red part of the image do not differ in any properties -whatever from those, which go to the upper and -violet part of it; but that the colours of the spectrum are -produced only by some new modifications of the rays, made -at their incidence upon the paper by the different terminations -of light and shadow: if indeed this assertion can -be allowed any place, after what has been said; for it seems -to be sufficiently obviated by the latter part of the preceding -experiment, that by intercepting the inferior part -of the light, which comes from the prism, the white spot -shall receive a bluish cast, and by stopping the upper part the -spot shall turn red, and in both cases recover its colour, when -the intercepted light is permitted to pass again; though -in all these trials there is the like termination of light and -shadow. However our author has contrived some experiments -expresly to shew the absurdity of this supposition; -all which he has explained and enlarged upon in so distinct -and expressive a manner, that it would be wholly unnecessary -to repeat them in this place<a name="FNanchor_280_280" id="FNanchor_280_280"></a><a href="#Footnote_280_280" class="fnanchor">[280]</a>. I shall only mention -that of them, which may be tried in the experiment -before us. If you draw upon the paper H G I K, and through -the spot N, the straight line <i>w x</i> parallel to the horizon, -and then if the paper be much inclined into the situation -<i>r s v t</i> the line <i>w x</i> still remaining parallel to the horizon, -the spot N shall lose its whiteness and receive a blue tincture; -but if it be inclined as much the contrary way, the -same spot shall exchange its white colour for a reddish dye.<span class="pagenum"><a name="Page_326" id="Page_326">[326]</a></span> -All which can never be accounted for by any difference in -the termination of the light and shadow, which here is -none at all; but are easily explained by supposing the upper -part of the rays, whenever they enter the eye, disposed -to give the sensation of the dark colours blue, indigo and -violet; and that the under part is fitted to produce the -bright colours yellow, orange and red: for when the paper -is in the situation <i>r s t u</i>, it is plain that the upper part of -the light falls more directly upon it, than the under part, -and therefore those rays will be most plentifully reflected -from it; and by their abounding in the reflected light will -cause it to incline to their colour. Just so when the paper -is inclined the contrary way, it will receive the inferior rays -most directly, and therefore ting the light it reflects with their -colour.</p> - -<p>14. <span class="smcap gesperrt">It</span> is now to be proved that these dispositions of the -rays of light to produce some one colour and some another, -which manifest themselves after their being refracted, are not -wrought by any action of the prism upon them, but are -originally inherent in those rays; and that the prism only -affords each species an occasion of shewing its distinct quality -by separating them one from another, which before, -while they were blended together in the direct beam of the -sun’s light, lay conceal’d. But that this is so, will be proved, -if it can be shewn that no prism has any power upon -the rays, which after their passage through one prism are -rendered uncompounded and contain in them but one colour, -either to divide that colour into several, as the sun’s<span class="pagenum"><a name="Page_327" id="Page_327">[327]</a></span> -light is divided, or so much as to change it into any other -colour. This will be proved by the following experiment<a name="FNanchor_281_281" id="FNanchor_281_281"></a><a href="#Footnote_281_281" class="fnanchor">[281]</a>. -The same thing remaining, as in the first experiment, let -another prism N O (in fig. 128.) be placed either immediately, -or at some distance after the first, in a perpendicular -posture, so that it shall refract the rays issuing from the -first sideways. Now if this prism could divide the light -falling upon it into coloured rays, as the first has done, it -would divide the spectrum breadthwise into colours, as -before it was divided lengthwise; but no such thing is observed. -If L M were the spectrum, which the first prism -D E F would paint upon the paper H G I K; P Q lying in -an oblique posture shall be the spectrum projected by the -second, and shall be divided lengthwise into colours corresponding -to the colours of the spectrum L M, and occasioned -like them by the refraction of the first prism, but -its breadth shall receive no such division; on the contrary -each colour shall be uniform from side to side, as much -as in the spectrum L M, which proves the whole assertion.</p> - -<p>15. <span class="smcap gesperrt">The</span> same is yet much farther confirmed by another -experiment. Our author teaches that the colours of -the spectrum L M in the first experiment are yet compounded, -though not so much as in the sun’s direct light. He -shews therefore how, by placing the prism at a distance from -the hole, and by the use of a convex glass, to separate the -colours of the spectrum, and make them uncompounded -to any degree of exactness<a name="FNanchor_282_282" id="FNanchor_282_282"></a><a href="#Footnote_282_282" class="fnanchor">[282]</a>. And he shews when this<span class="pagenum"><a name="Page_328" id="Page_328">[328]</a></span> -is done sufficiently, if you make a small hole in the paper -whereon the spectrum is received, through which any one sort -of rays may pass, and then let that coloured ray fall so upon a -prism, as to be refracted by it, it shall in no case whatever -change its colour; but shall always retain it perfectly as at -first, however it be refracted<a name="FNanchor_283_283" id="FNanchor_283_283"></a><a href="#Footnote_283_283" class="fnanchor">[283]</a>.</p> - -<p>16. <span class="smcap gesperrt">Nor</span> yet will these colours after this full separation -of them suffer any change by reflection from bodies of different -colours; on the other hand they make all bodies placed -in these colours appear of the colour which falls upon -them<a name="FNanchor_284_284" id="FNanchor_284_284"></a><a href="#Footnote_284_284" class="fnanchor">[284]</a>: for minium in red light will appear as in open day -light; but in yellow light will appear yellow; and which -is more extraordinary, in green light will appear green, in blue, -blue; and in the violet-purple coloured light will appear of a -purple colour; in like manner verdigrease, or blue bise, will -put on the appearance of that colour, in which it is placed; -so that neither bise placed in the red light shall be able to -give that light the least blue tincture, or any other different -from red; nor shall minium in the indigo or violet -light exhibit the least appearance of red, or any other colour -distinct from that it is placed in. The only difference -is, that each of these bodies appears most luminous and bright -in the colour, which corresponds with that it exhibits in -the day light, and dimmed in the colours most remote from -that; that is, though minium and bise placed in blue light -shall both appear blue, yet the bise shall appear of a bright -blue, and the minium of a dusky and obscure blue: but<span class="pagenum"><a name="Page_329" id="Page_329">[329]</a></span> -if minium and bise be compared together in red light, the -minium shall afford a brisk red, the bise a duller colour, -though of the same species.</p> - -<p><a name="c329" id="c329">17.</a> <span class="smcap gesperrt">And</span> this not only proves the immutability of all -these simple and uncompounded colours; but likewise unfolds -the whole mystery, why bodies appear in open day-light -of such different colours, it consisting in nothing more -than this, that whereas the white light of the day is composed -of all sorts of colours, some bodies reflect the rays -of one sort in greater abundance than the rays of any other<a name="FNanchor_285_285" id="FNanchor_285_285"></a><a href="#Footnote_285_285" class="fnanchor">[285]</a>. -Though it appears by the fore-cited experiment, that almost -all these bodies reflect some portion of the rays of every -colour, and give the sense of particular colours only by the -predominancy of some sorts of rays above the rest. And what -has before been explained of composing white by mingling -all the colours of the spectrum together shews clearly, that -nothing more is required to make bodies look white, than -a power to reflect indifferently rays of every colour. But -this will more fully appear by the following method: if -near the coloured spectrum in our first experiment a piece -of white paper be so held, as to be illuminated equally by -all the parts of that spectrum, it shall appear white; whereas -if it be held nearer to the red end of the image, than to the -other, it shall turn reddish; if nearer the blue end, it shall -seem bluish<a name="FNanchor_286_286" id="FNanchor_286_286"></a><a href="#Footnote_286_286" class="fnanchor">[286]</a>.</p> - -<p><span class="pagenum"><a name="Page_330" id="Page_330">[330]</a></span></p> - -<p>18. <span class="smcap gesperrt">Our</span> indefatigable and circumspect author farther -examined his theory by mixing the powders which painters -use of several colours, in order if possible to produce -a white powder by such a composition<a name="FNanchor_287_287" id="FNanchor_287_287"></a><a href="#Footnote_287_287" class="fnanchor">[287]</a>. But in this he -found some difficulties for the following reasons. Each -of these coloured powders reflects but part of the light, which -is cast upon them; the red powders reflecting little green -or blue, and the blue powders reflecting very little red or -yellow, nor the green powders reflecting near so much of -the red or indigo and purple, as of the other colours: and -besides, when any of these are examined in homogeneal light, -as our author calls the colours of the prism, when well separated, -though each appears more bright and luminous in -its own day-light colour, than in any other; yet white bodies, -suppose white paper for instance, in those very colours -exceed these coloured bodies themselves in brightness; so -that white bodies reflect not only more of the whole light -than coloured bodies do in the day-light, but even more -of that very colour which they reflect most copiously. All -which considerations make it manifest that a mixture of these -will not reflect so great a quantity of light, as a white body of -the same size; and therefore will compose such a colour as -would result from a mixture of white and black, such as -are all grey and dun colours, rather than a strong white. -Now such a colour he compounded of certain ingredients, -which he particularly sets down, in so much that when the -composition was strongly illuminated by the sun’s direct -beams, it would appear much whiter than even white paper,<span class="pagenum"><a name="Page_331" id="Page_331">[331]</a></span> -if considerably shaded. Nay he found by trials how -to proportion the degree of illumination of the mixture -and paper, so that to a spectator at a proper distance it -could not well be determined which was the more perfect -colour; as he experienced not only by himself, but by the -concurrent opinion of a friend, who chanced to visit him -while he was trying this experiment. I must not here omit -another method of trying the whiteness of such a mixture, -proposed in one of our author’s letters on this subject<a name="FNanchor_288_288" id="FNanchor_288_288"></a><a href="#Footnote_288_288" class="fnanchor">[288]</a>: -which is to enlighten the composition by a beam of -the sun let into a darkened room, and then to receive the -light reflected from it upon a piece of white paper, observing -whether the paper appears white by that reflection; -for if it does, it gives proof of the composition’s being white; -because when the paper receives the reflection from any -coloured body, it looks of that colour. Agreeable to this -is the trial he made upon water impregnated with soap, -and agitated into a froth<a name="FNanchor_289_289" id="FNanchor_289_289"></a><a href="#Footnote_289_289" class="fnanchor">[289]</a>: for when this froth after some -short time exhibited upon the little bubbles, which composed -it, a great variety of colours, though these colours to a -spectator at a small distance discover’d themselves distinctly; -yet when the eye was so far removed, that each little bubble -could no longer be distinguished, the whole froth by -the mixture of all these colours appeared intensly white.</p> - -<p>19. <span class="smcap gesperrt">Our</span> author having fully satisfied himself by these -and many other experiments, what the result is of mixing<span class="pagenum"><a name="Page_332" id="Page_332">[332]</a></span> -together all the prismatic colours; he proceeds in the next -place to examine, whether this appearance of whiteness be -raised by the rays of these different kinds acting so, when -they meet, upon one another, as to cause each of them to -impress the sense of whiteness upon the optic nerve; or whether -each ray does not make upon the organ of sight the -same impression, as when separate and alone; so that the -idea of whiteness is not excited by the impression from any -one part of the rays, but results from the mixture of all those -different sensations. And that the latter sentiment is the -true one, he evinces by undeniable experiments.</p> - -<p>20. <span class="smcap gesperrt">In</span> particular the foregoing experiment<a name="FNanchor_290_290" id="FNanchor_290_290"></a><a href="#Footnote_290_290" class="fnanchor">[290]</a>, wherein -the convex glass was used, furnishes proofs of this: in that -when the paper is brought into the situation θ γ η ϰ, beyond, beyond -N the colours, that at N disappeared, begin to emerge again; -which shews that by mingling at N they did not lose their -colorific qualities, though for some reason they lay concealed. -This farther appears by that part of the experiment, -when the paper, while in the focus, was directed to be enclined -different ways; for when the paper was in such a -situation, that it must of necessity reflect the rays, which -before their arrival at the point N would have given a blue -colour, those rays in this very point itself by abounding in -the reflected light tinged it with the same colour; so when the -paper reflects most copiously the rays, which before they -come to the point N exhibit redness, those same rays tincture<span class="pagenum"><a name="Page_333" id="Page_333">[333]</a></span> -the light reflected by the paper from that very point -with their own proper colour.</p> - -<p>21. <span class="smcap gesperrt">There</span> is a certain condition relating to sight, which -affords an opportunity of examining this still more fully: -it is this, that the impressions of light remain some short -space upon the eye; as when a burning coal is whirl’d about -in a circle, if the motion be very quick, the eye shall not -be able to distinguish the coal, but shall see an entire circle -of fire. The reason of which appearance is, that the impression -made by the coal upon the eye in any one situation -is not worn out, before the coal returns again to the same -place, and renews the sensation. This gives our author the -hint to try, whether these colours might not be transmitted -successively to the eye so quick, that no one of the colours -should be distinctly perceived, but the mixture of the sensations -should produce a uniform whiteness; when the rays -could not act upon each other, because they never should -meet, but come to the eye one after another. And this thought -he executed by the following expedient<a name="FNanchor_291_291" id="FNanchor_291_291"></a><a href="#Footnote_291_291" class="fnanchor">[291]</a>. He made an instrument -in shape like a comb, which he applied near the -convex glass, so that by moving it up and down slowly -the teeth of it might intercept sometimes one and sometimes -another colour; and accordingly the light reflected from the -paper, placed at N, should change colour continually. But -now when the comb-like instrument was moved very quick, -the eye lost all preception of the distinct colours, which came -to it from time to time, a perfect whiteness resulting from the<span class="pagenum"><a name="Page_334" id="Page_334">[334]</a></span> -mixture of all those distinct impressions in the sensorium. -Now in this case there can be no suspicion of the several -coloured rays acting upon one another, and making any -change in each other’s manner of affecting the eye, seeing -they do not so much as meet together there.</p> - -<p>22. <span class="smcap gesperrt">Our</span> author farther teaches us how to view the spectrum -of colours produced in the first experiment with another -prism, so that it shall appear to the eye under the -shape of a round spot and perfectly white<a name="FNanchor_292_292" id="FNanchor_292_292"></a><a href="#Footnote_292_292" class="fnanchor">[292]</a>. And in this -case if the comb be used to intercept alternately some of -the colours, which compose the spectrum, the round spot -shall change its colour according to the colours intercepted; -but if the comb be moved too swiftly for those changes to -be distinctly perceived, the spot shall seem always white, as -before<a name="FNanchor_293_293" id="FNanchor_293_293"></a><a href="#Footnote_293_293" class="fnanchor">[293]</a>.</p> - -<p><a name="c334" id="c334">23.</a> <span class="smcap gesperrt">Besides</span> this whiteness, which results from an universal -composition of all sorts of colours, our author particularly -explains the effects of other less compounded mixtures; -some of which compound other colours like some -of the simple ones, but others produce colours different from -any of them. For instance, a mixture of red and yellow -compound a colour like in appearance to the orange, which -in the spectrum lies between them; as a composition of yellow -and blue is made use of in all dyes to make a green. -But red and violet purple compounded make purples unlike -to any of the prismatic colours, and these joined with<span class="pagenum"><a name="Page_335" id="Page_335">[335]</a></span> -yellow or blue make yet new colours. Besides one rule is here -to be observed, that when many different colours are mixed, the -colour which arises from the mixture grows languid and degenerates -into whiteness. So when yellow green and blue -are mixed together, the compound will be green; but if -to this you add red and purple, the colour shall first grow dull -and less vivid, and at length by adding more of these colours -it shall turn to whiteness, or some other colour<a name="FNanchor_294_294" id="FNanchor_294_294"></a><a href="#Footnote_294_294" class="fnanchor">[294]</a>.</p> - -<p>24. <span class="smcap gesperrt">Only</span> here is one thing remarkable of those compounded -colours, which are like in appearance to the simple -ones; that the simple ones when viewed through a prism shall -still retain their colour, but the compounded colours seen -through such a glass shall be parted into the simple ones of -which they are the aggregate. And for this reason any body -illuminated by the simple light shall appear through a prism -distinctly, and have its minutest parts observable, as may easily -be tried with flies, or other such little bodies, which have -very small parts; but the same viewed in this manner when -enlighten’d with compounded colours shall appear confused, -their smallest parts not being distinguishable. How the -prism separates these compounded colours, as likewise how -it divides the light of the sun into its colours, has not yet -been explained; but is reserved for our third chapter.</p> - -<p>25. <span class="smcap gesperrt">In</span> the mean time what has been said, I hope, will -suffice to give a taste of our author’s way of arguing, and<span class="pagenum"><a name="Page_336" id="Page_336">[336]</a></span> -in some measure to illustrate the proposition laid down in -this chapter.</p> - -<p>26. <span class="smcap gesperrt">There</span> are methods of separating the heterogeneous -rays of the sun’s light by reflection, which perfectly -conspire with and confirm this reasoning. One of which -ways may be this. Let A B (in fig. 129) represent the window -shutter of a darkened room; C a hole to let in the sun’s -rays; D E F, G H I two prisms so applied together, that the -sides E F and G I be contiguous, and the sides D F, G H -parallel; by this means the light will pass through them without -any separation into colours: but if it be afterwards received -by a third prism I K L, it shall be divided so as to -form upon any white body P Q the usual colours, violet -at <i>m</i>, blue at <i>n</i>, green at <i>o</i>, yellow at <i>r</i>, and red at <i>s</i>. But -because it never happens that the two adjacent surfaces E F -and G I perfectly touch, part only of the light incident upon -the surface E F shall be transmitted, and part shall be -reflected. Let now the reflected part be received by a fourth -prism Δ Θ Λ, and passing through it paint upon a white body -Ζ Γ the colours of the prism, red at <i>t</i>, yellow at <i>u</i>, green -at <i>w</i>, blue at <i>x</i>, violet at <i>y</i>. If the prisms D E F, G H I -be slowly turned about while they remain contiguous, the -colours upon the body P Q shall not sensibly change their -situation, till such time as the rays become pretty oblique -to the surface E F; but then the light incident upon the -surface E F shall begin to be wholly reflected. And first -of all the violet light shall be wholly reflected, and thereupon -will disappear at <i>m</i>, appearing instead thereof<span class="pagenum"><a name="Page_337" id="Page_337">[337]</a></span> -at <i>y</i>, and increasing the violet light falling there, the -other colours remaining as before. If the prisms D E F, G H I -be turned a little farther about, that the incident rays become -yet more inclined to the surface E F, the blue shall -be totally reflected, and shall disappear in <i>n</i>, but appear at -<i>x</i> by making the colour there more intense. And the same -may be continued, till all the colours are successively removed -from the surface P Q to Ζ Γ. But in any case, suppose -when the violet and the blue have forsaken the surface P Q, and -appear upon the surface Ζ Γ, Ζ Γ, the green, yellow, and red only -remaining upon the surface P Q; if the light be received upon -a paper held any where in its whole passage between the -light’s coming out of the prisms D E F, G I H and its incidence -upon the prism I K L, it shall appear of the colour -compounded of all the colours seen upon P Q; and the reflected -ray, received upon a piece of white paper held any -where between the prisms D E F and Δ Θ Σ shall exhibit the colour -compounded of those the surface P Q is deprived of mixed -with the sun’s light: whereas before any of the light was reflected -from the surface E F, the rays between the prisms G H I and -I K L would appear white; as will likewise the reflected ray -both before and after the total reflection, provided the difference -of refraction by the surfaces D F and D E be inconsiderable. -I call here the sun’s light white, as I have all along done; but it -is more exact to ascribe to it something of a yellowish tincture, -occasioned by the brighter colours abounding in it; which -caution is necessary in examining the colours of the reflected -beam, when all the violet and blue are in it: for this<span class="pagenum"><a name="Page_338" id="Page_338">[338]</a></span> -yellowish turn of the sun’s light causes the blue not to be -quite so visible in it, as it should be, were the light perfectly -white; but makes the beam of light incline rather towards -a pale white.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c338" id="c338"><span class="smcap"><em class="gesperrt">Chap</em>. II.</span></a><br /> -Of the properties of BODIES, upon which -their COLOURS depend.</h2> - -<p class="drop-cap16">AFTER having shewn in the last chapter, that the -difference between the colours of bodies viewed in open -day-light is only this, that some bodies are disposed to -reflect rays of one colour in the greatest plenty, and other -bodies rays of some other colour; order now requires us -to examine more particularly into the property of bodies, -which gives them this difference. But this our author shews -to be nothing more, than the different magnitude of the -particles, which compose each body: this I question not -will appear no small paradox. And indeed this whole chapter -will contain scarce any assertions, but what will be almost -incredible, though the arguments for them are so strong -and convincing, that they force our assent. In the former -chapter have been explained properties of light, not in the -least thought of before our author’s discovery of them; yet -are they not difficult to admit, as soon as experiments are -known to give proof of their reality; but some of the propositions -to be stated here will, I fear, be accounted almost -past belief; notwithstanding that the arguments, by which<span class="pagenum"><a name="Page_339" id="Page_339">[339]</a></span> -they are established are unanswerable. For it is proved by -our author, that bodies are rendered transparent by the minuteness -of their pores, and become opake by having them large; -and more, that the most transparent body by being reduced -to a great thinness will become less pervious to the light.</p> - -<p>2. <span class="smcap gesperrt">But</span> whereas it had been the received opinion, and -yet remains so among all who have not studied this philosophy, -that light is reflected from bodies by its impinging -against their solid parts, rebounding from them, as a tennis -ball or other elastic substance would do, when struck against -any hard and resisting surface; it will be proper to -begin with declaring our author’s sentiment concerning this, -who shews by many arguments that reflection cannot be -caused by any such means<a name="FNanchor_295_295" id="FNanchor_295_295"></a><a href="#Footnote_295_295" class="fnanchor">[295]</a>: some few of his proofs I shall -set down, referring the reader to our author himself for -the rest.