,transcriber's ,note4 ,apparent errors in mathematical expressions have been retained1 although apparent typographical errors elsewhere in the text have been corrected4 ,inconsistencies in hyphenation have been retained4 ,gesperrt font has been condensed4 ,small capitals have been replaced by full capitals4 ,brackets extending over several columns have been replaced by columns of standard brackets4 ,words that are stacked one over the other are rendered thus3 upperlower4 ,italicised text is indicated by underscores4 ,where an italicised sentence or paragraph includes a word in ordimary font this is also indicated by underscores4 ,mathematical variables are usually italicised4 ,in order to avoid an excessive number of underscores1 and where it is possible without ambiguity1 complete mathematical expressions have instead been encased in underscores4 ,these usually extend over mathematical operators 7such as 71 or ,greek characters1 that are not italicised4 ,the more complex mathematical expressions have been separated out from the surrounding text4 ,fifth roots and nth roots are indicated by and respectively4 ,the decimal point may be indicated by a 4 or 1 while illustrations are referred to as a ,plate or a ,tab4 ,the ,table of ,discourses has been amended to include one omitted title and to correct erroneous page numbers4 ,illustration1 probably of ,charles ,,ii3 ,m3 ,v ,gucht ,sculp3 ,miscellanea ,curiosa4 ,,containing ,a ,,collection ,of some of the ,principal ,,ph,,nomena ,,in ,,nature1 ,accounted for by the ,greatest ,philosophers of this ,age2 ,,being ,,the ,most ,valuable ,,discourses1 ,read and ,delivered to the ,,royal ,,society1 for the ,advancement of ,physical and ,mathematical ,knowledge4 ,as also a ,collection of ,curious ,travels1 ,voyages1 ,antiquities1 and ,natural ,histories of ,countries2 ,presented to the same ,society4 ,in ,three ,,volumes4 ,the ,second ,edition2 ,to which is added1 ,a ,discourse of the ,influence of the ,sun and ,moon on ,humane ,bodies1 c4 ,by ,r4 ,,mead1 ,m4 ,d4 ,f4 ,r4 ,s4 ,and also ,fontenelle's ,preface of the ,usefulness of ,mathematical ,learning4 ,,vol4 ,i4 ,,london3 ,printed by ,f4 ,m4 for ,r4 ,smith1 at the ,bible under the ,piazza of the ,royal ,exchange in ,cornhill4 #agjh4 ,,to ,,the ,,reader4 ,some of the ,principal ,discoveries and ,enquiries1 both in ,physical and ,mathematical ,learning1 being register'd in the ,voluminous ,journals of the ,royal ,society1 are amongst a multitude of less useful ,matters1 so ,obscurely hid1 that but very few inquisitive ,gentlemen ever so much as heard of them4 ,the ,design therefore of the ensuing ,collection1 is to digest in a convenient ,method1 all the most curious ,philosophical and ,mathematical ,discoveries1 as they are to be met with1 which may any way tend to the ,use of ,life or ,advancement of ,arts and ,sciences4 ,and on this ,occasion1 it will be convenient to intimate to the ,reader2 ,first1 ,that the ,theories and ,discourses here collected1 have already past the ,censure of the ,learned ,world3 ,who have acknowleg'd them the most satisfactory ,accounts of ,nature's ,proceedings1 wherein some of her greatest ,depths are fathom'd1 and a ,foundation laid for ,posterity to build an infinite ,superstructure4 ,secondly1 ,that they are related 7,verbatim7 just as they were delivered in1 or read before the ,royal ,society3 ,for it has been the ,opinion of the most ,judicious among those ,honourable ,members1 that it is impossible so to abridge them1 7which are but ,abridgments themselves7 as not to render them obscure and unintelligible4 ,a ,,table ,,of ,,the ,discourses contain'd in this ,volume4 ,an ,estimate of the ,quantity of ,vapours raised out of the ,sea1 as derived from ,experiment3 ,together with an ,account of the ,circulation of the wat'ry ,vapours of the ,sea1 and of the ,cause of ,springs4 ,presented to the ,royal ,society by ,mr4 ,e4 ,halley1 ,f4 ,r4 ,s4 ,pag4 #a ,the ,true ,theory of the ,tides1 extracted from that admired ,treatise of ,mr4 ,isaac ,newton1 ,intituled ,philosophi ,naturalis ,principia ,mathematica2 being a ,discourse presented with that ,book to the late ,king ,james1 by ,mr4 ,e4 ,halley4 #ac ,a ,theory of the ,variation of the ,magnetical ,compass1 by ,mr4 ,e4 ,halley4 #bg ,an ,account of the ,cause of the ,change of the ,variation of the ,magnetical ,needle1 with an ,hypothesis of the ,structure of the ,internal ,parts of the ,earth2 as it was presented to the ,royal ,society in one of their late ,meetings1 by ,mr4 ,e4 ,halley4 #dc ,an ,historical ,account of the ,trade-,winds and ,monsoons1 observable in the ,seas between and near the ,tropicks2 with an ,attempt to assign the ,physical ,cause of the said ,winds1 by ,mr4 ,e4 ,halley4 #fa ,a ,discourse of the ,rule of the ,decrease of the ,heighth of the ,mercury in the ,barometer1 according as ,places are elevated above the ,surface of the ,earth2 with an ,attempt to discover the true ,reason of the rising and falling of the ,mercury1 upon ,change of ,weather1 by ,mr4 ,e4 ,halley4 #ha ,a ,letter from ,mr4 ,isaac ,newton1 while ,professor of the ,mathematicks in the ,university of ,cambridge2 containing his new ,theory about ,light and ,colours3 ,sent from ,cambridge1 ,feb4 #f4 #afga_/gb4 in order to be communicated to the ,royal ,society4 #ig ,a farther ,explanation of the same ,theory4 #aad ,a ,demonstration concerning the ,motion of ,light1 communicated from ,paris4 #aah ,an ,introductory ,essay to the ,doctrine of ,sounds1 containing some ,proposals for the ,improvement of ,acousticks2 as it was presented to the ,dublin ,society1 by the ,right ,reverend ,father in ,god ,narcissus1 ,lord ,bishop of ,ferns and ,leighlin4 #aba ,a ,discourse concerning the ,modern ,theory of ,generation1 by ,dr4 ,geo4 ,garden1 of ,aberdeen1 being part of a ,letter to ,dr4 ,william ,musgrave1 ,l4 ,l4 ,d4 ,reg4 ,soc4 ,s4 and by him communicated to the ,royal ,society4 #adb ,a short ,discourse concerning ,concoction ,read at a ,meeting of the ,royal ,society1 by ,clopton ,havers1 ,m4 ,d4 ,fellow of the ,royal ,society4 #aec ,a ,discourse concerning some ,influence of ,respiration on the ,motion of the ,heart hitherto unobserved4 ,by ,j4 ,drake1 ,m4 ,d4 ,f4 ,r4 ,s4 #aga ,some ,thoughts and ,experiments concerning ,vegetation4 ,by ,john ,woodward1 ,m4 ,d4 of the ,college of ,physicians and ,royal ,society1 and ,professor of ,physick in ,gresham-,college4 #bjc ,an ,account of the ,measure of ,gold upon ,gilt ,wire2 together with a ,demonstration of the exceeding ,minuteness of the ,atoms1 or constituent ,parts of ,gold2 as it was read before the ,royal ,society1 by ,mr4 ,e4 ,halley4 #bdc ,an ,account of the several ,species of ,infinite ,quantity1 and of the ,proportions they bear one to the other2 as it was read before the ,royal ,society1 by ,e4 ,halley4 #bdf ,an ,account of ,dr4 ,robert ,hook's ,invention of the ,marine ,barometer1 with it's ,description and ,uses4 ,published by ,order of the ,royal ,society by ,mr4 ,e4 ,halley4 #bej ,a ,discourse concerning the ,proportional ,heat of the ,sun in all ,latitudes2 with the ,method of collecting the same1 as it was read before the ,royal ,society in one of their late ,meetings1 by ,mr4 ,e4 ,halley4 #bef ,concerning the ,distance of the ,fixed ,stars1 by the ,honourable ,fran4 ,roberts1 ,esq2 ,f4 ,r4 ,s4 #bfe ,mr4 ,isaac ,newton's ,theory of the ,moon4 #bfh ,an estimate of the ,degrees of the ,mortality of ,mankind1 drawn from ,curious ,tables of ,births and ,funerals at the ,city of ,breslaw2 with an ,attempt to ascertain the ,price of ,annuities upon ,lives1 by ,mr4 ,e4 ,halley4 #bhj ,a ,discourse concerning ,gravity1 and its ,properties1 wherein the ,descent of ,heavy ,bodies1 and the ,motion of ,projects is briefly1 but fully handled3 ,together with the ,solution of a ,problem of great ,use in ,gunnery1 by ,mr4 ,e4 ,halley4 #cjb ,a ,proposition of ,general ,use in the ,art of ,gunnery1 shewing the ,rule of laying a ,mortar to pass1 in order to strike any ,object above or below the ,horizon1 by ,mr4 ,e4 ,halley4 #cbf ,a ,discourse concerning the ,measure of the ,air's ,resistance to ,bodies moved in it4 ,by the ,learned ,john ,wallis1 ,s4 ,t4 ,d4 and ,f4 ,r4 ,s4 #ccb ,an ,instance of the ,excellency of the ,modern ,algebra1 in the ,resolution of the ,problem of finding the ,foci of ,optick ,glasses universally4 ,by ,mr4 ,e4 ,halley1 ,s4 ,r4 ,s4 #cdh ,,appendix4 ,an ,analytical ,resolution of certain ,equations of the #c;d1 #eth1 #gth1 #ith ,powers1 and so on ad ,infinitum1 in finite ,terms1 after the manner of ,cardan's ,rules for ,cubicks4 ,by ,mr4 ,a4 ,moivre1 ,f4 ,r4 ,s4 #cfe ,a ,discourse concerning the ,action of the ,sun and ,moon on ,animal ,bodies2 and the ,influence which this may have in many ,diseases4 ,by ,richard ,mead1 ,m4 ,d4 ,f4 ,r4 ,s4 #cga ,a ,translation of ,part of ,monsieur ,fontenelle's ,preface to the ,memoirs of the ,royal ,academy at ,paris1 in the ,year #afii4 treating of the ,usefulness of ,mathematical ,learning4 ,but to what purpose should ,people become fond of the ,mathematicks and ,natural ,philosophy4 ,of what use are the ,transactions of the ,academy8 ,these are common ,questions1 which most do not barely propose as ,questions2 and it will not be improper to clear them4 ,people very readily call useless1 what they do not understand4 ,it is a sort of ,revenge2 and as the ,mathematicks and ,natural ,philosophy are known but by few1 they are generally look'd upon as useless4 ,the reason of this is2 because they are crabbed and not easily learnt4 ,we have a ,moon to light us in the ,night2 ,what is it to us1 say they1 whether ,jupiter hath four8 ,why so many laborious ,observations1 so many tedious ,calculations to know exactly their ,course8 ,they'll not afford us the more ,light for it2 and ,nature1 which hath plac'd these little ,planets without the reach of our ,eyes1 doth not seem to have made them for us4 ,according to this plausible ,argument they ought not to have been observ'd with a ,telescope1 nor study'd4 ,but it is certain1 that we had been considerable ,loosers by it3 ,for those who have some insight into the ,principles of ,geography and ,navigation know1 that since these four ,moons about ,jupiter have been discover'd1 they have been more useful to those ,sciences than our own ,moon2 and that they serve1 and shall more and more serve to make new ,sea-,charts1 infinitely more exact than the ,old2 and are likely to save the ,lives of a vast many ,seamen4 ,did we reap no other advantage from ,astronomy than this from these ,satellites of ,jupiter1 that wou'd be sufficient to justifie those prodigious ,calculations1 those assiduous and nice ,observations1 this great number of elaborate ,instruments1 and this ,noble ,edifice built only for this ,science4 ,however the greatest part of ,mankind know nothing of these ,satellites of ,jupiter1 unless perhaps by hear-say1 and that too confusedly2 or else they are ignorant of what ,affinity they have with ,navigation1 or of the great ,improvements which have been lately made in it4 ,this is the ,fate of ,sciences1 which are study'd and improv'd by few4 ,most ,people are not sensible of their ,progress1 and especially when made in some mean ,callings4 ,but what doth it signifie1 that we can now more easily direct the ,course of ,rivers1 cut out ,canals1 and settle new ,navigations2 because our ,method of taking the ,level and making ,sluces is infinitely better than heretofore8 ,some ,masons and ,seamen have thereby found their ,business easier1 but they themselves were not sensible of the ,skill of the ,geometrician who directed them4 ,they were mov'd1 as the ,body by a ,soul1 it doth not know4 ,others are yet less sensible of the ,genius that presided over the ,undertaking2 and the ,world is the better for its succeeding well1 but not altogether free from ,ingratitude4 ,anatomy1 which is some time since so carefully study'd1 can't become more exact1 but ,chyrurgical ,operations must also be more sure4 ,surgeons know this2 but those who receive the ,benefit of their ,art know nothing of it4 ,and indeed how should they8 ,they would be oblig'd to compare ,old with ,modern ,surgery2 and this wou'd take too much ,time1 and go against the ,grain3 ,so that since the ,operation hath succeeded well1 they do not think it material to know whether it had succeeded as well in another ,century4 ,it is strange that so many things are before our ,eyes1 and that we do not see them4 ,your ,handycraft ,shops are full of ingenious ,works2 but yet we hardly mind them3 ,and very useful and well contriv'd ,instruments and ,experiments want ,spectators1 who wou'd be wonderfully pleas'd1 wou'd they take the pains to admire them4 ,if a ,learned ,society have made some ,improvements in ,geometry1 ,anatomy1 ,mechanicks1 or any other useful ,science1 it must not be expected1 that the ,world will go back to so remote a ,spring to thank and applaud them for the ,usefulness of their ,productions3 ,for it will be more easie to enjoy the ,benefit of their ,discoveries and ,improvements than to know them4 ,the ,determination of ,longitude by the ,satellites1 the ,discovery of the ,ductus ,thoracicus1 a more convenient1 and more exact ,level1 are not ,novelties so fit to make a noise as a pleasant ,poem1 or a handsome ,piece of ,oratory4 ,altho' the ,usefulness of ,mathematicks and ,natural ,philosophy is obscure1 yet it is real4 ,to consider ,mankind in their ,natural ,state1 nothing is more useful to them1 than what may preserve their ,lives1 and produce those ,arts1 which are both great ,helps and ,ornaments to ,publick ,societies4 ,as for what concerns the ,preservation of ,life1 it peculiarly belongs to ,physick2 which for that reason is divided in the ,academy into three ,branches1 which make three different sorts of ,members of this ,society1 ,anatomy1 ,chymistry1 and ,botanicks4 ,every ,body knows of what ,importance it is to have an exact ,knowledge of ,human ,body1 and of what ,medicines may be extracted from ,minerals and ,plants4 ,as for ,arts1 too tedious to be reckon'd1 they depend some upon ,natural ,philosophy1 others upon ,mathematicks4 ,one wou'd think at first1 that if the ,mathematicks were to be confin'd to what is useful in them1 they ought only to be improv'd in those things1 which have an immediate and sensible affinity with ,arts1 and the rest ought to be neglected as a ,vain ,theory4 ,but this wou'd be a very wrong ,notion4 ,as for ,instance1 the ,art of ,navigation hath a necessary ,connexion with ,astronomy1 and ,astronomy can never be too much improv'd for the ,benefit of ,navigation4 ,astronomy cannot be without ,opticks by reason of ,perspective ,glasses2 and both1 as all other ,parts of ,mathematicks1 are grounded upon ,geometry1 and to go as far as you can1 even upon ,algebra4 ,geometry1 and especially ,algebra1 are the ,keys of all the ,inquiries1 that can be made concerning ,magnitude4 ,these ,sciences which are only conversant about abstruse ,relations1 and simple ,ideas1 may seem dry and barren1 whilst they keep within the ,verge of the ,intellectual ,world2 but mixt ,mathematicks1 which stoop to ,matter1 and consider the ,motion of the ,stars1 the ,augmentation of moving ,forces1 the different ,passages of the ,rays of ,light through different ,mediums2 the different ,effects of ,sound by the ,vibration of ,things2 to conclude all those ,sciences1 which discover the particular ,relations of ,sensible ,magnitudes go on farther and more securely1 when the ,art of discovering ,relations in ,general is more perfect4 ,the ,universal ,instrument cannot be too extensive1 too handy1 or too easily apply'd3 ,it is useful to all the ,sciences1 and they cannot be without it3 ,and therefore among the ,mathematicians of the ,academy1 who are design'd to be useful to the ,publick1 the ,geometricians and ,algebrists make a ,class1 as well as the ,astronomers and ,mechanicks4 ,however1 it is certain1 that ,speculations purely of ,geometry1 or of ,algebra1 are not about useful things3 ,but it is certain too1 that those that are not1 either lead or belong to those that are4 ,it is in it self a very barren thing to know1 that in a ,parabola a ,subtangant is double the corresponding ,absciss2 but yet it is a ,degree of ,knowledge necessary to the ,art of throwing ,bombs1 so exactly as they can do now4 ,there are not by far so many evident ,uses as ,propositions or ,truths in the ,mathematicks3 ,yet it is enough if the ,concourse of several ,truths is generally of some use4 ,farther1 a ,geometrical ,speculation1 which was not at first applicable to any use1 becomes so afterwards4 ,when the greatest ,geometricians in the ,seventeenth ,century set about to study a new ,curve1 which they call'd a ,cycloide1 they only engag'd themselves in a meer ,speculation out of ,vanity1 striving to outdo one another by the ,discovery of difficult ,theorems4 ,they did not even pretend that this was for the ,publick ,good2 however by diving into the ,nature of the ,cycloide it was found1 that it was destin'd to make ,pendulums as perfect as may be1 and carry the ,measure of ,time as far as it can go4 ,it is the same thing with ,natural ,philosophy as with ,geometry4 ,the ,anatomy of ,animals seems insignificant2 and it only concerns us to know that of ,human ,body4 ,but yet some ,parts of it1 which are of so nice1 or so confus'd a ,make1 that they are invisible1 are sensible and manifest in the ,body of an ,animal4 ,hence it is1 that ,monsters themselves are not to be neglected4 ,the ,mechanism conceal'd in a particular ,kind or in a common ,make1 is unfolded in another kind1 or in an extraordinary ,make2 and one wou'd be almost apt to say1 that ,nature by multiplying and varying so much her ,works1 can't sometimes forbear betraying her ,secrets4 ,all that the ,antients knew of the ,load-stone1 was1 that it attracts ,iron4 ,but whether they did not value a ,curiosity1 which promis'd them nothing2 or that their ,genius did not lead them to make ,experiments1 they have not examin'd this ,stone as carefully as they might4 ,one ,experiment taught them1 that it turns of its self towards the ,poles of the ,world1 and did put into their ,hands the inestimable ,treasure of the ,mariners ,compass4 ,they might easily have made this ,discovery important1 and yet they did not do it2 and if they had spent a little more time upon a ,curiosity which seem'd useless to them1 the ,latent use of it had soon appear'd4 ,let us always make a ,collection of ,mathematical and ,physical ,truths2 happen what it will we can't hazard much by it4 ,it is certain1 that they shall be drawn from ,springs1 whence a great many useful ones have already been drawn4 ,we have reason to presume1 that we shall draw from thence1 some that shall shine as soon as they are discover'd1 and convince us of their ,usefulness4 ,other ,truths shall stay some time till a piercing ,meditation1 or some happy ,accident discovers their ,use4 ,some ,truths being consider'd by themselves shall be barren1 till they are consider'd with reference to one another4 ,lastly1 let the worse come to the worse1 some shall be eternally useless4 ,i mean useless with reference to sensible and gross ,uses2 for otherwise they shall not be so4 ,an ,object upon which alone you cast your ,eyes is the clearer and brighter1 when the neighbouring ,objects1 which however you do not look upon1 are also enlighten'd2 because it hath the ,benefit of the ,rays1 which are reflected from them4 ,thus those ,discoveries1 which are palpably useful1 and deserve our chiefest ,attention1 are in some measure enlighten'd by those1 which may be call'd useless4 ,for all ,truths make one another more lucid4 ,it is always useful to have right ,notions1 even of useless ,subjects4 ,and tho' we cou'd reap no benefit by the ,knowledge of ,numbers and ,sines1 yet it wou'd still be the only certain ,knowledge granted to our ,natural ,light1 and they wou'd serve to give our ,reason the first ,habit of and ,inclination to ,truth4 ,they wou'd teach us to operate upon ,truths2 to take the ,thread of them1 which is generally very fine and almost imperceptible2 and to follow it as far as it reaches3 ,in a word1 they wou'd make ,truth so familiar1 that we might on other ,occasions know it at first sight1 and almost by ,instinct4 ,a ,geometrical ,genius is not so confin'd to ,geometry1 but that it may be capable of learning other ,sciences4 ,a ,tract of ,morality1 ,politicks1 or ,criticism1 and even a ,piece of ,oratory1 supposing the ,author qualify'd otherwise for those ,performances1 shall be the better for being compos'd by a ,geometrician4 ,that ,order1 ,perspicuity1 ,precision and ,exactness1 which some time since are found in good ,books1 may originally proceed from that ,geometrical ,genius1 which is now more common than ever1 and in some manner is communicated by one ,relation to another1 nay even to those that do not understand ,geometry4 ,sometimes a ,great ,man draws all his ,cotemporaries after him2 and he who hath the justest ,claim to the ,glory of having settled a new ,art of ,arguing1 was an ,excellent ,geometrician4 ,lastly1 whatever raises us to ,great and ,noble ,reflexions1 tho' they be purely ,speculative1 afford a ,spiritual and ,philosophical ,utility4 ,the ,wants of the ,mind are perhaps as many as those of the ,body4 ,she desires to extend her ,knowledge3 ,all that can be known1 is necessary to her1 and there can be no better ,proof than this1 that she is design'd for ,truth4 ,nothing perhaps can redound more to her ,glory1 than the ,pleasure that is felt sometimes1 in spight of ones self1 in the dry and crabbed ,questions of ,algebra4 ,but without running counter to the common ,notions1 and recurring to ,advantages which may seem too far fetch'd and refin'd1 it may fairly be own'd1 that the ,mathematicks and ,natural ,philosophy have some things which are only subservient to ,curiosity2 and so have those ,sciences which are most generally acknowledg'd to be useful1 as ,history1 c4 ,history doth not in every ,part of it supply us with ,examples of ,vertue and ,rules for our ,behaviour4 ,for besides these1 therein you have a ,view of the perpetual ,revolutions of ,human ,affairs1 of the ,beginning and ,fall of ,empires1 of ,manners1 ,customs1 and ,opinions which continually succeed one another2 and in a word1 of all that rapid1 tho' insensible1 ,motion that carries all before it1 and incessantly alters the ,face of the ,earth4 ,had we a mind to oppose ,curiosity to ,curiosity1 we shou'd find that instead of the ,motion1 which agitates ,nations1 and gives birth to1 and destroys ,states2 ,natural ,philosophy considers that ,great and ,universal ,motion1 which hath put the whole ,frame of ,nature in ,order1 and suspended the ,clestial ,bodies in several ,spheres1 and which illuminates and extinguishes some ,stars2 and by following always unalterable ,laws1 diversifies its effects ad infinitum4 ,if the surprising difference of ,manners and ,opinions of ,mankind is so entertaining2 there is too a great deal of ,pleasure to study the prodigious diversity of the ,structure of the different ,species of ,animals1 with reference to their different ,functions1 to the ,elements they live in1 to the ,climates they inhabit1 and the ,aliments they are to take1 c4 ,the most curious strokes of ,history shall hardly be more curious than the ,phosphorus1 the cold ,liquors which being mixt together1 break out into a flame2 ,silver ,trees1 the almost ,magical ,operations of the ,load-,stone1 and a vast number of ,secrets1 which ,art hath discover'd by a near and diligent ,scrutiny of ,nature4 ,lastly1 ,natural ,philosophy doth as much as it is possible unravel the ,footsteps of that ,infinite ,intellect and ,wisdom1 who hath made all things3 ,whereas the ,object of ,history are the disorderly ,effects of the ,passion1 and of ,humane ,caprices2 and so odd a ,series of ,events1 that some formerly fancy'd that a ,blind and ,senseless ,deity had the ,direction of them4 ,we must not look upon the ,sublime ,reflexions which ,natural ,philosophy leads us to make concerning the ,author of the ,universe1 as meer ,curiosities4 ,for this stupendous ,work1 which appears always more wonderful the more we know it1 gives us such exalted ,notions of its ,maker1 that they fill our ,minds with ,admiration and ,respect4 ,but above all1 ,astronomy and ,anatomy are the two ,sciences which more palpably lay before us two grand ,attributes of our ,creator2 one his ,immensity by the distance1 ,magnitude and ,number of ,clestial ,bodies2 the other his ,infinite ,knowledge by the ,mechanism of ,animals4 ,true ,natural ,philosophy is a kind of ,theology4 ,the different views of ,humane ,understanding are almost infinite2 and ,nature is really so4 ,so that we may every day expect some ,discoveries1 either in ,mathematicks or ,natural ,philosophy1 which shall be of a new sort of ,utility or ,curiosity4 ,make a ,collection of all the different ,advantages which the ,mathematicks afforded a ,hundred ,years ago1 and you'll find nothing to be compar'd to the ,perspective ,glasses they have furnish'd since that time1 and which are a new ,organ to the ,sight1 and cou'd not be expected from ,art4 ,how surpriz'd had the ,ancients been1 if they had been told that their ,posterity1 by the help of some ,instruments1 shou'd one day see a vast number of ,objects which they did not see2 a ,heaven that was unknown to them2 and ,plants and ,animals they did not even suspect it was possible to exist4 ,naturalists had already a great many curious ,experiments2 but within about half a ,century1 the ,air-,pump hath produced a prodigious quantity of them wholly new1 and which by shewing ,bodies in a ,space void of ,air1 shews them as transported in a ,world different from ours1 where they undergo ,alterations whereof we had no ,notion4 ,the ,excellency of ,geometrical ,methods1 which are every day invented and improv'd1 may perhaps at last exhaust ,geometry2 that is1 ,the ,art of making ,geometrical ,discoveries1 and that is all3 ,whereas ,natural ,philosophy1 which contemplates an ,object of an unlimited ,variety1 and ,fcundity1 shall always find room for new ,observations1 and opportunities to increase its vast ,stock1 and shall have the ,advantage of never being a compleat ,science4 ,there are so many things to be discover'd1 whereof a great part1 in all likelyhood shall never be known2 that they give an opportunity to those who will not encounter with the ,thorns and ,difficulties of ,natural ,philosophy1 to affect a sort of ,discouragement4 ,a great many to vilify this ,natural ,science1 pretend a mighty veneration for the works of ,nature1 and that they are absolutely incomprehensible4 ,however1 ,nature is never so admirable1 nor so admir'd as when known4 ,true it is1 that what is known is inconsiderable in comparison of what is not yet known4 ,nay1 ,sometimes what is not known1 is exactly what seems shou'd be the soonest known4 ,as for instance1 it is not at least certainly known1 why a ,stone thrown up into the ,air falls down again2 but we certainly know the cause of the ,rainbow1 why it doth not exceed a certain height2 why its breadth is always the same2 why when there are two ,rainbows at the same time1 the ,colours of the one are overset with reference to the ,colours of the other2 and yet the fall of a ,stone in the ,air appears a more simple ,phnomenon1 than the ,rainbow4 ,but in a word1 altho' we do not know every thing1 we are not neither ignorant of every thing4 ,and altho' we are ignorant of the most simple ,events1 yet we have a knowledge of what seems the most ,complex4 ,so that if we have on the one hand reason to fear1 lest our ,vanity shou'd flatter us with the hopes of attaining to the knowledge of things above our reach2 on the other we ought to dread1 lest our ,slothfulness should also flatter us that we are condemn'd to a greater degree of ,ignorance than really we are4 ,people may think that the ,sciences do not begin to exert themselves1 either because they cou'd be but imperfect among the ,ancients2 or because we have almost lost the ,footsteps of them during the gloomy ,darkness of ,barbarity2 or because a better method hath been taken about #ajj ,years ago4 ,was the ,progress ,historically examin'd1 they have already made in so short a time1 notwithstanding the strong1 but false ,prejudices they had long to encounter with1 even sometimes the foreign ,obstacles they have met with from ,authority and ,power2 the want of ,zeal for ,sciences so remote from common use1 those few who apply'd themselves to this ,work1 and the weak ,motives which engag'd them in it2 a ,man would wonder at the ,greatness and ,rapidity of the ,progress of the ,sciences1 and even we might observe some new ones to start out of nothing1 and perhaps be tempted to have too great hopes of future ,improvements4 ,the greater reason we have of future ,success1 the greater we have to look upon the ,sciences as in their ,cradles1 at least ,natural ,philosophy4 ,and therefore the ,academy is only now employ'd to make an ample ,provision of ,observations1 and ,facts well attested1 which may one day be the foundation of a ,system4 ,for before the ,systematical ,natural ,philosophy can raise solid ,edifices2 ,experimental ,natural ,philosophy must be in a condition to supply it with good ,materials4 ,none but ,societies1 of those too countenanc'd and encourag'd by the ,prince1 can successfully make and prepare this ,collection of ,materials4 ,all the ,learning1 ,care1 ,life and ,wealth of one ,private ,man can never answer this ,design4 ,there are too many different ,experiments to be made1 which are to be too much vary'd1 and a long time prosecuted with the same ,temper and ,mind4 ,the ,cause of the least ,effect is so wrap'd up1 that unless you very carefully open all the various ,foldings1 you cannot come at it4 ,hitherto the ,academy of ,sciences hath consider'd ,nature but by parcels3 ,they have fix'd upon no general ,system1 for fear of falling into the inconveniency of hasty ,systems1 which are very grateful to the impatience of ,humane ,understanding2 and being once settled1 are ,obstacles to what ,truths are afterwards discover'd4 ,this day we are sure of a ,fact1 to morrow we shall be sure of another that hath no relation with the former4 ,however some ,conjectures are ventur'd at upon ,causes2 but they are only ,conjectures4 ,so that this ,collection1 which the ,academy gives to the ,publick1 is compos'd of separate ,fragments1 independant of one another2 whereof every one who is the ,author1 warrants the ,facts and ,experiments2 and whose ,arguments are approv'd by the ,academy1 but with ,restrictions becoming ,wise and ,wary ,scepticks4 ,time perhaps will come1 when these scatter'd ,fragments shall be united into one regular ,body2 and if they be such as they are wish'd1 they may of themselves ,unite4 ,a great many ,truths1 when their ,numbers is considerable1 shew so near a ,relation to1 and so mutual a ,dependance upon one another1 that it seems1 that notwithstanding their violent ,separation1 they have a natural ,tendency to be re-united4 ,,miscellanea ,,curiosa4 ,an ,estimate of the ,quantity of the ,vapours raised out of the ,sea derived from ,experiment3 ,together with an ,account of the ,circulation of the watry ,vapours of the ,sea1 and of the ,cause of ,springs1 presented to the ,royal ,society4 ,by ,mr4 ,e4 ,halley1 ,f4 ,r4 ,s4 ,that the ,quantity of ,aqueous ,vapours contain'd in the ,medium of the ,air1 is very considerable1 seems most evident from the great ,rains and ,snows which are sometimes observ'd to fall1 to that degree1 that the ,water thus discharg'd out of the ,interstices of the ,particles of ,air1 is in weight a very sensible part of the incumbent ,atmosphere3 ,but in what proportion these ,vapours rise1 which are the ,sources not only of ,rains1 but also of ,springs or ,fountains 7as ,i design to prove7 has not1 that ,i know of1 been any where well examin'd1 tho' it seem to be one of the most necessary ,ingredients of a ,real and ,philosophical ,meteorology1 and1 as such2 to deserve the ,consideration of this ,honourable ,society4 ,i thought it might not be unacceptable to attempt by ,experiment to determine the ,quantity of the ,evaporations of ,water1 as far as they arise from ,heat1 which upon ,trial succeeded as follows4 ,we took a ,pan of ,water1 about #d inches deep1 and #g ,inches #i_/aj ,diameter1 in which we placed a ,thermometer1 and by means of a ,pan of ,coals1 we brought the ,water to the same degree of ,heat1 which is observed to be that of the ,air in our hottest ,summer2 the ,thermometer nicely shewing it3 ,this done1 we affixed the ,pan of ,water1 with the ,thermometer in it1 to one end of the ,beam of a ,pair of ,scales1 and exactly counterpois'd it with weights in the other ,scale2 and by the application or removal of the ,pan of ,coals1 we found it very easie to maintain the ,water in the same degree of ,heat precisely4 ,doing thus we found the weight of the ,water sensibly to decrease2 and at the end of two hours we observed that there wanted half an ,ounce ,troy1 all but #g grains1 or #bcc grains of ,water1 which in that time had gone off in ,vapour2 tho' one could hardly perceive it smoke1 and the ,water were not sensibly warm4 ,this ,quantity in so short a time seem'd very considerable1 being little less than #f ounces in #bd hours1 from so small a ,surface as a ,circle of #h inches ,diameter4 ,to reduce this ,experiment to an exact ,calculus1 and determine the thickness of the ,skin of ,water that had so evaporated1 ,i assume the ,experiment alledg'd by ,dr4 ,edward ,bernard to have been made in the ,oxford ,society1 viz4 ,that the ,cube-foot ,english of ,water weighs exactly #gf ,pounds ,troy2 this divided by #agbh1 the number of ,inches in a ,foot1 will give #bec grains1 or ounce #ac grains for the weight of a ,cube-inch of ,water2 wherefore the weight of #bcc grains is #bcc_/bec or #ce ,parts of #ch of a ,cube-inch of ,water4 ,now the ,area of the ,circle whose ,diameter is #g-i_/aj ,inches1 is #di square ,inches3 by which dividing the ,quantity of ,water evaporated1 viz4 #ce_/ch of an ,inch1 the ,quote #ce_/ahfb or #a_/ec shews that the thickness of the ,water evaporated was the #ec;d part of an ,inch2 but we will suppose it only the #fjth part1 for the ,facility of ,calculation4 ,if therefore ,water as warm as the ,air in ,summer1 exhales the thickness of a #fjth part of an ,inch in two hours from its whole ,surface1 in #ab hours it will exhale the of an ,inch2 which ,quantity will be found abundantly sufficient to serve for all the ,rains1 ,springs1 and ,dews2 and account for the ,caspian ,sea1 being always at a stand1 neither wasting nor overflowing2 as likewise for the ,current said to set always in at the ,streights of ,gibralter1 tho' those ,mediterranean ,seas receive so many and so considerable ,rivers4 ,to estimate the ,quantity of ,water arising in ,vapours out of the ,sea1 ,i think ,i ought to consider it only for the time the ,sun is up1 for that the ,dews return in the ,night1 as much if not more ,vapours than are then emitted2 and in ,summer the ,days being no longer than #ab hours1 this ,excess is ballanc'd by the weaker ,action of the ,sun1 especially when rising before the ,water be warmed3 ,so that if ,i allow of an ,inch of the ,surface of the ,sea1 to be raised per diem in ,vapours1 it may not be an improbable ,conjecture4 ,upon this ,supposition1 every #aj square ,inches of the ,surface of the ,water1 yields in ,vapour per diem a ,cube-inch of ,water2 and each square ,foot half a ,wine-pint2 every ,space of #d ,foot square1 a ,gallon2 a ,mile square1 #fiad ,tons2 a square ,degree suppose of #fi ,english ,miles1 will evaporate #cc ,millions of ,tons3 ,and if the ,mediterranean be estimated at forty degrees long and four broad1 allowances being made for the ,places where it is broader1 by those where it is narrower 7and ,i am sure ,i guess at the least7 there will be #afj ,square degrees of ,sea2 and consequently1 the whole ,mediterranean must lose in ,vapour1 in a ,summer's day1 at least #ebhj ,millions of ,tons4 ,and this ,quantity of ,vapour1 tho' very great1 is as little as can be concluded from the ,experiment produced3 ,and yet there remains another ,cause1 which cannot be reduced to ,rule1 ,i mean the ,winds1 whereby the ,surface of the ,water is licked up some times faster than it exhales by the heat of the ,sun2 as is well known to those that have consider'd those drying ,winds which blow sometimes4 ,to estimate the ,quantity of ,water1 the ,mediterranean ,sea receives from the ,rivers that fall into it1 is a very hard ,task1 unless one had the ,opportunity to measure their ,chanels and ,velocity2 and therefore we can only do it by allowing more than enough2 that is1 by assuming these ,rivers greater than in all probability they be1 and then comparing the ,quantity of ,water voided by the ,thames1 with that of those ,rivers1 whose ,waters we desire to compute4 ,the ,mediterranean receives these considerable ,rivers2 the ,iberus1 the ,rhone1 the ,tiber1 the ,po1 the ,danube1 the ,neister1 the ,borystenes1 the ,tanais1 and the ,nile2 all the rest being of no great ,note1 and their ,quantity of ,water inconsiderable3 ,these nine ,rivers1 we will suppose each of them to bring down ten times as much ,water as the ,river ,thames2 not that any of them is great in reality1 but to comprehend with them all the small ,rivulets that fall into the ,sea1 which otherwise ,i know not how to allow for4 ,to calculate the ,water of the ,thames1 ,i assume that at ,kingston ,bridge where the ,flood never reaches1 and the ,water always runs down1 the breadth of the ,chanel is #ajj ,yards1 and its ,depth #c1 it being reduced to an ,equality 7in both which ,suppositions ,i am sure ,i take with the most7 hence the ,profil of the ,water in this ,place is #cjj square ,yards3 ,this multiplied by #dh ,miles 7which ,i allow the ,water to run in #bd hours1 at #b ,miles an hour7 or #hddhj ,yards1 gives #becddjjj ,cubick-yards of ,water to be evacuated every ,day2 that is1 #bjcjjjjj ,tons per diem2 and ,i doubt not1 but in the excess of my ,measures of the ,chanel of the ,river1 ,i have made more than sufficient allowance for the ,waters of the ,brent1 the ,wandel1 the ,lea1 and ,darwent1 which are all worth notice1 that fall into the ,thames below ,kingston4 ,now if each of the aforesaid #i ,rivers yield #aj times as much ,water as the ,thames doth1 'twill follow that each of them yields but #bjc ,millions of ,ton per diem1 and the whole #i1 but #ahbg ,millions of ,tons in a day2 which is but little more than of what is proved to be raised in vapour out of the ,mediterranean in #ab hours time4 ,now what becomes of this ,vapour when rais'd1 and how it comes to pass that the ,current always sets in at the ,mouth1 of the ,streights of ,gibralter1 shall immediately be shew'd3 ,but first it is necessary to advertise the ,reader1 that in making the ,experiment herein mention'd1 the ,water used had been salted to the same degree as is the common ,sea-water1 by the ,solution of about a #djth part of ,salt4 ,having thus shew'd by ,experiment the ,quantity of ,water raised in ,vapour from the ,surface of the ,sea in a ,days time1 which was so far approv'd of by some ,honourable ,members of this ,society1 that ,i receiv'd their ,commands to prosecute these ,enquiries2 and particularly1 in relation to the ,method used by ,nature1 to return the said ,vapours again into the ,sea2 which is so justly perform'd1 that in many hundred of ,years we are sufficiently assured that the ,sea has not sensibly decreased by the loss in ,vapour2 nor yet abounded by the immense ,quantity of fresh it receives continually from the ,rivers4 ,to demonstrate this ,equilibre of ,receipt and ,expence in the whole ,sea1 is a ,task too hard for me to undertake1 yet in obedience to those whom ,i have the ,honour to serve1 ,i shall here offer1 what to me has hitherto seem'd the most satisfactory ,account of this grand ,phnomenon3 ,i have in another place attempted to explain the manner of the rising of ,vapour by ,warmth1 by shewing1 that if an ,atom of ,water were expanded into a ,shell or ,bubble1 so as to be ten times as big in ,diameter as when it was ,water2 such an ,atom would become specifically lighter than ,air1 and rise so long as that ,flatus or warm ,spirit that first separated it from the ,mass of ,water1 shall continue to distend it to the same ,degree2 and that ,warmth declining1 and the ,air growing cooler and also specifically lighter1 the ,vapours consequently shall stop at a certain ,region of the ,air1 or else descend1 which may happen upon several accounts1 as ,i shall by and by endeavour to make out2 yet ,i undertake not that this is the only principal of the rise of ,vapours1 and that there may not be a certain sort of ,matter1 whose ,conatus may be contrary to that of ,gravity2 as is evident in ,vegetation1 where in the ,tendency of the ,sprouts is directly upwards1 or against the ,perpendicular4 ,but what ever is the true ,cause1 it is in ,fact certain1 that warmth does separate the ,particles of ,water1 and emit them with a greater and greater ,velocity1 as the heat is more and more intense2 as is evident in the ,steam of a boiling ,cauldron1 wherein likewise the ,velocity of the ascent of the ,vapours does visibly decrease till they disappear1 being dispersed into and assimulated with the ,ambient ,air4 ,vapours being thus raised by warmth1 let us for a first ,supposition put1 that the whole ,surface of the ,globe were all ,water very deep1 or rather that the whole ,body of the ,earth were ,water1 and that the ,sun had its diurnal course about it3 ,i take it1 that it would follow1 that the ,air of it self would imbibe a certain ,quantity of aqueous ,vapours1 and retain them like ,salts dissolved in ,water2 that the ,sun warming the ,air1 and raising a more plentiful ,vapour from the ,water in the day-time1 the ,air would sustain a greater proportion of ,vapour1 as warm ,water will hold more dissolved ,salts1 which upon the absence of the ,sun in the ,nights would be all again discharged in ,dews1 analogous to the ,precipitation of ,salts on the cooling of the ,liquors2 nor is it to be believed that in such ,case there would be any diversity of ,weather1 other than periodically1 every ,year alike2 the mixture of all terrestrious1 saline1 heterogenious ,vapours being taken away1 which as they are variously compounded and brought by the ,winds1 seem to be the ,causes of those various ,seasons which we now find4 ,in this case the ,aiery ,regions every where1 at the same height1 would be equally replenished with the ,proportion of ,water it could contain1 regard being only to be had to the different degree of warmth1 from the nearness or distance of the ,sun2 and an eternal ,east-wind would blow all round the ,globe1 inclining only to the same side of the ,east1 as the ,latitude doth from the ,equator2 as is observed in the ,ocean between the ,tropicks4 ,next let us suppose this ,ocean interspersed with wide and spacious ,tracts of ,land1 with high ,ridges of ,mountains1 such as the ,pyrenean1 the ,alps1 the ,apennine1 the ,carpathian in ,europe1 ,taurus1 ,caucasus1 ,imaus1 and several others in ,asia2 ,atlas and the ,montes ,lun1 with other unknown ,ridges in ,africa1 whence came the ,nile1 the ,nigre1 and the ,zaire3 ,and in ,america1 the ,andes and the ,apalatean ,mountains2 each of which far surpass the usual height to which the ,aqueous ,vapours of themselves ascend1 and on the tops of which the ,air is so cold and rarified1 as to retain but a small part of those ,vapours1 that shall be brought thither by ,winds4 ,those ,vapours therefore that are raised copiously in the ,sea1 and by the ,wind1 are carried over the low ,land to those ,ridges of ,mountains1 are there compelled by the ,stream of the ,air to mount up with it to the tops of the ,mountains1 where the ,water presently precipitates1 gleeting down by the ,crannies of the ,stone2 and part of the ,vapour entering into the ,caverns of the ,hills1 the ,water thereof gathers as in an ,alembick into the ,basons of ,stone it finds2 which being once fill'd1 all the overplus of ,water that comes thither runs over by the lowest place1 and breaking out by the sides of the ,hills1 forms single ,springs4 ,many of these running down by the ,valleys or ,guts between the ,ridges of the ,hills1 and coming to unite1 form little ,rivulets1 or ,brooks3 ,many of these again1 meeting in one common ,valley and gaining the plain ,ground1 being grown less rapid1 become a ,river2 and many of these being united in one common ,channel1 make such ,streams as the ,rhine1 the ,rhone1 the ,danube2 which latter1 one would hardly think the ,collection of ,water condensed out of ,vapour1 unless we consider how vast a ,tract of ,ground that ,river drains1 and that it is the ,sum of all those ,springs which break out on the ,south side of the ,carpathian ,mountains1 and on the ,north side of the immense ,ridge of the ,alps1 which is one continued ,chain of ,mountains from ,switzerland1 to the ,black-,sea4 ,and it may almost pass for a ,rule1 that the magnitude of a ,river1 or the quantity of ,water it evacuates1 is proportionable to the length and height of the ,ridges from whence its ,fountains arise4 ,now this ,theory of ,springs is not a bare ,hypothesis1 but founded on ,experience1 which it was my luck to gain in my abode at ,st4 ,helena1 where in the ,night-time1 on the tops of the ,hills1 about #hjj ,yards above the ,sea1 there was so strange a condensation1 or rather precipitation of the ,vapours1 that it was a great ,impediment to my ,clestial ,observations2 for in the clear ,sky1 the ,dew would fall so fast1 as to cover1 each half quarter of an ,hour1 my ,glasses with little drops2 so that ,i was necessitated to wipe them so often1 and my ,paper on which ,i wrote my ,observations would immediately be so wet with ,dew1 that it would not bear ,ink3 ,by which it may be suppos'd how fast the ,water gathers in those mighty high ,ridges ,i but now nam'd4 ,thus is one part of the ,vapours blown upon the ,land return'd by the ,rivers into the ,sea1 from whence they came2 another part by the cool of the ,night falls in ,dews1 or else in ,rains1 again into the ,sea before it reaches the ,land1 which is by much the greatest part of the whole ,vapours1 because of the great extent of the ,ocean1 which the motion of the ,wind does not traverse in a very long space of ,time2 and this is the ,reason why the ,rivers do not return so much into the ,mediterranean1 as is extracted into ,vapour4 ,a third part falls on the ,low-,lands1 and is the ,pabulum of ,plants1 where yet it does not rest1 but is again exhaled in ,vapour by the action of the ,sun1 and is either carried by the ,winds to the ,sea to fall in ,rain or ,dew there1 or else to the ,mountains to be there turn'd into ,springs2 and tho' this does not immediately come to pass1 yet after several ,vicissitudes of rising in ,vapour1 and falling in ,rain or ,dews1 each ,particle of the ,water is at length return'd to the ,sea from whence it came4 ,add to this1 that the ,rain-waters after the ,earth is fully sated with moisture1 does1 by the ,vallies or lower parts of the ,earth1 find its way into the ,rivers1 and so is compendiously sent back to the ,sea4 ,after this manner is the ,circulation perform'd1 and ,i doubt not but this ,hypothesis is more reasonable than that of those who derive all ,springs from the ,rain-waters1 which yet are perpetual and without diminution1 even when no ,rain falls for a long space of time2 or that derive them from a ,filtration or ,percolation of the ,sea-waters1 thro' certain imaginary ,tubes or ,passages within the ,earth wherein they lose their ,saltness4 ,this1 besides many others1 labouring under this principal ,absurdity1 that the greatest ,rivers have their most copious ,fountains farthest from the ,sea1 and whether so great quantities of fresh ,water cannot reasonably be deriv'd any other way than in ,vapour4 ,this1 if we may allow final ,causes1 seems to be the design of the ,hills1 that their ,ridges being plac'd thro' the midst of the ,continents1 might serve1 as it were1 for ,alembicks to distil fresh ,water for the use of ,man and ,beast1 and their heights to give a descent to those ,streams to run gently1 like so many ,veins1 of the ,macrocosm to be the more beneficial to the ,creation4 ,if the difference between ,rain and ,dew1 and the cause why sometimes 'tis ,cloudy1 at other times ,serene1 be inquir'd1 ,i can offer nothing like a proper ,solution thereof1 only with submission to propose ,conjectures1 which are the best ,i can find1 viz4 ,that the ,air being heaped up by the meeting of two contrary ,winds1 when the ,mercury is high1 the ,vapours are the better sustain'd and kept from ,co-agulating or ,condensing into ,drops1 whereby ,clouds are not so easily generated1 and the ,night the ,vapours fall down single1 as they rose in imperceptible ,atoms of ,water3 ,whereas1 when the ,mercury is low1 ,and the ,air rarified by the ,exhaustion thereof1 by two contrary ,winds blowing from the place2 the ,atoms of ,air keep the ,vapours not so well separated1 and they coalesce into visible ,drops in the ,clouds1 and from thence are easily drawn into greater ,drops of ,rain2 to which 'tis possible and not improbable1 that some sort of ,saline or ,angular ,particles of ,terrestrial ,vapour being immix'd with the ,aqueous1 which ,i take to be ,bubbles1 may cut or break their ,skins or ,coats1 and so contribute to their more speedy ,condensation into ,rain4 ,the ,true ,theory of the ,tides1 extracted from that admired ,treatise of ,mr4 ,isaac ,newton1 ,intitled1 ,philosophi ,naturalis ,principia ,mathematica2 ,being a ,discourse presented with that ,book to the late ,king ,james1 by ,mr4 ,edmund ,halley4 ,it may1 perhaps1 seem strange1 that this ,paper1 being no other than a particular ,account of a ,book long since published1 should now appear here2 but the ,desires of several honourable ,persons1 which could not be withstood1 have obliged us to insert it here1 for the sake of such1 who being less knowing in ,mathematical ,matters1 and therefore not daring to adventure on the ,author himself1 are notwithstanding1 very curious to be inform'd of the ,causes of ,things2 particularly of so general and extraordinary ,phnomena1 as are those of the ,tides4 ,now this ,paper having been drawn up for the late ,king ,james's ,use1 7in whose ,reign the ,book was publish'd7 and having given good ,satisfaction to those that got ,copies of it2 it is hoped the ,savans of the higher ,form will indulge us this ,liberty we take to gratifie their ,inferiours in point of ,science2 and not be offended1 that we here insist more largely upon ,mr4 ,newton's ,theory of the ,tides1 which1 how plain and easie soever we find1 is very little understood by the common ,reader4 ,the sole ,principle upon which this ,author proceeds to explain most of the great and surprizing ,appearances of ,nature1 is no other than that of ,gravity1 whereby in the ,earth all ,bodies have a tendency towards its ,centre2 as is most evident3 ,and from undoubted ,arguments it's proved1 that there is such a ,gravitation towards the ,centre of the ,sun1 ,moon1 and all the ,planets4 ,from this ,principle1 as a necessary ,consequence1 follows the ,sphrical ,figure of the ,earth and ,sea1 and of all the other ,clestial ,bodies3 ,and tho' the tenacity and firmness of the ,solid ,parts1 support the ,inequalities of the ,land above the ,level2 yet the ,fluids1 pressing equally and easily yielding to each other1 soon restore the quilibrium1 if disturbed1 and maintain the exact ,figure of the ,globe4 ,now this force of ,descent of ,bodies towards the ,centre1 is not in all places alike1 but is still less and less1 as the distance from the ,center encreases3 ,and in this ,book it is demonstrated1 that this ,force decreases as the ,square of the distance increases2 that is1 the weight of ,bodies1 and the ,force of their ,fall is less1 in parts more removed from the ,center1 in the proportion of the ,squares of the ,distance4 ,so as for ,example1 a ,ton weight on the ,surface of the ,earth1 if it were raised to the height of #djjj ,miles1 which ,i suppose the ,semidiameter of the ,earth1 would weigh but of a ,ton1 or #e ,hundred weight3 ,if to #abjjj ,miles1 or #c ,semidiameters from the ,surface1 that is #d from the ,center1 it would weigh but #a_/af part of the ,weight on the ,surface1 or a ,hundred and ,quarter3 ,so that it would be as easie for the ,strength of a ,man at that height to carry a ,ton weight1 as here on the ,surface a #ajj4 ,and in the same ,proportion does the ,velocities of the fall of ,bodies decrease3 ,for whereas on the ,surface of the ,earth all things fall #af ,foot in a second2 at one ,semidiameter above1 this fall is but four ,foot2 and at three ,semidiameters1 or four from the ,centre1 it is but #a_/af of the ,fall at the ,surface1 or but one ,foot in a second3 ,and at greater ,distances both ,weight and ,fall become very small1 but yet at all given ,distances is still some thing1 tho' the ,effect become insensible4 ,at the distance of the ,moon 7which ,i will suppose #fj ,semidiameters of the ,earth7 #cfjj ,pounds weigh but one ,pound1 and the fall of ,bodies is but of #a_/cfjj a ,foot in a second1 or #af ,foot in a ,minute2 that is1 a ,body so far off descends in a ,minute no more than the same at the ,surface of the ,earth would do in a ,second of ,time4 ,as was said before1 the same force decreasing after the same manner is evidently found in the ,sun1 ,moon1 and all the ,planets2 but more especially in the ,sun1 whose ,force is prodigious2 becoming sensible even in the immense distance of ,saturn3 ,this gives room to suspect1 that the force of ,gravity is in the ,clestial ,globes proportional to the quantity of ,matter in each of them3 ,and the ,sun being at least ten ,thousand times as big as the ,earth1 its ,gravitation or attracting ,force1 is found to be at least ten ,thousand times as much as that of the ,earth1 acting on ,bodies at the same distance4 ,this ,law of the decrease of ,gravity being demonstratively proved1 and put past contradiction2 the ,author with great ,sagacity1 inquires into the necessary ,consequences of this ,supposition2 whereby he finds the genuine ,cause of the several ,appearances in the ,theory of the ,moon and ,planets1 and discovers the hitherto unknown ,laws of the ,motion of ,comets1 and of the ,ebbing and flowing of the ,sea4 ,each of which are ,subjects that have hitherto taken up much larger ,volumes2 but ,truth being uniform1 and always the same1 it is admirable to observe how easily we are enabled to make out very abstruse and difficult ,matters1 when once true and genuine ,principles are obtain'd3 ,and on the other hand it may be wondred2 that1 notwithstanding the great facility of truth1 and the perplexity and nonconsequences that always attend erroneous ,suppositions1 these great ,discoveries should have escaped the acute ,disquisitions of the best ,philosophical ,heads of all past ,ages1 and be reserv'd to these our ,times4 ,but that wonder will soon cease1 if it be consider'd how great improvements ,geometry has receiv'd in our ,memory1 and particularly from the profound ,discoveries of our incomparable ,author4 ,the ,theory of the ,motion of the primary ,planets is here shewn to be nothing else1 but the contemplation of the ,curve ,lines which ,bodies cast with a given ,velocity1 in a given ,direction1 and at the same time drawn towards the ,sun by its gravitating ,power1 would describe4 ,or1 which is all one1 that the ,orbs of the ,planets are such ,curve ,lines as a ,shot from a ,gun describes in the ,air1 being cast according to the direction of the ,piece1 but bent in a crooked ,line by the supervening ,tendency towards the ,earths ,centre3 ,and the ,planets being supposed to be projected with a given ,force1 and attracted towards the ,sun1 after the aforesaid manner1 are here proved to describe such ,figures1 as answer punctually to all that the ,industry of this and the last ,age has observed in the ,planetary ,motions4 ,so that it appears1 that there is no need of solid ,orbs and ,intelligences1 as the ,antients imagin'd1 nor yet of ,vortices or ,whirlpools of the ,clestial ,matter1 as ,des ,cartes supposes2 but the whole ,affair is simply and mechanically performed1 upon the sole ,supposition of a ,gravitation towards the ,sun2 which cannot be denied4 ,the ,motion of ,comets is here shewn to be compounded of the same ,elements1 and not to differ from ,planets1 but in their greater swiftness1 whereby overpowering the ,gravity that should hold them to the ,sun1 as it doth the ,planets1 they flie off again1 and distance themselves from the ,sun and ,earth1 so that they soon are out of our sight4 ,and the imperfect ,accounts and ,observations ,antiquity has left us1 are not sufficient to determine whether the same ,comet ever return again4 ,but this ,author has shewn how ,geometrically to determine the ,orb of a ,comet from ,observations1 and to find his ,distance from the ,earth and ,sun1 which was never before done4 ,the third thing here done is the ,theory of the ,moon1 all the ,inequalities of whose ,motion are proved to arise from the same ,principles1 only here the effect of two ,centers operating on1 or attracting a projected ,body1 comes to be considered2 for the ,moon1 though principally attracted by the ,earth1 and moving round it1 does together with the ,earth1 move round the ,sun once a ,year1 and is1 according as she is nearer or farther from the ,sun1 drawn by him more or less than the ,center of the ,earth1 about which she moves2 whence arise several ,irregularities in her ,motion1 of all which1 the ,author in this ,book1 with no less ,subtility than ,industry1 has given a full account4 ,and though by reason of the great ,complication of the ,problem1 he has not yet been able to make it purely ,geometrical1 'tis to be hoped1 that in some farther ,essay he may surmount the difficulty3 ,and having perfected the ,theory of the ,moon1 the long desir'd ,discovery of the ,longitude 7which at ,sea is only practicable this way7 may at length be brought to light1 to the great ,honour of your ,majesty1 and ,advantage of your ,subjects4 ,all the surprising ,phnomena of the ,flux and ,reflux of the ,sea1 are in like manner shewn to proceed from the same ,principle2 which ,i design more largely to insist on1 since the ,matter of ,fact is in this ,case much better known to your ,majesty than in the foregoing4 ,if the ,earth were alone1 that is to say1 not affected by the ,actions of the ,sun and ,moon1 it is not to be doubted1 but the ,ocean1 being equally press'd by the force of ,gravity towards the ,center1 would continue in a perfect ,stagnation1 always at the same height1 without either ,ebbing or ,flowing2 but it being here demonstrated1 that the ,sun and ,moon have a like ,principle of ,gravitation towards their ,centers1 and that the ,earth is within the ,activity of their ,attractions1 it will plainly follow1 that the ,equality of the pressure of ,gravity towards the ,center will thereby be disturb'd2 and though the smallness of these ,forces1 in respect of the ,gravitation towards the ,earth's ,center1 renders them altogether imperceptible by any ,experiments we can devise1 yet the ,ocean being fluid and yielding to the least force1 by its rising shews where it is less press'd1 and where it is more press'd by its sinking4 ,now if we suppose the force of the ,moon's ,attaction to decrease as the ,square of the ,distance from its ,center increases 7as in the ,earth and other ,clestial ,bodies7 we shall find1 that where the ,moon is perpendicularly either above or below the ,horizon1 either in ,zenith or ,nadir1 there the force of ,gravity is most of all diminished1 and consequently that there the ,ocean must necessarily swell by the coming in of the ,water from those parts where the ,pressure is greatest1 viz4 in those places where the ,moon is near the ,horizon3 ,but that this may be the better understood1 ,i thought it needful to add the following ,figure1 7,vide ,fig4 #a4 ,plate #a47 where ,m is the ,moon1 ,e the ,earth1 ,c its ,center1 and ,z the place where the ,moon is in the ,zenith1 ,n where in the ,nadir4 ,now by the ,hypothesis it is evident1 that the ,water in ,z1 being nearer1 is more drawn by the ,moon1 than the ,center of the ,earth ,c1 and that again more than the ,water in ,n2 wherefore the ,water in ,z hath a tendency towards the ,moon1 contrary to that of ,gravity1 being equal to the excess of the ,gravitation in ,z1 above that in ,c3 ,and in the other case1 the ,water in ,n1 tending less towards the ,moon than the ,center ,c1 will be less pressed1 by as much as is the difference of the ,gravitation towards the ,moon in ,c and ,n4 ,this rightly understood1 it follows plainly1 that the ,sea1 which otherwise would be ,spherical1 upon the ,pressure of the ,moon1 must form it self into a ,spheroidal or ,oval ,figure1 whose longest ,diameter is where the ,moon is vertical1 and shortest where she is in the ,horizon2 and that the ,moon shifting her ,position as she turns round the ,earth once a ,day1 this ,oval of ,water shifts with her1 occasioning thereby the two ,floods and ,ebbs observable in each #be ,hours4 ,and this may suffice1 as to the general ,cause of the ,tides2 it remains now to shew how naturally this ,motion accounts for all the ,particulars that have been observ'd about them2 so that there can be no room left to doubt1 but that this is the true cause thereof4 ,the ,spring ,tides upon the ,new and ,full ,moons1 and ,neap ,tides on the ,quarters1 are occasion'd by the attractive ,force of the ,sun in the ,new and ,full1 conspiring with the ,attraction of the ,moon1 and producing a ,tide by their united ,forces3 ,whereas in the ,quarters1 the ,sun raises the ,water where the ,moon depresses it1 and the contrary2 so as the ,tides are made only by the difference of their ,attractions4 ,that the force of the ,sun is no greater in this ,case1 proceeds from the very small ,proportion the ,semi-diameter of the ,earth bears to the vast distance of the ,sun4 ,it is also observ'd1 that cteris paribus1 the quinoctial ,spring ,tides in ,march and ,september1 or near them1 are the ,highest1 and the ,neap ,tides the lowest2 which proceeds from the greater ,agitations of the ,waters1 when the fluid ,spheroid revolves about a great ,circle of the ,earth1 than when it turns about in a lesser ,circle2 it being plain that if the ,moon were constituted in the ,pole1 and there stood1 that the ,spheroid would have a fix'd ,position1 and that it would be always high ,water under the ,poles1 and low ,water every where under the quinoctial3 ,and therefore the nearer the ,moon approaches the ,poles1 the less is the agitation of the ,ocean1 which is of all the greatest1 when the ,moon is in the quinoctial1 or farthest distant from the ,poles4 ,whence the ,sun and ,moon1 being either conjoined or opposite in the quinoctial1 produce the greatest ,spring ,tides2 and the subsequent ,neap ,tides1 being produc'd by the ,tropical ,moon in the ,quarters1 are always the least ,tides2 whereas in ,june and ,december1 the ,spring ,tides are made by the ,tropical ,sun and ,moon1 and therefore less vigorous2 and the ,neap ,tides by the quinoctial ,moon1 which therefore are the stronger3 ,hence it happens1 that the difference between the ,spring and ,neap ,tides in these ,months1 is much less considerable than in ,march and ,september4 ,and the reason why the very highest ,spring ,tides are found to be rather before the ,vernal and after the ,autumnal ,equinox1 viz4 in ,february and ,october1 than precisely upon them1 is1 because the ,sun is nearer the ,earth in the ,winter ,months1 and so comes to have a greater effect in producing the ,tides4 ,hitherto we have consider'd such ,affections of the ,tides as are ,universal1 without relation to particular ,cases2 what follows from the differing ,latitudes of places1 will be easily understood by the following ,fig4 7,vide ,fig4 #b4 ,plate #a47 ,let ,ap,e,p be the ,earth cover'd over with very deep ,waters1 ,c its ,center1 ,p1 p1 its ,poles1 ,,ae the quinoctial1 ,f1 f1 the parallel of ,latitude of a ,place1 ,d1 d1 another ,parallel at equal distance on the other side of the quinoctial1 ,h1 h1 the two ,points where the ,moon is vertical1 and let ,k1 k1 be the great ,circle1 wherein the ,moon appears ,horizontal4 ,it is evident1 that a ,spheroid describ'd upon ,hh1 and ,kk1 shall nearly represent the ,figure of the ,sea1 and ,cf1 ,,cd1 ,,cf1 ,cd1 shall be the heighths of the ,sea in the places f1 ,d1 ,f1 d1 in all which it is ,high-water3 ,and seeing that in twelve ,hours time1 by the diurnal ,rotation of the ,earth1 the ,point ,f is transferr'd to f1 and d to ,d3 ,the height of the ,sea ,,cf will be that of the ,high-water when the ,moon is present1 and ,cf that of the other ,high-water1 when the ,moon is under the ,earth3 ,which in the case of this ,figure is less than the former ,,cf4 ,and in the opposite ,parallel ,dd1 the contrary happens4 ,the ,rising of the ,water being always alternately greater and less in each place1 when it is produc'd by the ,moon declining sensibly from the quinoctial2 that being the greatest of the two ,high-waters in each diurnal ,revolution of the ,moon1 wherein she approaches nearest either to the ,zenith or ,nadir of the place3 ,whence it is1 that the ,moon in the ,northern ,signs1 in this part of the ,world1 makes the greatest ,tides when above the ,earth1 and in ,southern ,signs1 when under the ,earth2 the ,effect being always the greatest where the ,moon is farthest from the ,horizon1 either above or below it4 ,and this alternate ,increase and ,decrease of the ,tides has been observ'd to hold true on the ,coast of ,england1 at ,bristol by ,captain ,sturmy1 and at ,plymouth by ,mr4 ,colepresse4 ,but the ,motions hitherto mentioned are somewhat alter'd by the ,libration of the ,water1 whereby1 though the ,action of the ,luminaries should cease1 the ,flux and ,reflux of the ,sea would for some time continue3 ,this ,conservation of the impress'd ,motion diminishes the differences that otherwise would be between two consequent ,tides1 and is the reason why the highest ,spring-,tides are not precisely on the ,new and ,full ,moons1 nor the ,neaps on the ,quarters2 but generally they are the third ,tides after them1 and sometimes later4 ,all these things would regularly come to pass1 if the whole ,earth were cover'd with ,sea very deep2 but by reason of the shoalness of some places1 and the narrowness of the ,streights1 by which the ,tides are in many cases propagated1 there arises a great diversity in the ,effect1 and not to be accounted for1 without an exact ,knowledge of all the ,circumstances of the ,places1 as of the ,position of the ,land1 and the ,breadth and ,depth of the ,channels by which the ,tide flows2 for a very slow and imperceptible ,motion of the whole ,body of the ,water1 where it is 7for ,example7 #b ,miles deep1 will suffice to raise its ,surface #aj or #ab ,feet in a ,tides time2 whereas1 if the same quantity of ,water were to be convey'd up a ,channel of #dj ,fathoms deep1 it would require a very great ,stream to effect it1 in so large ,inlets as are the ,channel of ,england1 and the ,german ,ocean2 whence the ,tide is found to set strongest in those places where the ,sea grows narrowest2 the same quantity of ,water being to pass through a smaller ,passage3 ,this is most evident in the ,streights1 between ,portland and ,cape de ,hague in ,normandy1 where the ,tide runs like a ,sluce2 and would be yet more between ,dover and ,calais1 if the ,tide coming about the ,island from the ,north did not check it4 ,and this force being once impress'd upon the ,water1 continues to carry it above the level of the ordinary height in the ,ocean1 particularly where the ,water meets a direct ,obstacle1 as it is at ,st4 ,malo's2 and where it enters into a long ,channel1 which running far into the ,land1 grows very streight at its ,extremity2 as it is in the ,severn-,sea at ,chepstow and ,bristol4 ,this shoalness of the ,sea1 and the intercurrent ,continents are the reason1 that in the open ,ocean the time of ,high water is not at the ,moons appulse to the ,meridian1 but always some ,hours after it2 as it is observ'd upon all the ,west ,coast of ,europe and ,africa1 from ,ireland to the ,cape of ,good ,hope3 ,in all which a ,s4 ,w4 ,moon makes ,high-water1 and the same is reported to be on the ,west side of ,america4 ,but it would be endless to account all the particular ,solutions1 which are easie ,corollaries of this ,hypothesis2 as why the ,lakes1 such as the ,caspian ,sea1 and ,mediterranean ,seas1 such as the ,black ,sea1 the ,streights and ,baltick1 have no sensible ,tides3 ,for ,lakes having no ,communication with the ,ocean1 can neither increase nor diminish their ,water1 whereby to rise and fall2 and ,seas that communicate by such narrow ,inlets1 and are of so immense an ,extent1 cannot in a few ,hours time receive or empty ,water enough to raise or sink their ,surface any thing sensibly4 ,lastly1 to demonstrate the ,excellency of this ,doctrine1 the ,example of the ,tides in the ,port of ,tunking in ,china1 which are so extraordinary1 and differing from all others we have yet heard of1 may suffice4 ,in this ,port there is but one ,flood and ,ebb in #bd ,hours2 and twice in each ,month1 viz4 when the ,moon is near the quinoctial there is no ,tide at all1 but the ,water is stagnant2 but with the ,moons ,declination there begins a ,tide1 which is greatest when she is in the ,tropical ,signs3 ,only with this difference1 that when the ,moon is to the ,northward of the quinoctial1 it ,flows when she is above the ,earth1 and ,ebbs when she is under1 so as to make ,high-water at ,moons-setting1 and ,low-water at ,moons-rising3 ,but on the contrary1 the ,moon being to the ,southward1 makes ,high-water at rising1 and ,low-water at setting2 it ,ebbing all the time she is above the ,horizon4 ,as may be seen more at large in the ,philosophical ,transactions1 ,numb4 #afb4 ,the ,cause of this odd ,appearance is propos'd by ,mr4 ,newton1 to be from the concurrence of two ,tides2 the one propagated in six ,hours out of the great ,south-,sea along the ,coast of ,china2 the other out of the ,indian-,sea1 from between the ,islands in twelve ,hours1 along the ,coast of ,malacca and ,cambodia4 ,the one of these ,tides1 being produc'd in ,north ,latitude1 is1 as has been said1 greater1 when the ,moon being to the ,north of the ,equator is above the ,earth1 and less when she is under the ,earth4 ,the other of them1 which is propagated from the ,indian ,sea1 being raised in ,south-,latitude1 is greater when the ,moon declining to the ,south1 is above the ,earth1 and less when she is under the ,earth3 ,so that of these ,tides alternately greater and lesser1 there comes always successively two of the greater and two of the lesser together every ,day2 and the ,high-water falls always between the times of the arrival of the two greater ,floods2 and the ,low-water between the arrival of the two lesser ,floods4 ,and the ,moon coming to the quinoctial1 and the alternate ,floods becoming equal1 the ,tide ceases1 and the ,water stagnates3 ,but when she has pass'd to the other side of the ,equator1 those ,floods which in the former ,order were the least1 now becoming the greatest1 that ,that before was the time of ,high-water1 now becomes the ,low-water1 and the ,converse4 ,so that the whole appearance of these strange ,tides1 is without any forcing naturally deduc'd from these ,principles1 and is a great ,argument of the ,certainty of the whole ,theory4 ,a ,theory of the ,variation of the ,magnetical ,compass4 ,by ,mr4 ,ed4 ,halley1 ,fellow of the ,royal ,society4 ,the ,variation of the ,compass 7by which ,i mean the ,deflection of the ,magnetical ,needle from the true ,meridian7 is of that great ,concernment in the ,art of ,navigation1 that the neglect thereof1 does little less than render useless one of the noblest ,inventions ,mankind ever yet attained to4 ,and for this cause all ,ships of ,consequence 7especially those bound beyond the ,equator7 carry with them ,instruments on purpose to observe this ,variation3 ,that so the ,course steer'd by the ,compass1 may be reduc'd to the true ,course in respect of the ,meridian4 ,now although the great utility that a perfect ,knowledge of the ,theory of the ,magnetical ,direction would afford to ,mankind in general1 and especially to those concern'd in ,sea ,affairs1 seems as sufficient incitement to all ,philosophical and ,mathematical ,heads1 to take under serious ,consideration the several ,phnomena1 and to endeavour to reconcile them by some general ,rule3 ,yet so it is2 that almost all the ,authors1 from whom a ,discourse of this kind ought to have been expected1 pass by in silence the ,difficulties they here ,encounter4 ,and those that mention this ,variation3 ,by affirming it to proceed from ,causes altogether uncertain 7as are the casual lying of ,iron ,mines and ,loadstones in the ,earth7 put a stop to all further ,contemplation2 and give discouragement to those that would otherwise undertake this ,enquiry4 ',tis true1 that not long since one ,mr4 ,bond1 an old ,teacher of ,navigation1 put forth a small ,treatise1 wherein he pretends to calculate the ,variation3 ,but he limits his ,hypothesis to the ,city of ,london1 affirming himself 7as he had a great deal of reason7 that the same ,calculus is not sufficient for other ,places2 whereby it appears that this ,rule is far short of the so much desir'd general one4 ,now although 7through want of sufficient ,observations1 and some other ,difficulties1 which ,i shall anon shew7 ,i cannot pretend perfectly to establish the ,numbers and ,rules of a ,calculus1 which shall precisely answer to the ,variations of all parts of the ,world3 ,yet ,i suppose it will not be unacceptable to the ,curious to propose something of a ,light into this abstruse ,mystery2 which1 if no other1 may have this good ,effect1 to stir up the ,philosophical ,genii of the ,age to apply themselves more attentively to this useful ,speculation4 ,but before ,i proceed1 'twill be necessary to lay down the ,grounds upon which ,i raise my ,conclusions2 and at once to give a ,synopsis of those ,variations1 which ,i have reason to look upon as sure1 being mostly the ,observations of ,persons of good ,skill and ,integrity4 ,a ,,table ,,of ,,variations4 ,names of ,longitude ,latitude4 ,anno ,variation ,places4 from ,lon4 ,dom4 ,observ'd4 d m d m d m ,london #j #j #ea #cb ,n #aehj #aa #ae ,e #afbb #f #j ,e #afcd #d #e ,e #afgb #b #cj ,w ,paris #b #be ,e #dh #ea ,n #afhc #d #cj ,w #afdj #c #jj ,e #afff #j #j #afha #b #cj ,w ,uraniburg #ac #j ,e #ee #ed ,n #afgb #b #ce ,w ---------------------------------------- ------------------------------ ,copenhagen #ab #ec ,e #ee #da ,n #afdi #a #cj ,e #afgb #c #ce ,w ,dantzick #ai #j ,e #ed #bc ,n #afgi #g #jj ,w ,mompelier #d #j ,e #dc #cg ,n #afgd #a #aj ,w ,brest #d #be ,w #dh #bc ,n #afhj #a #de ,w ---------------------------------------- ------------------------------ ,rome #ac #j ,e #da #ej ,n #afha #e #j ,w ,bayonne #a #bj ,w #dc #cj ,n #afhj #a #bj ,w ,hudson's ,bay #gi #dj ,w #ea #jj ,n #affh #ai #ae ,w ,in ,hud4 ,straights #eg #jj ,w #fa #jj ,n #affh #bi #cj ,w ,in ,baffin's ,bay at ,sir ,thomas ,smith's #hj #jj ,w #gh #jj ,n #afaf #eg #jj ,w ,sound ---------------------------------------- ----------------------------- ,at ,sea #ej #j ,w #ch #dj ,n #afhb #g #cj ,w ,at ,sea #ca #cj ,w #dc #ej ,n #afhb #e #cj ,w ,at ,sea #db #j ,w #ba #j ,n #afgh #j #dj ,e ,cape ,st4 ,aug4 of ,brazile #ce #cj ,w #h #j ,s #afgj #e #cj ,e ,cape ,frio #da #aj ,w #bb #dj ,s #afgj #ab #aj ,e ---------------------------------------- ------------------------------ ,at ,sea off of the ,mou4 of the ,river ,plate #ec #jj ,w #ci #cj ,s #afgj #bj #cc ,e ,at the ,east ,entrance of ,magellan ,straits #fh #jj ,w #eb #cj ,s #afgj #ag #jj ,e ,at the ,w4 ,entrance of the ,magellan ,straits #ge #jj ,w #ec #jj ,s #afgj #ad #aj ,e ,baldivia #gc #jj ,w #dj #jj ,s #afgj #h #aj ,e ---------------------------------------- ------------------------------ ,at ,cape d',agulbas #af #cj ,e #cd #ej ,s #afbb #b #jj ,w #afge #h #jj ,w ,at ,sea #a #j ,e #cd #cj ,s #afge #j #jj ,at ,sea #bj #j ,w #cd #j ,s #afge #aj #cj ,e ,at ,sea #cb #j ,w #bd #j ,s #afge #aj #cj ,e ---------------------------------------- ------------------------------ ,at ,st4 ,helena #f #cj ,w #af #jj ,s #afgg #j #dj ,e ,at ,ascension #ad #cj ,w #g #ej ,s #afgh #a #jj ,e ,at ,johanna #dd #jj ,e #ab #ae ,s #afge #ai #cj ,w ,at ,monbasa #dj #jj ,e #d #jj ,s #afge #af #jj ,w ,at ,zocatra #ef #jj ,e #ab #cj ,n #afgd #ag #jj ,w ---------------------------------------- ------------------------------ ,at ,aden1 at the ,mo4 of the ,red ,sea #dg #cj ,e #ac #jj ,n #afgd #ae #jj ,w ,at ,diego ,roiz #fa #j ,e #bj #j ,s #afgf #bj #cj ,w ,at ,sea #fd #cj ,e #j #j #afgf #ae #cj ,w ,at ,sea #ee #j ,e #bg #j ,s #afgf #bd #jj ,w ---------------------------------------- ------------------------------ ,at ,bombay #gb #cj ,e #ai #j ,n #afgf #ab #jj ,w ,at ,cape ,comorin #gf #jj ,e #h #ae ,n #afhj #h #dh ,w ,at ,ballafore #hg #jj ,e #ba #cj ,n #afhj #h #bj ,w ,at ,fort ,st4 ,george #hj #jj ,e #ac #ae ,n #afhj #h #aj ,w ,at the ,w4 ,point of ,java #ajd #jj ,e #f #dj ,s #afgf #c #aj ,w ---------------------------------------- ------------------------------ ,at ,sea #eh #jj ,e #ci #j ,s #afgg #bg #cj ,w ,at the ,isle of ,st4 ,paul #gb #j ,e #ch #j ,s #afgg #bc #cj ,w ,at ,van ,dimen's ,land #adb #j ,e #db #be ,s #afdb #j #j ,at ,new ,zealand #agj #j ,e #dj #ej ,s #afdb #i #j ,e ,at ,three ,kings ,isle in ,new ,zealand4 #afi #cj ,e #cd #ce ,s #afdb #h #dj ,e ---------------------------------------- ------------------------------ ,at the ,isle ,rotterdam in the ,south ,sea #ahd #jj ,e #bj #ae ,s #afdb #f #bj ,e ,on the ,coast of ,n4 ,guin4 #adi #jj ,e #d #cj ,s #afdc #h #de ,e ,at the ,w4 ,p4 of ,n4 ,guin4 #abf #jj ,e #j #bf ,s #afdc #e #cj ,e ,tho' ,i could wish we could obtain from the ,spaniards what ,variations they find in their ,voyages from the ,manilhas towards ,acapulco1 through the ,north part of the ,south ,sea2 as likewise what it is at ,japan from the ,dutch3 ,yet 7considering the number of these ,observations ,i have collected1 and that they are made in parts of the ,world so remote from ,europe1 and from one another7 ,i suppose that the ,theory that answers these will scarce fail in those ,regions from whence we have as yet no account4 ,but first we must make some ,remarks upon the foregoing ,table3 ,and1 ,first1 ,that in all ,europe the ,variation at this time is ,west1 and more in the ,eastern ,parts thereof than the ,western3 ,as likewise1 that it seems throughout to be upon the increase that way4 ,secondly1 ,that on the ,coast of ,america1 about ,virginia1 ,new-,england and ,new-,foundland1 the ,variation is likewise ,westerly2 and that it increases all the way as you go ,northerly along the ,coast1 so as to be above #bj ,degrees at ,new-,found-,land1 nearly #cj gr4 in ,hudson's ,straights1 and not less than #eg ,degrees in ,baffin's ,bay2 also1 that as you ,sail ,eastward from this ,coast1 the ,variation diminishes4 ,from these two it is a ,legitimate ,corollary3 ,that ,somewhere between ,europe1 and the ,north part of ,america1 there ought to be an ,easterly ,variation1 or at least no ,westerly4 ,and so ,i conjecture it is about the ,eastermost of the ,tercera ,islands4 ,thirdly1 ,that on the ,coast of ,brasile there is ,east ,variation1 which increases very notably as you go to the ,southward1 so as to be #ab ,degrees at ,cape ,frio1 and over against the ,river of ,plate #bj ,degrees3 ,and from thence ,sailing ,south-,westerly to the ,straits of ,magellan it decreases #ag ,degrees1 and at the ,west ,entrance but #ad ,degrees4 ,fourthly1 ,that at the ,eastward of ,brasile1 properly so call'd1 this ,easterly ,variation decreases1 so as to be very little at ,st4 ,helena and ,ascension1 and to be quite gone1 and the ,compass ,point true about #ah ,degrees of ,longitude ,west from the ,cape of ,good-hope4 ,fifthly1 ,that to the ,eastward of the aforesaid ,places a ,westward ,variation begins1 which ,reigns in the whole ,indian ,sea1 and arises to no less than ,eighteen ,degrees under the ,equator it self1 about the ,meridian of the ,northern part of ,madagascar2 and near the same ,meridian1 but in #ci ,degrees ,south ,latitude it is found full #bg ,degrees3 ,from thence ,easterly the ,west ,variation decreases1 so as to be little more than eight ,degrees at ,cape ,comorin1 and than three ,degrees upon the ,coast of ,java2 and to be quite extinct about the ,molucca ,islands1 as also a little to the ,westwards of ,van ,diemens ,land found out by the ,dutch in #afdb4 ,sixthly1 ,that to the ,eastward of the ,molucca's and ,van ,diemens ,land in ,south ,latitude there arises another ,easterly ,variation1 which seems not so great as the former1 nor of so large ,extent2 for that at the ,island ,rotterdam it is sensibly less than upon the ,east ,coast of ,new ,guinea2 and1 at the rate it decreases1 it may well be suppos'd1 that about #bj ,degrees farther ,east1 or #bbe ,degrees ,east ,longitude from ,london1 in the ,latitude of #bj ,degrees ,south1 a ,westerly ,variation begins4 ,seventhly1 ,that the ,variations observ'd by the ,honourable ,sir ,john ,norborough at ,baldivia1 and at the ,west ,entrance of the ,straights of ,magellan do plainly shew1 that ,that ,east ,variation1 noted in our third ,remark1 is decreasing apace2 and that it cannot reasonably extend many ,degrees into the ,south ,sea from the ,coast of ,peru and ,chili1 leaving room for a small ,westerly ,variation1 in that ,tract of the unknown ,world that lies in the mid-way between ,chili and ,new-,zealand1 and between ,hounds-,island and ,peru4 ,eighthly1 ,that in ,sailing ,north-,west from ,st4 ,helena by ,ascension1 as far as the ,equator1 the ,variation continues very small ,east1 and as it were constantly the same3 ,so that in this part of the ,world the ,course1 wherein there is no ,variation1 is evidently no ,meridian1 but rather ,north-,west4 ,ninthly1 ,that the ,entrance of ,hudson's ,straights1 and the ,mouth of the ,river of ,plate1 being nearly under the same ,meridian1 at the one place the ,needle varies #bi ,degrees to the ,west2 at the other #bj ,degrees to the ,east4 ,this plainly demonstrates the impossibility of reconciling these ,variations by the ,theory of ,bond2 which is by two ,magnetical ,poles and an ,axis1 inclin'd to the ,axis of the ,earth2 from whence it would follow1 ,that under the same ,meridian the ,variation should be in all places the same way4 ,these things being premised may serve as a sure ,foundation to raise the ,superstructure of a ,theory upon4 ,but first it would not be amiss to shew hereby the mistake of ,gilbert and ,des ,cartes3 ,the first whereof supposes1 that the ,earth it self being in all its parts ,magnetical1 and the ,water not2 wheresoever the ,land is1 thither also should the ,needle turn1 as to the greater quantity of ,magnetical ,matter4 ,but this in many ,instances is not true2 but most remarkably upon the ,coast of ,brazile1 where the ,needle is so far from being attracted by the ,land1 that it turns the quite contrary way1 leaving the ,meridian to lye ,n b ,e1 which is just along the ,coast4 ,as to the ,position of ,des ,cartes1 that the ,iron and ,loadstones hid in the ,bowels of the ,earth and the ,bottom of the ,sea1 may be the ,causes that the ,needle varies2 if we consider for how great a part of the ,earths ,surface1 ex4 gr4 in the whole ,indian ,sea1 the ,needle declines the same way1 and that regularly1 'twill follow that the attracting ,substance that occasions it1 must be very far distant4 ,now by ,experience we find the little force that ,iron ,guns have upon the ,compass in ,ships 7their ,vertue1 though they be ,demiculverin1 or greater ,cannon1 being not perceptible at four or five ,yards distance7 and the ,experiments now before the ,royal ,society do plainly shew1 how little a ,magnetism there is in most crude ,iron ,oars3 ,what quantity thereof must be then suppos'd to make so powerful a ,diversion at two or three ,thousand ,miles distance8 ,yet ,i cannot deny that in some places near the ,shoar1 or in ,shoal-,water1 the ,needle may be irregularly directed from the aforesaid ,causes1 and that not a little1 as ,gassendus gives a notable instance of the ,island ,elba in the ,mediterranean ,sea3 ,but these differences from the general ,direction are always signs of the nearness of those ,magnetical ,substances1 for the ,production whereof that ,island ,elba has been famous from all ,antiquity4 ,besides1 against both ,des ,cartes and ,gilbert1 the change of the ,variation1 which has been within these ,hundred ,years last past more than #ae gr4 at ,london1 is an entire ,demonstration2 tho' ,des ,cartes does not stick to say1 that the transportation of ,iron from place to place1 and the growth of new ,iron within the ,earth1 where there was none before1 may be the cause thereof4 ,the same holds likewise against the ,hypothesis of ,magnetical ,fibres1 which ,kircher maintains4 ,now to propose something that may answer the several appearances1 and introduce nothing strange in ,philosophy1 after a great many close ,thoughts1 ,i can come to no other ,conclusion than that1 ,the whole ,globe of the ,earth is one great ,magnet1 having four ,magnetical ,poles1 or ,points of ,attraction1 near each ,pole of the ,equator4 ,two2 and that1 in those parts of the ,world which lie near adjacent to any one of those ,magnetical ,poles1 the ,needle is govern'd thereby1 the nearest ,pole being always predominant over the more remote4 ,the parts of the ,earth wherein these ,magnetical ,poles lie1 cannot as yet be exactly determin'd for want of sufficient ,data to proceed ,geometrically2 but1 as near as ,conjecture can reach1 ,i reckon that the ,pole1 which is at present nearest to us1 lies in or near the ,meridian of the ,lands-end of ,england1 and not above seven ,degrees from the ,pole ,arctick2 by this ,pole the ,variations in all ,europe and ,tartary1 and the ,north ,sea are principally govern'd1 though with regard to the other ,northern ,pole1 whose situation is in a ,meridian passing about the middle of ,california1 and about #ae gr4 from the ,north ,pole of the ,world2 to this the ,needle has chiefly respect in all the ,north ,america1 and in the two ,oceans on either side thereof1 from the ,azores ,westward to ,japan1 and farther4 ,the two ,southern ,poles are rather farther distant from the ,south ,pole of the ,world3 ,the one about sixteen ,degrees therefrom1 is in a ,meridian1 some twenty ,degrees to the ,westward of ,magellan ,straights1 or ninety five ,degrees ,west from ,london3 ,this commands the ,needle in all the ,south-,america1 in the ,pacifick ,sea1 and the greatest part of the ,ethiopick ,ocean4 ,the ,fourth and last ,pole seems to have the greatest ,power1 and largest ,dominions of all1 as it is the most remote from the ,pole of the ,world1 being little less than #bj ,degrees distant therefrom in the ,meridian1 which passes through ,hollandia ,nova1 and the ,island ,celebes about one hundred and twenty ,degrees ,east from ,london2 this ,pole is predominant in the ,south part of ,africa1 in ,arabia and the ,red ,sea1 in ,persia1 ,india1 and its ,islands1 and all over the ,indian ,sea1 from the ,cape of ,good-,hope ,eastwards to the middle of the great ,south ,sea1 that divides ,asia from ,america4 ,this seems to be the present ,disposition of the ,magnetical ,vertue throughout the whole ,globe of the ,earth2 it remains to shew how this ,hypothesis makes out all the ,variations that have been observ'd of late2 and how it answers to our several ,remarks drawn from the ,table4 ,and first it is plain1 that 7our ,european ,north ,pole being in the ,meridian of the ,lands-end of ,england7 all places more ,easterly than that will have it on the ,west side of their ,meridian1 and consequently the ,needle1 respecting it with its ,northern ,point1 will have a ,westerly ,variation1 which will still be greater as you go to the ,eastwards1 till you come to some ,meridian of ,russia1 where 'twill be greatest1 and from thence decrease again4 ,thus at ,brest the ,variation is but #a ,degrees1 at ,london #d ,degrees2 but at ,dantzick seven ,degrees ,west4 ,to the ,westward of the ,meridian of the ,lands-end1 the ,needle ought to have an ,easterly ,variation2 were it not that 7by approaching the ,american ,northern ,pole1 which lies on the ,west side of the ,meridian1 and seems to be of greater force than this other7 the ,needle is drawn thereby ,westwards1 so as to counterballance the ,direction given by the ,european ,pole1 and to make a small ,west ,variation in the ,meridian of the ,lands-end it self4 ,yet ,i suppose that about the ,meridian of the ,isle ,tercera1 our nearest ,pole may so far prevail as to give the ,needle a little turn to the ,east1 though but for a very small space3 ,the ,counterballance of those two ,poles permitting no considerable ,variation in all the ,eastern ,parts of the ,atlantick ,ocean2 nor upon the ,west ,coasts of ,england and ,ireland1 ,france1 ,spain and ,barbary4 ,but to the ,westwards of the ,azores the ,power of the ,american ,pole overcoming that of the ,european1 the ,needle has chiefly respect thereto1 and turns still more and more towards it as you approach it4 ,whence it comes to pass1 that on the ,coast of ,virginia1 ,new-,england1 ,new-found-,land1 and in ,hudson's-,straights the ,variation is ,westward2 that it decreases as you go from thence towards ,europe1 and that it is less in ,virginia and ,new-,england1 than in ,new-found-,land1 and ,hudson's-,straights4 ,this ,westerly ,variation again decreases1 as you pass over the ,north ,america2 and about the ,meridian of the middle of ,california the ,needle again points due ,north2 and from thence ,westward to ,yedzo and ,japan1 ,i make no doubt but the ,variation is ,easterly1 and half the ,sea over no less than fifteen ,degrees1 if there be any truth in this ,hypothesis of mine4 ,therefore ,i propose this as a ,trial1 that the whole may be scann'd thereby2 and ,i conceive it will not be hard to know of the ,spaniards how it is1 who so frequently sail through that ,ocean1 in their return from the ,manilha ,isles4 ,this ,east ,variation extends over ,japan1 ,yedzo1 ,east-,tartary1 and part of ,china1 till it meet with the ,westerly1 which is govern'd by the ,european ,north ,pole1 and which ,i said was greatest some where in ,russia4 ,towards the ,southern ,pole the effect is much the same1 only that here the ,south ,point of the ,needle is attracted4 ,hence it will follow1 that the ,variation on the ,coast of ,brazile1 at the ,river of ,plate1 and so on to the ,straights of ,magellan1 should be ,easterly 7as in our third ,remark72 if we suppose a ,magnetical ,pole situate about twenty ,degrees more ,westerly than the ,straights of ,magellan4 ,and this ,easterly ,variation doth extend ,eastward over the greatest part of the ,ethiopick ,sea1 till it be counterpoised by the ,vertue of the other ,southern ,pole2 as it is about mid-way between the ,cape of ,good-,hope1 and the ,isles of ,tristan d' ,acuntia4 ,from thence ,eastwards1 the ,asian ,south ,pole 7as ,i must take the liberty to call it7 becoming prevalent1 and the ,south point of the ,needle being attracted thereby1 there arises a ,west ,variation1 very great in quantity and extent1 because of the great distance of this ,magnetical ,pole of the ,world4 ,hence it is1 that in all the ,indian ,sea as far as ,hollandia ,nova1 and farther1 there is constantly ,west ,variation2 at that under the ,equator it self it arises to no less than eighteen ,degrees1 where 'tis most4 ,about the ,meridian of the ,island ,celebes1 being likewise that of this ,pole1 this ,westerly ,variation ceases1 and an ,easterly begins2 which reaches1 according to my ,hypothesis1 to the middle of the ,south-,sea1 between ,zelandia ,nova1 and ,chili1 leaving room for a small ,west ,variation govern'd by the ,american ,south ,pole1 which ,i shew'd to be in the ,pacifick ,sea1 in the sixth and seventh ,remark4 ,what ,i have now said1 does plainly shew the sufficiency of this ,hypothesis for solving the ,variations that are at this time observ'd in the temperate and frigid ,zones1 where the ,direction of the ,needle chiefly depends upon the ,counterpoise of the forces of two ,magnetical ,poles of the same ,nature2 and ,i suppose ,i have shewn how it comes to pass1 that under the same ,meridian the ,variation should be in one place #bi ,west1 and another #bj ,east2 as ,i have noted in my ninth ,remark4 ,in the ,torrid ,zone1 and particularly under the ,equinoctial1 respect must be had to all four ,poles1 and their ,positions well consider'd1 otherwise it will not be easie to determine what the ,variations shall be2 the nearest ,pole being always the strongest2 yet not so1 as not to be counterballanc'd sometimes by the united forces of two more remote2 a notable ,instance whereof is in our eighth ,remark1 where ,i took notice1 that in sailing from ,st4 ,helena by the ,isle of ,ascension1 to the ,equator1 on a ,n4 ,w4 ,course1 the ,variation is very little ,easterly1 and in that whole ,tract unalterable2 for which ,i give this ,reason1 ,that the ,south ,american ,pole 7which is considerably the nearest in the aforesaid ,places7 requiring a great ,easterly ,variation1 is counterpoised by the contrary ,attraction of the ,north-,american and the ,asian-,south-,pole2 each whereof singly are in these ,parts1 weaker than the ,american-,south-,pole2 and upon the ,north ,west ,course1 the ,distance from this latter is very little varied2 and as you recede from the ,asian-,south-,pole1 the ,ballance is still preserv'd by the access towards the ,north-,american-,pole4 ,i mention not in this ,case the ,european-,north-,pole1 its ,meridian being little remov'd from those of these places2 and of it self requiring the same ,variations we here find4 ,after the same manner we might proceed to conclude the ,variations in other places under and near the ,equator2 but ,i purposely leave it for an ,exercise to the ,thoughts of the serious ,reader1 who is desir'd to help his ,imagination1 by having before him a ,map or ,globe of the ,earth3 ,and to mark thereon the ,magnetical ,poles in the ,longitudes and ,latitudes ,i assign them4 7,vide ,plate #b47 ,thus1 ,i hope1 ,i have not lost my ,pains and ,study in this difficult ,subject2 believing that ,i have put it past doubt1 ,that there are in the ,earth four such ,magnetical ,points or ,poles1 which occasion the great variety and seeming irregularity which is observed in the ,variations of the ,compass4 ,but to calculate exactly what it is1 in any place assign'd1 is what ,i dare not yet pretend to1 though ,i could wish it were my happiness to be able to oblige the ,world with so useful a piece of ,knowledge2 there are ,difficulties that occur1 that render the thing as yet not feasible2 for first there are a great many ,observations requisite1 which ought to be made at the same time2 not at ,sea1 but ashore1 with greater ,care and ,attention than the generality of ,sailors apply4 ,and besides1 it remains undetermin'd in what proportion the attractive ,power decreases1 as you remove from the ,pole of a ,magnet1 without which it were a vain attempt to go about to calculate4 ,there is yet a further ,difficulty1 which is the ,change of the ,variation1 one of the ,discoveries of this last ,century2 which shews1 that it will require some hundreds of ,years to establish a compleat ,doctrine of the ,magnetical ,system4 ,from the foregoing ,table it should seem1 that all the ,magnetical ,poles had a motion ,westward3 ,but if it be so1 'tis evident1 that it is not a ,rotation about the ,axis of the ,earth2 for then the ,variations would continue the same1 in the same parallel of ,latitude 7the ,longitude only chang'd7 as much as is the motion of the ,magnetical ,poles1 but the contrary is found by ,experience2 for there is no where in the ,latitude of #ae ,north between ,england and ,america1 a ,variation of eleven ,degrees ,east at this time2 as it was once here at ,london2 it seems therefore1 that our ,european ,pole is grown nearer the ,pole ,arctick than it was heretofore1 or else that it has lost part of its ,vertue4 ,but whether these ,magnetical ,poles move altogether with one motion1 or with several2 whether equally or unequally2 whether ,circular or ,libratory3 ,if ,circular1 about what ,center2 if ,libratory1 after what manner2 are ,secrets as yet utterly unknown to ,mankind1 and are reserv'd for the ,industry of future ,ages4 ,an ,account of the ,cause of the ,change of the ,variation of the ,magnetical ,needle1 with an ,hypothesis of the ,structure of the ,internal ,parts of the ,earth2 as it was proposed to the ,royal ,society in one of their late ,meetings4 ,by ,mr4 ,edmund ,halley4 ,having in the precedent ,discourse delivered a ,theory of the ,variation of the ,magnetical ,compass1 wherein ,i did collect as many ,observations as at that time ,i could procure1 and having carefully compar'd them together1 ,i came at length to this general conclusion1 ,that the ,globe of the ,earth might be supposed to be one great ,magnet1 having four ,magnetical ,poles or ,points of ,attraction1 near each ,pole of the ,equator two2 and that in those parts of the ,world which lie near adjacent to any one of those ,magnetical ,poles1 the ,needle is chiefly govern'd thereby2 the nearest ,pole being always predominant ever the more remote4 ,and ,i there have endeavour'd to state and limit the present ,position of those ,poles in the ,surface of our ,globe1 which the ,reader pleasing to consult1 will save us the pains of repeating4 ,but after all1 tho' that ,discourse was favourably receiv'd both at home and abroad1 as seeming to render a tolerable account of the observ'd ,variations1 yet ,i found two ,difficulties not easie to surmount2 the one was1 that no ,magnet ,i had ever seen or heard of1 had more than two opposite ,poles1 whereas the ,earth had visibly four1 and perhaps more4 ,and secondly1 it was plain that these ,poles were not1 at least all of them1 fixt in the ,earth1 but shifted from place to place1 as appear'd by the great ,changes in the ,needles ,direction within this last ,century of ,years1 not only at ,london1 7where this great ,discovery was first made7 but almost all over the ,globe of ,earth2 whereas it is not known or observ'd that the ,poles of a ,load-stone ever shifted their place in the ,stone1 nor 7considering the compact hardness of that ,substance7 can it easily be suppos'd2 though the ,matter of ,fact be too notorious and universal1 not to be accounted for4 ,these ,difficulties had wholly made me despond1 and ,i had long since given over an ,inquiry ,i had so little hopes of1 when in accidental ,discourse1 and least expecting it1 ,i stumbl'd on the following ,hypothesis2 in delivering whereof1 if ,i shall seem to advance any thing that looks like ,extravagant or ,romantick1 the ,reader is desir'd to suspend his ,censure1 till he have consider'd the force and number of the many ,arguments which concur to make good so new and so bold a ,supposition4 ,though it be sufficiently known and allow'd1 that the ,needles ,variation changes1 it will be necessary however to give a few ,instances1 whereby it may appear that this ,change is gradual and universal1 and the effect of a great and permanent motion3 ,for which take the following ,examples4 ,at ,london1 in the ,year #aehj1 the ,variation was observ'd by ,mr4 ,burrows to be #aa #ae' ,east4 ,in ,anno #afbb1 the same was found by ,mr4 ,gunter to be but #f #j' ,east4 ,in the ,year #afcd1 ,mr4 ,gellibrand found it #d #e' ,east4 ,in #afeg1 ,mr4 ,bond observ'd that there was no ,variation at ,london4 ,anno #afgb1 my self observ'd it #b #cj' to the ,west2 and in the ,year #afib1 ,i again found it #f #jj' ,west4 ,so that in #aab ,years the ,direction of the ,needle has chang'd no less than seventeen ,degrees4 ,at ,paris1 ,orontius ,finus about the ,year #aeej1 did account it about eight or nine ,degrees ,east ,variation4 ,anno #afdj1 it was found three ,degrees ,east4 ,anno #affj1 there was no ,variation there1 and ,anno #afha1 ,i found it to be #b #cj' to the ,west4 ,at ,cape d' ,agulhas1 the most ,southerly ,promontary of ,africa1 about the ,year #afjj1 the ,needle pointed due ,north and ,south without ,variation1 whence the ,portugueze gave its name4 ,anno #afbb1 there was two ,degrees ,west ,variation4 ,anno #afge1 it was #h #ej' ,west2 and in the ,year #afia1 it was curiously observ'd not less than eleven ,degrees ,west4 ,at ,st4 ,helena1 about the ,year #afjj1 the ,needle declin'd eight ,degrees to the ,east4 ,anno #afbc1 it was but #f #j' ,east4 ,anno #afgg1 when ,i was there1 ,i observ'd it accurately on ,shoar to be #j #dj' ,east2 and in #afib it was found about #a to the ,westward of the ,north4 ,at ,cape ,comorine in ,india1 in the ,year #afbj1 there was #ad #bj' ,west ,variation4 ,in the ,year #afhj1 there was #h #dh'1 but now lately in the ,year #afhh1 it was no more than #g #cj'1 so that here the ,needle has return'd to the ,east about seven ,degrees in seventy ,years4 ,in all the other ,examples the ,needle has gradually mov'd towards the ,west1 and the places are too far asunder to be influenc'd by the removal of any ,magnetical ,matter1 which may by accident be transplac'd within the ,bowels1 or on the ,surface of the ,earth4 ,if more ,examples are desir'd1 the ,reader may be furnished with them in the ,portugueze ,routier of ,aleixo de ,motta 7written about the ,year #afjj7 and in the ,voyage of ,beaulieu1 both publish'd in ,mr4 ,thevenot's first ,collection of curious ,voyages1 ,printed at ,paris1 ,anno #affc2 which he is to compare with the ,journals of our late ,east ,india ,voyagers1 and ,i am assur'd1 that it will be thereby evident1 that the ,direction of the ,needle is in no place fix'd and constant1 tho' in some it change faster than in others3 ,and where for a long time it has continu'd as it were unalter'd1 it is there to be understood1 that the ,needle has its greatest ,deflection1 and is become ,stationary in order to return1 like the ,sun1 in the ,tropick4 ,this1 at present1 is in the ,indian ,sea1 about the ,island ,mauritius1 where is the highest ,west ,variation1 and in a ,tract tending from thence into the ,n4 ,n4 ,w4 towards the ,red-,sea and ,egypt4 ,and in all ,places to the ,westward of this ,tract1 all over ,africa and the ,seas adjoining1 the ,west ,variation will be found to have encreas'd2 and to the ,eastwards thereof as in the ,example of ,cape ,comorine1 to have decreased1 viz4 all over the ,east-,indies1 and the ,islands near it4 ,after the like manner in that ,space of ,east ,variation1 which1 beginning near ,st4 ,helena1 is found all over the ,south ,america1 and which at present is highest about the ,mouth of ,rio de la ,plata1 it has been observ'd1 that in the ,eastern ,parts thereof1 the ,variation of the ,needle gradually decreases2 but whether on the contrary it increases in those places which lie more ,westerly than that ,tract wherein the highest ,east ,variation is found2 or how it may be in the vast ,pacifick ,sea1 we have not ,experience enough to ascertain1 only we may by ,analogy infer1 that both the ,east and ,west ,variations therein do gradually increase and decrease after the same ,rule4 ,these ,phnomena being well understood and duly consider'd1 do sufficiently evince1 ,that the whole ,magnetical ,system is by one1 or perhaps more motions translated1 whether ,eastwards or ,westwards1 ,i shall anon discuss2 that this moving thing is very great1 as extending its effects from ,pole to ,pole1 and that the motion thereof is not per saltum1 but a gradual and regular motion4 ,now considering the ,structure of our ,terraqueous ,globe1 it cannot be well suppos'd that a very great part thereof can move within it1 without notably changing its ,center of ,gravity and the ,equilibre of its ,parts1 which would produce very wonderful ,effects in changing the ,axis of diurnal ,rotation1 and occasion strange alteration in the ,seas ,surface1 by ,inundations and ,recesses thereof1 such as ,history never yet mention'd4 ,besides1 the solid parts of the ,earth are not to be granted permeably by any other than fluid ,substances1 of which we know none that are any ways ,magnetical4 ,so that the only way to render this motion intelligible and possible1 is to suppose it to turn about the ,center of the ,globe1 having its ,center of ,gravity fix'd and immoveable in the same common ,center of the ,earth3 ,and there is yet requir'd1 that this moving internal ,substance be loose and detached from the external ,parts of the ,earth whereon we live2 for otherwise1 were it affix'd thereto1 the whole must necessarily move together4 ,so then the ,external ,parts of the ,globe may well be reckon'd as the ,shell1 and the ,internal as a ,nucleus or inner ,globe1 included within ours1 with a fluid ,medium between1 which having the same ,common ,center and ,axis of diurnal ,rotation1 may turn about with our ,earth each twenty four ,hours2 only this outer ,sphere having its turbinating motion some small matter either swifter or slower than the internal ,ball3 ,and a very minute ,difference in length of time1 by many ,repetitions becoming sensible1 the ,internal ,parts will by degrees recede from the ,external1 and not keeping pace with one another1 will appear gradually to move either ,eastwards or ,westwards by the difference of their motions4 ,now supposing such an ,internal ,sphere having such a motion1 we shall solve the two great ,difficulties we encounter'd in my former ,hypothesis3 ,for if this exteriour ,shell of ,earth be a ,magnet1 having its ,poles at a distance from the ,poles of diurnal ,rotation2 and if the ,internal ,nucleus be likewise a ,magnet1 having its ,poles in two other places1 distant also from the ,axis2 and these latter by a gradual and slow motion change their place in respect of the ,external2 we may then give a reasonable account of the four ,magnetical ,poles ,i presume to have demonstrated before2 as likewise of the ,changes of the ,needles ,variations1 which till now hath been unattempted4 ,the ,period of this ,motion being wonderful great1 and there being hardly an hundred ,years since these ,variations have been duly observ'd1 it will be very hard to bring this ,hypothesis to a ,calculus1 especially since1 though the ,variations do increase and decrease regularly in the same place1 yet in differing places1 at no great distance1 there are found such casual ,changes thereof as can no ways be accounted for by a regular ,hypothesis2 as depending upon the unequal and irregular distribution of the ,magnetical ,matter within the ,substance of the ,external ,shell or ,coat of the ,earth1 which deflect the ,needle from the ,position it would acquire from the effect of the general ,magnetism of the whole4 ,of this the ,variations at ,london and ,paris give a notable ,instance1 for the ,needle has been constantly about #a more ,easterly at ,paris than at ,london2 though it be certain that according to the general effect1 the ,difference ought to be the contrary way3 ,notwithstanding which1 the ,variations in both places do change alike4 ,hence1 and from some other of like ,nature1 ,i conclude1 ,that the two ,poles of the ,external ,globe are fixt in the ,earth1 and that if the ,needle were wholly govern'd by them1 the ,variations thereof would be always the same1 with some little ,irregularities upon the account ,i but just now mention'd3 ,but the ,internal ,sphere having such a gradual translation of its ,poles1 does influence the ,needle1 and direct it variously1 according to the result of the attractive or directive ,power of each ,pole2 and consequently there must be a ,period of the ,revolution of this ,internal ,ball1 after which the ,variations will return again as before4 ,but if it shall in future ,ages be observ'd otherwise1 we must then conclude that there are more of these ,internal ,spheres1 and more ,magnetical ,poles than ,four1 which at present we have not a sufficient number of ,observations to determine1 and particularly in that vast ,mar del ,zur1 which occupies so great a part of the whole ,surface of the ,earth4 ,if then two of the ,poles be fixt and two moveable1 it remains to ascertain which they are that keep their place2 and though ,i could wish we had the ,experience of another ,century of ,years to found our ,conclusions upon1 yet ,i think we may safely determine1 ,that our ,european ,north ,pole 7which in the precedent ,discourse ,i suppos'd near the ,meridian of the ,lands-end of ,england1 and about seven ,degrees therefrom7 is that ,that is moveable of the two ,northern ,poles1 and that ,that has chiefly influenc'd the ,variations in these parts of the ,world3 ,for in ,hudson's ,bay1 which is under the ,direction of the ,american ,pole1 the ,change is not observ'd to be near so fast as in these parts of ,europe1 though that ,pole be much farther remov'd from the ,axis4 ,as to the ,south ,poles1 ,i take the ,asian ,pole1 which ,i place about the ,meridian of the ,island ,celebes to be the fixt1 and consequently the ,american ,pole to move2 from the like ,observation of the slow ,decrease of the ,variation on the ,coast of ,java1 and near the ,meridian of the ,asian ,pole2 though ,i must confess to have no account of the effects of the other beyond ,magellan's ,streights4 ,if this be allow'd me1 'tis plain that the fixt ,poles are the ,poles of this ,external ,shell or ,cortex of the ,earth1 and the other two the ,poles of a ,magnetical ,nucleus included and moveable within the other4 ,it likewise follows1 that this ,motion is ,westwards1 and by consequence that the aforesaid ,nucleus has not precisely attained the same degree of ,velocity with the exteriour ,parts in their diurnal ,revolution2 but so very nearly equals it1 that in #cfe ,revolves the difference is scarce sensible4 ,this ,i conceive to arise from the ,impulse whereby this diurnal ,motion was imprest on the ,earth1 being given to the ,external ,parts1 and from thence in time communicated to the ,internal2 but not so as perfectly to equal the ,velocity of the first ,motion impress'd on1 and still conserv'd by the superficial ,parts of the ,globe4 ,as to the quantity of this ,motion it is almost impossible to define it1 both from the ,nature of this kind of ,observation1 which cannot be very accurately perform'd1 as also from the small time these ,variations have been observ'd1 and their ,change discover'd4 ,it appears by all ,circumstances1 that its ,period is of many ,centuries of ,years1 and as far as may be collected from the ,change of the ,place1 where there was no ,variation1 by reason of the ,equilibre of the two ,southern ,magnetical ,poles1 viz4 from ,cape d' ,agulhas to the ,meridian of ,st4 ,helena 7which is about #bc degr4 in about ninety ,years7 and of the place where the ,westerly ,variation is in its or greatest ,deflection1 being about half so much1 viz4 from the ,isle of ,diego ,roiz to the ,south ,west ,parts of ,madagascar4 ,we may with some ,reason conjecture1 that the ,american ,pole has mov'd ,westwards forty six ,degrees in that time1 and that the whole ,period thereof is perform'd in seven hundred ,years1 or thereabouts2 so that the nice ,determination of this1 and of several other ,particulars in the ,magnetick ,system is reserv'd for remote ,posterity2 all that we can hope to do1 is to leave behind us ,observations that may be confided in1 and to propose an ,hypothesis which after ,ages may examine1 amend or refute4 ,only here ,i must take leave to recommend to all ,masters of ,ships1 and all others1 ,lovers of ,natural ,truths1 that they use their utmost ,diligence to make1 or procure to be made1 ,observations of these ,variations in all parts of the ,world1 as well in the ,north as ,south ,latitude 7after the laudable ,custom of our ,east ,india ,commanders7 and that they please to communicate them to the ,royal ,society1 in order to leave as compleat a ,history as may be to those that are hereafter to compare all together1 and to compleat and perfect this abstruse ,theory4 ,and by the way it will not be amiss to amend a receiv'd ,error in the ,practice of observing the ,variation1 which is1 to take it by the ,amplitude of the ,rising and ,setting ,sun1 when his ,center appears in the visible ,horizon2 whereas he ought to be observ'd when his under ,limb is still above the ,horizon about of his ,diameter1 or twenty ,minutes1 upon the score of the ,refraction1 and the height of the ,eye of the ,observer above the ,surface of the ,sea3 ,or else they are to work the ,amplitudes as they do the ,azimuth1 reckoning the ,suns ,distance from the ,zenith #ij #cf'3 ,this1 though it be of little consequence near the quinoctial1 will make a great ,error in high ,latitudes1 where the ,sun rises and sets obliquely4 ,but to return to our ,hypothesis1 ,in order to explain the ,change of the ,variations1 we have adventur'd to make the ,earth hollow1 and to place another ,globe within it2 and ,i doubt not but this will find ,opposers enough4 ,i know 'twill be ,objected1 ,that there is no ,instance in ,nature of the like thing2 that if there was such a middle ,globe it would not keep its place in the ,center1 but be apt to deviate therefrom1 and might possibly chock against the ,concave ,shell1 to the ruin1 or at least endammaging thereof2 ,that the ,water of the ,sea would perpetually leak through1 unless we suppose the ,cavity full of ,water2 ,that were it possible1 yet it does not appear of what use such an inward ,sphere can be of1 being shut up in ,eternal ,darkness1 and therefore unfit for the ,production of ,animals or ,plants2 with many more ,objections1 according to the ,fate of all such new ,propositions4 ,to these1 and all other that ,i can foresee1 ,i briefly ,answer1 ,that the ,ring environing the ,globe of ,saturn is a notable ,instance of this kind1 as having the same common ,center1 and moving along with the ,planet1 without sensibly approaching him on one side more than the other4 ,and if this ,ring were turn'd on one of its ,diameters1 it would then describe such a ,concave ,sphere as ,i suppose our ,external one to be4 ,and since the ,ring1 in any ,position given1 would1 in the same manner1 keep the ,centre of ,saturn in its own1 it follows1 that such a ,concave ,sphere may move with another included in it1 having the same common ,centre4 ,nor can it well be suppos'd otherwise1 considering the ,nature of ,gravity2 for should these ,globes be adjusted once to the same common ,centre1 the ,gravity of the parts of the ,concave would press equally towards the ,centre of the inner ,ball1 which equality must necessarily continue till some ,external ,force disturb it1 which is not easie to imagine in our ,case4 ,this perhaps ,i might more intelligibly express1 by saying that the inner ,globe being posited in the ,centre of the ,exteriour1 must necessarily ascend which way soever it move2 that is1 it must overcome the force of ,gravity pressing towards the common ,centre1 by an impulse it must receive from some outward ,agent2 but all outward ,efforts being sufficiently fenc'd against by the ,shell that surrounds it1 it follows1 that this ,nucleus being once fixt in the common ,centre1 must always there remain4 ,as to the leaking of the ,water through this ,shell1 when once a passage shall be found for it to run through1 ,i must confess it is an ,objection seemingly of weight2 but when we consider how tightly great ,beds of ,chalk or ,clay1 and much more ,stone do hold ,water1 and even ,caves arch'd with ,sand2 no ,man can doubt but the ,wisdom of the ,creator has provided for the ,macrocosm by many more ways than ,i can either imagine or express1 especially since we see the admirable and innumerable ,contrivances wherewith each worthless ,individual is furnish'd both to defend it self1 and propagate its ,species4 ,what ,curiosity in the ,structure1 what ,accuracy in the ,mixture and ,composition of the parts1 ought not we to expect in the ,fabrick of this ,globe1 made to be the lasting ,habitation of so many various ,species of ,animals1 in each of which there want not many ,instances that manifest the boundless ,power and ,goodness of their ,divine ,author2 and can we then think it a hard ,supposition1 that the ,internal ,parts of this ,bubble of ,earth should be replete with such ,saline and ,vitriolick ,particles as may contribute to ,petrefaction1 and dispose the transuding ,water to shoot and coagulate into ,stone1 so as continually to fortifie1 and1 if need were1 to consolidate any breach or flaw in the ,concave ,surface of the ,shell4 ,and this perhaps may not without ,reason be suppos'd to be the final ,cause of the admixture of the ,magnetical ,matter in the ,mass of the ,terrestrial parts of our ,globe1 viz4 ,to make good and maintain the ,concave ,arch of this ,shell3 ,for by what the ,excellent ,mr4 ,newton has shewn in his ,principia ,philosophi1 it will follow1 that according to the general ,principle of ,gravity1 visible throughout the whole ,universe1 all those ,particles that by length of time1 or otherwise1 shall moulder away1 or become loose on the ,concave ,surface of the ,external ,sphere1 would fall in1 and with great force descend on the ,internal1 unless those ,particles were of another sort of ,matter capable by their stronger tendency to each other1 to suspend the force of ,gravity2 but we know no other ,substances capable of supporting each other by their mutual ,attraction but the ,magnetical1 and these we see miraculously to perform that ,office1 even where the ,power of ,gravity has its full effect1 much more within the ,globe where it is weaker4 ,why then may we not suppose these said ,arches to be lin'd throughout with a ,magnetical ,matter1 or rather to be one great ,concave ,magnet1 whose two ,poles are the ,poles we have before observ'd to be fixt in the ,surface of our ,globe4 ,another ,argument1 favouring this ,hypothesis1 is drawn from a ,proposition of the same ,mr4 ,newton1 where he determines the force wherewith the ,moon moves the ,sea in producing the ,tides3 ,his ,words are1 ,densitas ,lun est ad densitatem ,terra ut #fhj ad #chg seu #i ad #e quamproxim4 ,est igitur corpus ,lun densius ac magis terrestre quam ,terra nostra1 p4 #dff4 ,now if the ,moon be more solid than the ,earth1 as #i to #e1 why may we not reasonably suppose the ,moon1 being a small ,body1 and a secondary ,planet1 to be solid ,earth1 ,water1 ,stone1 and this ,globe to consist of the same ,materials1 only four ,ninths thereof to be ,cavity1 within and between the ,internal ,spheres2 which ,i would render not improbable4 ,to those that shall enquire of what use these included ,globes can be1 it must be allow'd1 that they can be of very little service to the ,inhabitants of this outward ,world1 nor can the ,sun be serviceable to them1 either with his ,light or ,heat4 ,but since it is now taken for granted1 that the ,earth is one of the ,planets1 and they all are with ,reason suppos'd ,habitable1 though we are not able to define by what sort of ,animals2 and since we see all the parts of the ,creation abound with ,animate ,beings1 as the ,air with ,birds and ,flies1 the ,water with the numerous varieties of ,fish1 and the very ,earth with ,reptiles of so many sorts2 all whose ways of ,living would be to us incredible did not daily ,experience teach us4 ,why then should we think it strange that the prodigious ,mass of ,matter1 whereof this ,globe does consist1 should be capable of some other improvement than barely to serve to support its ,surface8 ,why may not we rather suppose that the exceeding small quantity of solid ,matter1 in respect of the fluid ther1 is so dispos'd by the ,almighty ,wisdom1 as to yield as great a ,surface for the use of living ,creatures1 as can consist with the conveniency and security of the whole8 ,we our selves1 in ,cities where we are pressed for ,room1 commonly build many ,stories one over the other1 and thereby accommodate a much greater multitude of ,inhabitants4 ,but still it will be said1 ,that without ,light there can be no living1 and therefore all this apparatus of our inward ,globes must be useless3 ,to this ,i ,answer1 ,that there are many ways of producing ,light which we are wholly ignorant of2 the ,medium it self may be always luminous after the manner of our ,ignes fatui4 ,the ,concave ,arches may in several places shine with such a ,substance as invests the ,surface of the ,sun2 nor can we1 without a boldness unbecoming a ,philosopher1 adventure to assert the impossibility of peculiar ,luminaries below1 of which we have no sort of ,idea4 ,i am sure the ,poets ,virgil and ,claudian have gone before me in this ,thought1 inlightning their ,elysian ,fields with ,sun and ,stars proper to those infernal1 or rather internal ,regions4 ,virg4 neid4 #f4 ,largior hic compos ther lumine vestit ,purpureo2 ,solemque suum sua ,sidera norunt4 ,and ,claudian lib #b4 ,de ,raptu ,proserpin4 ,amissum ne crede diem1 sunt altera nobis ,sidera1 sunt orbes alii1 lumnque videbis ,purius1 ,elysiumque magis mirabere ,solem4 ,and though this be not to be esteem'd as an ,argument1 yet ,i may take the liberty ,i see others do1 to quote the ,poets when it makes for my purpose4 ,lastly1 ,to explain yet farther what ,i mean1 ,i have adventur'd to adjoin the following ,scheme1 7,tab4 #a4 ,fig4 #c7 wherein the ,earth is represented by the outward ,circle1 and the three inward ,circles are made nearly proportionable to the ,magnitudes of the ,planets ,venus1 ,mars and ,mercury1 all which may be included within the ,globe of ,earth1 and all the ,arches more than sufficiently strong to bear their weight4 ,the ,concave of each ,arch1 which is shaded differently from the rest1 ,i suppose to be made up of ,magnetical ,matter2 and the whole to turn about the same common ,axis pp1 only with this difference1 that the ,outer ,sphere still moves somewhat faster than the ,inner4 ,thus the ,diameter of the ,earth being about eight thousand ,english ,miles1 ,i allow five hundred ,miles for the thickness of its ,shell1 and another space of five hundred ,miles for a ,medium between1 capable of an immense ,atmosphere for the use of the ,globe of ,venus3 ,venus again ,i give a ,shell of the same thickness1 and leave as great a space between her ,concave and ,mars2 so likewise from ,mars to ,mercury1 which latter ,ball we will suppose solid1 and about two thousand ,miles ,diameter4 ,thus ,i have shew'd a possibility of a much more ample ,creation1 than has hitherto been imagin'd2 and if this seem strange to those that are unacquainted with the ,magnetical ,system1 it is hop'd that all such will endeavour1 first1 to inform themselves of the ,matter of ,fact1 and then try if they can find out a more simple ,hypothesis1 at least a less absurd1 even in their own ,opinions4 ,and whereas ,i have adventur'd to make these ,subterraneous ,orbs capable of being ,inhabited1 'twas done designedly for the sake of those who will be apt to ask cui bono1 and with whom ,arguments drawn from ,final ,causes prevail much4 ,if this short ,essay shall find a kind ,acceptance1 ,i shall be encourag'd to enquire farther1 and to ,polish this rough ,draft of a ,notion till hitherto not so much as started in the ,world1 and of which we could have no ,intimation from any other of the ,phnomena of ,nature4 ,since this was written1 a ,discovery ,i have made in the ,clestial ,motions1 seems to render a farther ,account of the ,use of the ,cavity of the ,earth1 viz4 ,to diminish the ,specifick ,gravity thereof1 in respect of the ,moon2 for ,i think ,i can demonstrate that the ,opposition of the ther to the ,motions of the ,planets in long time becomes sensible2 and consequently the greater ,body must receive a less ,opposition than the smaller1 unless the ,specifick ,gravity of the smaller do proportionably exceed that of the greater1 in which case only they can move together2 so that the ,cavity ,i assign in the ,earth1 may well serve to adjust its weight to that of the ,moon1 for otherwise the ,earth would leave the ,moon behind it1 and she become another ,primary ,planet4 ,an ,historical ,account of the ,trade ,winds and ,monsoons1 observable in the ,seas between and near the ,tropicks1 with an attempt to assign the ,physical ,cause of the said ,winds1 by ,mr4 ,ed4 ,halley4 ,an exact ,relation of the constant and periodical ,winds1 observable in several ,tracts of the ,ocean1 is a part of ,natural ,history not less desireable and useful1 than it is difficult to obtain1 and its ,phnomena hard to explicate3 ,i am not ignorant that several ,writers have undertaken this ,subject1 and although ,varenius 7,lib4 #a4 ,chap4 #ba4 ,geo4 ,gen47 seems to have endeavour'd after the best information from ,voyagers1 yet cannot his ,accounts be admitted for accurate1 by those that shall attentively consider and compare them together1 and some of them are most evident ,mistakes2 which1 as near as ,i can1 ,i shall attempt to rectify1 having had the opportunity of conversing with ,navigators1 acquainted with all parts of ,india1 and having liv'd a considerable time between the ,tropicks1 and there made my own ,remarks4 ,the ,substance of what ,i have collected is briefly as follows4 ,the ,universal ,ocean may most properly be divided into three ,parts1 viz4 #a4 ,the ,atlantick and thiopick-,sea4 #b4 ,the ,indian ,ocean4 #c4 ,the ,great ,south ,sea1 or the ,pacifick ,ocean2 and though these ,seas do all communicate by the ,south1 yet as to our present purpose of the ,trade ,winds1 they are sufficiently separated by the interposition of great ,tracts of ,land2 the first lying between ,africa and ,america1 the second between ,africa and the ,indian ,islands1 and ,hollandia ,nova2 and the last between the ,phillipine ,isles1 ,china1 ,japan and ,hollandia ,nova on the ,west1 and the ,coast of ,america on the ,east4 ,now following this natural division of the ,seas1 so will we divide our ,history into three parts in the same order4 ,i4 ,in the ,atlantick and thiopick ,seas between the ,tropicks1 there is a general ,easterly ,wind all the ,year long1 without any considerable ,variation1 excepting that it is subject to be deflected therefrom1 some few ,points of the ,compass towards the ,north or ,south1 according to the ,position of the place4 ,the ,observations which have been made of these ,deflections1 are the following4 #a4 ,that near the ,coast of ,africa1 as soon as you have pass'd the ,canary ,isles1 you are sure to meet a fresh ,gale of ,north ,east ,wind1 about the ,latitude of #bh ,degrees ,north1 which seldom comes to the ,eastwards of the ,east ,north-,east1 or passes the ,north ,north-,east4 ,this ,wind accompanies those bound to the ,southward1 to the ,latitude of ten ,north1 and about a hundred ,leagues from the ,guinea ,coast1 where1 till the fourth ,degree of ,north ,latitude1 they fall into the ,calms and ,tornadoes2 of which more hereafter4 #b4 ,that those bound to the ,caribbee ,isles1 find1 as they approach the ,american side1 that the aforesaid ,north-,east ,wind becomes still more and more ,easterly1 so as sometimes to be ,east1 sometimes ,east by ,south1 but yet most commonly to the ,northward of the ,east a ,point or two1 seldom more4 ',tis likewise observ'd1 that the strength of these ,winds does gradually decrease1 as you sail to the ,westwards4 #c4 ,that the limits of the ,trade and variable ,winds1 in this ,ocean1 are farther extended on the ,american side than the ,african2 for whereas you meet not with this certain ,wind till after you have pass'd the ,latitude of twenty eight ,degrees on this side2 on the ,american side it commonly holds to thirty1 thirty one1 or thirty two ,degrees of ,latitude2 and this is verified likewise to the ,southwards of the quinoctial1 for near the ,cape of ,good-,hope the limits of the ,trade ,winds1 are three or four ,degrees nearer the ,line1 than on the ,coast of ,brazile4 #d4 ,that from the ,latitude of four ,degrees ,north1 to the aforesaid ,limits on the ,south of the quator1 the ,winds are generally and perpetually between the ,south and ,east1 and most commonly between the ,south-,east and ,east1 observing always this ,rule1 ,that on the ,african side they are more ,southerly1 on the ,brazilian more ,easterly1 so as to become almost due ,east1 the little deflection they have being still to the ,southwards4 ,in this part of the ,ocean it has been my fortune to pass a full ,year1 in an ,employment that oblig'd me to regard more than ordinary the ,weather1 and ,i found the ,winds constantly about the ,south-,east1 the most usual ,point ,s ,e b ,e2 when it was ,easterly1 it generally blew hard1 and was gloomy1 dark1 and sometimes rainy ,weather2 if it came to the ,southwards it was generally ,serene1 and a small ,gale next to a ,calm1 but this not very common4 ,but ,i never saw it to the ,westwards of the ,south1 or ,northwards of the ,east4 #e4 ,that the ,season of the ,year has some small effect on these ,trade ,winds1 for that when the ,sun is considerable to the ,northwards of the quator1 the ,south-,east ,winds1 especially in the ,straight of this ,ocean 7if ,i may so call it7 between ,brazile and the ,coast of ,guinea1 do vary a ,point or two to the ,southwards1 and the ,north-,east become more ,easterly2 and on the contrary1 when the ,sun is towards the ,tropick of ,capricorn the ,south-,easterly ,winds become more ,easterly1 and the ,north-,easterly ,winds on this side the ,line veere more to the ,northwards4 #f4 ,that as there is no general ,rule that admits not of some ,exception1 so there is in this ,ocean a ,tract of ,sea wherein the ,southerly and ,south-,west ,winds are perpetual1 viz4 all along the ,coast of ,guinea1 for above five hundred ,leagues together1 from ,sierra ,leona to the ,isle of ,st4 ,thomas2 for the ,south-,east ,trade ,wind having pass'd the ,line1 and approaching the ,coast of ,guinea within eighty or #ajj ,leagues1 inclines towards the ,shore1 and becomes ,s4 ,s4 ,e4 and by ,degrees1 as you come nearer1 it veeres about to ,south1 ,s4 ,s4 ,w4 and in with the ,land ,south-,west1 and sometimes ,west ,south-,west2 which ,variation is better express'd in the ,mapp hereto annexed1 7,vide ,plate #b7 than it can well be in ,words4 ,these are the ,winds which are observ'd on this ,coast when it blows true1 but there are frequent ,calms1 violent sudden ,gusts call'd ,tornado's1 from all ,points of the ,compass1 and sometimes unwholsome foggy ,easterly ,winds1 call'd ,hermitaa by the ,natives1 which too often infest the ,navigation of these parts4 #g4 ,that to the ,northwards of the ,line1 between four and ten ,degrees of ,latitude1 and between the ,meridians of ,cape ,virde1 and of the ,eastermost ,islands that bear that ,name1 there is a ,tract of ,sea wherein it were improper to say there is any ,trade ,wind1 or yet a ,variable2 for it seems condemn'd to perpetual ,calms1 attended with terrible ,thunder and ,lightning1 and ,rains so frequent1 that our ,navigators from thence call this part of the ,sea the ,rains2 the little ,winds that are1 be only some sudden uncertain ,gusts1 of very little ,continuance and less ,extent2 so that sometimes each ,hour you shall have a different ,gale1 which dies away into a ,calm before another succeed1 and in a ,fleet of ,ships in sight of one another1 each shall have the ,wind from a several ,point of the ,compass2 with these weak ,breezes ,ships are oblig'd to make the best of their way to the ,southward through the aforesaid six ,degrees1 wherein 'tis reported some have been detain'd whole ,months for want of ,wind4 ,from the three last ,observables is shewn the ,reason of two notable ,occurents in the ,east-,india and ,guinea ,navigations3 ,the one is1 why1 notwithstanding the narrowest part of the ,sea between ,guinea and ,brazile be about five hundred ,leagues over1 yet ,ships bound to the ,southward1 sometimes1 especially in the ,months of ,july and ,august1 find a great difficulty to pass it4 ,this happens because of the ,south-,east ,winds1 at that time of the ,year commonly extending some ,degrees beyond the ordinary limit of four ,degrees ,north ,latitude1 and withal they come so much ,southerly1 as to be sometimes ,south1 sometimes a ,point or two to the ,west2 there remains then only to ply to ,windward1 and if on the one side they stand away ,w4 ,s4 ,w4 they gain the ,wind still more and more ,easterly2 but there is danger of not weathering the ,brazilian ,shoar1 or at least the ,shoals upon that ,coast4 ,but if upon the other ,tack they go away ,e4 ,s4 ,e4 they fall into the ,neighbourhood of the ,coast of ,guinea1 from which there is no departing without running ,easterly1 as far as the ,isle of ,st4 ,thomas1 which is the constant practice of all the ,guinea ,ships1 and which may seem very strange1 without the consideration of the sixth ,remark1 which shews the ,reason of it3 ,for being in with the ,coast1 the ,wind blows generally at ,s4 ,w4 and ,w4 ,s4 ,w4 with which ,winds they cannot go to the ,northward for the ,land2 and on the other ,tack they can lie no nearer the ,wind than ,s4 ,s4 ,e4 or ,south2 with these ,courses they run off the ,shoar1 but in so doing they always find the ,winds more and more contrary2 so that when near the ,shoar they could lie ,south1 at a greater distance they can make their way no better than ,s4 ,e4 and afterwards ,e4 ,s4 ,e4 with which ,courses they fetch commonly the ,isle of ,st4 ,thomas and ,cape ,lopez1 where finding the ,winds to the ,eastward of the ,south1 they keep them favourable1 by running away to the ,westward in the ,south ,latitude1 of three or four ,degrees1 where the ,s4 ,e4 ,winds are perpetual4 ,for the sake of these general ,winds1 all those that use the ,west-,indian ,trade1 even those bound to ,virginia1 count it their best ,course to get as soon as they can to the ,southwards1 that so they may be certain of a fair and fresh ,gale to run before it to the ,westwards2 and for the same ,reason those homewards bound from ,america1 endeavour to gain the ,latitude of thirty ,degrees1 as soon as possible1 where they first find the ,winds begin to be variable2 tho' the most ordinary ,winds in the ,northern part of the ,atlantick ,ocean come from between the ,south and ,west4 ,as to those furious ,storms call'd ,hurricanes1 which are1 as it were1 peculiar to the ,caribbee ,isles2 and which so dreadfully afflict them in the ,month of ,august1 or not much before or after1 they do not so properly belong to this place1 both by ,reason of their small continuance and extent1 as likewise because they are not ,anniversary1 some ,years having more than one1 and sometimes for several ,years together there being none at all4 ,but their ,violence is so unconceivable1 and their other ,phnomena so surprising1 that they merit well to be consider'd apart4 ,what is here said1 is to be understood of the ,sea ,winds at some distance from the ,land2 for upon and near the ,shoars1 the ,land and ,sea ,breezes are almost every where sensible2 and the great ,variety which happens in their ,periods1 ,force and ,direction1 from the situation of the ,mountains1 ,vallies and ,woods1 and from the various ,texture of the ,soil1 more or less capable of retaining and reflecting ,heat1 and of exhaling or condensing ,vapours1 is such1 that it were an endless task1 to endeavour to account for them4 ,,ii4 ,in the ,indian ,ocean1 the ,winds are partly general1 as in the thiopick ,ocean1 partly ,periodical2 that is1 half the ,year they blow one way1 and the other half near upon the opposite ,points2 and these ,points and ,times of shifting are different in different parts of this ,ocean2 the limits of each ,tract of ,sea1 subject to the same ,change or ,monsoon1 are certainly very hard to determine1 but the diligence ,i have used to be rightly inform'd1 and the care ,i have taken therein1 has1 in a great measure1 surmounted that ,difficulty2 and ,i am perswaded that the following ,particulars may be relied upon4 #a4 ,that between the ,latitudes of ten ,degrees and thirty ,degrees ,south1 between ,madagascar and ,hollandia ,nova1 the general ,trade ,wind about the ,s4 ,e4 by ,e4 is found to blow all the ,year long1 to all ,intents and ,purposes after the same manner as in the same ,latitudes in the thiopick ,ocean1 as it is describ'd in the fourth ,remark aforegoing4 #b4 ,that the aforesaid ,s4 ,e4 ,winds extend to within two ,degrees of the quator1 during the ,months of ,june1 ,july1 ,august1 c4 to ,november2 at which time between the ,south ,latitudes of three and ten ,degrees1 being near the ,meridian of the ,north end of ,madagascar1 and between two and twelve ,south ,latitude1 being near ,sumatra and ,java1 the contrary ,winds from the ,n4 ,w4 or between the ,north and ,west1 set in and blow for half the ,year1 viz4 from the beginning of ,december till ,may2 and this ,monsoon is observ'd as far as the ,molucca ,isles1 of which more anon4 #c4 ,that to the ,northward of three ,degrees ,south ,latitude1 over the whole ,arabian or ,indian-,sea and ,gulph of ,bengall1 from ,sumatra to the ,coast of ,africa1 there is another ,monsoon1 blowing from ,october to ,april upon the ,north ,east ,points2 but in the other half ,year1 from ,april to ,october1 upon the opposite ,points of ,s4 ,w4 and ,w4 ,s4 ,w4 and that with rather more force than the other1 accompanied with dark rainy ,weather1 whereas the ,n4 ,e4 blows clear2 'tis likewise to be noted1 that the ,winds are not so constant1 either in strength or point in the ,gulph of ,bengall1 as they are in the ,indian-,sea1 where a certain and steady ,gale scarce ever fails4 ',tis also remarkable1 that the ,s4 ,w4 ,winds in these ,seas are generally more ,southerly on the ,african side1 more ,westerly on the ,indian4 #d4 ,that as an ,appendix to the last describ'd ,monsoon1 there is a ,tract of ,sea to the ,southwards of the quator1 subject to the same ,changes of the ,winds1 viz4 near the ,african ,coast1 between it and the ,island ,madagascar or ,st4 ,lawrence1 and from thence ,northwards as far as the ,line2 wherein from ,april to ,october there is found a constant fresh ,s4 ,s4 ,w4 ,wind1 which1 as you go more ,northerly1 becomes still more and more ,westerly1 so as to fall in with the ,w4 ,s4 ,w4 ,winds1 mention'd before1 in those ,months of the ,year to be certain to the ,northward of the quator3 ,what ,winds blow in these ,seas1 for the other half ,year1 from ,october to ,april1 ,i have not yet been able to obtain to my full satisfaction1 for that our ,navigators always return from ,india without ,madagascar1 and so are little acquainted in this ,matter2 the ,account that has been given me is only this1 that the ,winds are much ,easterly hereabouts1 and as often to the ,north of the true ,east as to the ,southwards thereof4 #e4 ,that to the ,eastward of ,sumatra and ,malacca1 to the ,northwards of the ,line1 and along the ,coast of ,cambodia and ,china1 the ,monsoons blow ,north and ,south1 that is to say1 the ,n4 ,e4 ,winds are much ,northerly1 and the ,s4 ,w4 much ,southerly3 ,this ,constitution reaches to the ,eastwards of the ,philippine ,isles1 and as far ,northerly as ,japan4 ,the ,northern ,monsoon setting in1 in these ,seas1 in ,october or ,november1 and the ,southern in ,may1 blowing all the ,summer ,months3 ,here it is to be noted1 ,that the ,points of the ,compass1 from whence the ,wind comes in these ,parts of the ,world1 are not so fixt as in those lately describ'd2 for the ,southerly will frequently pass a ,point or two to the ,eastwards of the ,south1 and the ,northerly as much to the ,westwards of the ,north1 which seems occasion'd by the great quantity of ,land1 which is interspers'd in these ,seas4 #f4 ,that in the same ,meridians1 but to the ,southwards of the quator1 being that ,tract lying between ,sumatra and ,java to the ,west1 and ,new ,guinea to the ,east1 the same ,northerly ,monsoons are observ'd1 but with this difference1 that the inclination of the ,northerly is towards the ,n4 ,west1 and of the ,southerly towards the ,s4 ,e4 but the plag venti are not more constant here than in the former1 viz4 variable five or six ,points2 besides the times of the ,change of these ,winds1 are not the same as in the ,chinese ,seas1 but about a ,month or six ,weeks later4 #g4 ,that these contrary ,winds do not shift all at once1 but in some places the time of the ,change is attended with ,calms1 in others with variable ,winds2 and it is particularly remarkable1 that the end of the ,westerly ,monsoon on the ,coast of ,coromandel1 and the two last ,months of the ,southerly ,monsoon in the ,seas of ,china1 are very subject to be tempestuous3 ,the violence of these ,storms is such1 that they seem to be of the ,nature of the ,west-,india ,hurricanes1 and render the ,navigation of these parts very unsafe about that time of the ,year4 ,these ,tempests are by our ,seamen usually term'd1 ,the breaking up of the ,monsoons4 ,by reason of the shifting of these ,winds1 all those that sail in these ,seas1 are oblig'd to observe the ,seasons proper for their ,voyages1 and so doing they fail not of a fair ,wind and speedy ,passage2 but if so be they chance to out-stay their time1 till the contrary ,monsoon sets in1 as it frequently happens1 they are forc'd to give over the hopes of accomplishing their intended ,voyages1 and either return to the ,port from whence they came1 or else put in to some other ,harbour1 there to spend the time till the ,winds shall come favourable4 ,,iii4 ,the third ,ocean call'd ,mare ,pacificum1 whose ,extent is equal to that of the other two 7it being from the ,west ,coast of ,america to the ,philippine ,islands1 not less than #aej ,degrees of ,longitude7 is that which is least known to our own or the ,neighbour ,nations2 that ,navigation that there is on it1 is by the ,spaniards1 who go ,yearly from the ,coast of ,new ,spain to the ,manilha's1 but that but by one beaten track2 so that ,i cannot be so particular here as in the other two4 ,what the ,spanish ,authors say of the ,winds they find in their ,courses1 and what is confirm'd by the old ,accounts of ,drake and ,cavendish2 and since by ,schooten1 who sail'd the whole breadth of this ,sea in the ,southern ,latitude of fifteen or sixteen ,degrees1 is1 that there is a great conformity between the ,winds of this ,sea1 and those of the ,atlantick and thiopick2 that is to say1 that to the ,northwards of the quator1 the predominant ,wind is between the ,east and ,north-,east2 and to the ,southwards thereof there is a constant steady ,gale between the ,east and ,south-,east1 and that on both sides the ,line with so much constancy1 that they scarce ever need to attend the ,sails1 and ,strength1 that it is rare to fail of crossing this vast ,ocean in ten ,weeks time1 which is about #acj ,miles per diem2 besides1 'tis said that ,storms and ,tempests are never known in these parts3 ,so that here is the very best of ,sailing2 no want of a fresh fair ,wind1 and yet no danger of having too much3 ,wherefore some have thought it might be as short a ,voyage to ,japan and ,china1 to go by the ,streights of ,magellan1 as by the ,cape of ,good ,hope4 ,the ,limits of these general ,winds are also much the same as in the ,atlantick ,sea1 viz4 about the thirtieth ,degree of ,latitude on both sides2 for the ,spaniards homewards bound from the ,manilha's1 always take the advantage of the ,southerly ,monsoon1 blowing there in the ,summer ,months1 and run up to the ,northwards of that ,latitude1 as high as ,japan1 before they meet with variable ,winds1 to shape their ,course to the ,eastwards4 ,and ,schooten and others that have gone about by the ,magellan ,streights1 have found the ,limits of ,s4 ,e4 ,winds1 much about the same ,latitude to the ,southwards2 besides a farther ,analogy between the ,winds of this ,ocean1 and the thiopick1 appears in that1 upon the ,coast of ,peru1 they are always much ,southerly1 like as they are found near the ,shoars of ,angola4 ,thus far ,matter of ,fact1 wherein if the information ,i have receiv'd be not in all parts ,accurate1 it has not been for want of inquiry from those ,i conceiv'd best able to instruct me2 and ,i shall take it for a very great ,kindness if any ,master of a ,ship1 or other ,person1 well inform'd of the ,nature of the ,winds1 in any of the aforemention'd parts of the ,world1 shall please to communicate their ,observations thereupon2 so that what ,i have here ,collected may be either confirm'd or amended1 or by the addition of some material ,circumstances enlarg'd4 ,it is not the work of one1 nor of few1 but of a multitude of ,observers1 to bring together the ,experience requisite to compose a perfect and compleat ,history of these ,winds2 however ,i am not much doubtful that ,i have err'd in1 or omitted any of the principal ,observables1 whatever lesser ,particulars may have escaped my ,knowledge4 ,to help the ,conception of the ,reader in a manner of so much difficulty1 ,i believ'd it necessary to adjoin a ,scheme1 7,plate #b47 shewing at one view all the various ,tracts and ,courses of these ,winds2 whereby 'tis possible the thing may be better understood1 than by any verbal ,description whatsoever4 ,the ,limits of these several ,tracts are design'd every where by prickt ,lines1 as well in the ,atlantick and thiopick1 where they are the boundaries of the ,trade and variable ,winds1 as in the ,indian ,ocean1 where they also shew the ,extent of the several ,monsoons4 ,i could think of no better way to design the ,course of the ,winds on the ,map1 than by drawing rows of stroaks in the same ,line that a ,ship would move going always before it2 the sharp end of each little stroak pointing out that part of the ,horizon1 from whence the ,wind continually comes2 and where there are ,monsoons1 the rows of the stroaks run alternately backwards and forwards1 by which means they are thicker there than elsewhere4 ,as to the great ,south ,sea1 considering its vast ,extent1 and the little ,variety there is in its ,winds1 and the great ,analogy between them1 and those of the ,atlantick and thiopick ,oceans2 besides1 that the greatest part thereof is wholly unknown to us2 ,i thought it unnecessary to lengthen the ,map therewith4 ,in the foregoing ,history are contained several ,problems1 that merit well the ,consideration of our acutest ,naturalists1 both by reason of the constancy of the ,effect1 and of the immense ,extent thereof2 near half the ,surface of the ,globe being concerned4 ,the chief of these ,problems are1 #a4 ,why these ,winds are perpetually from the ,east in the ,atlantic and thiopick2 as likewise in the ,pacifick ,ocean1 between the ,latitudes of #cj ,north and ,south8 #b4 ,why the said ,winds extend no farther with constancy than to the ,latitude of #cj ,degrees8 #c4 ,why there should be a constant ,south-,westerly ,wind upon and near the ,coast of ,guinea8 #d4 ,why in the ,north part of the ,indian ,ocean1 the ,winds1 which for one half ,year do agree with those of the other two ,oceans1 should change in other half ,year1 and blow from the opposite ,points2 whilst the ,southern part of that ,ocean follows the ,general ,rule1 and has perpetual ,winds about ,s4 ,e8 #e4 ,why in these ,general ,trade-,winds it should be always true1 that to the ,northward of the quator it is inclin'd to the ,northwards of the ,east2 and in ,south ,latitudes1 to the ,southward thereof8 #f4 ,why in these ,seas of ,china there should be so great an ,inclination from the ,east to the ,north1 more than elsewhere8 with many more1 which it would be much easier to propose than answer4 ,but lest ,i should seem to propose to others1 ,difficulties which ,i have not thought worth my own ,time and ,pains1 take here the result of an earnest ,endeavour after the true reason of the aforesaid ,phnomena2 wherein if ,i am not able to account for all ,particulars1 yet 'tis hoped the ,thoughts ,i have spent thereon1 will not be judged wholly lost1 by the ,curious in ,natural ,enquiries4 ,wind is most properly defined to be the ,stream or ,current of the ,air1 and where such a ,current is perpetual and fixt in its ,course1 'tis necessary that it proceed from a permanent un-intermitting ,cause4 ,wherefore some have been inclin'd to propose the diurnal ,rotation of the ,earth upon its ,axis1 by which1 as the ,globe turns ,eastwards1 the loose and fluid ,particles of the ,air1 being so exceeding light as they be1 are left behind1 so that in respect of the ,earths ,surface they move ,westwards1 and become a constant ,easterly ,wind4 ,this ,opinion seems confirm'd1 for that these ,winds are found only near the quinoctial1 in those ,parallels of ,latitude where the diurnal ,motion is swiftest2 and ,i should readily assent to it1 if the constant ,calms in the ,atlantick ,sea1 near the quator1 the ,westerly ,winds near the ,coast of ,guinea2 and the ,periodical ,westerly ,monsoons under the quator in the ,indian ,seas1 did not declare the insufficency of that ,hypothesis4 ,besides the ,air being kept to the ,earth by the ,principle of ,gravity1 would acquire the same degree of ,velocity that the ,earths ,surface moves with1 as well in respect of the diurnal ,rotation1 as of the ,annual about the ,sun1 which is about thirty times swifter4 ,it remains therefore to substitute some other ,cause1 capable of producing a like constant ,effect1 not liable to the same ,objections1 but agreeable to the known ,properties of the ,elements of ,air and ,water1 and the ,laws of the ,motion of fluid ,bodies4 ,such an one is1 ,i conceive1 the ,action of the ,sun ,beams upon the ,air and ,water1 as he passes every ,day over the ,oceans1 consider'd together with the ,nature of the ,soil1 and ,situation of the adjoining ,continents3 ,i say therefore1 first1 that according to the ,laws of ,staticks1 the ,air which is less rarified or expanded by heat1 and consequently more ponderous1 must have a ,motion towards those parts thereof1 which are more rarified1 and less ponderous1 to bring it to an quilibrium2 and secondly1 ,that the ,presence of the ,sun continually shifting to the ,westwards1 that part towards which the ,air tends1 by reason of the ,rarifaction made by his greatest ,meridian ,heat1 is with him carried ,westward1 and consequently the tendency of the whole ,body of the lower ,air is that way4 ,thus a general ,easterly ,wind is formed1 which being impressed upon all the ,air of a vast ,ocean1 the ,parts impel one the other1 and so keep moving till the next return of the ,sun1 whereby so much of the ,motion as was lost1 is again restored1 and thus the ,westerly ,wind is made perpetual4 ,from the same ,principle it follows1 that this ,easterly ,wind should on the ,north side of the quator1 be to the ,northwards of the ,east1 and in ,south ,latitudes to the ,southwards thereof2 for near the ,line1 the ,air is much more rarified1 than at a greater distance from it2 because of the ,sun twice in a ,year ,vertical1 and at no time distant above #bc ,degr4 and a half2 at which distance the ,heat1 being as the ,sine of the ,angle of ,incidence1 is but little short of that of the perpendicular ,ray4 ,whereas under the ,tropicks1 though the ,sun stay long ,vertical1 yet he is as long #dg ,degr4 off2 which is a kind of ,winter1 wherein the ,air so cools1 as that the ,summer-heat cannot warm it to the same degree with that under the quator4 ,wherefore the ,air to the ,northwards and ,southwards1 being less rarified than that in the middle1 it follows1 that from both sides it ought to tend towards the quator3 ,this ,motion compounded with the former ,easterly ,wind1 answers all the ,phnomena of the general ,trade-winds2 which1 if the whole ,surface of the ,globe were ,sea1 would undoubtedly blow all round the ,world1 as they are found to do in the ,atlantick1 and thiopick ,oceans4 ,but seeing that so great ,continents do interpose1 and break the continuity of the ,oceans1 regard must be had to the ,nature of the ,soil1 and the ,position of the high ,mountains1 which ,i suppose the two principal ,causes of the several ,variations of the ,winds1 from the former general ,rule3 ,for if a ,country lying near the ,sun1 prove to be flat1 sandy1 low ,land1 such as the ,desarts of ,lybia are usually reported to be1 the ,heat occasion'd by the ,reflection of the ,suns ,beams1 and the retention thereof in the ,sand1 is incredible to those that have not felt it2 whereby the ,air being exceedingly rarified1 it is necessary that the cooler and more dense ,air should run thitherwards to restore the quilibrium3 ,this ,i take to be the cause1 why near the ,coast of ,guinea the ,wind always sets in upon the ,land1 blowing ,westerly instead of ,easterly1 there being sufficient ,reason to believe1 that the ,inland ,parts of ,africa are prodigiously hot1 since the ,northern ,borders thereof were so intemperate1 as to give the ,ancients cause to conclude1 that all beyond the ,tropick1 was made uninhabitable by excess of ,heat3 ,from the same ,cause it happens1 that there are so constant ,calms in that part of the ,ocean1 called the ,rains1 7described in the #gth ,remark on the ,atlantick ,sea7 for this ,tract being placed in the middle1 between the ,westerly ,winds blowing on the ,coast of ,guinea1 and the ,easterly ,trade-winds1 blowing to the ,westwards thereof1 the tendency of the ,air here1 is indifferent to either1 and so stands in quilibrio between both2 and the weight of the incumbent ,atmosphere being diminished by the continual contrary ,winds blowing from hence1 is the reason that the ,air here holds not the copious ,vapour it receives1 but lets it fall into frequent ,rains4 ,but as the cool and dense ,air1 by reason of its greater ,gravity1 presses upon the hot and rarified1 'tis demonstrative that this latter must ascend in a continued ,stream as fast it rarifies2 and that being ascended1 it must disperse it self to preserve the quilibrium3 that is1 by a contrary ,current1 the upper ,air must move from those ,parts where the greatest ,heat is3 ,so by a kind of ,circulation1 the ,north-,east ,trade-,wind below1 will be attended with a ,south-,westerly above1 and the ,south-,easterly with a ,north-,west ,wind above2 that this is more than a bare ,conjecture1 the almost instantaneous ,change of the ,wind to the opposite ,point1 which is frequently found in passing the limits of the ,trade-winds1 seems to assure us2 but that which above all confirms this ,hypothesis is the ,phnomenon of the ,monsoons1 by this means most easily solved1 and without it hardly explicable4 ,supposing therefore such a ,circulation1 as above1 'tis to be considered that to the ,northward of the ,indian ,ocean there is every where ,land within the usual limit of the ,latitude of #cj1 viz4 ,arabia1 ,persia1 ,india1 c4 which for the same reason as the ,mediterranean ,parts of ,africa1 are subject to unsufferable ,heats when the ,sun is to the ,north1 passing nearly ,vertical2 but yet are temperate enough when the ,sun is removed towards the other ,tropick2 because of a ridge of ,mountains at some distance within the ,land1 said to be frequently in ,winter cover'd with ,snow1 over which the ,air1 as it passes1 must needs be much chill'd4 ,hence it comes to pass1 that the ,air coming according to the general ,rule1 out of the ,n4 ,e4 in the ,indian ,seas1 is sometimes hotter1 sometimes colder1 than that which by this ,circulation is return'd out of the ,s4 ,w4 and by consequence1 sometimes the under ,current or ,wind1 is from the ,n4 ,e4 sometimes from the ,s4 ,w4 ,that this has no other ,cause1 is clear from the times wherein these ,winds set in1 viz4 in ,april1 when the ,sun begins to warm those ,countries to the ,north1 the ,s4 ,w4 ,monsoon begins1 and blows during the ,heats till ,october2 when the ,sun being retir'd1 and all things growing cooler ,northward1 and the ,heat increasing to the ,south1 the ,north-,east ,winds enter and blow all the ,winter till ,april again4 ,and it is undoubtedly from the same ,principle that to the ,southwards of the quator1 in part of the ,indian ,ocean1 the ,north-,west ,winds succeed to the ,south-,east1 when the ,sun draws near the ,tropick of ,capricorn2 but ,i must confess1 that in this latter occurs a difficulty1 not well to be accounted for1 which is1 why this ,change of the ,monsoons should be any more in this ,ocean1 than in the same ,latitudes in the thopick1 where there is nothing more certain than a ,s4 ,e4 ,wind all the ,year4 ',tis likewise very hard to conceive why the limits of the ,trade-wind should be fixt1 about the thirtieth ,degree of ,latitude all round the ,globe2 and that they should so seldom transgress or fall short of those bounds2 as also that in the ,indian ,sea1 only the ,northern ,part should be subject to the changeable ,monsoons1 and in the ,southern there be a constant ,s4 ,e4 ,these are ,particulars that merit to be consider'd more at large1 and furnish a sufficient ,subject for a just ,volume1 which will be a very commendable ,task for such1 who being us'd to ,philosophick ,contemplation1 shall have leisure to apply their serious ,thoughts about it4 ,illustration3 ,plate #b pag4 #hj ,a new ,correct ,,sea ,,chart of the ,,whole ,,world ,shewing the ,variations of y ,,compass as they were found ,ao #agjj with a ,view of the ,generall and ,coasting ,trade ,winds and ,monsoons or shifting ,trade ,winds by the ,direction of ,cap4 ,edm4 ,halley4 ,a ,discourse of the ,rule of the ,decrease of the height of the ,mercury in the ,barometer1 according as ,places are elevated above the ,surface of the ,earth2 with an ,attempt to discover the true ,reason of the ,rising and ,falling of the ,mercury1 upon ,change of ,weather4 ,by ,edm4 ,halley4 ,the ,elastick ,property of the ,air has been long since made out1 by ,experiments before the ,royal ,society1 and elsewhere2 and the ,resistance of its ,spring is found to be nearly equal to the ,weight or ,force that compresses it2 as also1 that the ,spaces the same ,air occupies1 under differing ,pressures1 are reciprocally as those ,pressures3 ,it has been shewn likewise by undoubted ,experiment1 that the specifick ,gravity of the ,air1 near the ,earth's ,surface to that of ,water1 was once as #a to #hdj2 again as #a to #heb2 and a third time1 in a very large ,vessel holding #aj ,gallons1 as #a to #hfj2 all which1 considering the ,difficulty of the ,experiment1 agree well enough1 the ,mercury standing at all those times about #bi ,inches 3 ,but by ,reason 'twas ,summer-weather1 and consequently the ,air rarified1 when all these were tried1 we may without sensible ,error say in round numbers1 that the ,barometer standing at #cj ,inches1 and in a mean ,state of ,heat and ,cold1 the specifick ,gravity of the ,air to ,water1 is as #a to #hjj4 ,by the like ,trials the weight of ,mercury to ,water1 is as #ac to #a1 or very near it2 so that the weight of ,mercury to ,air1 is as #ajhjj to #a2 and a ,cylinder of ,air of #ajhjj ,inches or #ijj ,feet1 is equal to an ,inch of ,mercury2 and were the ,air of an equal density like ,water1 the whole ,atmosphere would be no more than #e1a ,miles high1 and in the ,ascent of every #ijj ,feet the ,barometer would sink an ,inch4 ,but the ,expansion of the ,air increasing in the same proportion as the incumbent weight of the ,atmosphere decreases2 that is1 as the ,mercury in the ,barometer sinks2 the upper ,parts of the ,air are much more rarified than the lower1 and each ,space answering to an ,inch of ,quicksilver1 grows greater and greater2 so that the ,atmosphere must be extended to a much greater height4 ,now1 upon these ,principles1 to determine the height of the ,mercury at any assigned height in the ,air2 and contra1 having the height of the ,mercury given1 to find the height of the ,place where the ,barometer stands1 are ,problems not more difficult than curious2 and which ,i thus resolve4 ,the ,expansions of the ,air being reciprocally as the heights of the ,mercury1 it is evident1 that by the help of the ,curve of the ,hyperbola and its ,asymptotes1 the said ,expansions may be expounded to any given height of the ,mercury3 ,for by the #feth ,prop4 lib4 #b4 ,conic4 ,mydorgii1 the ,rectangles1 ,,abce1 ,,akge1 ,,alde1 c4 7in ,plate #a4 ,fig4 #d47 are always equal1 and consequently the sides1 ,,cb1 ,,gk1 ,,ld1 c4 are reciprocally as the sides ,,ab1 ,,ak1 ,,al1 c4 ,if then the ,lines ,,ab1 ,,ak1 ,,al1 be supposed equal to the heights of the ,mercury1 or the pressures of the ,atmosphere1 the ,lines ,,cb1 ,,gk1 ,,ld1 answering thereto1 will be as the ,expansions of the ,air under those ,pressures1 or the ,bulks that the same quantity of ,air will occupy2 which ,expansions being taken infinitely many1 and infinitely little1 7according to the ,method of ,indivisibles7 their ,summ will give the ,spaces of ,air between the several heights of the ,barometer2 that is to say1 the ,summ of all the ,lines between ,,cb and ,,kg1 or the ,area ,,cbkg1 will be proportioned to the ,distance or ,space intercepted between the ,levels of two ,places in the ,air1 where the ,mercury would stand at the heights represented by the ,lines ,,ab1 ,,ak2 so then the ,spaces of ,air answering to equal ,parts of ,mercury in the ,barometer1 are as the ,area's ,,cbkg1 ,,gkld1 ,,dlfm1 c4 ,these ,area's again are1 by the ,demonstration of ,gregory of ,st4 ,vincent1 proportionate to the ,logarithms of the ,numbers expressing the ,rationes of ,,ak to ,,ab1 of ,,al to ,,ak1 of ,,am to ,,al1 c4 ,so then by the common ,table of ,logarithms1 the height of any ,place in the ,atmosphere1 having any assign'd height of the ,mercury1 may most easily be found3 ,for the ,line ,,cb in the ,hyperbola1 whereof the ,area's design the ,tabular ,logarithms1 being #j1jaddgfe2 'twill be1 as #j1jaddgfe1 to the difference of the ,logarithms of #cj1 or any other lesser ,number1 for #ijj ,feet1 or the ,space answering to an ,inch of ,mercury1 if the ,air were equally prest with #cj ,inches of ,mercury1 and every where alike1 to the height of the ,barometer in the ,air1 where it will stand at that lesser number of ,inches3 ,and by the ,converse of this ,proportion may the height of the ,mercury be found1 having the ,altitude of the ,place given4 ,from these ,rules ,i deriv'd the following ,tables4 ,a ,table shewing the ,altitude1 to given heights of the ,mercury4 ,inch4 ,feet4 #cj #j #bi #iae #bh #ahfb #bg #bhdd #bf #chfc #be #dibb #bj #ajidg #ae #ahgae #aj #biffb #e #dhcgh #a #iahca #j4e #aajedg #j4be #abibfb #j4a #bi mil4 or #aedjjj #j4ja #da m4 or #bafafi #j4jja #ec m4 #bghcch ,a ,table shewing the heights of the ,mercury1 at given ,altitudes4 ,feet4 ,inch4 #j #cj #jj #ajjj #bh #ia #bjjj #bg #hf #cjjj #bf #he #djjj #ce #hg #ejjj feet #bd #ic #a mile #bd #fg #b #bj #bi #c #af #fh #d #ac #gb #e #aa #bh #aj #d #bd #ae #a #fj #bj #j #ie #be #j #bc #cj #j #jh #dj #j #jab ,upon these ,suppositions it appears1 that at the height of #da ,miles the ,air is so rarified1 as to take up #cjjj times the ,space it occupies here1 and at #ec ,miles high it would be expanded above #cjjjj times2 but it's probable that the utmost ,power of its ,spring cannot exert it self1 to so great an ,extension1 and that no part of the ,atmosphere reaches above #de ,miles from the ,surface of the ,earth4 ,this seems confirm'd from the ,observations of the ,crepusculum1 which is observ'd commonly to begin and end when the ,sun is about #ah ,degrees below the ,horizon2 for supposing the ,air to reflect light from its most rarified ,parts1 and that as long as the ,sun illuminates any of its ,atoms1 they are visible to an ,eye not intercepted by the ,curvity of the ,earth1 it will follow from ,fig4 #e4 ,plate #a4 that the proportion of the height of the whole ,air1 to the ,semi-diameter of the ,earth1 is much about1 as #a to #ij1 or as the excess of the ,secant of about #h ,degrees to the ,radius4 ,for if ,e be the ,eye of the ,observer1 ,s a ,place where the ,sun sets at the end of ,twilight in ,e1 and the ,arch ,,ecs1 or ,,tca1 be found #ah ,degrees1 the excess of the ,secant of half thereof ,,ech1 would be the height of the ,air1 viz4 ,,gh3 ,but the ,beam of the ,sun ,,ash1 and the ,visual ,ray ,,eh1 do each of them suffer a ,refraction of about #cb or #cc ,minutes1 whereby being bent inwards from ,h towards ,g1 the height of the ,air need not be so great as if they went streight2 and having from the ,angle ,,ecs taken the double ,refraction of the ,horizontal ,ray1 the half of the ,remainder will be #h ,degrees circiter1 whose ,secant being #aj1aaa1 it follows1 that as #ajjjj to #aaa1 so the ,semi-diameter of the ,earth supposed #djjj ,miles1 to #dd1d ,miles2 which will be the height of the whole ,air1 if the ,places ,e1 ,s1 whose visible ,portions of the ,atmosphere ,,erzh1 and ,,shkb1 just touch one the other1 be #ah ,degrees asunder4 ,at this height the ,air is expanded into above #cjjj times the space it occupies here1 and we have seen the ,experience of condensing it into the #fjth part of the same ,space1 so that it should seem1 that the ,air is a ,substance capable of being compressed into the #ahjjjjth part of the ,space it would naturally take up1 when free from pressure4 ,now what ,texture or ,composition of ,parts shall be capable of this great ,expansion and ,contraction1 seems a very hard ,question2 and which1 ,i suppose1 is scarce sufficiently accounted for1 by comparing it to ,wool1 ,cotten1 and the like springy ,bodies4 ,hitherto ,i have only consider'd the ,air and ,atmosphere1 as one unalter'd ,body1 as having constantly at the ,earth's ,surface the #hjjth part of the weight of ,water1 and being capable of ,rarifaction and ,condensation in infinitum2 neither of which ,hypotheses are rigidly true3 ,for here in ,england it is notoriously known1 that the weight of the whole ,atmosphere is various1 being counterpoised sometimes by #bh ,inches of ,mercury1 and at other times by no less than #cj2 so that the under parts being pressed by about a #aeth part1 less weight1 the specifick ,gravity of the ,air upon that score will sometimes be a #aeth part lighter than another2 besides ,heat and ,cold1 does very considerably dilate and contract the ,air1 and consequently alter its ,gravity2 to which add the mixture of ,effluvia1 or steams arising from almost all ,bodies1 which assimulating into the ,form of ,air1 are kept suspended therein1 as ,salts dissolv'd in ,liquors1 or ,metals in corroding ,menstrua2 which ,bodies being all of them very much heavier than ,air1 their ,particles by their ,admixture must needs encrease the weight of that ,air they lie incorporated withal1 after the same manner as melted ,salts do augment the specifick ,gravity of ,water4 ,the other ,consideration is1 that the ,rarifaction and ,condensation of the ,air is not precisely according to the proportion here laid down2 for the ,experiment very nearly agrees thereto1 as may be seen in the #ehth ,chapter of ,mr4 ,hook's ,micrography2 yet are the ,condensations not possible beyond certain degrees3 ,for being compressed into an #hjjth part of the ,space it takes up here1 its consistence would be equally dense with that of ,water2 which yields not to any force whatsoever1 as hath been found by several ,experiments tried here1 and at ,florence1 by the ,academia del ,cimento4 ,nor can the ,rarifaction proceed in infinitum2 for supposing the ,spring whereby it dilates it self1 occasion'd by what ,texture of ,parts you please1 yet must there be a determinate ,magnitude of the natural ,state of each ,particle1 as we see it is in ,wool1 and the like1 whose ,bodies being compressable into a very small ,space1 have yet a determinate bulk which they cannot exceed1 when free'd from all manner of ,pressure4 ,these ,objections being true1 do disturb the ,geometrical ,accuracy of these ,conclusions1 drawn from the specifick ,gravity of the ,air observ'd at any time2 but the ,method here shewn will compute by a like ,calculation1 the heights of the ,quick-silver1 and the ,rarifactions of the ,air from any assign'd height of the ,barometer at the ,earth's ,surface1 and any specifick ,gravity given4 ,as to the ,condensation and ,rarifaction by ,heat and ,cold1 and the various mixture of ,aqueous and other ,vapours1 these two ,objections seem generally to compensate each other2 for when the ,air is rarified by ,heat1 they are raised most copiously2 so that though the ,air properly so call'd1 be expanded1 and consequently lighter1 yet the ,interstices thereof being crouded full of ,vapours of much heavier ,matters1 bulk for bulk1 the weight of the ,compositum may continue much the same1 at least a most curious ,experiment made by the ,ingenious ,mr4 ,john ,caswell1 of ,oxford1 upon the top of ,snowdon ,hill1 in ,carnarvanshire1 seems to prove1 that the first ,inches of ,mercury have their ,portions of ,air near enough to what ,i now determine3 ,for the height of the ,hill being #abdj ,yards1 or very near it1 he found the ,mercury to have subsided to #be1f ,inches1 or #d inches below the mean ,altitude thereof at the ,level of the ,sea1 7which is a greater difference than has been found in any of our former ,experiments17 and the ,space answering to #d ,inches1 by my ,calculation1 should be #abhh ,yards2 and it agrees as well with the ,observations in the ,appendix to ,mr4 ,pascall's ,book1 del ,equilibre des ,liqueurs1 made on the high ,hill in ,auvergne1 call'd le puy de ,domme4 ,so that the ,rarifaction and ,vapours seem not to have alter'd considerably1 the ,gravity of the under ,parts of the ,air2 and much above the height where these ,experiments were made1 do few ,vapours ascend1 and the ,cold is such that the ,snow lies continually1 so that for the more elevated ,parts of the ,sphere of ,air1 there is much less ,reason to doubt4 ,but now we have had occasion to mention the difference there is between the height of the ,mercury at one time1 from the height thereof at another1 it may not be unacceptable to offer at some ,reasons for the said difference2 which1 at least to my self1 seem to have some appearance of ,truth4 ,first1 ,then it's undoubtedly demonstrable1 that the height of the ,cylinder of ,mercury is equal to the weight of the whole incumbent ,air1 and consequently that that whole is sometimes a fifteenth more than at other times2 which cannot otherwise be1 but by the access of new ,matter when 'tis heavy1 and its diminution when 'tis light2 that ,hypothesis therefore that shews how the ,air shall be encreased or diminished1 in any particular place1 will give a ,reason for the greater and lesser height of the ,mercury in the ,baroscope3 ,but to direct us in the choice of the several ,causes1 which may be assign'd for the ,increase and ,decrease of the ,air1 'twill not be unnecessary to enumerate some of the principal ,observations made upon the ,barometer1 most whereof are sufficiently known already to all those that are curious in these ,matters4 ,the ,first is1 ,that in calm ,weather1 when the ,air is inclin'd to ,rain1 the ,mercury is commonly low4 #b4 ,that in serene good settled ,weather1 the ,mercury is generally high4 #c4 ,that upon very great ,winds1 though they be not accompanied with ,rain1 the ,mercury sinks lowest of all1 with relation to the ,point of the ,compass the ,wind blows upon4 #d4 ,that cteris paribus the greatest heights of the ,mercury are found upon ,easterly and ,north-,easterly ,winds4 #e4 ,that in calm frosty ,weather the ,mercury generally stands high4 #f4 ,that after very great ,storms of ,wind1 when the ,quicksilver has been low1 it generally rises again very fast4 #g4 ,that the more ,northerly places have greater ,alterations of the ,baroscope1 than the more ,southerly4 #h4 ,that within the ,tropicks and near them1 those ,accounts ,i have had from others1 and my own ,observation at ,st4 ,helena1 make very little or no ,variation of the height of the ,mercury in all ,weathers4 ,now that ,theory that can well account for all these appearances1 will1 in all probability1 approach nearer the true cause of the ,barometers ,variations1 than any thing hitherto afforded2 and such an one ,i am bound to believe1 is that which ,i here lay down with submission to better ,judgments4 ,i conceive that the principal ,cause of the rise and fall of the ,mercury1 is from the variable ,winds1 which are found in the ,temperate ,zones1 and whose great unconstancy here in ,england is most notorious4 ,i shall not at present inquire into the ,cause of its uncertainty1 but the ,matter of ,fact being most undoubted1 the ,legitimate ,consequences thereof must be allow'd me1 let it proceed from what it will4 ,a second ,cause is the uncertain ,exhalation and ,prcipitation of the ,vapours lodging in the ,air1 whereby it comes to be at one time much more crowded than at another1 and consequently heavier2 but this latter in a great measure depends upon the former4 ,now from these ,principles ,i shall endeavour to explicate the several ,phnomena of the ,barometer1 taking them in the same order ,i laid them down4 #a4 ,why in calm ,weather the ,air being inclin'd to ,rain1 the ,mercury is commonly low8 ,i ,answer1 ,that the ,mercury's being low1 inclines it to ,rain2 for the ,air being light1 the ,vapours are no longer supported thereby1 being become specifically heavier than the ,medium wherein they floated2 so that they descend towards the ,earth1 and in their fall meeting with other aqueous ,particles1 they incorporate together1 and form little drops of ,rain2 but the ,mercury's being at one time lower than another1 is the effect of two contrary ,winds blowing from the place whence the ,barometer stands2 whereby the ,air of that place is carried both ways from it1 and consequently the incumbent ,cylinder of ,air is diminished1 and accordingly the ,mercury sinks2 as for ,instance1 if in the ,german ,ocean it should blow a ,gale of ,westerly ,wind1 and at the same time an ,easterly ,wind in the ,irish ,sea2 or if in ,france it should blow a ,southerly ,wind1 and in ,scotland a ,northern2 it must be granted me1 that ,that part of the ,atmosphere impendent over ,england1 would thereby be exhausted and attenuated1 and the ,mercury would subside1 and the ,vapours which before floated in those parts of the ,air of equal ,gravity with themselves1 would sink to the ,earth4 #b4 ,why in serene good settled weather the ,mercury is generally high8 ,to this ,i ,answer1 ,that the greater height of the ,barometer1 is occasion'd by two contrary ,winds blowing towards the place of ,observation1 whereby the ,air of other places is brought thither and accumulated2 so that the incumbent ,cylinder of ,air being encreas'd both in height and weight1 the ,mercury press'd thereby must needs rise and stand high1 as long as the ,winds continue so to blow2 and then the ,air being specifically heavier1 the ,vapours are better kept suspended1 so that they have no inclination to ,prcipitate and fall down in ,drops1 which is the reason of the serene good ,weather1 which attends the greater heights of the ,mercury4 #c4 ,why upon very great ,winds or ,storms1 tho' accompanied with no ,rain1 the ,mercury sinks lowest of all1 with relation to the ,point of the ,compass upon which the ,wind blows8 ,this is caus'd by the very rapid ,motion of the ,air in these ,storms2 for the ,tract or ,region of the ,earths ,surface1 wherein these ,winds rage1 not extending all round the ,globe1 that stagnant ,air which is left behind1 as likewise that on the sides1 cannot come in so fast as to supply the ,evacuation made by so swift a ,current2 so that the ,air must necessarily be attenuated1 when and where the said ,winds continue to blow1 and that more or less1 according to their ,violence2 add to which1 that the ,horizontal ,motion of the ,air being so quick as it is1 may in all probability take off some part of the perpendicular pressure thereof2 and the great ,agitation of its ,particles1 is the ,reason why the ,vapours are dissipated1 and do not condense into ,drops1 so as to form ,rain1 otherwise the natural ,consequence of the ,airs ,rarifaction4 #d4 ,why cteris paribus the ,mercury stands highest upon an ,easterly or ,north-,easterly ,wind8 ,this happens because that in the great ,atlantick ,ocean1 on this side the thirty fifth ,degree of ,north ,latitude1 the ,westerly and ,south-,westerly ,trade-,winds blow almost always2 so that whenever here the ,wind comes up at ,east and ,north-,east1 'tis sure to be checked by a contrary ,gale1 as soon as it reaches the ,ocean2 wherefore1 according to what is made out in our second ,remark1 the ,air must needs be heaped over this ,island2 and consequently the ,mercury must stand high1 as often as these ,winds blow4 ,this holds true in this ,country1 but is not a general ,rule for others1 where the ,winds are under different ,circumstances2 and ,i have sometimes seen the ,mercury here as low as twenty nine ,inches1 upon an ,easterly ,wind1 but then it blows exceeding hard1 and so comes to be accounted for by what was observ'd upon the third ,remark4 #e4 ,why in calm ,weather the ,mercury generally stands high8 ,the cause hereof is1 as ,i conceive1 that it seldom freezes but when the ,winds come out of the ,northern and ,north-,eastern ,quarters1 or at least unless those ,winds blow at no great distance off2 for the ,northern ,parts of ,germany1 ,denmark1 ,sweden1 ,norway1 and all that ,tract from whence ,north-,eastern ,winds come1 are subject to almost continual ,frost all the ,winter2 and thereby the lower ,air is very much condens'd1 and in that ,state is brought hitherwards by these ,winds1 and being accumulated by the opposition of the ,westerly ,wind blowing in the ,ocean1 the ,mercury must needs be prest to a more than ordinary height1 and as a concurring ,cause1 the shrinking of the lower parts of the ,air into lesser room by cold1 must needs cause a descent of the upper parts of the ,atmosphere1 to reduce the ,cavity made by this contraction to an quilibrium4 #f4 ,why after very great ,storms of ,wind1 when the ,mercury has been very low1 it generally rises again very fast8 ,this ,i have frequently observed1 and once found it risen an ,inch and a half in less than six ,hours1 after a long continu'd ,storm of ,south-,west ,wind4 ,this seems to be occasion'd by the sudden ,accession of new ,air to supply the great ,evacuation which such continu'd ,storms make thereof1 in those places whence they happen 7as in the third ,remark7 and by the ,recoile of the ,air1 after the force ceases that impelled it2 and the ,reason why the ,mercury rises so fast1 is because the ,air being very much rarify'd beyond its mean density1 the ,neighbouring ,air runs in the more swiftly to bring it to an quilibration1 as we see ,water runs the faster for having a great declivity4 #g4 ,why in more ,northerly places the ,variations of the ,baroscope are greater than in the ,southerly8 ,the truth of the ,matter of ,fact is prov'd from ,observations made at ,clermont and ,paris1 compar'd with others1 made at ,stockholm1 as may be seen in the ,appendix to ,mr4 ,pascal's ,book before-cited4 ,the ,reason ,i conjecture to be1 that the more ,northerly ,parts have usually greater ,storms of ,wind than the more ,southerly1 whereby the ,mercury should sink lower in that ,extream2 and then the ,northerly ,winds bringing the condens'd and ponderous ,air from the ,neighbourhood of the ,pole1 and that again being check'd by a ,southerly ,wind1 at no great distance1 and so heaped1 must of necessity make the ,mercury in such case stand higher in the other ,extream4 #h4 ,and ,lastly1 ,why near the quinoctial1 as at ,barbadoes and ,st4 ,helena1 there is very little or no ,variation of the height of the ,barometer8 ,this ,remark1 above all others1 confirms the ,hypothesis of the variable ,winds1 being the cause of these ,variations of the height of the ,mercury2 for in the ,places above-named1 there is always an easie ,gale of ,wind blowing nearly upon the same ,point1 viz4 ,e4 ,n4 ,e4 at ,barbadoes1 and ,e4 ,s4 ,e4 at ,st4 ,helena2 so that there being no contrary ,currents of the ,air1 to exhaust or accumulate it1 the ,atmosphere continues much in the same ,state4 ,however1 upon ,hurricanes1 the most violent of ,storms1 the ,mercury has been observ'd very low1 but this is but for once in two or three ,years1 and it soon recovers its settled state of about #bi ,inches4 ,i doubt not but the same thing is in the ,east ,coast of ,africa1 and in ,india1 where the ,monsoons or ,trade-,winds are for half the ,year one way1 and half the ,year another2 only it's probable1 that there may something worth noting happen1 about the times of the change or shifting of the ,winds1 which might be obtain'd1 if any ,body had the ,curiosity to keep the ,barometer at our ,factories in ,india4 ,i doubt not but this ,doctrine will find some ,opposers1 and that one principal ,objection will be1 that ,i suppose the ,air sometimes to move from those ,parts where it is already evacuated below the quilibrium1 and sometimes again towards those parts1 where it is condens'd and crouded above the mean ,state1 which may be thought contradictory to the ,laws of ,staticks and the ,rules of the quilibrium of ,fluids4 ,but those that shall consider how1 when once an impetus is given to a ,fluid ,body1 it is capable of mounting above its ,level1 and checking others that have a contrary tendency to descent by their own ,gravity1 will no longer regard this as a material ,obstacle1 but will rather conclude1 that the great ,analogy there is between the rising and falling of the ,water upon the ,flux and ,reflux of the ,sea1 and this of the accumulating and extenuating the ,air1 is a great ,argument for the ,truth of this ,hypothesis3 ,for as the ,sea over against the ,coast of ,essex1 rises and swells by the meeting of the two contrary ,tides of ,flood1 7whereof the one comes from the ,s4 ,w4 along the ,channel of ,england1 and the other from the ,north72 and on the contrary sinks below its ,level upon the retreat of the ,water both ways in the ,tide of ,ebb2 so it is very probable that the ,air may ,ebb and ,flow1 after the same manner2 but by reason of the diversity of ,causes1 whereby the ,air may be set in moving1 the times of these ,fluxes and ,refluxes thereof1 are purely ,casual1 and not reducible to any ,rule1 as are the ,motions of the ,sea1 depending wholly upon the regular ,course of the ,moon4 ,illustration3 ,plate #a4 pag4 #ig ,a ,letter of ,mr4 ,isaac ,newton1 ,professor of the ,mathematicks in the ,university of ,cambridge2 containing his ,new ,theory about ,light and ,colours3 ,sent by the ,author to the ,publisher from ,cambridge1 ,feb4 #f4 #afga_/b2 in order to be communicated to the ,royal ,society4 ,,sir1 ,to perform my late promise to you1 ,i shall without further ,ceremony acquaint you1 ,that in the beginning of the ,year #afff 7at which time ,i apply'd my self to the grinding of ,optick-glasses of other ,figures than ,spherical17 ,i procur'd me a ,triangular ,glass-,prism1 to try therewith the celebrated ,phnomena of ,colours4 ,and in order thereto1 having darken'd my ,chamber1 and made a small hole in my ,window-shuts1 to let in a convenient quantity of the ,sun's ,light1 ,i plac'd my ,prism at his entrance1 that it might be thereby refracted to the opposite ,wall4 ,it was at first a very pleasing ,divertisement1 to view the vivid and intense ,colours produced thereby2 but after a while applying my self to consider them more circumspectly1 ,i became surpriz'd to see them in an oblong ,form2 which1 according to the received ,laws of ,rarefraction1 ,i expected should have been ,circular4 ,they were terminated at the sides with streight ,lines1 but at the ends1 the decay of ,light was so gradual1 that it was difficult to determine justly1 what was their ,figure2 yet they seem'd ,semicircular4 ,comparing the length of this colour'd ,spectrum with its breadth1 ,i found it about five times greater2 a disproportion so extravagant1 that it excited me to a more than ordinary ,curiosity of examining1 from whence it might proceed4 ,i could scarce think1 that the various thickness of the ,glass1 or the termination with shadow or darkness1 could have any ,influence on ,light to produce such an effect2 yet ,i thought it not amiss1 first to examine those ,circumstances1 and so try'd what would happen by transmitting ,light through parts of the ,glass of divers thicknesses1 or through holes in the ,window of divers bignesses1 or by setting the ,prism without1 so that the ,light might pass through it1 and be refracted before it was terminated by the hole3 ,but ,i found none of those ,circumstances material4 ,the fashion of the ,colours was1 in all these ,cases1 the same4 ,then ,i suspected1 whether by any unevenness in the ,glass1 or other contingent ,irregularity1 these ,colours might be thus dilated4 ,and to try this1 ,i took another ,prism like the former1 and so plac'd it1 that the ,light passing through them both1 might be refracted contrary ways1 and so by the latter return'd into that ,course1 from which the former had diverted it4 ,for1 by this means1 ,i thought the regular effects of the first ,prism would be destroy'd by the second ,prism1 but the irregular ones more augmented by the multiplicity of ,refractions4 ,the ,event was1 that the ,light1 which by the first ,prism was diffused into an oblong ,form1 was1 by the second1 reduc'd into an orbicular one1 with as much regularity1 as when it did not at all pass through them4 ,so that whatever was the cause of that length1 'twas not any contingent ,irregularity4 ,i then proceeded to examine more critically1 what might be effected by the difference of the incidence of ,rays coming from divers parts of the ,sun2 and to that end1 measur'd the several ,lines and ,angles belonging to the ,image4 ,its distance from the ,hole or ,prism was twenty two ,foot2 its utmost length #ac ,inches2 its breadth #b2 the ,diameter of the ,hole of an ,inch2 the ,angle1 with the ,rays1 tending towards the middle of the ,image1 made with those ,lines1 in which they would have proceeded without ,refraction1 was #dd #ef'4 ,and the ,vertical ,angle of the ,prism1 #fc #ab'4 ,also the ,refractions on both sides the ,prism1 that is1 of the ,incident1 and ,emergent ,rays1 were as near1 as ,i could make them1 equal1 and consequently about #ed #d'4 ,and the ,rays fell perpendicularly upon the ,wall4 ,now subducting the ,diameter of the ,hole from the length and breadth of the ,image1 there remains #ac ,inches the length1 and #b the breadth1 comprehended by those ,rays1 which passed thro' the ,center of the said ,hole1 and consequently the ,angle of the ,hole1 which that breadth subtended1 was about #ca'1 answerable to the ,sun's ,diameter2 but the ,angle1 which its length subtended1 was more than five such ,diameters1 namely #b #di'4 ,having made these ,observations1 ,i first computed from them the refractive ,power of that ,glass1 and found it measur'd by the ratio of the ,sines1 twenty to thirty one4 ,and then1 by that ratio1 ,i computed the ,refractions of two ,rays flowing from opposite parts of the ,sun's discus1 so as to differ #ca' in their obliquity of ,incidence1 and found that the emergent ,rays should have comprehended an ,angle of about #ca'1 as they did1 before they were incident4 ,but because this ,computation was founded on the ,hypothesis of the proportionality of the ,sines of ,incidence and ,refraction1 which1 tho' by my own ,experience ,i could not imagine to be so erroneous as to make that ,angle but #ca'1 which in reality was #b #di'2 yet my ,curiosity caus'd me again to take my ,prism4 ,and having plac'd it at my ,window1 as before1 ,i observ'd1 that by turning it a little about its ,axis to and fro1 so as to vary its obliquity to the light1 more than an ,angle of four or five ,degrees1 the ,colours were not thereby sensibly translated from their place on the ,wall1 and consequently by that ,variation of ,incidence1 the quantity of ,refraction was not sensibly varied4 ,by this ,experiment therefore1 as well as by the former ,computation1 it was evident1 that the difference of the ,incidence of ,rays1 flowing from divers parts of the ,sun could not make them1 after decussation1 diverge at a sensibly greater ,angle1 than that at which they before converged2 which being1 at most1 but about thirty one or thirty two ,minutes1 there still remain'd some other cause to be found out1 from whence it could be two ,deg4 #di ,min4 ,then ,i began to suspect1 whether the ,rays1 after their ,trajection through the ,prism1 did not move in curve ,lines1 and according to their more or less ,curvity1 tend to divers parts of the ,wall4 ,and it increas'd my suspicion1 when ,i remember'd that ,i had often seen a ,tennis-,ball1 struck with an oblique ,racket1 describe such a curve ,line4 ,for a ,circular as well as a ,progressive ,motion being communicated to it by that stroak1 its parts on that side1 where the ,motions conspire1 must press and beat the contiguous ,air more violently than on the other1 and there excite a ,reluctancy and ,reaction of the ,air proportionably greater4 ,and for the same ,reason1 if the ,rays of ,light should possibly be globular ,bodies1 and by their oblique ,passage out of one ,medium into another1 acquire a circulating ,motion1 they ought to feel the greater resistance from the ambient ther1 on that side1 where this ,motion conspires1 and thence be continually bowed to the other4 ,but notwithstanding this plausible ground of suspicion1 when ,i came to examine it1 ,i could observe no such ,curvity in them4 ,and besides 7which was enough for my purpose7 ,i observ'd1 that the difference 'twixt the length of the ,image1 and ,diameter of the ,hole1 through which the ,light was transmitted1 was proportionable to their distance4 ,the gradual removal of these suspicions1 at length led me to the ,experimentum ,crucis1 which was this2 ,i took two ,boards1 and plac'd one of them close behind the ,prism at the ,window1 so that the light might pass through a small hole1 made in it for the purpose1 and fall on the other ,board1 which ,i plac'd at about twelve ,feet distance1 having first made a small hole in it also1 for some of that incident ,light to pass through4 ,then ,i plac'd another ,prism behind this second ,board1 so that the ,light1 trajected through both the ,boards1 might pass thro' that also1 and be again refracted before it arrived at the ,wall4 ,this done1 ,i took the first ,prism in my ,hand1 and turn'd it to and fro slowly about its ,axis1 so much as to make the several parts of the ,image1 cast on the second ,board1 successively pass through the hole in it1 that ,i might observe to what places on the ,wall the second ,prism would refract them4 ,and ,i saw by the ,variation of those places1 that the ,light1 tending to that end of the ,image1 towards which the ,refraction of the first ,prism was made1 did1 in the second ,prism1 suffer a ,refraction considerably greater than the ,light tending to the other end4 ,and so the true cause of the length of that ,image was detected to be no other1 than that ,light consists of ,rays differently refrangible1 which1 without any respect to a difference in their incidence1 were1 according to their degrees of ,refrangibility1 transmitted towards divers parts of the ,wall4 ,when ,i understood this1 ,i left off my aforesaid ,glass ,works2 for ,i saw1 that the perfection of ,telescopes was hitherto limited1 not so much for want of ,glasses truly figur'd1 according to the prescriptions of ,optick ,authors 7which all ,men have hitherto imagin'd71 as because that ,light it self is a ,heterogeneous mixture of differently refrangible ,rays4 ,so that1 were a ,glass so exactly figur'd1 so as to collect any one sort of ,rays into one ,point1 it could not collect those also into the same ,point1 which having the same ,incidence upon the same ,medium1 are apt to suffer a different ,refraction4 ,nay1 ,i wonder'd1 that seeing the difference of ,refrangibility was so great1 as ,i found it1 ,telescopes should arrive to that perfection they are now at4 ,for1 measuring the ,refractions in one of my ,prisms1 ,i found1 that1 supposing the common ,sine of ,incidence upon one of its plains1 was forty four ,parts1 the ,sine of ,refraction of the utmost ,rays on the red end of the ,colours1 made out of the ,glass into the ,air1 would be sixty eight parts1 and the ,sine of ,refraction of the utmost ,rays on the other end1 sixty nine parts2 so that the difference is about a twenty fourth or twenty fifth part of the whole ,refraction4 ,and consequently the ,object glass of any ,telescope cannot collect all the ,rays1 which come from one point of an ,object1 so as to make them convene at its ,focus in less room than in a ,circular space1 whose ,diameter is the fiftieth part of the ,diameter of its ,aperture2 which is an irregularity1 some hundred of times greater1 than a circularly figur'd ,lens1 of so small a section as the ,object-glasses of long ,telescopes are1 would cause by the unfitness of its ,figure1 were ,light uniform4 ,this made me take ,reflections into ,consideration1 and finding them regular1 so that the ,angle of ,reflection of all sorts of ,rays was equal to their ,angle of ,incidence2 ,i understood1 that by their mediation1 ,optick ,instruments might be brought to any degree of ,perfection imaginable1 provided a ,reflecting ,substance could be found1 which would polish as finely as ,glass1 and reflect as much ,light as ,glass transmits2 and the art of communicating to it a ,parabolick ,figure be also attain'd4 ,but there seem'd very great ,difficulties1 and ,i have almost thought them insuperable1 when ,i further consider'd1 that every ,irregularity in a reflecting ,superficies makes the ,rays stray five or six times more out of their due course1 than the like ,irregularities in a refracting one2 ,so that a much greater ,curiosity would be here requisite1 than in ,figuring ,glasses for ,refraction4 ,amidst these ,thoughts ,i was forc'd from ,cambridge by the ,intervening ,plague1 and it was more than two ,years before ,i proceeded further4 ,but then having thought on a tender way of polishing1 proper for ,metal1 whereby1 as ,i imagin'd1 the ,figure also would be corrected to the last2 ,i began to try what might be effected in this kind1 and by degrees so far perfected an ,instrument 7in the essential parts of it like that ,i sent to ,london17 by which ,i could discern ,jupiter's four ,concomitants1 and shew'd them divers times to two others of my ,acquaintance4 ,i could also discern the ,moon-like ,phase of ,venus1 but not very distinctly1 nor without some niceness in disposing the ,instrument4 ,from that time ,i was interrupted1 till this last ,autumn1 when ,i made the other4 ,and as that was sensibly better than the first 7especially for ,day-,objects17 so ,i doubt not but they will be still brought to a much greater perfection by their ,endeavours1 who1 as you inform me1 are taking care about it at ,london4 ,i have sometimes thought to make a ,microscope1 which in like manner should have1 instead of an ,object-glass1 a reflecting piece of ,metal4 ,and this ,i hope they will also take into ,consideration3 ,for those ,instruments seem as capable of improvement as ,telescopes1 and perhaps more1 because but one reflective piece of ,metal is requisite in them1 as you may perceive in ,plate #c4 ,fig4 #a4 where ,,ab representeth the ,object ,metal1 ,,cd the ,eye-glass1 ,f their common ,focus1 and ,o the other ,focus of the ,metal1 in which the ,object is placed4 ,but to return from this digression1 ,i told you1 that ,light is not similar1 or homogeneal1 but consists of difform ,rays1 some of which are more refrangible than others3 ,so that of those1 which are alike incident on the same ,medium1 some shall be more refracted than others1 and that not by any virtue of the ,glass1 or other external ,cause1 but from a predisposition1 which every particular ,ray hath to suffer a particular degree of ,refraction4 ,i shall now proceed to acquaint you with another more notable deformity in its ,rays1 wherein the ,origin of ,colours is unfolded3 ,concerning which ,i shall lay down the ,doctrine first1 and then1 for its ,examination1 give you an ,instance or two of the ,experiments1 as a ,specimen of the rest4 ,the ,doctrine you will find comprehended and illustrated in the following ,propositions4 #a4 ,as the ,rays of ,light differ in degrees of ,refrangibility1 so they also differ in their disposition to exhibit this or that particular ,colour4 ,colours are not ,qualifications of ,light1 derived from ,refractions1 or ,reflections of natural ,bodies1 7as 'tis generally believed7 but ,original and connate ,properties1 which in divers ,rays are divers4 ,some ,rays are disposed to exhibit a red ,colour and no other2 some a yellow and no other1 some a green and no other1 and so of the rest4 ,nor are there only ,rays proper and particular to the more eminent ,colours1 but even to all their intermediate ,gradations4 #b4 ,to the same degree of ,refrangibility ever belongs the same ,colour1 and to the same ,colour ever belongs the same degree of ,refrangibility4 ,the least ,refrangible ,rays are all disposed to exhibit a ,red ,colour1 and contrarily those ,rays1 which are disposed to exhibit a ,red ,colour1 are all the least ,refrangible3 ,so the most ,refrangible ,rays are all disposed to exhibit a deep ,violet ,colour1 and contrarily those which are apt to exhibit such a ,violet ,colour1 are all the most ,refrangible4 ,and so to all the intermediate ,colours in a continued ,series belong intermediate degrees of ,refrangibility4 ,and this ,analogy 'twixt ,colours1 and ,refrangibility1 is very precise and strict2 the ,rays always either exactly agreeing in both1 or proportionally disagreeing in both4 #c4 ,the ,species of ,colour1 and ,degree of ,refrangibility proper to any particular sort of ,rays1 is not mutable by ,refraction1 nor by ,reflection from ,natural ,bodies1 nor by any other ,cause1 that ,i could yet observe4 ,when any one sort of ,rays hath been well parted from those of other kinds1 it hath afterwards obstinately retain'd its ,colour1 notwithstanding my utmost ,endeavours to change it4 ,i have refracted it with ,prisms1 and reflected it with ,bodies1 which in ,day-light were of other ,colours2 ,i have intercepted it with the colour'd ,film of ,air interceding two compressed ,plates of ,glass2 transmitted it through colour'd ,mediums1 and through ,mediums irradiated with other sorts of ,rays1 and diversly terminated it1 and yet could never produce any new ,colour out of it4 ,it would by contracting and dilating become more brisk1 or faint1 and by the loss of many ,rays in some ,cases very obscure and dark2 but ,i could never see it chang'd in specie4 #d4 ,yet seeming ,transmutations of ,colours may be made1 where there is any mixture of divers sorts of ,rays4 ,for in such mixtures1 the component ,colours appear not1 but by their mutual allaying each other1 constitute a midling ,colour4 ,and therefore1 if by ,refraction1 or any other of the aforesaid ,causes1 the difform ,rays1 latent in such a mixture1 be separated1 there shall emerge ,colours different from the colour of the ,composition4 ,which ,colours are not new generated1 but only made apparent by being parted2 for if they be again intirely mix'd and blended together1 they will again compose that ,colour1 which they did before separation4 ,and for the same reason1 ,transmutations made by the convening of divers ,colours are not real2 for when the difform ,rays are again severed1 they will exhibit the very same ,colours1 which they did before they entered the ,composition2 as you see1 ,blue and ,yellow ,powders1 when finely mixed1 appear to the naked ,eye ,green1 and yet the ,colours of the component ,corpuscles are not thereby really transmuted1 but only blended4 ,for1 when viewed with a good ,microscope1 they still appear ,blue and ,yellow interspersedly4 #e4 ,there are therefore two sorts of ,colours4 ,the one ,original and ,simple1 the other compounded of these4 ,the ,original or ,primary ,colours are1 ,red1 ,yellow1 ,green1 ,blue1 and a ,violet-purple1 together with ,orange1 ,indico1 and an indefinite variety of intermediate ,gradations4 #f4 ,the same ,colours in ,specie with these primary ,ones1 may be also produced by ,composition3 ,for1 a mixture of ,yellow and ,blue makes ,green2 of ,red and ,yellow1 makes ,orange2 of ,orange and ,yellowish ,green1 makes ,yellow4 ,and in general1 if any two ,colours be mix'd1 which in the ,series of those1 generated by the ,prism1 are not too far distant one from another1 they by their mutual ,alloy compound that ,colour1 which in the said ,series appeareth in the mid-way between them4 ,but those1 which are situated at too great a distance1 do not so4 ,orange and ,indico produce not the intermediate ,green1 nor ,scarlet and ,green the intermediate ,yellow4 #g4 ,but the most surprizing and wonderful ,composition was that of ,whiteness4 ,there is no one sort of ,rays which alone can exhibit this4 ',tis ever compounded1 and to its ,composition are requisite all the aforesaid primary ,colours1 mix'd in a due proportion4 ,i have often with admiration beheld1 that all the ,colours of the ,prism being made to converge1 and thereby to be again mixed as they were in the light before it was incident upon the ,prism1 reproduced light1 intirely and perfectly white1 and not at all sensibly differing from a direct light of the ,sun1 unless when the ,glasses1 ,i used1 were not sufficiently clear2 for then they would a little incline it to their ,colour4 #h4 ,hence therefore it comes to pass1 that ,whiteness is the usual ,colour of ,light2 for ,light is a confused aggregate of ,rays1 indued with all sorts of ,colours1 as they are promiscuously darted from the various parts of luminous ,bodies4 ,and of such a confused aggregate1 as ,i said1 is generated ,whiteness1 if there be a due proportion of the ,ingredients2 but if any one predominate1 the ,light must incline to that ,colour2 as it happens in the blue ,flame of ,brimstone1 the yellow ,flame of a ,candle1 and the various ,colours of the fixed ,stars4 #i4 ,these things consider'd1 the manner1 how ,colours are produced by the ,prism1 is evident4 ,for1 of the ,rays1 constituting the incident ,light1 since those which differ in ,colour proportionally differ in ,refrangibility1 they by their unequal ,refractions must be severed and dispersed into an oblong ,form1 in an orderly succession1 from the least refracted ,scarlet to the most refracted ,violet4 ,and for the same reason it is1 that ,objects1 when look'd upon through a ,prism1 appear coloured4 ,for the difform ,rays1 by their unequal ,refractions1 are made to diverge towards several parts of the ,retina1 and there express the ,images of things coloured1 as in the former case they did the ,sun's ,image upon a ,wall4 ,and by this inequality of ,refractions1 they become not only coloured1 but also very confused and indistinct4 #aj4 ,why the ,colours of the ,rainbow appear in falling drops of ,rain1 is also from hence evident4 ,for those drops1 which refract the ,rays1 disposed to appear ,purple1 in greatest quantity to the ,spectator's ,eye1 refract the ,rays of other sorts so much less1 as to make them pass beside it2 and such are the drops on the inside of the ,primary ,bow1 and on the outside of the ,secondary or ,exteriour one4 ,so those drops1 which refract in greatest plenty the ,rays1 apt to appear red1 toward the ,spectator's ,eye1 refract those of other sorts so much more1 as to make them pass beside it2 and such are the drops on the ,exteriour part of the ,primary1 and ,interiour part of the ,secondary ,bow4 #aa4 ,the odd ,phnomena of an infusion of ,lignum ,nephriticum1 ,leaf-gold1 ,fragments of colour'd ,glass1 and some other transparently coloured ,bodies1 appearing in one ,position of one ,colour1 and of another in another1 are on these grounds no longer ,riddles4 ,for those are ,substances apt to reflect one sort of ,light1 and transmit another2 as may be seen in a dark ,room1 by illuminating them with similar or uncompounded ,light4 ,for then they appear of that ,colour only1 with which they are illuminated2 but yet in one ,position more vivid and luminous than in another1 accordingly as they are disposed more or less to reflect or transmit the incident ,colour4 #ab4 ,from hence also is manifest the reason of an unexpected ,experiment1 which ,mr4 ,hook1 somewhere in his ,micrography1 relates to have made with two wedge-like transparent ,vessels fill'd1 the one with a red1 the other with a blue ,liquor2 namely1 that though they were severally transparent enough1 yet both together became opake3 ,for1 if one transmitted only red1 and the other only blue1 no ,rays could pass through both4 #ac4 ,i might add more ,instances of this ,nature2 but ,i shall conclude with this general one1 that the ,colours of all natural ,bodies have no other ,origin than this1 that they are variously qualified to reflect one sort of ,light in greater plenty than another4 ,and this ,i have experimented in a dark ,room1 by illuminating those ,bodies with uncompounded ,light of divers ,colours4 ,for by that means any body may be made to appear of any ,colour4 ,they have there no appropriate ,colour1 but ever appear of the ,colour of the ,light cast upon them2 but yet with this difference1 that they are most brisk and vivid in the ,light of their own day-light-colour4 ,minium appeareth there of any ,colour indifferently1 with which 'tis illustrated1 but yet most luminous in red2 and so ,bise appeareth indifferently of any ,colour with which 'tis illustrated1 but yet most luminous in blue4 ,and therefore ,minium reflecteth ,rays of any ,colour1 but most copiously those endu'd with red1 and consequently when illustrated with day-light1 that is1 with all sorts of ,rays promiscuously blended1 those qualified with red1 shall abound most in the reflected ,light1 and by their prevalence cause it to appear of that ,colour4 ,and for the same reason ,bise1 reflecting blue most copiously1 shall appear blue by the excess of those ,rays in its reflected ,light2 and the like of other ,bodies4 ,and that this is the intire and adequate cause of their ,colours1 is manifest1 because they have no power to change or alter the ,colours of any sort of ,rays incident apart1 but put on all ,colours indifferently1 with which they are enlightned4 ,these things being so1 it can be no longer disputed1 whether there be ,colours in the dark1 nor whether they be the ,qualities of the ,objects we see1 no nor perhaps1 whether ,light be a ,body4 ,for1 since ,colours are the ,qualities of ,light1 having its ,rays for their intire and immediate ,subject1 how can we think those ,rays ,qualities also1 unless one ,quality may be the ,subject of and sustain another2 which in effect is to call it ,substance8 ,we should not know ,bodies for ,substances1 were it not for their sensible ,qualities2 and the principal of those being now found due to something else1 we have as good reason to believe that to be a ,substance also4 ,besides1 whoever thought any ,quality to be a heterogeneous ,aggregate1 such as ,light is discovered to be8 ,but to determine more absolutely1 what ,light is1 after what manner refracted1 and by what ,modes or ,actions it produceth in our ,minds the ,phantasms of ,colours1 is not so easie4 ,and ,i shall not mingle ,conjectures with ,certainties4 ,reviewing what ,i have written1 ,i see the ,discourse it self will lead to divers ,experiments sufficient for its ,examination2 and therefore ,i shall not trouble you farther1 than to describe one of those1 which ,i have already insinuated4 ,in a darkned ,room1 make a hole in the shut of a ,window1 whose ,diameter may conveniently be about a third part of an ,inch1 to admit a convenient quantity of the ,sun's ,light4 ,and there place a clear and colourless ,prism1 to refract the entring ,light towards the farther part of the ,room2 which1 as ,i said1 will thereby be diffused into an oblong coloured ,image4 ,then place a ,lens of about three ,foot ,radius 7suppose a broad ,object-glass of a three ,foot ,telescope17 at the distance of about four or five ,foot from thence1 through which all those ,colours may at once be transmitted1 and made by its ,refraction to convene at a farther distance of about ten or twelve ,feet4 ,if at that distance you intercept this ,light with a ,sheet of white ,paper1 you will see the ,colours converted into whiteness again by being mingled4 ,but it is requisite1 that the ,prism and ,lens be placed steady1 and that the ,paper1 on which the ,colours are cast1 be moved to and fro2 for1 by such motion1 you will not only find at what distance the whiteness is most perfect1 but also see how the ,colours gradually convene1 and vanish into whiteness2 and afterwards1 having crossed one another in that place where they compound whiteness1 are again dissipated and severed1 and in an inverted order retain the same ,colours1 which they had before they entred the ,composition4 ,you may also see1 that1 if any of the ,colours at the ,lens be intercepted1 the whiteness will be changed into the other ,colours4 ,and therefore1 that the ,composition of whiteness be perfect1 care must be taken that none of the ,colours fall besides the ,lens4 ,in the annexed ,design1 ,tab4 #c4 ,fig4 #b4 of this ,experiment1 ,,abc expresseth the ,prism set end-wise to sight1 close by the hole ,f of the ,window ,,eg4 ,its vertical ,angle ,,abc may conveniently be about #fj ,degrees3 ,,mn designeth the ,lens4 ,its breadth #b or #c ,inches4 ,,sf one of the streight ,lines1 in which difform ,rays may be conceived to flow successively from the ,sun4 ,,fp1 and ,,fr two of those ,rays unequally refracted1 which the ,lens makes to converge towards ,q1 and after decussation to diverge again4 ,and ,,hi the ,paper1 at divers distances1 on which the ,colours are projected1 which in ,q constitute ,whiteness1 but are ,red and ,yellow in ,r1 r1 and 1 and ,blue and ,purple in ,p1 p1 and 4 ,if you proceed further to try the impossibility of changing any uncompounded ,colour 7which ,i have asserted in the third and thirteenth ,propositions17 'tis requisite that the ,room may be very dark1 lest any scattering light1 mixing with the ,colour1 disturb and allay it1 and render it compound1 contrary to the design of the ,experiment4 ',tis also requisite1 that there be a perfecter separation of the ,colours1 than1 after the manner above described1 can be made by the ,refraction of one single ,prism2 and how to make such farther separations1 will scarce be difficult to them1 that consider the discovered ,laws of ,refractions4 ,but if trial shall be made with ,colours not throughly separated1 there must be allowed changes proportionable to the mixture4 ,thus if compound ,yellow ,light fall upon blue ,bise1 the ,bise will not appear perfectly yellow1 but rather green1 because there are in the yellow mixture many ,rays indued with green1 and green being less remote from the usual blue ,colour of ,bise than yellow1 is the more copiously reflected by it4 ,in like manner1 if any one of the ,prismatick ,colours1 suppose red1 be intercepted1 on design to try the asserted impossibility of reproducing that ,colour out of the others which are pretermitted2 'tis necessary1 either that the ,colours be very well parted before the red be intercepted2 or that1 together with the red1 the neighbouring ,colours1 into which any red is secretly dispersed1 7that is1 the yellow1 and perhaps green too7 be intercepted2 or else1 that allowance be made for the emerging of so much red out of the yellow green1 as may possibly have been diffused1 and scatteringly blended in those ,colours4 ,and if these things be observed1 the new ,production of red1 or any intercepted ,colour1 will be found impossible4 ,this1 ,i conceive1 is enough for an ,introduction to ,experiments of this kind2 which if any of the ,royal ,society shall be so curious as to prosecute1 ,i should be very glad to be informed with what success3 ,that1 if any thing seem to be defective1 or to thwart this ,relation1 ,i may have an opportunity of giving farther ,direction about it1 or of acknowledging my ,errors1 if ,i have committed any4 ,since the ,publication of this ,theory1 some ,misunderstandings happening between a ,french ,philosopher at ,paris and ,mr4 ,newton1 he has endeavour'd to explain himself a little further in these ,things1 according to the following ,method4 ,,definitions4 #a4 ,i call that ,light ,homogeneal1 ,similar1 or ,uniform1 whose ,rays are equally refrangible4 #b4 ,and that ,heterogeneal1 whose ,rays are unequally refrangible4 ,note1 ,there are but three ,affections of ,light in which ,i have observ'd its ,rays to differ2 viz4 ,refrangibility1 ,reflexibility1 and ,colour2 and those ,rays which agree in ,refrangibility1 agree also in the other two1 and therefore may well be defined ,homogeneal2 especially since ,men usually call those things ,homogeneal1 which are so in all ,qualities that come under their ,knowledge1 tho' in other ,qualities1 that their ,knowledge extends not to1 there may possibly be some ,heterogeneity4 #c4 ,those ,colours ,i call ,simple or ,homogeneal1 which are exhibited by ,homogeneal ,light4 #d4 ,and those ,compound or ,heterogeneal1 which are exhibited by ,heterogeneal ,light4 #e4 ,different ,colours1 ,i call1 not only the more eminent ,species1 ,red1 ,yellow1 ,green1 ,blue1 ,purple1 but all other the minutest ,gradations2 much after the same manner1 that not only the more eminent ,degrees in ,musick1 but all the lead ,gradations1 are esteem'd different ,sounds4 ,,propositions4 #a4 ,the ,sun's ,light consists of ,rays differing by indefinite ,degrees of ,refrangibility4 #b4 ,rays which differ in ,refrangibility1 when parted from one another1 do proportionally differ in the ,colours which they exhibit4 ,these ,two ,propositions are ,matter of ,fact4 #c4 ,there are as many ,simple or ,homogeneal ,colours1 as ,degrees of ,refrangibility4 ,for to every ,degree of ,refrangibility belongs a different ,colour1 by ,prop4 #b4 and that ,colour is ,simple1 by ,def4 #a1 and #c4 #d4 ,whiteness1 in all respects like that of the ,sun's immediate ,light1 and of all the usual ,objects of our ,senses1 cannot be compounded of two ,simple ,colours alone4 ,for such a ,composition must be made by ,rays that have only two ,degrees of ,refrangibility1 by ,def4 #a and #c4 and therefore it cannot be like that of the ,sun's ,light4 by ,prop4 #a4 nor1 for the same ,reason1 like that of ordinary white ,objects4 #e4 ,whiteness1 in all respects1 like that of the ,sun's immediate ,light1 cannot be compounded of ,simple ,colours without an indefinite ,variety of them4 ,for to such a ,composition1 there are requisite ,rays endu'd with all the indefinite ,degrees of ,refrangibility1 by ,prop4 #a4 ,and those infer as many ,simple ,colours1 by ,def4 #a and #c4 and ,prop4 #b and #c4 ,to make these a little plainer1 ,i have added also the ,propositions that follow4 #f4 ,the ,rays of ,light do not act on one another1 in passing through the same ,medium4 #g4 ,the ,rays of ,light suffer not any change of their ,qualities from ,refraction4 #h4 ,nor afterwards from the adjacent quiet ,medium3 ,these two ,propositions are manifest de ,facto in ,homogeneal ,light1 whose ,colour and ,refrangibility is not at all changeable1 either by ,refraction1 or by the ,contermination of a quiet ,medium4 ,and as for ,heterogeneal ,light1 it is but an ,aggregate of several sorts of ,homogeneal ,light1 no one sort of which suffers any more alteration than if it were alone2 because the ,rays act not on one another1 by ,prop4 #f4 and therefore the ,aggregate can suffer none4 ,these two ,propositions also might be further proved apart1 by ,experiments too long to be here described4 #i4 ,there can no ,homogeneal ,colours be reduced out of ,light by ,refraction1 which were not commixt in it before4 ,because by ,prop4 #g4 and #h4 ,refraction changeth not the ,qualities of the ,rays1 but only separates those which have divers ,qualities1 by means of their different ,refrangibility4 #aj4 ,the ,sun's ,light is an ,aggregate of an indefinite variety of ,homogeneal ,colours1 by ,prop4 #a1 #c1 and #i4 ,and hence it is1 that ,i call ,homogeneal ,colours also ,primitive or ,original4 ,and thus much concerning ,colours4 ,for a further ,illustration of this ,doctrine1 ,mr4 ,newton1 in his ,book of ,opticks lately published1 has by undeniable ,experiments explained most of the ,principal ,phnomena of ,light and ,colours3 ,to which we refer the ,reader4 ,a ,demonstration concerning the ,motion of ,light1 communicated from ,paris4 ,philosophers have been labouring for many ,years to decide by some ,experiment1 whether the ,action of ,light be conveyed in an instant to distant ,places1 or whether it requireth time4 ,m4 ,romer1 of the ,royal ,academy of ,sciences1 hath devised a way taken from the ,observations of the first ,satellit of ,jupiter1 by which he demonstrates1 that for the distance of about #cjjj ,leagues1 such as is very near the bigness of the ,diameter of the ,earth1 ,light needs not one ,second of ,time4 ,let 7in ,fig4 #c4 ,plate #c47 ,a be the ,sun1 ,b ,jupiter1 ,c the first ,satellit of ,jupiter1 which enters into the shadow of ,jupiter1 to come out at ,d1 and let ,,efghkl be the ,earth1 placed at divers distances from ,jupiter4 ,now suppose the ,earth1 being in ,l1 towards the second ,quadrature of ,jupiter1 hath seen the first ,satellit1 at the time of its emersion1 or issuing out of the shadow at ,d1 and that about #db ,hours after 7viz4 after one ,revolution of this ,satellit7 the ,earth being in ,k1 do see it return'd in ,d3 ,it is manifest1 that if the ,light require time to traverse the ,interval ,,lk1 the ,satellit will be seen return'd later in ,d1 than it would have been if the ,earth had remained in ,l4 ,so that the ,revolution of the ,satellit being thus observ'd by the ,emersions1 will be retarded by so much time1 as the ,light shall have taken in passing from ,l to ,k2 and that on the contrary1 in the other ,quadrature ,,fg1 where the ,earth by approaching goes to meet the ,light1 the ,revolutions of the ,emersions will appear to be shortned1 by so much as those of the ,emersions had appear'd to be lengthned4 ,and because #db ,hours1 which this ,satellit very near takes to make one ,revolution1 the distance between the ,earth and ,jupiter1 in both the ,quadratures1 varies at least #baj ,diameters of the ,earth3 ,it follows1 that if for the ,account of every ,diameter of the ,earth there were required a ,second of ,time1 the ,light would take #c ,minutes for each of the ,intervals ,,gf1 ,,kl2 which would cause near half a quarter of an ,hour between two ,revolutions of the first ,satellit1 one observ'd in ,,fg1 and the other in ,,kl1 whereas there is not observed any sensible difference4 ,yet doth it not follow hence1 that ,light demands no time4 ,for after ,m4 ,romer had examin'd the thing more nearly1 he found that what was not sensible in two ,revolutions1 became very considerable in many being taken together2 and that1 for ,example1 forty ,revolutions observed on the side ,f1 might be sensibly shorter1 than forty others observ'd in any place of the ,zodiack where ,jupiter may be met with2 and that in proportion of ,twenty two for the whole ,interval of ,,he1 which is the double of the ,interval that is from hence to the ,sun4 ,the necessity of this new ,equation of the ,retardment of ,light1 is establish'd by all the ,observations that have been made in the ,royal ,academy1 and in the ,observatory1 for the space of eight ,years2 and it hath been lately confirmed by the ,emersion of the first ,satellit observ'd at ,paris1 the #ith of ,november last1 at #e a-clock #ce' #de at ,night1 #aj ,minutes later than it was to be expected1 by deducting it from those that had been observ'd in the ,month of ,august1 when the ,earth was much nearer to ,jupiter2 which ,m4 ,romer had predicted to the said ,academy from the beginning of ,september4 ,but to remove all doubt1 that this ,inequality is caused by the ,retardment of the ,light1 he demonstrates1 that it cannot come from any ,excentricity1 or other ,cause of those that are commonly alledged to explicate the ,irregularities of the ,moon1 and the other ,planets2 though he be well aware1 that the first ,satellit of ,jupiter was ,excentrick2 and that1 besides his ,revolutions were advanced or retarded1 according as ,jupiter did approach to or recede from the ,sun2 as also1 that the ,revolutions of the ,primum ,mobile were unequal3 ,yet1 saith he1 these three last ,causes of ,inequality do not hinder the first from being manifest4 ,an introductory ,essay to the ,doctrine of ,sounds1 containing some ,proposals for the improvement of ,acousticks2 ,as it was presented to the ,dublin ,society1 ,nov4 #ab4 #afhc1 by the ,right ,reverend ,father in ,god ,narcissus ,lord ,bishop of ,ferns and ,leighlin4 ,being to treat of the ,doctrine of ,sounds1 ,i hold it convenient to premise something in the general1 concerning this ,theory2 which may serve at once to ingage your ,attention1 and excuse my ,pains1 when ,i shall have recommended them1 as bestow'd on a ,subject not altogether useless and unfruitful4 ,and for this purpose ,i shall omit to speak any thing of the ,excellency of the ,matter in ,hand2 though it might be celebrated by ,arguments drawn from several ,topicks1 and particularly from this1 that new ,discoveries and ,improvements may be made1 both as to the ,generation1 ,propagation and ,reception of ,sounds into the ,sense2 which1 in a peculiar manner agrees to this1 above the ,object of any other ,sense whatsoever4 ,i shall1 ,i say1 omit these things1 and apply my self wholly to the ,usefulness of the ,theory1 that we are now falling upon1 which ,i think cannot better be discovered1 than by making a comparison 'twixt the ,senses of ,seeing and ,hearing1 as to their ,improvements4 ,i mean1 by shewing1 that this latter of ,hearing is capable of all those improvements which the ,sense of ,seeing has receiv'd from ,art1 besides many more advantages that the ,ear may enjoy1 by the help of our ,doctrine1 above the ,eye2 all which moreover will be of as great benefit to ,mankind1 as any thing that ,opticks have yet discover'd1 if not of greater2 which1 with some other pre-eminencies that it has upon another ,score1 will happily render ,acousticks the nobler ,science of the two4 ,in order to the making good what ,i but now premised of the ,comparison of these two ,faculties of ,seeing and ,hearing1 as to their ,improvements1 ,i observe2 ,that ,vision is threefold1 ,direct1 ,refracted1 and ,reflex'd2 answerable whereunto we have ,opticks1 ,dioptricks1 and ,catoptricks4 ,in like manner ,hearing may be divided into ,direct1 ,refracted and ,reflex'd2 whereto answer three parts of our ,doctrine of ,acousticks1 which are yet nameless1 unless we call them ,acousticks1 ,diacousticks1 and ,catacousticks1 or 7in another ,sense1 but to as good ,purpose7 ,phonicks1 ,diaphonicks1 and ,cataphonicks4 ,i4 ,direct ,vision has been improv'd two ways1 ex parte ,objecti1 and ex parte ,organi vel ,medii4 #a4 ,ex parte ,objecti1 ,direct ,vision has receiv'd advantages by the ,arts of ,producing1 ,conserving and ,imitating ,light and ,colours1 which are the ,objects of ,vision4 #a4 ,for the ,art of ,producing ,light1 we have the ,frication of all hard ,bodies that beget ,fire2 especially of the ,flint and ,steel2 and instead of the ,flint1 most hard ,stones 7as well as the ,cane7 may be us'd to the same effect1 as upon trial ,i have found4 ,add hereto the lately invented ,phosphorus1 which is a new and admirable way of producing a ,lucid ,substance by ,art1 out of a ,body in itself not ,lucid2 and therefore may not unfitly be term'd an ,artificial production of ,light4 ,and then of the ,art of ,conserving ,light1 the ,lapis ,bononiensis is a notable ,instance2 and so happily were the ,sepulchral ,lamps of the ,ancients4 #b4 ,as to ,colours1 'tis the greatest part of the ,art of ,dying to be able to make and fix 7that is preserve7 them2 and the ,painters and ,limners will own it to be no small part of their ,skill to be able well to ,mix 7that is1 in effect1 to ,generate7 ,colours4 #c4 ,for ,imitation of ,light and ,colours1 'tis well known how far ,perspective with the ,art of ,limning and ,shadowing have gone therein1 which all tend some way to the ,advance or ,improvement of ,direct ,vision4 ,add to all these1 ,that a due ,application of ,light to the ,object renders it ,visible1 if it were not so before2 as appears from a dark ,room illuminated2 or else makes it better and more truly discernable by the ,sense of ,seeing1 if before it might have been discern'd4 ,hence the same ,colour1 in a diverse ,light1 will appear different1 and no ,picture can well be discern'd or judg'd of but by its true ,light4 ,besides1 the ,limner will assure you1 that he can hardly make true ,work1 or hit the ,air of a ,face exactly1 unless he draw by a ,north-,light1 by reason of the steadiness of that1 and the uncertainty of all other ,lights whatsoever4 ,which things shew1 that the ,art of duly applying ,light to the ,object does very much help and improve ,vision4 ,so also does the due placing of the ,object1 as to ,height and ,distance4 ,but to enumerate all things that help ,direct ,vision1 would be infinite4 #b4 ,ex parte ,organi vel ,medii1 ,direct ,vision has been improv'd by making use of a ,tube1 without ,glasses1 or a ,man's clos'd ,hand1 to look thro'2 which admitting into the ,eye only the principal ,rays1 that come directly from the ,object1 do very much strengthen and clear the ,sight1 by excluding all the ,collateral ,rays1 that crouding into the ,eye1 together with the direct ones1 would confound and disturb it1 partly by mixing and interfering with the direct ,rays1 and partly 7or rather chiefly7 by too much enlightning the fund of the ,eye1 wherein ,vision is truly 7tho' then imperfectly7 made4 ,on this is founded the ,art of making ,spectacles without ,glasses2 7as well as ,tubes7 which is done by putting into the ,glass-holes 7instead of ,glasses7 two short ,tubes of between three and four ,inches long 7for their length is to be vary'd according to the ,age or ,eye of the ,beholder1 and so also is the ,diameter of the extream ends7 which ,tubes being made of ,spanish ,leather 7or ,past-board1 or some such like ,matter7 and black'd on the inside1 are so to be placed1 as that the visual ,rays1 receiv'd thro' them1 may meet in one point 7or rather issue out from one ,point7 of the ,object standing at such a due distance1 as the ,person may clearly and distinctly see it1 or according to his length of ,sight 7as ,,abc1 in the #dth ,fig4 ,tab4 #c47 ,and these ,spectacles may be suppos'd better for preserving the ,sight1 than the ordinary ones with ,glasses1 because they represent the ,object more naturally1 and withal more clearly and distinctly to the ,eye1 than the other1 whose refracted ,rays being collected together with the right ones in the ,glasses1 do somewhat confound good ,vision1 as before3 ,especially if the visive ,power be strong enough to be sufficiently determin'd by the right ,rays alone4 ,for ,i speak now of preserving a good ,eye by these ,spectacles1 which holds in proportion true also of a bad one4 ,because those ,rays 7both right and refracted7 being collected and brought so near the ,eye 7whether good or bad7 as the ,spectacles are usually plac'd1 do too much affect it1 both by their own brightness1 and also by the brightness of the ,colours of the ,object 7when they are bright7 which is brought very near also2 whereby the ,eye is dazl'd and confounded1 unless there be a strong attention and conatus of the ,spirits1 whereto the bright ,rays do certainly engage them1 which of necessity weakens ,vision1 especially if these ,glass-spectacles be much us'd4 ,wherefore the now describ'd new ,tube-spectacles1 contributing so much to the help and preservation of ,sight1 may well be counted an improvement of ,direct ,vision1 because they convey the ,rays to the ,eye without any kind of ,refraction whatsoever4 ,seeing the same ,object also through various holes1 plac'd at certain distances1 does somewhat alter ,vision2 but of this perhaps more hereafter4 ,now as ,direct ,vision has thus been improved1 so likewise ,direct ,hearing partly has already receiv'd1 and partly may by the ,doctrine whereof we are treating1 7if well cultivated7 farther receive as great and notable ,improvements1 both ex parte ,objecti1 and ex parte ,organi vel ,medii4 #a4 ,as to the ,object of ,hearing1 which is ,sound1 improvement has been and may be made1 both as to the ,begetting1 and as to the ,conveying and ,propagating 7which is a kind of ,conserving7 of ,sounds4 #a4 ,as to the ,begetting of ,sounds4 ,the ,art of imitating any ,sound1 whether by ,speaking 7that is pronouncing7 any kind of ,language1 7which really is an ,art1 and the ,art of ,speaking1 perhaps one of the greatest7 or by ,whistling1 or by ,singing 7which are allow'd ,arts7 or by ,hollowing or ,luring 7which the ,huntsman or ,faulkner would have to be an ,art also7 or by imitating with the ,mouth 7or otherwise7 the ,voice of any ,animal1 as of ,quails1 ,cats1 and the like2 or by representing any ,sound begotten by the ,collision of ,solid ,bodies1 or after any other manner2 these are all ,improvements of ,direct ,hearing1 and may be improv'd4 ,moreover the ,skill to make all sorts of ,musical ,instruments1 both ,ancient and ,modern1 whether ,wind ,instruments or ,string'd1 or of any other sort1 whereof there are very many 7as ,drums1 ,bells1 the ,systrum of the ,egyptians1 and the like7 that beget 7and not only propagate7 ,sounds2 the ,skill of making these1 ,i say1 is an ,art1 that has as much improv'd ,direct ,hearing1 as an ,harmonious ,sound exceeds a single and rude one1 that is1 an immusical ,tone2 which ,art is yet capable of farther improvement4 ,and ,i do hope1 that by the ,rules1 which may happily be laid down concerning the ,nature1 ,propagation and ,proportion1 or ,adapting of ,sounds1 a way may be found out1 both to improve ,musical ,instruments already in use1 and to invent new ones1 that shall be more sweet and luscious1 than any yet known4 ,besides that1 by the same means ,instruments may be made1 that shall imitate any ,sound in ,nature1 that is not ,articulate1 be it of ,bird1 ,beast1 or what thing else soever4 #b4 ,the ,conveying and ,propagating 7which is a kind of ,conserving7 of ,sounds1 is much help'd by duly placing the ,sonorous ,body1 and also by the ,medium4 ,for if the ,medium be ,thin and ,quiescent1 and the ,sounding ,body plac'd conveniently1 the ,sound will be easily and regularly propagated1 and mightily conserv'd4 ,i say1 #a4 ,if the ,medium be ,thin and ,quiescent1 because it otherwise causes a ,refracted ,sound1 of which afterwards4 ,hence in a still ,evening1 or the dead of the ,night 7when the ,wind ceases7 a ,sound is better sent out1 and to a greater distance than otherwise1 tho' much of this may be ascrib'd to its ,refraction also4 #b4 ,i say1 that the ,sonorous ,body must be plac'd conveniently1 near a ,smooth ,wall1 near ,water1 or a ,plain1 whose ,surface is even4 #a4 ,near a ,smooth ,wall1 either ,plain or ,arch'd 7,cycloidically or ,elliptically1 rather than otherwise1 tho' a ,circular or any ,arch will do1 but not so well47 ,hence in a ,church1 the nearer the ,preacher stands to the ,wall 7and certainly 'tis much the best way to place ,pulpits near the ,wall7 the better is he heard1 especially by those who stand near the ,wall also1 though at a greater distance from the ,pulpit2 those at the remotest end of the ,church1 by laying their ,ears somewhat close to the ,wall1 may hear him easier than those in the middle4 ,hence also do arise ,whispering ,places4 ,for the ,voice being apply'd to one end of an ,arch1 easily rowls to the other4 ,and indeed were the ,motion and ,propagation of ,sounds but rightly understood1 'twould be no hard matter to contrive ,whispering ,places of infinite variety and use4 ,and perhaps there could be no better or more pleasant hearing a ,consort of ,musick than at such a place as this1 where the ,sounds rowling along together1 before they come to the ,ear1 must needs consolidate and imbody into one2 which becomes a true composition of ,sounds1 and is the very ,life and ,soul of ,consort4 #b4 ,if the ,sonorous ,body be plac'd near ,water1 the ,sound will easily be convey'd1 yet mollified2 as ,experience teacheth us from a ,ring of ,bells near a ,river1 and a great ,gun shot off at ,sea1 which yet differ much in the strength1 and softness and continuance1 or propagation of their ,sounds1 from the same at ,land1 where the ,sound is more harsh and more perishing1 or much sooner decays4 #c4 ,in a ,plain a ,voice may be heard at a far greater distance than in uneven ,ground4 ,the ,reason of all which last nam'd ,phnomena is the same2 because the ,sonorous ,air meeting with little or no resistance upon a ,plane 7much less upon an ,arch'd7 smooth ,superficies1 easily rowls along it1 without being let or hinder'd in its ,motion1 and consequently without having its parts disfigured1 and put into another kind of ,revolution1 than what they had at the first begetting of the ,sound4 ,which is the true cause of its ,preservation or ,progression1 and fails much when the ,air passes over an uneven ,surface1 according to the degrees of its inequality1 and somewhat also1 when it passes over the plain ,superficies of a ,body that is hard and resisting4 ,wherefore the smooth ,top of the ,water 7by reason of its yielding to the ,arch'd ,air1 and gently arising again with a kind of ,resurge1 like to ,elasticity1 tho' it be not so1 by which ,resurge it quickens and hastens the motion of the ,air rowling over it1 and by its yielding preserves it in its ,arch'd ,cycloidical or ,elliptical ,figure7 the smooth ,top of the ,water1 ,i say1 for these ,reasons1 and by these ,means1 conveys a ,sound more entire1 and to a greater distance than the plain ,surface of a piece of ,ground1 a ,wall1 or any other ,solid ,body whatever1 can do4 ,as for the ,speaking ,trumpet1 by which a ,voice may be convey'd to a considerable distance1 ,i refer its consideration to that of ,refracted ,sounds1 or ,refracted ,audition4 ,thus much of the ,improvements of ,hearing1 that respect its ,object1 which is ,sound4 #b4 ,the ,organ and ,medium are to be consider'd4 ,and1 #a4 ,the ,organ1 which is the ,ear1 is helpt much by placing it near a ,wall 7especially at one end of an ,arch1 the ,sound being begotten at the other7 or near the ,surface of ,water1 or of the ,earth1 along which the ,sounds are most easily and naturally convey'd1 as was before declar'd4 ,and 'tis incredible how far a ,sound made upon the ,earth 7by the trampling of a ,troop of ,horses1 for ,example7 may be heard in a still ,night1 if a ,man lays his ,ear close to the ,ground in a large ,plain4 ,otacousticks here come in for helping the ,ear2 which may be so contriv'd 7by a right understanding the ,progression of ,sounds1 which is the principal thing to be known for the due regulating all such kinds of ,instruments7 as that the ,sound might enter the ,ear without any ,refraction1 but as now they are generally made ,i refer them to ,refracted ,audition4 #b4 ,as to the ,medium1 ,i know not how that1 by any contrivance of ,art1 can advantage ,direct ,hearing1 otherwise than ,i have declar'd already in the propagation or conveyance of ,sounds1 though to the ,refracting or ,reflecting of them it may very much conduce2 of which presently4 ,and so ,i have done with the first part of my present undertaking1 which is the ,comparison of ,direct ,vision and ,audition1 as to their ,improvements from ,art4 ,the rest follow4 ,wherefore1 ,,ii4 ,concerning ,refracted ,vision and its ,comparison1 ,i observe1 ,that ,refracted ,vision is always made ,ex parte ,medii1 as ,reflected is ex parte ,objecti4 ,and therefore1 though ,direct ,vision may be help'd ex parte ,objecti1 ,medii vel ,organi1 yet ,refracted can be improv'd only ex parte ,medii1 and ,reflected ex parte ,corporis oppositi alone4 ,unless it be in a mixt or compound ,vision1 that is ,refracto-,reflext1 when the reflext ,rays pass to the ,eye through a refracting ,medium1 such as the ,medium ,internum1 contain'd in the ,body of the ,eye1 always is4 ,so that in truth1 all ,vision is ,refracted by an internal ,refraction made in ipso ,oculo4 ,and all that ,i have spoken of ,vision holds true of ,hearing also1 both ,refracted and ,reflext1 and therefore need not be repeated4 ,refracted ,vision arises from the different ,density1 ,figure1 and ,magnitude of the ,medium1 which is somewhat alter'd also by the diverse incidence of the visible ,rays4 ,and so it is in ,refracted ,hearing1 all these ,causes concur to its ,production1 and some others to be hereafter consider'd4 ,now as any ,object 7a ,man for example7 seen through a thicken'd ,air1 by ,refraction appears greater than really he is3 ,so likewise a ,sound1 heard through the same thicken'd part of the ,atmosphere1 will be considerably vary'd from what it would seem to be1 if heard through a thinner ,medium4 ,and this ,i call a ,refracted ,sound3 ,but what this ,refraction of ,sound is1 and how caus'd1 may hereafter be discuss'd1 when the ,nature1 and ,motion1 or ,progression of ,sounds are well stated4 ,for the ,improvement of ,refracted ,vision artificial ,instruments have been made1 by grinding or blowing ,glasses1 into a certain ,figure1 and placing them at due distances1 whereby the ,object may be 7as 'twere7 enabled to send forth its ,rays more vigorously1 and the ,visive ,faculty impower'd the better to receive them4 ,and thus also ,instruments may be contriv'd for the assisting both the ,sonorous ,body1 to send forth its ,sound more strongly1 and the ,acoustick ,faculty1 to receive and discern it more easily and clearly4 ,for1 #a4 ,as a fine ,glass ,bubble1 fill'd with clear ,water1 and placed before a burning ,candle or ,lamp1 does help it to dart forth its ,rays to a prodigious ,length and ,brightness3 ,so an ,instrument may be invented1 that apply'd to the ,mouth 7or any ,sonorous ,body7 shall send forth the ,voice distinctly to as prodigious a ,distance and ,loudness4 ,for if the ,stentoro-phonecon 7which is but a rude and unartificial ,instrument7 does such great feats1 what might be done with one compos'd according to the ,rules of ,art8 whose make should comply with the ,laws of ,sonorous ,motion 7which that does not7 and therefore not so much ,refract1 as to alter and confound the ,tone of the ,voice and ,words 7as that somewhat does47 ,now of what use such an ,instrument might be for speaking clearly and articulately at a distance 7and that without altering the ,tone of the ,voice7 whether it be at ,sea or at ,land 7but especially at ,sea in tempestuous ,weather and in the ,night7 is obvious to any ,man to conceive4 #b4 ,as ,instruments have been invented to help the ,eye1 ,so likewise are there some1 and more such there may be1 for the ,ear4 ,for1 #a4 ,as ,spectacles and other ,glasses are made to help the ,purblind and weak ,eyes1 to see at any competent distance3 ,so there are ,otacousticks 7and better may be made7 to help weak ,ears to hear at a reasonable distance also4 ,which would be as great a help to the infirmity of ,old ,age1 as the other invention of ,spectacles is1 and perhaps greater2 forasmuch as the ,hearing what's spoken is of more daily use and concern to such ,men1 then to be able to read ,books or to view ,pictures4 #b4 ,as ,perspective-,glasses and ,telescopes help the ,eye to see ,objects at a very great distance1 which otherwise would not be discernable2 in like manner may a sort of ,otacousticks be so contriv'd1 as that they shall receive in ,sounds made at a very great distance also1 but with so much advantage1 that the ,ear shall be able to hear them1 which otherwise would have been inaudible4 ,and these ,otacousticks in some respects would be of greater use than ,perspectives4 ,for whereas at ,land ,perspectives are many times render'd almost useless1 by the interposition of ,woods and ,mountains1 which hinder the ,sight from reaching very far3 ,our ,otacousticks would1 notwithstanding these ,obstacles1 take in a ,sound made some ,leagues off4 ,which might be of notable use in the time of ,war1 for discovering the ,enemy at a good distance1 when he marches or lyes incamp'd behind a ,mountain or ,wood1 or any such place of shelter4 ,yea1 even at ,sea also1 where ,perspectives are of most use1 by reason of the plainess of the ,surface of the ,water2 yet sometimes there ,otacousticks may be of more benefit1 when in dark hazy ,weather the ,air is too thick1 or in ,stormy ,tempestuous ,weather the ,waves arise too high for the ,perspective to be made use of4 ,but1 whether at ,sea or ,land1 ,perspectives become altogether insignificant in the ,night-time 7unless it be for viewing the ,stars7 which is the chief time for using ,otacousticks2 as it is generally1 for ,soldiers to take their ,march1 when they would surprise their ,enemies4 ,and therefore this sort of ,otacousticks have then their chief use1 when ,perspectives are of no use at all2 besides that they may be imploy'd in the ,day-time1 as well as ,perspectives1 whence they may 7not unfitly7 be term'd the most useful ,instrument of the two4 #c4 ,as ,microscopes or ,magnifying-,glasses help the ,eye to see near ,objects1 that by reason of their smallness were ,invisible before2 which ,objects they ,magnify to a strange greatness3 ,so ,microphones or ,micracousticks1 that is ,magnifying ,ear ,instruments1 may be contriv'd after that manner1 that they shall render the most minute ,sound in nature distinctly audible1 by ,magnifying it to an unconceivable loudness4 ,by the help hereof we may hear the different ,cries and ,tones1 as well as by ,microscopes see the divers ,shapes and ,figures of the smallest ,animals4 #d4 ,as by ,polyscopes or ,multiplying-,glasses1 one thing is represented to the ,eye as many1 whether in the same or different ,shapes 7for so ,multiplying-,glasses may be contriv'd37 ,so by a ,polyphone or ,polyacoustick well order'd1 one ,sound may be heard as many1 either of the same or a different ,note4 ,insomuch1 that who uses this ,instrument1 he shall1 at the ,sound of a single ,viol1 seem to hear a whole ,consort and all true ,harmony4 ,by which means this ,instrument has much the advantage of the ,polyscope4 ,and thus much may suffice for comparing the ,improvements made upon ,refracted ,seeing and ,hearing2 ,i call it ,refracted ,hearing1 because made through a ,medium1 viz4 thick ,air1 or an ,instrument1 through which the ,sound passing is broken or refracted4 ,,iii4 ,reflected ,vision has been improv'd by the ,invention of ,looking-glasses and ,polished ,metals1 whether ,plane1 ,concave1 or ,convex2 and these two last1 either ,spherical1 ,oval1 ,cylindrical1 ,conical1 ,hyperbolical1 or of several other shapes2 all which cause a different ,reflection1 and vary the ,phnomena4 ,thus also ,reflext ,audition1 made by ,ecchoes1 may be improv'd1 by contriving several sorts of ,artificial ,ecchoes2 as 'tis no hard matter to do in almost any place4 ,for 7speaking in the general7 ,any ,sound1 falling directly or obliquely upon any dense ,body1 of a smooth 7whether ,plane or ,arch'd7 ,superficies1 is beat back again and reflected1 or does eccho more or less4 ,i say 7#a47 falling directly or obliquely2 because1 if the ,sound be sent out and propagated parallel to the ,surface of the ,dense ,body1 or be made so far off and so weak1 that it cannot reach it1 there will be no ,reflection of ,sound1 no ,eccho4 ,i say 7#b47 upon a ,body of a smooth ,superficies2 because if the ,surface of the ,corpus ,obstans be uneven1 the ,air by reverberation will be put out of its regular ,motion1 and the ,sound thereby broken and extinguish'd3 ,so that tho' in this case also the ,air be beaten back again1 yet ,sound is not reflected1 nor is there any ,eccho4 ,i say 7#c47 it does eccho more or less1 to shew1 that when all things are1 as is before describ'd1 there is still an ,ecchoing1 though it be not always heard2 either because the direct ,sound is too weak to be beaten quite back again to him that made it2 or that it does return home to him1 but so weak1 that without the help of a good ,otacoustick1 it cannot be discern'd2 or that he stands in a wrong place1 to receive the reflected ,sound1 which passes over his head1 under his ,feet1 or to one side of him2 which therefore may be heard by a ,man standing in that place1 where the reflected ,sound will come1 provided no interpos'd ,body does intercept it2 but not by him1 that first made it4 ,i shall further make out the comparison 'twixt ,reflex'd ,vision and ,audition1 by these following ,propositions4 #a4 ,as a ,plain ,speculum reflects the ,object in its due ,dimensions and ,colours2 allowing for their difference of appearance1 according to their distance3 ,so a ,plane ,corpus ,obstans reflects the ,sound back in its due ,tone and ,loudness2 if allowance be likewise made for the proportionable decrease of the ,sound1 according to its distance4 #b4 ,as a ,convex ,speculum reflects the ,object less1 but somewhat brighter or clearer3 ,so a ,convex ,corpus ,obstans repels the ,sound 7insensibly7 smaller2 but somewhat quicker 7though weaker7 than otherwise it would be4 #c4 ,as a ,concave ,speculum reflects the ,object bigger1 more obscure and ,inverted3 ,so a ,concave ,corpus ,obstans ecchoes back the ,sound 7insensibly7 bigger1 slower 7though stronger7 and also inverted2 but never according to the order of ,words4 ,nor do ,i think it possible for the ,art of ,man to contrive a ,single ,eccho1 that shall invert the ,sound1 and repeat backwards2 because then the ,words last spoken1 that is1 which do last occur to the ,corpus ,obstans1 must first be repell'd2 which cannot be3 ,for where1 in the mean time1 should the first ,words hang1 and be conceal'd1 or lie dormant8 ,or how1 after such a pause1 be reviv'd and animated again into ,motion8 ,yet in complicated or ,compound ,ecchoes1 where many receive from one another1 ,i know not whether something that way may not be done4 ,from the determinate ,concavity or ,archedness of these reflecting ,bodies1 it comes to pass1 that some of them1 from a certain distance or posture1 will eccho back but one determinate ,note1 and from no other place will they reverberate any2 because of the undue ,position of the sounding ,body4 ,such an one 7as ,i remember7 is the ,vault in ,merton ,college in ,oxford4 #d4 ,as a ,speculum takes in and reflects more of its ,object1 when plac'd at a great distance from it1 than when nearer2 because it reflects according to the apparent ,magnitude of the ,body at such a distance1 which is less3 ,so also the ,ecchoing ,body1 being remov'd farther off1 reflects more of the ,sound1 than when nearer4 ,and this is the reason1 why some ,ecchoes repeat but one ,syllable1 some one ,word1 and some many4 #e4 ,as ,specula's may be so plac'd1 that reflecting one upon or into the other1 either directly or obliquely1 one ,object shall appear many2 as in ,sir ,samuel ,moreland's ,glass-room3 ,after the same manner ,ecchoing ,bodies may be so contriv'd and plac'd1 as that reflecting the ,sound from one to the other1 either directly and mutually1 or obliquely and by ,succession1 out of one ,sound shall many ,ecchoes be begotten2 which in the first case will be all together1 and somewhat involv'd or swallow'd up of each other1 and thereby confus'd 7as a ,face in ,looking-glasses obverted7 in the other they will be distinct1 separate1 and succeeding one another2 as most multiple ,ecchoes do4 ,moreover a ,multiple-,eccho may be made1 by so placing the ,ecchoing ,bodies1 at unequal distances1 that they reflect all one way1 and not one on the other2 by which means a manifold successive ,sound will be heard 7not without astonishment7 one ,clap of the hands like many1 one ,ha1 like a laughter1 one single ,word like many of the same ,tone and ,accent1 and so one ,viol like many of the same kind imitating each other4 ,furthermore1 as ,specula's may be so order'd1 that by ,reflection they shall make one single thing appear many different things2 as one single ,man to seem many ,men1 differing as to ,shape and ,complexion 7or a company of ,men7 which ,i think ,sir ,samuel ,moreland's ,contrivance does not3 ,so may ,ecchoing ,bodies also be order'd1 that from any one ,sound given1 they shall produce many ,ecchoes1 different both as to their ,tone and ,intension4 7,the ground whereof has elsewhere been laid down in a ,treatise concerning the ,sympathy of ,lute-strings47 ,by this means a ,musical ,room may be so contriv'd1 that not only one ,instrument1 play'd on in it shall seem many of the same sort and size2 but even a ,consort of 7somewhat7 different ones2 only by placing certain ,ecchoing ,bodies so1 as that any ,note 7play'd7 shall be return'd by them in #c;ds1 #eths1 and #hths1 which is possible to be done otherwise than was mention'd before in ,refracted ,audition4 ,i have now done with my ,comparison of the two ,noblest ,senses1 and ,sciences1 as to their ,improvements2 wherein ,i have been thus large1 that ,i might give you a little prospect into the ,excellency and ,usefulness of ,acousticks2 and that thereby ,i might excite all that hear me1 to bend their ,thoughts towards the making of ,experiments for the compleating this 7yet very imperfect1 tho' noble7 ,science2 a ,specimen whereof ,i will give you in three ,problems1 and then present you with the ,semiplane of an ,acoustick or ,phonical ,sphere1 as an ,attempt to explicate the great ,principle in this ,science1 which is ,the ,progression of ,sounds4 ,the ,problems are these3 #a4 ,sonum intendere quousque velis2 or1 ,datum sonum ad datum gradum intendere4 #b4 ,sonum extendere quousque velis2 or1 ,datum sonum ad datum distantiam extendere seu propagare4 #c4 ,sonum transire ab extremo ad extremum non per ,medium4 #a4 ,the first is1 ,to make the least ,sound 7by the help of ,instruments7 as loud as the greatest2 a whisper to become as loud as the shot of a ,cannon4 ,by the help of this ,problem1 the most minute ,sounds in ,nature may be clearly and distinctly heard4 #b4 ,the second is1 ,to propagate any 7the least7 ,sound to the greatest distance4 ,by the help hereof any ,sound may be convey'd to any1 and therefore heard at any distance1 7,i must add1 within a certain1 tho' very large ,sphere47 ,moreover1 by this means1 a ,weather-cock may be so contriv'd1 as that with an ordinary blast of ,wind it shall cry 7or whistle7 loud enough to be heard many ,leagues3 ,which happily may be found of some use1 not only for ,pilots in mighty tempestuous ,weather1 when light ,houses are render'd almost useless1 but also for the measuring the strength of ,winds1 if allowance be made for their different moisture4 ,for ,i conceive1 that the more dry any ,wind is1 the louder it will whistle cteris paribus2 ,i say1 cteris paribus1 because1 besides the strength and dryness of ,winds or ,breath1 there are a great many other things 7hereafter to be considered7 that concur to the increase or magnifying of ,sounds1 begotten by them in an ,instrument exposed to their ,violence1 or blown into4 #c4 ,the third ,problem1 is1 ,that a ,sound may be convey'd from one extreme to the other 7or from one distant place to another7 so as not to be heard in the middle4 ,by the help of this ,problem a ,man may talk to his ,friend at a very considerable distance1 so that those in the middle space shall hear nothing of what passed betwixt them4 ,,fig4 ,v4 ,,tab4 ,,iii4 ,semiplanum ,sphr ,phonic seu ,acoustic4 ,you are to conceive that 7rude7 ,semiplane1 as parallel to the ,horizon3 ,for if it be perpendicular thereunto1 ,i suppose the upper extremity will be no longer ,circular1 but ,hyperbolical1 and the lower part of it suited to a greater ,circle of the ,earth4 ,so that the whole ,phonical ,sphere 7if ,i may so call it7 will be a solid ,hyperbola1 standing upon a ,concave ,spherical ,base4 ,i speak this concerning ,sounds made 7as usually they are7 nigh the ,earth1 and whose ,sonorous ,medium has a free passage every way4 ,for if they are generated high in the ,air1 or directed one way1 the case will be different2 which is partly design'd in the inequality of that ,draught4 ,a ,discourse concerning the ,modern ,theory of ,generation1 by ,dr4 ,george ,garden of ,aberdeen1 being part of a ,letter to ,dr4 ,william ,musgrave1 ,l4 ,l4 ,d4 ,reg4 ,soc4 ,s4 and by him communicated the ,royal ,society4 ,the ,subject ,i pitch upon1 is that of the ,formation of ,animals1 ,you know how wide and unsatisfying ,men's ,conjectures were upon this ,head1 until this ,age1 in which first the deservedly ,famous ,dr4 ,harvey discovered the proper place of the ,formation of the ,chick in the ,cicatricula of the ,egg1 and the ,formation of the ,parts so far as was discernable by the naked ,eye2 and after him ,malpighius1 by the help of exact ,glasses1 observ'd the first ,rudiments of it there1 both before and after ,incubation3 ,and ,r4 de ,graef1 and others1 having upon many ,observations concluded1 that the ,testes ,fminei were the ,ovaries of ,females1 and consequently that all ,animals were ex ovo2 they began from hence to infer1 that the ,rudiments of each ,animal were originally in the respective ,females1 and that the ,male contributed only to give a new ,ferment to the ,mass of the ,blood and ,spirits1 by which means a spirituous ,liquor 7which the ,blood in its ordinary ,ferment could not produce7 did insinuate it self into the same ,ducts and ,pores of the ,rudiments of those ,animals1 which were in greatest forwardness in the ,ovary1 and so extend and enlarge all their ,parts1 and at last bring them to perfection1 as ,mr4 ,perrault does ingeniously discourse in the third ,part of his ,essais de ,physique2 till now at last ,leowenhoek has discover'd an infinite number of ,animalcula in semine marium of all kinds1 which has made him condemn the former ,opinions about the ,propagation of all ,animals ex ,ovo4 ,now upon comparing the ,observations and ,discoveries which have been made with one another1 these three things seem to me very probable4 #a4 ,that ,animals are ex ,animalculo4 #b4 ,that these ,animalcles are originally in semine ,marium non in ,fminis4 #c4 ,that they can never come forward1 nor be formed into ,animals of the respective kind1 without the ,ova in ,fminis4 ,the first of these seems probable from these three ,observations4 #a4 ,that some such thing has been so often observ'd by ,malpighius1 in the ,cicatricula of an ,egg before ,incubation1 as the ,rudiments of an ,animal in the shape of a ,tadpole1 as may be seen in his first1 and in his repeated ,observations de formatione ,pulli in ,ovo4 #b4 ,the sudden appearance and displaying of all the ,parts after ,incubation1 makes it probable1 that they are not then actually formed out of a fluid1 but that the ,stamina of them have been formerly there existent1 and are now expanded4 ,the first ,part of the ,chick which is discovered with the naked ,eye1 is1 you know1 the ,punctum saliens1 and that not till three days and nights of ,incubation be past2 and then1 on the fifth day1 the ,rudiments of the ,head and ,body do appear4 ,this made ,dr4 ,harvey conclude1 that the ,blood had a being before any other ,part of the ,body2 and that from it1 all the ,organs of the ,ftus were both form'd and nourished3 ,but by ,malpighius's ,observations we find that the ,parts are then only so far extended1 as to be made visible to the naked ,eye1 and that they were actually existent before1 and discernable by ,glasses4 ,after an ,incubation of thirty hours1 are to be seen the ,head1 the ,eyes1 and the ,carina with the ,vertebr1 distinct1 and the ,heart4 ,after forty hours its ,pulse is visible1 and all the other ,parts more distinct1 which cannot be discerned by the naked ,eye before the beginning of the fifth day2 from whence it seems probable1 that even the so early discovery of those ,parts of the ,ftus by the ,microscope1 is not the discerning of ,parts newly formed1 but only more dilated and extended by receiving of ,nutriment from the ,colliquamentum2 so that they seem all to have been actually existent before the ,incubation of the ,hen4 ,and what ,swammerdam has discovered in the transformation of ,insects1 gives no small light to this2 whilst he makes appear in the ,explanation of the #acth ,table of the ,general ,history of ,insects1 that in those large ,eruca's which feed upon ,cabbage1 if they be taken about the time they retire to be transformed into ,aurelia's1 and plung'd often in warm ,water to make a ,rupture of the outer ,skin1 you will discern through the transparency of their second ,membrane1 all the ,parts of the ,butterfly1 the ,trunk1 ,wings1 ,feelers1 c4 folded up4 ,but that after the ,eruca is chang'd into an ,aurelia1 none of these ,parts can be discern'd1 they are so drencht with moisture1 tho' they be there actually form'd4 ,another ,consideration is from the ,analogy1 which we may suppose between ,plants and ,animals4 ,all ,vegetables we do see proceed ex ,plantula1 the ,seeds of ,vegetables being nothing else but little ,plants of the same kind folded up in ,coats and ,membranes2 and from hence we may probably conjecture1 that so curiously an organized ,creature as an ,animal1 is not the sudden ,product of a ,fluid or ,colliquamentum1 but does much rather proceed from an ,animalcle of the same kind1 and has all its little ,members folded up according to their several ,joints and ,plicatures1 which are afterwards enlarged and distended1 as we see in ,plants4 ,now tho' this ,consideration alone may seem not to bear much weight2 yet being join'd to the two former1 they do mutually strengthen each other4 ,and indeed all the ,laws of ,motion1 which are as yet discovered1 can give but a very lame account of the forming of a ,plant or ,animal4 ,we see how wretchedly ,des ,cartes came off when he began to apply them to this ,subject2 they are formed by ,laws yet unknown to ,mankind2 and it seems most probable1 that the ,stamina of all the ,plants and ,animals that have been1 or ever shall be in the ,world1 have been form'd1 ab ,origine ,mundi1 by the ,almighty ,creator within the first of each respective kind4 ,and he who considers the ,nature of ,vision1 that it does not give us the true magnitude1 but the proportion of things2 and that what seems to our naked ,eye but a ,point1 may truly be made up of as many ,parts as seem to us to be in the whole visible ,world1 will not think this an absurd or impossible thing4 ,but the second thing which later ,discoveries have made probable1 is1 that these ,animalcles are originally in ,semine ,marium non in ,fminis4 ,and this ,i collect from these ,considerations3 #a4 ,that there are innumerable ,animalcula discover'd in ,semine ,masculo omnium ,animalium4 ,mr4 ,leewenhoeck has made this so evident by so many ,observations1 that ,i do not in the least question the truth of the thing4 ,the reason of their ,multitude1 and some of the ,difficulties which arise thereupon1 he has cleared to very good ,purpose1 so that ,i shall not repeat them4 #b4 ,the observing the ,rudiments of the ,ftus in ,eggs1 which have been fecundated by the ,male1 and the seeing no such thing in those which are not fecundated1 as appears from ,malpighius his ,observations1 make it very probable that these ,rudiments proceed originally from the ,male1 and not from the ,female4 #c4 ,the resemblance between the ,rudiments of the ,ftus in ,ovo1 both before and after ,incubation1 and the ,animalcle1 makes it very probable1 that they are one and the same4 ,the same ,shape and ,figure which ,mr4 ,leewenhoeck gives us of the ,animalcle1 ,malpighius likewise gives of the ,rudiments of the ,ftus1 both before and after ,incubation2 yea1 and even the ,ftus's of ,animals do appear so at first to the naked ,eye1 so that ,dr4 ,harvey does acknowledge that all ,animals1 even the most perfect1 are begotten of a ,worm1 ,de ,gen4 ,anim4 ,ex4 #ah4 #d4 ,this gives a rational account of many ,ftus's at one ,birth1 especially that of the ,countess of ,holland1 and how at least a whole ,cluster of ,eggs in a ,hen are fecundated by one ,coition of the ,male4 #e4 ,this gives a new light1 as it were1 to the first ,prophecy concerning the ,messiah1 that the ,seed of the ,woman shall bruise the ,head of the ,serpent1 all the rest of ,mankind being thus most properly and truly the ,seed of the ,man4 #f4 ,the ,analogy ,i have already mentioned1 which we may rationally suppose between the manner of the propagation of ,plants and ,animals1 does likewise make this probable4 ,every ,herb and ,tree bears its ,seed after its kind2 which ,seed is nothing else but a little ,plant of the same kind1 which being thrown into the ,earth1 as into its ,uterus1 spreads forth its ,roots1 and receives its ,nourishment1 but has its form within its self1 and we may rationally conjecture some such ,analogy in the ,propagation of ,animals4 ,the third ,particular which later ,discoveries make probable1 is1 that ,animals cannot be formed of these ,animalcula without the ,ova in fminis1 which are necessary for supplying of them with proper ,nutriment3 ,and this these ,considerations seem to evince4 #a4 ,it is probable that an ,animalcle cannot come forward1 if it do not fall into a proper ,nidus4 ,this we see is the ,cicatricula in ,eggs2 and tho' a ,million of them should fall into an ,egg1 none of them would come forward1 but what were in the ,center of the ,cicatricula2 and perhaps the ,nidus necessary for their formation is so proportion'd to their bulk1 that it can hardly contain more than one ,animalcle2 and this may be the reason why there are so few ,monsters4 ,this we see is absolutely necessary in ,oviparis2 and the only difference which seems to be between them and the ,vivipara1 in this matter1 is in this1 that in the latter the ,ova are properly nothing more but the ,cicatricula1 with its ,colliquamentum1 so that the ,ftus must spread forth its ,roots into the ,uterus to receive its nourishment2 but the ,eggs in ,oviparis may be properly term'd an ,uterus1 in relation to the ,ftus2 for they contain not only the ,cicatricula1 with its ,amnion and the ,colliquamentum1 which is the immediate nourishment of the ,ftus1 but also the materials which are to be converted into that ,colliquamentum2 so that the ,ftus spreads forth its ,roots no farther than into the ,white and ,yolk of the ,egg1 from whence it derives all its nourishment4 ,now that an ,animalcle cannot come forward without some such proper ,nidus1 ,mr4 ,leewenhoeck will not readily deny2 for if there were nothing needful1 but their being thrown into the ,uterus1 ,i do not see why many hundreds of them should not come forward at once2 for as to what ,mr4 ,leewenhoeck says1 that one of them would be-dwarf and choak the rest2 this might fall out in process of time3 ,but at first ,i do not see why many of them should not grow together1 whilst scatter'd in so large a ,field 7and yet no such thing is observed7 if there were not an absolute necessity of a ,cicatricula for their growth and thriving4 ,now1 #b4 ,that this ,cicatricula is not originally in ,utero1 seems evident from the frequent ,conceptions which have been found extra ,uterum3 ,such as the ,child which continued ,twenty six ,years in the ,woman of ,tholouse's ,belly1 mention'd ,numb4 #aci4 of the ,philos4 ,trans4 ,and the little ,ftus found in the ,abdomen de ,st4 ,mere1 together with the ,testicle torn and full of clotted ,blood1 recorded ,numb4 #aej4 both taken out of the ,journals des ,savans3 ,such also seem to be the ,ftus in the ,abdomen of the ,woman of ,copenhagen1 mention'd in the ,nouvelles des ,lettres1 for ,sept4 #he4 pag4 #iif4 all the ,members of which were easily to be felt through the ,skin of the ,belly1 and which she had carried in her ,belly for four ,years2 and the seven ,years ,gravidation1 related by ,dr4 ,cole1 ,numb4 #agb4 of the ,transact4 ,that these two were undoubtedly extra ,uterum1 is uncertain1 because the last was not open'd after her death1 and the former may be yet still alive4 ,now granting once the necessity of a proper ,nidus1 for the formation of an ,animalcle into the ,animal of its respective kind2 these ,observations make it probable1 that the ,testes are the ,ovaria appropriated for this use2 for tho' the ,animalcles coming thither in such ,cases may seem to be extraordinary1 and that usually the ,impregnation is in ,utero2 yet it may be collected from hence1 that the ,cicatricul or ,ova to be impregnated1 are in ,testibus fmineis2 for if it were not so1 the accidental coming of ,animalcles thither could not make them come forward more than in any other part of the ,body1 since they cannot be formed and nourished without a proper ,nidus4 ,but #c4 ,it is acknowledg'd by all1 that the ,ftus in ,utero1 for some considerable time after ,conception1 has no connexion with the ,womb1 that it sits wholly loose to it1 and is perfectly a little round ,egg with the ,ftus in the midst1 which sends forth its ,umbilical ,vessels by degrees1 and at last lays hold on the ,uterus4 ,now from hence it seems evident1 that the ,cicatricula1 which is the ,fountain of the ,animalcles nourishment1 does not sprout from the ,uterus1 but has its ,origin elsewhere1 and falls in thither as into a fit ,soil1 from whence it may draw ,nutriment for the growth of the ,ftus1 else it cannot be easily imagin'd1 how it should not have an immediate ,connexion with the ,uterus from the time of ,conception4 ,if you join all these three ,considerations together1 viz4 that an ,animalcle cannot come forward without a proper ,nidus or ,cicatricula2 that there have been frequent ,ftus's extra ,uterum2 and that they have no ,adhsion to the ,uterus1 for a considerable time after ,conception1 they seem to make it evident1 that ,animals cannot be form'd ex ,animalculis without the ,ova in ,fminis4 ,to all these ,i shall subjoin the ,proposal of an ,experimentum ,crucis1 which may seem to determine1 whether the ,testes ,fmine be truly the ,ovaria1 viz4 ,open the ,abdomen of the ,females of some kinds1 and cut out these ,testicles1 and this will determine1 whether they be absolutely necessary for the formation of ,animals4 ,there are some ,difficulties proposed against this ,conjecture1 which ,i think may be easily resolved4 ,some object the distance between the ,tub or ,cornua ,uteri1 and the ,testicles2 but to this is opposed by ,swammerdam1 and others1 the like distance between the ,infundibulum1 in ,hens and ,frogs1 and the ,ovary2 and yet it cannot be denied that the ,eggs are transmitted thro' this into the ,uterus3 ,and besides ,r4 de ,graef1 and others1 have by repeated ,observations found that the ,cornua ,uteri do at certain times after ,conception1 embrace the ,testes on both sides the ,uterus4 ,they object in the second place the great disproportion between the pretended ,eggs in the ,ovary1 and the ,aperture of the ,tub or ,cornua ,uteri1 the former being a great deal bigger than the latter3 ,but both ,r4 de ,graef and ,malpighius have clear'd that ,matter1 by making appear1 that these ,bladders in the ,ovary are not the ,ova1 but serve to form the ,glandules within which the ,ova are formed1 which break through a small ,papilla opening in the ,glandule1 which bears a proportion to the ,aperture of the ,tube4 ,they object #c1 ,the difficulty to conceive how these ,eggs should be impregnated per semen ,maris1 both because there is no ,connexion between the ,tub and the ,ovary for its transmission1 and for that ,dr4 ,harvey could never discover any thing of it in ,utero4 ,as to the last1 ,mr4 ,leewenhoeck has cleared that difficulty1 by the discovery of innumerable ,animalcula ,seminis ,maris in ,cornubus ,uteri1 and those living a considerable time after ,coition4 ,numb4 #agd4 of the ,transact4 ,and as to the former1 we may either suppose that there is such an ,inflation of the ,tub or ,cornua ,uteri tempore ,coitionis1 as makes them embrace the ,ovaria1 and such an approach of the ,uterus and its ,cornua1 as that ,i may easily transmit the ,seed into the ,ovary2 or else1 that the ,ova are impregnated by the ,animalcles after they descend into the ,uterus1 and not in the ,ovary2 the former seems probable for this ,reason1 that at least a whole ,cluster of ,eggs in a ,hen will be fecundated by one ,tread of the ,cock3 ,now this ,fecundation seems to be in the ,vitellary1 and not in the ,uterus1 as the ,eggs pass along from day to day2 for it can hardly be supposed that the ,animalcles should subsist so long1 being scattered loosely in the ,uterus1 as to wait there for many days for the ,fecundation of the ,eggs as they pass along4 ,the latter ,conjecture has this to strengthen it1 that the ,animalcles are found to live a considerable time in the ,uterus2 and that if they should impregnate the ,ova in the ,ovary it self1 the ,ftus would increase so fast1 that the ,ova could not pass through the ,tub ,uteri1 but would either burst the ,ovary1 or fall down into the ,abdomen from the ,orifices of the ,tub2 and that from hence proceed those extraordinary ,conceptions in ,abdomine extra ,uterum4 ,but1 #d4 ,mr4 ,leewehoeck1 ,numb4 #adg4 of the ,transact4 to weaken the third ,consideration about the ,conceptions1 being like unto an ,ovum in the ,womb1 proposes a ,parallel between these ,animalcles and ,insects2 and insinuates1 that as the latter cast their ,skins1 and appear of another ,shape1 so the other which at first seem like ,tadpoles1 may cast their outer ,skin1 and then be round2 and that this may be the occasion of the round ,figure of the ,conception in the ,womb4 ,to this it may be replied1 that according to ,mr4 ,leewenhoeck's own ,sentiment1 the ,animalcles cannot come forward1 if they do not find the ,punctum or proper place for their ,nourishment1 to which it seems they must have some ,adhsion4 ,now the ,conception in ,viviparis is not fastned unto the ,womb for many days1 nor does adhere to any point of it2 so that it seems this roundish ,body is not the ,animalcle thus chang'd after having cast an outer ,skin1 but is rather the ,cicatricula or little ,egg1 into which the ,animalcle has entred as its ,punctum or place of nourishment2 else ,i do not see why they should not be adhering to the ,womb from the first ,conception1 or why 7as ,i have said7 many hundreds of them are not conceiv'd and formed together1 c4 ,a short ,discourse concerning ,concoction3 ,read at a ,meeting of the ,royal ,society1 ,may 444 #afii1 by ,clopton ,havers1 ,m4 ,d4 ,fellow of the ,royal ,society4 ,the manner in which the ,digestion of the ,aliment is performed1 is a thing not very easie to be understood and explained4 ,however1 it has not escap'd the ,conjectures of some ,philosophical ,men1 who having curiously observ'd the ,phnomena of ,nature1 and enquired into their ,causes1 have1 amongst other things1 endeavour'd to account for this4 ,but their ,sentiments about it have been various1 and the ,hypothesis1 by which they have studied to explain it1 very different4 ,some have thought the ,concoction of the ,food to be a kind of ,elixation2 and that the grosser and more solid ,parts being1 as it were1 boil'd in the ,liquid by the ,heat of the ,stomach1 and the ,parts adjacent to it1 as the ,liver1 ,spleen1 and ,omentum1 are by a long and continued ,elixation1 first render'd more tender1 and then colliquated1 and dissolved into minuter ,particles1 so as to mix more equally with the ,fluid1 and with that to make one ,pulpament1 or chylous ,mass4 ,and ,hippocrates1 tho' he does not plainly call it an ,elixation1 yet seems to attribute the ,concoction of the ,food to the ,heat of the ,stomach1 as the ,cause of it1 ,sect4 #d4 ,libro de salubri victus ratione4 ,so where he takes notice of the voiding of such ,fces1 as appear to be like the ,food that has been eaten2 he adds1 ,constat enim1 sane ventriculum1 ciborum copiam1 ut concoquat1 calefacere non posse4 ,and there are other ,passages in the same ,book1 from which we may conclude1 that he suppos'd the ,heat of the ,stomach to be the great ,cause of the ,digestion of the ,food4 ,there are others that make the ,stomach itself to be the great ,instrument of ,digestion1 but in a different manner3 ,and they suppose it to be perform'd by an ,attrition1 as if the ,stomach1 by those repeated ,motions1 which are the necessary ,effects of ,respiration1 when it is distended by the ,aliment1 did both rub or grind off some minuter ,particles from the grosser ,parts2 and by continually agitating the ,mass of ,food1 make those ,parts1 which are not contiguous to the ,stomach1 strike one against another1 and break one another in pieces1 until they are all attenuated4 ,it is evident enough1 that the sides of the ,stomach do in ,expiration press upon the ,contenta1 so as to oblige1 at least some ,parts of them1 every time the ,muscles of the ,abdomen are contracted1 to move and shift their places4 ,so in ,inspiration1 when the ,diaphragm and ,liver press upon the upper part of the ,stomach1 the ,aliment must be moved again4 ,so that by these reciprocal ,motions1 that part of the ,food which is contiguous to the ,stomach1 and moves in a ,line parallel to it1 must rub against it2 and all the other ,parts being moved by such a ,compression1 as gives them a different ,tendency1 it is certain they must be continually striking one against another4 ,and for ,bread1 and such things as are made of ,flower1 that will be softned and dissolv'd with any common ,liquid1 that ,agitation of the ,stomach which moves them in ,respiration1 might seem sufficient to break and dissolve them1 when they are sufficiently moisten'd with a ,fluid4 ,yet this cannot be thought enough to break and digest ,flesh-meat1 ,fruits1 or any other thing that will not be softned and dissolv'd in ,water1 or some such ,liquid4 ,but although this ,motion of the ,aliment1 caused by ,respiration1 does not actually digest it1 yet it has a great and necessary ,use in ,concoction1 and makes all the grosser ,parts1 as they are attenuated1 mix equally with the ,fluid4 ,some think that the ,bilious ,juice2 others1 that the ,spirits are chiefly concern'd in this ,affair4 ,galen1 in his ,book de ,neutralibus ,facultatibus1 makes it to be the ,effect1 not of one1 but of several ,causes2 as a pituitous ,juice in the ,stomach1 the ,bile1 c4 which appears from what he has said1 and the ,translator thus render'd3 ',verum quanto ii 7cibi7 qui mansi sunt1 iis1 qui inhserunt1 magis sunt alterati2 tanto etiam his magis ii1 qui devorati sunt4 ,siquidem incomparabilis erit horum alterationis excessus1 si qu in ventre est ,pituita ,bilis1 ,spiritus1 ,calor1 tota ,ventris substantia1 stimentur4' ,some there are that will have the ,food to be dissolv'd by a ,menstruum1 which is supply'd from the ,glands of the ,stomach1 or some other way3 ,but those that do so far agree in the ,general1 as to think ,concoction is perform'd by a ,dissolvent1 do differ in their ,notions of the ,nature of the ,menstruum3 ,for there are some that suppose it to be an ,acid1 which does erode the grosser parts of the ,food1 and dissolves them in the same manner as ,vinegar1 ,spirit of ,vitriol1 or any such-like ,acid1 will dissolve even so solid a ,body as ,iron4 ,and it cannot be deny'd1 but that ,oil of ,vitriol will dissolve ,flesh-meat1 and reduce it to a ,pulp2 but it is not to be suppos'd1 that the ,fibres of the ,stomach can admit any such strong and corroding ,acid1 without something to correct it1 but it must be injur'd in its ,tone1 and labour under great and extraordinary ,pains4 ,neither does such a ,menstruum1 tho' it will digest some things1 seem capable of dissolving so great a ,variety of ,things as we eat1 especially when a great many of them are of a contrary ,nature4 ,some will have the ,menstruum to be a nitro-aerius ,spirit1 that is1 quick1 and very penetrating1 and included in its proper ,vehicle2 which1 being in its own ,nature apt to penetrate the ,mass of the ,aliment1 does diffuse it self through the ,whole1 and breaking the ,vinculum of the more solid ,parts1 does dissolve their ,compages4 ,by others1 it is thought to be some saline ,juice in the ,stomach1 by which the ,parts of the ,aliment are divided and dissolved1 and those which are fit for ,nourishment1 are volatiliz'd4 ,lastly1 ,there are some others who reject the ,opinions ,i have already mention'd1 and suppose the ,digestion of the ,food to be perform'd by the ,benefit of a ,ferment2 which1 when it is mixed with the ,aliment1 excites in the ,mass an intestine motion2 and the different and contrary motions and tendency of the ,parts1 making some kind of ,collision1 gradually break off ,particles from the grosser1 and more solid ,parts1 till they are so attenuated as to be apt to mix more equally with the ,fluid1 and with them to make one soft or chylous ,substance4 ,but yet there is not amongst them an universal ,consent1 either about the ,nature of this ,ferment1 or the manner how it is supply'd4 ,for first1 some think it to be the ,remains of the ,food that was last digested2 which having lain some time in the ,stomach1 after the rest is carried down into the ,intestines1 contracts an ,acid1 or some other ,quality1 and is so alter'd1 as to partake of the ,nature of a ,leaven4 ,and this ,leaven being a part of the ,food1 which has been already digested1 is so soft and liquid as to be capable of mixing with the ,aliment1 which is next taken into the ,stomach2 and being agitated with it by the repeated ,pressures of the ,diaphragm1 ,liver1 and ,abdominal ,muscles upon the ,stomach in ,respiration1 does diffuse it self through the whole ,mass2 and being mixed with it1 like ,leaven1 or ,yest added to new ,wort1 c4 puts it into a ,state of ,fermentation2 and by this ,fermentation1 or the ,expansion of the ,ferment1 and the more tenuious ,parts1 which are first put into motion by it1 those which are more solid1 and with which they are intermixed1 are rent1 and divided1 and so attenuated1 as to become a soft and pulpous matter4 ,and altho' the greatest part of the ,food1 that is thus broken and concocted1 is by the ,contraction of the ,fibres of the ,stomach press'd into the ,duodenum2 yet they do not contract themselves so as to force out all the ,aliment1 but leave between the ,rug or ,folds1 on the inside of the ,stomach1 a sufficient ,quantity to be a ,leaven to the next ,meal2 and so from time to time4 ,some have a ,notion1 ,that this ,ferment1 or ,principle of ,fermentation1 is in the ,aliment it self2 which being a ,congeries of ,matter1 consisting of various ,parts of a different ,nature1 is no sooner enclosed in the ,stomach1 and digested in the ,heat of that1 and the adjacent ,parts1 but the more spirituous and subtil ,particles are put into motion both from that ,warmth1 and the difference of their ,natures1 and enter upon a ,fermentation4 ,and so by their intestine ,commotion1 and the ,violence they offer to those ,parts which oppose the tendency of any of them1 they break and dissolve what is more solid4 ,again3 ,some suppose1 that this ,ferment is supply'd from the ,glands of the ,stomach4 ,and ,lastly1 ,others1 and perhaps with much better ,reason1 contend for the ,saliva1 and make that to be the ,ferment1 which serves principally for the ,digestion of the ,food2 which in ,mastication being mix'd with our ,aliment1 is with that carried down into the ,stomach1 where the ,parts of it being put into motion by a kindly and agreeable ,heat1 they do ferment with1 and exagitate first those ,parts of the ,food which are most apt to ferment with it1 and then both conspire to break and dissolve the grosser and more stubborn ,parts4 ,and ,galen1 in the ,book ,i have before-mention'd1 plainly allows that the ,saliva is concern'd in the business of ,concoction1 tho' he supposes the ,alteration1 which is produc'd by this ,juice1 to be made in the ,mouth1 as appears from these ,words3 ,qu 7alteratio7 in ore agitur mutat quidem id 7nutrimentum7 in alteram speciem manifest1 non tamen ad perfectionem transmutat--,qui mansi sunt cibi primum quidem hac ,pituita 7oris7 imbuunter1 cum ea miscentur----,itaque majorem mutationem consecuti sunt1 quam ii1 qui in vacuis dentium intervallis fuere impacti4 ,now ,i have given this short ,account of the various ,opinions of some ,ingenious ,men1 concerning the manner how ,concoction is perform'd2 ,i come now to propose my own ,hypothesis1 by which ,i shall endeavour to explain it4 ,in order to the more easie and effectual ,digestion of the ,food1 ,nature has appointed some ,parts for the breaking our ,aliment1 and reducing whatever is gross into smaller ,parts1 before it is put upon ,digestion3 ,others to supply the ,ferment1 by which it is to be dissolv'd and concocted1 and which1 before it comes to be included in the ,stomach1 does moisten1 and make it more soft1 that it may more easily be penetrated1 and broken by those ,parts which serve to divide every ,morsel into smaller ,pieces1 and prevents the ,inconvenience and ,trouble which would arise from the ,nourishment sticking about or between them1 when it is dry or viscous4 ,for the breaking of that part of our ,food1 which is not liquid1 ,nature has furnish'd us with ,teeth1 and those of two sorts3 ,for some are ordain'd to divide and break off smaller ,morsels from a larger ,mass2 others are made for the grinding those ,morsels into much smaller parts4 ,the ,teeth1 which serve to break off ,pieces of a convenient ,magnitude from a larger ,mass1 are of two sorts1 accommodated to the ,nature of the ,substance which we eat4 ,these are the ,incisores1 and the ,dentes ,canini4 ,if the ,substance1 which we have to eat1 be not hard1 but more easily penetrated and divided1 then the ,incisores are capable of making an ,impression upon it1 and fix'd firmly enough in the ,jaws to break off that part which they take hold of4 ,but if it be more solid1 and not easily penetrated1 nor any ,piece without difficulty to be separated from that ,body1 whereof it is a part2 then we apply the ,dentes ,canini1 or ,eye-,teeth1 to it1 which are not spread1 nor have such an edge as the ,incisores1 but are sharp and pointed like an ,awl1 and so do more readily penetrate a ,substance that is hard1 and which the ,incisores can scarcely make any ,impression upon4 ,and as the ,parts of a more solid ,body are commonly with more difficulty separated1 and there must be a greater stress put upon those ,teeth which pull it into pieces2 so these ,teeth are much more firmly fixed in the ,jaws than the ,incisores1 tho' they have but one single ,root4 ,besides1 the ,position of all these ,teeth is accommodated to their use1 as being planted opposite to the ,aperture of the ,mouth2 so that they may be conveniently apply'd to the ,substance which we have to eat1 before it is broken1 and when it is too large to be admitted within the ,mouth4 ,the ,teeth which do by a ,compression and ,attrition reduce the little ,morsels to smaller ,parts1 are from the manner in which they break the ,aliment1 called ,dentes ,molares1 because they do1 like so many ,mill-stones1 grind the ,food between them4 ,and that they might be render'd fit for this purpose1 they are made broad at that ,extremity1 which stands out of the ,gums1 by which means they retain some ,quantity of the ,food between them every time the lower ,jaw is pulled up and forc'd against the ,maxilla superior4 ,and as they are broad1 so they are formed with ,inequalities and ,protuberances2 and by the motion of the lower ,jaw1 from one side towards the other1 they grind what they have between them into pieces4 ,the ,position of these ,teeth too is as convenient as that of the ,incisores1 and the ,dentes ,canini3 ,for being design'd to break those pieces of our solid ,food1 which are taken into the ,mouth1 and these pieces1 when they are compress'd1 and mov'd by the ,dentes ,molares1 being apt to fly out of the ,mouth1 if there were no ,contrivance to prevent it1 they are placed beyond the ,aperture of the ,mouth1 and opposite to the ,cheeks1 which keep the ,food within that ,cavity1 and not only so1 but press it in between the ,dentes ,molares on one side1 as the ,tongue does on the other1 until they have sufficiently broken and divided it4 ,at the same time1 whilst the ,dentes ,molares are breaking the ,food1 there flows into the ,mouth a ,salival ,juice1 which mixes with it1 and not only serves to moisten it1 and to render it more apt and easie to be divided1 but seems to be the ,ferment1 by the ,benefit of which the ,food is dissolved and digested4 ,and therefore it is intimately mixed with it1 by the ,teeth agitating or stirring them together in ,mastication4 ,this ,liquor1 which we commonly call the ,saliva1 or ,spittle1 seems to be a ,composition made of two several ,juices1 very different in their ,nature3 ,and therefore the several ,parts of it are separated by their proper ,glands1 and ,nature has planted no fewer than four ,pair about the ,mouth1 which supply the ,juices that make the ,saliva2 to wit1 the ,parotides1 and the ,glandul ,nuckian1 the ,glandul ,maxillares intern1 and ,sublinguales4 ,whereas if the ,saliva were but one more simple ,liquor1 a less number of ,glands might have been sufficient4 ,at least there appears no ,reason why one of every ,pair should disembogue itself into the ,mouth so very near to the ,orifice1 by which a ,gland of some other ,pair throws in its ,juice2 and they are not rather all planted at more equal distances from one another1 so to flow in upon every part of the ,aliment at the same time4 ,not that ,i suppose1 as there are four ,pair of salivatory ,glands1 so there are four sorts of ,juices supply'd from them1 to make the ,saliva2 but1 as ,i hinted before1 that there are only two different ,juices that constitute it4 ,and these are not only sufficient1 but more proper to excite and secure that ,fermentation1 which is necessary to ,concoction4 ,for we find that most of those ,fermentations1 which arise upon ,mixtures made for ,experiments1 are produced from the mixture of two things2 and it is not so easie to find out three or four such ,liquors of a different ,nature1 as will1 upon the mixtion of them all1 produce a ,fermentation1 and from the omission of any one of them discover no ,discord or ,disposition to ferment3 ,besides1 it is certain that two do better secure the ,end1 which ,nature designs4 ,for1 if there were three or four different ,juices1 of which the ,saliva naturally consists1 these must all have their proper ,qualities preserved to them1 or else the ,fermentation1 which should arise between them1 will not necessarily follow upon their mixture2 and it is certain1 that there would be more ,danger1 that one of three or four should be deprived of its ,natural ,quality1 than one of two4 ,what ,nature these two ,juices are of1 ,i do not pretend positively to determine2 but so far as ,i have been able to make my ,conjectures about it from ,experiments1 ,i do think one of them to be an acid ,juice2 the other an oleaginous ,liquor1 something like ,oil of ,turpentine4 ,for amongst the many ,experiments ,i have made1 there was no one that gave me so much ,satisfaction1 as that which ,i made with ,oil of ,turpentine1 and ,oil of ,vitriol1 though ,i try'd several other things1 that will produce a ,fermentation upon their ,mixture4 ,and it was for this ,reason1 that ,i made the ,experiment with ,oil of ,turpentine and the other ,oil4 ,i took a piece of raw ,flesh1 and having cut it into pieces1 but much larger than what our more solid ,food is reduc'd to by due ,mastication1 ,i mix'd some ,crums of ,bread with it1 then ,i pour'd in the ,oil of ,turpentine to them1 and upon that the ,oil of ,vitriol2 and having shak'd them together1 ,i digested them about four ,hours in ,balneo ,mari1 and then shaking them again in the ,glass1 ,i found the ,meat dissolv'd1 and they all became a thickish ,pulp4 ,i could not but take notice1 that ,oil of ,camphire 7though it does not otherwise seem much different in its ,nature from ,oil of ,turpentine7 and ,oil of ,vitriol1 which upon mixture will produce an ,effervescence as well as the ,oil of ,turpentine and ,oil of ,vitriol1 yet did not touch the ,meat1 upon which ,i poured them1 so as in the least to dissolve them4 ,i cannot deny but that an ,acid1 and a ,solution of ,salt of ,tartar1 did dissolve some part of the ,flesh-meat1 which ,i mix'd them with1 but yet neither so soon1 nor so perfectly as the two forementioned ,oils4 ,and ,i do the rather think one of those ,juices1 which constitute the ,saliva1 to be of the ,nature of ,oil of ,turpentine1 than of a fix'd ,salt1 because it will correct and temper even ,oil of ,vitriol1 so as to render it more tolerable to the ,fibres of the ,stomach4 ,not that ,i suppose the acid part of the ,saliva to come near to the ,acidity of ,oil of ,vitriol4 ,for though1 when they are mix'd1 they will make a ,liquor that may not be injurious to the ,stomach2 yet the acid ,juice1 if it were so corrosive as ,oil of ,vitriol1 would certainly be injurious and painful to the ,salivatory ,ducts1 which convey it to the ,mouth before it is mix'd with the oleaginous ,liquor4 ,but ,i only say it is an ,acid1 and in some degree approaches to the ,nature of that ,oil4 ,and ,nature1 which can much better adapt several ,causes for the ,production of such an ,effect than ,art1 may attain her ,end by a more temperate ,acid2 though1 at the same time1 we may be able to make some probable and true ,conjectures about the ,nature of those ,causes from ,experiments4 ,it being most reasonable to suppose1 that there are but two sorts of ,juices1 of a different ,quality1 that make the ,saliva1 ,i do conceive1 that four of the eight ,salivatory ,glands1 or two ,pair of the four1 do supply one of these ,juices1 and the other four ,glands the other4 ,and this seems to be a very good ,reason1 why they are so planted1 and the ,orifice of their ,ducts so order'd1 that the ,juice1 which is supply'd by one ,gland1 is discharg'd into the ,mouth1 very near to the ,orifice1 by which the ,juice of a different ,nature is transmitted from another1 so that they must necessarily meet and mix together4 ,thus the ,glandul ,nuckian1 and ,parotides1 throw in two different ,juices by ,orifices1 which open into the ,mouth very near to one another2 and the ,glandul ,maxillares intern1 and ,sublinguales1 do below supply the same kind of ,juices by ,orifices1 that open so near to one another as to secure the mixture of the two different ,juices4 ,these ,glands1 ,i say1 do between them afford two divers sorts of ,liquors1 of such a ,nature as are apt to ferment upon their first ,mixture1 but perhaps more considerably when they come to be digested by the ,heat of the ,stomach4 ,so that the ,colluctation1 or ,fermentation1 which attenuates and concocts the ,food in the ,stomach1 does not ordinarily arise between the ,aliment and the ,saliva1 but between the several ,parts of the ,saliva it self4 ,and indeed1 if the ,saliva did not consist of two ,juices1 whose ,nature is in such a manner different1 as to render them apt to ferment upon their mixture1 it would be very hard to conceive how it should so readily and indifferently serve for the ,digestion of all ,eatables2 how it should ferment with1 and dissolve so great a variety of ,things1 not only of a different1 but of a contrary ,nature2 how it should ferment with ,acids as well as ,alkalies1 digest things that are cold1 as well as hot or temperate2 some things that are salt1 others that are insipid1 bitter and sweet1 mucilaginous1 oily1 c4 ,but if we suppose1 that the ,fermentation1 which serves for the ,digestion of the ,food1 arises from a peculiar difference in the ,nature of two ,juices1 which constitute the ,saliva1 it will be easie to give a rational ,account of our ,concoction of innumerable things of a different ,nature4 ,and this seems to be as effectual1 and a more certain way to attenuate and dissolve the grosser ,parts of our ,food1 than if the ,fermentation were made only between the ,saliva and the ,aliment3 ,besides1 the ,saliva seems to discover a ,fermentation upon the mixture of its constituent ,juices1 even at those times when we do not actually eat2 for it is always attended with ,bubbles1 and a ,froth1 when it has not been at all agitated in the ,mouth1 and many of those ,bubbles will remain for some considerable time after we have spit it out4 ,nature therefore having appointed the ,saliva for the digestion of the ,food1 has taken care that it shall be thrown in upon the ,aliment on every side4 ,thus the ,glandul ,nuckian1 and the ,parotides1 supply their ,juices to that part of the ,food1 which lies on the outside of the ,gums1 between the ,cheeks and the ,teeth1 and the ,glandul ,maxillares intern1 and ,sublinguales1 do bestow their ,liquor upon the ,meat1 which is within the ,teeth and ,gums4 ,neither has she had a ,regard only to that ,supply1 which is due to all the parts of our ,food1 but likewise to the mixture of the two different ,juices of the ,saliva1 which is necessary to its ,fermentation4 ,and therefore1 as ,i have already observ'd1 the ,orifices of the ,ducts1 which belong to one sort of ,glands1 are placed near the ,aperture of a ,duct1 which conveys a ,juice from one of the other ,glands4 ,so the ,ducts of the ,glandul ,nuckian1 and the ,ductus ,stenoniani1 do on each side open into the ,mouth1 near one another2 and the salivatory ,ducts of the ,glandul ,sublinguales1 and the ,maxillares intern1 though they have distinct ,orifices1 empty themselves under the same ,papill1 and the ,juices1 which are supply'd by them1 meet there1 and flow into the ,mouth together4 ,the several ,parts of the ,saliva being discharg'd into the ,mouth in such a manner as to meet and begin a ,fermentation1 the ,saliva does1 partly as it is agitated1 with the ,food by the ,teeth1 and some other parts of the ,mouth2 partly by its own ,fluidity1 insinuate it self into1 and mixes with the ,food1 and not only moistens and softens it1 but excites the ,fermentation1 which is to dissolve it4 ,and when the ,aliment is thus mix'd with the ,saliva1 which serves to ferment the whole ,mass1 it is then to be convey'd into the ,stomach1 that great digestive ,vessel of the ,body1 where the ,fermentation is not only continued1 but improved4 ,the ,nourishment being convey'd into the ,cavity of the ,stomach1 is there kept for some time in a digestive ,heat1 all which time it is under a ,fermentation1 produc'd by the different ,parts or ,juices of the ,saliva1 which are mix'd with it2 which ,fermentation does first agitate the more tenuious or subtil parts of the ,food1 and puts them into motion1 and so with the ,fermentation of its own1 and those ,alimentary ,parts1 which it first communicates a ,motion to1 improved by the ,heat of the ,stomach1 the ,saliva must necessarily act upon the grosser ,parts4 ,for the intestine ,motion1 which is excited in the ,mass1 does not give the ,particles1 which are fermented1 the same ,tendency1 but what is so various and confus'd1 that they must inevitably strike not only one against another1 but against those which are more gross1 so as to attenuate them1 sometimes by a ,collision1 which strikes off smaller ,particles from the larger ,parts2 sometimes by a ,compression1 when the ,particles which are in ,motion1 happen to strike directly against any grosser ,part1 on every side of it1 sometimes by a kind of ,explosion4 ,for without doubt the ,saliva1 which is fluid1 insinuates it self into the ,interstices of the more crass ,parts of the ,aliment1 and whatever is agitated and expanded in those ,interstices1 requiring a larger space for the ,freedom of its ,motion1 and offering a ,violence to every thing that opposes its ,tendency1 will1 like ,gun-powder included in a ,shell1 force its way out1 and tear to pieces that ,matter1 which does endeavour to confine it4 ,thus the grosser ,parts are broken and divided1 until they are at last so far attenuated as to mix more equally with the ,fluid1 and with them to make one ,pulp or ,chylous ,mass4 ,and although ,i do not apprehend how the ,stomach should by its reciprocal ,motions in ,inspiration and ,expiration1 be able to break and attenuate any ,matter1 that will not be softned and dissolved by ,agitation in a ,liquid2 yet it is certain that these ,motions1 caused by the ,diaphragm and ,abdominal ,muscles in ,respiration1 do make those ,parts1 which are broken off1 as they are dissolv'd1 mix intimately with the more ,liquid2 as the ,meat which ,i digested with ,oil of ,turpentine1 and ,oil of ,vitriol1 did by ,agitation mix more equally with the ,oils1 and became a ,pulpament4 ,as the ,juices1 which constitute the ,saliva1 do ferment upon their mixture1 so it is probable1 that from their ,mixture and ,fermentation there results such a ,tertium quid1 as is apt to ferment with the ,bile4 ,and therefore1 when the ,aliment has been under the ,fermentation1 excited by the ,saliva1 a sufficient time1 it is then thrown into the ,duodenum1 where it meets with the bilious ,juice1 which flows into that ,intestine from the ,liver1 from which a new ,fermentation seems to begin2 and the ,commotion of the ,parts of the ,aliment being still continued1 does carry on the ,business of ,digestion until the ,food is perfectly concocted3 ,though it is probable1 that this new ,fermentation serves not only for the more perfect ,digestion of the ,food1 but likewise for the ,separation of the ,chyle from the feculent ,parts4 ,neither do ,i by a random ,guess1 and an ungrounded ,conjecture1 suppose that from the ,mixture and ,fermentation of the two ,juices1 which constitute the ,saliva1 there results a ,matter1 which is apt to ferment with the ,bile4 ,but to me the ,notion seem'd to be confirmed by an ,experiment that ,i made4 ,for considering with my self1 that the ,bile is generally allow'd to have much of a saponary ,nature1 ,i made a ,solution of ,soap in fair ,water1 and mix'd it with the ,oils of ,turpentine and ,vitriol first put together1 and from their ,mixture ,i observ'd a very easie and gentle ,fermentation1 which continued for a considerable time4 ,a ,discourse concerning some ,influence of ,respiration on the ,motion of the ,heart1 hitherto unobserved4 ,by ,j4 ,drake1 ,m4 ,d4 ,f4 ,r4 ,s4 ,tho' divers accurate ,treatises of the ,heart1 and its ,action1 have been written by ,learned ,men of several ,nations1 especially by two of our own ,country2 the ,great ,dr4 ,harvey1 to whose happy ,sagacity this ,nation owes the ,glory of the ,invention of the ,circulation of the ,blood2 and the incomparable ,dr4 ,lower1 to whom we are beholden for a compleat ,display of the ,mechanical ,structure of the ,heart1 and a most ingenious ,rationale of its ,action4 ,yet there remain several ,doubts and ,difficulties about it 7in my ,opinion7 not sufficiently accounted for2 towards the resolving some of which1 ,i shall offer what my own ,thoughts have suggested to me1 and leave it to the ,consideration of the ,reader4 ,the ,learned ,dr4 ,lower 7whose accurate ,piece on this ,argument will insure his ,reputation so long as ,physical ,knowledge shall last in esteem7 has so well accounted for the ,systole1 or ,contraction of the ,heart1 from the ,mechanical ,structure of it1 that he seems almost to have exhausted the ,subject2 and had he been as happy in discovering the true cause of the ,diastole1 he had left little room for the ,industry and ,sagacity of others about this ,viscus4 ,but having judiciously and solidly explain'd the ,systole1 he contents himself to ascribe the ,diastole to a motion of ,restitution1 which account gives me no ,satisfaction3 ,because the ,systole being the proper1 and 7as himself confesses7 the only motion of the ,heart1 a ,state of ,contraction seems to be the natural ,state1 and consequently without ,external ,violence1 it shou'd have no ,diastole at all4 ,this will appear more plain1 if we consider the ,circumstances of it1 and its ,motion1 as a ,muscle1 with respect to other ,muscles4 ,that ,contraction is the proper ,action1 and ,state of all ,muscles1 is evident from ,experience of ,fact1 as well as ,reason4 ,for1 if any ,muscle be freed from the power of its ,antagonist1 it is immediately contracted1 and is not by any ,action of the ,will1 or ,spirits1 to be reduced to a ,state of ,dilatation4 ,thus1 if the ,musculi ,flexores of any ,joint be divided1 the ,extensores of that ,joint being by that means free'd from the contrary ,action of their ,antagonists1 that ,joint is immediately extended without any consent of the ,will1 and in that ,state it remains2 and so ,vice versa1 if the ,extensores be divided4 ,from whence it is plain1 that the ,muscles have no restitutive ,motion1 but what they derive from the ,action of their ,antagonists1 by which they are balanc'd4 ,thus likewise the ,sphincters of the ,gula1 ,anus and ,vesica1 having no proper ,antagonists1 are always in a ,state of ,contraction1 and suffer nothing to pass them1 but what is forced through them by the contrary ,action of some stronger ,muscles1 which1 though not properly to be call'd ,antagonists1 yet on all necessary ,occasions perform the ,office of such4 ,that the ,heart is a ,muscle1 furnish'd and instructed for ,motion like other ,muscles1 is 7in my ,opinion at least7 demonstrated beyond ,contradiction by ,dr4 ,lower and others4 ,and1 as it is a ,solitary ,muscle without any proper ,antagonist1 and not directly under the power of the ,will1 nor exercising ,voluntary ,motion1 it approaches nearest to the ,sphincter kind1 which only has these ,conditions in common with it4 ,but in constant and regular ,alternations of ,contraction and ,dilatation1 it differs exceedingly from all the ,muscles of the ,body4 ,this reciprocal stus of the ,heart has given the ,learned abundance of trouble2 who1 finding nothing peculiar in the ,structure1 which shou'd necessarily occasion it1 nor any ,antagonist1 whose re-action should produce it1 have been extreamly perplex'd to find out the cause of it4 ,but passing over the various ,opinions of ,authors1 to avoid being tedious1 ,i shall take notice here only of the very ,learned ,dr4 ,lower's1 in whose ,account of the ,systole1 however solid and ingenious1 ,i observe something deficient1 and whose ,hypothesis of the ,diastole ,i think to be precarious and false4 ,this ,excellent ,author1 having by sound ,arguments drawn from the ,structure and ,mechanism of the ,heart1 establish'd the ,certainty of its ,muscular ,motion1 rests satisfied1 without taking notice of any ,assistance1 that the ,heart receives from any other ,part1 except from the ,brain1 by the means of the eight pair of ,nerves4 ,sidenote3 ,part #b;d4 ,prop4 #fg4 ,prop4 #gc4 ,sidenote3 ,prop4 #gf4 ,the ,accurate ,borellus1 in his ,oeconomia ,animalis1 computes the ,motive ,power of the ,machine of the ,heart to be equal to1 or to surmount that of a ,weight of #cjjjl4 ,the ,obstacles to the ,motion of the ,blood thro' the ,arteries he esteems equivalent to #ahj1jjjl4 which is #fj times as much as he rates the ,force of the ,heart at4 ,then deducting #de1jjjl4 for the adventitious ,help of the ,muscular ,elastic ,coat of the ,arteries1 he leaves the ,heart with a ,force of #c1jjjl4 to overcome a resistance of #ace1jjjl4 that is1 with #a1 to remove #de4 ,this stupendous ,effect he contents himself to ascribe to the ,energy of ,percussion4 ,but1 had he proceeded in his ,calculation to the ,veins1 which he allows to contain constantly a quantity of ,blood1 quadruple to the ,contents of the ,arteries1 and to which this ,energy of ,percussion does either not reach at all1 or but very languidly1 he might probably have seen a necessity for some other ,expedient to remove so insuperable a ,difficulty4 ,but not to insist rigorously on the ,exactness of this ,calculation1 7though the great ,abilities of the ,author in this way1 and his ,ingenuity and ,modesty1 are a sufficient ,warrant for the ,accuracy of his ,computations1 and the ,fidelity of his ,accounts7 we may allow a much greater ,deduction1 than would be justifiable1 without lessening the ,difficulty4 ,but this ,account ,i have taken notice of purely for the sake of the ,calculation1 which may be of use in the ,sequel2 the account it self being in other respects more defective than ,dr4 ,lower's1 to which we will return4 ,the ,doctor1 notwithstanding his great ,sagacity1 appears 7to me7 to have overlook'd something of very great moment1 and importance in the explication of the ,action of the ,heart4 ,for1 tho' it should be granted1 that the ,muscular ,fibres of the ,heart acted by the ,nerves1 are the immediate ,instruments of its ,constriction or ,systole1 yet it must not be denied1 that the ,intercostal ,muscles and ,diaphragm are of great service to aid and facilitate this ,contraction1 by opening a ,passage for the ,blood through the ,lungs1 which denied would be an invincible ,obstacle4 ,neither do they promote it that way only4 ,the manner how they farther assist the ,heart in its ,contraction1 will appear manifestly1 if we consider the different ,posture1 ,situation1 and ,capacity of the ,blood-,vessels of the ,lungs in the several times of ,elevation and ,depression of the ,cost4 ,the ,pulmonary ,artery rises from the right ,ventricle of the ,heart1 and runs in one ,trunk1 till it comes to the ,aspera ,arteria1 where it is divided1 and sends a ,branch along with each ,division of the ,aspera ,arteria1 according to all the minutest ,subdivisions1 of which it is likewise subdivided1 accompanying all the ,bronchi1 in their whole progress through the ,lungs4 ,the ,pulmonary ,vein1 which empties itself into the ,left ,ventricle of the ,heart1 spreads it self on the ,aspera ,arteria and ,bronchi1 in the same manner that the ,artery does4 ,the necessary confluence of this ,disposition if1 that this ,artery and ,vein being co-extended with1 and fasten'd to the ,bronchi1 must needs suffer such alteration of ,superficial ,dimensions1 as the ,bronchi do in the ,elevation or ,depression of the ,cost4 ,while the ,ribs are in a ,state of ,depression 7whether before ,commerce with the ,external ,air or after7 the ,annular ,cartilages of the ,bronchi shrink one into another1 and by that means their ,dimensions are exceedingly contracted4 ,in conformity to this condition of the ,bronchi1 the ,pulmonary ,artery and ,vein must likewise1 either by means of their ,muscular ,coats1 contract themselves to the same ,dimensions1 or lye in ,folds or ,corrugations1 which is less probable4 ,on the other hand1 when the ,ribs are elevated1 and the ,diaphragm bears downward1 the ,air rushing into the ,lungs1 shoots out the ,cartilaginous ,rings1 and divaricates the ,branches of the ,trachea1 and by them extends and divaricates the several ,divisions of the ,pulmonary ,artery and ,veins1 and thereby lengthens and enlarges their ,cavities4 ,this enlargement of their ,cavities is very considerable1 not only upon the score of the addition1 which they receive in length thereby1 but also upon the account of their ,divarication4 ,for whereas1 when the ,ribs are depress'd1 and the ,lungs subside1 the ,blood-vessels are not only contracted1 7as ,i have already observ'd7 but their ,branches1 which are exceeding numerous1 approach one another1 and lie in juxta-position1 by which their ,cavities are very much compress'd and streighten'd3 ,when the ,ribs are elevated1 and the ,lungs turgid with ,air1 not only the ,fibres1 by which their ,coats in the opposite state were contracted1 are extended2 but those innumerable ,vessels1 which lying before in lines almost parallel upon one another1 compress'd one another1 making an acute ,angle at their ,junctures1 are divaricated and separated from each other1 and make an obtuse1 whereby their ,channels are widened4 ,thus a passage is open'd to the ,blood1 from the ,right ,ventricle of the ,heart to the ,left1 through the ,lungs1 to which it could not otherwise pass2 and the opposition1 which the ,blood contain'd in that ,ventricle1 must otherwise necessarily have made to its ,constriction1 is taken off1 and the ,systole thereby facilitated4 ,nor is that all4 ,for the ,diastole being caus'd 7as ,i shall in the ,sequel shew7 by the force of the ,blood rushing into the ,ventricles1 this ,ampliation and ,extension of the ,pulmonary ,artery is a sort of ,check or ,counterpoise to it1 and prevents an endeavour towards two contrary ,actions at once1 which must necessarily frustrate both4 ,for the ,heart being a ,springy1 ,compressible ,body1 whose proper ,action1 which is ,contraction1 depends on the influx of certain ,fluids into its ,fibers1 or ,substance2 and containing besides a ,fluid in its ,ventricles1 or great ,cavities1 in one of which is the ,mouth of this ,artery1 the action of this ,vessel must in great measure resemble that of a ,syringe1 whose extremity is immers'd in ,water1 the ,enlargement or ,expansion of the ,chanels of the ,artery answering the drawing of the ,embolum1 as the constrictive motion of the ,muscle of the ,heart does the pressure of the ,atmosphere