</p> - -<p><a name="c339" id="c339">3.</a> <span class="smcap gesperrt">It</span> is well known, that when light falls upon any -transparent body, glass for instance, part of it is reflected and -part transmitted; for which it is ready to account, by saying -that part of the light enters the pores of the glass, and -part impinges upon its solid parts. But when the transmitted -light arrives at the farther surface of the glass, in passing -out of glass into air there is as strong a reflection caused, -or rather something stronger. Now it is not to be conceived, -how the light should find as many solid parts in the -air to strike against as in the glass, or even a greater number<span class="pagenum"><a name="Page_340" id="Page_340">[340]</a></span> -of them. And to augment the difficulty, if water -be placed behind the glass, the reflection becomes much -weaker. Can we therefore say, that water has fewer solid -parts for the light to strike against, than the air? And if -we should, what reason can be given for the reflection’s being -stronger, when the air by the air-pump is removed -from behind the glass, than when the air receives the rays -of light. Besides the light may be so inclined to the hinder -surface of the glass, that it shall wholly be reflected, -which happens when the angle which the ray makes with -the surface does not exceed about 49⅓ degrees; but if the -inclination be a very little increased, great part of the light -will be transmitted; and how the light in one case should -meet with nothing but the solid parts of the air, and by -so small a change of its inclination find pores in great plenty, -is wholly inconceivable. It cannot be said, that the light -is reflected by striking against the solid parts of the surface -of the glass; because without making any change in that -surface, only by placing water contiguous to it instead of -air, great part of that light shall be transmitted, which could -find no passage through the air. Moreover in the last experiment -recited in the preceding chapter, when by turning -the prisms D E F, G H I, the blue light became wholly -reflected, while the rest was mostly transmitted, no possible -reason can be assigned, why the blue-making rays should -meet with nothing but the solid parts of the air between -the prisms, and the rest of the light in the very same obliquity -find pores in abundance. Nay farther, when two glasses -touch each other, no reflection at all is made; though<span class="pagenum"><a name="Page_341" id="Page_341">[341]</a></span> -it does not in the least appear, how the rays should avoid -the solid parts of glass, when contiguous to other glass, any -more than when contiguous to air. But in the last place -upon this supposition it is not to be comprehended, how -the most polished substances could reflect the light in that -regular manner we find they do; for when a polished looking -glass is covered over with quicksilver, we cannot suppose -the particles of light so much larger than those of the quicksilver -that they should not be scattered as much in reflection, -as a parcel of marbles thrown down upon a rugged pavement. -The only cause of so uniform and regular a reflection must be -some more secret cause, uniformly spread over the whole surface -of the glass.</p> - -<p><a name="c341" id="c341">4.</a> <span class="smcap gesperrt">But</span> now, since the reflection of light from bodies -does not depend upon its impinging against their solid parts, -some other reason must be sought for. And first it is -past doubt that the least parts of almost all bodies are transparent, -even the microscope shewing as much<a name="FNanchor_296_296" id="FNanchor_296_296"></a><a href="#Footnote_296_296" class="fnanchor">[296]</a>; besides that -it may be experienced by this method. Take any thin plate -of the opakest body, and apply it to a small hole designed -for the admission of light into a darkened room; however -opake that body may seem in open day-light, it shall under -these circumstances sufficiently discover its transparency, -provided only the body be very thin. White metals indeed -do not easily shew themselves transparent in these trials, they -reflecting almost all the light incident upon them at their -first superficies; the cause of which will appear in what<span class="pagenum"><a name="Page_342" id="Page_342">[342]</a></span> -follows<a name="FNanchor_297_297" id="FNanchor_297_297"></a><a href="#Footnote_297_297" class="fnanchor">[297]</a>. But yet these substances, when reduced into parts -of extraordinary minuteness by being dissolved in aqua fortis -or the like corroding liquors do also become transparent.</p> - -<p><a name="c342" id="c342">5.</a> <span class="smcap gesperrt">Since</span> therefore the light finds free passage through -the least parts of bodies, let us consider the largeness of -their pores, and we shall find, that whenever a ray of light -has passed through any particle of a body, and is come -to its farther surface, if it finds there another particle contiguous, -it will without interruption pass into that particle; -just as light will pass through one piece of glass into another -piece in contact with it without any impediment, or -any part being reflected: but as the light in passing out of -glass, or any other transparent body, shall part of it be reflected -back, if it enter into air or other transparent body -of a different density from that it passes out of; the same -thing will happen in the light’s passage through any particle -of a body, whenever at its exit out of that particle it -meets no other particle contiguous, but must enter into a -pore, for in this case it shall not all pass through, but part -of it be reflected back. Thus will the light, every time it -enters a pore, be in part reflected; so that nothing more -seems necessary to opacity, than that the particles, which compose -any body, touch but in very few places, and that the -pores of it are numerous and large, so that the light may -in part be reflected from it, and the other part, which enters -too deep to be returned out of the body, by numerous -reflections may be stifled and lost<a name="FNanchor_298_298" id="FNanchor_298_298"></a><a href="#Footnote_298_298" class="fnanchor">[298]</a>; which in all probability<span class="pagenum"><a name="Page_343" id="Page_343">[343]</a></span> -happens, as often as it impinges against the solid part -of the body, all the light which does so not being reflected -back, but stopt, and deprived of any farther motion<a name="FNanchor_299_299" id="FNanchor_299_299"></a><a href="#Footnote_299_299" class="fnanchor">[299]</a>.</p> - -<p>6. <span class="smcap gesperrt">This</span> notion of opacity is greatly confirmed by the -observation, that opake bodies become transparent by filling -up the pores with any substance of near the same density -with their parts. As when paper is wet with water or -oyl; when linnen cloth is either dipt in water, oyled, or -varnished; or the oculus mundi stone steeped in water<a name="FNanchor_300_300" id="FNanchor_300_300"></a><a href="#Footnote_300_300" class="fnanchor">[300]</a>. -All which experiments confirm both the first assertion, that -light is not reflected by striking upon the solid parts of -bodies; and also the second, that its passage is obstructed -by the reflections it undergoes in the pores; since we find -it in these trials to pass in greater abundance through bodies, -when the number of their solid parts is increased, only -by taking away in great measure those reflections; which -filling the pores with a substance of near the same density -with the parts of the body will do. Besides as filling -the pores of a dark body makes it transparent; so on the -other hand evacuating the pores of a body transparent, or -separating the parts of such a body, renders it opake. As -salts or wet paper by being dried, glass by being reduced to -powder or the surface made rough; and it is well known that -glass vessels discover cracks in them by their opacity. Just -so water itself becomes impervious to the light by being -formed into many small bubbles, whether in froth, or by -being mixed and agitated with any quantity of a liquor<span class="pagenum"><a name="Page_344" id="Page_344">[344]</a></span> -with which it will not incorporate, such as oyl of turpentine, -or oyl olive.</p> - -<p>7. <span class="smcap gesperrt">A certain</span> electrical experiment made by Mr. <span class="smcap">Hauksbee</span> -may not perhaps be useless to clear up the present speculation, -by shewing that something more is necessary besides -mere porosity for transmitting freely other fine substances. -The experiment is this; that a glass cane rubbed -till it put forth its electric quality would agitate leaf brass -inclosed under a glass vessel, though not at so great a distance, -as if no body had intervened; yet the same cane -would lose all its influence on the leaf brass by the interposition -of a piece of the finest muslin, whose pores are -immensely larger and more patent than those of glass.</p> - -<p><a name="c344" id="c344">8.</a> <span class="smcap gesperrt">Thus</span> I have endeavoured to smooth my way, as much -as I could, to the unfolding yet greater secrets in nature; -for I shall now proceed to shew the reason why bodies appear -of different colours. My reader no doubt will be -sufficiently surprized, when I inform him that the knowledge -of this is deduced from that ludicrous experiment, with -which children divert themselves in blowing bubbles of water -made tenacious by the solution of soap. And that these -bubbles, as they gradually grow thinner and thinner till -they break, change successively their colours from the same -principle, as all natural bodies preserve theirs.</p> - -<p>9. <span class="smcap gesperrt">Our</span> author after preparing water with soap, so as to -render it very tenacious, blew it up into a bubble, and placing<span class="pagenum"><a name="Page_345" id="Page_345">[345]</a></span> -it under a glass, that it might not be irregularly agitated -by the air, observed as the water by subsiding changed the -thickness of the bubble, making it gradually less and less till -the bubble broke; there successively appeared colours at the -top of the bubble, which spread themselves into rings surrounding -the top and descending more and more, till they vanished -at the bottom in the same order in which they appeared<a name="FNanchor_301_301" id="FNanchor_301_301"></a><a href="#Footnote_301_301" class="fnanchor">[301]</a>. -The colours emerged in this order: first red, then blue; to which -succeeded red a second time, and blue immediately followed; -after that red a third time, succeeded by blue; to which -followed a fourth red, but succeeded by green; after this a -more numerous order of colours, first red, then yellow, -next green, and after that blue, and at last purple; then -again red, yellow, green, blue, violet followed each other -in order; and in the last place red, yellow, white, blue; -to which succeeded a dark spot, which reflected scarce any -light, though our author found it did make some very obscure -reflection, for the image of the sun or a candle might -be faintly discerned upon it; and this last spot spread itself -more and more, till the bubble at last broke. These colours -were not simple and uncompounded colours, like those -which are exhibited by the prism, when due care is taken -to separate them; but were made by a various mixture of -those simple colours, as will be shewn in the next chapter: -whence these colours, to which I have given the name of -blue, green, or red, were not all alike, but differed as follows. -The blue, which appeared next the dark spot, was a -pure colour, but very faint, resembling the sky-colour; the<span class="pagenum"><a name="Page_346" id="Page_346">[346]</a></span> -white next to it a very strong and intense white, brighter -much than the white, which the bubble reflected, before -any of the colours appeared. The yellow which preceded -this was at first pretty good, but soon grew dilute; and -the red which went before the yellow at first gave a tincture -of scarlet inclining to violet, but soon changed into -a brighter colour; the violet of the next series was deep -with little or no redness in it; the blue a brisk colour, but -came much short of the blue in the next order; the green -was but dilute and pale; the yellow and red were very -bright and full, the best of all the yellows which appeared -among any of the colours: in the preceding orders the purple -was reddish, but the blue, as was just now said, the brightest -of all; the green pretty lively better than in the order -which appeared before it, though that was a good willow -green; the yellow but small in quantity, though bright; the -red of this order not very pure: those which appeared before -yet more obscure, being very dilute and dirty; as were -likewise the three first blues.</p> - -<p>10. <span class="smcap gesperrt">Now</span> it is evident, that these colours arose at the -top of the bubble, as it grew by degrees thinner and thinner: -but what the express thickness of the bubble was, where -each of these colours appeared upon it, could not be determined -by these experiments; but was found by another -means, viz. by taking the object glass of a long telescope, -which is in a small degree convex, and placing it upon a -flat glass, so as to touch it in one point, and then water being -put between them, the same colours appeared as in the<span class="pagenum"><a name="Page_347" id="Page_347">[347]</a></span> -bubble, in the form of circles or rings surrounding the -point where the glasses touched, which appeared black for -want of any reflection from it, like the top of the bubble -when thinnest<a name="FNanchor_302_302" id="FNanchor_302_302"></a><a href="#Footnote_302_302" class="fnanchor">[302]</a>: next to this spot lay a blue circle, and -next without that a white one; and so on in the same order -as before, reckoning from the dark spot. And henceforward -I shall speak of each colour, as being of the first, second, -or any following order, as it is the first, second, or any -following one, counting from the black spot in the center -of these rings; which is contrary to the order in which -I must have mentioned them, if I should have reputed -them the first, second, or third, &c. in order, as they arise -after one another upon the top of the bubble.</p> - -<p>11. But now by measuring the diameters of each of these -rings, and knowing the convexity of the telescope glass, the -thickness of the water at each of those rings may be determined -with great exactness: for instance the thickness of it, -where the white light of the first order is reflected, is about -3⅞ such parts, of which an inch contains 1000000<a name="FNanchor_303_303" id="FNanchor_303_303"></a><a href="#Footnote_303_303" class="fnanchor">[303]</a>. -And this measure gives the thickness of the bubble, where -it appeared of this white colour, as well as of the water -between the glasses; though the transparent body which -surrounds the water in these two cases be very different: -for our author found, that the condition of the ambient -body would not alter the species of the colour at all, though -it might its strength and brightness; for pieces of Muscovy -glass, which were so thin as to appear coloured by being<span class="pagenum"><a name="Page_348" id="Page_348">[348]</a></span> -wet with water, would have their colours faded and made -less bright thereby; but he could not observe their species -at all to be changed. So that the thickness of any transparent -body determines its colour, whatever body the light -passes through in coming to it<a name="FNanchor_304_304" id="FNanchor_304_304"></a><a href="#Footnote_304_304" class="fnanchor">[304]</a>.</p> - -<p>12. <span class="smcap gesperrt">But</span> it was found that different transparent bodies -would not under the same thicknesses exhibit the same colours: -for if the forementioned glasses were laid upon each -other without any water between their surfaces, the air itself -would afford the same colours as the water, but more -expanded, insomuch that each ring had a larger diameter, -and all in the same proportion. So that the thickness of the -air proper to each colour was in the same proportion larger, -than the thickness of the water appropriated to the same<a name="FNanchor_305_305" id="FNanchor_305_305"></a><a href="#Footnote_305_305" class="fnanchor">[305]</a>.</p> - -<p>13. <span class="smcap gesperrt">If</span> we examine with care all the circumstances of these -colours, which will be enumerated in the next chapter, -we shall not be surprized, that our author takes them to -bear a great analogy to the colours of natural bodies<a name="FNanchor_306_306" id="FNanchor_306_306"></a><a href="#Footnote_306_306" class="fnanchor">[306]</a>. For -the regularity of those various and strange appearances relating -to them, which makes the most mysterious part of the action -between light and bodies, as the next chapter will shew, -is sufficient to convince us that the principle, from which -they flow, is of the greatest importance in the frame of -nature; and therefore without question is designed for no -less a purpose than to give bodies their various colours, to -which end it seems very fitly suited. For if any such transparent<span class="pagenum"><a name="Page_349" id="Page_349">[349]</a></span> -substance of the thickness proper to produce -any one colour should be cut into slender threads, -or broken into fragments, it does not appear but -these should retain the same colour; and a heap of such -fragments should frame a body of that colour. So that this -is without dispute the cause why bodies are of this or the -other colour, that the particles of which they are composed -are of different sizes. Which is farther confirmed by -the analogy between the colours of thin plates, and the colours -of many bodies. For example, these plates do not -look of the same colour when viewed obliquely, as when -seen direct; for if the rings and colours between a convex -and plane glass are viewed first in a direct manner, and then at -different degrees of obliquity, the rings will be observed to dilate -themselves more and more as the obliquity is increased<a name="FNanchor_307_307" id="FNanchor_307_307"></a><a href="#Footnote_307_307" class="fnanchor">[307]</a>; -which shews that the transparent substance between the glasses -does not exhibit the same colour at the same thickness in all -situations of the eye: just so the colours in the very same -part of a peacock’s tail change, as the tail changes posture -in respect of the sight. Also the colours of silks, cloths, -and other substances, which water or oyl can intimately -penetrate, become faint and dull by the bodies being wet -with such fluids, and recover their brightness again when -dry; just as it was before said that plates of Muscovy glass -grew faint and dim by wetting. To this may be added, that -the colours which painters use will be a little changed by being -ground very elaborately, without question by the diminution -of their parts. All which particulars, and many more that<span class="pagenum"><a name="Page_350" id="Page_350">[350]</a></span> -might be extracted from our author, give abundant proof of the -present point. I shall only subjoin one more: these transparent -plates transmit through them all the light they do not reflect; -so that when looked through they exhibit those colours, -which result from the depriving white light of the colour reflected. -This may commodiously be tryed by the glasses so -often mentioned; which if looked through exhibit coloured -rings as by reflected light, but in a contrary order; for the middle -spot, which in the other view appears black for want -of reflected light, now looks perfectly white, opposite to -the blue circle; next without this spot the light appears -tinged with a yellowish red; where the white circle appeared -before, it now seems dark; and so of the rest<a name="FNanchor_308_308" id="FNanchor_308_308"></a><a href="#Footnote_308_308" class="fnanchor">[308]</a>. -Now in the same manner, the light transmitted through foliated -gold into a darkened room appears greenish by the -loss of the yellow light, which gold reflects.</p> - -<p>14. <span class="smcap gesperrt">Hence</span> it follows, that the colours of bodies -give a very probable ground for making conjecture concerning -the magnitude of their constituent particles<a name="FNanchor_309_309" id="FNanchor_309_309"></a><a href="#Footnote_309_309" class="fnanchor">[309]</a>. My reason for -calling it a conjecture is, its being difficult to fix certainly the -order of any colour. The green of vegetables our author -judges to be of the third order, partly because of the intenseness -of their colour; and partly from the changes they -suffer when they wither, turning at first into a greenish or -more perfect yellow, and afterwards some of them to an orange -or red; which changes seem to be effected from their -ringing particles growing denser by the exhalation of their<span class="pagenum"><a name="Page_351" id="Page_351">[351]</a></span> -moisture, and perhaps augmented likewise by the accretion -of the earthy and oily parts of that moisture. How the mentioned -colours should arise from increasing the bulk of those particles, -is evident; seeing those colours lie without the ring of -green between the glasses, and are therefore formed where -the transparent substance which reflects them is thicker. And -that the augmentation of the density of the colorific -particles will conspire to the production of the same effect, -will be evident; if we remember what was said of the different -size of the rings, when air was included between the -glasses, from their size when water was between them; -which shewed that a substance of a greater density than -another gives the same colour at a less thickness. Now -the changes likely to be wrought in the density or magnitude -of the parts of vegetables by withering seem not -greater, than are sufficient to change their colour into those of -the same order; but the yellow and red of the fourth order -are not full enough to agree with those, into which these substances -change, nor is the green of the second sufficiently -good to be the colour of vegetables; so that their colour -must of necessity be of the third order.</p> - -<p>15. <span class="smcap gesperrt">The</span> blue colour of syrup of violets our author -supposes to be of the third order; for acids, as vinegar, with -this syrup change it red, and salt of tartar or other alcalies -mixed therewith turn it green. But if the blue colour -of the syrup were of the second order, the red colour, -which acids by attenuating its parts give it, must be of the -first order, and the green given it by alcalies by incrassating<span class="pagenum"><a name="Page_352" id="Page_352">[352]</a></span> -its particles should be of the second; whereas neither of those -colours is perfect enough, especially the green, to answer -those produced by these changes; but the red may well enough -be allowed to be of the second order, and the green -of the third; in which case the blue must be likewise of -the third order.</p> - -<p>16. <span class="smcap gesperrt">The</span> azure colour of the skies our author takes to -be of the first order, which requires the smallest particles -of any colour, and therefore most like to be exhibited by -vapours, before they have sufficiently coalesced to produce -clouds of other colours.</p> - -<p>17. <span class="smcap gesperrt">The</span> most intense and luminous white is of the -first order, if less strong it is a mixture of the colours of -all the orders. Of the latter sort he takes the colour of linnen, -paper, and such like substances to be; but white metals -to be of the former sort. The arguments for it are -these. The opacity of all bodies has been shewn to arise -from the number and strength of the reflections made within -them; but all experiments shew, that the strongest reflection -is made at those surfaces, which intercede transparent -bodies differing most in density. Among other instances -of this, the experiments before us afford one; for -when air only is included between the glasses, the coloured -rings are not only more dilated, as has before been said, -than when water is between them; but are likewise much -more luminous and bright. It follows therefore, that whatever -medium pervades the pores of bodies, if so be there<span class="pagenum"><a name="Page_353" id="Page_353">[353]</a></span> -is any, those substances must be most opake, the density of -whose parts differs most from the density of the medium, -which fills their pores. But it has been sufficiently proved in -the former part of this tract, that there is no very dense -medium lodging in, at least pervading at liberty the pores -of bodies. And it is farther proved by the present experiments. -For when air is inclosed by the denser substance -of glass, the rings dilate themselves, as has been said, by being -viewed obliquely; this they do so very much, that at -different obliquities the same thickness of air will exhibit all -sorts of colours. The bubble of water, though surrounded -with the thinner substance of air, does likewise change its -colour by being viewed obliquely; but not any thing near -so much, as in the other case; for in that the same colour -might be seen, when the rings were viewed most obliquely, -at more than twelve times the thickness it appeared at under -a direct view; whereas in this other case the thickness -was never found considerably above half as much again. -Now the colours of bodies not depending only on the light, -that is incident upon them perpendicularly, but likewise -upon that, which falls on them in all degrees of obliquity; -if the medium surrounding their particles were denser than -those particles, all sorts of colours must of necessity be reflected -from them so copiously, as would make the colours of all bodies -white, or grey, or at best very dilute and imperfect. But on the -other hand, if the medium in the pores of bodies be much rarer -than their particles, the colour reflected will be so little -changed by the obliquity of the rays, that the colour produced -by the rays, which fall near the perpendicular, may<span class="pagenum"><a name="Page_354" id="Page_354">[354]</a></span> -so much abound in the reflected light, as to give the body -their colour with little allay. To this may be added, that -when the difference of the contiguous transparent substances -is the same, a colour reflected from the denser substance -reduced into a thin plate and surrounded by the rarer will -be more brisk, than the same colour will be, when reflected -from a thin plate formed of the rarer substance, and surrounded -by the denser; as our author experienced by -blowing glass very thin at a lamp furnace, which exhibited -in the open air more vivid colours, than the air does between -two glasses. From these considerations it is manifest, -that if all other circumstances are alike, the densest bodies -will be most opake. But it was observed before, that these -white metals can hardly be made so thin, except by being -dissolved in corroding liquors, as to be rendred transparent; -though none of them are so dense as gold, which proves -their great opacity to have some other cause besides their -density; and none is more fit to produce this, than such a -size of their particles, as qualifies them to reflect the white -of the first order.</p> - -<p>18. <span class="smcap gesperrt">For</span> producing black the particles ought to be -smaller than for exhibiting any of the colours, viz. of a -size answering to the thickness of the bubble, where by reflecting -little or no light it appears colourless; but -yet they must not be too small, for that will make them -transparent through deficiency of reflections in the inward -parts of the body, sufficient to stop the light from going -through it; but they must be of a size bordering upon that<span class="pagenum"><a name="Page_355" id="Page_355">[355]</a></span> -disposed to reflect the faint blue of the first order, which -affords an evident reason why blacks usually partake a little -of that colour. We see too, why bodies dissolved by fire -or putrefaction turn black: and why in grinding glasses upon -copper plates the dust of the glass, copper, and sand -it is ground with, become very black: and in the last place -why these black substances communicate so easily to others -their hue; which is, that their particles by reason of the -great minuteness of them easily overspread the grosser particles -of others.</p> - -<p><a name="c355" id="c355">19.</a> <span class="smcap gesperrt">I shall</span> now finish this chapter with one remark -of the exceeding great porosity in bodies necessarily required -in all that has here been said; which, when duly considered, -must appear very surprizing; but perhaps it will be matter -of greater surprize, when I affirm that the sagacity of our -author has discovered a method, by which bodies may easily -become so; nay how any the least portion of matter may -be wrought into a body of any assigned dimensions how -great so ever, and yet the pores of that body none of -them greater, than any the smallest magnitude proposed at -pleasure; notwithstanding which the parts of the body shall -so touch, that the body itself shall be hard and solid<a name="FNanchor_310_310" id="FNanchor_310_310"></a><a href="#Footnote_310_310" class="fnanchor">[310]</a>. The -manner is this: suppose the body be compounded of particles of -such figures, that when laid together the pores found between -them may be equal in bigness to the particles; how -this may be effected, and yet the body be hard and solid, -is not difficult to understand; and the pores of such a body<span class="pagenum"><a name="Page_356" id="Page_356">[356]</a></span> -may be made of any proposed degree of smallness. But -the solid matter of a body so framed will take up only half -the space occupied by the body; and if each constituent -particle be composed of other less particles according to -the same rule, the solid parts of such a body will be but a -fourth part of its bulk; if every one of these lesser particles -again be compounded in the same manner, the solid -parts of the whole body shall be but one eighth of its bulk; -and thus by continuing the composition the solid parts of -the body may be made to bear as small a proportion to the -whole magnitude of the body, as shall be desired, notwithstanding -the body will be by the contiguity of its parts capable -of being in any degree hard. Which shews that this -whole globe of earth, nay all the known bodies in the universe -together, as far as we know, may be compounded -of no greater a portion of solid matter, than might be reduced -into a globe of one inch only in diameter, or even -less. We see therefore how by this means bodies may easily -be made rare enough to transmit light, with all that -freedom pellucid bodies are found to do. Though what -is the real structure of bodies we yet know not.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c356" id="c356"><span class="smcap"><em class="gesperrt">Chap. III.</em></span></a><br /> -Of the <span class="smcap">Refraction</span>, <span class="smcap">Reflection,</span> -and <span class="smcap">Inflection</span> of <span class="smcap">Light</span>.</h2> - -<p class="drop-cap04">THUS much of the colours of natural bodies; our -method now leads us to speculations yet greater, no<span class="pagenum"><a name="Page_357" id="Page_357">[357]</a></span> -less than to lay open the causes of all that has hitherto been -related. For it must in this chapter be explained, how the -prism separates the colours of the sun’s light, as we found -in the first chapter; and why the thin transparent plates -discoursed of in the last chapter, and consequently the particles -of coloured bodies, reflect that diversity of colours -only by being of different thicknesses.</p> - -<p><a name="c357" id="c357">2.</a> <span class="smcap gesperrt">For</span> the first it is proved by our author, that the colours -of the sun’s light are manifested by the prism, from the rays -undergoing different degrees of refraction; that the violet-making -rays, which go to the upper part of the coloured -image in the first experiment of the first chapter, are the -most refracted; that the indigo-making rays are refracted, -or turned out of their course by passing through the prism, -something less than the violet-making rays, but more than -the blue-making rays; and the blue-making rays more than -the green; the green-making rays more than the yellow; -the yellow more than the orange; and the orange-making -rays more than the red-making, which are least of all refracted. -The first proof of this, that rays of different colours -are refracted unequally is this. If you take any body, -and paint one half of it red and the other half blue, then -upon viewing it through a prism those two parts shall appear -separated from each other; which can be caused no -otherwise than by the prism’s refracting the light of one -half more than the light of the other half. But the blue -half will be most refracted; for if the body be seen through -the prism in such a situation, that the body shall appear<span class="pagenum"><a name="Page_358" id="Page_358">[358]</a></span> -lifted upwards by the refraction, as a body within a bason -of water, in the experiment mentioned in the first chapter, -appeared to be lifted up by the refraction of the water, so -as to be seen at a greater distance than when the bason is -empty, then shall the blue part appear higher than the red; -but if the refraction of the prism be the contrary way, the -blue part shall be depressed more than the other. Again, -after laying fine threads of black silk across each of the colours, -and the body well inlightened, if the rays coming -from it be received upon a convex glass, so that it -may by refracting the rays cast the image of the body -upon a piece of white paper held beyond the glass; then -it will be seen that the black threads upon the red part of -the image, and those upon the blue part, do not at the same -time appear distinctly in the image of the body projected -by the glass; but if the paper be held so, that the threads -on the blue part may distinctly appear, the threads cannot -be seen distinct upon the red part; but the paper -must be drawn farther off from the convex glass to make the -threads on this part visible; and when the distance is great enough -for the threads to be seen in this red part, they become -indistinct in the other. Whence it appears that the rays proceeding -from each point of the blue part of the body are -sooner united again by the convex glass than the rays which -come from each point of the red parts<a name="FNanchor_311_311" id="FNanchor_311_311"></a><a href="#Footnote_311_311" class="fnanchor">[311]</a>. But both these experiments -prove that the blue-making rays, as well in the small -refraction of the convex glass, as in the greater refraction -of the prism, are more bent, than the red-making rays.</p> - -<p><span class="pagenum"><a name="Page_359" id="Page_359">[359]</a></span></p> - -<p>3. <span class="smcap gesperrt">This</span> seems already to explain the reason of the coloured -spectrum made by refracting the sun’s light with a prism, -though our author proceeds to examine that in particular, -and proves that the different coloured rays in that spectrum -are in different degrees refracted; by shewing how to place -the prism in such a posture, that if all the rays were refracted -in the same manner, the spectrum should of necessity -be round: whereas in that case if the angle made by -the two surfaces of the prism, through which the light -passes, that is the angle D F E in fig. 126, be about 63 or 64 -degrees, the image instead of being round shall be near -five times as long as broad; a difference enough to shew -a great inequality in the refractions of the rays, which go to -the opposite extremities of the image. To leave no scruple -unremoved, our author is very particular in shewing by a -great number of experiments, that this inequality of refraction -is not casual, and that it does not depend upon any irregularities -of the glass; no nor that the rays are in their -passage through the prism each split and divided; but on -the contrary that every ray of the sun has its own peculiar -degree of refraction proper to it, according to which it is -more or less refracted in passing through pellucid substances -always in the same manner<a name="FNanchor_312_312" id="FNanchor_312_312"></a><a href="#Footnote_312_312" class="fnanchor">[312]</a>. That the rays are not split -and multiplied by the refraction of the prism, the third of -the experiments related in our first chapter shews very clearly; -for if they were, and the length of the spectrum in -the first refraction were thereby occasioned, the breadth -should be no less dilated by the cross refraction of the second<span class="pagenum"><a name="Page_360" id="Page_360">[360]</a></span> -prism; whereas the breadth is not at all increased, -but the image is only thrown into an oblique posture by the -upper part of the rays which were at first more refracted -than the under part, being again turned farthest out of their -course. But the experiment most expressly adapted to prove -this regular diversity of refraction is this, which follows<a name="FNanchor_313_313" id="FNanchor_313_313"></a><a href="#Footnote_313_313" class="fnanchor">[313]</a>. -Two boards A B, C D (in fig. 130.) being erected in a darkened -room at a proper distance, one of them A B being -near the window-shutter E F, a space only being left for -the prism G H I to be placed between them; so that the -rays entring at the hole M of the window-shutter may after -passing through the prism be trajected through a smaller -hole K made in the board A B, and passing on from thence -go out at another hole L made in the board C D of -the same size as the hole K, and small enough to transmit -the rays of one colour only at a time; let another prism -N O P be placed after the board C D to receive the rays passing -through the holes K and L, and after refraction by that -prism let those rays fall upon the white surface Q R. Suppose -first the violet light to pass through the holes, and to -be refracted by the prism N O P to <i>s</i>, which if the prism -N O P were removed should have passed right onto W. If the -prism G H I be turned slowly about, while the boards and -prism N O P remain fixed, in a little time another colour -will fall upon the hole L, which, if the prism N O P were -taken away, would proceed like the former rays to the same -point W; but the refraction of the prism N O P shall not carry -these rays to <i>s</i>, but to some place less distant from W as<span class="pagenum"><a name="Page_361" id="Page_361">[361]</a></span> -to <i>t</i>. Suppose now the rays which go to <i>t</i> to be the indigo-making -rays. It is manifest that the boards A B, C D, and -prism N O P remaining immoveable, both the violet-making -and indigo-making rays are incident alike upon the prism -N O P, for they are equally inclined to its surface O P, and enter it -in the same part of that surface; which shews that the indigo-making -rays are less diverted out of their course by the refraction -of the prism, than the violet-making rays under an -exact parity of all circumstances. Farther, if the prism G H I -be more turned about, ’till the blue-making rays pass -through the hole L, these shall fall upon the surface Q R -below I, as at <i>v</i>, and therefore are subjected to a less refraction -than the indigo-making rays. And thus by proceeding -it will be found that the green-making rays are -less refracted than the blue-making rays, and so of the rest, -according to the order in which they lie in the coloured -spectrum.</p> - -<p>4. <span class="smcap gesperrt">This</span> disposition of the different coloured rays to -be refracted some more than others our author calls their -respective degrees of refrangibility. And since this difference -of refrangibility discovers it self to be so regular, the -next step is to find the rule it observes.</p> - -<p><a name="c361" id="c361">5.</a> <span class="smcap gesperrt">It</span> is a common principle in optics, that the sine of -the angle of incidence bears to the sine of the refracted angle -a given proportion. If A B (in fig. 131, 132) represent -the surface of any refracting substance, suppose of -water or glass, and C D a ray of light incident upon that face<span class="pagenum"><a name="Page_362" id="Page_362">[362]</a></span> -in the point D, let D E be the ray, after it has passed the -surface A B; if the ray pass out of the air into the substance -whose surface is A B (as in fig. 131) it shall be turned -from the surface, and if it pass out of that substance into -air it shall be bent towards it (as in fig. 132) But if -F G be drawn through the point D perpendicular to the -surface A B, the angle under C D F made by the incident -ray and this perpendicular is called the angle of incidence; -and the angle under E D G, made by this perpendicular and the -ray after refraction, is called the refracted angle. And if -the circle H F I G be described with any interval cutting C D -in H and D E in I, then the perpendiculars H K, I L being -let fall upon F G, H K is called the sine of the angle -under C D F the angle of incidence, and I L the sine of -the angle under E D G the refracted angle. The first of -these sines is called the sine of the angle of incidence, or -more briefly the sine of incidence, the latter is the sine -of the refracted angle, or the sine of refraction. And it -has been found by numerous experiments that whatever -proportion the sine of incidence H K bears to the sine of -refraction I L in any one case, the same proportion shall -hold in all cases; that is, the proportion between these sines -will remain unalterably the same in the same refracting substance, -whatever be the magnitude of the angle under C D F.</p> - -<p>6. <span class="smcap gesperrt">But</span> now because optical writers did not observe that -every beam of white light was divided by refraction, as has -been here explained, this rule collected by them can only -be understood in the gross of the whole beam after refraction,<span class="pagenum"><a name="Page_363" id="Page_363">[363]</a></span> -and not so much of any particular part of it, or -at most only of the middle part of the beam. It therefore -was incumbent upon our author to find by what law the -rays were parted from each other; whether each ray apart -obtained this property, and that the separation was made -by the proportion between the sines of incidence and refraction -being in each species of rays different; or whether -the light was divided by some other rule. But he -proves by a certain experiment that each ray has its sine of -incidence proportional to its sine of refraction; and farther -shews by mathematical reasoning, that it must be so upon -condition only that bodies refract the light by acting -upon it, in a direction perpendicular to the surface of the -refracting body, and upon the same sort of rays always in -an equal degree at the same distances<a name="FNanchor_314_314" id="FNanchor_314_314"></a><a href="#Footnote_314_314" class="fnanchor">[314]</a>.</p> - -<p>7. <span class="smcap gesperrt">Our</span> great author teaches in the next place how from -the refraction of the most refrangible and least refrangible rays -to find the refraction of all the intermediate ones<a name="FNanchor_315_315" id="FNanchor_315_315"></a><a href="#Footnote_315_315" class="fnanchor">[315]</a>. The -method is this: if the sine of incidence be to the sine of refraction -in the least refrangible rays as A to B C, (in fig. 133) and -to the sine of refraction in the most refrangible as A to B D; -if C E be taken equal to C D, and then E D be so divided -in F, G, H, I, K, L, that E D, E F, E G, E H, E I, E K, E L, -E C, shall be proportional to the eight lengths of musical -chords, which found the notes in an octave, E D being -the length of the key, E F the length of the tone above<span class="pagenum"><a name="Page_364" id="Page_364">[364]</a></span> -that key, E G the length of the lesser third, E H of the -fourth, E I of the fifth, E K of the greater sixth, E L of -the seventh, and E C of the octave above that key; that is if -the lines E D, E F, E G, E H, E I, E K, E L, and E C bear the same -proportion as the numbers, 1, 9/8, 5/6, ¾, ⅓, ¾, 9/61, ½, respectively -then shall B D, B F, be the two limits of the sines of refraction of -the violet-making rays, that is the violet-making rays shall -not all of them have precisely the same sine of refraction, -but none of them shall have a greater sine than B D, nor -a less than B F, though there are violet-making rays which -answer to any sine of refraction that can be taken between -these two. In the same manner B F and B G -are the limits of the sines of refraction of the indigo-making -rays; B G, B H are the limits belonging to the blue-making -rays; B H, B I the limits pertaining to the green-making -rays, B I, B K the limits for the yellow-making rays; -B K, B L the limits for the orange-making rays; and lastly, -B L and B C the extreme limits of the sines of refraction -belonging to the red-making rays. These are the proportions -by which the heterogeneous rays of light are separated -from each other in refraction.</p> - -<p>8. <span class="smcap gesperrt">When</span> light passes out of glass into air, our author -found A to B C as 50 to 77, and the same A to B D as 50 -to 78. And when it goes out of any other refracting substance -into air, the excess of the sine of refraction of any -one species of rays above its sine of incidence bears a constant -proportion, which holds the same in each species, to -the excess of the sine of refraction of the same sort of rays<span class="pagenum"><a name="Page_365" id="Page_365">[365]</a></span> -above the sine of incidence into the air out of glass; provided -the sines of incidence both in glass and the other substance -are equal. This our author verified by transmitting the -light through prisms of glass included within a prismatic -vessel of water; and draws from those experiments the following -observations: that whenever the light in passing -through so many surfaces parting diverse transparent substances -is by contrary refractions made to emerge into the -air in a direction parallel to that of its incidence, it will -appear afterwards white at any distance from the prisms, -where you shall please to examine it; but if the direction -of its emergence be oblique to its incidence, in receding -from the place of emergence its edges shall appear tinged -with colours: which proves that in the first case there is -no inequality in the refractions of each species of rays, but -that when any one species is so refracted as to emerge parallel -to the incident rays, every sort of rays after refraction -shall likewise be parallel to the same incident rays, and -to each other; whereas on the contrary, if the rays of -any one sort are oblique to the incident light, the several -species shall be oblique to each other, and be gradually -separated by that obliquity. From hence he deduces -both the forementioned theorem, and also this other; -that in each sort of rays the proportion of the sine of incidence -to the sine of refraction, in the passage of the ray -out of any refracting substance into another, is compounded -of the proportion to which the sine of incidence would have to -the sine of refraction in the passage of that ray out of the -first substance into any third, and of the proportion which<span class="pagenum"><a name="Page_366" id="Page_366">[366]</a></span> -the sine of incidence would have to the sine of refraction -in the passage of the ray out of that third substance into -the second. From so simple and plain an experiment has -our most judicious author deduced these important theorems, -by which we may learn how very exact and circumspect -he has been in this whole work of his optics; that -notwithstanding his great particularity in explaining his -doctrine, and the numerous collection of experiments he -has made to clear up every doubt which could arise, yet -at the same time he has used the greatest caution to make -out every thing by the simplest and easiest means possible.</p> - -<p><a name="c366" id="c366">9.</a> <span class="smcap gesperrt">Our</span> author adds but one remark more upon refraction, -which is, that if refraction be performed in the manner -he has supposed from the light’s being pressed by the -refracting power perpendicularly toward the surface of the -refracting body, and consequently be made to move swifter -in the body than before its incidence; whether this power -act equally at all distances or otherwise, provided only its -power in the same body at the same distances remain without -variation the same in one inclination of the incident -rays as well as another; he observes that the refracting powers -in different bodies will be in the duplicate proportion -of the tangents of the lead angles, which the refracted light -can make with the surfaces of the refracting bodies<a name="FNanchor_316_316" id="FNanchor_316_316"></a><a href="#Footnote_316_316" class="fnanchor">[316]</a>. This -observation may be explained thus. When the light passes -into any refracting substance, it has been shewn above that -the sine of incidence bears a constant proportion to the sine<span class="pagenum"><a name="Page_367" id="Page_367">[367]</a></span> -of refraction. Suppose the light to pass to the refracting -body A B C D (in fig. 134) in the line E F, and to fall upon it at the -point F, and then to proceed within the body in the line -F G. Let H I be drawn through F perpendicular to the surface -A B, and any circle K L M N be described to the center -F. Then from the points O and P where this circle cuts -the incident and refracted ray, the perpendiculars O Q, P R -being drawn, the proportion of O Q to P R will remain -the same in all the different obliquities, in which the same ray -of light can fall on the surface A B. Now O Q is less than -F L the semidiameter of the circle K L M N, but the more -the ray E F is inclined down toward the surface A B, the -greater will O Q be, and will approach nearer to the magnitude -of F L. But the proportion of O Q to P R remaining -always the same, when O Q, is largest, P R will also be -greatest; so that the more the incident ray E F is inclined -toward the surface A B, the more the ray F G after refraction -will be inclined toward the same. Now if the line -F S T be so drawn, that S V being perpendicular to F I shall -be to F L the semidiameter of the circle in the constant proportion -of P R to O Q; then the angle under N F T is that -which I meant by the least of all that can be made by the -refracted ray with this surface, for the ray after refraction -would proceed in this line, if it were to come to the point -F lying on the very surface A B; for if the incident ray -came to the point F in any line between A F and F H, the -ray after refraction would proceed forward in some line -between F T and F I. Here if N W be drawn perpendicular -to F N, this line N W in the circle K L M N is called<span class="pagenum"><a name="Page_368" id="Page_368">[368]</a></span> -the tangent of the angle under N F S. Thus much being premised, -the sense of the forementioned proposition is this. Let there -be two refracting substances (in fig. 135) A B C D, and E F G H. -Take a point, as I, in the surface A B, and to the center I -with any semidiameter describe the circle K L M. In like -manner on the surface E F take some point N, as a center, -and describe with the same semidiameter the circle O P Q. -Let the angle under B I R be the least which the refracted -light can make with the surface A B, and the angle under -F N S the least which the refracted light can make with -the surface E F. Then if L T be drawn perpendicular to -A B, and P V perpendicular to E F; the whole power, wherewith -the substance A B C D acts on the light, will bear to -the whole power wherewith the substance E F G H acts on, -the light, a proportion, which is duplicate of the proportion, -which L T bears to P V.