upon the ,surface of the ,water1 the one making way for the fluid1 and the other forcing it to follow1 where the resistance is least4 ,in this ,sense we may allow a sort of ,attraction to the ,pulmonary-,artery1 depending wholly upon the ,action of the ,intercostal ,muscles and ,diaphragm1 which we must therefore confess to be very serviceable and instrumental in promoting the ,systole of the ,heart4 ,but if the ,learned ,author be deficient in his ,account of the ,systole2 that is1 if he has not observ'd all the ,mechanism and ,contrivance of ,nature for the ,contraction of the ,heart2 much less sufficiently has he accounted for the ,diastole1 or ,dilatation of it1 which he ascribes to a motion of ,restitution of the over-strain'd ,fibres1 which yet he confesses are made for ,constriction only4 ',tis true1 he immediately after joins the ,influx of the ,blood as a concurrent ,cause2 but from the slight notice that he takes of it1 'tis plain1 that he did not so much as dream of any great share it had in that ,action4 ,his ,words are these3 ,sidenote3 ,de ,corde1 ,pag4 #ge4 ,quin 7ut obiter hoc moneam7 omnis motus contractione perficiatur1 ,cordis ,fibr ad constrictionem solum fact sint1 apparet quoque ,cordis motum totum in ,systole positum esse2 cumque ,fibr ultra tonum suum in omni constrictione eius tendantur1 idcirco ubi nixus iste absolvitur1 motu quasi restitutionis ,cor iterum relaxatur1 sanguine ,venis influente rursus distenditur2 nullo enim cordis motu1 nisi tensionem suam remittente1 ab irruente sanguine ,diastole ejus libratis adeo viribus succedit4 ,i have transcrib'd the intire ,paragraph1 because it contains his whole ,hypothesis of the ,diastole1 and all the notice that he takes of it through his whole ,work4 ,but how slender soever this may prove1 it is the most substantial that ,i have any where met with1 except a late one of ,mr4 ,cowper1 which is properly an ,improvement of this1 and shall be consider'd in the ,sequel4 ,but if ,contraction be the sole ,action of these ,fibres 7as this ,great ,man confesses it to be7 and as indeed it is of all ,muscular ,fibres1 ,i wonder how so judicious a ,writer came to slip into such an ,absurdity1 as to call their ,distention 7vulgarly but improperly call'd ,relaxation7 a ,motion of ,restitution4 ,for from the ,nature of those ,fibres1 and their disposition in the ,structure of the ,heart1 the natural ,state of the ,heart appears manifestly to be ,tonical1 and its ,dilatation a ,state of ,violence2 and consequently1 the ,constriction is the true motion of ,restitution1 and the ,state to which it will spontaneously return1 when the ,force is taken off1 which is the work of the ,intercostal ,muscles and ,diaphragm4 ,thus we are left still to seek for the true ,cause of the ,diastole1 which seems to me to be the main and most difficult ,phnomenon1 relating to the ,heart and the ,circulation of the ,blood4 ,but in ,mr4 ,cowper's ingenious ,introduction to his ,anatomy of ,humane ,bodies1 ,i find the ,share which ,dr4 ,lower hints the ,blood to have in that ,action1 further prosecuted1 and improved into the main ,instrument of the ,dilatation of the ,heart1 wherein ,i agree intirely with him4 ,but as to the manner1 and reasons of its being so very instrumental1 ,i can't be so perfectly of his mind4 ,the ,heart 7says this accurate ,anatomist7 of an ,animal bears a great ,analogy to the ,pendulums of those ,artificial ,automata1 ,clocks and ,watches1 whilst its motion is performed like that of other ,muscles1 the ,blood doing the ,office of a ,pondus4 ,this ,explication1 being but a ,simile without a distinct application to ,particulars1 is beside so very short1 that ,i can at best but give a conjecture at the meaning2 which if ,i mistake1 ,i shall deserve to be excused1 and expect to be better inform'd4 ,by the ,bloods doing the ,office of a ,pondus1 ,i suppose he means1 that the ,blood contributes in the same manner to the motion of the ,heart1 as the ,weights do to that of the ,pendulum of a ,clock4 ,if so1 the ,blood1 according to him1 must be the ,instrument of ,constriction2 and ,dilatation must be the ,natural ,state1 or ,spontaneous ,motion1 to which it wou'd1 when under no violence1 return2 the contrary of which1 ,i presume1 will appear e're ,i have done4 ,but if he means1 that the ,blood in its reflux1 by gravitating on the ,auricles and ,ventricles1 dilates and expands 'em1 acting therein as a ,counterpoise to its contractions as a ,muscle1 ,i cou'd wish his ,design had not bound him up to so narrow a compass1 and that he had given us an explication at large of so abstruse and so important a ,phnomenon3 ,because the ,specifick ,gravity of the ,blood seems to me a cause by no means alone adequate to the effect1 which it is here suppos'd to produce4 ,for1 if the ,blood acts only as a weight by meer gravitation1 then that part of it only which descends from the ,parts above the ,heart can be employ'd in that ,action4 ,this at the largest computation can't amount to ,five pound weight1 and must1 according to the computation of ,borellus1 force a ,machine1 that is able to overcome a resistance of #ace1jjjl4 ,i leave every ,man to deduct what he shall upon examination find reasonably to be deducted1 and yet shall rest secure1 that it is not to be effected in the least with so small a ,weight4 ,but neither does the ,refluent ,blood gravitate in any such proportion1 as ,i have here assign'd4 ,for to make a true estimate of its ,gravitation1 we must consider the ,circumstances of the ,liquor suppos'd to gravitate2 in which it very much resembles ,water inclos'd in a recurve ,tube1 of which1 if the length of the two ,legs be equal1 it may be suspended in the ,air full of ,water1 with the ,extremities downwards1 without losing a drop1 although the ,diameter of those ,legs should be very unequal4 ,the ,case of the ,arteries and ,veins is pretty near a parallel to a ,tube1 so fill'd and inverted4 ,for1 if the ,arteries and ,veins be continued ,tubes1 7as by the ,microscope they are made to appear7 then supposing their contents to have no other determination of motion1 than their own weight wou'd give them1 the contain'd ,fluids must be ,counterpoises to each other4 ,for the ,veins and ,arteries being join'd at the smaller ,extremities1 and the larger of both terminating in the same parallel ,line1 it is impossible1 according to the ,laws of ,hydrostaticks1 that the contents of either shou'd overbalance t'other4 ,how far then must it fall short of forcing the natural ,power and ,resistance of so strong a ,muscle as the ,heart1 by meer ,gravitation8 ,the ,blood indeed has a ,progressive ,motion through its ,vessels1 wherein it differs from ,water1 in a recurve ,tube1 in the ,experiment above-stated4 ,but1 if the natural ,gravitation of the ,blood contributes nothing to the ,dilatation of the ,heart1 this progressive ,motion will not be found much more sufficient4 ,for1 as this ,motion is deriv'd intirely from the ,heart's ,constriction 7as all ,accounts hitherto derive it7 cou'd the ,blood be suppos'd to re-act upon it by the ,heart1 with all the force first impress'd upon it by the ,heart1 it would be insufficient1 unless we will suppose the ,force communicated to be superiour to the ,power ,communicant1 which is absurd4 ,but when the just and necessary ,deductions for the ,impediments1 which the ,blood meets with in its ,progress through the ,vessels1 shall be made1 the remaining ,force will be found so exceeding weak1 that to prop the ,blood through the ,veins may be a task alone too great for so small a ,power1 without charging it with the additional difficulty of forcing the ,muscle of the ,heart4 ,alphonsus ,borellus1 after a great deal of solemn pains taken to shew his ,care and ,exactness1 and to possess his ,reader of the ,truth of his ,calculations1 casts up the force of the ,heart1 and the ,muscular ,coat of the ,arteries1 to be together equal to a weight of #c1gejl4 and allots them a ,resistance equal to #ahj1jjjl4 to overcome which is #de to #a4 ,to make up for a disproportion1 by his own confession1 incredible to those who have not consider'd the ,matter as he had done1 he flings into the ,scale the additional ,force of ,percussion1 which he leaves indefinite1 and thinks sufficient to force any quiescent finite ,resistance whatsoever4 ,but as this ,account and ,hypothesis are part of a ,posthumous ,work 7if a liberty of ,conjecture may be allow'd in so uncertain a ,matter17 ,i shou'd suspect1 that these ,papers were left unfinish'd by ,borellus2 or at least1 that in many places the last ,hand was never put to them4 ,for neither in this ,place1 nor any other of this ,work1 does he account for any more than the ,systole of the ,heart1 and the resistance which is made to the progressive motion of the ,blood in the ,arteries only4 ,this alone he found to exceed the ,power of the ,heart so prodigiously1 that he seems to shuffle it off his ,hands with a general and precarious ,solution1 as a difficulty that he was desirous to be rid of4 ,for1 having ascrib'd this stupendous 7as he himself calls it7 effect to the ,energy of ,percussion1 he takes no care to satisfie his ,reader any farther about it1 or to refer him1 or give him the expectation of ,satisfaction any where else2 although he has an express ,treatise on the ,force of ,percussion1 which was written preparatory to this1 and to which he frequently refers in other ,places of this ,work4 ,but what confirms my suspicion1 that this part was intended for a farther ,revise by the ,author1 is1 that he has left the ,progress of the ,blood through the ,veins1 and the ,diastole of the ,heart1 absolutely untouch'd1 tho' they are ,difficulties of a much greater magnitude than this1 which he has attempted to account so slightly for3 ,for1 in these he is excluded the benefit of ,percussion1 and has yet a greater resistance to overcome without it4 ,omissions of this kind are so unusual with this ,author1 where-ever he knows himself to go upon sure grounds1 that it is to me an ,argument1 that he doubted the sufficience of his ,percussion1 and reserv'd these important ,phnomena for farther ,consideration1 without plunging himself into such an ,absurdity1 as to ascribe to ,percussion any such ,energy as to be able 7so broken as it returns to the ,heart7 by its re-action to force that ,power1 from whence only it was at first deriv'd4 ,dr4 ,lower1 and ,mr4 ,cowper1 deliver their ,opinions of the ,cause of the ,dilatation of the ,heart so very short1 and without any ,arguments to support them1 that by exposing them naked1 they seem rather to discourse of it transiently1 as ,men oblig'd by the ,nature of their ,subjects to say something of it1 than solicitous to give any full or satisfactory ,account2 and therefore ,i shall proceed no farther upon them here4 ,but though the ,hypothesis of ,borellus may1 in this ,case1 be found precarious or insufficient 7a ,misfortune that has befallen him in divers other ,particulars7 his ,theory holds still good4 ,at least it ought to be allow'd1 in justice to his great ,abilities and ,exactness1 till some ,body convicts him of some material ,error in his ,calculations1 which has not as yet been done by any ,body1 that ,i know of4 ,supposing then the force of the ,heart1 and of the ,muscular ,coat of the ,arteries1 as likewise of the resistance1 which they must overcome1 to be computed with any degree of accuracy1 there remains yet such a prodigious disproportion to be accounted for1 as requires some more powerful ,agent1 than any yet assign'd1 to make up the deficiency4 ,what assistance the ,heart receives from the action of the ,thorax towards the facilitating its ,contraction1 without which assistance there cou'd have been no ,systole1 has been already shewn4 ,but neither the ,intercostal ,muscles1 or ,diaphragm1 which are so instrumental in that part of its action1 can contribute any thing to the ,diastole2 because they serve only to enlarge the ,cavity of the ,thorax1 and thereby to open a passage to the ,blood from the ,heart1 and promote its ,constriction4 ,whatever therefore the force is1 that dilates the ,heart1 and is the cause of the ,diastole1 it must be equal to that of the ,heart1 the ,intercostal ,muscles and ,diaphragm2 to all which it acts as an ,antagonist4 ,i take no notice of the ,serratus ,major ,anticus1 and other ,muscles2 which have an obscure share in the ,elevation of the ,cost1 because as much may reasonably be deducted upon the account of the ,obliquus externus ,abdominis1 and other ,muscles2 which having their ,insertions on some of the lower ,ribs are as instrumental towards the ,depression of them1 and so balance the ,account4 ,but the chief use of these is in violent ,respiration3 ,in ordinary ,respiration their share is small4 ,such a real ,power 7which may in the least be suspected of any share in this ,action7 is hard1 perhaps impossible to be found in the ,machine of any ,animal ,body2 and yet without some such ,antagonist1 it is as impossible the ,circulation of the ,blood should be maintain'd4 ,all the ,engines yet discover'd within the ,body1 conspire towards the ,constriction of the ,heart1 which is the ,state of ,quiescence1 to which it naturally tends4 ,yet we find it alternately in a ,state of ,violence1 that is1 of ,dilatation2 and this upon necessity1 because upon this ,alternation depends all ,animal ,life4 ,some sufficient ,cause ,external must therefore be found1 to produce this great ,phnomenon2 which ,cause must be either in the ,air1 or ,atmosphere1 because we have no constant and immediate ,commerce with any other ,mediums4 ,some great ,physicians observing this1 and that depriv'd by whatsoever means of ,communication with the external ,air1 we became instantly extinct1 have imagin'd1 that in the ,act of ,inspiration certain purer parts of the ,air1 mixed with the ,blood in the ,lungs1 and was convey'd with it to the ,heart1 where it nourish'd a sort of ,vital ,flame1 which was the ,cause of this reciprocal stus of the ,heart4 ,others not quite so gross1 rejecting an ,actual ,flame1 have fancied1 that these fine ,parts of ,air mixing with the ,blood in the ,ventricles of the ,heart1 produc'd an ,effervescence which dilated it4 ,but these ,fancies have been long since exploded and condemn'd upon ample ,conviction2 and 'tis a ,point yet undetermin'd1 whether any ,air does mix with the ,blood at all in the ,lungs1 or not4 ,but supposing1 that some ,air may insinuate it self into the ,pulmonary ,vein1 it can no other way dilate the ,heart than by an ,effervescence in the ,left ,ventricle1 which wou'd not dilate the ,right4 ,but this ,opinion is contradicted by ,autopsie1 and too laboriously confuted by others1 to be brought upon the ,stage again here4 ,there remains therefore only the gross ,body of the ,atmosphere to be considered1 which is undoubtedly the true ,antagonist to all those ,muscles1 which serve for ordinary ,inspiration1 and the ,constriction of the ,heart4 ,this will appear more evidently1 if we consider not only the ,power1 but the ,necessity of its ,action upon ,animal ,bodies1 as well as the want of other sufficient ,agents4 ,the ,heart is a ,solitary ,muscle of very great strength1 and the ,intercostal ,muscles and ,diaphragm1 which likewise have no ,antagonists1 are a vast additional ,force1 which must be balanc'd by the contrary ,action of some equivalent ,power or other4 ,for1 tho' the ,action of the ,intercostal ,muscles be voluntary1 that does not exempt them from the condition of all other ,muscles serving for voluntary motion1 which wou'd be in a ,state of perpetual ,contraction1 notwithstanding any ,influence of the ,will1 were it not for the ,libration of ,antagonist ,muscles4 ,this ,libration between other ,muscles1 is answer'd by the ,weight of the incumbent ,atmosphere1 which presses upon the ,thorax and other parts of the ,body4 ,and1 as in all other voluntary ,motions the influence of the ,will only gives a prevalence to one of its two ,powers before equilibrated1 so here it serves to enable those ,muscles to lift up a weight too ponderous for their strength not so assisted2 and therefore as soon as that assistance is withdrawn1 the ,cost are again depress'd by the meer ,gravitation of the ,atmosphere1 which wou'd otherwise remain elevated through the natural ,tendency of those ,muscles to ,contraction4 ,this is evidently prov'd from the ,torricellian ,experiments1 and those made upon ,animals in ,mr4 ,boyle's ,engine2 where1 as soon as the ,air is withdrawn1 and the pressure thereby taken off1 the ,intercostal ,muscles and ,diaphragm are contracted1 and the ,ribs elevated in an instant1 and can't by any ,power of the ,will be made to subside1 till the ,air is again let in to bear them forcibly down4 ,sidenote3 ,de ,respirationis ,organis ,usu4 ,it were scarce worth while to take notice here of a ,mistake of the ,learned ,dr4 ,willis1 were it not for the great ,authority of the ,man1 which is almost sufficient to keep ,error in countenance4 ,the ,doctor having observ'd1 that the ,fibres of the ,external and ,internal ,intercostal ,muscles ran in a contrary order1 as it were1 decussating each other1 takes occasion from thence to fansie1 that there was an opposition in their ,office2 and that as the ,external serv'd to raise up the ,ribs1 the ,internal drew them down again1 forgetting at that time1 ,that1 when a contractile ,body is fasten'd at the several ends to ,points unequally moveable1 let the ,contraction happen in what part or manner soever1 the more moveable ,point must be drawn towards the less moveable3 ,by which ,rule1 whether ,external or ,internal ,intercostals be contracted1 the lower ,ribs will be forc'd to approach the upper1 that is1 be rais'd up4 ,as in the ,elevation of the ,cost1 the ,blood1 by the passage that is open'd for it1 is in a manner solicited into the ,lungs2 so in the ,depression of them1 by the subsidence of the ,lungs1 and the ,contraction of the ,blood-,vessels1 both which are consequent thereof1 the ,blood is forcibly driven1 as it were with an ,embolum1 through the ,pulmonary ,vein into the ,left ,ventricle of the ,heart4 ,and this1 together with the general ,compression of the ,body by the weight of the ,atmosphere1 which surrounds and presses upon the whole ,surface of it1 is that ,power which causes the ,blood to mount in the ,veins1 after the force impress'd upon it by the ,heart is broken and spent1 and which is sufficient to force the ,heart from its natural ,state to ,dilatation4 ,he that is able to compute the weight of a ,column of ,air1 equal to the ,surface of the whole ,body1 will readily grant it a power sufficient for the ,effects1 which are here ascrib'd to it4 ,and when he considers1 that the ,bodies of ,animals are compressible ,machines1 he will find that it must of necessity affect them in the manner here laid down4 ,but though our ,bodies be entirely compos'd of ,tubuli1 or ,vessels fill'd with ,fluids2 yet this pressure1 how great soever1 being equal1 cou'd have no effect upon them1 if the superficial ,dimensions were not easily variable2 because being compress'd on all parts with the same degree of ,force1 the contain'd ,fluids cou'd not any where begin to recede1 and make way for the rest to follow1 but wou'd remain as fix'd and immoveable as if they were actually solid4 ,but by the ,dilatation of the ,thorax1 room is made for the ,fluids to move1 and by the ,coarctation of it1 fresh motion is imprest1 which is the main ,spring whereby the ,circulation is set and kept going4 ,this reciprocal ,dilatation and ,contraction of the superficial ,dimensions of the ,body1 seems so necessary to ,animal ,life1 that there is not any ,animal so imperfect as to want it1 at least none to the inward ,structure1 of which our ,anatomical ,discoveries have yet reach'd4 ,for1 tho' most kinds of ,fish and ,insects1 want both moveable ,ribs and ,lungs1 and consequently have no dilatable ,thorax1 yet that want is made up to 'em by an ,analogous ,mechanism1 answering sufficiently the ,necessities of their ,life4 ,those ,fishes which have no ,lungs1 have ,gills1 which do the ,office of ,lungs1 receiving and expelling alternately the ,water1 whereby the ,blood-,vessels suffer the same alteration of ,dimensions1 that they do in the ,lungs of more perfect ,animals4 ,the ,lungs or ,air-,vessels of ,insects1 are yet exceedingly more different in ,structure1 ,distribution1 and ,situation from those of perfect ,animals1 than those of ,fishes are1 and yet in their ,use and ,action agree perfectly with both2 that is1 receiving and expelling the ,air1 and varying the ,dimensions and ,capacities of the ,blood-,vessels4 ,these having no ,thorax1 or separate ,cavity for the ,heart and ,air-,vessels1 have the latter distributed through the whole ,trunk of their ,bodies1 by which they communicate with the ,external ,air through several ,spiracula or ,vent-holes1 to which are fasten'd so many little ,trache1 or ,wind-pipes1 which thence send their ,branches to all the ,muscles and ,viscera1 and seem to accompany the ,blood-,vessels all over the ,body1 as they do in the ,lungs only of perfect ,animals4 ,by this disposition in every ,inspiration1 the whole ,body of these little ,animals is inflated1 and in every ,expiration compress'd2 and consequently the ,blood-,vessels must suffer a ,vicissitude of ,extension and ,contraction1 and a greater motion must thereby be impress'd upon the ,fluids contain'd in them1 than the ,heart1 which does not in those ,creatures appear to be ,muscular1 seems capable of giving4 ,the only ,animal that is exempted from this necessary condition of ,breathing1 or receiving and expelling alternately some ,fluid into and out of the ,body1 is a ,ftus4 ,but this1 while included in the ,womb1 has little more than a vegetative ,life1 and ought scarce to be reckon'd among the number of ,animals4 ,for1 were it not for that small share of ,muscular ,motion1 which it exercises in the ,womb1 it might without absurdity be accounted for as a ,graft upon1 or ,branch of the ,mother4 ,sidenote3 ,boyle of the ,elasticity of ,air4 ,pechlinus de ,aeris ,alimenti defectu4 ,concerning the immediate ,matter1 and ,means of ,life1 and ,nutrition1 ,authors are not agreed1 nor is it the business of this place to reconcile1 or decide their ,differences1 but to account for the ,motion of the ,blood through the ,vessels only4 ,in order to this1 it will be necessary to observe1 that the ,pulsation of the ,heart in a ,ftus is so very weak and obscure1 and the ,motion of the ,blood so extream slow and languid1 as to be scarce1 if at all perceivable1 as has been experienced in the ,dissection of ,puppies before ,respiration had4 ,to produce such a feeble ,palpitation1 and creeping ,motion1 no greater force seems to be required1 than may be deriv'd from the ,communication between the ,vessels of the ,mother and ,ftus in the ,placenta4 ,i am not ignorant1 that divers very ,learned ,anatomists 7whom the ,crowd have implicitly follow'd7 have absolutely rejected all ,communication between these ,vessels4 ,but1 with submission to ,great ,authorities1 ,i think they have acted arbitrarily1 and without sufficient ,warrant from ,reason or ,experiment3 ,for neither are the ,arguments which they bring against it conclusive1 nor the ,office which they assign to the ,umbilical ,vessels in lieu of it1 proper1 or natural to those ,vessels1 or the reality of the ,fact made out by any substantial ,reasons4 ,those that reject this ,communication usually do it in favour of one or both of these ,opinions1 that the ,arteries of the ,uterus do deposite a ,nutritive ,juice1 or a ,juice impregnate with ,air in the ,placenta1 which is suck'd in by the ,umbilical ,vein1 and convey'd to the ,ftus1 for the necessary ,uses of ,nutrition and ,life4 ,now those that patronize either of these ,opinions1 lead ,nature an unnecessary ,dance4 ,for if the ,maternal ,blood does really contain any such ,nutritious1 or any such necessary ,aerial ,particles1 why shou'd they be separated and extravasated1 to be with difficulty receiv'd into the ,umbilical ,vein1 and again mixt with the ,blood1 when they might more easily have been imparted by the plain simple way of ,transfusion from the ,arteries of the ,mother to the ,veins of the ,ftus4 ,and1 that this is the course which ,nature takes in this ,case1 ,i am perswaded from the easiness and simplicity of the ,method1 which readily performs what might be perhaps in vain expected from the other1 and wou'd over and above find them1 what they seem to grope so blindly about for1 a first ,mover of the ,blood in a ,ftus4 ,those that contend for the conveyance of the ,nutricious ,juice1 through the ,umbilical ,vein from the ,placenta1 are forc'd upon two ,difficulties next to ,absurdities4 ,for first they are oblig'd to make this ,vein1 which1 as all other ,veins1 seems dedicated to the ,re-conveyance of ,blood only1 the proper and immediate ,chanel1 thro' which a very different ,liquour is to be carried2 and next1 to give a ,power of ,attraction or ,suction to it2 because the ,nutricious ,juice1 which it is thus destin'd to carry1 is both viscous and stagnant1 and has neither force to drive1 nor subtilty to penetrate1 or insinuate it self into the ,capillary ,veins2 and therefore must be drawn or suck'd as ,milk is from the ,breast1 to which the ,placenta and its ,nutricious ,juice are by the ,favourers of them expresly compar'd4 ,but if this were the sole use of the ,placenta1 and ,umbilical ,vessels1 why were the ,umbilical ,arteries sent along with the ,vein8 ,their business is not to bring any thing back to the ,ftus1 nor can they contribute any thing to the benefit of the ,mother2 for the ,uterine ,arteries bring all to the ,placenta1 the ,umbilical ,vein carries it to the ,ftus1 and the ,uterine ,veins convey back again the ,surcharge of the ,mother's ,blood2 the ,umbilical ,arteries only1 have nothing to do1 and are superfluous and impertinent1 which is contrary to the constant ,practice of ,nature4 ,yet if ,autopsie did in the least countenance this ,hypothesis1 some ,defence might still be made2 but we find in the ,umbilical ,vein of a ,ftus nothing but ,florid ,blood1 such as in all probability it received immediately from the ,arteries of the ,mother without any mixture4 ,and therefore ,i can't help concluding1 that this ,opinion engages its ,favourers in some ,absurdity1 without ,necessity and without ,proof4 ,they that from the ,placenta supply the ,body of the ,ftus with ,air1 are as much distress'd as t'other2 for they are forc'd to beg the ,question twice1 which1 even when granted1 will not answer their ,ends4 ,first1 they suppose1 that an intimate mixture or confusion of ,air with the ,blood1 is necessary for the support of ,animal ,life1 a ,postulatum1 which perhaps the former part of this ,discourse may have render'd unnecessary2 and next1 that the ,ftus is supply'd with ,air from1 and its ,blood mix'd with it in the ,placenta4 ,but here again they fetch a ,compass without necessity or proof4 ,for if a mixture of ,air were necessary to a ,ftus1 why should it be separated from the ,mother's ,blood1 and not rather both communicated together1 since it is so much more easie and commodious8 ,but neither does the ,placenta seem to be instructed and provided for the separation of ,air1 but of a much grosser ,fluid1 destin'd to some other use1 which ,autopsie confirms3 ,yet1 were both these ,opinions true1 they are however defective1 and the ,circular ,motion of the ,blood unprovided for4 ,by the way of ,transfusion1 this great ,phnomenon is naturally accounted for1 and the ,ends1 for which the other two ,hypotheses were devis'd1 might both be answer'd with more ease4 ,for the ,hysterick ,arteries transmitting their ,blood immediately to the ,umbilical ,vein1 may very easily transmit such ,nutricious ,juices or ,aeral ,particles1 as are contain'd in the ,blood1 along with it1 without depositing them by the way4 ,by this means so much of the ,impulse of the ,mother's ,blood is preserv'd1 as suffices to maintain that languid ,circulation which a ,ftus enjoys4 ,for the ,blood being driven through the ,arteries of the ,uterus into the ,umbilical ,vein1 is convey'd directly to the ,sinus of the ,porta1 and thence by a short and direct ,passage through the ,cava to the ,heart2 where passing through the ,foramen ,ovale to the ,left ,ventricle1 and through the ,canalis ,arteriosus from the ,right and ,pulmonary ,artery1 it is all deliver'd without coming at the ,lungs to the ,aorta1 and from thence again by the ,umbilical ,arteries to the ,veins of the ,uterus1 making a sort of ,epicycle to the main ,circulation in the ,mother4 ,as this ,opinion is ,favour'd by the ,structure and ,disposition of the ,blood-,vessels on both ,parts1 so there is nothing in it difficult to be conceiv'd1 or repugnant to ,experience4 ,late ,discoveries have made it appear1 that the ,arteries and ,veins are continu'd ,tubes1 and that the latter contain nothing but what they receive from the former1 and no ,reason appears why we shou'd think this ,method to be varied in the ,placenta4 ,on the other hand1 if the ,arteries of the ,uterus were continued to the ,veins of the same part1 and those of the ,ftus in like manner1 without communicating with each other1 their ,confluence in the ,placenta seems to be altogether impertinent1 and of no use1 and the ,umbilical ,arteries and ,vein fram'd for no other ,service or ,purpose1 than to give the ,blood room for an idle ,sally4 ,thus the ,reasonableness of this old ,opinion may be vindicated1 but the ,certainty of it rests upon stronger ,proof4 ,mr4 ,cowper1 to whose happy ,industry we owe the ,confirmation of many ancient ,discoveries1 and the ,benefit of some new ones1 has the ,honour to re-establish this old1 but long exploded ,truth4 ,for by pouring ,mercury into a ,branch of the ,uterine ,arterie of a ,cow1 that went into one of the ,cotyledones of the ,uterus1 he fill'd those ,branches of the ,umbilical ,veins1 which went from that ,cotyledon to the ,navel of the ,ftus2 which1 with a part of the ,uterus1 he keeps prepared by him4 ,it would be a weak ,objection1 to alledge1 ,that the ,observation and ,experiment being made on the ,uterus of a ,cow1 the ,inference would not hold from thence to a ,woman1 the one being ,glanduliferous1 and the other ,placentiferous2 since every one of these ,cotyledones1 or ,uterine ,glandules1 is in all respects a little ,placenta1 and all the difference between them is in number1 name1 and magnitude4 ,why ,ruminants differ in this ,particular from other ,viviparous ,animals1 is beside the ,subject of our present ,enquiry4 ,but the great ,flux of ,blood1 which constantly follows upon drawing the ,placenta from ,women 7which is frequently so great as to cost them their ,lives7 is as plain a demonstration to ,reason of the ,continuity of the ,vessels1 as ,mr4 ,cowper's ,experiments is to the ,eye4 ,i have heard it objected by very ,learned ,men1 that if there were such a ,continuity of ,vessels1 and such ,transfusion of ,blood1 the ,ftus must necessarily perish through loss of ,blood1 upon the separation of the ,placenta from the ,uterus2 but that1 on the contrary1 no visible ,flux of ,blood does follow while the ,ftus continues wrapt in the ,membrane1 in which ,condition it may be kept alive some ,hours4 ,to this it may be answer'd1 that the ,circulation in the ,ftus1 being deriv'd from the ,mother1 may be suppos'd wholly to cease upon the cutting off the ,communication between them1 till it is again renew'd more forcibly by ,respiration4 ,but if we allow the motion already impress'd upon the ,blood to be sufficient to keep it going a little while2 yet it must needs be so exceeding languid1 that the meer resistance of the ,external ,air must be more than enough to hinder any ,efflux of ,blood from a ,ftus before ,respiration4 ,how long ,life may be preserv'd without an actual ,circulation of the ,blood1 is a ,question not of this place4 ,but we have been convinc'd by many and notorious ,observations and ,experiments1 that ,life has been recover'd a long time after all tokens of ,respiration1 ,circulation1 or even ,life it self1 have disappear'd2 so that we can't think the first ,solution either impossible or improbable4 ,i expect to be told1 that in the early ,days of ,gestation in ,viviparous ,animals1 there is no ,placenta1 or any ,adhesion of the ,umbilical ,vessels to any part of the ,mother1 and consequently no such ,transfusion2 and that in ,oviparous there is no continuity1 or communication of ,vessels of any kind1 during the whole time of ,incubation4 ,but these ,objections carry neither the ,weight nor ,difficulty along with them1 that they may be suppos'd to do2 for in those ,days there is neither ,blood or ,blood-,vessels1 and consequently there can be no ,circulation of the ,blood2 and the ,embryo1 of what ,species soever1 is no more than a ,vegetable at that time2 nor does the ,ftus of any ,viviparous ,creature enjoy any ,circulation1 or shew any signs of ,animal ,life1 till after those ,vessels1 as well as others requisite to the ,circulation1 are compleated4 ,it must be confess'd1 that ,oviparous ,animals are denied the benefit of this ,communication2 but that want is sufficiently compensated by a peculiar ,mechanism1 which directly answers the ends of ,respiration1 and the pressure of the ,atmosphere upon the ,ftus4 ,there is at the obtuse end of an ,egg a small ,cavity fill'd with ,air1 which is the succedaneous ,instrument to the ,respiratory ,organs4 ,for as soon as the ,contents begin to be warm'd by the ,incubation of the ,hen1 or any analogous ,heat of ,furnace or ,dunghill1 the several ,humours of the ,egg require a fermentative motion1 and the ,air contain'd in the ,cavity or ,vesicle1 at the obtuse end of the ,egg1 is rarefied1 and the ,vesicle extended and enlarg'd1 and consequently the other ,contents are comprest2 to which the fermentative motion naturally resists4 ,but both ,bodies being as well compressible as dilatable1 and both having an expansive motion imprest upon them by ,incubation1 the ,compression and ,renitency will be mutual1 but varied in degree1 according as either1 through the variation of ,circumstances1 shall prevail4 ,by this means1 an ,alternation of ,compression and ,dilatation will be produc'd in both1 answering the respiratory motion1 by which a motion will be communicated1 which1 as soon as the ,organs by which it should be regulated are compleated1 will in the ,body of the ,pullus be regular and circulatory4 ,fabricius ab ,aquapendente1 and after him1 our ,great ,dr4 ,harvey1 have assign'd divers ,uses to this ,cavity or ,air ,vesicle1 the ,extravagance of which have perhaps deterr'd others from enquiring so much into the ,use1 as the ,importance of it requir'd4 ,but though ,i can't agree to that ,perspiration1 ,refrigeration1 and ,respiration1 which they make it the ,instrument of2 yet perhaps the ,air1 that was inclos'd in that ,cavity1 may through the ,augmentation of the ,body of the ,pullus1 and its own ,rarefaction 7which is at last so great as to occupy half the ,shell7 break the ,membrane1 which separated it from the ,pullus1 and thereby give so much ,respiration as to form the chirping ,voice1 which is often heard before the breaking of the ,shell1 and with it give an addition of ,strength to enable it to break the ,shell4 ,but how it should respire sooner1 is to me inconceivable4 ,there are many ,problems of great seeming ,difficulty1 the ,solutions of which flow naturally from what has been laid down here3 ,but intending to prosecute this ,subject farther1 and to treat of the ,impediments of ,respiration1 and the ,consequences of ,respiration obstructed or intermitted1 ,i shall reserve them for that ,opportunity1 and content my self here to attempt the ,harveyan ,problem only1 which has given abundance of ,authors so much perplexity4 ,that incomparable ,philosopher enquires1 ,why a ,ftus1 taken out of the ,uterus with the ,membranes intire1 shall live in ,water some ,hours without communication with the ,external ,air2 whereas if it be taken out and suffer'd once to breath1 it can't afterwards survive a ,moment without the benefit of ,respiration4 ,granting the ,fact to be as he has deliver'd it1 which yet is not so in all ,cases1 the main ,difficulty is grounded on a ,mistake1 which from the stating of the ,question ,i find this ,great ,man to have slipt into4 ,for he thinks1 that a ,ftus is sooner suffocated after having once breath'd1 than if it had not breath'd at all1 and that by breathing it had contracted something which render'd it more perishable4 ,idem tamen secundis exutus1 7says he7 si semel aerem intra ,pulmones attraxerit1 postea ne momentum quidem temporis absque eo durare possit1 sed confestim moriatur4 ,and presently after1 ,siquidem constat1 ftum1 postquam eum semel hauserit1 citius suffocari2 quam cum ab illo prorsus accebatur4 ,the ,doctor observing a ,ftus to live longer without ,respiration1 and to dispence better with the want of ,air while included in the ,membranes intire1 than it cou'd afterwards2 infers thence1 that the ,air does in the first ,act of ,inspiration impress upon the ,lungs some quality1 which renders it ever after more indispensably necessary4 ,but allowing his ,observation1 ,i must yet deny his ,inference to be good3 ,for deprive a ,ftus of means of respiring1 and then take it out of the ,membranes1 and it shall be as soon suffocated1 as if it had respired before4 ,this proves1 that this necessity of intercourse with the ,air1 by way of the ,lungs1 is not the ,offspring1 but the ,parent of ,respiration1 and that1 that ,learned ,man was drawn into a ,fallacy of ,non causa pro causa4 ,the ,reason of this ,necessity is the pressure of the ,external ,air upon the ,surface of the ,body1 from which it was defended by the ,interposition of the ,membranes1 and the ,humours contain'd1 which are not so compressible as the ,body of the ,ftus it self4 ,so soon therefore as the ,ftus is excluded1 and expos'd to the immediate contact of the ambient ,atmosphere1 the ,vessels and all the ,cavities of the ,body must necessarily be so compress'd1 that the ,fluids can't have room for motion1 and consequently the ,ftus could have no ,life1 if ,nature had not contriv'd by the motion of the ,thorax to remove and admit that pressure alternately1 and thereby to impress a motion on the ,fluids1 which is the ,spring of ,life4 ,but this motion of the ,thorax being any way suppress'd1 the equal pressure of the ,atmosphere on all parts1 occasions a total ,cessation of motion1 which is ,death4 ,i shall prosecute this ,subject no farther now1 nor trouble the ,reader with any ,apology1 for dissenting from those ,great ,men herein named2 because1 ,i hope1 ,i have done it with ,modesty1 and all the ,respect due to so great ,authorities1 and have assign'd nothing which is not ,matter of ,fact uncontroverted1 or deduc'd from it by plain ,mechanical ,necessity4 ,some ,thoughts and ,experiments concerning ,vegetation4 ,by ,john ,woodward1 ,m4 ,d4 of the ,college of ,physicians1 and ,r4 ,s4 and ,professor of ,physick in ,gresham ,college4 ,the ,ancients generally intitled the ,earth to the ,production of the ,animals1 ,vegetables1 and other ,bodies upon and about it2 and that for that ,reason 'twas1 that they gave it so frequently the ,epithets of ,parent and ,mother#a4 ,they were of opinion1 that it furnished forth the ,matter whereof those ,bodies consist2 and receiv'd it all back again at their ,dissolution for the ,composure of others4 ,even those who asserted four ,elements1 supposed that the ,earth was the ,matter that constituted those ,bodies2 and that ,water and the rest1 serv'd only for the ,conveyance and ,distribution of that ,matter1 in order to the forming and composition of them4 ',tis true1 ,thales1 a ,philosopher of the first ,rank in those early ,ages1 has been thought to have ,sentiments very different from these2 but that without just ,grounds1 as ,i think ,i have sufficiently prov'd in another ,paper1 which ,i am ready to produce4 ,but though ,antiquity thus gave its ,vote for ,terrestrial ,matter1 several of the ,moderns1 and some of very great ,name too1 both here and abroad1 have gone quite counter1 and given theirs in behalf of ,water4 ,the ,dignity of the ,persons that have espoused it1 as well as their ,numbers1 renders this ,doctrine very considerable1 and well worth our enquiring into4 ,the great ,restorer of ,philosophy in this last ,age1 my ,lord ,bacon1 is of ,opinion1 ,that for ,nourishment of ,vegetables1 the ,water is almost all in all2 and that the ,earth doth but keep the ,plant upright1 and save it from over-heat1 and over-cold#b4 ,others there are who are still more express2 and assert ,water to be the only ,principle or ,ingredient of all ,natural ,things4 ,they suppose that1 ,i cannot tell by what ,process of ,nature1 ,water is transmuted into ,stones1 into ,plants1 and in brief1 all other ,substances whatever4 ,helmont1#c particularly1 and his ,followers1 are very positive in this2 and offer some ,experiments to render it credible4 ,nay1 a very ,extraordinary ,person of our own ,nation#d tries those ,experiments over again2 and discovers a great ,propensity to the same ,thoughts and ,opinion they had2 declaring for this ,transmutation of ,water into ,plants and other ,bodies1 though with great ,modesty and ,deference1 which was his usual manner4 ,the ,experiments they insist upon are chiefly two2 the first is1 that ,mint1 and several other ,plants prosper and thrive very greatly in ,water4 ,the other is this2 they take a certain quantity of ,earth1 and bake it in an ,oven2 then they weigh it1 and put it into an ,earthen ,pot4 ,having well water'd this ,earth1 they make choice of some fit ,plant1 which1 being first carefully weigh'd1 they set in it4 ,there they let it grow1 continuing to water it for some time1 till 'tis much advanced in bigness3 ,then they take it up2 and though the ,bulk and ,weight of the ,plant be much greater than when first set1 yet upon baking the ,earth1 and weighing it1 as at first1 they find it little or not at all diminished in weight2 and therefore conclude1 'tis not the ,earth but ,water1 that nourishes and is turn'd into the ,substance of the ,plant4 ,i must confess ,i cannot see how this ,experiment can ever be made with the nicety and justness that is requisite1 in order to build upon it so much as these ,gentlemen do4 ',tis hard to weigh ,earth in that quantity1 or ,plants of the size of those they mention1 with any great exactness2 or to bake the ,earth with that accuracy1 as to reduce it twice to just the same ,driness4 ,but ,i may wave all this2 for though the ,experiment be never so easily practicable1 and all the ,accidents of it exactly as they set forth1 yet nothing like what they infer can possibly be concluded from it2 unless ,water1 which they so plentifully bestow upon the ,plant in this ,experiment1 be pure1 homogeneous1 and not charged with any terrestrial ,mixture2 for if it be1 the ,plant after all may owe its ,growth and ,encrease intirely to that4 ,some ,waters are indeed so very clear and transparent1 that one would not easily suspect any terrestrial ,matter were latent in them2 but they may be highly saturated with such ,matter1 though the ,eye be not presently able to descry or discern it4 ',tis true1 ,earth is an ,opake ,body2 but it may be so far dissolved1 reduced to so extreme small ,particles1 and these so diffused through the watry ,mass1 as not sensibly to impede ,vision1 or render the ,water much the less diaphanous4 ,silver is an ,opake1 and indeed a very dense ,body2 and yet1 if perfectly dissolved in ,spirit of ,nitre1 or ,aqua ,fortis1 that is rectified and thorowly fine1 it does not darken the ,menstruum1 or render it less pellucid than before#e4 ,and other ,instances there are1 that oftentimes great quantities of ,opake ,matter are sustain'd in ,fluids1 without considerably striking the ,eye1 or being perceiv'd by it4 ,so that were there ,water any where found so pure1 that the quickest ,eye could discover in it no terrestrial ,intermixture2 that would be far short of a ,proof1 that in reality there was none4 ,but after all1 even the clearest ,water is very far from being pure and wholly defecate1 in any part of the ,world that ,i can learn4 ,for ours here1 ,i have had an ,opportunity of examining it over a good part of ,england2 and cannot say ,i ever met with any1 that1 however fresh and newly taken out of the ,spring1 did not exhibit1 even to the naked ,eye1 great numbers of exceeding small terrestrial ,particles disseminated through all parts of it4 ,thicker and crasser ,water exhibits them in still greater ,plenty4 ,these are of two general kinds4 ,the one a vegetable terrestrial ,matter1 consisting of very different ,corpuscles2 some whereof are proper for the formation and increment of one sort of ,plant1 and some of another2 as also some for the ,nourishment of one part of the same ,plant1 and some of another4 ,the other kind of ,particles sustain'd in ,water are of a ,mineral ,nature4 ,these likewise are of different sorts4 ,in some ,springs we find common ,salt1 in others ,vitriol1 in others ,alum1 ,nitre1 ,sparr1 ,ochre1 c4 nay1 frequently several of these1 or other ,minerals1 all in the same ,spring2 the ,water as it drains and passes thorough the ,strata of ,stone1 ,earth1 and the like1 taking up and bearing along such loose ,mineral ,corpuscles1 as it meets with in the ,pores and ,interstices of those ,strata1 and bringing them on with it quite to the ,spring4 ,all ,water whatever is much charg'd with the ,vegetable ,matter1 this being fine1 light1 and easily moveable4 ,for the ,mineral1 the ,water of ,springs contains more of it than that of ,rivers1 especially when at distance from their ,sources2 and that of ,rivers more than the ,water that falls in ,rain4 ,this ,i have learn'd from several ,trials1 which ,i must not give ,account of here2 my ,drift in this place being only to evince the ,existence of ,terrestrial ,matter in ,water4 ,any one who desires farther ,satisfaction in this1 may easily obtain it1 if he only put ,water into a clear ,glass ,viol1 stopping it close1 to keep ,dust and other exterior ,matter out1 and letting it stand1 without stirring it for some ,days3 ,he will then find a considerable ,quantity of terrestrial ,matter in the ,water1 however pure and free it might appear when first put into the ,viol4 ,he will in a very short time observe1 as ,i have frequently done1 the ,corpuscles that were at first1 while the ,water was agitated and kept in motion1 separate1 and hardly visible#f1 by degrees1 as the ,water permits1 by its becoming more still and at rest1 assembling and combining together2 by that means forming somewhat larger and more conspicuous ,molecul4 ,afterwards he may behold these joining and fixing each to other1 by that means forming large thin ,masses1 appearing like ,nubecul1 or ,clouds in the ,water2 which grow more thick and opake1 by the continual appulse and accretion of fresh ,matter4 ,if the said ,matter be chiefly of the ,vegetable kind1 it will be sustain'd in the ,water2 and discover at length a green ,colour1 becoming still more and more of that ,colour1 ,i mean an higher and more saturate ,green1 as the ,matter thickens and encreases4 ,that this ,matter inclines so much to that ,colour1 is the less strange1 since we see so large a share of it1 when constituting ,vegetables wearing the same ,colour in them4 ,but if there be any considerable quantity of meer ,mineral ,matter in the ,water1 this1 being of a greater specifick ,gravity than the ,vegetable1 as the ,particles of it unite and combine in such ,number1 till they form a ,molecula1 the ,impetus of whose ,gravity surpasses that of the ,resistance of the ,water1 subsides a great deal of it to the bottom4 ,nor does it only fall down it self1 but frequently entangling with the ,vegetable ,nubecul1 forces them down along with it4 ,the ,reason why ,bodies1 when dissolved and reduced to extreme small ,parts1 are sustain'd in ,liquors that are of less specifick ,gravity than those ,bodies are1 hath been pointed at by a late ingenious ,member of this ,society#g4 ,he is indeed far from having adjusted all the ,momenta of this ,affair2 however it must be admitted1 that1 in the dividing or solution of ,bodies1 their ,surfaces do not decrease in the same ,proportion that their ,bulk does4 ,now the ,gravity of a ,body1 which is the ,cause of its sinking or tendency downwards1 is commensurate to its ,bulk2 but the resistance that the ,liquor makes1 is proportion'd1 not to the ,bulk1 but to the ,extent of the ,surface of the ,body immersed in it4 ,whence 'tis plain1 a ,body may be so far divided1 that its ,parts may be sustain'd in a ,fluid1 whose specifick ,gravity is less than that of the said ,body4 ,nay1 'tis ,matter of ,fact1 that they frequently are so2 and we daily see ,menstrua supporting the ,parts of ,metals1 and other ,bodies1 that are of six1 ten1 nay1 almost twenty times the specifick ,gravity of those ,menstrua4 ,and as the ,parts of ,bodies when divided1 are thus supported in a ,fluid2 so when they occur and unite again1 they must sink of course1 and fall to the ,bottom4 ,upon the whole1 'tis palpable and beyond reasonable ,contest1 that ,water contains in it a very considerable ,quantity of terrestrial ,matter4 ,now the ,question is1 to which of these1 the ,water1 or the ,earthly ,matter sustain'd in it1 ,vegetables owe their ,growth and ,augment3 ,for deciding of which1 ,i conceive the following ,experiments may afford some ,light2 and ,i can safely say1 they were made with due ,care and ,exactness4 ,anno #afia4 ,i chose several ,glass ,vials1 that were all1 as near as possible1 of the same shape and bigness4 ,after ,i had put what ,water ,i thought fit into every one of them1 and taken an ,account of the weight of it1 ,i strain'd and ty'd over the ,orifice of each ,vial1 a ,piece of ,parchment1 having an hole in the middle of it1 large enough to admit the ,stem of the ,plant ,i design'd to set in the ,vial1 without confining or streightning it1 so as to impede its ,growth4 ,my ,intention in this1 was to prevent the inclosed ,water from evaporating1 or ascending any other way than only through the ,plant to be set therein4 ,then ,i made choice of several ,sprigs of ,mint1 and other ,plants1 that were1 as near as ,i could possibly judge1 alike fresh1 sound1 and lively4 ,having taken the weight of each1 ,i placed it in a ,vial1 order'd as above2 and as the ,plant imbib'd and drew off the ,water1 ,i took care to add more of the same from time to time1 keeping an ,account of the weight of all ,i added4 ,each of the ,glasses were1 for better distinction1 and the more easie keeping a ,register of all ,circumstances1 noted with a different ,mark or ,letter1 ,a1 ,b1 ,c1 c4 and all set in a ,row in the same ,window1 in such manner that all might partake alike of ,air1 ,light1 and ,sun4 ,thus they continued from ,july the ,twentieth1 to ,october the ,fifth1 which was just ,seventy ,seven ,days4 ,then ,i took them out1 weigh'd the ,water in each ,vial1 and the ,plant likewise1 adding to its weight that of all the ,leaves that had fallen off during the time it stood thus4 ,and ,lastly1 ,i computed how much each ,plant had gain'd2 and how much ,water was spent upon it4 ,the ,particulars are as follow4 7,a47 ,common ,spear-,mint1 set in ,spring-,water4 ,the ,planted weighed when put in1 ,july #bj4 just #bg ,grains2 when taken forth1 ,october #e4 #db ,grains3 ,so that in this space of #gg ,days1 it had gained in weight #ae ,grains4 ,the whole ,quantity of ,water expended1 during these #gg ,days1 amounted to #beeh ,grains4 ,consequently the weight of the ,water taken up1 was #agj-h_/ae times as much as the ,plant had got in weight4 7,b47 ,common ,spear-,mint1 ,rain-,water4 ,the ,mint weigh'd1 when put in1 ,gr4 #bh2 when taken out ,gr4 #de1 having gain'd in #gg ,days ,gr4 #ag4 ,the ,dispendium of the ,water ,gr4 #cjjd1 which was #aga-bb_/ce times as much as the ,plant had received in weight4 7,c47 ,common ,spear-,mint1 ,thames-water4 ,the ,plant when put in1 ,gr4 #bh1 when taken forth1 ,gr4 #ed4 ,so that in #gg ,days it had gained ,gr4 #bf4 ,the ,water expended1 amounted to ,gr4 #bdic4 which was #ie-bc_/bf times as much as the additional weight of the ,mint4 7,d47 ,common ,solanum1 or ,night-shade3 ,spring-water4 ,the ,plant weigh'd1 when put in1 ,gr4 #di2 when taken out1 #ajf2 having gain'd in #gg ,days #eg ,gr4 ,the ,water expended during the said time1 was #cgjh ,gr4 which was #fe-c_/eg times as much as the ,augment of the ,plant4 ,this ,specimen had several ,buds upon it1 when first set in the ,water4 ,these in some ,days became fair ,flowers1 which were at length succeeded by ,berries4 7,e47 ,lathyris seu ,cataputia ,gerh4 ,spring-,water4 ,it weigh'd1 when put in1 ,gr4 #ih4 when taken forth1 ,gr4 #aja4 ,the additional weight for the whole #gg ,days1 being but ,gr4 #c4 ,the ,quantity of ,water spent upon it during that time1 ,gr4 #beja4 which is #gad-d_/g times as much as the ,plant was augmented4 ,several other ,plants were try'd1 that did not thrive in ,water1 or succeed any better than the ,cataputia foregoing3 ,but 'tis besides my purpose to give a particular ,account of them here4 7,f1 ,g47 ,these ,two ,vials were fill'd1 the former 7,f7 with ,rain1 the other with ,spring-water1 at the same time as those above-mention'd were2 and stood as long as they did4 ,but they had neither of them any ,plant2 my ,design in these being only to inform my self1 whether any ,water exhaled out of the ,glasses1 otherwise than thorow the ,bodies of the ,plants4 ,the ,orifices of these two ,glasses were cover'd with ,parchment2 each piece of it being perforated with an hole of the same bigness with those of the ,vials above4 ,in this ,i suspended a bit of ,stick1 about the thickness of the ,stem of one of the aforesaid ,plants1 but not reaching down to the ,surface of the included ,water4 ,i put them in thus1 that the ,water in these might not have more ,scope to evaporate than that in the other ,vials4 ,thus they stood the whole #gg ,days in the same ,window with the rest2 when1 upon ,examination1 ,i found none of the ,water in these wasted or gone off4 ,tho' ,i observed both in these1 and the rest1 especially after hot ,weather1 small ,drops of ,water1 not unlike ,dew1 adhering to the ,insides of the ,glasses1 that ,part of them1 ,i mean1 that was above the ,surface of the enclosed ,water4 ,the ,water in these two ,glasses that had no ,plants in them1 at the end of the ,experiment1 exhibited a larger ,quantity of ,terrestrial ,matter than that in any of those that had the ,plants in them did4 ,the ,sediment at the bottom of the ,vials was greater2 and the ,nubecul1 diffus'd through the ,body of the ,water1 thicker4 ,and of that which was in the others1 some of it proceeded from certain small ,leaves that had fallen from that part of the ,stems of the ,plants that was within the ,water1 wherein they rotted and dissolved4 ,the ,terrestrial ,matter in the ,rain-water was finer than that in the ,spring-water4 ,anno #afib4 ,the ,glasses made use of in this1 were of the same sort with those in the former ,experiment2 and cover'd over with ,parchment in like manner4 ,the ,plants here were all ,spear-,mint2 the most kindly1 fresh1 sprightly ,shoots ,i could chuse4 ,the ,water1 and the ,plants were weigh'd as above2 and the ,vials set in a ,line1 in a ,south ,window3 where they stood from ,june the #b;d to ,july #bh4 which was just #ef ,days4 7,h47 ,hyde-,park ,conduit ,water1 alone4 ,the ,mint weighed1 when put in1 #abg ,gr4 when taken out1 #bee ,gr4 ,the whole ,quantity of ,water expended upon this ,plant1 amounted to #adaij ,gr4 ,this was all along a very kindly ,plant2 and had run up to above two ,foot in height4 ,it had shot but one considerable collateral ,branch2 but had sent forth many and long ,roots1 from which sprung very numerous1 though small and short1 lesser ,fibres4 ,these lesser ,roots came out of the larger on two opposite sides1 for the most part2 so that each ,root1 with its ,fibrill1 appear'd not unlike a small ,feather4 ,to these ,fibrill adher'd pretty must ,terrestrial ,matter4 ,in the ,water1 which was at last thick and turbid1 was a green ,substance1 resembling a fine thin ,conserva4 7,i47 ,the same ,water1 alone4 ,the ,mint weigh'd1 when put in1 #aaj ,gr4 when taken out1 #bdi4 ,water expended1 #acadj ,gr4 ,this ,plant was as kindly as the former1 but had shot no collateral ,branches4 ,its ,roots1 the ,water1 and the green ,substance1 all much as in the former4 7,k47 ,hyde-,park ,conduit-water1 in which was dissolved an ,ounce and half of ,common ,garden-earth4 ,the ,mint weigh'd1 when put in1 #gf ,gr4 when taken out1 #bdd ,gr4 ,water expended1 ,gr4 #ajgca4 ,this ,plant1 though it had the ,misfortune to be annoy'd with many small ,insects that hapn'd to fix upon it2 yet had shot very considerable collateral ,branches2 and at least as many ,roots as either that in ,h or ,i2 which had a much greater ,quantity of ,terrestrial ,matter adhering to the ,extremities of them4 ,the same green ,substance here1 that was in the two preceding4 7,l47 ,hyde-,park ,water1 with the same ,quantity of ,garden-mould as in the former4 ,the ,mint weigh'd1 when put in1 #ib ,gr4 when taken out1 #cgf ,gr4 ,the ,water expended #adiej ,gr4 ,this ,plant was far more flourishing than any of the precedent2 had several very considerable collateral ,branches1 and very numerous ,roots1 to which ,terrestrial ,matter adhered very copiously4 ,the ,earth in both these ,glasses was very sensibly and considerably wasted1 and less than when first put in4 ,the same sort of green ,substance here as in those above4 7,m47 ,hyde-,park ,water1 distilled off with a gentle ,still4 ,the ,mint weigh'd1 when put in1 #aad ,gr4 when taken out #aee4 ,the ,water expended1 #hhjc ,gr4 ,this ,plant was pretty kindly2 had two small collateral ,branches1 and several ,roots1 though not so many as that in ,h or ,i1 but as much ,terrestrial ,matter adhering to them as those had4 ,the ,water was pretty thick2 having very numerous small ,terrestrial ,particles swimming in it1 and some ,sediment at the bottom of the ,glass4 ,this ,glass had none of the green ,matter above mentioned1 in it4 7,n47 ,the ,residue of the ,water1 which remain'd in the ,still after that in ,m1 was distill'd off4 ,it was very turbid1 and as high-colour'd 7reddish7 as ordinary ,beer4 ,the ,mint weigh'd1 when put in1 #ha ,gr4 when taken out1 #age ,gr4 ,water expended1 #dcdd ,gr4 ,this ,plant was very lively2 and had sent out six collateral ,branches1 and several ,roots4 7,o47 ,hyde-,park ,conduit-water1 in which was dissolved a ,drachm of ,nitre4 ,the ,mint set in this suddenly began to wither and decay2 and died in a few ,days3 ,as likewise did two more ,sprigs1 that were set in it1 successively4 ,in another ,glass ,i dissolv'd an ,ounce of good ,garden-mould1 and a ,drachm of ,nitre1 and in a third1 half an ,ounce of ,wood ashes1 and a ,drachm of ,nitre2 but the ,plants in these succeeded no better than in the former4 ,in other ,glasses ,i dissolved several other sorts of ,earths1 ,clays1 ,marles1 and variety of ,manures1 c4 ,i set ,mint in distill'd ,mint-water2 and other ,experiments ,i made1 of several kinds1 in order to get ,light and ,information1 what hastened or retarded1 promoted or impeded ,vegetation2 but these do not belong to the ,head ,i am now upon4 7,p47 ,hyde-,park ,conduit-water4 ,in this ,i fix'd a ,glass-,tube about ten ,inches long1 the ,bore about one sixth of an ,inch in ,diameter1 fill'd with very fine and white ,sand1 which ,i kept from falling down out of the ,tube into the ,vial1 by tying a thin piece of ,silk over that end of the ,tube that was downwards4 ,upon ,immersion of the lower end of it into the ,water1 this by little and little ascended quite to the upper ,orifice of the ,tube4 ,and yet1 in all the fifty six ,days which it stood thus1 a very inconsiderable ,quantity of ,water had gone off1 viz4 scarce twenty ,grains2 though the ,sand continued moist up to the top till the very last4 ,the ,water had imparted a green ,tincture to the ,sand1 quite to the very top of the ,tube4 ,and1 in the ,vial1 it had precipitated a greenish ,sediment1 mix'd with black4 ,to the bottom and sides of the ,tube1 as far as 'twas immers'd in the ,water1 adher'd pretty much of the green ,substance describ'd above4 ,other like ,tubes ,i fill'd with ,cotton1 ,lint1 ,pith of ,elder1 and several other porous ,vegetable ,substances2 setting some of them in clear ,water2 others in ,water tinged with ,saffron1 ,cochinele1 c4 ,and several other ,trials were made1 in order to give a mechanical ,representation of the motion and distribution of the ,juices in ,plants2 and of some other ,phnomena observable in ,vegetation1 which ,i shall not give the ,particulars of here1 as being not of use to my present design4 7,q1 ,r1 ,s1 c47 ,several ,plants set in ,vials1 ordered in like manner as those above1 in ,october1 and the following colder ,months4 ,these throve not near so much2 nor did the ,water ascend in nigh the quantity it did in the better ,seasons1 in which the before recited ,trials were made4 ,some ,reflections upon the foregoing ,experiments4 #a4 ,in ,plants of the same kind1 the less they are in ,bulk1 the smaller the ,quantity of the fluid ,mass1 in which they are set1 is drawn off2 the ,dispendium of it1 where the ,mass is of equal thickness1 being pretty nearly proportion'd to the ,bulk1 of the ,plant4 ,thus that in the ,glass mark'd ,a1 which weigh'd only #bg ,grains1 drew off but #beeh ,grains of the ,fluid2 and that in ,b1 which weigh'd only #bh1 took up but #cjjd ,grains2 whereas that in ,h1 which weigh'd #abg ,grains1 spent #adaij ,grains of the ,liquid ,mass4 ,the ,water seems to ascend up the ,vessels of ,plants1 in much the same manner as up a ,filtre2 and 'tis no great wonder that a larger ,filtre should draw off more ,water than a lesser2 or that a ,plant that has more and larger ,vessels1 should take up a greater share of the ,fluid in which it is set1 than one that has fewer and smaller ones can4 ,nor do ,i note this as a thing very considerable in it self1 but chiefly in regard to what ,i am about to offer beneath2 and that it may be seen that1 in my other ,collations of ,things1 ,i made due ,allowance for this ,difference4 #b4 ,the much greatest part of the fluid ,mass1 that is thus drawn off and convey'd into the ,plants1 does not settle or abide there2 but passes through the pores of them1 and exhales up into the ,atmosphere4 ,that the ,water in these ,experiments ascended only through the ,vessel of the ,plants1 is certain4 ,the ,glasses ,f and ,g1 that had no ,plants in them1 though disposed of in like manner as the rest1 remain'd at the ,end of the ,experiment1 as at first2 and none of the ,water was gone off4 ,and that the greatest part of it flies off from the ,plant into the ,atmosphere1 is as certain4 ,the least ,proportion of the ,water expended1 was to the ,augment of the ,plant1 as #df or #ej to #a4 ,and in some the weight of the ,water drawn off1 was #ajj1 #bjj1 nay1 in one above #gjj times as much as the ,plant had received of ,addition4 ,this so continual an ,emission and ,detachment of ,water1 in so great ,plenty from the ,parts of ,plants1 affords us a manifest ,reason why ,countries that abound with ,trees1 and the larger ,vegetables especially1 should be very obnoxious to ,damps1 great ,humidity in the ,air1 and more frequent ,rains1 than others that are more open and free4 ,the great ,moisture in the ,air1 was a mighty inconvenience and annoyance to those who first settled in ,america2 which at that time was much overgrown with ,woods and ,groves4 ,but as these were burnt and destroy'd1 to make way for ,habitation and ,culture of the ,earth1 the ,air mended and clear'd up apace1 changing into a ,temper much more dry and serene than before4 ,nor does this ,humidity go off pure and alone2 but usually bears forth with it many ,parts of the same ,nature with those whereof the ,plant1 through which it passes1 consists4 ,the ,crasser indeed are not so easily born up into the ,atmosphere2 but are usually deposited on the ,surface of the ,flowers1 ,leaves1 and other ,parts of the ,plants3 ,hence comes our ,manna's1 our ,honeys1 and other ,gummous ,exsudations of ,vegetables4 ,but the finer and lighter ,parts are with greater ease sent up into the ,atmosphere4 ,thence they are conveyed to our ,organs of ,smell1 by the ,air we draw in ,respiration2 and are pleasant or offensive1 beneficent or injurious to us1 according to the ,nature of the ,plants from whence they arise4 ,and since these owe their ,rise to the ,water1 that ascends out of the ,earth through the ,bodies of ,plants1 we cannot be far to seek for the ,cause why they are more numerous in the ,air1 and we find a greater quantity of ,odors exhaling from ,vegetables1 in warm1 humid ,seasons1 than in any other whatever4 #c4 ,a great part of the ,terrestrial ,matter that is mix'd with the ,water1 ascends up into the ,plant as well as the ,water4 ,there was much more ,terrestrial ,matter at the end of the ,experiment1 in the ,water of the ,glasses ,f and ,g1 that had no ,plants in them1 than in those that had ,plants4 ,the ,garden-mould dissolved in the ,glasses ,k and ,l1 was considerably diminished1 and carried off4 ,nay1 the ,terrestrial and ,vegetable ,matter was born up in the ,tubes fill'd with ,sand1 ,cotton1 c4 in that ,quantity1 as to be evident even to ,sense4 ,and the ,bodies in the ,cavities of the other ,tubes1 that had their lower ,ends immers'd in ,water1 wherein ,saffron1 ,cochinele1 c4 had been infused1 were tinged with ,yellow1 ,purple1 c4 ,if ,i may be permitted to look abroad a while1 towards our ,shores and ,parts within the ,verge of the ,sea1 these will present us with a large ,scene of ,plants1 that1 along with the ,vegetable1 take up into them meer mineral ,matter also in great abundance4 ,such are our ,sea-,purslains1 the several sorts of ,alga's1 of ,sampires1 and other marine ,plants4 ,these contain common ,sea-salt1 which is all one with the ,fossil1 in such plenty1 as not only to be plainly distinguish'd on the ,palate1 but may be drawn forth of them in considerable ,quantity4 ,nay1 there want not those who affirm1 there are ,plants found that will yield ,nitre1 and other mineral ,salts2 of which indeed ,i am not so far satisfied1 that ,i can depend on the ,thing1 and therefore give this only as an hint for ,enquiry4 ,to go on with the ,vegetable ,matter1 how apt and how much disposed this1 being so very fine and light1 is to attend ,water in all its ,motions1 and follow it into each of its ,recesses1 is manifest1 not only from the ,instances above alledg'd1 but many others4 ,percolate it withal the ,care imaginable3 ,filter it with never so many ,filtrations1 yet some ,terrestrial ,matter will remain4 ',tis true1 the ,fluid will be thinner every time than other1 and more disingaged of the said ,matter2 but never wholly free and clear4 ,i have filtred ,water thorough several wholly free and clear ,sheets of thick ,paper2 and1 after that1 through very close fine ,cloth twelve times doubled4 ,nay1 ,i have done this over and over2 and yet a considerable quantity of this ,matter discover'd it self in the ,water after all4 ,now if it thus pass ,interstices1 that are so very small and fine along with the ,water1 'tis the less strange it should attend it in its passage through the ,ducts and ,vessels of ,plants4 ',tis true1 filtering and distilling of ,water intercepts and makes it quit some of the ,earthy ,matter it was before impregnated withal3 ,but then that which continues with the ,water after this1 is fine and light2 and such consequently1 as is in a peculiar manner fit for the ,growth and ,nourishment of ,vegetables4 ,and this is the ,case of ,rain-water4 ,the ,quantity of ,terrestrial ,matter it bears up into the ,atmosphere1 is not great4 ,but that which it does bear up1 is mainly of that light kind of ,vegetable ,matter2 and that too perfectly dissolved1 and reduced to single ,corpuscles1 all fit to enter the ,tubules and ,vessels of ,plants3 ,on which ,account 'tis1 that this ,water is so very fertile and prolifick4 ,the ,reason1 why in this ,proposition1 ,i say1 only a great part of the ,terrestrial ,matter that is mix'd with the ,water1 ascends up with it into the ,plant1 is1 because all of it cannot4 ,the ,mineral ,matter is a great deal of it1 not only gross and ponderous1 but scabrous and inflexible2 and so not disposed to enter the ,pores of the ,roots4 ,and a great many of the simple ,vegetable ,particles by degrees unite1 and form some of them small ,clods or ,molecul2 such as those mention'd in ,h1 ,k1 and ,l1 sticking to the ,extremities of the ,roots of those ,plants4 ,others of them intangle in a looser manner2 and form the ,nubecul1 and green ,bodies1 so commonly observ'd in stagnant ,water4 ,these1 when thus conjoin'd1 are too big to enter the ,pores1 or ascend up the ,vessels of ,plants1 which singly they might have done4 ,they who are conversant in ,agriculture1 will easily subscribe to this4 ,they are well aware that1 be their ,earth never so rich1 so good1 and so fit for the production of ,corn or other ,vegetables1 little will come of it1 unless the ,parts of it be separated and loose4 ',tis on this ,account they bestow the ,pains they do in ,culture of it1 in ,digging1 ,plowing1 ,harrowing1 and ,breaking of the ,clodded ,lumps of ,earth4 ',tis the same way that ,sea-salt1 ,nitre1 and other ,salts1 promote ,vegetation4 ,i am sorry ,i cannot subscribe to the ,opinion of those ,learned ,gentlemen1 who imagine ,nitre to be essential to ,plants2 and that nothing in the ,vegetable ,kingdom is transacted without it4 ,by all the ,trials ,i have been able to make1 the thing is quite otherwise2 and when contiguous to the ,plant1 it rather destroys than nourishes it4 ,but this ,nitre and other ,salts certainly do2 they loosen the ,earth1 and separate the concreted ,parts of it2 by that means fitting and disposing them to be assumed by the ,water1 and carried up into the ,seed or ,plant1 for its ,formation and ,augment4 ,there's no ,man but must observe1 how apt all sorts of ,salts are to be wrought upon by ,moisture2 how easily they liquate and run with it2 and when these are drawn off1 and have deserted the ,lumps wherewith they were incorporated1 those must moulder immediately1 and fall asunder of ,course4 ,the hardest ,stone we meet with1 if it happen1 as frequently it does1 to have any sort of ,salt intermix'd with the ,sand1 of which it consists1 upon being expos'd to an humid ,air1 in a short time dissolves and crumbles all to pieces2 and much more will clodded ,earth or ,clay1 which is not of near so compact and solid a ,constitution as ,stone is4 ,the same way likewise is ,lime serviceable in this ,affair4 ,the ,husbandmen say of it1 that it does not fatten1 but only mellows the ,ground3 ,by which they mean1 that it does not contain any thing in it self that is of the same ,nature with the ,vegetable ,mould1 or afford any ,matter fit for the ,formation of ,plants2 but meerly softens and relaxes the ,earth2 by that means rendering it more capable of entering the ,seeds and ,vegetables set in it1 in order to their ,nourishment1 than otherwise it would have been4 ,the ,properties of ,lime are well known2 and how apt 'tis to be put into ,ferment and ,commotion by ,water4 ,nor can such ,commotion ever happen when ,lime is mix'd with ,earth1 however hard and clodded that may be1 without opening and loosening of it4 #d4 ,the ,plant is more or less nourish'd and augmented1 in ,proportion as the ,water1 in which it stands1 contains a greater or smaller ,quantity of proper terrestrial ,matter in it4 ,the ,truth of this ,proportion is so eminently discernable through the whole ,process of these ,trials1 that ,i think no doubt can be made of it4 ,the ,mint in the ,glass ,c1 was of much the same ,bulk and ,weight with those in ,a and ,b4 ,but the ,water1 in which that was1 being ,river-water1 which was apparently stored more copiously with terrestrial ,matter1 than the ,spring or ,rain-water1 wherein they stood1 were2 it had thriven to almost double the ,bulk that either of them had1 and with a less ,expence of ,water too4 ,so likewise the ,mint in ,l1 in whose ,water was dissolved a small quantity of good ,garden-mould1 though it had the disadvantage#h to be less1 when first set1 than either of the ,mints in ,h or ,i1 whose ,water was the very same with this in ,l1 but had none of that ,earth mix'd with it2 yet1 in a short time the ,plant not only overtook1 but much out-strip'd those and at the end of the ,experiment was very considerably bigger and heavier than either of them4 ,in like manner the ,mint in ,n1 though less at the beginning than that in ,m1 being set in that thick1 turbid1 feculent ,water1 that remained behind1 after that wherein ,m was placed1 was still'd off1 had in fine more than double its original weight and bulk2 and receiv'd above twice the additional ,encrease1 than that in ,m1 which stood in the thinner distill'd ,water1 had done4 ,and1 which is not less considerable1 had not drawn off half the ,quantity of ,water that that had4 ,why1 in the beginning of this ,article1 ,i limit the ,proportion of the ,augment of the ,plant to the ,quantity of proper ,terrestrial ,matter in the ,water1 is1 because all1 even the ,vegetable ,matter1 to say nothing of the ,mineral1 is not proper for the ,nourishment of every ,plant4 ,there may be1 and doubtless are1 some ,parts in different ,species of ,plants1 that may be much alike1 and so owe their ,supply to the same common ,matter2 but 'tis plain all cannot4 ,and there are other ,parts so differing1 that 'tis no ways credible they should be formed all out of the same sort of ,corpuscles4 ,so far from it1 that there want not good ,indications1 as we shall see by and by1 that every kind of ,vegetable requires a peculiar and specifick ,matter for its ,formation and ,nourishment4 ,yea1 each ,part of the same ,vegetable does so2 and there are very many and different ,ingredients go to the ,composition of the same individual ,plant4 ,if therefore the ,soil1 wherein any ,vegetable or ,seed is planted1 contains all or most of these ingredients1 and those in due quantity1 it will grow and thrive there2 otherwise 'twill not4 ,if there be not as many sorts of ,corpuscles as are requisite for the ,constitution of the main and more essential ,parts of the ,plant1 'twill not prosper at all4 ,if there be these1 and not in sufficient ,plenty1 'twill starve1 and never arrive to its natural ,stature3 ,or if there be any the less necessary and essential ,corpuscles wanting1 there will be some failure in the ,plant2 'twill be defective in ,taste1 in ,smell1 in ,colour1 or some other way4 ,but though a ,tract of ,land may happen not to contain ,matter proper for the ,constitution of some one peculiar kind of ,plant2 yet it may for several others1 and those much differing among themselves4 ,the ,vegetative ,particles are commix'd and blended in the ,earth1 with all the diversity and variety1 as well as all the uncertainty1 conceivable4 ,i have given some intimations of this elsewhere#i1 and shall not repeat them here1 but hope in due time to put them into a much better ,light than that they there stand in4 ,it is not possible to imagine1 how one uniform1 homogeneous ,matter1 having its ,principles or ,original ,parts all of the same ,substance1 ,constitution1 ,magnitude1 ,figure1 and ,gravity1 should ever constitute ,bodies so egregiously unlike1 in all those respects1 as ,vegetables of different kinds are2 nay1 even as the different ,parts of the same ,vegetable4 ,that one should carry a resinous1 another a milky1 a third a yellow1 a fourth a red ,juice1 in its ,veins2 one afford a fragrant1 another an offensive ,smell2 one be sweet to the ,taste1 another bitter1 acid1 acerbe1 austere1 c4 that one should be nourishing1 another poisonous1 one purging1 another astringent3 ,in brief1 that there should be that vast difference in them1 in their several ,constitutions1 ,makes1 ,properties1 and ,effects1 and yet all arise from the very same sort of ,matter1 would be very strange4 ,and1 to note by the by1 this ,argument makes equally strong against those1 who suppose meer ,water the ,matter1 out of which all ,bodies are form'd4 ,the ,cataputia in the ,glass ,e1 received but very little ,encrease1 only three ,grains and an half all the while it stood1 though #beja ,grains of ,water were spent upon it4 ,i will not say the ,reason was1 because that ,water did not contain in it ,matter fit and proper for the ,nourishment of that peculiar and remarkable ,plant4 ,no1 it may be the ,water was not a proper ,medium for it to grow in2 and we know there are very many ,plants that will not thrive in it4 ,too much of that ,liquor1 in some ,plants1 may probably hurry the ,terrestrial ,matter thorough their ,vessels too fast for them to arrest and lay hold of it4 ,be that as it will1 'tis most certain there are peculiar ,soils that suit particular ,plants4 ,in ,england1 ,cherries are observ'd to succeed best in ,kent2 ,apples in ,herefordshire2 ,saffron in ,cambridgeshire2 ,wood in two or three of our ,midland ,counties2 and ,teazles in ,somersetshire4 ,this is an ,observation that hath held in all ,parts1 and indeed in all ,ages of the ,world4 ,the most ancient ,writers of ,husbandry#aj took notice of it2 and are not wanting in their ,rules for making choice of ,soils suited to the ,nature of each kind of ,vegetable they thought valuable1 or worth propagating4 ,but1 which is a further ,proof of what ,i am here endeavouring to advance1 that ,soil that is once proper and fit for the ,production of some one sort of ,vegetable1 does not ever continue to be so4 ,no1 in ,tract of time it loses that ,property2 but sooner in some ,lands1 and later in others3 ,this is what all who are conversant in these things know very well4 ,if ,wheat1 for ,example1 be sown upon a ,tract of ,land that is proper for that ,grain1 the first ,crop will succeed very well2 and perhaps the second1 and the third1 as long as the ,ground is in ,heart1 as the ,farmers speak2 but in a few ,years 'twill produce no more1 if sowed with that ,corn3 ,some other ,grain indeed it may1 as ,barley4 ,and after this has been sown so often1 that the ,land can bring forth no more of the same1 it may afterwards yield good ,oats2 and1 perhaps1 ,pease after them4 ,at length 'twill become barren2 the ,vegetative ,matter1 that at first it abounded withal1 being educed forth of it by those successive ,crops1 and most of it born off4 ,each sort of ,grain takes forth that peculiar ,matter that is proper for its own ,nourishment4 ,first1 the ,wheat draws off those ,particles that suit the ,body of that ,plant2 the rest lying all quiet and undisturbed the while4 ,and when the ,earth has yielded up all them1 those that are proper for ,barley1 a different ,grain1 remain still behind1 till the successive ,crops of that ,corn fetch them forth too4 ,and so the ,oats and ,pease1 in their ,turn2 till in fine all is carried off1 and the ,earth in great measure drain'd of that sort of ,matter4 ,after all which1 that very ,tract of ,land may be brought to produce another ,series of the same ,vegetables2 but never till 'tis supplied with a new ,fund of ,matter1 of like sort with that it at first contain'd4 ,this ,supply is made several ways3 ,by the ,grounds lying fallow for some time1 till the ,rain has pour'd down a fresh ,stock upon it3 ,or1 by the ,tiller's ,care in manuring of it4 ,and for farther ,evidence that this ,supply is in reality of like sort1 we need only reflect a while upon those ,manures that are found by constant ,experience best to promote ,vegetation1 and the ,fruitfulness of the ,earth4 ,these are chiefly either parts of ,vegetables1 or of ,animals2 which indeed either derive their own ,nourishment immediately from ,vegetable ,bodies1 or from other ,animals that do so4 ,in particular1 the ,blood1 ,urine1 and ,excrements of ,animals2 ,shavings of ,horns1 and of ,hoofs2 ,hair1 ,wool1 ,feathers2 calcin'd ,shells2 ,lees of ,wine1 and of ,beer2 ,ashes of all sorts of ,vegetable ,bodies2 ,leaves1 ,straw1 ,roots1 and ,stubble1 turn'd into the ,earth by ,plowing or otherwise to rot and dissolve there3 ,these1 ,i say1 are our best ,manures2 and1 being ,vegetable ,substances1 when refunded back again into the ,earth1 serve for the ,formation of other like ,bodies4 ,not wholly to confine our ,thoughts to the ,fields1 let us look a while into our ,gardens2 where we shall meet with still further ,confirmations of the same thing4 ,the ,trees1 ,shrubs1 and ,herbs cultivated in these1 after they have continued in one ,station1 till they have derived thence the greater part of the ,matter fit for their ,augment1 will decay and degenerate1 unless either fresh ,earth1 or some fit ,manure1 be applied unto them4 ',tis true1 they may maintain themselves there for some time1 by sending forth ,roots further and further to a great ,extent all round1 to fetch in more remote ,provision2 but at last all will fail2 and they must either have a fresh ,supply brought to them1 or they themselves be removed and transplanted to some ,place better furnished with ,matter for their ,subsistence4 ,and accordingly ,gardiners observe1 that ,plants that have stood a great while in a ,place1 have longer ,roots than usual2 part of which they cut off1 when they transplant them to a fresh ,soil1 as now not of any further use to them4 ,all these ,instances1 to pass over a great many others that might be alledg'd1 point forth a particular ,terrestrial ,matter1 and not ,water1 for the ,subject to which ,plants owe their ,increase4 ,were it ,water only1 there would be no need of ,manures2 or of transplanting them from place to place4 ,the ,rain falls in all ,places alike2 in this ,field and in that indifferently2 in one side of an ,orchard or ,garden1 as well as another4 ,nor could there be any ,reason1 why a ,tract of ,land should yield ,wheat one ,year1 and not the next2 since the ,rain showers down alike in each4 ,but ,i am sensible ,i have carried on this ,article to too great a length2 which yet on so ample and extensive a ,subject1 'twas not easie to avoid4 #e4 ,vegetables are not form'd of ,water2 but of a certain peculiar ,terrestrial ,matter4 ,it hath been shewn1 that there is a considerable ,quantity of this ,matter contain'd both in ,rain1 ,spring1 and ,river-water3 ,that the much greatest part of the fluid ,mass that ascends up into ,plants1 does not settle or abide there1 but passes through the ,pores of them1 and exhales up into the ,atmosphere2 ,that a great part of the ,terrestrial ,matter1 mix'd with the ,water1 passes up into the ,plant along with it2 and that the ,plant is more or less augmented in proportion1 as the ,water contains a greater or smaller ,quantity of that ,matter4 ,from all which we may very reasonably infer1 that ,earth1 and not ,water1 is the ,matter that constitutes ,vegetables4 ,the ,plant in ,e1 drew up into it #beja ,grains of the fluid ,mass2 and yet had received but ,grains #c and a half of ,increase from all that4 ,the ,mint in ,l1 though it had at first the disadvantage to be much less than that in ,i2 yet being set in ,water wherewith ,earth was plentifully mix'd1 and that in ,i1 only in ,water without any such additional ,earth1 it had vastly outgrown the other1 weighing at last #ade ,grains more than that did1 and so having gain'd about twice as much as that had4 ,in like manner that in ,k1 though 'twas a great deal less when put in than that in ,i1 and also was impair'd and offended by ,insects2 yet being planted in ,water wherein ,earth was dissolved1 whereas the ,water in which it stood had none1 it not only over-took1 but considerably surpass'd the other2 weighing at last #bi ,grains more than that in ,i1 and yet had not expended so much ,water as that1 by above #bdjj ,grains4 ,the ,plant in ,n1 tho' at first a great deal less than that in ,m2 yet being set in the foul crass ,water that was left in the ,still1 after that1 in which ,m was set1 was drawn off1 in ,conclusion had gain'd in weight above double what that in the finer and thinner ,water had4 ,the ,proportion of the ,augment of that ,plant that throve most was1 to the fluid ,mass spent upon it1 but as #a to #df4 ,in others1 'twas but as #a to #fj1 #ajj1 #bjj2 nay1 in the ,cataputia1 'twas but as #a to #gad4 ,the ,mint in ,b took up #ci ,grains of ,water a-day1 one day with another2 which was much more than the whole weight of the ,plant originally2 and yet1 with all this1 it gain'd not one fourth of a ,grain a-day in weight4 ,nay1 that in ,h took up #bec ,grains a day of the ,fluid3 ,which was near twice as much as its original ,weight1 it weighing1 when first set in the ,water1 but #abg ,grains4 ,and1 after all1 the daily ,encrease of the ,plant was no more than ,grains #b-ae_/ef4 #f4 ,spring1 and ,rain-water1 contain pretty near an equal ,charge of ,vegetable ,matter2 ,river-water more than either of them4 ,the ,plants in the ,glasses ,a1 ,b1 and ,c1 were at first of much the same size and weight4 ,at the ,end of the ,experiment1 the ,mint in ,a had gain'd #ae ,grains out of #beeh ,grains of ,spring-water2 that in ,b1 ,grains #ag and an half1 out of #cjjd ,grains of ,rain-water2 but that in ,c had got #bf ,grains out of only #bdic ,grains of ,river-water4 ,i do not found this ,proposition solely upon these ,trials2 having made some more1 which ,i do not relate here1 that agree well enough with these4 ,so that the ,proportions here deliver'd1 will hold for the main2 but a strict and just ,comparison is hardly to be expected4 ,so far from it1 that ,i make no doubt1 but the ,water that falls in ,rain1 at some times1 contains a greater share of ,terrestrial ,matter than that which falls at others4 ,a more powerful and intense ,heat must needs hurry up a larger quantity of that ,matter along with the humid ,vapours that form ,rain1 than one more feeble and remiss ever possibly can4 ,the ,water of one ,spring may flow forth with an higher ,charge of this ,matter1 than that of another2 this depending partly upon the quickness of the ,ebullition of the ,water1 and partly upon the ,quantity of that ,matter latent in the ,strata1 through which the ,fluid passes1 and the greater or less laxity of those ,strata4 ,for the same ,reason1 the ,water of one ,river may abound with it more than that of another4 ,nay1 the same ,river1 when much agitated1 and in commotion1 must bear up more of it1 than when it moves with less rapidity and violence4 ,that there is a great ,quantity of this ,matter in ,rivers2 and that it contributes vastly to the ordinary ,fertility of the ,earth1 we have an illustrious ,instance in the ,nile1 the ,ganges1 and other ,rivers that yearly overflow the neighbouring ,plains4 ,their ,banks shew the fairest and largest ,crops of any in the whole ,world4 ,they are even loaded with the multitude of their ,productions2 and those who have not seen them1 will hardly be induced to believe the mighty ,returns those ,tracts make in comparison of others1 that have not the ,benefit of like ,inundations4 #g4 ,water serves only for a ,vehicle to the ,terrestrial ,matter1 which forms ,vegetables2 and does not it self make any addition unto them4 ,where the proper ,terrestrial ,matter is wanting1 the ,plant is not augmented1 though never so much ,water ascend into it4 ,the ,cataputia in ,e1 took up more ,water than the ,mint in ,c1 and yet had grown but very little1 having received only three ,grains and an half of additional weight2 whereas the other had received no less than twenty six ,grains4 ,the ,mint in ,i1 was planted in the same sort of ,water as that in ,k1 was2 only the latter had ,earth dissolved in the ,water2 and yet that drew off #acadj ,grains of the ,water1 gaining it self no more than #aci ,grains in weight2 whereas the other took up but #ajgca ,grains of the ,water1 and was augmented #afh ,grains in weight4 ,consequently that spent #bdji ,grains more of the ,water than this in ,k1 did1 and yet was not so much encreased in weight as this by #bi ,grains4 ,the ,mint in ,m1 stood in the very same kind of ,water as that in ,n1 did4 ,but the ,water in ,m1 having much less ,terrestrial ,matter in it than that in ,n had1 the ,plant bore up #hhjc ,grains of it1 gaining it self only #da ,grains the while2 whereas that in ,n drew off no more than #dcdd ,grains1 and yet was augmented #id ,grains4 ,so that it spent #ddei ,grains of ,water more than that did2 and yet was not it self so much increased in weight1 as that was1 by #ec ,grains4 ,this is both a very fair1 and a very conclusive ,instance2 on which ,account 'tis that ,i make oftner use of it4 ,indeed they are all so2 and to add any thing further on this ,head1 will not be needful4 ',tis evident therefore ,water is not the ,matter that composes ,vegetable ,bodies4 ',tis only the ,agent that conveys that ,matter to them2 that introduces and distributes it to their several ,parts for their ,nourishment4 ,that ,matter is sluggish and unactive1 and would lie eternally confin'd to its ,beds of ,earth1 without ever advancing up into ,plants1 did not ,water1 or some like ,instrument1 fetch it forth and carry it unto them4 ,that therefore there is that plentiful ,provision1 and vast ,abundance of it supplied to all ,parts of the ,earth1 is a mark of a natural ,providence superintending over the ,globe we inhabit2 and ordaining a due ,dispensation of that ,fluid1 without the ,ministry of which the ,noble ,succession of ,bodies we behold1 ,animals1 ,vegetables1 and ,minerals1 would be all at a stand#aa4 ,but to keep to ,plants1 'tis manifest ,water1 as well on this1 as upon the other ,hypothesis1 is absolutely necessary in the ,affair of ,vegetation2 and it will not succeed without it3 ,which indeed gave occasion to the ,opinion1 that ,water it self nourished1 and was changed into ,vegetable ,bodies4 ,they saw1 though these were planted in a ,soil never so rich1 so happy1 so advantageous1 nothing came of it unless there was ,water too in a considerable quantity4 ,and it must be allow'd ,vegetables will not come on or prosper where that is wanting3 ,but yet what those ,gentlemen inferr'd thence1 was not1 we see1 well grounded4 ,this ,fluid is capacitated for the ,office here assign'd it several ways3 ,by the ,figure of its ,parts1 which1 as appears from many ,experiments1 is exactly and mathematically ,spherical2 their ,surfaces being perfectly polite1 and without any the least ,inequalities4 ',tis evident1 ,corpuscles of such a ,figure are easily susceptible of ,motion1 yea1 far above any others whatever2 and consequently the most capable of moving and conveying other ,matter1 that is not so active and voluble4 ,then the ,intervals of ,bodies of that ,figure are1 with respect to their ,bulk1 of all others the largest2 and so the most fitted to receive and entertain foreign ,matter in them4 ,besides1 as far as the ,trials hitherto made inform us1 the constituent ,corpuscles of ,water are1 each singly consider'd1 absolutely solid2 and do not yield to the greatest ,external ,force4 ,this secures their ,figure against any ,alteration2 and the ,intervals of the ,corpuscles must be always alike4 ,by the latter1 'twill be ever disposed to receive ,matter into it2 and by the former1 when once received1 to bear it on along with it4 ,water is further capacitated to be a ,vehicle to this ,matter1 by the tenuity and fineness of the ,corpuscles of which it consists4 ,we hardly know any ,fluid in all ,nature1 except ,fire1 whose constituent ,parts are so exceeding subtle and small as those of ,water are4 ,they'll pass ,pores and ,interstices1 that neither ,air nor any other ,fluid will4 ,this enables them to enter the finest ,tubes and ,vessels of ,plants1 and to introduce the ,terrestrial ,matter1 conveying it to all ,parts of them2 whilst each1 by means of ,organs 'tis endowed with for the ,purpose1 intercepts and assumes into it self such ,particles as are suitable to its own ,nature1 letting the rest pass on through the common ,ducts4 ,nay1 we have almost every where ,mechanical ,instances of much the same ,tenor4 ',tis obvious to every one1 how easily and suddenly ,humidity1 or the ,corpuscles of ,water sustained in the ,air1 pervade and insinuate themselves into ,cords1 however tightly twisted1 into ,leather1 ,parchment1 ,vegetable ,bodies1 ,wood1 and the like4 ,this it is that fits them for ,hygrometers2 and to measure and determine the different quantities of ,moisture in the ,air1 in different ,places and ,seasons4 ,how freely ,water passes and carries with it ,terrestrial ,matter1 through ,filtres1 ,colatures1 ,distillations1 c4 hath been intimated already4 #h4 ,water is not capable of performing this ,office to ,plants1 unless assisted by a due ,quantity of ,heat2 and this must concur1 or ,vegetation will not succeed4 ,the ,plants that were set in the ,glasses ,q1 ,r1 ,s1 c4 in ,october1 and the following colder ,months1 had not near the quantity of ,water sent up into them1 or so great an additional ,encrease by much1 as those that were set in ,june1 ,july1 and the hotter4 ',tis plain ,water has no power of moving it self2 or rising to the vast height it does in the more tall and lofty ,plants4 ,so far from this1 that it does not appear from any ,discovery yet made1 that even its own ,fluidity consists in the intestine ,motion of its ,parts2 whatever some1 otherwise very learned and knowing1 ,persons may have thought4 ,there is no need of any thing more1 for solving all the ,phnomena of ,fluidity1 than such a ,figure and ,disposition of the ,parts1 as ,water has4 ,corpuscles of that make1 and that are all absolutely ,spherical1 must stand so very tickle and nicely upon each other1 as to be susceptible of every ,impression2 and though not perpetually in ,motion1 yet must be ever ready and liable to be put into it1 by any the slightest ,force imaginable4 ,it is true1 the ,parts of ,fire or ,heat are not capable of moving themselves any more than those of ,water2 but they are more subtil1 light1 and active1 than those are1 and so more easily put into ,motion4 ,in fine1 'tis evident and matter of ,fact1 that ,heat does operate upon1 and move the ,water1 in order to its carrying on the ,work of ,vegetation3 ,but how 'tis agitated it self1 and where the ,motion first begins1 this is no fit ,place to enquire4 ,that the ,concourse of ,heat in this ,work is really necessary1 appears1 not only from the ,experiments before us1 but from all ,nature2 from our ,fields and ,forests1 our ,gardens and our ,orchards4 ,we see in ,autumn1 as the ,sun's ,power grows gradually less and less1 so its ,effects on ,plants is remitted1 and their ,vegetation slackens by little and little4 ,its ,failure is first discernible in ,trees4 ,these are raised highest above the ,earth2 and require a more intense ,heat to elevate the ,water1 charged with their ,nourishment1 to the ,tops and ,extremities of them4 ,so that for want of fresh ,support and ,nutriment1 they shed their ,leaves1 unless secur'd by a very firm and hardy ,constitution indeed1 as our ever-,greens are4 ,next the ,shrubs part with theirs2 and then the ,herbs and lower ,tribes2 the ,heat being at length not sufficient to supply even these1 though so near the ,earth1 the ,fund of their ,nourishment4 ,as the ,heat returns the succeeding ,spring1 they all recruit again2 and are furnish'd with fresh ,supplies and ,verdure3 ,but first1 those which are lowest and nearest the ,earth1 ,herbs1 and they that require a lesser degree of ,heat to raise the ,water with its ,earthy ,charge into them3 ,then the ,shrubs and higher ,vegetables in their ,turns2 and lastly1 the ,trees4 ,as the ,heat increases1 it grows too powerful1 and hurries the ,matter with too great ,rapidity thorough the finer and more tender ,plants3 ,these therefore go off1 and decay2 and others that are more hardy and vigorous1 and require a greater share of ,heat1 succeed in their ,order4 ,by which ,mechanism1 provident ,nature furnishes us with a very various and differing ,entertainment2 and what is best suited to each ,season1 all the ,year round4 ,as the ,heat of the several ,seasons affords us a different ,face of ,things2 so the several distant ,climates shew different ,scenes of ,nature1 and ,productions of the ,earth#ab4 ,the ,hotter ,countries yield ordinarily the largest and tallest ,trees2 and those in too much greater variety than the colder ever do4 ,even those ,plants which are common to both1 attain to a much greater ,bulk in the ,southern than in the ,northern ,climes4 ,nay1 there are some ,regions so bleak and chill1 that they raise no ,vegetables at all to any considerable ,size4 ,this we learn from ,greenland1 from ,iseland1 and other ,places of like cold ,site and ,condition4 ,in these no ,tree ever appears2 and the very ,shrubs they afford1 are few1 little1 and low4 ,again1 in the warmer ,climates1 and such as do furnish forth ,trees and the larger ,vegetables1 if there happen a remission or diminution of the usual ,heat1 their ,productions will be impeded and diminished in proportion4 ,our late ,colder ,summers have given us proof enough of this4 ,for though the ,heat we have had1 was sufficient to raise the ,vegetative ,matter into the lower ,plants1 into our ,corns1 our ,wheat1 ,barley1 ,pease and the like2 and we have had plenty of ,straw-berries1 ,ras-berries1 ,currans1 ,goosberries1 and the ,fruits of such other ,vegetables as are low and near the ,earth3 ,yea1 and a moderate store of ,cherries1 ,mulberries1 ,plumbs1 ,filberts1 and some others that grow somewhat at a greater ,height2 yet our ,apples1 our ,pears1 ,walnuts1 and the ,productions of the taller#ac ,trees have been fewer1 and those not so kindly1 so thoroughly ripen'd1 and brought to that ,perfection they were in the former more benign and their warm ,seasons4 ,nay1 even the lower ,fruits and ,grains have had some share in the common ,calamity2 and fallen short both in ,number and ,goodness of what the hotter and kinder ,seasons were wont to shew us4 ,as to our ,grapes1 ,abricots1 ,peaches1 ,nectarens1 and ,figs1 being transplanted hither out of hotter ,climes1 'tis the less wonder we have of late had so general a ,failure of them4 ,nor is it the ,sun1 or the ordinary emission of the ,subterranean ,heat only1 that promotes ,vegetation2 but any other indifferently1 according to its ,power and ,degree3 ,this we are taught by our ,stoves1 hot ,beds1 and the like4 ,all ,heat is of like kind2 and where-ever is the same ,cause1 there will be constantly the same ,effect4 ,there's a ,procedure in every part of ,nature1 that is perfectly regular and geometrical1 if we can but find it out2 and the further our ,searches carry us1 the more shall we have occasion to admire this1 and the better 'twill compensate our ,industry4 #a ,terra ,parens4 4 ,terra ,matter4 #b ,nat4 ,history1 ,cent4 #e4 4 #daa4 #c ,complexionum atque ,mistion4 ,element4 ,figm4 #d ,mr4 ,boyle1 ,scept4 ,chym4 par4 #b4 #e ,provided the ,silver be pure and absolutely refin'd3 ,for the least admixture of ,copper will produce a blue ,tincture in the ,menstruum2 as that of some other ,bodies1 one different4 #f ,to say nothing of those that were not discernible4 #g ,mr4 ,w4 ,molineux1 ,philosophical ,trans4 ,no4 #aha4 #h ,confer4 ,prop4 #a4 supra4 #i ,nat4 ,hist4 ,earth1 p4 #bbh4 seq4 #aj ,vid4 ,varronem1 ,columellam1 reliquos ,rei ,rustic ,scriptores4 #aa ,conf4 ,nat4 ,hist4 ,earth1 p4 #dg4 seq4 uti p4 #abh1 c4 #ab ,conf4 ,nat4 ,hist4 ,earth1 ,pag4 #bfg4 seq4 #ac ,the ,dwarf ,apple and ,pear trees have succeeded better4 ,and indeed in ,trees of the same kind1 those that keep closest to the ,earth always produce the most and best ,fruit4 ,for which ,reason 'tis that the ,gardiners check and restrain the ,growth of better ,fruit-trees1 and prevent their running up to too great a ,height4 ,an ,account of the ,measure of the thickness of ,gold upon ,gilt ,wire2 together with ,demonstration of the exceeding ,minuteness of the ,atoms or constituent ,particles of ,gold2 as it was read before the ,royal ,society1 by ,e4 ,halley4 ,what are the constituent ,parts of ,matter1 and how there comes to be so great a diversity in the weight of ,bodies1 to all appearance equally solid and dense1 such as are ,gold and ,glass1 7whose specifick ,gravities are nearly as #g to #a7 seems a very hard ,question to those that shall rightly consider it3 ,for from undoubted ,experiment1 ,gravity is in all ,bodies proportionable to the ,quantity of ,matter in each2 and there is no such thing as a ,propension of some more1 others less1 towards the ,earth's ,center2 since the ,impediment of the ,air being removed1 all ,bodies descend1 be they never so loose or compact in ,texture1 with equal ,velocity4 ,it follows therefore1 ,that there is #g times as much ,matter in ,gold1 as in a piece of ,glass of the same ,magnitude2 and consequently1 that at least six parts of seven in the ,bulk of ,glass1 must be ,pore or ,vacuity3 ,this some ,favourers of the ,atomical ,philosophy have endeavoured to solve1 by supposing the primary or constituent ,atoms of ,gold to be much larger than those of other ,bodies1 and consequently the ,pores fewer2 whereas in other ,bodies1 the great multitude of the interspersed ,vacuities does diminish their ,weights4 ,being desirous to examine this ,notion of the ,magnitude of ,atoms of ,gold1 ,i bethought my self of the extreme ,ductility of that ,metal1 which is seen in the beating of it into ,leaf1 and above all in the drawing fine ,gilt-wire1 by means whereof1 ,i believed ,i might most exactly obtain the true thickness of the ,coat of ,gold1 that appears1 even with the ,microscope1 so well to represent ,gold it self1 that not the least point of ,silver appears through it4 ,in order to this1 ,i inform'd my self among the ,wire-drawers1 what ,gold they us'd to their ,silver2 and they told me1 ,that the very best double ,gilt ,wire was made out of ,cylindrick ,ingots1 #d ,inches in ,circumference1 and #bh ,inches long1 which weigh #af ,pounds ,troy2 on these they bestow #d ,ounces of ,gold1 that is1 to every #dh ,ounces of ,silver one of ,gold2 and that two ,yards of the super-fine ,wire weighs a ,grain4 ,hence at first sight it appear'd1 that the length of #ih ,yards is in weight #di ,grains1 and that a single ,grain of ,gold covers the said #ih ,yards1 and that the #ajjjjth part of a ,grain is above of an ,inch long2 which yet may be actually divided into #aj1 and so the #ajjjjjth part of a ,grain of ,gold be visible without a ,microscope4 ,but being desirous to compute the thickness of the ,skin of ,gold1 by means of the specifick ,gravities of the ,metals1 viz4 ,silver #aj1 and ,gold #ah1 ,i found the ,diameter of such ,wire the #a_/chf part of an ,inch1 and its ,circumference the #a_/abc part2 but the ,gold in thickness not to exceed the #a_/acdejj part of an ,inch2 whence it may be concluded1 that the ,cube of the hundredth part of an ,inch would contain above #bdccjjjjjj1 7or the ,cube of #acde7 of such ,atoms4 ,and it may likewise be marvelled at1 that ,gold being stretcht to so great a degree1 as is here demonstrated1 should yet shew it self of so even and united a ,texture1 as not to let the white ,colour of the ,silver under it appear through any the least ,pores2 which argues1 that even in this exceeding thinness very many of those ,atoms may still lie one over the other3 ,which is a ,consideration may merit the ,thoughts of this ,honourable ,society1 as tending to examine that renowned ,atomical ,doctrine1 which has of late much obtain'd among the ,learned4 ,an ,account of the several ,species of ,infinite ,quantity1 and of the ,proportions they bear one to the other2 as it was read before the ,royal ,society1 by ,e4 ,halley4 ,that all ,magnitudes infinitely great1 or such as exceed any assignable ,quantity1 are equal among themselves1 though it be vulgarly received for a ,maxim1 is not yet so common as it is erroneous2 and the ,reason of the mistake seems to be1 ,that the ,mind of ,man1 coming to contemplate the ,extensions of what exceeds the bounds of its ,capacity1 and of which the very ,idea does include a ,negation of ,limits2 it comes to pass that we acquiesce generally1 and it suffices to say such a ,quantity is infinite4 ,but if we come more nearly to examine this ,notion1 we shall find1 that there are really besides infinite ,length and infinite ,area1 no less than three several sorts of infinite ,solidity2 all of which are ,quantitates sui generis1 having no more relation or proportion the one to the other1 than a ,line to a ,plane1 or a ,plane to a ,solid1 or a ,finite to an ,infinite4 ,but that among themselves1 each of those ,species of ,infinites are in given ,proportions1 is what ,i now intend to make plain1 if possible4 ,but first1 infinite ,length1 or a ,line infinitely long1 is to be considered either as beginning at a ,point1 and so infinitely extended one way1 or else both ways from the same ,point2 in which case the one1 which is a beginning infinity1 is the one half of the whole1 which is the ,summ of the beginning and ceasing ,infinity2 or1 as ,i may say1 of ,infinity1 parte ante1 and parte post3 ,which is analogous to ,eternity in ,time or ,duration1 in which there is always as much to follow as is past1 from any point or moment of ,time3 ,nor doth the ,addition or ,subduction of finite ,length or ,space of time alter the case either in ,infinity or ,eternity1 since both the one or the other cannot be any part of the whole4 ,as to infinite ,surface or ,area1 any right ,line1 infinitely extended both ways on an infinite ,plane1 does divide that infinite ,plane into equal ,parts2 the one to the right1 and the other to the left of the said ,line3 ,but if from any ,point in such a ,plane1 two right ,lines be infinitely extended1 so as to make an ,angle1 the infinite ,area1 intercepted between those infinite right ,lines1 is to the whole infinite ,plane1 as the ,arch of a ,circle1 on the ,point of ,concourse of those ,lines1 as a ,centre1 intercepted between the said ,lines1 is to the ,circumference of the ,circle2 or as the ,degrees of the ,angle to the #cfj ,degrees of a ,circle4 ,for ,example1 two right ,lines meeting at a right ,angle do include1 on an infinite ,plane1 a quarter part of the whole infinite ,area of such a ,plane4 ,but if so be1 two parallel infinite ,lines be supposed drawn on such an infinite ,plane1 the ,area intercepted between them will be likewise infinite2 but at the same time will be infinitely less1 than that ,space which is intercepted between two infinite ,lines that are inclined1 though with never so small an ,angle2 for that in the one ,case1 the given finite distance of the parallel ,lines diminishes the ,infinity in one ,degree of ,dimension2 whereas in a ,sector1 there is ,infinity in both ,dimensions2 and consequently1 the ,quantities are the one infinitely greater than the other1 and there is no proportion between them4 ,from the same ,consideration arise the ,three several ,species of infinite ,space or ,solidity1 as has been said2 for a ,parallelepipede1 or a ,cylinder1 infinitely long1 is greater than any finite ,magnitude how great soever2 and all such ,solids1 supposed to be formed on given ,bases1 are as those ,bases1 in proportion to one another4 ,but if two of these three ,dimensions are wanting1 as in the ,space intercepted between two parallel ,planes infinitely extended1 and at a finite distance2 or with infinite ,length and ,breadth1 with a finite ,thickness2 ,all such ,solids shall be as the given finite distances one to another3 ,but these ,quantities1 though infinitely greater than the other1 are yet infinitely less than any of those1 wherein all the three ,dimensions are infinite4 ,such are the ,spaces intercepted between two inclined ,planes infinitely extended2 the ,space intercepted by the ,surface of a ,cone1 or the sides of a ,pyramid likewise infinitely continued1 c4 of all which notwithstanding1 the ,proportions one to another1 and to the 1 or vast ,abyss of infinite ,space 7wherein is the ,locus of all things that are or can be2 or to the ,solid of infinite ,length1 ,breadth1 and ,thickness1 taken all manner of ways7 are easily assignable4 ,for the ,space between two ,planes1 is to the whole1 as the ,angle of those ,planes to the #cfj ,degrees of the ,circle4 ,as for ,cones and ,pyramids1 they are as the ,spherical ,surface1 intercepted by them1 is to the ,surface of the ,sphere2 and therefore ,cones are as the versed ,sines of half their ,angles1 to the ,diameter of the ,circle3 ,these three sorts of infinite ,quantity are analogous to a ,line1 ,surface and ,solid1 and after the same manner cannot be compared1 or have any proportion the one to the other4 ,besides these1 there are several other ,species of infinite ,quantity1 arising from the ,contemplation of ,curves1 and their ,asymptotes2 which1 by reason of the difficulty of the ,subject1 cannot be made so plain to most ,readers3 ,but what has been already said1 may be sufficient to evince what we undertook to explain4 ,an ,account of ,dr4 ,robert ,hook's ,invention of the ,marine ,barometer1 with its ,description and ,uses2 published by order of the ,royal ,society1 by ,e4 ,halley1 ,r4 ,s4 ,s4 ,since it was found that the ,torricellian ,tube1 commonly call'd the ,mercurial ,barometer1 by the rising and falling of the ,quick-silver therein1 doth presage the ,changes of the ,air1 in relation to fair and foul ,weather2 upon several ,years ,observation of it1 it has been proved and adjusted for that purpose by ,dr4 ,robert ,hook2 and there have been by him many attempts to improve the ,instrument1 and render the ,minute ,divisions on the ,scale thereof more sensible4 ,he also judging that it might be of great use at ,sea1 contrived several ways to make it serviceable on ,board of ,ship2 one of which he explain'd to the ,royal ,society at their ,weekly ,meeting in ,gresham ,college1 ,january #b4 #affg_/h4 ,since which time he hath further cultivated the ,invention1 and some ,years ago produced before the said ,society1 the ,instrument ,i am now to describe1 which for its subtilty and usefulness1 seemeth to surpass all other performances of the like ,nature4 ',till such time as the ,author's present ,indisposition will give him leave to bestow freely his ,thoughts on this ,subject upon the ,publick1 it is the ,opinion of the ,society1 that such an ,account be given of this ,contrivance1 as may render it known1 and recommend it to the ,mariners use1 for which it was principally intended4 ,the ,mercurial ,barometer requiring a perpendicular ,posture1 and the ,quick-silver vibrating therein with great ,violence upon any ,agitation1 is therefore uncapable of being used at ,sea 7tho' it hath lately been contrived to be made portable71 so it remain'd to find out some other ,principle1 wherein the ,position of the ,instrument was not so indispensably necessary3 ,for this1 all those that use the ,sea are obliged to the great facility ,dr4 ,hook has always shewn1 in applying ,philosophical ,experiments to their proper uses4 ,it is about forty ,years since1 that the ,thermometers of ,robert de ,fluctibus1 depending on the ,dilatation and ,contraction of included ,air by ,heat and ,cold1 have been disused1 upon discovery that the ,airs pressure is unequal2 that inequality mixing it self with the ,effects of the warmth of the ,air in that ,instrument4 ,and instead thereof was substituted the seal'd ,thermometer1 including ,spirit of ,wine 7first brought into ,england1 out of ,italy1 by ,sir ,robert ,southwell7 as a proper ,standard of the temper of the ,air1 in relation to ,heat and ,cold2 that therial ,spirit being of all the known ,liquors the most susceptible of ,dilatation and ,contraction1 especially with a moderate degree of either ,heat or ,cold4 ,now this being allow'd as a ,standard1 and the other ,thermometer that includes ,air1 being graduated with the same ,divisions1 so as at the time when the ,air was included1 to agree with the ,spirit-,thermometer in all the degrees of ,heat and ,cold1 noting at the same time the precise height of the ,mercury in the common ,barometers3 ,it will readily be understood1 that whensoever these two ,thermometers shall agree1 the pressure of the ,air is the same it was1 when the ,air was included1 and the ,instrument graduated3 ,that if in the ,air-,thermometer the ,liquor stand higher than the ,division marked thereon1 corresponding with that on the ,spirit-glass1 it is an indication that there is a greater pressure of the ,air at that time1 than when the ,instrument was graduated4 ,and the contrary is to be concluded1 when the ,air-glass stands lower than the ,spirit1 viz4 that then the ,air is so much lighter1 and the ,quick silver1 in the ordinary ,barometer lower than at the said time of ,graduation4 ,and the ,spaces answering to an ,inch of ,mercury1 will be more or less1 according to the quantity of ,air so included1 and the smallness of the ,glass ,cane1 in which the ,liquor rises and falls1 and may be augmented almost in any proportion1 under that of the ,specifick ,gravity of the ,liquor of the ,thermometer to ,mercury4 ,so as to have a ,foot or more for an ,inch of ,mercury1 which is another great convenience4 ,it has been observed by some1 that in long keeping this ,instrument1 the ,air included either finds a means to escape1 or deposites some ,vapours mixt with it1 or else for some other cause becomes less ,elastick1 whereby1 in process of time1 it gives the height of the ,mercury somewhat greater than it ought2 but this1 if it should happen in some of them1 hinders not the usefulness thereof1 for that it may at any time very easily be corrected by ,experiment1 and the rising and falling thereof are the things chiefly remarkable in it1 the just height being barely a ,curiosity4 ,in these ,parts of the ,world1 long ,experience has told us1 that the rising of the ,mercury forebodes fair ,weather after foul1 and an ,easterly or ,northerly ,wind2 and that the falling thereof1 on the contrary1 signifies ,southerly or ,westerly ,winds1 with ,rain1 or stormy ,winds1 or both2 which latter it is of much more consequence to provide against at ,sea than at ,land2 and in a ,storm1 the ,mercury beginning to rise is a sure sign that it begins to abate1 as has been experienced in high ,latitudes1 both to the ,northwards and ,southwards of the quator4 ,the ,form of this ,instrument is shown in the ,cut1 by ,tab4 #d4 ,fig4 #a4 wherein1 ,,ab represents the ,spirit-,thermometer1 graduated from #j1 or the freezing ,point1 through all the possible degrees of the ,heat or ,cold of the ,air1 at least in these ,climates4 ,,cd1 is the ,air-,thermometer1 graduated after the same manner with the like ,degrees4 ,,ef1 is a ,plate applied to the side of the ,thermometer ,,cd1 graduated into ,spaces answering to ,inches and parts of an ,inch of ,mercury1 in the common ,barometers4 ,g1 a ,hand standing on the ,plate at the height of the ,mercury thereon1 as it was when the ,instrument was graduated1 as suppose here at #bi ,inches4 ,,lm1 a ,wire on which the ,plate ,,ef1 slips up and down1 parallel to the ,cane of the ,thermometer ,,cd4 ,k1 any ,point at which the ,spirit stands at the time of ,observation2 suppose at #ch on the ,spirit-,thermometer2 ,slide the ,plate ,,ef till the ,hand ,g stand at #ch on the ,air-,thermometer1 and if the ,liquor therein stand at #ch likewise1 then is the pressure of the ,air the same as at the time of ,graduation1 viz4 #bi1e2 but if it stand higher1 as at #cj1 at ,i2 then is the pressure of the ,air greater2 and the division on the sliding ,plate against the ,liquor1 shews the present height of the ,mercury to be twenty nine ,inches seven ,tenths4 ,and this may suffice as to the manner of using it4 ,i had one of these ,barometers with me in my late ,southern ,voyage1 and it never failed to prognostick and give early notice of all the bad ,weather we had1 so that ,i depended thereon1 and made provision accordingly2 and from my own ,experience ,i conclude that a more useful ,contrivance hath not for this long time been offer for the benefit of ,navigation4 ,these ,instruments are made according to the ,direction of ,dr4 ,hook1 by ,mr4 ,henry ,hunt1 ,operator to the ,royal ,society1 who will furnish any ,gentlemen with them1 and give them ,directions how to use them4 ,a ,discourse concerning the ,proportional ,heat of the ,sun in all ,latitudes1 with the ,method of collecting the same2 as it was read before the ,royal ,society1 in one of their late ,meetings4 ,by ,e4 ,halley4 ,there having lately arisen some ,discourse about that part of the ,heat of ,weather1 simply produced by the ,action of the ,sun2 and ,i having affirmed1 that if that were considered1 as the only ,cause of the ,heat of the ,weather1 ,i saw no ,reason1 but that under the ,pole the solstitical ,day ought to be as hot as it is under the quinoctial1 when the ,sun comes vertical1 or over the ,zenith3 ,for this ,reason1 that for all the #bd ,hours of that ,day under the ,pole1 the ,sun's ,beams are inclined to the ,horizon1 with an ,angle of #bc ,degrees2 and under the quinoctial1 though he come vertical1 yet he shines no more than #ab ,hours1 and is again #ab ,hours absent2 and that for #c ,hours #h ,minutes of that #ab ,hours1 he is not so much elevated as under the ,pole2 so that he is not #i of the whole #bd1 higher than 'tis there1 and is #ae ,hours lower4 ,now the simple ,action of the ,sun is1 as all other ,impulses or ,stroaks1 more or less forceable1 according to the ,sinus of the ,angle of ,incidence1 or to the ,perpendicular let fall on the ,plain1 whence the vertical ,ray 7being that of the greatest ,heat17 being put ,radius1 the force of the ,sun on the ,horizontal ,surface of the ,earth will be to that1 as the ,sinus of the ,sun's ,altitude at any other time4 ,this being allow'd for true1 it will then follow1 that the time of the continuance of the ,sun's shining being taken for a ,basis1 and the ,sines of the ,sun's ,altitudes erected thereon as ,perpendiculars1 and a ,curve drawn through the ,extremities of those ,perpendiculars1 the ,area comprehended shall be proportionate to the ,collection of the ,heat of all the ,beams of the ,sun in that space of time4 ,hence it will follow1 that under the ,pole the ,collection of all the ,heat of a tropical ,day1 is proportionate to a ,rectangle of the ,sine of #bc gr4 into #bd ,hours1 or the ,circumference of a ,circle2 that is1 the ,sine of #bc gr4 being nearly #d ,tenths of ,radius2 as #c_/aj into #ab ,hours4 ,or the ,polar ,heat is equal to that of the ,sun containing #ab ,hours above the ,horizon1 at #ec gr4 height1 than which the ,sun is not #e ,hours more elevated under the quinoctial4 ,but that this ,matter may the better be understood1 ,i have exemplified it by a ,scheme1 7,tab4 #d4 ,fig4 #b7 wherein the ,area ,,zghh1 is equal to the ,area of all the ,sines of the ,sun's ,altitude under the quinoctial1 erected on the respective ,hours from ,sun-rise to the ,zenith2 and the ,area ,,hh is in the same proportion to the ,heat of the same #f ,hours under the ,pole on the ,topical ,day2 and ,,hhq1 is proportional to the collected ,heat of #ab ,hours1 or half a ,day under the ,pole1 which space ,,hhq1 is visibly greater than the other ,area ,,hzgh1 by as much as the ,area ,,hgq is greater than the ,area ,,zg2 which1 that it is so1 is visible to sight1 by a great excess2 and so much in proportion does the ,heat of the #bd ,hours ,sun-shine under the ,pole1 exceed that of the #ab ,hours under the quinoctial3 ,whence1 ,cteris paribus1 it is reasonable to conclude1 that were the ,sun perpetually under the ,tropick1 the ,pole would be at least as warm1 as it is now under the ,line it self4 ,but whereas the ,nature of ,heat is to remain in the ,subject1 after the ,cause that heated is removed1 and particularly in the ,air2 under the quinoctial1 the #ab ,hours absence of the ,sun does very little still the ,motion impressed by the part ,action of his ,rays1 wherein ,heat consists1 before he arise again3 ,but under the ,pole the long absence of the ,sun for #f ,months1 wherein the extremity of ,cold does obtain1 has so chill'd the ,air1 that it is as it were frozen1 and cannot1 before the ,sun has got far towards it1 be any way sensible of his presence1 his ,beams being obstructed by thick ,clouds1 and perpetual ,fogs and ,mists1 and by that ,atmosphere of ,cold1 as the late ,honourable ,mr4 ,boyle was pleased to term it1 proceeding from the everlasting ,ice1 which in immense ,quantities does chill the ,neighbouring ,air1 and which the too soon retreat of the ,sun leaves unthawed1 to encrease again1 during the long ,winter that follows this short interval of ,summer4 ,but the differing ,degrees of ,heat and ,cold1 in differing ,places1 depend in great measure upon the ,accidents of the ,neighbourhood of high ,mountains1 whose height exceedingly chills the ,air brought by the ,winds over them2 and of the ,nature of the ,soil1 which variously retains the ,heat1 particularly the ,sandy1 which in ,africa1 ,arabia1 and generally where such ,sandy ,desarts are found1 do make the ,heat of the ,summer incredible to those that have not felt it4 ,in the prosecution of this first ,thought1 ,i have solved the ,problem generally1 viz4 to give the proportional ,degree of ,heat1 or the ,sum of all the ,sines of the ,sun's ,altitude1 while he is above the ,horizon in any oblique ,sphere1 by reducing it to the finding of the ,curve ,surface of a ,cylindrick ,hoof1 or of a given part thereof4 ,now this ,problem is not of that difficulty as appears at first sight1 for in ,tab4 #d4 ,fig4 #c4 let the ,cylinder ,,abcd be cut obliquely with the ,ellipse ,,bkdi1 and by the ,center thereof ,h1 describe the ,circle ,,iklm2 ,i say1 the ,curve ,surface ,,iklb is equal to the ,rectangle of ,,ik and ,,bl1 or of ,,hk and #b ,,bl or ,,bc3 ,and if there be supposed another ,circle1 as ,,nqpo1 cutting the said ,ellipse in the ,points ,p1 ,q2 draw ,,ps1 ,,qr1 parallel to the ,cylinders ,axe1 till they meet with the aforesaid ,circle ,,iklm in the ,points ,r1 ,s1 and draw the ,lines ,,rts1 ,,qvp bisected in ,t and ,v4 ,i say again1 that the ,curve ,surface ,,rmsqdp is equal to the ,rectangle of ,,bl or ,,md and ,,rs1 or of #b ,,bl or ,,ad and ,,st or ,,vp2 and the ,curve ,surface ,,qnpd is equal to ,,rs ,,md----the ,arch ,,rms ,,sp1 or the ,arch ,,ms #b ,,sp3 ,or it is equal to the ,surface ,,rmsqdp1 substracting the ,surface ,,rmsqnp4 ,so likewise the ,curve ,surface ,,qbpo is equal to the ,sum of the ,surface ,,rmsqdp1 or ,,rs ,,md1 and of the ,surface ,,rlsqop1 or the ,arch ,,ls #b ,,sp4 ,this is the most easily demonstrated from the ,consideration1 ,that the ,cylindrick ,surface ,,iklb is to the inscrib'd ,spherical ,surface ,,ikle1 either in the whole1 or in its ,analogous ,parts1 as the tangent ,,bl is to the ,arch ,,el1 and from the ,demonstrations of ,archimedes de ,sphra ,cylindro1 ,lib4 ,i4 ,prop4 ,,xxx1 and ,,xxxvii1 ,,xxxiix4 which ,i shall not repeat here1 but leave the ,reader the pleasure of examining it himself2 nor will it be amiss to consult ,dr4 ,barrow's ,learned ,lectures on that ,book1 ,publish'd at ,london1 ,anno #afhd1 viz4 ,probl4 ,,ix4 and the ,corollaries thereof4 ,now to reduce our ,case of the ,sum of all the ,sines of the ,sun's ,altitude in a given ,declination and ,latitude to the aforesaid ,problem1 let us consider 7,tab4 #d4 ,fig4 #d47 which is the ,analemma projected on the ,plain of the ,meridian1 ,z the ,zenith1 ,p the ,pole1 ,,hh the ,horizon1 the quinoctial1 1 the two ,tropicks1 #a the ,sine of the ,meridian ,altitude in 2 and equal thereto1 but perpendicular to the ,tropick1 erect ,i1 and draw the ,line ,,ti intersecting the ,horizon in ,t1 and the ,hour ,circle of #f1 in the ,point #d1 and #fd shall be equal to #f,r1 or to the ,sine of the ,altitude at #f3 ,and the like for any other ,point in the ,tropick1 erecting a ,perpendicular thereat1 terminated by the ,line ,t ,i3 ,through the ,point #d draw the ,line #d1 #e1 #g parallel to the ,tropick1 and representing a ,circle equal thereto2 then shall the ,tropick in ,fig4 #d4 answer to the ,circle ,,nopq1 in ,fig4 #c4 the ,circle #deg shall answer the ,circle ,,iklm1 ,t#d;,i shall answer to the ,elliptick ,segment ,,qibkp1 #f,r or #fd shall answer to ,,sp1 and #e;,i to ,,bl1 and the ,arch ,t1 to the ,arch ,,ls1 being the semidiurnal ,arch in that ,latitude and ,declination2 the ,sine whereof1 tho' not expressible in ,fig4 #d4 must be conceived as ,analogous to the ,line ,,ts or ,,up in ,fig4 #c4 ,the ,relation between these two ,figures being well understood1 it will follow from what precedes1 ,that1 the sum of the ,sines of the ,meridian ,altitudes of the ,sun in the two ,tropicks1 7and the like for any two opposite ,parallels7 being multiplied by the ,sine of the semidiurnal ,arch1 will give an ,area ,analogous to the ,curve ,surface ,,rimsqdp2 and thereto adding in ,summer1 or substracting in ,winter1 the ,product of the length of the semidiurnal ,arch1 7taken according to ,van ,ceulen's ,numbers7 into the difference of the above-said ,sines of the ,meridian ,altitude3 ,the sum in one case1 and difference in another1 shall be as the ,aggregate of all the ,sines of the ,sun's ,altitude1 during his appearance above the ,horizon2 and consequently of all his ,heat and ,action on the ,plain of the ,horizon in the proposed ,day4 ,and this may also be extended to the parts of the same ,day2 for if the aforesaid ,sum of the ,sines of the ,meridian ,altitudes1 be multiplied by half the ,sum of the ,sines of the ,sun's ,horary distance from ,noon1 when the ,times are before and after ,noon2 or by half their difference1 when both are on the same side of the ,meridian2 and thereto in ,summer1 or therefrom in ,winter1 be added or substracted the ,product of half the ,arch answerable to the proposed interval of ,time1 into the difference of the ,sines of ,meridian ,altitudes1 the ,sum in one case and ,difference in the other1 shall be proportional to all the ,action of the ,sun during that space of time4 ,i fore-see it will be ,objected1 that ,i take the ,radius of my ,circle on which ,i erect my ,perpendiculars always the same1 whereas the ,parallels of ,declination are unequal2 but to this ,i answer1 ,that our said ,circular ,bases ought not to be ,analogous to the ,parallels1 but to the ,times of ,revolution1 which are equal in all of them4 ,it may perhaps be useful to give an ,example of the ,computation of this ,rule1 which may seem difficult to some4 ,let the ,solstitical ,heat in and be required at ,london1 ,lat4 #ea #cb'4 #chj-b'h ,co-,lat4 #bc -#cj ,decl4 ------ #fa -#eh ,sinus 1#hhbfgd #ad -#eh ,sinus 1#behbeg ------ ,summa #a1adjica ,diff4 1#fbddag ,diff4 ,ascen4 #ccjj-a'a4 ,arch4 ,semid4 stiv4 #abc-aa4 ,ar4 ,sem4 hyb4 #ef-di4 ,s4 1#fchibc ,arch4 stiv4 mensura #b1adiiee ,arc4 hyb4 mensura 1#iiafhc ,then #a1adjica in 1#hcfibc1 #fbddag in #b1adiiee #b1bigcd4 ,and #a1adjica in #hcfibi - 1#fbddag in 1#iiafch #cchie4 ,so that #b1bigcd will be as the ,tropical ,summers ,day ,heat1 and #j1cchie as the ,action of the ,sun in the ,day of the ,winter ,solstice4 ,after this manner ,i computed the following ,table for every tenth ,degree of ,latitude1 to the quinoctial and ,tropical ,sun1 by which an ,estimate may be made of the intermediate ,degrees4 ---------------------------------------- -------- ,sun in ,sun in ,sun in ,lat4 ---------------------------------------- -------- #j #bjjjj #ahcda #ahcda #aj #aifif #bjbij #aehcd #bj #ahgid #bagcg #acaff #cj #agcba #bbfea #ajabd #dj #aecba #bcjdh #fidd ---------------------------------------- -------- #ej #abhee #bbiia #cgih #fj #ajjjj #bbggc #ajge #gj #fhdj #bcedc #jjj #hj #cdgc #bdfgc #jjj #ij #jjjj #bejee #jjj ---------------------------------------- -------- ,those that desire more of the ,nature of this ,problem1 as to the ,geometry thereof1 would do well to compare the ,,xiii4 ,prop4 ,cap4 ,v4 of the ,learned ,treatise1 ,de ,calculo ,centri ,gravitatis1 by the ,reverend ,dr4 ,wallis1 ,published ,anno #afgj4 ,from this ,rule there follow several ,corollaries worth ,note3 ,as ,i4 ,that the quinoctial ,heat1 when the ,sun comes ,vertical1 is as twice the ,square of ,radius1 which may be proposed as a ,standard to compare with1 in all other ,cases4 ,,ii4 ,that under the quinoctial1 the ,heat is as the ,sine of the ,sun's ,declination4 ,,iii4 ,that in the ,frigid ,zones when the ,sun sets not1 the ,heat is as the ,circumference of a ,circle into the ,sine of the ,altitude at #f4 ,and consequently1 that in the same ,latitude these ,aggregates of ,warmth1 are as the ,sines of the ,sun's ,declinations2 and in the same ,declination of ,sol1 they are as the ,sines of the ,latitude1 and generally they are as the ,sines of the ,latitude into the ,sines of ,declination4 ,,iv4 ,that the quinoctial ,days ,heat is every where as the ,co-sine of the ,latitude4 ,v4 ,in all places where the ,sun sets1 the difference between the ,summer and ,winter ,heats1 when the ,declinations are contrary1 is equal to a ,circle into the ,sine of the ,altitude at six in the ,summer ,parallel1 and consequently those differences are as the ,sines of ,latitude into1 or multiplied by the ,sines of ,declination4 ,,vi4 ,from the ,table ,i have added1 it appears1 that the ,tropical ,sun under the quinoctial1 has1 of all others1 the least ,force4 ,under the ,pole it is greater than any other ,days ,heat whatsoever1 being to that of the quinoctial as #e to #d4 ,from the ,table and these ,corollaries may a general ,idea be conceived of the ,sum of all the ,actions of the ,sun in the whole ,year1 and that part of the ,heat that arises simply from the ,presence of the ,sun be brought to a ,geometrical ,certainty3 ,and if the like could be performed for ,cold2 which is something else than the bare ,absence of the ,sun1 as appears by many ,instances1 we might hope to bring what relates to this part of ,meteorology to a perfect ,theory4 ,concerning the ,distance of the ,fix'd ,stars4 ,by the ,honourable ,francis ,roberts1 ,esq2 ,s4 ,r4 ,s4 ,the ,ancient ,astronomers1 who had no other way of computing the ,distances of the ,heavenly ,bodies1 but by their ,parallax to the ,semi-diameter of the ,earth2 and being never able to discover any in the fix'd ,stars1 did from thence rightly enough infer1 that their ,distance was very great1 and much exceeding that of the ,planets1 but could go no farther otherwise than by uncertain guess4 ,since the ,pythagorean ,system of the ,world has been reviv'd by ,copernicus1 7and now by all ,mathematicians accepted for the true one7 there seem'd ,ground to imagine that the ,diameter of the ,earth's ,annual ,course 7which1 according to our best ,astronomers1 is at least #djjjj times bigger than the ,semi-diameter of the ,earth7 might give a sensible ,parallax to the fix'd ,stars1 though the other could not1 and thereby determine their ,distance more precisely4 ,but though we have a ,foundation to build on so vastly exceeding that of the ,ancients1 there are some ,considerations may make us suspect that even this is not large enough for our purpose4 ,monsieur ,hugens 7who is very exact in his ,astronomical ,observations7 tells us1 he could never discover any visible ,magnitude in the fix'd ,stars1 though he used ,glasses which magnified the apparent ,diameter above #ajj times4 ,now1 since in all likelyhood the fix'd ,stars are ,suns1 7perhaps of a different ,magnitude7 we may as a reasonable ,medium presume they are generally about the bigness of the ,sun4 ,let us then 7for ,example7 suppose the ,dog-,star to be so4 ,the ,distance from us to the ,sun being about #ajj times the ,sun's ,diameter 7as is demonstrable from the ,sun's ,diameter being #cb ,minutes7 it is evident1 that the ,angle under which the ,dog-,star is seen in ,mr4 ,hugens's ,telescope1 must be near the same with the ,angle of its ,parallax to the ,sun's ,distance1 or ,semi-diameter of the ,earth's ,annual ,course2 so that the ,parallax to the whole ,diameter1 can be but double such a quantity1 as even to ,mr4 ,hugens's nice ,observation is altogether insensible4 ,the ,distance therefore of the fix'd ,stars seems hardly within the reach of any of our ,methods to determine2 but from what has been laid down1 we may draw some ,conclusions that will much illustrate the prodigious vastness of it4 #a4 ,that the ,diameter of the ,earth's ,annual ,orb 7which contains at least #afj ,millions of ,miles7 is but as a ,point in comparison of it2 at least it must be above #fjjj times the ,distance of the ,sun4 ,for if a ,star should appear thro' the aforesaid ,telescope half a ,minute broad 7which is a pretty sensible ,magnitude7 the true apparent ,diameter would not exceed #ah #c;d ,minutes1 which is less than the #fjjjth part of the apparent ,diameter of the ,sun1 and consequently the ,sun's ,distance not the #fjjjth part of the ,distance of the ,star4 #b4 ,that could we advance towards the ,stars #ii ,parts of the whole ,distance1 and have only #a_/ajj ,part remaining1 the ,stars would appear little bigger to us than they do here2 for they would shew no otherwise than they do through a ,telescope1 which magnifies an ,hundred-fold4 #c4 ,that at least ,nine ,parts in ,ten of the ,space between us and the fix'd ,stars1 can receive no greater ,light from the ,sun1 or any of the ,stars1 than what we have from the ,stars in a clear ,night4 #d4 ,that ,light takes up more time in travelling from the ,stars to us1 than we in making a ,west-,india ,voyage 7which is ordinarily perform'd in six ,weeks47 ,that a ,sound would not arrive to us from thence in #ejjjj ,years1 nor a ,cannon-bullet in a much longer time4 ,this is easily computed1 by allowing 7according to ,mr4 ,newton7 ,ten ,minutes for the ,journey of ,light from the ,sun hither1 and that a ,sound moves about #acjj ,foot in a ,second4 ,the ,famous ,mr4 ,isaac ,newton's ,theory of the ,moon4 ,this ,theory which hath been long expected by all the true ,lovers of ,astronomy1 was communicated from ,mr4 ,newton to ,dr4 ,gregory1 ,astronomy ,professor at ,oxford1 and by him published in his ,astron4 ,elem4 ,philos4 and ,geomet4 p4 #ccf4 ,from whence1 as it was lately translated into ,english1 ,i thought fit to insert it here4 ,by this ,theory1 what by all ,astronomers was thought most difficult and almost impossible to be done1 the ,excellent ,mr4 ,newton hath now effected2 viz4 to determine the ,moon's ,place even in her ,quadratures1 and all other ,parts of her ,orbit1 besides the ,syzygys1 so accurately by ,calculation1 that the ,difference between that and her true ,place in the ,heavens1 shall scarce be above two minutes in her ,syzygys1 or above three in her ,quadratures1 and is usually so small1 that it may well enough be reckon'd only as a ,defect in the ,observation4 ,and this ,mr4 ,newton experienced1 by comparing it with very many ,places of the ,moon1 observ'd by ,mr4 ,flamsteed1 and communicated to him4 ,the ,royal ,observatory at ,greenwich1 is to the ,west of the ,meridian of ,paris1 #b degrees1 #ai minutes4 ,of ,uraniburgh1 #ab degrees1 #ea minutes1 #cj seconds4 ,and of ,gedanum1 #ah degrees1 #dh minutes4 ,the mean ,motions of the ,sun and ,moon1 accounted from the ,vernal quinox at the ,meridian of ,greenwich1 ,i make to be as followeth4 ,the last ,day of ,december #afhj1 at ,noon 7,old ,stile7 the mean ,motion of the ,sun was #i ,signs1 #bj degrees1 #cd minutes1 #df seconds4 ,of the ,sun's ,apogum1 was #c ,s4 #g deg4 #bc min4 #cj seconds4 ,that the mean ,motion of the ,moon at that time1 was #f ,s4 #a degree1 #de minutes1 #de seconds4 ,and of her ,apogee1 #h ,s4 #d degrees1 #bh minutes1 #e seconds4 ,of the ascending ,node of the ,moon's ,orbit1 #e ,s4 #bd deg4 #ad min4 #ce seconds1 c4 ,and on the last ,day of ,december1 #agjj1 at ,noon1 the mean ,motion of the ,sun was #i ,s4 #bj degrees1 #dc minutes1 #ej seconds4 ,of the ,sun's ,apogee1 #c ,s4 #g degrees1 #dd minutes1 #cj seconds4 ,the mean ,motion of the ,moon was #aj ,s4 #ae degrees1 #ai minutes1 #ej seconds4 ,of the ,moon's ,apogee1 #aa ,s4 #h degrees1 #ah minutes1 #bj seconds4 ,and of her ascending ,node1 #d ,s4 #bg degrees1 #bd minutes1 #bj seconds4 ,for in #bj ,julian ,years1 or #gcje ,days1 the ,sun's ,motion is #bj ,revol4 #j ,s4 #j degrees1 #i minutes1 #d seconds4 ,and the ,motion of the ,sun's ,apogee1 #ba minutes1 #j seconds4 ,the ,motion of the ,moon in the same time1 is #bfg ,revol4 #d ,s4 #ac degrees1 #cd minutes1 #e seconds4 ,and the ,motion of the ,lunar ,apogee1 is #b ,revol4 #c ,s4 #c degrees1 #ej minutes1 #ae seconds4 ,and the ,motion of her ,node1 #a ,revol4 #j ,s1 #bf degrees1 #ej minutes1 #ae seconds4 ,all which ,motions are accounted from the ,vernal quinox3 ,wherefore if from them there be subtracted the ,recession or ,motion of the quinoctial ,point1 in ,antecedentia1 during that space1 which is #af minutes1 #dj seconds1 there will remain the ,motions in reference to the fix'd ,stars in #bj ,julian ,years2 viz4 the ,sun's #ai ,revol4 #aa ,s4 #bi degrees1 #eb minutes1 #bd seconds4 ,of his ,apogee1 #d minutes1 #bj seconds4 ,and the ,moon's #bfg ,revol4 #d ,s4 #ac degrees1 #ag minutes1 #be seconds4 ,of her ,apogee1 #b ,revol4 #c ,s4 #c degrees1 #cc minutes1 #ce seconds4 ,and of the ,node of the ,moon1 #a ,revol4 #j ,s4 #bg degrees1 #f minutes1 #ee seconds4 ,according to this ,computation1 the ,tropical ,year is #cfe ,days1 #e ,hours1 #dh ,minutes1 #eg ,seconds4 ,and the ,sydereal ,year is #cfe ,days1 #f ,hours1 #i ,minutes1 #ad ,seconds4 ,these mean ,motions of the ,luminaries are affected with various ,inequalities3 ,of which1 #a4 ,there are the ,annual ,equations of the aforesaid mean ,motions of the ,sun and ,moon1 and of the ,apogee and ,node of the ,moon4 ,the ,annual ,equation of the mean ,motion of the ,sun1 depends on the ,eccentricity of the ,earth's ,orbit round the ,sun1 which is #af-aa_/ab of such ,parts1 as that the ,earth's mean ,distance from the ,sun shall be #ajjj3 ,whence 'tis call'd the ,equation of the ,centre2 and is1 when greatest1 #a degree1 #ef minutes1 #bj seconds4 ,the greatest ,annual ,equation of the ,moon's mean ,motion1 is #aa degrees1 #di seconds2 of her ,apogee1 #bj minutes1 and of her ,node1 #i minutes1 #cj seconds4 ,and these four ,annual ,equations are always mutually proportional one to another3 ,wherefore when any of them is at the greatest1 the other three will also be greatest2 and when any one lessens1 the other three will also be diminished in the same ,ratio4 ,the ,annual ,equation of the ,sun's ,centre being given1 the three other corresponding ,annual ,equations will be also given2 and therefore a ,table of that will serve for all4 ,for if the ,annual ,equation of the ,sun's ,centre be taken from thence1 for any ,time1 and be call'd ,p1 and let #a_/aj,p ,q1 ,q #a_/fj,q ,r1 #a_/f,p ,d1 ,d #a_/cj;,d ,e1 and ,d - #a_/ej;,d #b;,f2 then shall the ,annual ,equation of the ,moon's mean ,motion for that time be ,r1 that of the ,apogee of the ,moon will be ,e1 and that of the ,node ,f4 ,only observe here1 ,that if the ,equation of the ,sun's ,centre be required to be added2 then the ,equation of the ,moon's mean ,motion must be subtracted1 that of her ,apogee must be added1 and that of the ,node subducted1 ,and on the contrary1 if the ,equation of the ,sun's ,centre were to be subducted1 the ,moon's ,equation must be added1 the ,equation of her ,apogee subducted1 and that of her ,node added4 ,there is also an ,equation of the ,moon's mean ,motion1 depending on the situation of her ,apogee1 in respect of the ,sun2 which is greatest when the ,moon's ,apogee is in an ,octant with the ,sun1 and is nothing at all when it is in the ,quadratures or ,syzygys4 ,this ,equation1 when greatest1 and the ,sun in ,perigo1 is #c ,minutes1 #ef ,seconds4 ,but if the ,sun be in ,apogo1 it will never be above #c ,minutes1 #cd ,seconds4 ,at other ,distances of the ,sun from the ,earth1 this ,equation1 when greatest1 is reciprocally as the ,cube of such ,distance4 ,but when the ,moon's ,apogee is any where but in the ,octants1 this ,equation grows less1 and is mostly at the same distance between the ,earth and ,sun1 as the ,sine of the double ,distance of the ,moon's ,apogee1 from the next ,quadrature or ,syzygy1 to the ,radius4 ,this is to be added to the ,moon's ,motion1 while her ,apogee passes from a ,quadrature with the ,sun to a ,syzygy2 but this is to be subtracted from it1 while the ,apogee moves from the ,syzygy to the ,quadrature4 ,there is moreover another ,equation of the ,moon's ,motion1 which depends on the ,aspect of the ,nodes of the ,moon's ,orbit with the ,sun3 ,and this is greatest1 when her ,nodes are in ,octants to the ,sun1 and vanishes quite1 when they come to their ,quadratures or ,syzygys4 ,this ,equation is proportional to the ,sine of the double ,distance of the ,node from the next ,syzygy1 or ,quadrature2 and at greatest1 is but #dg seconds4 ,this must be added to the ,moon's mean ,motion1 while the ,nodes are passing from their ,syzygys with the ,sun1 to their ,quadratures with him2 but subtracted while they pass from the ,quadratures to the ,syzygys4 ,from the ,sun's true ,place1 take the equated mean ,motion of the ,lunar ,apogee1 as was above shew'd1 the ,remainder will be the ,annual ,argument of the said ,apogee4 ,from whence the ,eccentricity of the ,moon1 and the second ,equation of her ,apogee may be computed after the manner of the following 7which takes place also in the ,computation of any other intermediate ,equations74 ,tab4 #c4 ,fig4 #f4 ,let ,t represent the ,earth1 ,,ts1 a ,right ,line joining the ,earth and ,sun1 ,,tacb1 a ,right ,line drawn from the ,earth to the middle or mean ,place of the ,moon's ,apogee1 equated1 as above3 ,let the ,angle ,,sta be the ,annual ,argument of the aforesaid ,apogee1 ,,ta the least ,eccentricity of the ,moon's ,orbit1 ,,tb the greatest4 ,bissect ,,ab in ,g2 and on the ,centre ,c1 with the ,distance ,,ac describe a ,circle ,,afb1 and make the ,angle ,,bcf to the double of the ,annual ,argument4 ,draw the ,right ,line ,,tf1 that shall be the ,eccentricity of the ,moon's ,orbit2 and the ,angle ,,btf1 is the second ,equation of the ,moon's ,apogee required4 ,in order to whose ,determination1 let the mean ,distance of the ,earth from the ,moon1 or the ,semi-diameter of the ,moon's ,orbit1 be #ajjjjj2 then shall its greatest ,eccentricity ,,tb be #ffghb such ,parts2 and the least ,,ta1 #dccai4 ,so that the greatest ,equation of the ,orbit1 viz4 when the ,apogee is in the ,syzygys1 will be #g degrees1 #ci minutes1 #cj seconds1 or perhaps #g degrees1 #dj minutes1 7for ,i suspect there will be some ,alteration1 according to the ,position of the ,apogee in ,cancer and ,capricorn47 ,but when it is ,quadrate to the ,sun1 the greatest ,equation aforesaid will be #d degrees1 #eg minutes1 #ef seconds2 and the greatest ,equation of the ,apogee1 #ab degrees1 #ae minutes1 #d seconds4 ,having from these ,principles made a ,table of the ,equation of the ,moon's ,apogee1 and of the ,eccentricities of her ,orbit to each degree of the ,annual ,argument1 from whence the ,eccentricity ,,tf1 and the ,angle ,,btf 7viz4 the second and the principal ,equation of the ,apogee7 may easily be had for any ,time required2 let the ,equation thus found be added to the first ,equated ,place of the ,moon's ,apogee1 if the ,annual ,argument be less than #ij degrees1 or greater than #ahj degrees1 and less than #bgj2 otherwise it must be subducted from it2 and the ,sum or ,difference shall be the ,place of the ,lunar ,apogee secondarily equated2 which being taken from the ,moon's ,place equated a third time1 shall leave the mean ,anomaly of the ,moon corresponding to any given ,time4 ,moreover1 from this mean ,anomaly of the ,moon1 and the before-found ,eccentricity of her ,orbit1 may be found 7by means of a ,table of ,equations of the ,moon's ,centre made to every degree of the mean ,anomaly1 and some ,eccentricities1 viz4 #dejjj1 #ejjjj1 #eejjj1 #fjjjj1 and #fejjj7 the ,prostaphresis1 or ,equation of the ,moon's ,centre1 as in the common way3 ,and this being taken from the former ,semi-circle of the middle ,anomaly1 and added in the latter to the ,moon's ,place thus thrice equated1 will produce the ,place of the ,moon a fourth time equated4 ,the greatest ,variation of the ,moon 7viz4 that which happens when the ,moon is in an ,octant with the ,sun7 is nearly1 reciprocally as the ,cube of the ,distance of the ,sun from the ,earth4 ,let that be taken #cg minutes1 #be seconds1 when the ,sun is in ,perigo1 and #cc minutes1 #dj seconds1 when he is in ,apogo3 ,and let the ,differences of this ,variation in the ,octants be made reciprocally1 as the ,cubes of the ,distances of the ,sun from the ,earth2 and so let a ,table be made of the aforesaid ,variation of the ,moon in her ,octants 7or its ,logarithms7 to every ,tenth1 ,sixth1 or ,fifth ,degree of the mean ,anomaly3 ,and for the ,variation out of the ,octants1 make1 as ,radius to the ,sine of the double ,distance of the ,moon from the next ,syzygy1 or ,quadrature 33 so let the afore-found ,variation in the ,octant be to the ,variation congruous to any other ,aspect2 and this added to the ,moon's ,place before found in the first and third ,quadrant 7accounting from the ,sun7 or subducted from it in the second and fourth1 will give the ,moon's ,place equated a fifth time4 ,again1 as ,radius to the ,sine of the ,summ of the ,distances of the ,moon from the ,sun1 and of her ,apogee from the ,sun's ,apogee 7or the ,sine of the ,excess of that ,summ above #cfj degrees17 33 so is #b minutes1 #aj seconds1 to a sixth ,equation of the ,moon's ,place1 which must be subtracted1 if the aforesaid ,summ or ,excess be less than a ,semi-circle2 but added1 if it be greater4 ,let it be made also1 as ,radius to the ,sine of the ,moon's distance from the ,sun 33 so #b degrees1 #bj secants1 to a seventh ,equation2 which when the ,moon's ,light is increasing1 add2 but when decreasing1 subtract2 and the ,moon's ,place will be equated a seventh time1 and this is her ,place in her proper ,orbit4 ,note here1 the ,equation thus produced by the mean ,quantity #b degrees1 #bj seconds1 is not always of the same magnitude2 but is increased and diminished1 according to the ,position of the ,lunar ,apogee4 ,for if the ,moon's ,apogee be in ,conjunction with the ,sun's1 the aforesaid ,equation is about #ed seconds greater3 ,but when the ,apogees are in ,opposition1 'tis about as much less2 and it librates between its greatest ,quantity #c minutes1 #ad seconds1 and its least1 #a minute1 #bf seconds4 ,and this is1 when the ,lunar ,apogee is in ,conjunction1 or ,opposition with the ,sun's3 ,but in the ,quadratures1 the aforesaid ,equation is to be lessen'd about #ej seconds1 or #a minute1 when the ,apogees of the ,sun and ,moon are in ,conjunction2 but if they are in ,opposition1 for want of a sufficient number of ,observations1 ,i cannot determine1 whether it is to be lessen'd or increas'd4 ,and even as to the ,argument or ,decrement of the ,equation1 #b minutes1 #bj seconds1 above mentioned1 ,i dare determine nothing certain1 for the same ,reason1 viz4 the want of ,observations accurately made4 ,if the sixth and seventh ,equations are augmented or diminished in a reciprocal ,ratio of the distance of the ,moon from the ,earth2 i4 e4 in a direct ,ratio of the ,moon's ,horizontal ,parallax1 they will become more accurate3 ,and this may be readily done1 if ,tables are first made to each minute of the said ,parallax1 and to every sixth or fifth degree of the ,argument of the sixth ,equation for the ,sixth1 as of the distance of the ,moon from the ,sun1 for the ,seventh ,equation4 ,from the ,sun's ,place1 take the mean motion of the ,moon's ascending ,node1 equated as above2 the ,remainder shall be the ,annual ,argument of the ,node1 whence its second ,equation may be computed after the following manner in the preceding ,figure4 ,let ,t1 as before1 represent the ,earth2 ,,ts a ,right ,line1 conjoining the ,earth and ,sun3 ,let also the ,line ,,tacb1 be drawn to the ,place of the ascending ,node of the ,moon1 as above equated2 and let ,,sta be the ,annual ,argument of the ,node4 ,take ,,ta from a ,scale1 and let it be to ,,ab 33 as #ef to #c1 or as #aa to #a4 ,then bissect ,,ba in ,c1 and on ,c as a ,centre1 with the ,distance ,,ca1 describe a ,circle1 as ,,afb1 and make the ,angle ,,bcf1 equal to double the ,annual ,argument of the ,node before-found3 ,so shall the ,angle ,,btf1 be the second ,equation of the ascending ,node2 which must be added1 when the ,node is passing from the ,quadrature to a ,syzygy with the ,sun2 and subducted1 when the ,node moves from a ,syzygy towards a ,quadrature4 ,by which means1 the true ,place of the ,node of the ,lunar ,orbit will be gained3 ,whence from ,tables made after the common way1 the ,moon's ,latitude1 and the ,reduction of her ,orbit to the ,ecliptick1 may be computed1 supposing the ,inclination of the ,moon's ,orbit to the ,ecliptick1 to be #d degrees1 #ei minutes1 #ce seconds1 when the ,nodes are in ,quadrature with the ,sun2 and #e degrees1 #ag minutes1 #bj seconds1 when they are in the ,syzygys4 ,and from the ,longitude and ,latitude thus found1 and the given ,obliquity of the ,ecliptick1 #bc degrees1 #bi minutes1 the ,right ,ascension and ,declination of the ,moon will be found4 ,the ,horizontal ,parallax of the ,moon1 when she is in the ,syzygys1 at a mean distance from the ,earth1 ,i make to be #eg minutes1 #cj seconds2 and her ,horary ,motion1 #cc minutes1 #cb seconds1 #cb thirds2 and her apparent ,diameter #ca minutes1 #cj seconds4 ,but in her ,quadratures at a mean ,distance from the ,earth1 ,i make the ,horizontal ,parallax of the ,moon to be #ei minutes1 #dj seconds1 her ,horary ,motion #cb minutes1 #ab seconds1 #b thirds1 and her apparent ,diameter1 #ca minutes1 #c seconds4 ,the ,moon in an ,octant to the ,sun1 and at a mean distance1 hath her ,centre distant from the ,centre of the ,earth about #fj-b_/i of the ,earth's ,semi-diameters4 ,the ,sun's ,horizontal ,parallax ,i make to be #aj seconds1 and its apparent ,diameter at a mean distance from the ,earth1 ,i make #cb minutes1 #ae seconds4 ,the ,atmosphere of the ,earth1 by dispersing and refracting the ,sun's ,light1 casts a ,shadow1 as if it were an ,opake ,body1 at least to the height of #dj or #ej ,geographical ,miles 7by a ,geographical ,mile1 ,i mean the sixtieth part of a ,degree of a great ,circle1 on the ,earth's ,surface47 ,this ,shadow falling upon the ,moon in a ,lunar ,eclipse1 makes the ,earth's ,shadow be the larger or broader4 ,and to each ,mile of the ,earth's ,atmosphere1 is correspondent a ,second in the ,moon's ,disk1 so that the ,semi-diameter of the ,earth's shadow projected upon the ,disk of the ,moon1 is to be increased about #ej seconds3 ,or1 which is all one1 in a ,lunar ,eclipse1 the ,horizontal ,parallax of the ,moon is to be increased in the ,ratio of about #gj to #fi4 ,thus far the ,theory of this ,incomparable ,mathematician4 ,and if we had many ,places of the ,moon accurately observ'd1 especially about her ,quadratures1 and these well compar'd with her ,places1 at the same time calculated according to this ,theory2 it would then appear1 whether there yet remain any other sensible ,equations2 which when accounted for1 might serve to improve and enlarge this ,theory4 ,an ,estimate of the ,degrees of the ,mortality of ,mankind1 drawn from curious ,tables of the ,births and ,funerals at the ,city of ,breslaw2 with an ,attempt to ascertain the ,price of ,annuities upon ,lives4 ,by ,mr4 ,e4 ,halley1 ,r4 ,s4 ,s4 ,the ,contemplation of the ,mortality of ,mankind1 has besides the ,moral1 its ,physical and ,political ,uses1 both which have been some ,years since most judiciously consider'd by the ,curious ,sir ,william ,petty1 in his ,natural and ,political ,observations on the ,bills of ,mortality of ,london1 own'd by ,captain ,john ,graunt3 ,and since in a like ,treatise on the ,bills of ,mortality of ,dublin4 ,but the ,deduction from those ,bills of ,mortality seemed even to their ,authors to be defective3 ,first1 ,in that the ,number of the ,people was wanting4 ,secondly1 ,that the ,ages of the ,people dying was not to be had4 ,and ,lastly1 ,that both ,london and ,dublin1 by reason of the great and casual ,accession of ,strangers who die therein1 7as appeared in both1 by the great ,excess of the ,funerals above the ,births7 rendred them incapable of being ,standards for this purpose2 which requires1 if it were possible1 that the ,people we treat of1 should not at all be changed1 but die where they were born1 without any adventitious ,increase from ,abroad1 or ,decay by ,migration elsewhere4 ,illustration3 ,plate #c4 pag4 #bhj4 ,this ,defect seems in a great measure to be satisfied by the late curious ,tables of the ,bills of ,mortality at the ,city of ,breslaw1 lately communicated to this ,honourable ,society by ,mr4 ,justell1 wherein both the ,ages and ,sexes of all that die1 are ,monthly delivered1 and compared with the number of the ,births1 for ,five ,years last past1 viz4 #afhg1 #hh1 #hi1 #ij1 #ia1 seeming to be done with all the ,exactness and ,sincerity possible4 ,this ,city of ,breslaw is the ,capital ,city of the ,province of ,silesia2 or1 as the ,germans call it1 ,schlesia1 and is situated on the ,western ,bank of the ,river ,oder1 anciently call'd ,viadrus1 near the ,confines of ,germany and ,poland1 and very nigh the ,latitude of ,london4 ,it is very far from the ,sea1 and as much a ,mediterranean ,place as can be desired1 whence the ,confluence of ,strangers is but small1 and the ,manufacture of ,linnen employs chiefly the poor ,people of the ,place1 as well as of the ,country round about2 whence comes that sort of ,linnen we usually call your ,sclesi ,linnen2 which is the chief1 if not the only ,merchandize of the ,place4 ,for these ,reasons1 the ,people of this ,city seem most proper for a ,standard2 and the rather1 for that the ,births do a small matter exceed the ,funerals4 ,the only thing wanting1 is the ,number of the whole ,people1 which in some measure ,i have endeavour'd to supply1 by the comparison of the ,mortality of the ,people of all ,ages1 which ,i shall from the said ,bills trace out with all the ,accuracy possible4 ,it appears that in the ,five ,years mentioned1 viz4 from #hg to #ia inclusive1 there were born #faic ,persons1 and buried #ehfi2 that is1 born per ,annum #abch1 and buried #aagd2 whence an ,increase of the ,people may be argued of #fd per ,annum1 or of about a #bjth