</p> - -<p><a name="c368" id="c368">10.</a> <span class="smcap gesperrt">Upon</span> comparing according to this rule the refractive -powers of a great many bodies it is found, that unctuous -bodies which abound most with sulphureous parts -refract the light two or three times more in proportion to -their density than others: but that those bodies, which seem -to receive in their composition like proportions of sulphureous -parts, have their refractive powers proportional to their -densities; as appears beyond contradiction by comparing -the refractive power of so rare a substance as the air with -that of common glass or rock crystal, though these substances -are 2000 times denser than air; nay the same proportion<span class="pagenum"><a name="Page_369" id="Page_369">[369]</a></span> -is found to hold without sensible difference in comparing -air with pseudo-topar and glass of antimony, though -the pseudo-topar be 3500 times denser than air, and glass -of antimony no less than 4400 times denser. This power -in other substances, as salts, common water, spirit of -wine, &c. seems to bear a greater proportion to their densities -than these last named, according as they abound with -sulphurs more than these; which makes our author conclude -it probable, that bodies act upon the light chiefly, if not -altogether, by means of the sulphurs in them; which kind -of substances it is likely enters in some degree the composition -of all bodies. Of all the substances examined by -our author, none has so great a refractive power, in respect -of its density, as a diamond.</p> - -<p><a name="c369" id="c369">11.</a> <span class="smcap gesperrt">Our</span> author finishes these remarks, and all he offers -relating to refraction, with observing, that the action between -light and bodies is mutual, since sulphureous bodies, -which are most readily set on fire by the sun’s light, when -collected upon them with a burning glass, act more upon -light in refracting it, than other bodies of the same density -do. And farther, that the densest bodies, which have -been now shewn to act most upon light, contract the greatest -heat by being exposed to the summer sun.</p> - -<p>12. <span class="smcap gesperrt">Having</span> thus dispatched what relates to refraction, -we must address ourselves to discourse of the other operation -of bodies upon light in reflecting it. When light -passes through a surface, which divides two transparent bodies<span class="pagenum"><a name="Page_370" id="Page_370">[370]</a></span> -differing in density, part of it only is transmitted, -another part being reflected. And if the light pass out of -the denser body into the rarer, by being much inclined to -the foresaid surface at length no part of it shall pass through, -but be totally reflected. Now that part of the light, which -suffers the greatest refraction, shall be wholly reflected with -a less obliquity of the rays, than the parts of the light -which undergo a less degree of refraction; as is evident -from the last experiment recited in the first chapter; where, -as the prisms D E F, G H I, (in fig. 129.) were turned about, -the violet light was first totally reflected, and then -the blue, next to that the green, and so of the rest. In consequence -of which our author lays down this proportion; that -the sun’s light differs in reflexibility, those rays being most reflexible, -which are most refrangible. And collects from this, -in conjunction with other arguments, that the refraction -and reflection, of light are produced by the same cause, -compassing those different effects only by the difference of -circumstances with which it is attended. Another proof -of this being taken by our author from what he has discovered -of the passage of light through thin transparent -plates, viz. that any particular species of light, suppose, -for instance, the red-making rays, will enter and pass out -of such a plate, if that plate be of some certain thicknesses; -but if it be of other thicknesses, it will not break through -it, but be reflected back: in which is seen, that the thickness -of the plate determines whether the power, by which -that plate acts upon the light, shall reflect it, or suffer it to -pass through.</p> - -<p><span class="pagenum"><a name="Page_371" id="Page_371">[371]</a></span></p> - -<p>13. <span class="smcap gesperrt">But</span> this last mentioned surprising property of the -action between light and bodies affords the reason of all -that has been said in the preceding chapter concerning the -colours of natural bodies; and must therefore more particularly -be illustrated and explained, as being what will -principally unfold the nature of the action of bodies upon -light.</p> - -<p><a name="c371" id="c371">14.</a> <span class="smcap gesperrt">To</span> begin: The object glass of a long telescope being -laid upon a plane glass, as proposed in the foregoing chapter, -in open day-light there will be exhibited rings of various -colours, as was there related; but if in a darkened -room the coloured spectrum be formed by the prism, as in -the first experiment of the first chapter, and the glasses be -illuminated by a reflection from the spectrum, the rings -shall not in this case exhibit the diversity of colours before -described, but appear all of the colour of the light -which falls upon the glasses, having dark rings between. -Which shews that the thin plate of air between the -glasses at some thicknesses reflects the incident light, at -other places does not reflect it, but is found in those places -to give the light passage; for by holding the glasses in -the light as it passes from the prism to the spectrum, suppose -at such a distance from the prism that the several sorts -of light must be sufficiently separated from each other, when -any particular sort of light falls on the glasses, you will find -by holding a piece of white paper at a small distance beyond -the glasses, that at those intervals, where the dark -lines appeared upon the glasses, the light is so transmitted,<span class="pagenum"><a name="Page_372" id="Page_372">[372]</a></span> -as to paint upon the paper rings of light having that colour -which falls upon the glasses. This experiment therefore -opens to us this very strange property of reflection, -that in these thin plates it should bear such a relation to the -thickness of the plate, as is here shewn. Farther, by carefully -measuring the diameters of each ring it is found, that -whereas the glasses touch where the dark spot appears in -the center of the rings made by reflexion, where the air -is of twice the thickness at which the light of the first ring -is reflected, there the light by being again transmitted makes -the first dark ring; where the plate has three times -that thickness which exhibits the first lucid ring, it again -reflects the light forming the second lucid ring; when -the thickness is four times the first, the light is again transmitted -so as to make the second dark ring; where the air -is five times the first thickness, the third lucid ring is made; -where it has six times the thickness, the third dark ring appears, -and so on: in so much that the thicknesses, at which -the light is reflected, are in proportion to the numbers 1, 3, -5, 7, 9, &c. and the thicknesses, where the light is transmitted, -are in the proportion of the numbers 0, 2, 4, 6, 8, -&c. And these proportions between the thicknesses which -reflect and transmit the light remain the same in all situations -of the eye, as well when the rings are viewed obliquely, -as when looked on perpendicularly. We must farther here -observe, that the light, when it is reflected, as well as when it is -transmitted, enters the thin plate, and is reflected from its farther -surface; because, as was before remarked, the altering -the transparent body behind the farther surface alters the degree<span class="pagenum"><a name="Page_373" id="Page_373">[373]</a></span> -of reflection as when a thin piece of Muscovy glass -has its farther surface wet with water, and the colour of -the glass made dimmer by being so wet; which shews that -the light reaches to the water, otherwise its reflection could -not be influenced by it. But yet this reflection depends -upon some power propagated from the first surface to the -second; for though made at the second surface it depends -also upon the first, because it depends upon the distance -between the surfaces; and besides, the body through -which the light passes to the first surface influences the reflection: -for in a plate of Muscovy glass, wetting the surface, -which first receives the light, diminishes the reflection, -though not quite so much as wetting the farther surface will -do. Since therefore the light in passing through these thin -plates at some thicknesses is reflected, but at others transmitted -without reflection, it is evident, that this reflection is -caused by some power propagated from the first surface, -which intermits and returns successively. Thus is every ray -apart disposed to alternate reflections and transmissions at -equal intervals; the successive returns of which disposition -our author calls the fits of easy reflection, and of easy transmission. -But these fits, which observe the same law of -returning at equal intervals, whether the plates are viewed -perpendicularly or obliquely, in different situations of the -eye change their magnitude. For what was observed before -in respect of those rings, which appear in open day-light, -holds likewise in these rings exhibited by simple lights; namely, -that these two alter in bigness according to the different -angle under which they are seen: and our author<span class="pagenum"><a name="Page_374" id="Page_374">[374]</a></span> -lays down a rule whereby to determine the thicknesses of -the plate of air, which shall exhibit the same colour under -different oblique views<a name="FNanchor_317_317" id="FNanchor_317_317"></a><a href="#Footnote_317_317" class="fnanchor">[317]</a>. And the thickness of the aereal -plate, which in different inclinations of the rays will exhibit -to the eye in open day-light the same colour, is also varied -by the same rule<a name="FNanchor_318_318" id="FNanchor_318_318"></a><a href="#Footnote_318_318" class="fnanchor">[318]</a>. He contrived farther a method -of comparing in the bubble of water the proportion between -the thickness of its coat, which exhibited any colour -when seen perpendicularly, to the thickness of it, where the -same colour appeared by an oblique view; and he found -the same rule to obtain here likewise<a name="FNanchor_319_319" id="FNanchor_319_319"></a><a href="#Footnote_319_319" class="fnanchor">[319]</a>. But farther, if the -glasses be enlightened successively by all the several species -of light, the rings will appear of different magnitudes; in -the red light they will be larger than in the orange colour, -in that larger than in the yellow, in the yellow larger than -in the green, less in the blue, less yet in the indigo, and -least of all in the violet: which shew that the same thickness -of the aereal plate is not fitted to reflect all colours, but -that one colour is reflected where another would have been -transmitted; and as the rays which are most strongly refracted -form the least rings, a rule is laid down by our author -for determining the relation, which the degree of refraction -of each species of colour has to the thicknesses of -the plate where it is reflected.</p> - -<p>15. <span class="smcap gesperrt">From</span> these observations our author shews the reason -of that great variety of colours, which appears in these thin -plates in the open white light of the day. For when this white<span class="pagenum"><a name="Page_375" id="Page_375">[375]</a></span> -light falls on the plate, each part of the light forms rings of -its own colour; and the rings of the different colours not -being of the same bigness are variously intermixed, and form -a great variety of tints<a name="FNanchor_320_320" id="FNanchor_320_320"></a><a href="#Footnote_320_320" class="fnanchor">[320]</a>.</p> - -<p><a name="c375a" id="c375a">16.</a> <span class="smcap gesperrt">In</span> certain experiments, which our author made with -thick glasses, he found, that these fits of easy reflection and -transmission returned for some thousands of times, and thereby -farther confirmed his reasoning concerning them<a name="FNanchor_321_321" id="FNanchor_321_321"></a><a href="#Footnote_321_321" class="fnanchor">[321]</a>.</p> - -<p><a name="c375b" id="c375b">17.</a> <span class="smcap gesperrt">Upon</span> the whole, our great author concludes from -some of the experiments made by him, that the reason why all -transparent bodies refract part of the light incident upon them, -and reflect another part, is, because some of the light, when it -comes to the surface of the body, is in a fit of easy transmission, -and some part of it in a fit of easy reflection; and from -the durableness of these fits he thinks it probable, that the -light is put into these fits from their first emission out of the -luminous body; and that these fits continue to return at equal -intervals without end, unless those intervals be changed -by the light’s entring into some refracting substance<a name="FNanchor_322_322" id="FNanchor_322_322"></a><a href="#Footnote_322_322" class="fnanchor">[322]</a>. He -likewise has taught how to determine the change which is -made of the intervals of the fits of easy transmission and reflection, -when the light passes out of one transparent space or -substance into another. His rule is, that when the light passes -perpendicularly to the surface, which parts any two transparent -substances, these intervals in the substance, out of<span class="pagenum"><a name="Page_376" id="Page_376">[376]</a></span> -which the light passes, bear to the intervals in the substance, -whereinto the light enters, the same proportion, as the sine of -incidence bears to the sine of refraction<a name="FNanchor_323_323" id="FNanchor_323_323"></a><a href="#Footnote_323_323" class="fnanchor">[323]</a>. It is farther to be -observed, that though the fits of easy reflection return at constant -intervals, yet the reflecting power never operates, but at -or near a surface where the light would suffer refraction; and -if the thickness of any transparent body shall be less than the -intervals of the fits, those intervals shall scarce be disturbed by -such a body, but the light shall pass through without any reflection<a name="FNanchor_324_324" id="FNanchor_324_324"></a><a href="#Footnote_324_324" class="fnanchor">[324]</a>.</p> - -<p><a name="c376" id="c376">18.</a> <span class="smcap gesperrt">What</span> the power in nature is, whereby this action -between light and bodies is caused, our author has not discovered. -But the effects, which he has discovered, of this -power are very surprising, and altogether wide from any conjectures -that had ever been framed concerning it; and from -these discoveries of his no doubt this power is to be deduced, -if we ever can come to the knowledge of it. Sir <span class="smcap">Isaac -Newton</span> has in general hinted at his opinion concerning it; -that probably it is owing to some very subtle and elastic substance -diffused through the universe, in which such vibrations -may be excited by the rays of light, as they pass through -it, that shall occasion it to operate so differently upon the -light in different places as to give rise to these alternate fits -of reflection and transmission, of which we have now been -speaking<a name="FNanchor_325_325" id="FNanchor_325_325"></a><a href="#Footnote_325_325" class="fnanchor">[325]</a>. He is of opinion, that such a substance may produce -this and other effects also in nature, though it be so -rare as not to give any sensible resistance to bodies in motion<a name="FNanchor_326_326" id="FNanchor_326_326"></a><a href="#Footnote_326_326" class="fnanchor">[326]</a>;<span class="pagenum"><a name="Page_377" id="Page_377">[377]</a></span> -and therefore not inconsistent with what has been said -above, that the planets move in spaces free from resistance<a name="FNanchor_327_327" id="FNanchor_327_327"></a><a href="#Footnote_327_327" class="fnanchor">[327]</a>.</p> - -<p><a name="c377a" id="c377a">19.</a> <span class="smcap gesperrt">In</span> order for the more full discovery of this action between -light and bodies, our author began another set of experiments, -wherein he found the light to be acted on as it passes -near the edges of solid bodies; in particular all small bodies, -such as the hairs of a man’s head or the like, held in a -very small beam of the sun’s light, cast extremely broad shadows. -And in one of these experiments the shadow was -35 times the breadth of the body<a name="FNanchor_328_328" id="FNanchor_328_328"></a><a href="#Footnote_328_328" class="fnanchor">[328]</a>. These shadows are also -observed to be bordered with colours<a name="FNanchor_329_329" id="FNanchor_329_329"></a><a href="#Footnote_329_329" class="fnanchor">[329]</a>. This our author calls -the inflection of light; but as he informs us, that he was interrupted -from prosecuting these experiments to any length, I need -not detain my readers with a more particular account of them.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c377b" id="c377b"><em class="gesperrt"><span class="smcap">Chap. IV.</span></em></a><br /> -Of OPTIC GLASSES.</h2> - -<p class="drop-cap08">SIR <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> having deduced from his doctrine -of light and colours a surprising improvement of telescopes, -of which I intend here to give an account, I shall -first premise something in general concerning those instruments.</p> - -<p><span class="pagenum"><a name="Page_378" id="Page_378">[378]</a></span></p> - -<p><a name="c378" id="c378">2.</a> <span class="smcap gesperrt">It</span> will be understood from what has been said above, -that when light falls upon the surface of glass obliquely, after -its entrance into the glass it is more inclined to the line -drawn through the point of incidence perpendicular to that -surface, than before. Suppose a ray of light issuing from the -point A (in fig. 136) falls on a piece of glass B C D E, whose -surface B C, whereon the ray falls, is of a spherical or globular -figure, the center whereof is F. Let the ray proceed in -the line A G falling on the surface B C in the point G, and draw -F G H. Here the ray after its entrance into the glass will -pass on in some line, as G I, more inclined toward the line F G H -that the line A G is inclined thereto; for the line F G H is perpendicular -to the surface B C in the point G. By this means, -if a number of rays proceeding from any one point -fall on a convex spherical surface of glass, they shall be -inflected (as is represented in fig. 137,) so as to be gathered -pretty close together about the line drawn through the center -of the glass from the point, whence the rays proceed; which -line henceforward we shall call the axis of the glass: or the -point from whence the rays proceed may be so near the glass, -that the rays shall after entring the glass still go on to spread -themselves, but not so much as before; so that if the rays -were to be continued backward (as in fig. 138,) they should -gather together about the axis at a place more remote from -the glass, than the point is, whence they actually proceed. In -these and the following figures A denotes the point to which -the rays are related before refraction, B the point to which they -are directed afterwards, and C the center of the refracting surface. -Here we may observe, that it is possible to form the glass of -such a figure, that all the rays which proceed from one point<span class="pagenum"><a name="Page_379" id="Page_379">[379]</a></span> -shall after refraction be reduced again exactly into one point on -the axis of the glass. But in glasses of a spherical form though this -does not happen; yet the rays, which fall within a moderate distance -from the axis, will unite extremely near together. If the -light fall on a concave spherical surface, after refraction it shall -spread quicker than before (as in fig. 139,) unless the rays proceed -from a point between the center and the surface of the glass. If -we suppose the rays of light, which fall upon the glass, not to -proceed from any point, but to move so as to tend all to some -point in the axis of the glass beyond the surface; if the glass -have a convex surface, the rays shall unite about the axis -sooner, than otherwise they would do (as in fig. 140,) unless -the point to which they tended was between the surface and -the center of that surface. But if the surface be concave, -they shall not meet so soon: nay perhaps converge. (See -fig. 141 and 142.)</p> - -<p>5. <span class="smcap gesperrt">Farther</span>, because the light in passing out of glass into -the air is turned by the refraction farther off from the -line drawn through the point of incidence perpendicular to -the refracting surface, than it was before; the light which -spreads from a point shall by parting through a convex surface -of glass into the air be made either to spread less than -before (as in fig. 143,) or to gather about the axis beyond -the glass (as in fig. 144.) But if the rays of light were proceeding -to a point in the axis of the glass, they should by -the refraction be made to unite sooner about that axis -(as in fig. 145.) If the surface of the glass be concave, rays which -proceed from a point shall be made to spread faster (as in -fig 146,) but rays which are tending to a point in the axis of<span class="pagenum"><a name="Page_380" id="Page_380">[380]</a></span> -the glass, shall be made to gather about the axis farther from -the glass (as in fig. 147) or even to diverge (as in fig. 148,) -unless the point, to which the rays are directed, lies between -the surface of the glass and its center.</p> - -<p>4. <span class="smcap gesperrt">The</span> rays, which spread themselves from a point, are -called diverging; and such as move toward a point, are called -converging rays. And the point in the axis of the glass, about -which the rays gather after refraction, is called the focus of -those rays.</p> - -<p><a name="c380" id="c380">5.</a> <span class="smcap gesperrt">If</span> a glass be formed of two convex spherical surfaces -(as in fig. 149,) where the glass AB is formed of the surfaces -A C B and A D B, the line drawn through the centers of the -two surfaces, as the line E F, is called the axis of the glass; -and rays, which diverge from any point of this axis, by the -refraction of the glass will be caused to converge toward some -part of the axis, or at least to diverge as from a point more -remote from the glass, than that from whence they proceeded; -for the two surfaces both conspire to produce this effect -upon the rays. But converging rays will be caused by such a -glass as this to converge sooner. If a glass be formed of two -concave surfaces, as the glass A B (in fig. 150,) the line C D -drawn through the centers, to which the two surfaces are -formed, is called the axis of the glass. Such a glass shall -cause diverging rays, which proceed from any point in the -axis of the glass, to diverge much more, as if they came from -some place in the axis of the glass nearer to it than the point, -whence the rays actually proceed. But converging rays will -be made either to converge less, or even to diverge.</p> - -<div class="figcenter"> - <img src="images/ill-449.jpg" width="400" height="519" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_381" id="Page_381">[381]</a></span></p> - -<p><a name="c381" id="c381">6.</a> <span class="smcap gesperrt">In</span> these glasses rays, which proceed from any point -near the axis, will be affected as it were in the same manner, -as if they proceeded from the very axis it self, and such as -converge toward a point at a small distance from the axis will -suffer much the same effects from the glass, as if they converged to -some point in the very axis. By this means any luminous body -exposed to a convex glass may have an image formed upon -any white body held beyond the glass. This may be easily -tried with a common spectacle-glass. For if such a glass -be held between a candle and a piece of white paper, if the -distances of the candle, glass, and paper be properly adjusted, -the image of the candle will appear very distinctly upon the -paper, but be seen inverted; the reason whereof is this. -Let A B (in fig. 151) be the glass, C D an object placed -cross the axis of the glass. Let the rays of light, which issue -from the point E, where the axis of the glass crosses the object, -be so refracted by the glass, as to meet again about the -point F. The rays, which diverge from the point C of the -object, shall meet again almost at the same distance from -the glass, but on the other side of the axis, as at G; for the -rays at the glass cross the axis. In like manner the rays, -which proceed from the point D, will meet about H on the -other side of the axis. None of these rays, neither those -which proceed from the point E in the axis, nor those which -issue from C or D, will meet again exactly in one point; but -yet in one place, as is here supposed at F, G, and H, they<span class="pagenum"><a name="Page_382" id="Page_382">[382]</a></span> -will be crouded so close together, as to make a distinct -image of the object upon any body proper to reflect it, -which shall be held there.</p> - -<p>7. <span class="smcap gesperrt">If</span> the object be too near the glass for the rays to -converge after the refraction, the rays shall issue out of the -glass, as if they diverged from a point more distant from -the glass, than that from whence they really proceed (as -in fig. 152,) where the rays coming from the point E -of the object, which lies on the axis of the glass A B, issue -out of the glass, as if they came from the point F -more remote from the glass than E; and the rays proceeding -from the point C issue out of the glass, as if they proceeded -from the point G; likewise the rays which issue -from the point D emerge out of the glass, as if they came -from the point H. Here the point G is on the same side -of the axis, as the point C; and the point H on the same -side, as the point D. In this case to an eye placed beyond -the glass the object should appear, as if it were in the situation -G F H.</p> - -<p>8. <span class="smcap gesperrt">If</span> the glass A B had been concave (as in, fig. 153,) to -an eye beyond the glass the object C D would appear in -the situation G H, nearer to the glass than really it is. Here -also the object will not be inverted; but the point G is on -the same side the axe with the point C, and H on the -same side as D.</p> - -<p><span class="pagenum"><a name="Page_383" id="Page_383">[383]</a></span></p> - -<p>9. <span class="smcap gesperrt">Hence</span> may be understood, why spectacles made -with convex glasses help the sight in old age: for the eye -in that age becomes unfit to see objects distinctly, except -such as are remov’d to a very great distance; whence all -men, when they first stand in need of spectacles, are observed -to read at arm’s length, and to hold the object at a -greater distance, than they used to do before. But when an -object is removed at too great a distance from the sight, -it cannot be seen clearly, by reason that a less quantity of -light from the object will enter the eye, and the whole -object will also appear smaller. Now by help of a convex -glass an object may be held near, and yet the rays of -light issuing from it will enter the eye, as if the object -were farther removed.</p> - -<p>10. <span class="smcap gesperrt">After</span> the same manner concave glasses assist such, -as are short sighted. For these require the object to be -brought inconveniently near to the eye, in order to their -seeing it distinctly; but by such a glass the object may be -removed to a proper distance, and yet the rays of light -enter the eye, as if they came from a place much nearer.</p> - -<p><a name="c383" id="c383">11.</a> <span class="smcap gesperrt">Whence</span> these defects of the sight arise, that in -old age objects cannot be seen distinct within a moderate -distance, and in short-sightedness not without being brought -too near, will be easily understood, when the manner of -vision in general shall be explain’d; which I shall now endeavour -to do, in order to be better understood in what<span class="pagenum"><a name="Page_384" id="Page_384">[384]</a></span> -follows. The eye is form’d, as is represented in fig. 154. -It is of a globular figure, the fore part whereof scarce -more protuberant than the rest is transparent. Underneath -this transparent part is a small collection of an humour in -appearance like water, and it has also the same refractive -power as common water; this is called the aqueous humour, -and fills the space A B C D in the figure. Next beyond -lies the body D E F G; this is solid but transparent, it is -composed with two convex surfaces, the hinder surface E F G -being more convex, than the anterior E D G. Between the -outer membrane A B C, and this body E D G F is placed that -membrane, which exhibits the colours, that are seen round -the sight of the eye; and the black spot, which is called the -sight or pupil, is a hole in this membrane, through which the -light enters, whereby we see. This membrane is fixed only -by its outward circuit, and has a muscular power, whereby -it dilates the pupil in a weak light, and contracts it in -a strong one. The body D E F G is called the crystalline -humour, and has a greater refracting power than water. -Behind this the bulk of the eye is filled up with what is -called the vitreous humor, this has much the same refractive -power with water. At the bottom of the eye toward -the inner side next the nose the optic glass enters, as at -H, and spreads it self all over the inside of the eye, till -within a small diftance from A and C. Now any object, as -I K, being placed before the eye, the rays of light issuing -from each point of this object are so refracted by the convex -surface of the aqueous humour, as to be caused to converge; -after this being received by the convex surface E D G<span class="pagenum"><a name="Page_385" id="Page_385">[385]</a></span> -of the crystalline humour, which has a greater refractive -power than the aqueous, the rays, when they are entered -into this surface, still more converge, and at going out of -the surface E F G into a humour of a less refractive power -than the crystalline they are made to converge yet farther. By -all these successive refractions they are brought to converge at -the bottom of the eye, so that a distinct image of the object -as L M is impress’d on the nerve. And by this means -the object is seen.</p> - -<p>11. <span class="smcap gesperrt">It</span> has been made a difficulty, that the image of -the object impressed on the nerve is inverted, so that the -upper part of the image is impressed on the lower part of -the eye. But this difficulty, I think, can no longer remain, -if we only consider, that upper and lower are terms -merely relative to the ordinary position of our bodies: -and our bodies, when view’d by the eye, have their image as -much inverted as other objects; so that the image of our -own bodies, and of other objects, are impressed on the eye -in the same relation to one another, as they really have.</p> - -<p><a name="c385" id="c385">12.</a> <span class="smcap gesperrt">The</span> eye can see objects equally distinct at very -different distances, but in one distance only at the same -time. That the eye may accomodate itself to different -distances, some change in its humours is requir’d. It is -my opinion, that this change is made in the figure of the -crystalline humour, as I have indeavoured to prove in another -place.</p> - -<p><span class="pagenum"><a name="Page_386" id="Page_386">[386]</a></span></p> - -<p>13. <span class="smcap gesperrt">If</span> any of the humours of the eye are too flat, -they will refract the light too little; which is the case in -old age. If they are too convex, they refract too much; -as in those who are short-sighted.</p> - -<p>14. <span class="smcap gesperrt">The</span> manner of direct vision being thus explained, -I proceed to give some account of telescopes, by which we -view more distinctly remote objects; and also of microscopes, -whereby we magnify the appearance of small objects. In -the first place, the most simple sort of telescope is composed -of two glasses, either both convex, or one convex, -and the other concave. (The first sort of these is represented -in fig. 155, the latter in fig. 156.)</p> - -<p><a name="c386" id="c386">15.</a> <span class="smcap gesperrt">In</span> fig. 155 let A B represent the convex glass next -the object, C D the other glass more convex near the eye. -Suppose the object-glass A B to form the image of the object -at E F; so that if a sheet of white paper were to be -held in this place, the object would appear. Now suppose -the rays, which pass the glass A B, and are united about -F, to proceed to the eye glass C D, and be there refracted. -Three only of these rays are drawn in the figure, -those which pass by the extremities of the glass A B, and -that which passes its middle. If the glass C D be -placed at such a distance from the image E F, that the rays, -which pass by the point F, after having proceeded through -the glass diverge so much, as the rays do that come from -an object, which is at such a distance from the eye as<span class="pagenum"><a name="Page_387" id="Page_387">[387]</a></span> -to be seen distinctly, these being received by the eye will -make on the bottom of the eye a distinct representation of -the point F. In like manner the rays, which pass through -the object glass A B to the point E after proceeding through -the eye-glass C D will on the bottom of the eye make a -distinct representation of the point E. But if the eye be -placed where these rays, which proceed from E, cross those, -which proceed from F, the eye will receive the distinct impression -of both these points at the same time; and consequently -will also receive a distinct impression from all the -intermediate parts of the image E F, that is, the eye will -see the object, to which the telescope is directed, distinctly. -The place of the eye is about the point G, where the rays -H E, H F cross, which pass through the middle of the object-glass -A B to the points E and F; or at the place where -the focus would be formed by rays coming from the point -H, and refracted by the glass C D. To judge how much -this instrument magnifies any object, we must first observe, -that the angle under E H F, in which the eye at the point H -would see the image E F, is nearly the same as the angle, -under which the object appears by direct vision; but when -the eye is in G, and views the object through the telescope, -it sees the same under a greater angle; for the rays, which -coming from E and F cross in G, make a greater angle than -the rays, which proceed from the point H to these points E -and F. The angle at G is greater than that at H in the -proportion, as the distance between the glasses A B and C D -is greater than the distance of the point G from the glass -C D.</p> - -<p><span class="pagenum"><a name="Page_388" id="Page_388">[388]</a></span></p> - -<p><a name="c388a" id="c388a">16.</a> <span class="smcap gesperrt">This</span> telescope inverts the object; for the rays, which -came from the right-hand side of the object, go to the -point E the left side of the image; and the rays, which -come from the left side of the object, go to F the right -side of the image. These rays cross again in G, so that -the rays, which come from the right side of the object, go -to the right side of the eye; and the rays from the left -side of the object go to the left side of the eye. Therefore -in this telescope the image in the eye has the same -situation as the object; and seeing that in direct vision -the image in the eye has an inverted situation, here, where -the situation is not inverted, the object must appear so. -This is no inconvenience to astronomers in celestial observations; -but for objects here on the earth it is usual to add -two other convex glasses, which may turn the object again -(as is represented in fig. 157,) or else to use the other kind of -telescope with a concave eye-glass.</p> - -<p><a name="c388b" id="c388b">17.</a> <span class="smcap gesperrt">In</span> this other kind of telescope the effect is founded -on the same principles, as in the former. The distinctness -of the appearance is procured in the same manner. But -here the eye-glass C D (in fig. 156) is placed between the -image E F, and the object glass A B. By this means the rays, -which come from the right-hand side of the object, and proceed -toward E the left side of the image, being intercepted -by the eye-glass are carried to the left side of the eye; and -the rays, which come from the left side of the object, go -to the right side of the eye; so that the impression in the -eye being inverted the object appears in the same situation,<span class="pagenum"><a name="Page_389" id="Page_389">[389]</a></span> -as when view’d by the naked eye. The eye must here be -placed close to the glass. The degree of magnifying in -this instrument is thus to be found. Let the rays, which -pass through the glass A B at H, after the refraction of -the eye-glass C D diverge, as if they came from the point -G; then the rays, which come from the extremities of the -object, enter the eye under the angle at G; so that here -also the object will be magnified in the proportion of the -distance between the glasses, to the distance of G from -the eye-glass.</p> - -<p>18. <span class="smcap gesperrt">The</span> space, that can be taken in at one view in -this telescope, depends on the breadth of the pupil of the -eye; for as the rays, which go to the points E, F of the -image, are something distant from each other, when they -come out of the glass C D, if they are wider asunder -than the pupil, it is evident, that they cannot both enter -the eye at once. In the other telescope the eye is placed -in the point G, where the rays that come from the points -E or F cross each other, and therefore must enter the eye -together. On this account the telescope with convex glasses -takes in a larger view, than those with concave. But in -these also the extent of the view is limited, because the eye-glass -does not by the refraction towards its edges form so -distinct a representation of the object, as near the middle.</p> - -<p><a name="c389" id="c389">18.</a><span class="smcap">Microscopes</span> are of two sorts. One kind is only a -very convex glass, by the means of which the object may -be brought very near the eye, and yet be seen distinctly.<span class="pagenum"><a name="Page_390" id="Page_390">[390]</a></span> -This microscope magnifies in proportion, as the object by -being brought near the eye will form a broader impression -on the optic nerve. The other kind made with convex -glasses produces its effects in the same manner as the telescope. -Let the object A B (in fig. 158) be placed under the glass C D, -and by this glass let an image be formed of this object. -Above this image let the glass G H be placed. By this glass -let the rays, which proceed from the points A and B, be -refracted, as is expressed in the figure. In particular, let -the rays, which from each of these points pass through the -middle of the glass C D, cross in I, and there let the eye -be placed. Here the object will appear larger, when seen -through the microscope, than if that instrument were removed, -in proportion as the angle, in which these rays cross -in I, is greater than the angle, which the lines would make, -that should be drawn from I to A and B; that is, in the -proportion made up of the proportion of the distance of the -object A B from I, to the distance of I from the glass G H; -and of the proportion of the distance between the glasses, -to the distance of the object A B from the glass C D.</p> - - -<p><a name="c390" id="c390">19.</a> <span class="smcap gesperrt">I shall</span> now proceed to explain the imperfection in -these instruments, occasioned by the different refrangibility of -the light which comes from every object. This prevents the -image of the object from being formed in the focus of the object -glass with perfect distinctness; so that if the eye-glass magnify -the image overmuch, the imperfections of it must be visible, -and make the whole appear confused. Our author more fully -to satisfy himself, that the different refrangibility of the<span class="pagenum"><a name="Page_391" id="Page_391">[391]</a></span> -several sorts of rays is sufficient to produce this irregularity, -underwent the labour of a very nice and difficult experiment, -whose process he has at large set down, to prove, -that the rays of light are refracted as differently in the small -refraction of telescope glasses as in the larger of the prism; -so exceeding careful has he been in searching out the true -cause of this effect. And he used, I suppose, the greater -caution, because another reason had before been generally -assigned for it. It was the opinion of all mathematicians, -that this defect in telescopes arose from the figure, in -which the glasses were formed; a spherical refracting surface -not collecting into an exact point all the rays which -come from any one point of an object, as has before been -said<a name="FNanchor_330_330" id="FNanchor_330_330"></a><a href="#Footnote_330_330" class="fnanchor">[330]</a>. But after our author has proved, that in these small -refractions, as well as in greater, the sine of incidence into -air out of glass, to the sine of refraction in the red-making -rays, is as 50 to 77, and in the blue-making rays -50 to 78; he proceeds to compare the inequalities of refraction -arising from this different refrangibility of the rays, -with the inequalities, which would follow from the figure -of the glass, were light uniformly refracted. For this purpose -he observes, that if rays issuing from a point so remote -from the object glass of a telescope, as to be esteemed -parallel, which is the case of the rays, which come from the -heavenly bodies; then the distance from the glass of the -point, in which the least refrangible rays are united, will -be to the distance, at which the most refrangible rays unite, -as 28 to 27; and therefore that the least space, into which<span class="pagenum"><a name="Page_392" id="Page_392">[392]</a></span> -all the rays can be collected, will not be less than the 55th -part of the breadth of the glass. For if A B (in fig. 159) be -the glass, C D its axis, E A, F B two rays of the light parallel -to that axis entring the glass near its edges; after refraction -let the least refrangible part of these rays meet in G, -the most refrangible in H; then, as has been said, G I will -be to I H, as 28 to 27; that is, G H will be the 28th -part of G I, and the 27th part of H I; whence if K L be -drawn through G, and M N through H, perpendicular to -C D, M N will be the a 28th part of A B, the breadth of -the glass, and K L the 27th part of the same; so that O P -the least space, into which the rays are gathered, will be -about half the mean between these two, that is the 55th -part of A B.</p> - -<p>20. <span class="smcap gesperrt">This</span> is the error arising from the different refrangibility -of the rays of light, which our author finds -vastly to exceed the other, consequent upon the figure of -the glass. In particular, if the telescope glass be flat on -one side, and convex on the other; when the flat side is -turned towards the object, by a theorem, which he has -laid down, the error from the figure comes out above 5000 -times less than the other. This other inequality is so -great, that telescopes could not perform so well as they -do, were it not that the light does not equally fill all the -space O P, over which it is scattered, but is much more dense -toward the middle of that space than at the extremities. -And besides, all the kinds of rays affect not the sense equally -strong, the yellow and orange being the strongest, -the red and green next to them, the blue indigo and violet -being much darker and fainter colours; and it is shewn -that all the yellow and orange, and three fifths of the -brighter half of the red next the orange, and as great a -share of the brighter half of the green next the yellow, -will be collected into a space whose breadth is not above -the 250th part of the breadth of the glass.</p> - -<div class="figcenter"> - <img src="images/ill-463.jpg" width="400" height="509" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_393" id="Page_393">[393]</a></span></p> - -<p>And the remaining -colours, which fall without this space, as they are -much more dull and obscure than these, so will they be -likewise much more diffused; and therefore call hardly affect -the sense in comparison of the other. And agreeable -to this is the observation of astronomers, that -telescopes between twenty and sixty feet in length represent -the fixed stars, as being about 5 or 6, at most -about 8 or 10 seconds in diameter. Whereas other arguments -shew us, that they do not really appear to us of any -sensible magnitude any otherwise than as their light is -dilated by refraction. One proof that the fixed stars do -not appear to us under any sensible angle is, that when -the moon passes over any of them, their light does not, like -the planets on the same occasion, disappear by degrees, but -vanishes at once.</p> - -<p><a name="c393" id="c393">21.</a> <span class="smcap gesperrt">Our</span> author being thus convinced, that telescopes -were not capable of being brought to much greater perfection -than at present by refractions, contrived one by reflection, in -which there is no separation made of the different coloured -light; for in every kind of light the rays after reflection -have the same degree of inclination to the surface, from -whence they are reflected, as they have at their incidence, so<span class="pagenum"><a name="Page_394" id="Page_394">[394]</a></span> -that those rays which come to the surface in one line, will go -off also in one line without any parting from one another. Accordingly -in the attempt he succeeded so well, that a short -one, not much exceeding six inches in length, equalled an ordinary -telescope whose length was four feet. Instruments of -this kind to greater lengths, have of late been made, which -fully answer expectation<a name="FNanchor_331_331" id="FNanchor_331_331"></a><a href="#Footnote_331_331" class="fnanchor">[331]</a>.</p> - -</div> - -<div class="chapter"> - -<h2 class="p4"><a name="c394a" id="c394a"><span class="smcap"><em class="gesperrt">Chap. V.</em></span></a><br /> -Of the RAINBOW.</h2> - -<p class="drop-cap00">I SHALL now explain the rainbow. The manner of its -production was understood, in the general, before Sir -<em class="gesperrt"><span class="smcap">Isaac Newton</span></em> had discovered his theory of colours; but -what caused the diversity of colours in it could not then be -known, which obliges him to explain this appearance particularly; -whom we shall imitate as follows. The first person, -who expressly shewed the rainbow to be formed by the -reflection of the sun-beams from drops of falling rain, -was <span class="smcap">Antonio de Dominis</span>. But this was afterwards -more fully and distinctly explained by <span class="smcap">DesCartes</span>.</p> - -<p><a name="c394b" id="c394b">2.</a> <span class="smcap gesperrt">There</span> appears most frequently two rainbows; both -of which are caused by the foresaid reflection of the sun-beams -from the drops of falling rain, but are not produced -by all the light which falls upon and are reflected -from the drops. The inner bow is produced by those -rays only which enter the drop, and at their entrance are -so refracted as to unite into a point, as it were, upon the farther -surface of the drop, as is represented in fig. 160; -where the contiguous rays <i>a b</i>, <i>c d</i>, <i>e f</i>, coming from the<span class="pagenum"><a name="Page_395" id="Page_395">[395]</a></span> -sun, and therefore to sense parallel, upon their entrance into -the drop in the points <i>b, d, f</i>, are so refracted as to meet -together in the point <i>g</i>, upon the farther surface of the drop. -Now these rays being reflected nearly from the same point -of the surface, the angle of incidence of each ray upon -the point g being equal to the angle of reflection, the -rays will return in the lines <i>g h, g k, g l</i>, in the same manner -inclined to each other, as they were before their incidence -upon the point <i>g</i>, and will make the same angles with -the surface of the drop at the points <i>b, k, l</i>, as at the points -<i>b, d, f</i>, after their entrance; and therefore after their emergence -out of the drop each ray will be inclined to the surface -in the same angle, as when it first entered it; whence -the lines <i>b m, k n, l o</i>, in which the rays emerge, must be -parallel to each other, as well as the lines <i>a b, c d, e f</i>, in -which they were incident. But these emerging rays being -parallel will not spread nor diverge from each other in -their passage from the drop, and therefore will enter the -eye conveniently situated in sufficient plenty to cause a -sensation. Whereas all the other rays, whether those nearer -the center of the drop, as <i>p q, r s</i>, or those farther off, as -<i>t u, w x</i>, will be reflected from other points in the hinder -surface of the drop; namely, the ray <i>p q</i> from the point -<i>y, r s</i> from <i>z, t v</i> from α, and <i>w x</i> from β. And for this -reason by their reflection and succeeding refraction they -will be scattered after their emergence from the forementioned -rays and from each other, and therefore cannot enter -the eye placed to receive them copious enough to excite -any distinct sensation.</p> - -<p><span class="pagenum"><a name="Page_396" id="Page_396">[396]</a></span></p> - -<p><a name="c396" id="c396">3.