part1 which may perhaps be balanc'd by the ,levies for the ,emperor's ,service in his ,wars4 ,but this being contingent1 and the ,births certain1 ,i will suppose the ,people of ,breslaw to be increased by #abch ,births annually4 ,of these it appears by the same ,tables1 that #cdh do die yearly in the first ,year of their ,age1 and that but #hij do arrive at a full ,year's ,age2 and likewise1 that #aih do die in the ,five ,years between #a and #f compleat1 taken at a ,medium2 so that but #fib of the ,persons born do survive ,six whole ,years4 ,from this ,age the ,infants being arrived at some degree of ,firmness1 grow less and less ,mortal2 and it appears1 that of the whole ,people of ,breslaw there die yearly1 as in the following ,table1 wherein the upper ,line shews the ,age1 and the next under it1 the ,number of ,persons of that ,age dying yearly4 #g #h #i #ad #ah #ba #bg #bh #ce #aa #aa #f #e #b #c #e #f #d #f #i #h #g #g #cf #db #de #ci #ed #ee #ef #fc #h #i #h #i #g #g #aj #aa #i #i #aj #ab #gj #ga #gb #gg #ha #hd #ij #ia #i #ad #i #aa #i #f #g #c #d #b #a #a #a #ih #ii #ajj #j ,and where no ,figure is placed over1 it is to be understood of those that die between the ,ages of the precedent and consequent ,column4 ,from this ,table it is evident1 that from the ,age of #i to about #be1 there does not die above #f per ,annum of each ,age1 which is much about #a per ,cent4 of those that are of those ,ages3 ,and whereas in the #ad1 #ae1 #af1 #ag ,years1 there appear to die much fewer1 as #b and #c2 yet that seems rather to be attributed to ,chance1 as are the other ,irregularities in the ,series of ,ages1 which would rectifie themselves1 were the number of ,years much more considerable1 as #bj instead of #e4 ,and by our own ,experience in ,christ-,church ,hospital1 ,i am inform'd there die of the ,young ,lads1 much about #a per ,cent4 per ,annum1 they being of the aforesaid ,ages4 ,from #be to #ej1 there seem to die from #g to #h and #i per ,annum of each ,age2 and after that to #gj1 they growing more crasie1 though the number be much diminished1 yet the ,mortality increases1 and there are found to die #aj or #aa of each ,age per ,annum3 ,from thence the number of the ,living being grown very small1 they gradually decline till there be none left to die2 as may be seen at one ,view in the ,table4 ,from these ,considerations ,i have form'd the adjoined ,table1 whose ,uses are manifold1 and give a more just ,idea of the ,state and ,condition of ,mankind1 than any thing yet extant that ,i know of4 ,it exhibits the ,number of ,people in the ,city of ,breslaw of all ,ages1 from the ,birth to extreme ,old ,age1 and thereby shews the ,chances of ,mortality at all ,ages1 and likewise how to make a certain ,estimate of the ,value of ,annuities for ,lives1 which hitherto has been only done by an imaginary ,valuation3 ,also the ,chances that there are that a ,person of any ,age proposed does live to any other ,age given2 with many more1 as ,i shall hereafter shew4 ,this ,table does shew the ,number of ,persons that are living in the ,age current annexed thereto1 as follows3 ---------------------------------------- ----- ,age4 ,persons4 ,age4 ,persons4 ,age4 ,persons4 ,curt4 ,curt4 ,curt4 ---------------------------------------- ----- #a #ajjj #h #fhj #ae #fbh #b #hee #i #fgj #af #fbb #c #gih #aj #ffa #ag #faf #d #gfj #aa #fec #ah #faj #e #gcb #ab #fdf #ai #fjd #f #gaj #ac #fdj #bj #eih #g #fib #ad #fcd #ba #eib ---------------------------------------- ----- #bb #ehf #bi #eci #cf #dha #bc #egi #cj #eca #cg #dgb #bd #egc #ca #ebc #ch #dfc #be #efg #cb #eae #ci #ded #bf #efj #cc #ejg #dj #dde #bg #eec #cd #dii #da #dcf #bh #edf #ce #dij #db #dbg ---------------------------------------- ----- #dc #dag #ej #cdf #eg #bgb #dd #djg #ea #cce #eh #bfb #de #cig #eb #cbd #ei #beb #df #chg #ec #cac #fj #bdb #dg #cgg #ed #cjb #fa #bcb #dh #cfg #ee #bib #fb #bbb #di #ceg #ef #bhb #fc #bab ---------------------------------------- ----- #fd #bjb #ga #aca #gh #eh #fe #aib #gb #abj #gi #di #ff #ahb #gc #aji #hj #da #fg #agb #gd #ih #ha #cd #fh #afb #ge #hh #hb #bh #fi #aeb #gf #gh #hc #bc #gi #adb #gg #fh #hd #bj ---------------------------------------- ----- ,age4 ,persons4 #g #eedg #ad #dehd #ba #dbgj #bh #cifd #ce #cfjd #db #cgjh #di #bgji #ef #baid #fc #afid #gj #abjd #gg #fib #hd #bec #ajj #ajg ----------- #cdjjj ----------- ,sum ,total4 ,thus it appears1 that the whole ,people of ,breslaw does consist of #cdjjj ,souls1 being the ,sum ,total of the ,persons of all ,ages in the ,table3 ,the first use hereof is to shew the ,proportion of ,men able to bear ,arms in any ,multitude1 which are those between #ah and #ef1 rather than #af and #fj2 the one being generally too weak to bear the ,fatigues of ,war1 and the ,weight of ,arms2 and the other too crasie and infirm from ,age1 notwithstanding particular ,instances to the contrary4 ,under #ah from the ,table1 are found in this ,city #aaiig ,persons1 #ciej above #ef1 which together make #aeidg1 so that the ,residue to #cdjjj being #ahjec1 are ,persons between those ,ages4 ,at least one half thereof are ,males1 or #ijbg3 ,so that the whole ,force this ,city can raise of ,fencible ,men1 as the ,scotch call them1 is about #ijjj1 or #i_/cd1 or somewhat more than a quarter of the ,number of ,souls2 which may parhaps pass for a ,rule for all other places4 ,the ,second ,use of this ,table1 is1 to shew the differing degrees of ,mortality1 or rather ,vitality1 in all ,ages2 for if the ,number of ,persons of any ,age remaining after one ,year1 be divided by the difference between that and the number of the ,age proposed1 it shews the ,odds that there is1 that a ,person of that ,age does not die in a ,year4 ,as for ,instance1 a ,person of #be ,years of ,age has the ,odds of #efj to #g1 or #hj to #a1 that he does not die in a ,year3 ,because that of #efg1 living of #be ,years of ,age1 there do die no more than #g in a ,year1 leaving #efj of #bf ,years old4 ,so likewise for the ,odds1 that any ,person does not die before he attain any proposed ,age3 ,take the number of the remaining ,persons of the ,age proposed1 and divide it by the difference between it and the number of those of the ,age of the ,party proposed2 and that shews the ,odds there is between the ,chances of the ,party's living or dying4 ,as for ,instance2 ,what is the ,odds that a ,man of #dj lives #g ,years3 ,take the number of ,persons of #dg ,years1 which in the ,table is #cgg1 and subtract it from the number of ,persons of #dj ,years1 which is #dde1 and the difference is #fh3 ,which shews that the ,persons dying in that #g ,years1 are #fh1 and that it is #cgg to #fh1 or #e to #a1 that a ,man of #dj does live #g ,years4 ,and the like for any other number of ,years4 ,use ,,iii4 ,but if it be enquired at what number of ,years1 it is an even ,lay that a ,person of any ,age shall die1 this ,table readily performs it2 ,for if the number of ,persons living of the ,age proposed1 be halfed1 it will be found by the ,table at what ,year the said ,number is reduced to half by ,mortality2 and that is the ,age1 to which it is an even ,wager1 that a ,person of the ,age proposed shall arrive before he die4 ,as for ,instance2 ,a ,person of #cj ,years of ,age is proposed1 the number of that ,age is #eca1 the half thereof is #bfe1 which number ,i find to be between #eg and #eh ,years2 so that a ,man of #cj may reasonably expect to live between #bg and #bh ,years4 ,use ,,iv4 ,by what has been said1 the ,price of ,insurance upon ,lives ought to be regulated1 and the difference is discovered between the ,price of insuring the ,life of a ,man of #bj and #ej4 ,for ,example2 ,it being #ajj to #a1 that a ,man of #bj dies not in a ,year1 and but #ch to #a1 for a ,man of #ej ,years of ,age4 ,use ,v4 ,on this depends the ,valuation of ,annuities upon ,lives2 for it is plain1 that the ,purchaser ought to pay for only such a part of the ,value of the ,annuity1 as he has ,chances that he is living2 and this ought to be computed yearly1 and the ,sum of all those yearly ,values being added together1 will amount to the ,value of the ,annuity for the ,life of the ,person proposed4 ,now the present ,value of ,money payable after a ,term of ,years1 at any given ,rate of ,interest1 either may be had from ,tables already computed2 or almost as compendiously1 by the ,table of ,logarithms3 ,for the ,arithmetical ,complement of the ,logarithm of ,unity1 and its yearly ,interest1 7that is1 of #a1jf for ,six per ,cent4 being #i1igdfid47 being multiplied by the number of ,years proposed1 gives the present ,value of ,one ,pound payable after the end of so many ,years4 ,then by the foregoing ,proposition1 it will be as the number of ,persons living after that ,term of ,years1 to the number dead2 so are the ,odds that any one ,person is alive or dead4 ,and by consequence1 as the ,sum of both1 or the number of ,persons living of the ,age first proposed1 to the number remaining after so many ,years1 7both given by the ,table7 so the present ,value of the yearly ,sum payable after the ,term proposed1 to the ,sum which ought to be paid for the ,chance the ,person has to enjoy such an ,annuity after so many ,years4 ,and this being repeated for every ,year of the ,person's ,life1 the ,sum of all the present ,values of those ,chances is the true ,value of the ,annuity4 ,this will without doubt appear to be a most laborious ,calculation2 but it being one of the principal ,uses of this ,speculation1 and having found some ,compendia for the ,work1 ,i took the pains to compute the following ,table1 being the short ,result of a not ordinary number of ,arithmetical ,operations3 ,it shews the ,value of ,annuities for every ,fifth ,year of ,age1 to the ,seventieth1 as follows4 ---------------------------------------- -------------- ,age4 ,years ,pur4 ,age4 ,years ,pur4 ,age4 ,years ,pur4 ---------------------------------------- -------------- #a #aj1bh #be #ab1bg #ej #i1ba #e #ac1dj #cj #aa1gb #ee #h1ea #aj #ac1dd #ce #aa1ab #fj #g1fj #ae #ac1cc #dj #aj1eg #fe #f1ed #bj #ab1gh #de #i1ia #gj #e1cb ---------------------------------------- -------------- ,this shews the great ,advantage of putting ,money into the present ,fund lately granted to ,their ,majesties1 giving #ad per ,cent4 per ,annum1 or at the ,rate of #g ,years ,purchase for a ,life2 when young ,lives1 at the usual ,rate of ,interest1 are worth above #ac ,years ,purchase4 ,it shews likewise the ,advantage of young ,lives over those in ,years2 a ,life of ,ten ,years being almost worth #ac ,years ,purchase1 whereas one of #cf is worth but #aa4 ,use ,,vi4 ,two ,lives are likewise valuable by the same ,rule2 for the number of ,chances of each single ,life1 found in the ,table1 being multiplied together1 become the ,chances of the ,two ,lives4 ,and after any certain ,term of ,years1 the ,product of the two remaining ,sums is the ,chances that both the ,persons are living4 ,the ,product of the two ,differences1 being the numbers of the ,dead of both ,ages1 are the ,chances that both the ,persons are dead4 ,and the two ,products of the remaining ,sums of the one ,age multiplied by those dead of the other1 shew the ,chances that there are1 that each ,party survives the other3 ,whence is derived the ,rule to estimate the ,value of the ,remainder of one ,life after another4 ,now as the ,product of the ,two ,numbers in the ,table for the ,two ,ages proposed1 is to the difference between that ,product1 and the ,product of the two numbers of ,persons deceased in any space of time2 so is the ,value of a ,sum of ,money to be paid after so much time1 to the ,value thereof under the ,contingency of ,mortality4 ,and as the aforesaid ,product of the two ,numbers answering to the ,ages proposed1 to the ,product of the ,deceased of one ,age multiplied by those remaining alive of the other2 so the ,value of a ,sum of ,money to be paid after any time proposed1 to the ,value of the ,chances1 that the one ,party has that he survives the other1 whose number of ,deceased you made use of1 in the second ,term of the ,proportion4 ,this perhaps may be better understood1 by putting ,n for the number of the younger ,age1 and n for that of the ,elder2 ,y1 y the ,deceased of both ,ages respectively1 and ,r1 r for the ,remainders2 and ,r ,y ,n1 and r y n4 ,then shall ,nn be the whole ,number of ,chances2 ,nn - ,yy be the ,chances that one of the two ,persons is living1 ,yy the ,chances that they are both dead2 ,ry the ,chances that the elder ,person is dead1 and the younger living2 and r,y the ,chances1 that the elder is living1 and the younger dead4 ,thus two ,persons of #ah and #ce are proposed1 and after #h ,years these ,chances are required4 ,the ,numbers for #ah and #ce1 are #faj and #dij2 and there are #ej of the ,first ,age dead in #h ,years1 and #gc of the ,elder ,age4 ,there are in all #faj #dij1 or #bihijj ,chances2 of these there are #ej #gc1 or #cfej1 that they are both dead4 ,and as #bihijj1 to #bihijj - #cfej1 or #biebej3 ,so is the present ,value of a ,sum of ,money to be paid after #h ,years1 to the present ,value of a ,sum to be paid1 if either of the two live4 ,and as #efj #gc1 so are the ,chances that the ,elder is dead1 leaving the ,younger2 and as #dag #ej1 so are the ,chances that the ,younger is dead1 leaving the ,elder4 ,wherefore as #faj #dij to #efj #gc1 so is the present ,value of a ,sum to be paid at #h ,years end1 to the ,sum to be paid for the ,chance of the ,younger's ,survivance2 and as #faj #dij to #dag #ej1 so is the same present ,value to the ,sum to be paid for the ,chance of the ,elder's ,survivance4 ,this possibly may be yet better explained1 by expounding these ,products by ,rectangular ,parallelograms1 as in ,fig4 #g4 wherein ,,ab or ,,cd represents the number of ,persons of the younger ,age1 and ,,de1 ,,bh those remaining alive after a certain ,term of ,years2 whence ,,ce will answer the number of those dead in that time3 ,so ,,ac1 ,,bd may represent the number of the elder ,age2 ,,af1 ,,bi the ,survivors after the same ,term2 and ,,cf1 ,,di1 those of that ,age that are dead at that time4 ,then shall the whole ,parallelogram ,,abcd be ,nn1 or the ,product of the two ,numbers of ,persons1 representing such a number of ,persons of the two ,ages given2 and by what was said before1 after the ,term proposed1 the ,rectangle ,,hd shall be as the number of ,persons of the younger ,age that survive1 and the ,rectangle ,,ae as the number of those that die4 ,so likewise the ,rectangles ,,ai1 ,,fd shall be as the ,numbers1 living and dead1 of the other ,age4 ,hence the ,rectangle ,,hi shall be as an equal number of both ,ages surviving4 ,the ,rectangle ,,fe being the ,product of the ,deceased1 or ,yy1 an equal number of both dead4 ,the ,rectangle ,,gd or ,ry1 a number living of the younger ,age1 and dead of the elder3 ,and the ,rectangle ,,ag or r,y a number living of the elder ,age1 but dead of the younger4 ,this being understood1 it is obvious1 that as the whole ,rectangle ,,ad or ,nn is to the ,gnomon ,,fabdeg or ,nn - ,yy1 so is the whole number of ,persons or ,chances1 to the number of ,chances that one of the two ,persons is living3 ,and as ,,ad or ,nn is to ,,fe or ,yy1 so are all the ,chances1 to the ,chances that both are dead2 whereby may be computed the ,value of the ,reversion after both ,lives4 ,and as ,,ad to ,,gd or ,ry1 so the whole number of ,chances1 to the ,chances that the younger is living1 and the other dead2 whereby may be cast up what ,value ought to be paid for the ,reversion of one ,life after another1 as in the ,case of providing for ,clergy-men's ,widows1 and others1 by such ,reversions4 ,and as ,,ad to ,,ag1 or r,y1 so are all the ,chances1 to those that the elder survives the younger4 ,i have been the more particular1 and perhaps tedious1 in this ,matter1 because it is the ,key to the ,case of ,three ,lives1 which of it self would not have been so easie to comprehend4 ,,vii4 ,if ,three ,lives are proposed1 to find the ,value of an ,annuity during the continuance of any of those three ,lives2 the ,rule is1 ,as the ,product of the continual ,multiplication of the ,three ,numbers1 in the ,table1 answering to the ,ages proposed1 is to the difference of that ,product1 and of the ,product of the ,three ,numbers of the ,deceased of those ,ages1 in any given ,term of ,years3 ,so is the present ,value of a ,sum of ,money1 to be paid certainly after so many ,years1 to the present ,value of the same ,sum to be paid1 provided one of those ,three ,persons be living at the ,expiration of that ,term4 ,which ,proportion being yearly repeated1 the ,sum of all those present ,values will be the ,value of an ,annuity granted for three such ,lives4 ,but to explain this1 together with all the ,cases of ,survivance in ,three ,lives3 ,let ,n be the ,number in the ,table for the younger ,age1 n for the second1 and for the elder ,age2 let ,y be those dead of the younger ,age in the ,term proposed1 y those dead of the second ,age1 and those of the elder ,age2 and let ,r be the ,remainder of the younger ,age1 r that of the middle ,age1 and the ,remainder of the elder ,age4 ,then shall ,r ,y be equal to ,n1 r y to n1 and to 1 and the continual ,product of the three ,numbers ,n1 n1 1 shall be equal to the continual ,product of ,r ,y r y 1 which being the whole ,number of ,chances for three ,lives1 is compounded of the eight ,products following4 7#a7 ,rr1 which is the ,number of ,chances that all three of the ,persons are living4 7#b7 r,y1 which is the ,number of ,chances that the two elder ,persons are living1 and the younger dead4 7#c7 ,ry the ,number of ,chances that the middle ,age is dead1 and the younger and elder living4 7#d7 ,rr being the ,chances that the two younger are living1 and the elder dead4 7#e7 ,yy the ,chances that the two younger are dead1 and the elder living4 7#f7 r,y the ,chances that the younger and elder are dead1 and the middle ,age living4 7#g7 ,ry1 which are the ,chances that the younger is living1 and the two other dead4 ,and ,lastly and ,eighthly1 ,yy1 which are the ,chances that all three are dead4 ,which latter subtracted from the whole ,number of ,chances ,nn1 leaves ,nn - ,yy the ,sum of all the other seven ,products2 in all of which one or more of the three ,persons are surviving4 ,to make this yet more evident1 ,i have added ,fig4 #h4 wherein these eight several ,products are at one view exhibited4 ,let the rectangled ,parallelepipedon ,,abcdefgh be constituted of the sides ,,ab1 ,,gh1 c4 proportional to ,n the ,number of the younger ,age2 ,,ac1 ,,bd1 c4 proportional to n2 and ,,ag1 ,,ce1 c4 proportional to the ,number of the elder1 or 4 ,and the whole ,parallelepipedon shall be as the ,product ,nn1 or our whole ,number of ,chances4 ,let ,,bp be as ,r1 and ,,ap as ,y2 let ,,cl be as r1 and ,ln as y2 and ,,gn as 1 and ,,na as 2 and let the ,plain ,p,rea be made parallel to the ,plain ,,acge2 the ,plain ,n,vb,y parallel to ,,abcd2 and the ,plain ,,lxtq parallel to the ,plain ,,abgh4 ,and our first ,product ,rr shall be as the ,solid ,s,t,w,i,f,zeb4 ,the ,second1 or r,y will be as the ,solid ,e,y,ze,q,s,m,i4 ,the ,third1 ,ry1 as the ,solid ,,rhovwist4 ,and the ,fourth1 ,rr1 as the ,solid ,zab,d,w,x,i,k4 ,fifthly1 ,yy1 as the ,solid ,,gqrsimno4 ,sixthly1 r,y1 as ,,iklmgyza4 ,seventhly1 ,ry1 as the ,solid ,,ikpobxvw4 ,and ,lastly1 ,,aiklmnop will be as the ,product of the #c ,numbers of ,persons dead1 or ,yy4 ,i shall not apply this in all the ,cases thereof1 for brevity sake2 only to shew in one how all the rest may be performed1 let it be demanded what is the ,value of the ,reversion of the younger ,life after the two elder proposed4 ,the proportion is as the whole ,number of ,chances1 or ,nn to the ,product ,ry2 so is the certain present ,value of the ,sum payable after any ,term proposed1 to the ,value due to such ,chances as the younger ,person has to bury both the elder1 by the ,term proposed2 which therefore he is to pay for4 ,here it is to be noted1 that the first ,term of all these ,proportions is the same throughout1 viz4 ,nn4 ,the second changing yearly according to the ,decrease of ,r1 r1 1 and ,increase of ,y1 y1 4 ,and the third are successively the present ,values of ,money payable after one1 two1 three1 c4 years1 according to the ,rate of ,interest agreed on4 ,these ,numbers1 which are in all ,cases of ,annuities of necessary ,use1 ,i have put into the following ,table1 they being ,decimal ,values of one ,pound payable after the ,number of ,years in the ,margent1 at the ,rate of #f per ,cent4 ---------------------------------------- ----------------------- ,years4 ,pres4 ,value ,years4 ,pres4 ,value ,years4 ,pres4 ,value of #a l4 of #a l4 of #a l4 ---------------------------------------- ----------------------- #a #j1idcd #ai #j1ccje #cg #j1aaeh #b #j1hijj #bj #j1caah #ch #j1ajib #c #j1hcif #ba #j1bida #ci #j1ajca #d #j1giba #bb #j1bgge #dj #j1jigb #e #j1gdgc #bc #j1bfah #de #j1jgbf #f #j1gjej #bd #j1bdgj #ej #j1jedc ---------------------------------------- ----------------------- #g #j1ffej #be #j1bccj #ee #j1jdjf #h #j1fbgd #bf #j1baih #fj #j1jcjc #i #j1eiai #bg #j1bjgd #fe #j1jbbg #aj #j1eehd #bh #j1aief #gj #j1jafi #aa #j1ebfh #bi #j1ahde #ge #j1jabf #ab #j1digj #cj #j1agda #hj #j1jjid ---------------------------------------- ----------------------- #ac #j1dfhh #ca #j1afdc #he #j1jjga #ad #j1ddbc #cb #j1aeej #ij #j1jjec #ae #j1dagc #cc #j1adfb #ie #j1jjci #af #j1cicf #cd #j1acgi #ajj #j1jjbi #ag #j1cgad #ce #j1acja #ah #j1cejc #cf #j1abbg ---------------------------------------- ----------------------- ,it were needless to advertise1 that the great trouble of working so many ,proportions will be very much alleviated by using ,logarithms2 and that instead of using ,nn - ,yy for the second ,term of the ,proportion in finding the ,value of ,three ,lives1 it may suffice to use only ,yy1 and then deducting the fourth ,term so found out of the third1 the ,remainder shall be the present ,value sought2 or all these fourth ,terms being added together1 and deducted out of the ,value of the certain ,annuity for so many ,years1 will leave the ,value of the contingent ,annuity upon the ,chance of ,mortality of all those ,three ,lives4 ,for ,example2 ,let there be ,three ,lives of #aj1 #cj1 and #dj ,years of ,age proposed1 and the ,proportions will be thus2 ,as #ffa in #eca in #dde or #aefaijiie1 or ,nn to #h in #h in #i1 or #egf1 or ,yy for the first ,year1 so #j1idcd4 to #j1jjjjjcdh4 ,to #ae in #af in #ah1 or #dcbj1 for the second ,year1 so #j1hijj4 to #j1jjjjbdfb4 ,to #ba in #bd in #bh1 or #adaab for the third ,year1 so #j1hcif4 to #j1jjjjhabh4 ,to #bg in #cb in #ch1 for the fourth ,year1 so #j1giba4 to #j1jjjaffej4 ,to #cc in #da in #dh1 for the fifth ,year1 so #j1gdgc4 to #j1jjjcajga4 ,to #ci in #ej in #eh1 for the sixth ,year1 so #j1gjej4 to #j1jjjeajea4 ,and so forth to the #fjth ,year1 when we suppose the elder ,life of ,forty certainly to be expired2 from whence till ,seventy we must compute for the ,first and ,second only1 and from thence to ,ninety for the single youngest ,life4 ,then the ,sum ,total of all these ,fourth ,proportionals being taken out of the ,value of a certain ,annuity for #ij ,years1 being #af1eh ,years ,purchase1 shall leave the just ,value to be paid for an ,annuity during the whole ,term of the ,lives of ,three ,persons of the ,ages proposed4 ,and note1 that it will not be necessary to compute for every ,year singly2 but that in most ,cases every #dth or #eth ,year may suffice1 interpoling for the intermediate ,years seceundum artem4 ,it may be objected1 that the different ,salubrity of ,places does hinder this ,proposal from being universal2 nor can it be denied4 ,but by the ,number that die1 being #aagd4 per ,annum in #cdjjj1 it does appear that about a #cjth part die yearly1 as ,sir ,william ,petty has computed for ,london2 and the ,number that die in ,infancy1 is a good ,argument that the ,air is but indifferently salubrious4 ,so that by what ,i can learn1 there cannot perhaps be one better ,place proposed for a ,standard4 ,at least 'tis desired1 that in ,imitation hereof the ,curious in other ,cities would attempt something of the same ,nature1 than which nothing perhaps can be more useful4 ,were this ,calculus founded on the ,experience of a very great number of ,years1 it would be very well worth the while to think of ,methods for facilitating the ,computation of the ,value of two1 three1 or more ,lives2 which1 as proposed in my former1 seems 7as ,i am inform'd7 a ,work of too much ,difficulty for the ordinary ,arithmetician to undertake4 ,i have sought1 ,if it were possible1 to find a ,theorem that might be more concise than the ,rules there laid down1 but in vain2 for all that can be done to expedite it1 is1 by ,tables of ,logarithms ready computed1 to exhibit the ,rationes of ,n to ,y in each single ,life1 for every third1 fourth1 or fifth ,year of ,age1 as occasion shall require2 and these ,logarithms being added to the ,logarithms of the present ,value of ,money payable after so many ,years1 will give a ,series of ,numbers1 the ,sum of which will shew the ,value of the ,annuity sought4 ,however1 for each ,number of this ,series1 two ,logarithms for a single ,life1 three for two ,lives1 and four for three ,lives1 must necessarily be added together4 ,if you think the ,matter1 under the ,uncertainties ,i have mentioned1 to deserve it1 ,i shall shortly give you such a ,table of ,logarithms1 as ,i speak of1 and an ,example or two of the use thereof3 ,but by ,vulgar ,arithmetick1 the ,labour of these ,numbers were immense2 and nothing will more recommend the useful ,invention of ,logarithms to all ,lovers of ,numbers1 than the advantage of ,dispatch in this and such like ,computations4 ,besides the ,uses mentioned1 it may perhaps not be an unacceptable thing to infer from the same ,tables1 how unjustly we repine at the shortness of our ,lives1 and think our selves wronged if we attain not old ,age2 whereas it appears hereby1 that the one half of those that are born are dead in ,seventeen ,years time1 #abch being in that time reduced to #faf4 ,so that instead of murmuring at what we call an untimely ,death1 we ought with ,patience and ,unconcern to submit to that ,dissolution which is the necessary ,condition of our perishable ,materials1 and of our nice and frail ,structure and ,composition3 ,and to account it as a ,blessing that we have survived1 perhaps by many ,years1 that ,period of ,life1 whereat the one half of the whole ,race of ,mankind does not arrive4 ,a second ,observation ,i make upon the said ,table1 is that the ,growth and ,increase of ,mankind is not so much stinted by any thing in the ,nature of the ,species1 as it is from the cautious difficulty most ,people make to adventure on the ,state of ,marriage1 from the ,prospect of the ,trouble and ,charge of providing for a ,family4 ,nor are the poorer sort of ,people herein to be blamed1 since their difficulty of subsisting is occasion'd by the unequal ,distribution of ,possessions1 all being necessarily fed from the ,earth1 of which yet so few are ,masters4 ,so that besides themselves and ,families1 they are yet to work for those who own the ,ground that feeds them3 ,and of such does by very much the greater part of ,mankind consist2 otherwise it is plain1 that there might well be four times as many ,births as we now find4 ,for by ,computation from the ,table1 ,i find that there are nearly #aejjj ,persons above #af1 and under #de1 of which at least #gjjj are ,women capable to bear ,children4 ,of these notwithstanding there are but #abch born yearly1 which is but little more than a sixth part3 ,so that about one in six of these ,women do breed yearly2 whereas were they all married1 it would not appear strange or unlikely1 that four of six should bring a ,child every ,year4 ,the ,political ,consequences hereof ,i shall not insist on2 only the ,strength and ,glory of a ,king being in the multitude of his ,subjects1 ,i shall only hint1 that above all things1 ,celibacy ought to be discouraged1 as1 by extraordinary ,taxing and ,military ,service3 ,and those who have numerous ,families of ,children to be countenanced and encouraged by such ,laws as the ,jus trium ,liberorum among the ,romans4 ,but especially1 by an effectual ,care to provide for the ,subsistence of the ,poor1 by finding them ,employments1 whereby they may earn their ,bread1 without being chargeable to the ,publick4 ,a ,discourse concerning ,gravity1 and its ,properties1 wherein the ,descent of ,heavy ,bodies1 and the ,motion of ,projects is briefly1 but fully handled3 ,together with the ,solution of a ,problem of great ,use in ,gunnery4 ,by ,e4 ,halley4 ,nature1 amidst the great ,variety of ,problems1 wherewith ,she exercises the ,wits of ,philosophical ,men1 scarce affords any one wherein the ,effect is more visible1 and the ,cause more concealed1 than in those of the ,phnomena of ,gravity4 ,before we can go alone1 we must learn to defend our selves from the ,violence of its ,impulse1 by not trusting the ,center of ,gravity of our ,bodies beyond our reach2 and yet the acutest ,philosophers1 and the subtilest ,enquirers into the ,original of this ,motion1 have been so far from satisfying their ,readers1 that they themselves seem little to have understood the ,consequences of their own ,hypotheses4 ,des ,cartes his ,notion1 ,i must needs confess to be to me incomprehensible1 while he will have the ,particles of his ,clestial ,matter1 by being reflected on the ,surface of the ,earth1 and so ascending therefrom1 to drive down into their ,places those ,terrestrial ,bodies they find above them3 ,this is1 as near as ,i can gather1 the ,scope of the #bj1 #ba1 #bb1 and #bc ,sections of the last ,book of his ,principia ,philosophi2 yet neither he1 nor any of his ,followers1 can shew how a ,body suspended in ,libero there1 shall be carried downwards by a continual ,impulse tending upwards1 and acting upon all its ,parts equally3 ,and besides the ,obscurity wherewith he expresses himself1 particularly1 ,sect4 #bc4 does sufficiently argue according to his own ,rules1 the confused ,idea he had of the thing he wrote4 ,others1 and among them ,dr4 ,vossius1 assert the ,cause of the ,descent of heavy ,bodies1 to be the ,diurnal ,rotation of the ,earth upon its ,axis1 without considering1 that according to the ,doctrine of ,motion fortified with ,demonstration1 all ,bodies moved in ,circulo1 would recede from the ,center of their ,motion2 whereby the contrary to ,gravity would follow1 and all loose ,bodies would be cast into the ,air in a ,tangent to the ,parallel of ,latitude1 without the intervention of some other ,principle to keep them fast1 such as is that of ,gravity4 ,besides1 the ,effect of this ,principle is throughout the whole ,surface of the ,globe found nearly equal2 and certain ,experiments have proved it rather less near the quinoctial1 than towards the ,poles2 which could not be by any means1 if the ,diurnal ,rotation of the ,earth upon its ,axis were the ,cause of ,gravity2 for where the ,motion was swiftest1 the ,effect would be most considerable4 ,others assign the ,pressure of the ,atmosphere1 to be the ,cause of this ,tendency towards the ,center of the ,earth2 but unhappily they have mistaken the ,cause for the ,effect2 it being from undoubted ,principles plain1 that the ,atmosphere has no other ,pressure but what it derives from its ,gravity2 and that the ,weight of the upper ,parts of the ,air1 pressing on the lower ,parts thereof1 do so far bend the ,springs of that ,elastick ,body1 as to give it a ,force equal to the ,weight that compress'd it1 having of it self no force at all3 ,and supposing it had1 it will be very hard to explain the ,modus1 how that ,pressure should occasion the ,descent of a ,body circumscribed by it1 and pressed equally above and below1 without some other ,force to draw1 or thrust it downwards4 ,but to demonstrate the contrary of this ,opinion1 an ,experiment was long since shewn before the ,royal ,society1 whereby it appeared1 that the ,atmosphere was so far from being the ,cause of ,gravity1 that the ,effects thereof were much more vigorous1 where the ,pressure of the ,atmosphere was taken off2 for a long ,glass-,receiver having a light ,down-feather included1 being evacuated of ,air1 the ,feather1 which in the ,air would hardly sink1 did in vacuo descend with nearly the same ,velocity1 as if it had been a ,stone4 ,some think to illustrate this ,descent of ,heavy ,bodies1 by comparing it with the ,vertue of the ,loadstone2 but setting aside the difference there is in the manner of their ,attractions1 the ,loadstone drawing only in and about its ,poles1 and the ,earth near equally in all ,parts of its ,surface1 this ,comparison avails no more than to explain ignotum per que ignotum4 ,others assign a certain ,sympthetical ,attraction between the ,earth and its ,parts1 whereby they have1 as it were1 a desire to be united1 to be the ,cause we enquire after3 ,but this is so far from explaining the ,modus1 that it is little more1 than to tell us in other ,terms1 that ,heavy ,bodies descend1 because they descend4 ,this1 ,i say1 not that ,i can pretend to substitute any ,solution of this ,important ,philosophical ,problem1 that shall more happily explicate the ,appearances of ,gravity2 only it may be serviceable to those with whom the ,credit of great ,authors sways much1 and who too readily assent in ,verba ,magistri1 to let them see that their ,books are not always infallible3 ,besides1 the detection of ,errors is the first and surest ,step towards the discovery of ,truth4 ,though the efficient ,cause of ,gravity be so obscure1 yet the final ,cause thereof is clear enough2 for it is by this single ,principle1 that the ,earth and all the ,clestial ,bodies are kept from ,dissolution2 the least of their ,particles not being suffer'd to recede far from their ,surfaces1 without being immediately brought down again by ,virtue of this ,natural ,tendency2 which1 for their ,preservation1 the ,infinite ,wisdom of their ,creator has ordained to be towards each of their ,centers2 nor can the ,globes of the ,sun and ,planets otherwise be destroy'd1 but by taking from them this ,power of keeping their ,parts united4 ,the ,affections or ,properties of ,gravity1 and its manner of acting upon ,bodies falling1 have been in a great measure discovered1 and most of them made out by ,mathematical ,demonstration in this our ,century1 by the accurate diligence of ,galilus1 ,torricellius1 ,hugenius1 and others1 and now lately by our worthy ,countryman1 ,mr4 ,isaac ,newton1 which ,properties it may be very material here to enumerate1 that they may serve for a ,foundation to all those that shall be willing to spend their ,thoughts in search of the true ,cause of this ,descent of ,bodies4 ,the first ,property is1 ,that by this ,principle of ,gravitation1 all ,bodies do descend towards a ,point1 which either is1 or else is very near to the ,center of ,magnitude of the ,earth and ,sea1 about which the ,sea forms it self exactly into a ,spherical ,surface1 and the ,prominences of the ,land1 considering the ,bulk of the whole1 differ but insensibly therefrom4 ,secondly1 ,that this ,point or ,center of ,gravitation1 is fix'd within the ,earth1 or at least has been so1 ever since we have any ,authentick ,history3 ,for a ,consequence of its ,change1 though never so little1 would be the over-flowing of the low ,lands on that side of the ,globe towards which it approached1 and the leaving new ,islands bare on the opposite side1 from which it receded2 but for this ,two ,thousand ,years it appears1 that the low ,islands of the ,mediterranean ,sea 7near to which the ancientest ,writers liv'd7 have continued much at the same height above the ,water1 as they now are found2 and no ,inundations or ,recesses of the ,sea arguing any such ,change1 are recorded in ,history2 excepting the ,universal ,deluge1 which can no better way be accounted for1 than by supposing this ,center of ,gravitation removed for a time1 towards the middle of the then inhabited ,parts of the ,world2 and a change of its ,place1 but the ,two ,thousandth ,part of the ,radius of this ,globe1 were sufficient to bury the ,tops of the highest ,hills under ,water4 ,thirdly1 ,that in all ,parts of the ,surface of the ,earth1 or rather in all ,points equidistant from its ,center1 the ,force of ,gravity is nearly equal2 so that the length of the ,pendulum vibrating ,seconds of ,time1 is found in all ,parts of the ,world to be very near the same4 ',tis true at ,st4 ,helena1 in the ,latitude of #af ,degrees ,south1 ,i found that the ,pendulum of my ,clock1 which vibrated ,seconds1 needed to be made shorter than it had been in ,england1 by a very sensible ,space 7but which at that time ,i neglected to observe accurately7 before it would keep time2 and since the like ,observations have been made by the ,french ,observers1 near the quinoctial3 ,yet ,i dare not affirm1 that in mine it proceeded from any other ,cause1 than the great ,height of my ,place of ,observation above the ,surface of the ,sea1 whereby the ,gravity being diminished1 the length of the ,pendulum vibrating ,seconds1 is proportionably short'ned4 ,fourthly1 ,that ,gravity does equally affect all ,bodies1 without regard either to their ,matter1 ,bulk1 or ,figure2 so that the ,impediment of the ,medium being removed1 the most compact and most loose1 the greatest and smallest ,bodies would descend the same ,spaces in equal ,times2 the ,truth thereof will appear from the ,experiment ,i before-cited4 ,in these two last ,particulars1 is shewn the great difference between ,gravity and ,magnetism1 the one affecting only ,iron1 and that towards its ,poles1 the other all ,bodies alike in every part4 ,as a ,corollary1 from hence it will follow1 that there is no such thing as positive ,levity1 those things that appear light1 being only comparatively so2 and whereas several things rise and swim in ,fluids1 'tis because1 ,bulk for ,bulk1 they are not so heavy as those ,fluids2 nor is there any ,reason why ,cork1 for ,instance1 should be said to be light1 because it swims on ,water1 any more than ,iron1 because it swims on ,mercury4 ,fifthly1 ,that this ,power increases as you descend1 and decreases as you ascend from the ,center1 and that in the ,proportion of the ,squares of the ,distances therefrom reciprocally1 so as at a double ,distance to have but a quarter of the ,force2 this ,property is the ,principle on which ,mr4 ,newton has made out all the ,phnomena of the ,clestial ,motions1 so easily and naturally1 that its ,truth is past ,dispute4 ,besides that1 it is highly rational1 that the attractive or gravitating ,power should exert it self more vigorously in a small ,sphere1 and weaker in a greater1 in proportion as it is contracted or expanded2 and if so1 seeing that the ,surfaces of ,spheres are as the ,squares of their ,radii1 this ,power1 at several ,distances1 will be as the ,squares of those ,distances reciprocally2 and then its whole ,action upon each ,spherical ,surface1 be it great or small1 will be always equal4 ,and this is evidently the ,rule of ,gravitation towards the ,centers of the ,sun1 ,jupiter1 ,saturn and the ,earth1 and thence is reasonably inferred1 to be the general ,principle observed by ,nature1 in all the rest of the ,clestial ,bodies4 ,these are the principal ,affections of ,gravity1 from which the ,rules of the ,fall of ,bodies1 and the ,motion of ,projects are ,mathematically deducible4 ,mr4 ,isaac ,newton has shew'd how to define the ,spaces of the ,descent of a ,body1 let fall from any given height1 down to the ,center1 supposing the ,gravitation to increase1 as in the fifth ,property2 but considering the smallness of heighth1 to which any ,project can be made ascend1 and over how little an ,arch of the ,globe it can be cast by any of our ,engines1 we may well enough suppose the ,gravity equal throughout1 and the ,descents of ,projects in parallel ,lines1 which in ,truth are towards the ,center1 the difference being so small as by no means to be discovered in ,practice4 ,the ,opposition of the ,air1 'tis true1 is considerable against all light ,bodies moving through it1 as likewise against small ones 7of which more hereafter7 but in great and ponderous ,shot1 this ,impediment is found by ,experience but very small1 and may safely be neglected4 ,propositions concerning the ,descent of ,heavy ,bodies1 and the ,motion of ,projects4 ,prop4 ,i4 ,the ,velocities of ,falling ,bodies1 are proportionate to the ,times from the beginning of their ,falls4 ,this follows1 for that the ,action of ,gravity being continual1 in every ,space of ,time1 the falling ,body receives a new ,impulse1 equal to what it had before1 in the same ,space of ,time1 received from the same ,power3 ,for ,instance1 in the first ,second of ,time1 the falling ,body has acquired a ,velocity1 which in that time would carry it to a certain ,distance1 suppose #cb ,foot1 and were there no new ,force1 would descend at that rate with an equable ,motion3 ,but in the next ,second of ,time1 the same ,power of ,gravity continually acting thereon1 superadds a new ,velocity equal to the former2 so that at the end of two ,seconds1 the ,velocity is double to what it was at the end of the first1 and after the same manner may it be proved to be triple1 at the end of the third ,second1 and so on4 ,wherefore the ,velocities of falling ,bodies1 are proportionate to the ,time of their ,falls1 ,q4 ,e4 ,d4 ,illustration3 ,plate #d4 pag4 #caj ,prop4 ,,ii4 ,the ,spaces described by the ,fall of a ,body1 are as the ,squares of the ,times1 from the beginning of the ,fall4 ,demonstration4 ,let ,,ab 7,fig4 #i4 ,tab4 #d47 represent the ,time of the ,fall of a ,body1 ,,bc perpendicular to ,,ab1 the ,velocity acquired at the end of the ,fall1 and draw the ,line ,,ac2 then divide the ,line ,,ab representing the ,time1 into as many equal ,parts as you please1 as b1 b1 b1 b1 c4 and through these ,points draw the ,lines bc1 bc1 bc1 bc1 c4 parallel to ,,bc1 'tis manifest that the several ,lines1 bc1 represent the several ,velocities of the falling ,body1 in such ,parts of the ,time as ,ab is of ,,ab1 by the former ,proposition4 ,it is evident likewise1 that the ,area ,,abc is the ,sum of all the ,lines bc being taken1 according to the ,method of ,indivisibles1 infinitely many2 so that the ,area ,,abc represents the ,sum of all the ,velocities1 between none and ,,bc supposed infinitely many2 which ,sum is as the ,space descended in the ,time represented by ,,ab4 ,and by the same ,reason the ,areas ,abc1 will represent the ,spaces descended in the ,times ,ab2 so then the ,spaces descended in the ,times ,,ab1 ,ab1 are as the ,areas of the ,triangles ,,abc1 ,abc1 which by the #bjth of the #f of ,euclid1 are as the ,squares of their ,homologous ,sides ,,ab1 ,ab1 that is to say1 of the ,times3 ,wherefore the ,descents of falling ,bodies1 are as the ,squares of the ,times of their ,fall1 ,q4 ,e4 ,d4 ,prop4 ,,iii4 ,the ,velocity which a falling ,body acquires in any ,space of time1 is double to that1 wherewith it would have moved the ,space1 descended by an equable ,motion1 in the same time4 ,demonstration4 ,draw the ,line ,,ec parallel to ,,ab1 and ,,ae parallel to ,,bc in the same ,fig4 #i4 and compleat the ,parallelogram ,,abce1 it is evident that the ,area thereof may represent the ,space1 a ,body moved equably with the ,velocity ,,bc would describe in the ,time ,,ab1 and the ,triangle ,,abc represents the ,space describ'd by the ,fall of a ,body1 in the same ,time ,,ab1 by the second ,proposition4 ,now the ,triangle ,,abc is half of the ,parallelogram ,,abce1 and consequently the ,space described by the ,fall1 is half what would have been described by an equable ,motion with the ,velocity ,,bc1 in the same ,time2 wherefore the ,velocity ,,bc at the end of the ,fall1 is double to that ,velocity1 which in the ,time ,,ab1 would have described the ,space fallen1 represented by the ,triangle ,,abc with an equable ,motion1 ,q4 ,e4 ,d4 ,prop4 ,,iv4 ,all ,bodies on or near the ,surface of the ,earth1 in their ,fall1 descend so1 as at the end of the first ,second of ,time1 they have described #af ,feet1 #a ,inch1 ,london ,measure1 and acquired the ,velocity of #cb ,feet1 #b ,inches1 in a ,second4 ,this is made out from the #beth ,proposition of the second ,part of that excellent ,treatise of ,mr4 ,hugenius de ,horologio ,oscillatorio2 wherein he demonstrates the time of the least ,vibrations of a ,pendulum1 to be to the ,time of the ,fall of a ,body1 from the heighth of half the length of the ,pendulum1 as the ,circumference of a ,circle to its ,diameter2 whence1 as a ,corollary1 it follows1 ,that as the ,square of the ,diameter to the ,square of the ,circumference1 so half the length of the ,pendulum vibrating ,seconds1 to the ,space described by the ,fall of a ,body in a ,second of ,time3 ,and the ,length of the ,pendulum vibrating ,seconds1 being found #ci1 #abe1 or ,inches1 the ,descent in a ,second will be found by the aforesaid ,analogy #af ,foot and #a ,inch2 and1 by the third ,proposition1 the ,velocity will be double thereto2 and near to this it hath been found by several ,experiments1 which by reason of the swiftness of the ,fall1 cannot so exactly determine its ,quantity4 ,the ,demonstration of ,hugenius being the ,conclusion of a long ,train of ,consequences1 ,i shall for brevity sake omit2 and refer you to his ,book1 where these things are more amply treated of4 ,from these ,four ,propositions1 all ,questions concerning the ,perpendicular ,fall of ,bodies1 are easily solved1 and either ,time1 ,height1 or ,velocity being assign'd1 one may readily find the other two4 ,from them likewise is the ,doctrine of ,projects deducible1 assuming the two following ,axioms2 viz4 ,that a ,body set a moving1 will move on continually in a right ,line with an equable ,motion1 unless some other ,force or ,impediment intervene1 whereby it is accelerated1 or retarded1 or deflected4 ,secondly1 ,that a ,body being agitated by two ,motions at a time1 does by their compounded ,forces pass through the same ,points1 as it would do1 were the two ,motions divided and acted successively4 ,as for ,instance1 ,suppose a ,body moved in the ,line ,,gf1 7,fig4 #a4 ,tab4 #e47 from ,g to ,r1 and there stopping1 by another ,impulse1 suppose it moved in a ,space of ,time equal to the former1 from ,r towards ,k1 to ,v4 ,i say1 the ,body shall pass through the ,point to ,v1 though these two several ,forces acted both in the same time4 ,prop4 ,v4 ,the ,motion of all ,projects is in the ,curve of a ,parabola3 ,let the ,line ,,grf 7in ,fig4 #a47 be the ,line in which the ,project is directed1 and in which by the first ,axiom it would move equal ,spaces in equal ,times1 were it not deflected downwards by the ,force of ,gravity4 ,let ,,gb be the ,horizontal ,line1 and ,,gc a ,perpendicular thereto4 ,then the ,line ,,grf being divided into equal ,parts1 answering to equal ,spaces of ,time1 let the ,descents of the ,project be laid down in ,lines parallel to ,,gc1 proportioned as the ,squares of the ,lines ,,gs1 ,,gr1 ,,gl1 ,,gf1 or as the ,squares of the ,times1 from ,s to ,t1 from ,r to ,v1 from ,l to ,x1 and from ,f to ,b1 and draw the ,lines ,,th1 ,,vd1 ,,xy1 ,,bc parallel to ,,gf2 ,i say1 the ,points ,t1 ,v1 ,x1 ,b1 are ,points in the ,curve described by the ,project1 and that that ,curve is a ,parabola4 ,by the second ,axiom1 they are ,points in the ,curve2 and the ,parts of the ,descent ,,gh1 ,,gd1 ,,gy1 ,,gc1 to ,,st1 ,,rv1 ,,lx1 ,,fb1 being as the ,squares of the ,times 7by the ,second ,proposition7 that is1 as the ,squares of the ,ordinates1 ,,ht1 ,,du1 ,,yx1 ,,bc1 equal to ,,gs1 ,,gr1 ,,gl1 ,,gf1 the ,spaces measured in those ,times2 and there being no other ,curve but the ,parabola1 whose ,parts of the ,diameter are as the ,squares of the ,ordinates1 it follows that the ,curve describ'd by a ,project1 can be no other than a ,parabola3 ,and saying1 as ,,ru the ,descent in any time1 to ,,gr or ,,ud the direct ,motion in the same time1 so is ,,ud to a third proportional2 that third will be the ,line call'd by all ,writers of ,conicks1 the ,parameter of the ,parabola to the ,diameter ,,gc1 which is always the same in ,projects cast with the same ,velocity3 ,and the ,velocity being defined by the ,number of ,feet moved in a ,second of ,time1 the ,parameter will be found by dividing the ,square of the ,velocity1 by #af ,feet1 #a ,inch1 the ,fall of a ,body in the same ,time4 ,lemma4 ,the ,sine of the double of any ,arch1 is equal to twice the ,sine of that ,arch into its ,co-sine1 divided by ,radius2 and the versed ,sine of the double of any ,arch is equal to twice the ,square of the ,sine thereof divided by ,radius4 ,let the ,arch ,,bc 7in ,fig4 #b4 ,tab4 #e47 be double the ,arch ,,bf1 and ,a the ,center2 draw the ,radii ,,ab1 ,,af1 ,,ac1 and the ,chord ,,bdc1 and let fall ,,be perpendicular to ,,ac1 and the ,angle ,,ebc1 will be equal to the ,angle ,,abd1 and the ,triangle ,,bce1 will be like to the ,triangle ,,bda2 wherefore it will be as ,,ab to ,,ad1 so ,,bc or twice ,,bd1 to ,,be2 that is1 as ,radius to ,co-sine1 so twice ,sine to ,sine of the double ,arch4 ,and as ,,ab to ,,bd1 so twice ,,bd or ,,bc to ,,ec1 that is1 as ,radius to ,sine1 so twice that ,sine1 to the ,versed ,sine of the double ,arch2 which two ,analogies resolved into ,equations1 are the ,propositions contained in the ,lemma to be proved4 ,prop4 ,,vi4 ,the ,horizontal ,distances of ,projections made with the same ,velocity1 at several ,elevations of the ,line of ,direction1 are as the ,sines of the doubled ,angles of ,elevation4 ,let ,,gb 7,fig4 #a7 the ,horizontal ,distance be z1 the ,sine of the ,angle of ,elevation1 ,,fgb1 be s1 its ,co-sine c1 ,radius r1 and the ,parameter p4 ,it will be as c to s2 so z to sz_/c ,,fb ,,gc1 and by reason of the ,parabola psz_/c to the ,square of ,,cb1 or ,,gf2 ,now as c to r1 so is z to zr_/c ,,gf1 and its ,square zzrr_/cc will be therefore to psz_/c3 ,which ,equation reduced will be psc_/rr z4 ,but by the former ,lemma #bsc_/r is equal to the ,sine of the double ,angle1 whereof s is the ,sine3 ,wherefore 'twill be as ,radius to ,sine of double the ,angle ,,fgb1 so is half the ,parameter1 to the ,horizontal ,range or ,distance sought2 and at the several ,elevations1 the ,ranges are as the ,sines of the double ,angles of ,elevation1 ,q4 ,e4 ,d4 ,corollary4 ,hence it follows1 that half the ,parameter is the greatest ,randon1 and that that happens at the ,elevation of #de ,degrees1 the ,sine of whose double is ,radius4 ,likewise that the ,ranges equally distant above and below #de are equal1 as are the ,sines of all double ,arches1 to the ,sines of their doubled ,complements4 ,prop4 ,,vii4 ,the ,altitudes of ,projections made with the same ,velocity1 at several ,elevations1 are as the versed ,sines of the doubled ,angles of ,elevation3 ,as c is to s2 so is psc_/rr ,,gb to pss_/rr ,,bf3 and ,,uk ,,ru ,,bf_/#d1 the ,altitude of the ,projection psc_/#drr4 ,now by the foregoing ,lemma #bss_/r to the versed ,sine of the double ,angle1 and therefore it will be as ,radius1 to versed ,sine of double the ,angle ,,fgb1 so an #hth of the ,parameter to the height of the ,projection ,,vk2 and so these heights at several ,elevations1 are as the said versed ,sines1 ,q4 ,e4 ,d4 ,corollary4 ,from hence it is plain1 that the greatest ,altitude of the perpendicular ,projection is a #dth of ,parameter1 or half the greatest ,horizontal ,range2 the versed ,sine of #ahj ,degrees being #br4 ,prop4 ,,viii4 ,the ,lines ,,gf1 or ,times of the ,flight of a ,project cast with the same ,degree of ,velocity at different ,elevations1 are as the ,sines of the ,elevations4 ,as c is to r2 so is psc_/rr ,,gb by the #f ,prop4 to ps_/r ,,gf2 that is1 as ,radius to ,sine of ,elevation1 so the ,parameter to the ,line ,,gf2 so the ,lines ,,gf are as the ,sines of ,elevation1 and the ,times are proportional to those ,lines2 wherefore the ,times are as the ,sines of ,elevation3 ,ergo constat propositio4 ,prop4 ,,ix4 ,problem4 ,a ,projection being made as you please1 having the ,distance and ,altitude1 or ,descent1 of an ,object1 through which the ,project passes1 together with the ,angle of ,elevation of the ,line of ,direction2 to find the ,parameter and ,velocity1 that is 7in ,fig4 #a47 having the ,angle ,,fgb1 ,,gm1 and ,,mx4 ,solution4 ,as ,radius to ,secant of ,,fgb1 so ,,gm the ,distance given to ,,gl2 and as ,radius to ,tangent of ,,fgb1 so ,,gm to ,,lm4 ,then ,,lm - ,,mx in ,heights1 or ,,mx in ,descents2 or else ,,mx - ,,ml1 if the ,direction be below the ,horizontal ,line1 is the ,fall in the ,time that the direct ,impulse given in ,g would have carried the ,project from ,g to ,l ,,lx ,,gy2 then by ,reason of the ,parabola1 as ,,lx or ,,gy1 is to ,,gl or ,,yx1 so is ,,gl to the ,parameter sought4 ,to find the ,velocity of the ,impulse3 by ,prop4 #b1 and #d1 find the ,time in ,seconds that a ,body would fall the ,space ,,lx2 and by that dividing the ,line ,,gl1 the ,quote will be the ,velocity1 or ,space moved in a ,second sought1 which is always a mean ,proportional between the ,parameter1 and #af ,feet1 #a ,inch4 ,prop4 ,x4 ,problem #b4 ,having the ,parameter1 ,horizontal ,distance1 and ,height or ,descent of an ,object1 to find the ,elevations of the ,line of ,direction necessary to hit the given ,object2 that is1 having ,,gm1 ,,mx1 and the greatest ,randon equal to half the ,parameter2 to find the ,angles ,,fgb4 ,let the ,tangent of the ,angle sought be t1 the ,horizontal ,distance ,,gm b1 the ,altitude of the ,object ,,mx h1 the ,parameter p1 and ,radius r1 and it will be1 ,as r to t1 so b to tb_/r ,,ml and tb_/r h in ascentsin descents ,,lx1 and ptb_/r ph ,,gl quad4 ,,xy quad4 ratione ,parabol2 but bb ttbb_/rr ,,gl quad4 #dg4 #a4 ,euclid4 ,wherefore ptb_/r ph bb ttbb_/rr which ,equation transposed1 is ttbb_/rr ptb_/r ph - bb1 divided by bb is tt_/rr pt_/br ph_/bb - #a4 this ,equation shews the ,question to have #b ,answers1 and the ,roots thereof are t_/r p_/#b;h 77pp #dph7_/#d;bb7 - #a2 from which ,i derive the following ,rule4 ,divide half the ,parameter by the ,horizontal distance1 and keep the ,quote2 viz4 p_/#b;b then say1 as square of the distance given to the half ,parameter1 so half ,parameter double heightdescent to the square of a ,secant 7pp #dph7_/7#d;bb74 ,the ,tangent answering to that ,secant1 will be 77pp #dph7_/#d;bb7 - #a or ,square of ,radius1 so then the sum and difference of the afore-found ,quote1 and this ,tangent will be the ,roots of the ,equation1 and the ,tangents of the ,elevations sought4 ,note here1 that in ,descents1 if the ,tangent exceed the ,quote1 as it does when ph is more than bb1 the direction of the lower ,elevation will be below the ,horizon1 and if ph bb1 it must be directed ,horizontal1 and the ,tangent of the upper ,elevation will be pr_/b3 ,note likewise1 that if #d;bb #dph in ,ascents1 or #d;bb - #dph in ,descents1 be equal to pp1 there is but one ,elevation that can hit the ,object1 and its ,tangent is pr_/#b;b4 ,and if #d;bb #dph in ,ascents1 or #d;bb - #dph in descents1 do exceed pp1 the ,object is without the reach of a ,project cast with that ,velocity1 and so the thing impossible4 ,from this ,equation #d;bb #dph pp are determined the utmost limits of the reach of any ,project1 and the ,figure assigned1 wherein are all the heights upon each ,horizontal distance beyond which it cannot pass2 for by reduction of that ,equation1 h will be found p - bb_/p in heights1 and bb_/p - p in descents2 from whence it follows1 that all the ,points h are in the ,curve of the ,parabola1 whose ,focus is the ,point from whence the ,project is cast1 and whose ,latus rectum1 or ,parameter ad ,axem is p4 ,likewise from the same ,equation may the least ,parameter or ,velocity be found capable to reach the ,object proposed2 for bb pp ph being reduced1 p will be 7bb hh7 h in ascentsin descents which is the ,horizontal ,range at #de degrees1 of a ,project cast with the least ,velocity that would just reach the ,object1 and the ,elevation requisite will be easily had2 for dividing the so found ,semi-parameter by the ,horizontal distance given b1 the ,quote into ,radius will be the ,tangent of the ,elevation sought4 ,this ,rule may be of good use to all ,bombardiers and ,gunners1 not only that they may use no more ,powder than is necessary1 to cast their ,bombs into the place assigned1 but that they may shoot with much more certainty1 for that a small ,error committed in the ,elevation of the ,piece1 will produce no sensible ,difference in the fall of the ,shot3 ,for which ,reasons the ,french ,engineers in their late ,sieges have used ,mortar-pieces inclin'd constantly to the ,elevation of #de1 proportioning their ,charge of ,pouder according to the distance of the ,object they intend to strike on the ,horizon4 ,and this is all that need to be said concerning this ,problem of shooting upon ,heights and ,descents4 ,but if a ,geometrical ,construction thereof be required2 ,i think ,i have one that is as easy as can be expected1 which ,i deduce from the foregoing ,analytical ,solution1 viz4 t_/r p_/#b;b 77pp ph - bb7_/bb71 and 'tis this1 having made the right ,angle ,,gdf1 7,tab4 #e4 ,fig4 #c47 make ,,df p1 or greatest ,range1 and ,,gd b the ,horizontal ,distance1 and ,,db h the perpendicular heighth of the ,object2 to be laid upwards from ,d1 if the ,object be above the ,horizon1 or downwards if below it4 ,parallel to ,,gd draw ,,fa1 and make it equal to ,,gb the ,hypothenusal ,distance of the ,object2 and with the ,center ,a and ,radius ,,fb p h1 sweep an ,arch1 which shall if the thing be possible1 intersect the indeterminate ,perpendicular ,,df in two ,points ,k and ,l1 to which draw the ,lines1 ,,gl1 ,,gk2 ,i say1 the ,angles ,,dgk1 ,,dgl1 are the ,elevations requisite to strike the ,object ,b4 ,demonstration4 ,the ,square of ,,fk or ,,fl1 is equal to ,,fbq - ,,gbq3 or 7p h7 - bb - hh or pp ph - bb1 and therefore 7pp ph - bb7 is ,,fk ,,fl1 and by ,consequence ,,dk1 ,,dl p 7pp ph - bb74 ,and as ,,dg3 ,,dk and ,,dl 33 ,radius3 ,tangents sought1 which coincides with our ,algebraical ,expression thereof4 ,prop4 ,,xi4 ,to determine the ,force or ,velocity of a ,project1 in every ,point of the ,curve it describes4 ,to do this we need no other ,prcognita1 but only the third ,proposition1 viz4 ,that the ,velocity of falling ,bodies1 is double to that which in the same time1 would have described the ,space fallen by an equable ,motion3 ,for the ,velocity of a ,project1 is compounded of the constant equal ,velocity of the impressed ,motion1 and the ,velocity of the ,fall1 under a given ,angle1 viz4 the ,complement of the ,elevation3 ,for ,instance1 in ,fig4 #b4 in the time wherein a ,project would move from ,g to ,l1 it descends from ,l to ,x1 and by the third ,proposition has acquired a ,velocity1 which in that time would have carried it by an equable ,motion from ,l to ,z1 or twice the ,descent ,,lx2 and drawing the ,line ,,gz1 ,i say1 the ,velocity in the ,point ,x1 compounded of the ,velocities ,,gl and ,,lz under the ,angle ,,glz1 is to the ,velocity impress'd in the ,point ,g1 as ,,gz is to ,,gl2 this follows from our second ,axiom1 and by the #bj and #ba ,prop4 lib4 #a4 conic4 ,midorgii1 ,,xo parallel and equal to ,,gz shall touch the ,parabola in the ,point ,x4 ,so that the ,velocities in the several ,points1 are as the lengths of the ,tangents to the ,parabola in those ,points1 intercepted between any two ,diameters3 ,and these again are as the ,secants of the ,angles1 which those ,tangents continued make with the ,horizontal ,line ,,gb4 ,from what is here laid down1 may the comparative ,force of a ,shot in any two ,points of the ,curve1 be either ,geometrically or ,arithmetically discover'd4 ,corollary4 ,from hence it follows1 that the force of a ,shot is always least at ,u1 or the ,vertex of the ,parabola1 and that at equal distances therefrom1 as at ,t and ,x1 ,g and ,b its force is always equal1 and that the least force in ,u is to that in ,g and ,b1 as ,radius to the ,secant of the ,angle of ,elevation ,,fgb4 ,these ,propositions considered1 there is no question relating to ,projects1 which1 by the help of them1 may not easily be ,solved2 and tho' it be true that most of them are to be met withal1 in ,galileus1 ,torricellius and others1 who have taken them from those ,authors1 yet their ,books being ,foreign1 and not easy to come by1 and their ,demonstrations long and difficult1 ,i thought it not amiss to give the whole ,doctrine here in ,english1 with such short ,analytical ,proof of my own1 as might be sufficient to evince their ,truth4 ,the ,tenth ,proposition contains a ,problem1 untouch'd by ,torricellius1 which is of the greatest use in ,gunnery1 and for the sake of which this ,discourse was principally intended3 ,it was first ,solved by ,mr4 ,anderson1 in his ,book of the ,genuine ,use and ,effects of the ,gun1 ,printed in the ,year #afgd2 but his ,solution required so much ,calculation1 that it put me upon search1 whether it might not be done more easily1 and thereupon in the ,year #afgh ,i found out the ,rule ,i now ,publish1 and from it the ,geometrical ,construction3 ,since which time there has a large ,treatise of this ,subject1 ,intituled1 ,l',art dejetter les ,bombes1 been ,published by ,monsieur ,blondel1 wherein he gives the ,solutions of this ,problem by ,messieurs ,buot1 ,romer and de la ,hire3 ,but none of them being the same with ,mine1 or1 in my ,opinion1 more easy1 and most of them more ,operose1 and besides mine finding the ,tangent1 which generally determines the ,angle better than its ,sine1 ,i thought my self obliged to ,print it for the use of all such1 as desire to be informed in the ,mathematical part of the ,art of ,gunnery4 ,now these ,rules were rigidly true1 were it not1 as ,i said before1 for the ,opposition of the ,medium1 whereby not only the direct imprest ,motion is continually retarded1 but likewise the increase of the ,velocity of the ,fall1 so that the ,spaces described thereby1 are not exactly as the ,squares of the ,times3 ,but what this ,opposition of the ,air is1 against several ,velocities1 ,bulks1 and ,weights1 is not so easie to determine4 ',tis certain that the weight of ,air to that of ,water1 is nearly as #a to #hjj1 whence the weight thereof1 to that of any ,project is given2 'tis very likely1 that to the same ,velocity and ,magnitude1 but of different ,matter1 the ,opposition should be reciprocally as the weights of the ,shot2 as likewise that to ,shot of the same ,velocity and ,matter1 but of different ,sizes1 it should be as the ,diameters reciprocally3 ,whence generally the ,opposition to ,shot with the same ,velocity1 but of differing ,diameters1 and ,materials1 should be as their ,specifick ,gravities into their ,diameters reciprocally2 but whether the ,opposition1 to differing ,velocities of the same ,shot1 be as the ,squares of those ,velocities1 or as the ,velocities themselves1 or otherwise1 is yet a harder ,question4 ,however it be1 'tis certain1 that in large ,shot of ,metal1 whose weight many ,thousand times surpasses that of the ,air1 and whose force is very great1 in proportion to the ,surface wherewith they press thereon2 this ,opposition is scarce discernable2 ,for by several ,experiments made with all ,care and ,circumspection with a ,mortarpiece1 ,extraordinary well fix'd to the ,earth on purpose1 which carried a solid ,brass ,shot of four ,inches and a half ,diameter1 and of about fourteen ,pound ,weight1 the ,ranges above and below forty five ,degrees were found nearly equal2 if there were any difference1 the under ,ranges went rather the farthest1 but those differences were usually less than the ,errors committed in ordinary ,practice1 by the unequal ,goodness and ,dryness of the same sort of ,powder1 by the ,unfitness of the ,shot to the ,bore1 and by the ,loosness of the ,carriage4 ,in a smaller ,brass-,shot of about an ,inch and half ,diameter1 cast by a ,cross-,bow which ranged it1 at most about four ,hundred ,foot1 the ,force being much more equal than in the ,mortarpiece1 this difference was found more ,curiously3 and ,constantly and most ,evidently1 the under ,ranges out-went the upper4 ,from which ,trials ,i conclude1 that although in small and light ,shot1 the ,opposition of the ,air1 ought and must be accounted for2 yet in ,shooting of great and weighty ,bombs1 there need be very little or no allowance made2 and so these ,rules may be put in practice to all ,intents and ,purposes1 as if this ,impediment were absolutely remov'd4 ,a ,proposition of general ,use in the ,art of ,gunnery1 shewing the ,rule of laying a ,mortar to pass1 in order to strike an ,object above or below the ,horizon4 ,it was formerly the ,opinion of those concerned in ,artillery1 that there was a certain requisite of ,powder for each ,gun1 and that in ,mortars1 where the distance was to be varied1 it must be done by giving a greater or lesser ,elevation to the ,piece4 ,but now our later ,experience has taught us that the same thing may be more certainly and readily performed by increasing and diminishing the quantity of ,powder1 whether regard be had to the ,execution to be done1 or to the ,charge of doing it4 ,for when ,bombs are discharged with great ,elevations of the ,mortar1 they fall too ,perpendicular1 and bury themselves too deep in the ,ground1 to do all that damage they might1 if they came more ,oblique1 and broke upon or near the ,surface of the ,earth2 which is a thing acknowledg'd by the ,besieged in all ,towns1 who unpave their ,streets1 to let the ,bombs bury themselves1 and thereby stifle the force of their ,splinters4 ,a ,second ,convenience is1 that at the extream ,elevation1 the ,gunner is not obliged to be so curious in the direction of his ,piece1 but it will suffice to be within a ,degree or two of the ,truth2 whereas in the other ,method of ,shooting he ought to be very curious4 ,but a ,third1 and no less considerable ,advantage is1 in the saving the ,prince's ,powder1 which in so great and so numerous ,discharges1 as we have lately seen1 must needs amount to a considerable ,value4 ,and for ,sea-,mortars1 it is scarce practicable otherwise to use them1 where the agitation of the ,sea continually changes the ,direction of the ,mortar1 and would render the ,shot very uncertain1 were it not that they are placed about #de ,degrees ,elevation1 where several ,degrees above or under1 make very little difference in the ,effect4 ,in the precedent ,discourse1 ,i considered all the ,propositions relating to the ,motion of ,projectiles1 and gave a ,solution to this ,problem2 viz4 ,to hit an ,object above or below the ,horizontal ,line with the greatest ,certainty and least ,force4 ,that is1 that the ,horizontal distance of the ,object being put b1 and the ,perpendicular ,heighth b1 the ,charge requisite to strike the ,object with the greatest ,advantage1 was that which with an ,elevation of #de would cast the ,shot on the ,horizontal ,line1 to the distance of 7bb hh71 when the ,object was above the ,horizon2 or if it were below it1 the ,charge must be lesser1 so as to reach on the ,horizon1 at #de ,elevation1 no greater a ,distance than 7bb hh7 - h2 that is1 in the one ,case1 the ,sum of the ,hypothenusal ,distance of the ,object from the ,gun1 and the ,perpendicular ,heighth thereof above the ,gun2 and in the other ,case1 when the ,object is below the ,horizon1 the difference of the same per #dg4 ,i ,eucl4 ,and ,i then shew'd how to find the ,elevation proper for the ,gun so charged1 viz4 ,as the ,horizontal ,distance of the ,object1 to the ,sum or ,difference of the ,hypothenusal ,distance and ,perpendicular ,height3 ,so ,radius to the ,tangent of the ,elevation sought4 ,but ,i was not at that time aware that the aforesaid ,elevation did constantly bisect the ,angle between the ,perpendicular and the ,object1 as is demonstrated from the ,difference and ,sum of the ,tangent and ,secant of any ,arch being always equal to the ,tangent and ,cotangent of the half ,complement thereof to a ,quadrant4 ,having discovered this1 ,i think nothing can be more compendious1 or bids fairer to compleat the ,art of ,gunnery1 it being as easie to shoot with a ,mortar at any ,object on demand1 as if it were on the ,level2 neither is there need of any ,computation1 but only simply laying the ,gun to pass1 in the middle ,line between the ,zenith and the ,object1 and giving it its due ,charge4 ,nor is there any great need of ,instruments for this purpose3 ,for if the ,muzzle of the ,mortar be turned truly ,square to the ,bore of the ,piece1 as it usually is or ought to be1 a piece of ,looking-glass ,plate applied parallel to the ,muzzle1 will by its ,reflection give the true ,position of the ,piece1 the ,bombardeer having no more to do1 but to look perpendicularly down on the ,looking-glass1 along a small ,thread with a ,plumbet1 and to raise or depress the ,elevation of the ,piece1 till the ,object appear reflected on the same ,point of the ,speculum1 on which the ,plumbet falls2 for the ,angle of ,incidence and ,reflection being equal1 in this ,case a ,line at ,right ,angles to the ,speculum1 as is the ,axis of the ,chase of the ,piece1 will bisect the ,angle between the ,perpendicular and the ,object1 according as our ,proposition requires4 ,so that it only remains by good and valid ,experiments to be assured of the ,force of ,gunpowder1 how to make and conserve it equal1 and to know the ,effect thereof in each ,piece2 that is1 how far differing ,charges will cast the same ,shot out of it2 which may most conveniently be engraven on the outside thereof1 as a standing ,direction to all ,gunners1 who shall from thence forward have occasion to use that ,piece3 ,and were this ,matter well ascertained1 it might be worth the while to make all ,mortars of the like ,diameter as near as may he1 alike in length of ,chase1 ,weight1 ,chamber1 and all other ,circumstances4 ,this ,discovery that the utmost ,range on an inclined ,plane1 is1 when the ,axis of the ,piece makes equal ,angles with the ,perpendicular and the ,object2 compared with what ,i have demonstrated of the same ,problem in the aforesaid ,discourse does lead to and discover two very ready ,theorems2 the one1 to find the greatest ,horizontal ,range at #de ,elevation1 by any ,shot made upon any inclined ,plane1 with any ,elevation of the ,piece whatsoever3 ,and the other to find the ,elevations proper to strike a given ,object1 with any ,force greater than what suffices to reach it with the aforesaid middle ,elevation4 ,both which being performed by one single ,proportion1 may be very serviceable to such as are concerned in the ,practice of ,gunnery1 but are unwilling to trouble themselves with tedious and difficult ,rules4 ,the two ,propositions are these4 ,,prop4 ,i4 ,a ,shot being made on an inclined ,plane1 having the ,horizontal ,distance of the ,object it strikes1 with the ,elevation of the ,piece1 and the ,angle at the ,gun between the ,object and the ,perpendicular2 to find the greatest ,horizontal ,range of that ,piece1 laden with the same ,charge2 that is1 half the ,latus rectum of all the ,parabol made with the same ,impetus4 ,,rule4 ,take half the ,distance of the ,object from the ,nadir1 and take the ,difference of the given ,elevation from that half2 the ,versed ,sine of twice that ,difference subtract from the ,versed ,sine of the ,distance of the ,object from the ,zenith3 ,then shall the ,difference of those ,versed ,sines be to the ,sine of the ,distance of the ,object from the ,zenith1 as the ,horizontal ,distance of the ,object strook1 to the greatest ,horizontal ,range at #de4 ,,prop4 ,,ii4 ,having the greatest ,horizontal ,range of a ,gun1 the ,horizontal ,distance and ,angle of ,inclination of an ,object to the ,perpendicular1 to find the two ,elevations necessary to strike that ,object4 ,,rule4 ,halve the ,distance of the ,object from the ,nadir2 this half is always equal to the half ,sum of the two ,elevations we seek4 ,then say1 ,as the greatest ,horizontal ,range is to the ,horizontal ,distance of the ,object3 ,so is the ,sine of the ,angle of ,inclination or ,distance of the ,object from the ,perpendicular1 to a fourth ,proportional2 which fourth being subtracted from the ,versed ,sine of the ,distance of the ,object from the ,zenith1 leaves the ,versed ,sine of the ,difference of the ,elevations sought2 which ,elevations are therefore had by adding and subtracting the half ,difference to and from the aforesaid half ,sum4 ,i shall not need to speak of the ,facility of these ,solutions1 ,i shall only observe that they are both ,general1 without ,exception or ,caution1 and derived from the ,knowledge that these two ,elevations are equidistant above and below the ,line1 bisecting the ,angle between the ,object and the ,zenith4 ,a ,discourse concerning the ,measure of the ,airs ,resistance to ,bodies moved in it4 ,by the ,learned ,john ,wallis1 ,s4 ,t4 ,d4 and ,r4 ,s4 ,s4 #a4 ,that the ,air 7and the like of any other ,medium7 doth considerably give ,resistance to ,bodies moved in it2 and doth thereby abate their ,celerity and ,force2 is generally admitted4 ,and ,experience doth attest it3 ,for otherwise1 a ,cannon ,bullet projected ,horizontally1 should 7supposing the ,celerity and ,force undiminished7 strike as hard against a ,perpendicular ,wall1 erected at a great distance1 as near at hand2 which we find it doth not4 #b4 ,but at what ,rate1 or in what ,proportion1 such ,resistance is2 and 7consequently1 at what ,rate the ,celerity and ,force is continually diminished7 seems not to have been so well examined4 ,whence it is1 that the ,motion of a ,project 7secluding this ,consideration7 is commonly reputed to describe a ,parabolick ,line2 as arising from an ,uniform or equal ,celerity in the ,line of ,projection1 and a ,celerity uniformly accelerated in the ,line of ,descent2 which two so compounded1 do create a ,parabola4 #c4 ,in order to the ,computation hereof1 ,i first premise this ,lemma1 7as the most rational that doth occur for my first footing17 ,that 7supposing other things equal7 the ,resistance is proportional to the ,celerity4 ,for in a double ,celerity1 there is to be removed 7in the same time7 twice as much ,air1 7which is a double ,impediment7 in a treble1 thrice as much2 and so in other ,proportions4 #d4 ,suppose we then the ,force impressed 7and consequently the ,celerity1 if there were no ,resistance7 as #a2 the ,resistance as r4 7which must be less than the ,force1 or else the ,force would not prevail over the ,impediment1 to create a ,motion47 ,and therefore the effective ,force at a first ,moment1 is to be reputed as #a - r3 ,that is1 so much as the ,force impressed1 is more than the ,impediment or ,resistance4 #e4 ,be it as #a - r to #a2 so one to m4 7which m is therefore greater than #a47 #f4 ,and therefore the effective ,force 7and consequently the ,celerity7 as to a first ,moment1 is to be #a_/m of what it would be1 had there been no ,resistance4 #g4 ,this #a_/m is also the remaining ,force after such first ,moment2 and this remaining ,force is 7for the same ,reason7 to be proportionally abated as to a second ,moment2 that is1 we are to take #a_/m thereof1 that is #a_/mm of the impressed ,force4 ,and for a third ,moment 7at equal distance of time7 #a_/mmm2 for a fourth #a_/m2 and so onward infinitely4 #h4 ,because the length dispatched 7in equal times7 is proportional to the ,celerities2 the ,lines of ,motion 7answering to those equal ,times7 are to be as #a_/m1 #a_/m1 #a_/m1 #a_/m1 c4 of what they would have been1 in the same ,times1 had there been no ,resistance4 #i4 ,this therefore is a ,geometrical ,progression2 and 7because of m greater than #a7 continually decreasing4 #aj4 ,this decreasing ,progression infinitely continued 7determining in the same ,point of ,rest1 where the ,motion is supposed to expire7 is yet of a finite ,magnitude2 and equal to #a_/7m - #a71 of what it would have been in so much ,time1 if there had been no ,resistance4 ,as is demonstrated in my ,algebra1 ,chap4 #ie4 ,prop4 #h4 ,for 7as ,i have elsewhere demonstrated7 the ,sum or ,aggregate of a ,geometrical ,progression is 7,,vr - ,a7_/7,r - #a7 7supposing ,v the greatest ,term1 ,a the least1 and ,r the common ,multiplier47 ,that is ,,vr_/7,r - #a7 - ,a_/7,r - #a74 ,now in the present ,case1 7supposing the ,progression infinitely continued7 the least ,term ,a1 becomes infinitely small1 or #j4 ,and consequently ,a_/7,r - #a7 doth also vanish1 and thereby the ,aggregate becomes ,,vr_/7,r - #a74 ,that is 7as will appear by dividing ,,vr by ,r - #a27 ,v ,v_/,r ,v_/,,rr ,v_/,r c4 ,,vr_/7,r - #a72ad 7supposing the ,progression to begin at ,v #a47 ,that is 7dividing all by ,r1 that so the ,progression may begin at ,v_/,r #a_/m37 ,v_/7,r - #a7 ,v_/,r ,v_/,,rr ,v_/,r c41 ,that is1 in our present ,case 7because of ,v #a1 ,r m37 #a_/m #a_/mm #a_/m c4 #a_/7m - #a74 ,that is1 7putting n m - #a7 #a_/n of what it would have been if there had been no ,resistance4 #aa4 ,this infinite ,progression is fitly expressed by an ,ordinate in the ,exterior ,hyperbola1 parallel to one of the ,asymptotes2 and the several ,members of that1 by the several ,members of this1 cut in continual ,proportion4 ,as is there demonstrated at ,prop4 #ae4 ,for let ,,sh1 7vid4 ,fig4 #d4 ,tab4 #e47 be an ,hyperbola between the ,asymptotes ,,ab1 ,,af3 ,and let the ,ordinate ,,dh 7in the ,exterior ,hyperbola1 parallel to ,,af17 represent the impressed ,force undiminished2 or the ,line to be described in such time1 by a ,celerity answerable to such undiminished ,force4 ,and let ,,bs 7a like ,ordinate7 be #a_/m thereof2 which therefore1 being less than ,,dh 7as being equal to a ,part of it7 will be farther than it from ,,af4 ,in ,,ab 7which ,i put #a7 let ,bd be such a ,part thereof1 as is ,,bs of ,,dh4 ,now because 7as is1 well known7 all the inscribed ,parallelograms1 in the ,exterior ,hyperbola1 ,,as1 ,,ah1 c4 are equal2 and therefore their sides reciprocal3 ,therefore as ,ad #a - #a_/m 7supposing ,bd to be taken1 from ,b towards ,a17 to ,,ab #a1 or as m - #a to m3 so is ,,bs 7#a_/m7,,dh1 to dh1 which is therefore equal to #a_/7m - #a7 of ,,dh2 that is 7as will appear by dividing #a1 by m - #a17 to #a_/m #a_/mm #a_/m1 c4 of ,,dh4#ae ,or if ,bd be taken beyond ,b2 then as ,ad #a #a_/m to ,,ab #a1 or as m #a to m1 so is 7#a_/m7,,dh to dh1 which is therefore equal to #a_/7m #a7;,,dh2 that is 7as will appear by like dividing of #a by m #a27 to #a_/m - #a_/mm #a_/m - c4 of ,,dh4 #ab4 ,let such ordinate dh1 or 7equal to it in the ,asymptote7 ,,af1 be so divided in ,l1 ,m1 ,n1 c4 7by ,perpendiculars cutting the ,hyperbola in l1 m1 n1 c47 as that ,,fl1 ,,lm1 ,,mn1 be as #a_/m1 #a_/mm1 #a_/m1 c4 ,that is1 so continually decreasing as that each ,antecedent be to its ,consequent1 as #a to #a_/m1 or as m to #a4 ,see ,fig4 #e4 ,tab4 #e4 #ac4 ,this is done by taking ,,af1 ,,al1 ,,an1 c4 in such proportion4 ,for1 of continual ,proportionals1 the ,differences are also continually proportional1 and in the same proportion4 ,for let ,a1 ,b1 ,c1 ,d1 c4 be such ,proportionals1 and their ,differences a1 b1 c1 c4 ,that is1 ,a - ,b a1 ,b - ,c b1 ,c - ,d c1 c4 ,then1 because ,a1 ,b1 ,c1 ,d1 c4 are in continual proportion1 ,that is1 ,a4 ,b 33 ,b4 ,c 33 ,c4 ,d 33 c4 ,and dividing 7,a - ,b74 ,b 33 7,b - ,c74 ,c 33 7,c - ,d74 ,d 33 c4 ,that is1 a4 ,b 33 b4 ,c 33 d4 ,d 33 c4 ,and alternly a4 b4 c4 c4 33 ,b4 ,c4 ,d4 c4 33 ,a4 ,b4 ,c4 c4 ,that is1 in continual proportion as ,a to ,b1 or as m to #a4 #ad4 ,this being done2 the ,hyperbolick ,spaces ,fl1 ,lm1 ,mn1 c4 are equal4 ,as is demonstrated by ,gregory ,san-,vincent2 and as such is commonly admitted4 #ae4 ,so that ,fl1 ,lm1 ,mn1 c4 may fitly represent equal ,times1 in which are dispatched unequal ,lengths1 represented by ,,fl1 ,,lm1 ,,mn1 c4 #af4 ,and because they are in ,number infinite 7though equal to a finite ,magnitude7 the ,duration is infinite3 ,and consequently the impressed ,force1 and ,motion thence arising1 never to be wholly extinguished 7without some further ,impediment7 but perpetually approaching to ,a1 in the ,nature of ,asymptotes4 #ag4 ,the ,spaces ,fl1 ,fm1 ,fn1 c4 are therefore as ,logarithms 7in ,arithmetical ,progression increasing7 answering to the ,lines ,,af1 ,,al1 ,,am1 c4 or to ,,fl1 ,,lm1 ,,mn1 c4 in ,geometrical ,progression decreasing4 #ah4 ,because ,,fl1 ,,lm1 ,,mn1 c4 are as #a_/m1 #a_/mm1 #a_/m1 c4 7infinitely7 terminated at ,a2 therefore 7by #aj7 their ,aggregate ,,fa or dh1 is to ,,dh1 7so much ,length as would have been dispatched1 in the same time1 by such impressed ,force undiminished7 as #a to m - #a n4 #ai4 ,if therefore we take1 as #a to n1 so ,,af to ,,dh2 this will represent the ,length to be dispatched1 in the same time1 by such undiminished ,force4 #bj4 ,and if such ,,dh be supposed to be divided into equal ,parts innumerable 7and therefore infinitely small27 these answer to those 7as many7 ,parts unequal in ,,fa1 or hd4 #ba4 ,but1 what is the ,proportion of r to #a1 or 7which depends on it7 of #a - r to #a1 or #a to m2 remains to be inquired by ,experiment8 #bb4 ,if the ,progression be not infinitely continued2 but end 7suppose7 at ,n1 and its least ,term be ,a ,,mn2 then1 out of ,v_/7,r - #a7 #a_/m #a_/mm #a_/m1 c4 is to be subducted ,a_/7,r - #a7 7as at #aj47 that is 7as by ,division will appear7 ,a_/,r ,a_/,r ,a_/,r c4 ,that is 7in our present ,case7 a_/m a_/mm a_/m c4 ,and so the ,aggregate will be 7#a-;a7_/m 7#a-;a7_/mm 7#a-;a7_/m c4 7#a-;a7_/n4 ,and thus as to the ,line of ,projection1 in which 7secluding the ,resistance7 the ,motion is reputed uniform2 dispatching equal ,lengths in equal ,times4 ,consider we next the ,line of ,descent4 #bc4 ,in the ,descent of ,heavy ,bodies1 it is supposed that to each ,moment of ,time1 there is superadded a new ,impulse of ,gravity to what was before3 ,and each of these1 secluding the ,consideration of the ,air's ,resistance1 to proceed equally 7from their several beginnings7 through the succeeding ,moments4 ,as 7in the erect ,lines7 #a #a #a #a1 c4 #a #a #a1 c4 #a #a1 c4 #a1 c4 and so continually1 as in the ,line of ,projection4#af #bd4 ,hence ariseth 7in the transverse ,lines7 for the first ,moment #a1 for the second #a #a1 for the third #a #a #a1 and so forth1 in ,arithmetical ,progression3 ,as are the ,ordinates in a ,triangle1 at equal distance4 #be4 ,and such are the continual ,increments of the ,diameter1 or of the ,ordinates in the exterior ,parabola1 answering to the interior ,ordinates1 or ,segments of the ,tangent1 equally increasing2 as is known1 and commonly admitted4 #bf4 ,if we take in the ,consideration of the ,air's ,resistance2 we are then1 for each of these equal ,progressions1 to substitute a decreasing ,progression ,geometrical2 in like manner 7and for the same ,reasons7 as in the ,line of ,projection4 #bg4 ,hence ariseth1 for the first ,moment #a_/m2 for the second #a_/m #a_/m2 for the third #a_/m #a_/m #a_/m1 c4#ag ,and such is therefore the ,descent of a heavy ,body falling by its own weight4 ,the several ,impulses of ,gravity being supposed equal4 #bh4 ,that is 7in the ,figure of #ab7 as ,,fl1 ,,fm1 ,,fn1 c4 in the ,line of ,descent1 answering to ,,fl1 ,,lm1 ,,mn1 c4 in the ,line of ,projection4 #bi4 ,but though the ,progressions for the ,line of ,projection1 are like to each of those many in the ,line of ,descent2 it is not to be thence inferred1 that therefore #a_/m in the one1 is equal to #a_/m in the other3 ,but in the ,line of ,projection 7suppose7 7#a_/m7f 7such a ,part of the ,force impressed1 and a ,celerity answerable37 in the ,line of ,descent1 7#a_/m7g such a ,part of the ,impulse of ,gravity4 #cj4 ,those for the ,line of ,descent 7of the some ,body7 are all equal1 each to other3 ,because g 7the new ,impulse of ,gravity7 in each ,moment is supposed to be the same4 #ca4 ,but what is the ,proportion of f to g 7that of the ,force impressed1 to the ,impulse of ,gravity in each ,body7 remains to be inquired by ,experiment4 #cb4 ,this ,proportion being found as to one known ,force2 the same is thence known as to any other ,force 7whose ,proportion to this is given7 in the same uniform ,medium4 #cc4 ,and this being known1 as to one ,medium2 the same is thence known as to any other ,medium1 the ,proportion of whose ,resistance to that of this is known4 #cd4 ,if a heavy ,body be projected downward in a perpendicular ,line2 it descends therefore at the ,rate #a_/m1 #a_/mm1 #a_/m1 c4 of f1 7the impressed ,force7 increased by #a_/m1 #a_/m #a_/m1 #a_/m #a_/m #a_/m1 c4 of g the impulse of ,gravity1 7by #g1 and #bg7 ,because both ,forces are here united4 #ce4 ,if in a perpendicular ,projection upwards2 it ascends in the rate of the former1 abated by that of the latter4 ,because here the impulse of ,gravity is contrary to the ,force impressed4 #cf4 ,when therefore this latter 7continually increasing7 becomes equal to that former 7continually decreasing7 it then ceaseth to ascend2 and doth thenceforth descend at the rate wherein the latter continually exceeds the former4 #cg4 ,in an ,horizontal1 or ,oblique ,projection3 ,if to a ,tangent1 whose ,increments are as ,,fl1 ,,lm1 ,,mn1 c4 that is as 7#a_/m7f1 c4 be fitted ,ordinates 7at a given ,angle7 whose ,increments are as ,,fl1 ,,fm1 ,,fn1 c4 that is1 as 7#a_/m7g1 c4 ,the ,curve answering to the ,compound of these ,motions1 is that wherein the ,project is to move4 #ch4 ,this ,curve 7being hitherto without a ,name7 may be call'd ,linea ,projectorum2 the ,line of ,projects1 or things projected2 which resembles a ,parabola deform'd4 #ci4 ,the ,celerity and ,tendency1 as to each ,point of this ,line1 is determined by a ,tangent at that ,point4 #dj4 ,and that against which it makes the greatest ,stroke or ,percussion1 is that which 7at that ,point7 is at right ,angles to that ,tangent4 #da4 ,if the ,projection 7at #bg7 be not infinitely continued1 but terminate 7suppose7 at ,n1 so that the last ,term in the first ,column or ,series erect be a2 and consequently in the second1 ma2 in the third1 mma1 c4 7each ,series having one ,term fewer than that before it37 ,then 7for the same ,reasons1 as at #bb7 the ,aggregates of the several ,columns 7or erect ,series7 will be 7#a - a7_/n1 7#a - ma7_/n1 7#a - mma7_/n1 and so forth1 till 7the ,multiple of a becoming #a7 the ,progression expire4 #db4 ,now all the ,abatements here1 a1 ma1 mma1 c4 are the same with the ,terms of the first ,column taken backward4 ,for a is the last1 ma the next before it2 and so of the rest4 #dc4 ,and the ,aggregate of all the ,numerators is so many times #a1 as is the ,number of ,terms 7suppose t17 wanting the first ,column2 that is t - 7#a - a7_/n1 or 7nt - #a a7_/n2 and this again divided by the common ,denominator n1 becomes 7nt - #a a7_/nn4 ,and therefore 77nt - #a a7_/nn7g1 is the ,line of ,descent by its own ,gravity4 #dd4 ,if therefore this be added to a projecting ,force downward in a ,perpendicular2 or subducted from such projecting ,force upward2 that is1 to or from 77#a - a7_/n7f3 ,the ,descent in the first ,case will be 77#a - a7_/n7f 77nt - #a a7_/nn7g2 and the ,ascent in the other ,case 77#a - a7_/n7f - 77nt - #a a7_/nn7g4 ,and in this latter ,case1 when the ablative ,part becomes equal to the positive ,part1 the ,ascent is at the highest2 and thenceforth 7the ablative ,part exceeding the positive7 will descend4 #de4 ,in an ,horizontal or ,oblique ,projection1 having taken 77#a - a7_/n7f1 in the ,line of ,projection1 and thence 7at the ,angle given7 77nt - #a a7_/nn7g1 in the ,line of ,descent2 the ,point in the ,curve answering to these1 is the ,place of the ,project answering to that ,moment4 #df4 ,i am aware of some ,objections to be made1 whether to some ,points of the ,process1 or to some of the ,suppositions4 ,but ,i saw not well how to wave it1 without making the ,computation much more perplex'd4 ,and in a ,matter so nice1 and which must depend upon ,physical ,observations1 'twill be hard to attain such ,accuracy1 as not to stand in need of some ,allowances4 #dg4 ,somewhat might have been farther added to direct the ,experiments suggested at #ba1 and #ca4 ,but that may be done at leisure1 after deliberation had1 which way to attempt the ,experiment4 #dh4 ,the like is to be said of the different resistance which different ,bodies may meet with in the same ,medium1 according to their different ,gravities 7extensively or intensively consider'd7 and their different ,figures and ,positions in ,motion4 ,whereof we have hitherto taken no account2 but supposed them1 as to all these1 to be alike and equal4 ,,postscript4 #di4 ,the ,computation in #da1 #db1 #dc1 may 7if that be also desired7 be thus represented by ,lines and ,spaces4 ,the ,ablatives a1 ma1 mma1 c4 7being the same with the first ,column taken backward7 are fitly represented by the ,segments of ,,nf 7beginning at ,n7 in ,figure #e and #f1 and therefore by ,parallelograms on these ,bases1 assuming the common height of ,fh1 or ,,nq2 the ,aggregate of which is ,nh1 or ,,fq4 ,and1 so many times #a1 by so many equal ,spaces1 on the same ,bases1 between the same ,parallels1 terminated at the ,hyperbola3 ,the ,aggregate of which is h,f,n,qn4 ,from whence if we subduct the ,aggregate of ,ablatives ,,fy2 the remaining ,trilinear h,qn1 represents the ,descent4 #ej4 ,if to this of ,gravity1 be joined a projecting ,force2 which is to the ,impulse of ,gravity as h,k to h,f 7be it greater1 less1 or equal7 taken in the same ,line2 the same ,parallels determine proportional ,parallelograms1 whose ,aggregate is ,,kq4 #ea4 ,and therefore if this be a perpendicular ,projection downwards2 then h,kkn 7the ,sum of this with the former7 represents the ,descent4 #eb4 ,if it be a ,perpendicular upwards2 then the difference of these two represents the ,motion2 which so long as ,,kq is the greater1 is ,ascendent2 but ,descendent1 when h,qn becomes greater2 and it is then at the highest when they be equal4 #ec4 ,if the ,projection be not in the same ,perpendicular1 7but ,horizontal1 or ,oblique7 then ,,kq represents the ,tangent of the ,curve2 and h,qn the ,ordinates to that ,tangent1 at the given ,angle4 #ed4 ,but the ,computation before given1 ,i take to be of better use than this ,representation in ,figure4 ,because in such ,mathematical ,enquiries1 ,i choose to separate 7as much as may be7 what purely concerns ,proportions2 and consider it abstractly from ,lines1 or other ,matter wherewith it is incumbred4 ,as to the ,question proposed2 whether the resistance of the ,medium do not always take off such a proportional part of the ,force moving through it1 as is the specifick ,gravity of the ,medium to that of the ,body moved in it3 7,for1 if so1 it will save us the trouble of ,observation47 ,i think this can by no means be admitted4 ,for there be many other things of ,consideration herein1 beside the intensive ,gravity 7or1 as some call it1 the specifick ,gravity7 of the ,medium4 ,a viscous ,medium shall more resist1 than one more fluid1 though of like intensive ,gravity4 ,and a sharp ,arrow shall bore his way more easily through the ,medium1 than a blunt-headed ,bolt1 though of equal ,weight1 and like intensive ,gravity4 ,and the same ,pyramid with the ,point1 than with the ,base forward4 ,and many other like ,varieties1 intended in my #dh4 ,but this ,i think may be admitted1 namely1 ,that different ,mediums1 equally liquid1 7and other ,circumstances alike17 do in such proportion resist1 as is their intensive ,gravity4 ,because there is1 in such proportion1 a heavier ,object to be removed1 by the same ,force4 ,which is one of the things to which #cc refers4 ,and again3 ,the heavier ,project once in ,motion1 7being equally swift1 and all other ,circumstances alike7 moves through the same ,medium in such proportion more strongly1 as is its intensive ,gravity4 ,for now the ,force is in such proportion greater1 for the removal of the same resistance4 ,and this ,part of what my #cb1 insinuates4 ,but where there is a ,complication of these ,considerations one with another1 and with many other ,circumstances1 whereof each is severally to be considered2 there must be respect had to all of them4 #ad ,r - #a,v7 ,r 7,v ,v_/,r1 ,v_/,,rr1 c4 ,,vr - ,v -------- ,v ,v_/,,vr ------- ,v_/,r ,,vv_/,,rrr -------- ,v_/,,rr c4 #ae m - #a7 #a 7#a_/m #a_/mm #a_/m c4 #a - #a_/m ------- #a_/m #a_/m - #a_/mm -------------- #a_/mm #a_/mm - #a_/mmm ---------------- #a_/mmm c4 #af #a #a #a #a #a #a #a #a #a #a c4 #ag #a --- m #a #a ----- --- m m #a #a #a ----- ----- --- m m m #a #a #a #a ----- ----- ----- --- m m m m ,an ,instance of the ,excellence of the ,modern ,algebra1 in the ,resolution of the ,problem of finding the ,foci of ,optick ,glasses ,universally4 ,by ,e4 ,halley1 ,s4 ,r4 ,s4 ,the ,excellence of the ,modern ,geometry is in nothing more evident1 than in those full and adequate ,solutions it gives to ,problems2 representing all the possible ,cases at one view1 and in one general ,theorem1 many times comprehending whole ,sciences2 which deduced at length into ,propositions1 and demonstrated after the manner of the ,ancients1 might well become the ,subjects of large ,treatises3 ,for whatsoever ,theorem solves the most complicated ,problem of the kind1 does with a due ,reduction reach all the subordinate ,cases4 ,of this ,i now design to give a notable ,instance in the ,doctrine of ,dioptricks4 ,this ,dioptrick ,problem is that of finding the ,focus of any sort of ,lens1 exposed either to converging1 diverging1 or parallel ,rays of ,light1 proceeding from1 or tending to a given ,point in the ,axis of the ,lens1 be the ,ratio of ,refraction what it will1 according to the ,nature of the transparent ,material whereof the ,lens is formed1 and also with allowance for the thickness of the ,lens between the ,vertices of the two ,spherical ,segments4 ,this ,problem being solved in one ,case1 mutatis mutandis1 will exhibit ,theorems for all the possible ,cases1 whether the ,lens be ,double-,convex or ,double-,concave1 ,plano-,convex1 or ,plano-,concave1 or ,convexo-,concave1 which sort are usually call'd ,menisci4 ,but this only to be understood of those ,beams which are nearest to the ,axis of the ,lens1 so as to occasion no sensible difference by their ,inclination thereto2 and the ,focus here formed1 is by ,dioptrick ,writers commonly call'd the principal ,focus1 being that of use in ,telescopes and ,microscopes4 ,let then 7in ,fig4 #g4 ,tab4 #e47 ,,be be a double ,convex ,lens1 ,c the ,center of the ,segment ,,eb1 and ,k the ,center of the ,segment ,e1 ,b the thickness of the ,lens1 ,d a ,point in the ,axis of the ,lens2 and it is required to find the ,point ,f1 at which the ,beams proceeding from the ,point ,d1 are collected therein1 the ,ratio of ,refraction being as m to n4 ,let the distance of the ,object ,,db ,,da d 7the ,point ,a being supposed the same with ,b1 but taken at a distance therefrom1 to prevent the coincidence of so many ,lines7 the ,radius of the ,segment towards the ,object ,,cb or ,,ca r1 and the ,radius of the ,segment from the ,object ,k or ,k 2 and let ,b the thickness of the ,lens be t1 and then let the ,sine of the ,angle of ,incidence ,,dag be to the ,sine of the refracted ,angle ,,hag or ,,ca as m to n3 ,and in very small ,angles1 the ,angles themselves will be in the same proportion2 whence it will follow that1 ,as d to r1 so the ,angle at ,c to the ,angle at ,d1 and d r will be as the ,angle of ,incidence ,,gad2 and again as m to n1 so d r to 7dn rn7_/m1 which will be as the ,angle ,,gah ,,ca2 ,this being taken from ,,acd which is as d1 will leave 7m - nd - nr7_/m analogous to the ,angle ,a,d2 and the ,sides being in this ,case proportional to the ,angles they subtend1 it will follow1 that as the ,angle ,a,d is to the ,angle ,,ad1 so is the ,side ,,ad or ,,bd to ,a or ,b3 ,that is1 ,b will be mdr_/7m - nd - nr71 which shews in what ,point the ,beams proceeding from ,d1 would be collected by means of the first ,refraction2 but if nr cannot be subtracted from m - nd1 it follows that the ,beams after ,refraction do still pass on diverging1 and the ,point is on the same side of the ,lens beyond ,d4 ,but if nr be equal to m - nd1 then they proceed parallel to the ,axis1 and the ,point is infinitely distant4 ,the ,point being found as before1 and ,b - ,b being given1 which we will call 1 it follows by a ,process like the former1 that ,f1 or the focal ,distance sought1 is equal to n_/7m - m7 f4 ,and in the room of substituting ,b - ,b mdr_/7m - nd - nr7 - t1 putting p for n_/7m - n71 after due ,reduction this following ,equation will arise1 7mpdr - ndt nprt7_/7mdr md - mpr - m - ndt nrt7 f4 ,which ,theorem1 however it may seem operose1 is not so1 considering the great ,number of ,data that enter the ,question2 and that one half of the ,terms arise from our taking in the thickness of the ,lens1 which in most ,cases can produce no great ,effect2 however it was necessary to consider it1 to make our ,rule perfect4 ,if therefore the ,lens consist of ,glass1 whose ,refraction is as #c to #b 'twill be 7#f;dr - #b;dt #drt7_/7#c;dr #c;d - #fr - dt #brt7 f4 ,if of ,water1 whose ,refraction is as #d to #c1 the ,theorem will stand thus 7#ab;dr - #c;dt #irt7_/7#d;dr #d;d - #abr - dt #crt7 f4 ,if it could be made of ,diamant1 whose ,refraction is as #e to #b1 it would be 77#aj_/c7;dr - #b;dt 7#d_/c7rt7_/7#e;dr #e;d - 7#aj_/c7r - #c;dt #brt7 f4 ,and this is the universal ,rule for the ,foci of double ,convex ,glasses exposed to diverging ,rays4 ,but if the thickness of the ,lens be rejected1 as not sensible1 the ,rule will be much shorter1 viz4 pdr_/7dr d - prt7 f1 or in ,glass #b;dr_/7dr d - #br7 f1 all the ,terms wherein t is found being omitted1 as equal to nothing4 ,in this ,case1 if d be so small1 as that #br exceed dr d1 then will it be - f1 or the ,focus will be ,negative1 which shews that the ,beams after both ,refractions still proceed diverging4 ,to bring this to the other ,cases1 as of converging ,beams1 or of ,concave ,glasses1 the ,rule is ever composed of the same ,terms1 only changing the ,signs of and -2 for the distance of the ,point of ,concourse of converging ,beams1 from the ,point ,b1 or the first ,surface of the ,lens1 ,i call a negative ,distance or - d2 and the ,radius of a ,concave ,lens ,i call a negative ,radius1 or - r if it be the first ,surface1 and - if it be the second ,surface4 ,let then converging ,beams fall on a double ,convex of ,glass1 and the ,theorem will stand thus - #b;dr_/7- dr - d - #brt7 f1 which shews that in this ,case the ,focus is always affirmative4 ,if the ,lens were a ,meniscus of ,glass1 exposed to diverging ,beams1 the ,rule is - #b;dr_/7- dr d #br7 f1 which is affirmative when #br is less than dr - d otherwise negative3 ,but in the ,case of converging ,beams falling on the same ,meniscus1 'twill be #b;dr_/7 dr - d #brp7 f1 and it will be f1 whilst d - dr is less than #br2 but if it be greater than #br1 it will always be found negative or - f4 ,if the ,lens be double ,concave1 the ,focus of converging ,beams is negative1 where it was affirmative in the ,case of diverging ,beams on a double ,convex1 viz4 - #b;dr_/7 dr d - #br7 f1 which is affirmative only when #br exceeds dr d3 ,but diverging ,beams passing a double ,concave1 have always a negative ,focus1 viz4 - #b;dr_/7 dr d #br7 - f4 ,the ,theorems for converging ,beams1 are principally of use to determine the ,focus resulting from any sort of ,lens placed in a ,telescope1 between the ,focus of the ,object-,glass and the ,glass it self2 the distance between the said ,focus of the ,object-,glass1 and the interposed ,lens being made - d4 ,i here suppose my ,reader acquainted with the ,rules of ,analytical ,multiplication and ,division1 as that multiplied by makes the ,product 1 by - makes -1 and - by - makes 2 so dividing by makes the ,quote 1 by - makes -1 and - by - makes 2 which will be necessary to be understood in the preceding ,examples4 ,in case the ,beams are parallel1 as coming from an infinite distance1 7which is supposed in the ,case of ,telescopes7 then will d be supposed ,infinite1 and in the ,theorem pdr_/7dr d - pr7 the ,term pr vanishes1 as being finite1 which is no part of the other infinite ,terms2 and dividing the ,remainder by the infinite ,part d1 the ,theorem will stand thus pr_/7r 7 f1 or in ,glass1 #br_/7r 7 f4 ,in case the ,lens were ,plano-,convex exposed to diverging ,beams1 instead of pdr_/7dr d - pr71 r being infinite1 it will be pd_/7d - p7 f1 or #b;d_/7d - #b7 if the ,lens be ,glass4 ,if the ,lens be ,double-,convex1 and r be equal to 1 as being formed of ,segments of equal ,spheres1 then will 7pdr7_/7dr d - pr7 be reduced to 7pdr_/7#b;d - pr77f2 and in case d be infinite1 then it will yet be farther contracted to pr1 and p being n_/7m - n71 the focal distance in ,glass will be r1 in ,water #ar1 but in ,diamant r4 ,i am sensible that these ,examples are too much for the compleat ,analyst1 though ,i fear too little for the less ,skilful2 it being very hard1 if possible1 in such ,matters1 so to write1 as to give satisfaction to both2 or to please the one1 and instruct the other4 ,but this may suffice to shew the extent of our ,theorem1 and how easie a ,reduction adapts any one case to all the rest4 ,nor is this only useful to discover the ,focus from the other proposed data1 but from the ,focus given1 we may thereby determine the distance of the ,object2 or from the ,focus and ,distance given1 we may find of what ,sphere it is requisite to take another ,segment1 to make any given ,segment of another ,sphere cast the ,beams from the distance d to the ,focus f4 ,as likewise from the ,lens1 ,focus1 and ,distance given1 to find the ,ratio of ,refraction1 or of m to n1 requisite to answer those ,data4 ,all which it is obvious1 are fully determined from the ,equation we have hitherto used1 viz4 pdr drf df - prf1 for to find d the ,theorem is 7prf7_/7rf f - pr7 d1 the distance of the ,object4 ,for the ,rule is drf_/7pdr df prf7 4 ,but for p will be 7drf df7_/7dr fr7 p1 which latter determines the ,ratio of ,refraction1 m being to n1 as #a p to p4 ,i shall not expatiate on these ,particulars1 but leave them for the ,exercise of those that are desirous to be informed in ,optical ,matters1 which ,i am bold to say are comprehended in these three ,rules1 as fully as the most ,inquisitive can desire them1 and in all possible ,cases2 regard being had to the ,signs and -1 as in the former ,cases of finding the ,focus4 ,i shall only shew two considerable ,uses of them2 the one to find the distance whereat an ,object being plac'd1 shall by a given ,lens be represented in a ,species as large as the ,object it self1 which may be of singular ,use in drawing ,faces and other things in their true ,magnitude1 by transmitting the ,species by a ,glass into a dark ,room1 which will not only give the true ,figure and ,shades1 but even the ,colours themselves1 almost as vivid as the ,life4 ,in this ,case d is equal to f1 and substituting d for f in the ,equation1 we shall have pdr ddr dd - dpr1 and dividing all by dpr dr d - pr1 that is1 #bpr_/7r 7 d2 but if the two ,convexities be of the same ,sphere so as r 1 then will the distance be pr2 that is1 if the ,lens be ,glass #br1 so that if an ,object be placed at the ,diameter of the ,sphere distant1 in this ,case the ,focus will be as far within as the ,object is without1 and the ,species represented thereby will be as big as the ,life2 but if it were a ,plano-,convex1 the same distance will be #bpr1 or in ,glass to four times the ,radius of the ,convexity2 but of this ,method ,i may entertain the ,curious at some other ,time1 and shew how to magnifie or diminish an ,object in any proportion assign'd1 7which yet will be obvious enough from what is here deliver'd7 as likewise how to erect the ,object which in this ,method is represented inverted4 ,a ,second ,use is to find what ,convexity or ,concavity is required1 to make a vastly distant ,object be represented at a given ,focus1 after the one ,surface of the ,lens is formed2 which is but a ,corollary of our ,theorem for finding 1 having p1 d1 r and f given2 for d being infinite1 that ,rule becomes rf_/7pr - f7 1 that is in ,glass rf_/7#br - f7 1 whence if f be greater than #br1 becomes ,negative1 and rf_/7f - #br7 is the ,radius of the ,concave sought4 ,those that are wholly to begin with this ,dioptrical ,science1 cannot do better than to read with ,attention a late ,treatise of ,dioptricks1 published by ,w4 ,molineux1 ,esq1 ,r4 ,s4 ,s4 who has at large shewn the ,nature of ,optick ,glasses1 and the ,construction and ,use of ,microscopes and ,telescopes2 and though some nicely ,critical have endeavour'd to spy ,faults1 and to traduce the ,book2 yet having long since examin'd it with ,care1 ,i affirm1 that if ,i can judge1 it hath but two things that with any ,colour may be call'd ,faults2 the one1 an over-careful acknowledgment of every ,trifle the ,author had receiv'd from others2 and the other that he labours to make easie this curious ,subject1 so little understood by most1 in a manner perhaps too familiar for the ,learned ,critick1 and which demonstrates that it was writ cum animo docendi1 both which require but very little ,friendship or good ,nature in the ,reader1 to pass for ,vertues in an ,author4 ,illustration3 ,tab4 #e4 pag4 #cei ,but to return to our first ,theorem1 which accounting for the thickness of the ,lens1 we will here again resume1 viz4 7mpdr - ndt nprt7_/7mdr md - mpr - m - ndt nrt7 f4 ,and let it be required to find the ,focus where a whole ,sphere will collect the ,beams proceeding from an ,object at the distance d3 ,here t is equal to #br1 and r equal to 4 ,and after due ,reduction1 the ,theorem will stand thus1 7mpdr - #bndr #bnprr7_/7#bnd #bnr - mpr7 f2 but if d be ,infinite1 it is contracted to mpr_/#bn - r 77#bn - m7_/7#bm - #bn77r f1 wherefore a ,sphere of ,glass collects the ,sun-,beams at half the ,semi-diameter of the ,sphere without it1 and a ,sphere of ,water at a whole ,semi-diameter4 ,but if the ,ratio of ,refraction m to n be as #b to #a1 the ,focus falls on the opposite ,surface of the ,sphere2 but if it be of greater ,inequality it falls within4 ,another ,example shall be when a ,hemisphere is exposed to parallel ,rays1 that is1 d and being infinite1 and t r1 and after due ,reduction the ,theorem results 7nn_/7mm - mn77r f4 ,that is1 in ,glass it is at #d_/cr1 in ,water at #i_/dr2 but if the ,hemisphere were ,diamant1 it would collect the ,beams at #a-d_/ae of the ,radius beyond the ,center4 ,lastly1 ,as to the ,effect of turning the two sides of a ,lens towards an ,object2 it is evident1 that if the thickness of the ,lens be very small1 so as that you neglect it1 or account t #j2 then in all ,cases the ,focus of the same ,lens1 to whatsoever ,beams1 will be the same1 without any difference upon the turning the ,lens3 ,but if you are so curious as to consider the thickness1 7which is seldom worth accounting for7 in the ,case of parallel ,rays falling on a ,plano-,convex of ,glass1 if the plain side be towards the ,object1 t does occasion no difference1 but the focal distance f #br4 ,but when the ,convex-side is towards the ,object1 it is contracted to #br - t1 so that the ,focus is nearer by t4 ,if the ,lens be double ,convex1 the difference is less2 if a ,meniscus1 greater4 ,if the ,convexity on both sides be equal1 the focal length is about t shorter than when t #j4 ,in a ,meniscus the ,concave-side towards the ,object increases the focal ,length1 but the ,convex towards the ,object diminishes it4 ,a ,general ,rule for the difference arising on turning the ,lens1 where the ,focus is ,affirmative1 is this 7#brt - #bt7_/7#cr #c - t71 for double ,convexes of differing ,spheres4 ,but for ,menisci the same difference becomes 7#brt #bt7_/7#cr - #c t72 of which ,i need give no other ,demonstration1 but that by a due ,reduction it will so follow from what is premised1 as will the ,theorems for all sorts of ,problems relating to the ,foci of ,optick-,glasses4 ,,appendix4 ,an ,analytical ,resolution of certain ,equations of the ,third1 ,fifth1 ,seventh1 ,ninth ,powers1 and so on ad ,infinitum1 in finite ,terms1 after the manner of ,cardan's ,rules for ,cubicks4 ,by ,mr4 ,a4 ,moivre1 ,transact4 ,n #cji4 ,let 7n7 be any ,number1 7y7 an unknown ,quantity1 or ,root of the ,equation1 7a7 a ,quantity altogether known1 or what they call ,homogeneum ,comparationis3 ,and let the ,relation of these ,quantities to each other be exprest by the ,equation4 ny 77nn - #a7_/7b #c77ny 77nn - #a7_/7b #c77 77nn - #i7_/7d #e77ny 77nn - #a7_/7b #c77 77nn - #i7_/7d #e77 77nn - #be7_/7f #g77ny1 c4 a4 ,its plain from the ,nature of this ,series1 that if n be any odd ,number 7that is an ,integer1 it matters not whether ,affirmative or ,negative7 then the ,series will ,terminate1 and the ,equation arising will be one of the above defin'd1 whose ,root is 7#a7 y 77#a aa7 a7 - _/77#a aa7 a7 or1 7#b7 y 77#a aa7 a7 - 77#a aa7 - a7 or1 7#c7 y _/77#a aa7 - a7 - 77#a aa7 - a7 or1 7#d7 y _/77#a aa7 - a7 - _/77#a aa7 a7 ,for ,example1 ,let the ,root of this ,equation of the ,fifth ,power be required #ey #bjy #afy #d in which case n is #e1 and a #d1 and the ,root1 according to the first ,form1 is y 77#ag #d77 - _/77#ag #d77 which is ,expeditiously resolved into ,numbers after this manner4 #ag #d is equal to #h4abca1 whose ,logarithm is #j1ijigafd1 and the fifth part of it is #j1ahaidcc1 the ,number answering it #a4ebjc 7#ag #d74 ,but the ,arithmetical ,complement of #j4fegg is #i4hahjefg1 the ,number answering is #j4ahaidcc #a_/7ag #d7 and the half difference of these ,numbers is #j1dcac y4 ,here we may observe1 that in the ,room of the general ,root1 we may advantageously take y 7#b;a7 - _/7#b;a7 if the quantity a be pretty large in respect of ,unity4 ,as if the ,equation were #ey #bjy #afy #fhb1 the ,logarithm of #b;a #c4acdhadc whose ,fifth part is #j4fbfifbh1 the ,number answering is #d4bcf1 and the ,number answering the ,arithmetical ,complement #i4cgcjcgb is #j4bcf1 the half difference of these ,numbers is #b y4 ,but if in the aforegoing ,equation the ,signs are alternately ,affirmative and ,negative2 or which is the same thing if the ,series be after this manner1 ny 77#a - nn7_/7#b #c77ny 77#a - nn7_/7#b #c77 77#i - nn7_/7#d #e77ny 77#a - nn7_/7#b #c77 77#i - nn7_/7#d #e77 77#be - nn7_/7#f #g77ny c4 a4 ,the ,root of it will be equal to 7#a7 y 7a 7aa - #a77 _/7a 7aa - #a771 or 7#b7 y 7a 7aa - #a77 7a - 7aa - #a771 or 7#c7 y _/7a - 7aa - #a77 7a - 7aa - #a771 or 7#d7 y _/7a - 7aa - #a77 _/7a 7aa - #a774 ,here it is to be noted1 that if 7n - #a7_/b be an odd ,number1 the ,sign of the ,root found must be contrary to it4 ,let an ,equation be propos'd #ey - #bjy #afy #f1 whence n #e1 and a #f1 and the ,root will be 7#f 7#ce77 _/7#f 7#ce77 or because #f #ce #aa4iaf whose ,logarithm is #a4jgfacjd1 and its ,fifth part is #j4baebefa1 whose ,arithmetical ,complement is #i4ghdgdci4 ,the ,numbers belonging to these ,logarithms are #a4fdae and #j4fjia1 whose half ,sum is #a4abec y4 ,but if it happen that a is less than ,unity then the ,second ,form1 as being more convenient1 ought to be pitch'd on4 ,so if the ,equation had been #ey - #bjy #afy #fa_/fd1 then y will be 7#fa_/fd 7-#cge_/djif77 7#fa_/fd - 7-#cge_/djif77 and if the ,root of the ,fifth ,power can by any means be ,extracted the true and possible ,root of the ,equation1 will thence ,emerge1 tho' the ,expression seems to insinuate an ,impossibility4 ,but the ,root of the ,fifth ,power of the ,binomial #fa_/fd 7-#cge_/djif7 is 7-#ae7 and so the same ,root of the ,binomial #fa_/fd 7-#cge_/djif7 is - 7-#ae7 the half ,sum of which ,roots is y4 ,but if that ,extraction can not be perform'd1 or may seem too difficult1 the thing may be solv'd by the help of a ,table of ,natural ,sines1 after the following manner2 ,to the ,radius #a let a #fa_/fd #j1ieaab the ,sine of some ,arch which is therefore #gb #bc'1 whose ,fifth part 7because n is equal to #e7 is #ad #bh' the ,sine of it is #j4bdiha nearly4 ,the same is the ,method of proceeding in ,equations of higher ,dimensions4 ,a ,discourse concerning the ,action of the ,sun and ,moon on ,animal ,bodies2 and the ,influence which ,this may have in many ,diseases4 ,by ,richard ,mead1 ,m4 ,d4 ,f4 ,r4 ,s4 ,,part ,i4 ,that some ,diseases are properly the ,effects of the ,influence of the ,heavenly ,bodies1 and that others do vary their ,periods and ,symptoms according to the different ,positions of one or other of those ,luminous ,globes1 is a very ancient and certain ,observation4 ,upon this score ,hippocrates#ah advises his ,son ,thessalus to the study of ,geometry and ,numbers1 because the ,knowledge of the ,stars is of very great use in ,physick#ai4 ,and the earliest ,histories of ,epidemic ,distempers1 particularly do all turn upon the alterations made in our ,bodies by the ,heavens4 ,but when in later ,times ,medicine came to be accommodated to the ,reasonings of ,philosophers2 no body being able to account for the manner of this ,celestial ,action1 ,it was allowed no farther share in affecting our ,health1 than what might be imputed to the changes in the manifest ,constitution of the ,air1 excepting perhaps something of ,truth which still remains disguised and blended with the ,jargon of ,judiciary ,astrology4 ,in order therefore to set this ,matter in a little clearer light1 ,i shall in the first place shew1 ,that the ,sun and ,moon regarding their ,nearness and ,direction to the ,earth only1 besides the ,effects of ,heat1 ,moisture1 c4 thereby caused in our ,atmosphere1 must at certain times make some ,alterations in all ,animal ,bodies2 then enumerate some ,histories and ,observations of such ,changes1 and enquire of what ,use such ,thoughts as these may be in the ,practice of ,physick4 ,it is a constant ,observation of those who write the ,history of the ,winds1 ,that the most ,windy ,seasons of the ,year1 are the ,time about the ,vernal and ,autumnal ,equinox2 for be the ,air never so calm before or after1 we never fail of having ,winds at that ,juncture4 ,every body likewise knows1 that in the most quiet ,weather we are sure of some ,breeze at ,mid-day and ,mid-night1 as also at ,full ,sea1 i4e4 always about the time the ,sun or ,moon arrive at the ,meridian4 ,seamen and ,country ,people reckon upon ,this1 and order their ,affairs accordingly4 ,and the changes of the ,weather as to ,winds or ,calms especially about the ,new and ,full ,moon1 are too well known to require any ,authority to confirm such ,remarks4 ,those who desire a fuller account of these ,observations1 may see it in ,de ,chales's ,navigation1 ,gassendus's ,natural ,philosophy1 and ,j4 ,goad1 his ,astro-,meteoro-,logica4 ,these things being ,matters of ,fact1 and in a manner ,regular and ,universal1 it may very well seem strange that ,philosophers have not been more accurate in their ,enquiries into the ,reason of such ,appearances4 ,true indeed it is1 that the ,origin of ,winds is various and uncertain1 but however1 so constant and uniform an ,effect must undoubtedly be owing to one necessary ,cause4 ,it has bin1 now a considerable time since1 sufficiently made out1 that our ,atmosphere is a thin ,elastic ,fluid1 one part of which gravitates upon another1 and whose ,pressure is communicated every way in a ,sphere to any given ,part thereof4 ,from hence it follows1 ,that if by any external ,cause the ,gravity of any one part shou'd be taken off or diminished1 that from all sides around this part1 the more heavy ,air would rush in to restore the ,equilibrium which must of necessity be preserved in all ,fluids4 ,now this violent running in of the heavier ,air would certainly produce a ,wind1 which is no more than a strong ,motion of the ,air in some determined ,direction4 ,if therefore we can find any outward ,cause that would at these stated ,seasons we have mentioned1 diminish the ,weight or ,pressure of the ,atmosphere2 we shall have the genuine ,reason of these ,periodical ,winds1 and the necessary ,consequences thereof4 ,the ,flux and ,reflux of the ,sea was a ,phnomenon too visible1 and too much conducing to the ,subsistance of ,mankind1 and all other ,animals1 to be neglected by those who applyed themselves to the ,study of ,nature2 however all their ,attempts to explain this ,admirable ,contrivance of infinite ,wisdom were unsuccessfull1 till ,sir ,isaac ,newton reveal'd to the ,world juster ,principles1 and by a truer ,philosophy than was formerly known1 shew'd us how by the ,united or ,divided ,forces of the ,sun and ,moon1 which are encreased and lessened by several ,circumstances1 all the ,varieties of the ,tides are to be accounted for4 ,and since all the ,changes we have enumerated in the ,atmosphere do fall out at the same times when those happen in the ,ocean2 and likewise whereas both the ,waters of the ,sea and the ,air of our ,earth1 are ,fluids subject1 in a great ,measure1 to the same ,laws of ,motion2 it is plain1 that the ,rule of our great ,philosopher takes place here1 viz4 ,that ,natural ,effects of the same kind are owing to the same ,causes4#bj ,what difference that known ,property of the ,air1 which is not in ,water1 makes in the ,case1 ,i shall shew anon2 setting aside the ,consideration of that for the present2 ,it is certain1 ,that as the ,sea is1 so must our ,air1 twice every #be ,hours1 be rais'd upwards to a considerable height1 by the ,attraction of the ,moon coming to the ,meridian2 so that instead of a ,spherical1 it must form it self into a ,spheroidal1 or ,oval ,figure1 whose longest ,diameter being produced1 would pass thro' the ,moon4 ,that the like ,raising must follow as often as the ,sun is in the ,meridian of any ,place1 either above or below the ,horizon4 ,moreover1 ,that this ,elevation is greatest upon the ,new and ,full ,moons1 because both ,sun and ,moon do then conspire in their ,attraction2 least on the ,quarters1 in that they then drawing different ways1 'tis only the ,difference of their ,actions produces the ,effect4 ,lastly1 ,that this ,intumescence will be of a middle degree1 at the time between the ,quarters1 and ,new and ,full ,moon4 ,from the same ,principles1 ,the ,motion upwards of the ,air will be strongest of all about the ,equinoxes2 the ,equinoctial ,line being over that ,circle of the ,globe1 which has the greatest ,diameter1 either of the ,luminaries when in that are nearer1 and the ,agitation of the ,fluid ,spheroid revolving about a greater ,circle1 is greater2 besides1 the ,centrifugal ,force 7arising from the ,diurnal ,rotation7 is there greatest of all4 ,this will still be more considerable about the ,new and ,full ,moons happening at these times1 for the ,reasons just now mentioned4 ,and the least ,attraction will be about the ,quadratures of these ,lunar ,months1 because the ,declination of the ,moon from the ,equator is then greatest4 ,the different distances of the ,moon in her ,perigum and ,apogum1 are the ,reason that these full changes fall out a little before the ,vernal1 and after the ,autumnal ,equinox4 ,now the ,inverse of all this happens when the ,luminaries are in the ,solstitial ,circles4 ,lastly1 ,in the same ,parallel1 when the ,moon's ,declination is towards the ,elevated ,pole1 the ,attraction is strongest when the ,moon is in that ,places ,meridian1 and weakest when she is in the ,opposite ,places ,meridian3 ,the contrary happens in the ,opposite ,parallel2 by reason of the ,spheroidal ,figure of the ,earth and its ,atmosphere4 ,whatever has been said on this ,head1 is no more that applying what ,sir ,isaac ,newton has ,demonstrated of the ,sea to our ,atmosphere2 and it is needless to shew how necessarily those ,appearances1 just now mentioned1 of ,winds1 at the ,stated ,times1 c4 must happen hereupon4 ,it will be of more use to consider the ,proportion of the ,forces of the two ,luminaries upon the ,air1 to that which they have upon the ,water of our ,globe2 that it may the more plainly appear what ,influence the ,alterations hereby made1 must have upon the ,animal ,body4 ,sir ,isaac ,newton has demonstrated#ba ,that the ,force of the ,sun to move the ,sea1 is to the ,force of ,gravity1 as #a to #abhfhbjj4 ,let that be ,s4 ,g 33 #a4 n4 ,hence1 ,s ,g_/n4 ,and that the ,force of the ,moon to raise the ,sea is to ,gravity1 as #a to #bjcahba4 ,let this be ,l4 ,g 33 #a4 s4 ,hence1 ,l ,g_/s4 ,and since the ,centrifugal force of the ,parts of the ,earth arising from its ,diurnal ,motion is to ,gravity1 as #a to #bia4 ,let this be ,c4 ,g 33 #a4 ,c4 ,then ,c ,g_/e4 ,hence1 7,s ,l74 ,c 33 7,g_/n ,g_/s74 ,g_/e 33 7#a_/n #a_/s74 #a_/;e 33 #a4 sn_/77s n7 e7 33 #a4 #fjca4 ,the same ,philosopher has taught us#bb that the ,centrifugal force raises the ,water at the ,equator above the ,water at the ,poles1 to the height of #hebjj ,feet4 ,wherefore if that ,force which is as #fjca1 raise the ,ocean to #hebjj ,feet1 the ,united forces of the ,sun and ,moon1 which are as #a4 will raise the same to #ad ,feet1 for #hebjj_/fjca #ad4 ,proxim4 ,now we know that the more easily the ,waters can obey the ,attraction1 with the more ,force are the ,tides moved2 but since1 as ,mr4 ,halley has determin'd it1#bc our ,atmosphere is extended to #de ,miles1 whereas the middle depth of the ,ocean is but about half a ,mile2 it is plain1 that the ,air revolving in a ,sphere about #ajj times larger than that of the ,ocean1 will have a proportionably greater ,agitation4 ,besides1 ,rocks1 ,shelves1 and the inequality of ,shoars are a great stop to the ,access and ,recess of the ,sea3 ,but nothing repels the rising ,air1 which is also of such thinness and fluidity1 that it is easily driven1 and runs every way4 ,nor ought we to omit1 that it is the universal ,law of ,bodies ,attracted1 that the ,force of ,attraction is reciprocally as the ,squares of their ,distances2 so that the ,action of the ,sun and ,moon will be greater upon the ,air than upon the ,water1 upon the ,account of its ,nearness4 ,but the ,consideration of the ,elasticity is still of greater ,moment here1 of which this is the nature1 that it is reciprocally as the ,pressure1 so that the incumbent ,weight being diminished by the ,attraction1 the ,air underneath will upon this score be mightily expanded4 ,these and such like ,causes will make the ,tides in the ,air to be much greater than those of the ,ocean2 nor is it necessary to our purpose to determine1 by nice ,calculations1 their particular ,forces2 it is sufficient to have proved that these ,motions must both be ,universal1 and also return at certain ,intervals4 ,now since the raising of the ,water of the ,ocean #ad ,feet1 produces ,torrents of such a prodigious ,force1 we may easily conceive what ,tempests of ,winds 7if not otherwise check'd7 the ,elevation of the ,air much higher 7perhaps above a ,mile7 will necessarily cause4 ,and there is no doubt to be made1 but that the same infinitely ,wise ,being1 who contrived the ,flux and ,reflux of the ,sea1 to secure that vast ,collection of ,waters from ,stagnation and ,corruption 7which would inevitably destroy all the ,animals and ,vegetables on this ,globe7 has ordered this ,ebb and ,flood of the ,air of our ,atmosphere1 with the like good design1 that is to preserve 7in ,case all other ,causes should fail1 as they may1 and at times do in some ,countries7 the sweet ,freshness1 and brisk ,temper of this ,fluid1 so necessary to ,life1 and keep it1 by a kind of continual ,circulation1 from ,deadness and ,stinking4 ,this ,reasoning is liable to only one ,objection that ,i know of1 and that is this3 ,that the ,appearances we have mention'd cannot be owing to the ,causes now assigned2 since by ,calculation from them1 the ,mercury must at ,new and ,full ,moon subside in the ,barometer to a certain degree1 which yet we do not observe to happen4 ,in answer to which1 7besides that there have been some ,observations made of the sinking of the ,mercury at those times2 and it may perhaps be the fault of the ,observers that these have not been reduced to any ,rule7 ,we are to ,consider1 ,that altho' ,winds and ,alterations in the ,pressure of the ,atmosphere1 are the necessary consequents of the ,lunar ,attraction1 and true ,causes of the different ,rise of the ,mercury in the ,barometer2 yet these may be produced many others ways too1 and therefore tho' regularly the ,mercury would always fall at the ,new and ,full ,moon1 those other ,causes may be strong enough1 even to raise it at those ,seasons2 in as much as two contrary ,winds1 for instance1 blowing towards the ,place of ,observation1 may accumulate the ,air there1 so as to increase both the height and weight of the incumbent ,cylinder2 in like manner1 the ,direction of two ,winds may be such1 as meeting at certain ,angle they may keep the ,gravity of the ,air in the middle place unaltered2 and a ,thousand such ,varieties there may be1 by which the ,regularity of ,appearances of this nature may be hindered4 ,now the other ,springs1 from which such ,changes in the ,air may arise1 are these4 #a4 ,elastic ,vapours forc'd from the ,bowels of the ,earth1 by ,subterraneous ,heats1 and condensed by whatever cause in the ,atmosphere4 #b4 ,a mixture of ,effluvia of different qualities in the ,air1 may by ,rarefactions1 ,fermentations1 c4 produce ,winds and other ,effects like those resulting from the ,combination of some ,chymical ,liquors2 and that such things happen1 we are assured from the ,nature of ,thunder1 ,lightning1 and ,meteors4 #c4 ,from the ,eruptions of ,vulcanoes and ,earthquakes in distant ,places1 ,winds may be propagated to remoter ,countries4 #d4 ,the divided or ,united ,forces of the other ,planets and of ,comets1 may variously disturb the influence of the ,sun and ,moon1 c4 ,we know that there happen violent ,tempests in the upper ,regions of the ,air1 while we below enjoy a ,calm2 and how many ,ridges of ,mountains there are on our ,globe1 which interrupt and check the ,propagation of the ,winds2 so that it is no wonder that the ,phnomena we have ascribed to the ,action of the ,sun and ,moon1 are not always constant and uniform1 and that every ,effect does not hereupon follow2 which1 were there no other ,powers in ,nature able to alter the influence of this1 might in a very regular and uniform manner be expected from it4 ,these things being premised1 it will not be difficult to shew 7as was proposed in the first ,place7 that these ,changes in our ,atmosphere at ,high ,water1 ,new and ,full ,moon1 the quinoxes1 c4 must occasion some ,alterations in all ,animal ,bodies2 and that from the following ,considerations4 #a4 ,all living ,creatures require ,air of a determined ,gravity to perform ,respiration easily1 and with ,advantage2 for it is by its weight that this ,fluid insinuates it self into the ,cavity of the ,breast and ,lungs4 ,now the ,gravity1 as we have proved1 being lessened at these ,seasons1 a smaller quantity only will insinuate it self1 and this must be of smaller force to comminute the ,blood1 and forward its ,passage into the left ,ventricle of the ,heart1 whence a slower ,circulation insues1 and the ,secretion of ,spirits is diminished4 #b4 ,this ,effect will be the more sure1 in that the ,elasticity of the ,atmosphere is likewise diminished4 ,animals want ,air as heavy so ,elastic to a certain degree2 ,for as this is by its weight forced into the ,cavity of the ,thorax in ,inspiration1 so the ,muscles of the ,abdomen press it into the ,bronchi in ,expiration1 where the bending force being somewhat taken off1 and ,springy ,bodies when unbended1 exerting their ,power every way1 in ,proportion to their ,pressures1 the ,parts of the ,air push against all the sides of the ,vesicul1 and promote the ,passage of the ,blood4 ,we have a convincing ,instance of all this1 in those who go to the top of high ,mountains1 for the ,air is there so pure 7as they call it7 that is1 wants so much of its ,gravity and ,elasticity1 that they ,breathe with very great difficulty4 #c4 ,all the ,fluids in ,animals have in them a mixture of ,elastic ,aura1 which when set at liberty1 shews its ,energy1 and causes those ,fermentations we observe in the ,blood and ,spirits3 ,now when the ,pressure of the ,atmosphere1 upon the ,surface of our ,body is diminished1 the inward ,air in the ,vessels must necessarily be inabled to exert its ,force1 in ,proportion to the lessening the ,gravity and ,elasticity of the outward2 hereupon the ,juices begin to ferment1 change the ,union and ,cohsion of their ,parts1 break their ,canals1 c4 ,this is very plain in living ,creatures put into the ,receiver1 exhausted by the ,air-,pump1 which always swell as the ,air is more and more drawn out2 their ,lungs at the same time contracting themselves1 and falling so together as to be hardly discernible4#bd ,e're we proceed to ,matters of ,fact1 it may be worth the while to take ,notice1 ,that ,effects depending on such ,causes as these1 must of necessity be most visible in ,weak ,bodies and ,morbid ,constitutions1 when other ,circumstances concur to their taking ,place4 ,for this reason1 whatever ,mischiefs do hence follow1 cannot in the least disparage the ,wise ,contrivance of ,infinite ,power in ordering these ,tides of our ,atmosphere4 ,the ,author of ,nature1 we know1 has made all things to the greatest ,advantage that could be1 for the whole ,system of ,animals on our ,globe1 but it was impossible that such a disposition shou'd not in some ,cases be prejudicial to a ,few4 ,the ,position and ,distance of the ,sun are so adjusted1 as to give in the most beneficial manner possible1 ,heat and ,light to the ,earth2 yet this notwithstanding1 some ,places may be too hot for some weakly ,bodies2 some ,autumns too sultry to agree with some ,animals1 and some ,winters too cold to be endured by some tender ,creatures3 ,the whole however we must own1 is most carefully provided for4 ,besides1 as most of these last mentioned ,inconveniencies are by easy shifts to be avoided2 so there are such ,powerful ,checks put to this ,aereal ,flux and ,reflux1 so many ways of abating the ,damages accruing from it now and then2 that these are of no account in comparison of the mighty ,benefits hence arising1 in which the ,race of ,mankind does universally share4 #ah ,epist4 ad ,thessalum ,filium4 #ai 4 ,de ,aere ,aquis ,locis4 #bj ,newton1 ,princip4 p4 #djb4 #ba ,princip4 ,lib4 #c4 ,prop4 #cf4 #bb ,ibid4 ,lib4 #c4 ,prop4 #cg4 #bc ,philos4 ,trans4 ,n #aha4 #bd ,esperienze dell' ,academia del ,cimento1 p4m4 #aac4 ,,part ,,ii4 ,there are no ,historys in ,physick which we may more safely take upon the ,credit of the ,authors who relate 'em1 than such as we are now going to mention4 ,in some ,cases a ,point may perhaps be strained to serve a darling ,hypothesis which the ,writer has taken up1 but here we are much more likely to have pure ,matter of ,fact1 because hitherto no one has pretended the ,appearances of this kind to be within the ,reach of any ,scheme of ,philosophy4 ,epileptical ,diseases besides the other ,difficultys with which they are attended1 have this also surprizing1 that in some the ,fits do constantly return every ,new and ,full ,moon2 the ,moon 7says ,galen#be7 governs the ,periods of ,epileptic ,cases4 ,upon this score1 ,they who were thus affected were called #bf and in the ,historys of the ,gospel #bg by some of the ,latins afterwards1 ,lunatici#bh4 ,bartholin#bi tells a ,story of one ,epileptic who had apparent ,spots in her ,face1 which according to the ,time of the ,moon1 varyed both their ,colour and ,magnitude4 ,but no greater ,consent in such ,cases was perhaps ever ,observed than what ,i saw some time since in a ,child about #e years old1 in which the ,convulsions were so strong and frequent1 that life was almost despair'd of1 and by ,evacuations and other ,medicines very difficultly saved4 ,the ,girl1 who was of a lusty full habit of ,body1 continued well for a few days1 but was at ,full ,moon again seized with a most violent ,fit1 after which1 the ,disease kept its ,periods constant and regular with the ,tides2 ,she lay always ,speechless during the whole time of ,flood1 and ,recovered upon the ,ebb4 ,the ,father who lives by the ,thames side1 and does business upon the ,river1 observed these ,returns to be so punctual1 that not only coming home ,he knew how the ,child was before he saw it1 but in the night has risen to his ,employ1 being warned by ,cries when coming out of her ,fit1 of the turning of the ,water4 ,this continued #ad days1 that is1 to the next great ,change of the ,moon1 and then a dry ,scab on the ,crown of the ,head1 7the effect of an ,epispastic ,plaister1 with which ,i had covered the whole ,occiput in the beginning of the ,illness7 broke1 and from the ,sore1 tho' there had been no sensible ,discharge this way for above a ,fortnight1 ran a considerable quantity of limpid ,serum2 upon which1 the ,fits returning no more1 ,i took great care to promote this new ,evacuation by proper ,applications1 with desired ,success1 for some time2 and when it ceased1 besides two or three ,purges with ,mercurius ,dulcis1 c4 ordered an ,issue in the ,neck1 which being thought troublesome1 was made in the ,arm2 the ,patient however has never since felt any ,attacks of those frightful ,symptoms4 ,whether or no it be thro' want of due ,heed and ,enquiry that we have not in all the ,collections of ,histories and ,cases1 any ,instance of the like ,nature so particular as this is1 ,i know not2 this is certain1 that as the ,vertigo is a ,disease nearly related to the ,epilepsy1 and the ,hysterical ,symptoms do partake of the same ,nature2 so both one and the other are frequently observed to obey the ,lunar ,influence4 ,in like manner1 the raving ,fits of ,mad ,people1 which keep ,lunar ,periods1 are generally in some degree ,epileptic too4 ,tulpius#cj and ,piso#ca afford us remarkable ,instances of ,periodical ,palseys4 ,every one knows how great a share the ,moon has in forwarding those ,evacuations of the weaker ,sex1 which have their ,name from the constant ,regularity they keep in their ,returns2 and there is no question to be made1 but the ,correspondency we here observe1 would be greater still1 and even ,universal1 did not many ,accidents1 and the infinite ,varieties in particular ,constitutions one way or other concur to make a difference4 ,it is very observable that in ,countries nearest to the quator1 where we have proved the ,lunar ,action to be strongest2 these ,monthly ,secretions are in much greater quantity than in those near the ,poles1 where this force is weakest4 ,this ,hippocrates#cb takes notice of1 and gives it as one ,reason why the ,women in ,scythia are not very fruitful4 ,the ,case being thus with ,females1 it is no wonder if we sometimes meet with ,periodical ,hmorrhages answering to the times of the ,moon in ,males also4 ,for as a greater quantity of ,blood in proportion to the bulk in one ,sex1 is the reason of its discharging it self thro' proper ,ducts1 at certain ,intervals1 when the pressure of the external ,air being diminish'd1 the internal ,aura can exert its ,elasticity2 so in the other1 if at any time there happens to be a ,superabundancy of the same ,fluid1 together with a weak ,tone of the ,fibres2 it is plain that the ,vessels will be most easily burst1 when the ,resistance of the ,atmosphere is least4 ,and this more especially1 if any accidental hurt1 or rarefying ,force has first given occasion to the other ,causes to take effect4 ,i know a ,gentleman of a tender frame of ,body1 who having once1 by over reaching1 strained the parts about the ,breast2 fell thereupon into a spitting of ,blood1 which for a ,year and half constantly return'd every ,new ,moon1 and decreasing gradually1 continued always #d or #e days4 ,the ,fits being more or less considerable1 according as his management about that time1 contributed to a greater or lesser fullness of the ,vessels4 ,we have two notable ,instances of the like nature in our ,philosophical ,transactions2 the one#cc of a ,person1 who from his ,infancy to the #bdth ,year of his ,age1 had every full ,moon an ,eruption of ,blood on the right side of the ,nail of his left ,thumb1 at first to #c or #d ,ounces1 and after his sixteenth ,year1 to half a ,pound each time2 which when by searing the part with a hot ,iron1 he stopp'd1 he fell into a ,sputum ,sanguinis1 and by frequent ,bleeding1 c4 was very difficultly saved from a ,consumption4 ,the other#cd is a ,story of an ,inn-,keeper in ,ireland1 who from the #dcrd ,year of his ,life1 to the #eeth 7in which it killed him7 suffered a ,periodical ,evacuation at the point of the ,fore-,finger of his ,right-hand2 and altho the ,fits here kept not their returns so certain as in the forementioned ,case1 7it may be either from the irregular way of living of the ,patient1 or the mighty change every ,effusion made in his habit of ,body1 the quantity seldom amounting to less than four ,pounds at a time7 yet there is this remarkable ,circumstance in the ,relation1 that the first beginning of this ,hmorrhage was at ,easter1 that is1 the next ,full ,moon after the ,vernal ,equinox1 which is one of the two ,seasons of the ,year1 at which we have proved the attraction of the ,air1 or lessening of its ,pressure1 to be greater than at any other time whatsoever4 ,but we are besides this to consider1 ,that the ,static ,chair1 and nice ,observation taught ,sanctorius1#ce ,that ,men do increase a ,pound or two in their weight every ,month1 which overplus is discharged at the ,months end1 by a ,crisis of copious1 or thick turbid ,urine4 ,it is not therefore at all strange that we should once a ,month be liable to the returns of such ,distempers as depend upon a ,fullness of the ,vessels1 that these should take place at those times especially1 when the ambient ,air is least able to repress the ,turgency2 and that tho' ,new and ,full ,moon are both of equal ,force1 yet that sometimes one1 and sometimes the other only should ,influence the ,periods1 according as this or that happens to fall in with the inward ,repletion4 ,the ,afflux of ,humours to ,ulcers is sometimes manifestly altered by this ,power2 #cf ,baglivi was acquainted with a ,learned ,young ,man at ,rome1 who labour'd under a ,fistula in the ,abdomen1 penetrating to the ,colon1 which discharged so plentifully in the ,increase1 and so sparingly in the ,decrease of the ,moon1 that he could make a very true judgment of the ,periods and ,quadratures of the ,planet1 from the different quantity of the ,matter that came from ,him4 ,nephritic ,paroxysms have frequently been observed to obey the ,lunar ,attraction3 ,tulpius#cg relates the ,case of ,mr4 ,ainsworth1 an ,english ,minister at ,amsterdam1 who had a ,fit of the ,gravel and suppression of ,urine every ,full ,moon1 of which he found no relief till the ,moon decreased1 unless by ,bleeding at the ,arm4 ,after his death two large ,stones were taken out of his ,bladder1 and the ,pelvis of the left ,kidney was enlarged to that degree by the quantity of ,urine so often stopt there1 as to contain almost as much as the ,bladder it self4 ,i was present1 not long since1 at the ,dissection of a ,child about #e or #f ,year old1 who dyed of the frequent returns of ,nephritic ,fits1 attended with ,vomitings and a ,diarrha4 ,the ,kidneys and ,ureters were quite stuffed with a slimy calculous ,matter1 and it was very instructive to see the different degrees of ,concretion in the several parts of it1 from a clear limpid ,water1 to a hard friable ,substance4 ,dr4 ,groenvelt1 who had tended the ,boy in his ,illness1 observed him to be seized with his ,pains at every ,full ,moon for several ,months together1 which generally ended with the voiding of a ,stone4 ,what ,influence the ,moon has in ,asthma's1#ch van ,helmont takes ,notice1 ,exacerbatur ,paroxysmus 7says he7 ,lun ,stationibus1 vi tempestatibus quas ideo prsentit prsagit4#ci ,and ,sir ,john ,floyer1 who has given us a more particular ,history of this ,disease than any ,author1 observes1 that ,the ,fits usually return once in a ,fortnight1 and frequently happen near the ,change of the ,moon4 ',tis a more uncommon ,effect of this ,attractive ,power that is related by the ,learned ,kerckringius4#dj ,he knew a ,young ,gentlewoman1 whose ,beauty depended upon the ,lunar ,force1 insomuch that at ,full ,moon she was ,plump and very ,handsome1 but in the decrease of the ,planet so ,wan and ill ,favoured1 that she was asham'd to go abroad till the return of the ,new ,moon gave ,fullness to her ,face1 and ,attraction to her ,charms4 ,tho' this is indeed no more than an ,influence of the same kind1 with that the ,moon has always been observed to have upon ,shell-,fish1 and some other living ,creatures4 ,for as the old ,latin ,poet ,lucilius says1#da ,luna alit ,ostrea implet ,echinos1 ,muribu' fibras ,et ,pecui addit---- ---- ---- ,and after him ,manilius#db ,sic submersa fretris concharum ,carcere clausa1 ,ad ,lun motum variant animalia corpus4 ,it is very well worth the pains to enquire what share such an ,alteration in the ,weight and ,pressure of the ,atmosphere may have in the ,crises or ,changes of ,acute ,diseases4 ,the ,ancients made great ,account of ,critical ,days1 and regulated their ,practice according to the ,expectation they had from them2 ,this ,part of ,physick is grown now into disuse1 quite slighted1 and even ridiculed2 and that ,i suppose chiefly for these two reasons4 ,in the first place1 because the earliest ,observations of this kind1 which were drawn into ,rules being made in ,eastern ,countries1 when these came to be applied to the ,distempers of ,northern ,regions1 without allowance given for the difference of the ,climate1 they were oftentimes found not to answer4 ,and secondly1 ,fevers of old were treated with few or no ,medicines1 the ,motions of ,nature were carefully watched1 and no ,violence offer'd to interrupt her ,work4 ,the ,histories therefore of ,crises1 tho' of great ,use1 and certainty under such ,management as this1 were at length unavoidably set aside and lost2 when ,acute ,cases came to be ,cured1 according to this or that ,hypothesis1 not only by ,evacuations1 but hot or cold ,alteratives too2 there being no longer any room for those ,laws of ,practice which supposed a regular and uniform ,progress of the ,distemper4 ,wherefore1 in order to understand a little both what might ,induce the first ,masters of our ,profession to so nice and strict an ,observance in this point2 and what grounds there may be now1 for a more due regard to their ,precepts1 even upon the score of the ,lunar ,attraction only1 ,i propose the following ,remarks4 #a4 ,all ,epidemic ,diseases do in their regular course require a stated time1 in which they come to their height1 decline1 and leave the ,body free4 ,this is so constant and certain1 that when a ,fever of any ,constitution which is continual in one ,subject1 happens from some other cause1 in another to be intermitting1 the ,paroxysms do always return so often as all together to make up just as many days of ,illness as he suffers1 whose ,distemper goes on from beginning to end1 without any abatement4 ,dr4 ,sydenham1 a sworn ,enemy to all ,theories1 learn'd thus much from downright ,observation2 and gives this reason why ,autumnal ,quartans hold six ,months1 because by computation the ,fits of so long a time amount to #ccf hours1 or #ad days1 the period of a continual ,fever of the same ,season4#dc ,so ,galen takes notice that when an ,exquisite ,tertian is terminated in seven ,paroxysms1 a true ,continual at the same time has its ,crisis in seven days2 that is1 the ,fever lasts as long in one as in the other1 in as much 7says he7 as a ,fit in an ,intermitting ,feaver answers to a day in a ,continual#dd4 ,now this so comes to pass1 because #b4 ,in these ,cases there is always a ,fermentation in the ,blood1 which goes not off till the active ,particles are thrown out by those ,organs of ,secretion1 which1 according to the ,laws of ,motion1 are most fitted to separate 'em4 ,and #c4 ,as different ,liquors put upon a ,ferment1 are depurated in different times1 so the ,arterial ,fluid takes up a determined ,period1 of which it is discharged of an induced ,effervescence4 #d4 ,the ,symptoms1 during this ,ebullition1 do not proceed all along in the same ,tenour2 but on some days particularly1 they give such evident ,marks of their good or bad ,quality1 that the nature of the ensuing ,solution may very well be guess'd at1 and foretold by 'em4 ,things being thus1 ,those days on which the ,disease was so evidently terminated one way or other1 might very justly be call'd the days of ,crisis2 and those upon which the tendency of ,illness was discovered by most visible ,tokens1 the ,indices of the ,critical ,days4 ,and thus far the ,foundation was good1 but when a false ,theory happen'd unluckily to be joined to true ,observations1 this did a little puzzle the ,cause4 ,hippocrates1 it is plain1 knew not to what to ascribe that remarkable regularity with which he saw the ,periods of ,feavers were ended on the ,seventh1 ,fourteenth1 ,one and ,twentieth day1 c4 ,pythagoras his ,philosophy was in those ,ages very ,famous1 of which ,harmony and the ,mysteries of ,numbers made a considerable part1 ,odd were more ,powerful than ,even1 and ,seven was the most perfect of all4 ,our great ,physician espoused these ,notions1#de and confined the ,stages of acute ,distempers to a ,septenary ,progression#df1 upon which this ,inconvenience follow'd1 that when a ,crisis fell out a day sooner or later than this ,computation required1 his ,measures were quite broken2 and that this must necessarily oftentimes happen1 will appear by and by4 ,upon this score ,asclepiades rejected this whole ,doctrine as vain1#dg and ,celsus finding it to be too nice and scrupulous1 observes that the ,pythagorean ,numbers led the ,ancients into the ,error4#dh ,galen being aware of this1 succeeded much better in his reasoning upon the ,matter1 and very happily imputed the ,critical ,changes not to the ,power of ,numbers1 but to the ,influence of the ,moon2 which he observes1 has a mighty ,action upon our ,earth1 exceeding the other ,planets1 not in ,energy1 but in ,nearness#di4 ,so that according to him1 the ,septenary ,periods in ,diseases are owing to the ,quarterly ,lunar ,phases1 which are the times of the greatest ,force1 and which return in about seven days4#ej ,the result of the whole ,affair1 in short is this1 ,a ,crisis is no more than the ,expulsion of the ,morbific ,matter out of the ,body1 thro' some or other of the ,secretory ,organs2 in order to which1 it is necessary that this should be prepar'd and comminuted to such a degree1 as is required to make it pass into the ,orifices of the respective ,glands2 and therefore as the most perfect ,crisis is by ,sweat1 7both by reason that the ,subcutaneous ,glands do naturally discharge more than all the other put together1 and also that their ,ducts being the smallest of any1 whatsoever comes this way is certainly wery well divided and broken7 so the most imperfect is an ,hmorrhage1 because ,this is an ,argument that what ,offends is not fit to be cast off in any ,part1 and consequently breaks the ,vessels by the ,effervescence of the ,blood4 ,an ,abscess in those ,organs which separate thick1 slimy ,juices is of a middle nature betwixt these two4 ,now it is very plain1 ,that if the time1 in which either the ,peccant ,humour is prepar'd for ,secretion1 or the ,fermentation of the ,blood is come to its height1 falls in with those ,changes in the ,atmosphere which diminish its pressure2 the ,crisis will then be more compleat and large4 ,and also1 that this ,work may be forwarded or delay'd a day1 upon the account of such an ,alteration in the ,air2 the ,distention of the ,vessels upon which it depends1 being hereby made more easie1 and a weak ,habit of ,body in some ,cases standing in need of this outward ,assistance4 ,thus a ,fever which requires about a ,week to its ,period1 may sometimes1 as ,hippocrates observed1 have a good ,crisis on the sixth1 and sometimes not till the eighth day4 ,in ,order therefore to make true ,observations of this kind1 the time of ,invasion is to be considered1 ,the genuine course of the ,distemper must first be watched1 which is not to be interrupted by any violent ,methods3 ,the strength of ,nature in the ,patient is to be considered1 and by what ,secretions the ,crisis is most likely to be performed2 and it will then be found1 that not only the ,new and ,full ,moons1 but even the ,southings1 whether visible or latent1 of the ,planet1 are here of considerable ,moment4 ,for ,confirmation of which1 we need only to reflect on what ,mr4 ,paschal has remark'd1 concerning the ,motions of ,diseases and ,births and ,deaths#ea4 ,dividing the into ,four ,senaries of ,hours1 the first consists of three hours before the ,southing of the ,moon1 and three after2 the second of the six hours following1 and the third and fourth of the remaining ,quarters of the natural day2 ,he takes notice that none are born1 or die a natural ,death in the first and third ,senaries1 which he calls first and second ,tides1 but all either in the second or fourth ,senaries1 which he calls first and second ,ebbs4 ,in like manner1 that in ,agues1 the tumult of the ,fits generally lasts all the ,tiding time1 and then goes off in kindly ,sweats in the ,ebbs4 ,from whence he very rationally concludes1 that ,motion1 ,vigour1 ,action1 ,strength1 c4 appear most1 and do best in the ,tiding ,senaries2 and that ,rest1 ,relaxation1 ,decay1 ,dissolution1 c4 belong to the ,ebbing ,senaries4 #be 4 ,de ,dieb4 ,critic4 lib4 #c4 #bf ,alexand4 ,trallian4 lib4 #a4 c4 #ae4 #bg ,matth4 c4 #ag4 v4 #ae4 #bh ,apuleius de ,virtutib4 ,herbar4 cap4 #f4 #ie4 #bi ,anatom4 ,centur4 #b4 ,h4 #gb4 #cj ,observ4 ,med4 lib4 #a4 cap4 #ab4 #ca ,de ,morb4 seros ,colluvie1 ,obs4 #bh4 #cb ,de ,aere ,aquis ,locis4 #cc ,n #bgb4 #cd ,philos4 ,trans4 ,n #aga4 #ce ,medicin4 ,static4 ,sect4 #a4 ,aph4 #fe4 #cf ,de ,experiment4 circa ,sanguin4 p4 m4 #cda4 #cg ,observat4 ,lib4 #b4 c4 #dc4 vid4 etiam ,observ4 #eb4 #ch ,asthma ,tuss4 #bb4 #ci ,treatise of the ,asthma1 p4 #ag4 #dj ,observat4 ,anatomic4 #ib4 #da ,apud ,a4 ,gellium1 lib4 #bj4 c4 #h4 #db ,astronomic4 lib4 #b4 #dc ,de ,feber4 ,intermit4 ,ann4 #affa4 pag4 m4 #fe4 #dd ,comment4 in ,aphor4 #ei4 lib4 #d4 de ,crisib4 lib4 #b4 c4 #f4 #de ,epidem4 lib4 #a4 ,sect4 #c4 #df 1 1 4 de ,septimestri ,partu4 #dg ,vid4 ,celsum lib4 #c4 c4 #d4 #dh ,ibid4 #di ,de diebus ,decretor4 lib4 #c4 #ej ,ibid4 #ea ,philos4 ,transact4 ,n #bjb4 ,a ,,corollary4 ,it having bin explained in the ,beginning of this ,discourse1 how those ,influences of the ,heavens1 which favour the ,returns of ,diseases1 may likewise raise ,winds at the same times2 and that ,we feel the different ,effects of ,these according as other ,causes do concurr to the ,motion of the ,air2 it will not be amiss1 to shew in one ,instance or two1 how much ,natural ,history confirms this ,reasoning4 ,there happened on the #bfth of ,november1 #agjc4 a little before ,midnight1 a most terrible ,storm of ,wind1 the ,fury of it is still fresh in every ones ,mind1 which lasted above six ,hours4 ,it is not to the present purpose to relate its ,history and ,causes2 ,what we observe is1 ,that the ,moon was at that time in ,perigo1 and just upon the change to ,new4 ,upon both which accounts its ,action in raising the ,atmosphere must be great2 ,and hence indeed the ,tides which followed were also very great1 and the ,mercury in the ,barometer1 at least1 in most places1 fell very low4 ,this ,influence was1 without all doubt1 assisted by some such other ,causes of ,winds1 as we have mentioned2 ,these we can't know1 but may however take notice how much the manifest ,state of the ,air contributed to this ,calamity4 ,after a greater quantity of ,rains than ordinary had fallen in the ,summer and ,autumn1 in those places where the ,storm was felt1 the ,winter came on much warmer than usual2 so that the ,liquor in a ,thermometer1 of which the #hdth ,degree notes ,frost1 never fell below the #ajjth4#eb ,hence we may very well believe1 that the ,atmosphere was at that time fill'd with ,atoms of ,salts and ,sulphur1 out of the ,vapours raised by the ,heat from the moist ,earth1 which being variously combined and agitated1 gave that deadly force to the ,motion of the ,air4 ,a ,proof of this we have not only from the frequent ,flashes of ,lightning1 observed a little before the ,storm1 but also from what the ,country ,people took notice of the next day1 that the ,grass and ,twiggs of the ,trees1 in ,fields remote from the ,sea1 tasted very salt1 so that the ,cattle wou'd not feed on them4 ,our ,histories mention another ,storm1 which if not equal to this last in ,violence1 is however thought the greatest that had then ever been known and memorable from the time at which it happened1 viz4 on the #c;d of ,september1 #afeh4 the day on which the ,usurper ,o4 ,cromwel died4 ,no ,ephemerides that ,i know of relate the ,condition of the ,air that ,year1 but it is sufficient to remark1 ,that whatever other ,causes concurr'd1 their force was accompanied with a ,full ,moon1 just before the time of the ,atumnal ,equinox4 ,upon the same score it comes to pass1 ,that in those ,countries which are ,subject to frequent ,inundations1 these ,calamities are observed to happen at the times of the ,moon's greatest ,influence1 so that the ,learned ,baccius#ec has rightly enough laid the ,cause of such ,mischiefs upon immoderate ,tides of the ,ocean1 being unhappily accompanied with the attractive ,force of some or other ,stars4 ,dr4 ,childrey in his ,britannia ,baconica#ed has from several ,instances shewn the ,lunar ,action in ,damages of this kind4 ,such and the like ,natural ,causes have ,storms and ,tempests2 for as to the ,question of ,divine ,power1 whether or no ,calamities of this kind do not sometimes1 by the ,anger of ,heaven1 happen out of the ,course of ,nature1 it is not my ,business to ,dispute1 nor would ,i by any means indeavour to absolve ,mens ,minds from the ,bands of ,religion4 ,for although we must allow all the ,parts of the ,machine of this ,world to be framed and moved by ,established ,laws1 and that the same ,disposition of its ,fabrick1 which is most beneficial to the ,whole1 must of necessity1 in some few ,places now and then occasion ,hurts and ,mischiefs2 it is however most highly reasonable1 that we should yield to the ,supreme ,creator an absolute ,power over all his ,works2 ,concluding withal1 that it was perhaps agreeable to ,divine ,wisdom1 to order the ,make of the ,world after such a manner as might sometimes bring ,mischiefs and ,calamities upon ,mankind1 whom it was necessary by the ,frights of ,storms1 ,thunder and ,lightning to keep in a continual ,sence of their ,duty4 #eb ,vid4 ,philos4 ,transact4 ,n #bhi4 #ec ,del ,tevere1 lib4 #c4 p4 #bbh4 #ed ,pag4 #ig4 ,the ,end4