</a> <span class="smcap gesperrt">The</span> external rainbow is formed by two reflections -made between the incidence and emergence of the rays; -for it is to be noted, that the rays <i>g h, g k, g l</i>, at the -points <i>h, k, l</i>, do not wholly pass out of the drop, but -are in part reflected back; though the second reflection -of these particular rays does not form the outer bow. -For this bow is made by those rays, which after their entrance -into the drop are by the refraction of it united, before -they arrive at the farther surface, at such a distance from -it, that when they fall upon that surface, they may be reflected -in parallel lines, as is represented in fig. 161; -where the rays <i>a b, c d, e f</i>, are collected by the refraction -of the drop into the point <i>g</i>, and passing on from thence -strike upon the surface of the drop in the points <i>h, k, l</i>, and -are thence reflected to <i>m, n, o</i>, passing from <i>h</i> to <i>m</i>, from <i>k</i> to -<i>n</i>, and from <i>l</i> to <i>o</i> in parallel lines. For these rays after -reflection at <i>m, n, o</i>, will meet again in the point <i>p</i>, at -the same distance from these points of reflection <i>m, n, o</i>, -as the point <i>g</i> is from the former points of reflection <i>h, -k, l</i>. Therefore these rays in passing from <i>p</i> to the surface -of the drop will fall upon that surface in the points <i>q, -r, s</i> in the same angles, as these rays made with the surface -in <i>b, d, f</i>, after refraction. Consequently, when these rays -emerge out of the drop into the air, each ray will make -with the surface of the drop the same angle, as it made at -its first incidence; so that the lines <i>q t, r v, s w</i>, in which -they come from the drop, will be parallel to each other, as -well as the lines <i>a b, c d, e f</i>, in which they came to the<span class="pagenum"><a name="Page_397" id="Page_397">[397]</a></span> -drop. By this means these rays to a spectator commodiously -situated will become visible. But all the other rays, as well -those nearer the center of the drop <i>x y</i>, <i>z</i> α, as those more -remote from it β γ, δ ε, will be reflected in lines not parallel -to the lines <i>h m, k n, l o</i>; namely, the ray <i>x y</i>, in the -line ζ η, the ray ϰ α in the line θ ϰ, the ray β γ in the line -λ μ, and the ray δ ε in the line ν χ. Whence these rays -after their next reflection and subsequent refraction will be -scattered from the forementioned rays, and from one another, -and by that means become invisible.</p> - -<p>4. <span class="smcap gesperrt">It</span> is farther to be remarked, that if in the first case -the incident rays <i>a b, c d, e f</i>, and their correspondent emergent -rays <i>h m, k n, l o</i>, are produced till they meet, -they will make with each other a greater angle, than any -other incident ray will make with its corresponding emergent -ray. And in the latter case, on the contrary, the emergent -rays <i>q t, r v, s w</i> make with the incident rays an -acuter angle, than is made by any other of the emergent -rays.</p> - -<p>5. <span class="smcap gesperrt">Our</span> author delivers a method of finding each of -these extream angles from the degree of refraction being -given; by which method it appears, that the first of these -angles is the less, and the latter the greater, by how much -the refractive power of the drop, or the refrangibility of -the rays is greater. And this last consideration fully compleats -the doctrine of the rainbow, and shews, why the colours -of each bow are ranged in the order wherein they -are seen.</p> - -<p><span class="pagenum"><a name="Page_398" id="Page_398">[398]</a></span></p> - -<p>6. <span class="smcap gesperrt">Suppose</span> A (in fig. 162.) to be the eye, B, C, D, E, F, drops -of rain, M <i>n</i>, O <i>p</i>, Q <i>r</i>, S <i>t</i>, V <i>w</i> parcels of rays of the sun, -which entring the drops B, C, D, E, F after one reflection -pass out to the eye in A. Now let M <i>n</i> be produced to η -till it meets with the emergent ray likewise produced, let -O <i>p</i> produced meet its emergent ray produced in ϰ, let -Q <i>r</i> meet its emergent ray in λ, let S <i>t</i> meet its emergent -ray in μ, and let V <i>w</i> meet its emergent ray produced in ν. If -the angle under M η A be that, which is derived from the -refraction of the violet-making rays by the method we have -here spoken of, it follows that the violet light will only -enter the eye from the drop B, all the other coloured rays -passing below it, that is, all those rays which are not -scattered, but go out parallel so as to cause a sensation. For -the angle, which these parallel emergent rays makes with -the incident in the most refrangible or violet-making rays, -being less than this angle in any other sort of rays, none of -the rays which emerge parallel, except the violet-making, -will enter the eye under the angle M η A, but the rest making -with the incident ray M η a greater angle than this will -pass below the eye. In like manner if the angle under O ϰ A -agrees to the blue-making rays, the blue rays only shall enter -the eye from the drop C, and all the other coloured rays -will pass by the eye, the violet-coloured rays passing above, -the other colours below. Farther, the angle Q λ A corresponding -to the green-making rays, those only shall enter -the eye from the drop D, the violet and blue-making rays -passing above, and the other colours, that is the yellow and<span class="pagenum"><a name="Page_399" id="Page_399">[399]</a></span> -red, below. And if the angle S μ A answers to the refraction -of the yellow-making rays, they only shall come to -the eye from the drop E. And in the last place, if the angle -V ν A belongs to the red-making and least refrangible -rays, they only shall enter the eye from the drop F, all the -other coloured rays passing above.</p> - -<p>7. <span class="smcap gesperrt">But</span> now it is evident, that all the drops of water -found in any of the lines A ϰ, A λ, A μ, A ν, whether farther -from the eye, or nearer than the drops B, C, D, E, F, will -give the same colours as these do, all the drops upon each -line giving the same colour; so that the light reflected from -a number of these drops will become copious enough to be -visible; whereas the reflection from one minute drop alone -could not be perceived. But besides, it is farther manifest, -that if the line A Ξ be drawn from the sun through the eye, -that is, parallel to the lines M <i>n</i>, O <i>p</i>, Q <i>r</i>, S <i>t</i>, V <i>w</i>, and -if drops of water are placed all round this line, the same -colour will be exhibited by all the drops at the same distance -from this line. Hence it follows, that when the sun is -moderately elevated above the horizon, if it rains opposite -to it, and the sun shines upon the drops as they fall, a -spectator with his back turned to the sun must observe a coloured -circular arch reaching to the horizon, being red without, -next to that yellow, then green, blue, and on the inner -edge violet; only this last colour appears faint by being -diluted with the white light of the clouds, and from another -cause to be mentioned hereafter<a name="FNanchor_332_332" id="FNanchor_332_332"></a><a href="#Footnote_332_332" class="fnanchor">[332]</a>.</p> - -<p><span class="pagenum"><a name="Page_400" id="Page_400">[400]</a></span></p> - -<p>8. <span class="smcap gesperrt">Thus</span> is caused the interior or primary bow. The -drops of rain at some distance without this bow will cause -the exterior or secondary bow by two reflections of the sun’s -light. Let these drops be G, H, I, K, L; X <i>y</i>, Z α, Γ β, -Δ ι, Θ ζ denoting parcels of rays which enter each drop. -Now it has been remarked, that these rays make with the -visible refracted rays the greatest angle in those rays, which -are most refrangible. Suppose therefore the visible refracted -rays, which pass out from each drop after two reflections, and -enter the eye in A, to intersect the incident rays in π, ρ, σ, τ, -φ respectively. It is manifest, that the angle under Θ φ A is -the greatest of all, next to that the angle under Δ τ A, -the next in bigness will be the angle under Γ σ A, the next -to this the angle under Z ρ A, and the least of all the angle -under X π A. From the drop L therefore will come to -the eye the violet-making, or most refrangible rays, from -K the blue, from I the green, from H the yellow, and -from G the red-making rays; and the like will happen to -all the drops in the lines A π, A ρ, A τ, A φ, and also to all -the drops at the same distances from the line A Ξ all round -that line. Whence appears the reason of the secondary -bow, which is seen without the other, having its colours -in a contrary order, violet without and red within; -though the colours are fainter than in the other bow, as being -made by two reflections, and two refractions; whereas -the other bow is made by two refractions, and one reflection -only.</p> - -<p><span class="pagenum"><a name="Page_401" id="Page_401">[401]</a></span></p> - -<p><a name="c401" id="c401">9.</a> <span class="smcap gesperrt">There</span> is a farther appearance in the rainbow particularly -described about five years ago<a name="FNanchor_333_333" id="FNanchor_333_333"></a><a href="#Footnote_333_333" class="fnanchor">[333]</a>, which is, that under the -upper part or the inner bow there appears often two or -three orders of very faint colours, making alternate arches -of green, and a reddish purple. At the time this appearance -was taken notice of, I gave my thoughts concerning the -cause of it<a name="FNanchor_334_334" id="FNanchor_334_334"></a><a href="#Footnote_334_334" class="fnanchor">[334]</a>, which I shall here repeat. Sir <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> -has observed, that in glass, which is polished and quick-silvered, -there is an irregular refraction made, whereby some -small quantity of light is scattered from the principal reflected -beam<a name="FNanchor_335_335" id="FNanchor_335_335"></a><a href="#Footnote_335_335" class="fnanchor">[335]</a>. If we allow the same thing to happen in the -reflection whereby the rainbow is caused, it seems sufficient -to produce the appearance now mentioned.</p> - -<p>10. <span class="smcap gesperrt">Let</span> A B (in fig. 162.) represent a globule of water, -B the point from whence the rays of any determinate species -being reflected to C, and afterwards emerging in the -line C D, would proceed to the eye, and cause the appearance -of that colour in the rainbow, which appertains to -this species. Here suppose, that besides what is reflected regularly, -some small part of the light is irregularly scattered -every way; so that from the point B, besides the rays -that are regularly reflected from B to C, some scattered rays -will return in other lines, as in B E, B F, B G, B H, on -each side the line B C. Now it has been observed above<a name="FNanchor_336_336" id="FNanchor_336_336"></a><a href="#Footnote_336_336" class="fnanchor">[336]</a>, -that the rays of light in their passage from one superficies -of a refracting body to the other undergo alternate fits of<span class="pagenum"><a name="Page_402" id="Page_402">[402]</a></span> -easy transmission and reflection, succeeding each other at -equal intervals; insomuch that if they reach the farther superficies -in one sort of those fits, they shall be transmitted; -if in the other kind of them, they shall rather be reflected -back. Whence the rays that proceed from B to C, and -emerge in the line C D, being in a fit of easy transmission, -the scattered rays, that fall at a small distance without these -on either side (suppose the rays that pass in the lines B E, -B G) shall fall on the surface in a fit of easy reflection, and -shall not emerge; but the scattered rays, that pass at some -distance without these last, shall arrive at the surface of the -globule in a fit of easy transmission, and break through that -surface. Suppose these rays to pass in the lines B F, B H; -the former of which rays shall have had one fit more of easy -transmission, and the latter one fit less, than the rays that -pass from B to C. Now both these rays, when they go out -of the globule, will proceed by the refraction of the water -In the lines F I, H K, that will be inclined almost equally to -the rays incident on the globule, which come from the sun; but -the angles of their inclination will be less than the angle, in -which the rays emerging in the line C D are inclined to -those incident rays. And after the same manner rays scattered -from the point B at a certain distance without these -will emerge out of the globule, while the intermediate rays -are intercepted; and these emergent rays will be inclined -to the rays incident on the globule in angles still less than -the angles, in which the rays F I and H K are inclined to -them; and without these rays will emerge other rays, that -shall be inclined to the incident rays in angles yet less.</p> - -<div class="figcenter"> - <img src="images/ill-475.jpg" width="400" height="515" - alt="" - title="" /> -</div> - -<p><span class="pagenum"><a name="Page_403" id="Page_403">[403]</a></span></p> - -<p>Now by this means may be formed of every kind of rays, besides -the principal arch, which goes to the formation of the rainbow, -other arches within every one of the principal of the -same colour, though much more faint; and this for divers -successions, as long as these weak lights, which in every -arch grow more and more obscure, shall continue visible. -Now as the arches produced by each colour will be variously -mixed together, the diversity of colours observ’d in -these secondary arches may very possibly arise from them.</p> - -<p>11. <span class="smcap gesperrt">In</span> the darker colours these arches may reach below -the bow, and be seen distinct. In the brighter colours these -arches are lost in the inferior part of the principal light of the -rainbow; but in all probability they contribute to the red tincture, -which the purple of the rainbow usually has, and is most -remarkable when these secondary colours appear strongest. -However these secondary arches in the brightest colours may -possibly extend with a very faint light below the bow, and -tinge the purple of these secondary arches with a reddish hue.</p> - -<p>12. <span class="smcap gesperrt">The</span> precise distances between the principal arch -and these fainter arches depend on the magnitude of the -drops, wherein they are formed. To make them any degree -separate it is necessary the drop be exceeding small. It is -most likely, that they are formed in the vapour of the cloud, -which the air being put in motion by the fall of the rain -may carry down along with the larger drops; and this may -be the reason, why these colours appear under the upper<span class="pagenum"><a name="Page_404" id="Page_404">[404]</a></span> -part of the bow only, this vapour not descending very low. -As a farther confirmation of this, these colours are seen -strongest, when the rain falls from very black clouds, which -cause the fiercest rains, by the fall whereof the air will be -most agitated.</p> - -<p>13. <span class="smcap gesperrt">To</span> the like alternate return of the fits of easy transmission -and reflection in the passage of light through the -globules of water, which compose the clouds, Sir <span class="smcap">Isaac -Newton</span> ascribes some of those coloured circles, which -at times appear about the sun and moon<a name="FNanchor_337_337" id="FNanchor_337_337"></a><a href="#Footnote_337_337" class="fnanchor">[337]</a>.</p> - -<div class="figcenter"> - <img src="images/ill-478.jpg" width="300" height="176" - alt="" - title="" /> -</div> - -</div> - -<p><span class="pagenum"><a name="Page_405" id="Page_405">[405]</a></span></p> - -<div class="chapter"> - -<div class="figcenter"> - <img src="images/ill-479.jpg" width="400" height="204" - alt="" - title="" /> -</div> - -<h2 class="p4"><a name="c405" id="c405">CONCLUSION.</a></h2> - -<div> - <img class="dcap1" src="images/ds1.jpg" width="80" height="81" alt=""/> -</div> -<p class="cap13">SIR <em class="gesperrt"><span class="smcap">Isaac Newton</span></em> having concluded -each of his philosophical treatises with -some general reflections, I shall now -take leave of my readers with a short -account of what he has there delivered. -At the end of his mathematical principles -of natural philosophy he has -given us his thoughts concerning the Deity. Wherein he -first observes, that the similitude found in all parts of the -universe makes it undoubted, that the whole is governed by -one supreme being, to whom the original is owing of the -frame of nature, which evidently is the effect of choice -and design. He then proceeds briefly to state the best metaphysical -notions concerning God. In short, we cannot -conceive either of space or time otherwise than as necessarily<span class="pagenum"><a name="Page_406" id="Page_406">[406]</a></span> -existing; this Being therefore, on whom all others depend, -must certainly exist by the same necessity of nature. -Consequently wherever space and time is found, there God -must also be. And as it appears impossible to us, that space -should be limited, or that time should have had a beginning, -the Deity must be both immense and eternal.</p> - -<p>2. <span class="smcap gesperrt">At</span> the end of his treatise of optics he has proposed -some thoughts concerning other parts of nature, which he -had not distinctly searched into. He begins with some -farther reflections concerning light, which he had not fully -examined. In particular he declares his sentiments at large -concerning the power, whereby bodies and light act on each -other. In some parts of his book he had given short hints -at his opinion concerning this<a name="FNanchor_338_338" id="FNanchor_338_338"></a><a href="#Footnote_338_338" class="fnanchor">[338]</a>, but here he expressly declares -his conjecture, which we have already mentioned<a name="FNanchor_339_339" id="FNanchor_339_339"></a><a href="#Footnote_339_339" class="fnanchor">[339]</a>, -that this power is lodged in a very subtle spirit of a great elastic -force diffused thro’ the universe, producing not only this, but -many other natural operations. He thinks it not impossible, -that the power of gravity itself should be owing to it. On -this occasion he enumerates many natural appearances, the -chief of which are produced by chymical experiments. From -numerous observations of this kind he makes no doubt, that -the smallest parts of matter, when near contact, act strongly -on each other, sometimes being mutually attracted, at other -times repelled.</p> - -<p>3. <span class="smcap gesperrt">The</span> attractive power is more manifest than the other, -for the parts of all bodies adhere by this principle. And the<span class="pagenum"><a name="Page_407" id="Page_407">[407]</a></span> -name of attraction, which our author has given to it, has -been very freely made use of by many writers, and as much -objected to by others. He has often complained to -me of having been misunderstood in this matter. What -he lays upon this head was not intended by him as a philosophical -explanation of any appearances, but only to point -out a power in nature not hitherto distinctly observed, the -cause of which, and the manner of its acting, he thought -was worthy of a diligent enquiry. To acquiesce in the -explanation of any appearance by asserting it to be a general -power of attraction, is not to improve our knowledge in -philosophy, but rather to put a stop to our farther search.</p> - -<p>FINIS.</p> - -<div class="figcenter"> - <img src="images/ill-481.jpg" width="300" height="206" - alt="" - title="" /> -</div> - -<hr class="chap" /> - -</div> - -<div class="chapter"> - -<h2 class="p4">FOOTNOTES:</h2> - -<div class="footnotes"> - -<p class="pfn4"><span class="ln1"><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a></span> -Philosoph. Nat. princ. math. L. iii. introduct.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a></span> -Nov. Org. Scient. L. i. Aphorism. 9.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a></span> -Nov. Org. L. i. Aph. 19.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a></span> -Ibid. Aph. 25.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a></span> -Aph. 30. Errores radicales & in prima digestione -mentis ab excellentia functionum & remediorum -sequentium non curantur.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a></span> -Aph. 38.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a></span> -Aph. 39.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a></span> -Aph. 41.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a></span> -Aph. 10, 24.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a></span> -Aph. 45.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a></span> -De Cartes Princ. Phil. Part. 3. §. 52.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a></span> -Fermat, in Oper. pag. 156, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a></span> -Nov. Org. Aph. 46.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a></span> -Aph. 50.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a></span> -Aph 53.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a></span> -Aph. 54.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a></span> -Aph. 56.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a></span> -Aph. 55.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a></span> -Locke, On human understanding, B. iii.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a></span> -Nov. Org. Aph. 59.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a></span> -In the conclusion.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">[24]</span></a></span> -Nov. Org. L. i. Aph. 59.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a></span> -Ibid. Aph. 60.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a></span> -Ibid. Aph. 62.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a></span> -Aph. 63.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a></span> -Aph. 64.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a></span> -Aph. 65.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a></span> -See above, § 4, 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a></span> -Nov. Org. L. i. Aph. 69.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a></span> -Ibid. Aph. 109.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a></span> -Book III. Chap. iv.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a></span> -Book I. Chap. 2. § 14.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_36_36" id="Footnote_36_36"></a><a href="#FNanchor_36_36"><span class="label">[36]</span></a></span> -Ibid. § 85, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_37_37" id="Footnote_37_37"></a><a href="#FNanchor_37_37"><span class="label">[37]</span></a></span> -See Book II. Ch. 3. § 3, 4. of this treatise.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_38_38" id="Footnote_38_38"></a><a href="#FNanchor_38_38"><span class="label">[38]</span></a></span> -See Book II. Ch. 3. of this treatise.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_39_39" id="Footnote_39_39"></a><a href="#FNanchor_39_39"><span class="label">[39]</span></a></span> -See Chap. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_40_40" id="Footnote_40_40"></a><a href="#FNanchor_40_40"><span class="label">[40]</span></a></span> -At the end of his Optics. in Qu. 21.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_41_41" id="Footnote_41_41"></a><a href="#FNanchor_41_41"><span class="label">[41]</span></a></span> -See the same treatise, in Advertisement 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_42_42" id="Footnote_42_42"></a><a href="#FNanchor_42_42"><span class="label">[42]</span></a></span> -Nov. Org. Lib. i. Ax. 105.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_43_43" id="Footnote_43_43"></a><a href="#FNanchor_43_43"><span class="label">[43]</span></a></span> -Princip. philos. pag. 13, 14.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_44_44" id="Footnote_44_44"></a><a href="#FNanchor_44_44"><span class="label">[44]</span></a></span> -Princ. Philos. L. II. prop. 24. corol. 7. See also B. II. Ch. 5. § 3. of this treatise.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_45_45" id="Footnote_45_45"></a><a href="#FNanchor_45_45"><span class="label">[45]</span></a></span> -How this degree of elasticity is to be found by experiment, will be shewn below in § 74.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_46_46" id="Footnote_46_46"></a><a href="#FNanchor_46_46"><span class="label">[46]</span></a></span> - In oper. posthum de Motu corpor. ex percussion. prop. 9.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_47_47" id="Footnote_47_47"></a><a href="#FNanchor_47_47"><span class="label">[47]</span></a></span> - In the above-cited place.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_48_48" id="Footnote_48_48"></a><a href="#FNanchor_48_48"><span class="label">[48]</span></a></span> -In the place above-cited.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_49_49" id="Footnote_49_49"></a><a href="#FNanchor_49_49"><span class="label">[49]</span></a></span> -These experiments are described in § 73.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_50_50" id="Footnote_50_50"></a><a href="#FNanchor_50_50"><span class="label">[50]</span></a></span> -Book II. Chap. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_51_51" id="Footnote_51_51"></a><a href="#FNanchor_51_51"><span class="label">[51]</span></a></span> -Chap. 1. § 25, 26, 27, compared with § 15, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_52_52" id="Footnote_52_52"></a><a href="#FNanchor_52_52"><span class="label">[52]</span></a></span> -Book II. Chap. 5. § 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_53_53" id="Footnote_53_53"></a><a href="#FNanchor_53_53"><span class="label">[53]</span></a></span> -See Euclid’s Elements, Book XII. prop. 13.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_54_54" id="Footnote_54_54"></a><a href="#FNanchor_54_54"><span class="label">[54]</span></a></span> -Archimed. de æquipond. prop. 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_55_55" id="Footnote_55_55"></a><a href="#FNanchor_55_55"><span class="label">[55]</span></a></span> -Ibid. prop. 12.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_56_56" id="Footnote_56_56"></a><a href="#FNanchor_56_56"><span class="label">[56]</span></a></span> -Lucas Valerius De centr. gravit. solid. L. I. -prop. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_57_57" id="Footnote_57_57"></a><a href="#FNanchor_57_57"><span class="label">[57]</span></a></span> -Idem L. II. prop. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_58_58" id="Footnote_58_58"></a><a href="#FNanchor_58_58"><span class="label">[58]</span></a></span> -§ 25.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_59_59" id="Footnote_59_59"></a><a href="#FNanchor_59_59"><span class="label">[59]</span></a></span> -§ 27.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_60_60" id="Footnote_60_60"></a><a href="#FNanchor_60_60"><span class="label">[60]</span></a></span> -Pag. 65, 68.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_61_61" id="Footnote_61_61"></a><a href="#FNanchor_61_61"><span class="label">[61]</span></a></span> -§ 23.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_62_62" id="Footnote_62_62"></a><a href="#FNanchor_62_62"><span class="label">[62]</span></a></span> -§ 20</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_63_63" id="Footnote_63_63"></a><a href="#FNanchor_63_63"><span class="label">[63]</span></a></span> -§ 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_64_64" id="Footnote_64_64"></a><a href="#FNanchor_64_64"><span class="label">[64]</span></a></span> -§ 27.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_65_65" id="Footnote_65_65"></a><a href="#FNanchor_65_65"><span class="label">[65]</span></a></span> -Hugen. Horolog. oscillat. pag. 141, 142.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_66_66" id="Footnote_66_66"></a><a href="#FNanchor_66_66"><span class="label">[66]</span></a></span> -See Hugen. Horolog. Oscillat. p. 142.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_67_67" id="Footnote_67_67"></a><a href="#FNanchor_67_67"><span class="label">[67]</span></a></span> -Princip. Philos. pag. 22.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_68_68" id="Footnote_68_68"></a><a href="#FNanchor_68_68"><span class="label">[68]</span></a></span> -Chap. 1. § 29.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_69_69" id="Footnote_69_69"></a><a href="#FNanchor_69_69"><span class="label">[69]</span></a></span> -Princip. Philos. pag. 25.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_70_70" id="Footnote_70_70"></a><a href="#FNanchor_70_70"><span class="label">[70]</span></a></span> -§ 71.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_71_71" id="Footnote_71_71"></a><a href="#FNanchor_71_71"><span class="label">[71]</span></a></span> -See Method. Increment. prop. 25.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_72_72" id="Footnote_72_72"></a><a href="#FNanchor_72_72"><span class="label">[72]</span></a></span> -Lib. XI. Def.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_73_73" id="Footnote_73_73"></a><a href="#FNanchor_73_73"><span class="label">[73]</span></a></span> -Chap. 2. § 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_74_74" id="Footnote_74_74"></a><a href="#FNanchor_74_74"><span class="label">[74]</span></a></span> -See above Ch. 2. § 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_75_75" id="Footnote_75_75"></a><a href="#FNanchor_75_75"><span class="label">[75]</span></a></span> -From B II. Ch. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_76_76" id="Footnote_76_76"></a><a href="#FNanchor_76_76"><span class="label">[76]</span></a></span> -Prin. Philos. pag. 7, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_77_77" id="Footnote_77_77"></a><a href="#FNanchor_77_77"><span class="label">[77]</span></a></span> -See Newton, princip. philos. pag. 9. lin. 30.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_78_78" id="Footnote_78_78"></a><a href="#FNanchor_78_78"><span class="label">[78]</span></a></span> -Princip. Philos. pag. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_79_79" id="Footnote_79_79"></a><a href="#FNanchor_79_79"><span class="label">[79]</span></a></span> -Renat. Des Cart. Princ. Philos. Part. II. § 25.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_80_80" id="Footnote_80_80"></a><a href="#FNanchor_80_80"><span class="label">[80]</span></a></span> -Ibid. § 30.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_81_81" id="Footnote_81_81"></a><a href="#FNanchor_81_81"><span class="label">[81]</span></a></span> -§ 85, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_82_82" id="Footnote_82_82"></a><a href="#FNanchor_82_82"><span class="label">[82]</span></a></span> -Princip. Philos. Lib. I. prop. 9.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_83_83" id="Footnote_83_83"></a><a href="#FNanchor_83_83"><span class="label">[83]</span></a></span> -§ 92.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_84_84" id="Footnote_84_84"></a><a href="#FNanchor_84_84"><span class="label">[84]</span></a></span> -Ch. II. § 22.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_85_85" id="Footnote_85_85"></a><a href="#FNanchor_85_85"><span class="label">[85]</span></a></span> -Viz. L. I. prop. 30, 29, & 26.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_86_86" id="Footnote_86_86"></a><a href="#FNanchor_86_86"><span class="label">[86]</span></a></span> - Ch. II. § 21, 22.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_87_87" id="Footnote_87_87"></a><a href="#FNanchor_87_87"><span class="label">[87]</span></a></span> -viz. His doctrine of prime and ultimate ratios.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_88_88" id="Footnote_88_88"></a><a href="#FNanchor_88_88"><span class="label">[88]</span></a></span> -§ 57</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_89_89" id="Footnote_89_89"></a><a href="#FNanchor_89_89"><span class="label">[89]</span></a></span> -§ 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_90_90" id="Footnote_90_90"></a><a href="#FNanchor_90_90"><span class="label">[90]</span></a></span> -Ch. 2. § 22.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_91_91" id="Footnote_91_91"></a><a href="#FNanchor_91_91"><span class="label">[91]</span></a></span> -§ 12.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_92_92" id="Footnote_92_92"></a><a href="#FNanchor_92_92"><span class="label">[92]</span></a></span> -Ch. 1. sect. 21, 22.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_93_93" id="Footnote_93_93"></a><a href="#FNanchor_93_93"><span class="label">[93]</span></a></span> -Elem. Book I. p. 37.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_94_94" id="Footnote_94_94"></a><a href="#FNanchor_94_94"><span class="label">[94]</span></a></span> -§ 12.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_95_95" id="Footnote_95_95"></a><a href="#FNanchor_95_95"><span class="label">[95]</span></a></span> -Ch 1 § 24.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_96_96" id="Footnote_96_96"></a><a href="#FNanchor_96_96"><span class="label">[96]</span></a></span> -Ch 2 select. 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_97_97" id="Footnote_97_97"></a><a href="#FNanchor_97_97"><span class="label">[97]</span></a></span> -Newt. Princ. L. II. prop. 2; 5, 6, 7; 11, 12.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_98_98" id="Footnote_98_98"></a><a href="#FNanchor_98_98"><span class="label">[98]</span></a></span> -Prop. 3; 8, 9; 13, 14.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_99_99" id="Footnote_99_99"></a><a href="#FNanchor_99_99"><span class="label">[99]</span></a></span> -Prop. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_100_100" id="Footnote_100_100"></a><a href="#FNanchor_100_100"><span class="label">[100]</span></a></span> -Prælect. Geometr. pag. 123.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_101_101" id="Footnote_101_101"></a><a href="#FNanchor_101_101"><span class="label">[101]</span></a></span> -Newton. Princ. Lib. II. prop. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_102_102" id="Footnote_102_102"></a><a href="#FNanchor_102_102"><span class="label">[102]</span></a></span> -Newton. Princ. Lib II. prop 10. in schol.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_103_103" id="Footnote_103_103"></a><a href="#FNanchor_103_103"><span class="label">[103]</span></a></span> -Torricelli de motu gravium.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_104_104" id="Footnote_104_104"></a><a href="#FNanchor_104_104"><span class="label">[104]</span></a></span> -Ch. 2 § 85, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_105_105" id="Footnote_105_105"></a><a href="#FNanchor_105_105"><span class="label">[105]</span></a></span> -Newt. Princ L. II. sect 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_106_106" id="Footnote_106_106"></a><a href="#FNanchor_106_106"><span class="label">[106]</span></a></span> -L. II. sect. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_107_107" id="Footnote_107_107"></a><a href="#FNanchor_107_107"><span class="label">[107]</span></a></span> -See B. II. Ch 6. § 7. of this treatise.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_108_108" id="Footnote_108_108"></a><a href="#FNanchor_108_108"><span class="label">[108]</span></a></span> -Lib. I. sect. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_109_109" id="Footnote_109_109"></a><a href="#FNanchor_109_109"><span class="label">[109]</span></a></span> -De la Pesanteur, pag. 169, and the following.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_110_110" id="Footnote_110_110"></a><a href="#FNanchor_110_110"><span class="label">[110]</span></a></span> -Newton. Princ. L. II. prop 4. schol.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_111_111" id="Footnote_111_111"></a><a href="#FNanchor_111_111"><span class="label">[111]</span></a></span> -See his Tract on the admirable rarifaction of -the air.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_112_112" id="Footnote_112_112"></a><a href="#FNanchor_112_112"><span class="label">[112]</span></a></span> -Book II. Ch. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_113_113" id="Footnote_113_113"></a><a href="#FNanchor_113_113"><span class="label">[113]</span></a></span> -Princ. philos. Lib. II. prop. 23.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_114_114" id="Footnote_114_114"></a><a href="#FNanchor_114_114"><span class="label">[114]</span></a></span> -Book I. Ch. 2. § 30.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_115_115" id="Footnote_115_115"></a><a href="#FNanchor_115_115"><span class="label">[115]</span></a></span> -Princ. philos. Lib. II. prop. 23, in schol.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_116_116" id="Footnote_116_116"></a><a href="#FNanchor_116_116"><span class="label">[116]</span></a></span> -Princ. philos. Lib. II. prop. 33. coroll.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_117_117" id="Footnote_117_117"></a><a href="#FNanchor_117_117"><span class="label">[117]</span></a></span> -Lib. II. Ch. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_118_118" id="Footnote_118_118"></a><a href="#FNanchor_118_118"><span class="label">[118]</span></a></span> -Ibid. Prop. 35. coroll. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_119_119" id="Footnote_119_119"></a><a href="#FNanchor_119_119"><span class="label">[119]</span></a></span> -Ibid. coroll. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_120_120" id="Footnote_120_120"></a><a href="#FNanchor_120_120"><span class="label">[120]</span></a></span> -Vid. ibid. coroll. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_121_121" id="Footnote_121_121"></a><a href="#FNanchor_121_121"><span class="label">[121]</span></a></span> -In § 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_122_122" id="Footnote_122_122"></a><a href="#FNanchor_122_122"><span class="label">[122]</span></a></span> -Princ. philos. Lib. II. Prop. 35.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_123_123" id="Footnote_123_123"></a><a href="#FNanchor_123_123"><span class="label">[123]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_124_124" id="Footnote_124_124"></a><a href="#FNanchor_124_124"><span class="label">[124]</span></a></span> -Id.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_125_125" id="Footnote_125_125"></a><a href="#FNanchor_125_125"><span class="label">[125]</span></a></span> -h. 1. § 29.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_126_126" id="Footnote_126_126"></a><a href="#FNanchor_126_126"><span class="label">[126]</span></a></span> -Princ. philos. Lib. II. Prop. 38, compared with -coroll. 1 of prop. 35.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_127_127" id="Footnote_127_127"></a><a href="#FNanchor_127_127"><span class="label">[127]</span></a></span> -L. II. Lem. 7. schol. pag. 341.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_128_128" id="Footnote_128_128"></a><a href="#FNanchor_128_128"><span class="label">[128]</span></a></span> -Lib. II. Prop. 34.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_129_129" id="Footnote_129_129"></a><a href="#FNanchor_129_129"><span class="label">[129]</span></a></span> -Lib. II. Lem. 7. p. 341.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_130_130" id="Footnote_130_130"></a><a href="#FNanchor_130_130"><span class="label">[130]</span></a></span> -Schol. to Lem. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_131_131" id="Footnote_131_131"></a><a href="#FNanchor_131_131"><span class="label">[131]</span></a></span> -Prop. 34. schol.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_132_132" id="Footnote_132_132"></a><a href="#FNanchor_132_132"><span class="label">[132]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_133_133" id="Footnote_133_133"></a><a href="#FNanchor_133_133"><span class="label">[133]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_134_134" id="Footnote_134_134"></a><a href="#FNanchor_134_134"><span class="label">[134]</span></a></span> -Book II. Ch. I. § 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_135_135" id="Footnote_135_135"></a><a href="#FNanchor_135_135"><span class="label">[135]</span></a></span> -Vid. Newt. princ. in schol. to Lem. 7, of -Lib. II. pag. 341.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_136_136" id="Footnote_136_136"></a><a href="#FNanchor_136_136"><span class="label">[136]</span></a></span> -Sect. 17. of this chapter.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_137_137" id="Footnote_137_137"></a><a href="#FNanchor_137_137"><span class="label">[137]</span></a></span> -See Princ. philos. Lib. II. prop. 34.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_138_138" id="Footnote_138_138"></a><a href="#FNanchor_138_138"><span class="label">[138]</span></a></span> -Vid. Princ. philos. Lib. II. Lem. 5. p. 314.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_139_139" id="Footnote_139_139"></a><a href="#FNanchor_139_139"><span class="label">[139]</span></a></span> -Lemm. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_140_140" id="Footnote_140_140"></a><a href="#FNanchor_140_140"><span class="label">[140]</span></a></span> -Ibid. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_141_141" id="Footnote_141_141"></a><a href="#FNanchor_141_141"><span class="label">[141]</span></a></span> - Newt. Princ. Lib. II. prop. 40, in schol.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_142_142" id="Footnote_142_142"></a><a href="#FNanchor_142_142"><span class="label">[142]</span></a></span> - Lib. II. in schol. post prop. 31.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_143_143" id="Footnote_143_143"></a><a href="#FNanchor_143_143"><span class="label">[143]</span></a></span> -Book I. ch. 2 § 82.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_144_144" id="Footnote_144_144"></a><a href="#FNanchor_144_144"><span class="label">[144]</span></a></span> -Book I. Ch. 3 § 29.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_145_145" id="Footnote_145_145"></a><a href="#FNanchor_145_145"><span class="label">[145]</span></a></span> -Ch. 3. of this present book.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_146_146" id="Footnote_146_146"></a><a href="#FNanchor_146_146"><span class="label">[146]</span></a></span> -Ch. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_147_147" id="Footnote_147_147"></a><a href="#FNanchor_147_147"><span class="label">[147]</span></a></span> -In Princ. philos. part. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_148_148" id="Footnote_148_148"></a><a href="#FNanchor_148_148"><span class="label">[148]</span></a></span> -Philos. princ. mathem. Lib. II. prop. 2. & schol.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_149_149" id="Footnote_149_149"></a><a href="#FNanchor_149_149"><span class="label">[149]</span></a></span> -Ibid. prop 53.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_150_150" id="Footnote_150_150"></a><a href="#FNanchor_150_150"><span class="label">[150]</span></a></span> -Philos. princ. prop. 52. coroll. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_151_151" id="Footnote_151_151"></a><a href="#FNanchor_151_151"><span class="label">[151]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_152_152" id="Footnote_152_152"></a><a href="#FNanchor_152_152"><span class="label">[152]</span></a></span> -Coroll. 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_153_153" id="Footnote_153_153"></a><a href="#FNanchor_153_153"><span class="label">[153]</span></a></span> -See ibid. schol. post prop. 53.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_154_154" id="Footnote_154_154"></a><a href="#FNanchor_154_154"><span class="label">[154]</span></a></span> -Princ. philos. pag. 316, 317.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_155_155" id="Footnote_155_155"></a><a href="#FNanchor_155_155"><span class="label">[155]</span></a></span> -Ch. I. § 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_156_156" id="Footnote_156_156"></a><a href="#FNanchor_156_156"><span class="label">[156]</span></a></span> -Book I. Ch. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_157_157" id="Footnote_157_157"></a><a href="#FNanchor_157_157"><span class="label">[157]</span></a></span> -Book I. Ch. 3. § 29.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_158_158" id="Footnote_158_158"></a><a href="#FNanchor_158_158"><span class="label">[158]</span></a></span> -Ibid. Ch. 2. § 30, 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_159_159" id="Footnote_159_159"></a><a href="#FNanchor_159_159"><span class="label">[159]</span></a></span> -Book I. Ch. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_160_160" id="Footnote_160_160"></a><a href="#FNanchor_160_160"><span class="label">[160]</span></a></span> -Ch. 1. § 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_161_161" id="Footnote_161_161"></a><a href="#FNanchor_161_161"><span class="label">[161]</span></a></span> -Chap. 5. § 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_162_162" id="Footnote_162_162"></a><a href="#FNanchor_162_162"><span class="label">[162]</span></a></span> -Princ. pag. 60.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_163_163" id="Footnote_163_163"></a><a href="#FNanchor_163_163"><span class="label">[163]</span></a></span> -Street, in Astron. Carolin.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_164_164" id="Footnote_164_164"></a><a href="#FNanchor_164_164"><span class="label">[164]</span></a></span> -See Chap. 5. §9, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_165_165" id="Footnote_165_165"></a><a href="#FNanchor_165_165"><span class="label">[165]</span></a></span> -In the foregoing page.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_166_166" id="Footnote_166_166"></a><a href="#FNanchor_166_166"><span class="label">[166]</span></a></span> -See Newton. Princ. Lib. III. prop. 13.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_167_167" id="Footnote_167_167"></a><a href="#FNanchor_167_167"><span class="label">[167]</span></a></span> -Chap. 5. § 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_168_168" id="Footnote_168_168"></a><a href="#FNanchor_168_168"><span class="label">[168]</span></a></span> -Princ. Lib. I. prop. 60.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_169_169" id="Footnote_169_169"></a><a href="#FNanchor_169_169"><span class="label">[169]</span></a></span> -Book I, Chap. 2. § 80.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_170_170" id="Footnote_170_170"></a><a href="#FNanchor_170_170"><span class="label">[170]</span></a></span> -Princ. philos. Lib. I. prop. 58. coroll. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_171_171" id="Footnote_171_171"></a><a href="#FNanchor_171_171"><span class="label">[171]</span></a></span> -Newt. Optics. pag. 378.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_172_172" id="Footnote_172_172"></a><a href="#FNanchor_172_172"><span class="label">[172]</span></a></span> -Newton. Princ. Lib. III. prop. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_173_173" id="Footnote_173_173"></a><a href="#FNanchor_173_173"><span class="label">[173]</span></a></span> -Newton, Princ. Lib. III. pag. 390,391. compared -with pag. 393.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_174_174" id="Footnote_174_174"></a><a href="#FNanchor_174_174"><span class="label">[174]</span></a></span> -Book I. Ch. 3. § 29.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_175_175" id="Footnote_175_175"></a><a href="#FNanchor_175_175"><span class="label">[175]</span></a></span> -Princ. philos. Lib. I. prop. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_176_176" id="Footnote_176_176"></a><a href="#FNanchor_176_176"><span class="label">[176]</span></a></span> -Ibid. coroll.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_177_177" id="Footnote_177_177"></a><a href="#FNanchor_177_177"><span class="label">[177]</span></a></span> - Newt. Princ. philos. Lib. III. pag. 390.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_178_178" id="Footnote_178_178"></a><a href="#FNanchor_178_178"><span class="label">[178]</span></a></span> -Newt. Princ. philos. Lib. III. pag. 391, 392.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_179_179" id="Footnote_179_179"></a><a href="#FNanchor_179_179"><span class="label">[179]</span></a></span> -Book III. Ch. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_180_180" id="Footnote_180_180"></a><a href="#FNanchor_180_180"><span class="label">[180]</span></a></span> -Newt. Princ. philos. Lib. III. pag. 391.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_181_181" id="Footnote_181_181"></a><a href="#FNanchor_181_181"><span class="label">[181]</span></a></span> -Ibid. pag. 392.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_182_182" id="Footnote_182_182"></a><a href="#FNanchor_182_182"><span class="label">[182]</span></a></span> -See Book I. Ch. 2. § 60, 64.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_183_183" id="Footnote_183_183"></a><a href="#FNanchor_183_183"><span class="label">[183]</span></a></span> -Book I. Ch. 2. § 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_184_184" id="Footnote_184_184"></a><a href="#FNanchor_184_184"><span class="label">[184]</span></a></span> -See Ch. II. § 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_185_185" id="Footnote_185_185"></a><a href="#FNanchor_185_185"><span class="label">[185]</span></a></span> -The second of the laws of motion laid down in Book I. Ch. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_186_186" id="Footnote_186_186"></a><a href="#FNanchor_186_186"><span class="label">[186]</span></a></span> -Newton. Princ. philos. Lib. III. prop. 6. pag. 401.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_187_187" id="Footnote_187_187"></a><a href="#FNanchor_187_187"><span class="label">[187]</span></a></span> -Newton’s Princ. philos. Lib. III. prop. 22, 23.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_188_188" id="Footnote_188_188"></a><a href="#FNanchor_188_188"><span class="label">[188]</span></a></span> -Newton. Princ. Lib. I. prop. 66. coroll. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_189_189" id="Footnote_189_189"></a><a href="#FNanchor_189_189"><span class="label">[189]</span></a></span> -Menelai Sphaeric. Lib. I. prop. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_190_190" id="Footnote_190_190"></a><a href="#FNanchor_190_190"><span class="label">[190]</span></a></span> -Vid. Newt. Princ. Lib. I. prop. 66. coroll. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_191_191" id="Footnote_191_191"></a><a href="#FNanchor_191_191"><span class="label">[191]</span></a></span> -Vid. Newt. Princ. Lib. III prop. 30. p. 440.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_192_192" id="Footnote_192_192"></a><a href="#FNanchor_192_192"><span class="label">[192]</span></a></span> -Ibid. Lib. I. prop. 66. coroll. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_193_193" id="Footnote_193_193"></a><a href="#FNanchor_193_193"><span class="label">[193]</span></a></span> -What this proportion is, may be known from Coroll. 2 prop. 44. Lib. I. Princ. philos. Newton.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_194_194" id="Footnote_194_194"></a><a href="#FNanchor_194_194"><span class="label">[194]</span></a></span> -Princ. Phil. Newt. Lib. I. prop. 45. Coroll. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_195_195" id="Footnote_195_195"></a><a href="#FNanchor_195_195"><span class="label">[195]</span></a></span> -Pr. Phil. Newt. Lib. I. prop. 66. Coroll. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_196_196" id="Footnote_196_196"></a><a href="#FNanchor_196_196"><span class="label">[196]</span></a></span> -See § 19 of this chapter.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_197_197" id="Footnote_197_197"></a><a href="#FNanchor_197_197"><span class="label">[197]</span></a></span> -Phil. Nat. Pr. Math Lib. I. prop. 66. cor. 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_198_198" id="Footnote_198_198"></a><a href="#FNanchor_198_198"><span class="label">[198]</span></a></span> -Ibid. Coroll. 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_199_199" id="Footnote_199_199"></a><a href="#FNanchor_199_199"><span class="label">[199]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_200_200" id="Footnote_200_200"></a><a href="#FNanchor_200_200"><span class="label">[200]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_201_201" id="Footnote_201_201"></a><a href="#FNanchor_201_201"><span class="label">[201]</span></a></span> -Newt. Princ. Lib. III. prop. 29.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_202_202" id="Footnote_202_202"></a><a href="#FNanchor_202_202"><span class="label">[202]</span></a></span> -Ibid. prop. 28.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_203_203" id="Footnote_203_203"></a><a href="#FNanchor_203_203"><span class="label">[203]</span></a></span> -Ibid. prop. 31.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_204_204" id="Footnote_204_204"></a><a href="#FNanchor_204_204"><span class="label">[204]</span></a></span> -Newt. Princ. pag. 459.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_205_205" id="Footnote_205_205"></a><a href="#FNanchor_205_205"><span class="label">[205]</span></a></span> -In Princ. philos. part. 3. § 41.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_206_206" id="Footnote_206_206"></a><a href="#FNanchor_206_206"><span class="label">[206]</span></a></span> -Chap. 1. § 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_207_207" id="Footnote_207_207"></a><a href="#FNanchor_207_207"><span class="label">[207]</span></a></span> -Newton. Princ. philos. Lib. III. Lemm. 4. -pag. 478.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_208_208" id="Footnote_208_208"></a><a href="#FNanchor_208_208"><span class="label">[208]</span></a></span> -Princ. philos. Lib. III. prop. 40.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_209_209" id="Footnote_209_209"></a><a href="#FNanchor_209_209"><span class="label">[209]</span></a></span> -Book I. chap. 2. § 82.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_210_210" id="Footnote_210_210"></a><a href="#FNanchor_210_210"><span class="label">[210]</span></a></span> -Princ. philos. Lib. III. pag. 499, 500.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_211_211" id="Footnote_211_211"></a><a href="#FNanchor_211_211"><span class="label">[211]</span></a></span> -Ibid. pag. 500, and 520, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_212_212" id="Footnote_212_212"></a><a href="#FNanchor_212_212"><span class="label">[212]</span></a></span> -Princ. Philos. Lib. III. prop. 40.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_213_213" id="Footnote_213_213"></a><a href="#FNanchor_213_213"><span class="label">[213]</span></a></span> -Ibid. prop. 41.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_214_214" id="Footnote_214_214"></a><a href="#FNanchor_214_214"><span class="label">[214]</span></a></span> -Ibid. pag. 522.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_215_215" id="Footnote_215_215"></a><a href="#FNanchor_215_215"><span class="label">[215]</span></a></span> -Ibid. prop. 42.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_216_216" id="Footnote_216_216"></a><a href="#FNanchor_216_216"><span class="label">[216]</span></a></span> -Newt. Princ. philos. edit. 2. p. 464, 465.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_217_217" id="Footnote_217_217"></a><a href="#FNanchor_217_217"><span class="label">[217]</span></a></span> -Ibid. edit. 3. p 501, 502.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_218_218" id="Footnote_218_218"></a><a href="#FNanchor_218_218"><span class="label">[218]</span></a></span> -Ibid. pag. 519.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_219_219" id="Footnote_219_219"></a><a href="#FNanchor_219_219"><span class="label">[219]</span></a></span> -Ibid. pag. 524.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_220_220" id="Footnote_220_220"></a><a href="#FNanchor_220_220"><span class="label">[220]</span></a></span> -Newt. Princ. philos. p. 525.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_221_221" id="Footnote_221_221"></a><a href="#FNanchor_221_221"><span class="label">[221]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_222_222" id="Footnote_222_222"></a><a href="#FNanchor_222_222"><span class="label">[222]</span></a></span> -Ibid. pag. 508.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_223_223" id="Footnote_223_223"></a><a href="#FNanchor_223_223"><span class="label">[223]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_224_224" id="Footnote_224_224"></a><a href="#FNanchor_224_224"><span class="label">[224]</span></a></span> -Ibid. pag. 484.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_225_225" id="Footnote_225_225"></a><a href="#FNanchor_225_225"><span class="label">[225]</span></a></span> -Ibid. pag. 482, 483.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_226_226" id="Footnote_226_226"></a><a href="#FNanchor_226_226"><span class="label">[226]</span></a></span> -Ibid. pag. 481.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_227_227" id="Footnote_227_227"></a><a href="#FNanchor_227_227"><span class="label">[227]</span></a></span> -Ibid. pag. 509.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_228_228" id="Footnote_228_228"></a><a href="#FNanchor_228_228"><span class="label">[228]</span></a></span> -See the fore-cited place.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_229_229" id="Footnote_229_229"></a><a href="#FNanchor_229_229"><span class="label">[229]</span></a></span> -Ibid. and Cartes. Princ. Phil. part. 3. § 134, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_230_230" id="Footnote_230_230"></a><a href="#FNanchor_230_230"><span class="label">[230]</span></a></span> -Vid. Phil. Nat. princ. Math. p. 511.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_231_231" id="Footnote_231_231"></a><a href="#FNanchor_231_231"><span class="label">[231]</span></a></span> -Book I. Ch. 4. § 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_232_232" id="Footnote_232_232"></a><a href="#FNanchor_232_232"><span class="label">[232]</span></a></span> -Ch. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_233_233" id="Footnote_233_233"></a><a href="#FNanchor_233_233"><span class="label">[233]</span></a></span> -All these arguments are laid down in Philos. Nat. Princ. Lib. III. from p. 509, to 517.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_234_234" id="Footnote_234_234"></a><a href="#FNanchor_234_234"><span class="label">[234]</span></a></span> -Philos. Nat. Princ. Lib. III. p. 515.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_235_235" id="Footnote_235_235"></a><a href="#FNanchor_235_235"><span class="label">[235]</span></a></span> -Ch. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_236_236" id="Footnote_236_236"></a><a href="#FNanchor_236_236"><span class="label">[236]</span></a></span> -See Ch. 1. § 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_237_237" id="Footnote_237_237"></a><a href="#FNanchor_237_237"><span class="label">[237]</span></a></span> -Newt. Princ. Philos. pag. 525, 526. An account -of all the stars of both these kinds, which -have appeared within the last 150 years may be -seen in the Philosophical transactions, vol. 29. -numb. 346.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_238_238" id="Footnote_238_238"></a><a href="#FNanchor_238_238"><span class="label">[238]</span></a></span> -Newt. Princ. Philos. Nat. Lib. III. prop. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_239_239" id="Footnote_239_239"></a><a href="#FNanchor_239_239"><span class="label">[239]</span></a></span> -Ch. 3. § 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_240_240" id="Footnote_240_240"></a><a href="#FNanchor_240_240"><span class="label">[240]</span></a></span> -Book I. Ch. 2. § 24.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_241_241" id="Footnote_241_241"></a><a href="#FNanchor_241_241"><span class="label">[241]</span></a></span> -Newt. Princ. Lib. III. prop. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_242_242" id="Footnote_242_242"></a><a href="#FNanchor_242_242"><span class="label">[242]</span></a></span> -Ch. 3. § 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_243_243" id="Footnote_243_243"></a><a href="#FNanchor_243_243"><span class="label">[243]</span></a></span> -Newt. Princ. philos. Lib. III. prop. 7. cor. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_244_244" id="Footnote_244_244"></a><a href="#FNanchor_244_244"><span class="label">[244]</span></a></span> -See Book I. Ch. 1. § 15.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_245_245" id="Footnote_245_245"></a><a href="#FNanchor_245_245"><span class="label">[245]</span></a></span> -Ibid. § 5, 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_246_246" id="Footnote_246_246"></a><a href="#FNanchor_246_246"><span class="label">[246]</span></a></span> -Chap. 2. § 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_247_247" id="Footnote_247_247"></a><a href="#FNanchor_247_247"><span class="label">[247]</span></a></span> -Newt. Princ. Lib. I. prop. 63.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_248_248" id="Footnote_248_248"></a><a href="#FNanchor_248_248"><span class="label">[248]</span></a></span> -§ 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_249_249" id="Footnote_249_249"></a><a href="#FNanchor_249_249"><span class="label">[249]</span></a></span> -See Introd. § 23.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_250_250" id="Footnote_250_250"></a><a href="#FNanchor_250_250"><span class="label">[250]</span></a></span> -§ 4, 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_251_251" id="Footnote_251_251"></a><a href="#FNanchor_251_251"><span class="label">[251]</span></a></span> -Newt. Princ. philos. Lib. I. prop. 74.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_252_252" id="Footnote_252_252"></a><a href="#FNanchor_252_252"><span class="label">[252]</span></a></span> -Ibid. coroll. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_253_253" id="Footnote_253_253"></a><a href="#FNanchor_253_253"><span class="label">[253]</span></a></span> -Lib. I. Prop. 75. and Lib. III. prop. 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_254_254" id="Footnote_254_254"></a><a href="#FNanchor_254_254"><span class="label">[254]</span></a></span> -Lib. I. Prop. 76.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_255_255" id="Footnote_255_255"></a><a href="#FNanchor_255_255"><span class="label">[255]</span></a></span> -Ibid. cor. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_256_256" id="Footnote_256_256"></a><a href="#FNanchor_256_256"><span class="label">[256]</span></a></span> -Vid. Lib. III. Prop. 7. coroll. 1</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_257_257" id="Footnote_257_257"></a><a href="#FNanchor_257_257"><span class="label">[257]</span></a></span> -Newt. Princ. Lib. III. prop. 8. coroll. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_258_258" id="Footnote_258_258"></a><a href="#FNanchor_258_258"><span class="label">[258]</span></a></span> -Ibid. coroll. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_259_259" id="Footnote_259_259"></a><a href="#FNanchor_259_259"><span class="label">[259]</span></a></span> -Book I. Ch. 4. § 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_260_260" id="Footnote_260_260"></a><a href="#FNanchor_260_260"><span class="label">[260]</span></a></span> -Newt. Princ. Lib. III. prop. 8. coroll. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_261_261" id="Footnote_261_261"></a><a href="#FNanchor_261_261"><span class="label">[261]</span></a></span> -Ibid. coroll. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_262_262" id="Footnote_262_262"></a><a href="#FNanchor_262_262"><span class="label">[262]</span></a></span> -Book I. Ch. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_263_263" id="Footnote_263_263"></a><a href="#FNanchor_263_263"><span class="label">[263]</span></a></span> -Lib. II. prop. 20. cor. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_264_264" id="Footnote_264_264"></a><a href="#FNanchor_264_264"><span class="label">[264]</span></a></span> -Chap. 4. § 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_265_265" id="Footnote_265_265"></a><a href="#FNanchor_265_265"><span class="label">[265]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_266_266" id="Footnote_266_266"></a><a href="#FNanchor_266_266"><span class="label">[266]</span></a></span> -Vid. Newt. Princ. Lib. II. prop. 46.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_267_267" id="Footnote_267_267"></a><a href="#FNanchor_267_267"><span class="label">[267]</span></a></span> -Princ. philos. Lib. II. prop. 49.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_268_268" id="Footnote_268_268"></a><a href="#FNanchor_268_268"><span class="label">[268]</span></a></span> -Chap. 3. § 18.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_269_269" id="Footnote_269_269"></a><a href="#FNanchor_269_269"><span class="label">[269]</span></a></span> -Newt. Princ. philos. Lib. I. prop. 66. coroll. 18.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_270_270" id="Footnote_270_270"></a><a href="#FNanchor_270_270"><span class="label">[270]</span></a></span> -§ 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_271_271" id="Footnote_271_271"></a><a href="#FNanchor_271_271"><span class="label">[271]</span></a></span> -Ch. 3. § 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_272_272" id="Footnote_272_272"></a><a href="#FNanchor_272_272"><span class="label">[272]</span></a></span> -Ch. 3 § 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_273_273" id="Footnote_273_273"></a><a href="#FNanchor_273_273"><span class="label">[273]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_274_274" id="Footnote_274_274"></a><a href="#FNanchor_274_274"><span class="label">[274]</span></a></span> - See below § 44.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_275_275" id="Footnote_275_275"></a><a href="#FNanchor_275_275"><span class="label">[275]</span></a></span> -Newton Princ. Lib. III. prop. 19.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_276_276" id="Footnote_276_276"></a><a href="#FNanchor_276_276"><span class="label">[276]</span></a></span> -Lib. III. prop. 19.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_277_277" id="Footnote_277_277"></a><a href="#FNanchor_277_277"><span class="label">[277]</span></a></span> -Lib. I. prop. 73.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_278_278" id="Footnote_278_278"></a><a href="#FNanchor_278_278"><span class="label">[278]</span></a></span> -Lib. III. prop. 20.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_279_279" id="Footnote_279_279"></a><a href="#FNanchor_279_279"><span class="label">[279]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_280_280" id="Footnote_280_280"></a><a href="#FNanchor_280_280"><span class="label">[280]</span></a></span> -Opt. B. I. part. 2. prop. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_281_281" id="Footnote_281_281"></a><a href="#FNanchor_281_281"><span class="label">[281]</span></a></span> -Newt. Opt. B. 1. part 1. experim. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_282_282" id="Footnote_282_282"></a><a href="#FNanchor_282_282"><span class="label">[282]</span></a></span> -Ibid. prop. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_283_283" id="Footnote_283_283"></a><a href="#FNanchor_283_283"><span class="label">[283]</span></a></span> -Newt. Opt. B. 1. part 2. exper. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_284_284" id="Footnote_284_284"></a><a href="#FNanchor_284_284"><span class="label">[284]</span></a></span> -Ibid exper. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_285_285" id="Footnote_285_285"></a><a href="#FNanchor_285_285"><span class="label">[285]</span></a></span> -Newton Opt. B. I. prop. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_286_286" id="Footnote_286_286"></a><a href="#FNanchor_286_286"><span class="label">[286]</span></a></span> -Ibid exp. 9.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_287_287" id="Footnote_287_287"></a><a href="#FNanchor_287_287"><span class="label">[287]</span></a></span> -Newt. Opt. B. I. part 1. exp 15.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_288_288" id="Footnote_288_288"></a><a href="#FNanchor_288_288"><span class="label">[288]</span></a></span> -Philos. Transact. N. 88, p. 5099.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_289_289" id="Footnote_289_289"></a><a href="#FNanchor_289_289"><span class="label">[289]</span></a></span> -Opt B. I. par. 2. exp. 14.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_290_290" id="Footnote_290_290"></a><a href="#FNanchor_290_290"><span class="label">[290]</span></a></span> -Ibid. exp. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_291_291" id="Footnote_291_291"></a><a href="#FNanchor_291_291"><span class="label">[291]</span></a></span> -Opt. pag. 122.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_292_292" id="Footnote_292_292"></a><a href="#FNanchor_292_292"><span class="label">[292]</span></a></span> -Opt. B. I. part 2. exp. 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_293_293" id="Footnote_293_293"></a><a href="#FNanchor_293_293"><span class="label">[293]</span></a></span> -Ibid prop. 4, 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_294_294" id="Footnote_294_294"></a><a href="#FNanchor_294_294"><span class="label">[294]</span></a></span> -Opt. pag. 51.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_295_295" id="Footnote_295_295"></a><a href="#FNanchor_295_295"><span class="label">[295]</span></a></span> -Opt. Book II. prop. 8.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_296_296" id="Footnote_296_296"></a><a href="#FNanchor_296_296"><span class="label">[296]</span></a></span> -Opt. Book II. par. 3. prop. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_297_297" id="Footnote_297_297"></a><a href="#FNanchor_297_297"><span class="label">[297]</span></a></span> -§ 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_298_298" id="Footnote_298_298"></a><a href="#FNanchor_298_298"><span class="label">[298]</span></a></span> -Opt. Book II. par. 3. prop. 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_299_299" id="Footnote_299_299"></a><a href="#FNanchor_299_299"><span class="label">[299]</span></a></span> -Opt. Book II. pag. 241.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_300_300" id="Footnote_300_300"></a><a href="#FNanchor_300_300"><span class="label">[300]</span></a></span> -Ibid. pag. 224.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_301_301" id="Footnote_301_301"></a><a href="#FNanchor_301_301"><span class="label">[301]</span></a></span> -Ibid. Obs. 17. &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_302_302" id="Footnote_302_302"></a><a href="#FNanchor_302_302"><span class="label">[302]</span></a></span> -Ibid. Obs. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_303_303" id="Footnote_303_303"></a><a href="#FNanchor_303_303"><span class="label">[303]</span></a></span> -Ibid. pag. 206.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_304_304" id="Footnote_304_304"></a><a href="#FNanchor_304_304"><span class="label">[304]</span></a></span> -Obser. 21.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_305_305" id="Footnote_305_305"></a><a href="#FNanchor_305_305"><span class="label">[305]</span></a></span> -Observ. 5. compared with Observ. 10</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_306_306" id="Footnote_306_306"></a><a href="#FNanchor_306_306"><span class="label">[306]</span></a></span> -Ibid. prop. 5.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_307_307" id="Footnote_307_307"></a><a href="#FNanchor_307_307"><span class="label">[307]</span></a></span> -Observ. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_308_308" id="Footnote_308_308"></a><a href="#FNanchor_308_308"><span class="label">[308]</span></a></span> -Observ. 9.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_309_309" id="Footnote_309_309"></a><a href="#FNanchor_309_309"><span class="label">[309]</span></a></span> -Ibid prop. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_310_310" id="Footnote_310_310"></a><a href="#FNanchor_310_310"><span class="label">[310]</span></a></span> -Opt. pag. 243.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_311_311" id="Footnote_311_311"></a><a href="#FNanchor_311_311"><span class="label">[311]</span></a></span> -Newt. Opt. B. I. part. 1. prop. I.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_312_312" id="Footnote_312_312"></a><a href="#FNanchor_312_312"><span class="label">[312]</span></a></span> -Opt. B. I. part. 1. prop. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_313_313" id="Footnote_313_313"></a><a href="#FNanchor_313_313"><span class="label">[313]</span></a></span> -Opt. B. I. part 1. Expec. 6.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_314_314" id="Footnote_314_314"></a><a href="#FNanchor_314_314"><span class="label">[314]</span></a></span> -Opt. pag. 67, 68, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_315_315" id="Footnote_315_315"></a><a href="#FNanchor_315_315"><span class="label">[315]</span></a></span> -Ibid. B. 1. par. 2. prop. 3.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_316_316" id="Footnote_316_316"></a><a href="#FNanchor_316_316"><span class="label">[316]</span></a></span> -Opt. B. II. par. 3. prop. 10.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_317_317" id="Footnote_317_317"></a><a href="#FNanchor_317_317"><span class="label">[317]</span></a></span> -Opt. B. II. par. 3. prop. 15.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_318_318" id="Footnote_318_318"></a><a href="#FNanchor_318_318"><span class="label">[318]</span></a></span> -Ibid. par. 1. observ. 7.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_319_319" id="Footnote_319_319"></a><a href="#FNanchor_319_319"><span class="label">[319]</span></a></span> -Ibid. Observ. 19.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_320_320" id="Footnote_320_320"></a><a href="#FNanchor_320_320"><span class="label">[320]</span></a></span> -Opt. B. II. par. 2. pag. 199. &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_321_321" id="Footnote_321_321"></a><a href="#FNanchor_321_321"><span class="label">[321]</span></a></span> -Ibid. par. 4</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_322_322" id="Footnote_322_322"></a><a href="#FNanchor_322_322"><span class="label">[322]</span></a></span> -Ibid. part. 3. prop. 13.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_323_323" id="Footnote_323_323"></a><a href="#FNanchor_323_323"><span class="label">[323]</span></a></span> -Ibid. prop. 17.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_324_324" id="Footnote_324_324"></a><a href="#FNanchor_324_324"><span class="label">[324]</span></a></span> -Ibid. prop. 13.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_325_325" id="Footnote_325_325"></a><a href="#FNanchor_325_325"><span class="label">[325]</span></a></span> -Opt. Qu. 18, &c.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_326_326" id="Footnote_326_326"></a><a href="#FNanchor_326_326"><span class="label">[326]</span></a></span> -See Concl. S. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_327_327" id="Footnote_327_327"></a><a href="#FNanchor_327_327"><span class="label">[327]</span></a></span> -B. II. Ch. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_328_328" id="Footnote_328_328"></a><a href="#FNanchor_328_328"><span class="label">[328]</span></a></span> -Opt. B. III. Obs. 1.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_329_329" id="Footnote_329_329"></a><a href="#FNanchor_329_329"><span class="label">[329]</span></a></span> -Ibid. Obs. 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_330_330" id="Footnote_330_330"></a><a href="#FNanchor_330_330"><span class="label">[330]</span></a></span> -§ 2.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_331_331" id="Footnote_331_331"></a><a href="#FNanchor_331_331"><span class="label">[331]</span></a></span> -Philos. Trans. No. 378.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_332_332" id="Footnote_332_332"></a><a href="#FNanchor_332_332"><span class="label">[332]</span></a></span> -§ 11.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_333_333" id="Footnote_333_333"></a><a href="#FNanchor_333_333"><span class="label">[333]</span></a></span> -Philos. Transact No. 375.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_334_334" id="Footnote_334_334"></a><a href="#FNanchor_334_334"><span class="label">[334]</span></a></span> -Ibid.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_335_335" id="Footnote_335_335"></a><a href="#FNanchor_335_335"><span class="label">[335]</span></a></span> -Opt. B. II. part 4.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_336_336" id="Footnote_336_336"></a><a href="#FNanchor_336_336"><span class="label">[336]</span></a></span> -Ch. 3. § 14.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_337_337" id="Footnote_337_337"></a><a href="#FNanchor_337_337"><span class="label">[337]</span></a></span> -Opt. B. II. part 4. obs. 13.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_338_338" id="Footnote_338_338"></a><a href="#FNanchor_338_338"><span class="label">[338]</span></a></span> -Opt. pag. 255.</p> - -<p class="pfn4"><span class="ln1"><a name="Footnote_339_339" id="Footnote_339_339"></a><a href="#FNanchor_339_339"><span class="label">[339]</span></a></span> -Ch. 3. § 18.</p></div> - -</div> - -</div> - - - - - - - -<pre> - - - - - -End of the Project Gutenberg EBook of A View of Sir Isaac Newton's Philosophy, by -Anonymous - -*** END OF THIS PROJECT GUTENBERG EBOOK SIR ISAAC NEWTON'S PHILOSOPHY *** - -***** This file should be named 53161-h.htm or 53161-h.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/3/1/6/53161/ - -Produced by Giovanni Fini, Markus Brenner, Irma Spehar and -the Online Distributed Proofreading Team at -http://www.pgdp.net (This file was produced from images -generously made available by The Internet Archive/Canadian -Libraries) - - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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