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This Institution reserves the right to refuse to accept a copy order If, in Its judgement, fulfillment of the order would Involve violation of the copyright law. A UTHOR: CHEYNE, GEORGE TITLE: PHILOSOPHICAL PRINCIPLES ... PLACE: LONDON DATE: 1725 (PT.1), 1716 (PT.2) COLUMBIA UNIVERSITY LIBRARIES PRESERVATION DEPARTMENT BIBLIOGRA PHIC MirROFORM TARHFT Master Negative # Original Material as Filmed - Existing Bibliographic Record (, teio C4? rhilosopl-iical pviTiciples o •^e,"©^; natuval arjd rev^eaUd... London i8B5.a6. ies o^ rc- ZV.'wt I, 74411 Restrictions on Use: TECHNICAL MICROFORM DATA FILM SIZE: Sfjf^ IMAGE PLACEMENT: L\ (fQ IB IIB REDUCTION RATIO: _//^ BIBLIOGRAPHIC IRREGULARITIES ENTRY; ^^^^^ Bibliographic IrrcgulariHes in the Ori ginal Documpnt list voliimes and pages affected; include name of institution if filming borrowed text. 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DATE BORROWED fin DATE DUE m ? •■ '"^ i? DATE BORROWED DATE DUE •■» 1 ' :, ^', 1 i 1 ■n' i t I 1 '"^ • 1 i t 1 1 1 ' C28 (1149) 100M •• 9 m bphical COL.COLL.N EiM^^lPLES N.YORK, oi IGION. NATVRAL zxi^REVEALET>: In Two Parts* Part I. Containing the Elements of Natu^ ral Philofophy^ and the Proofs of Natural Religion arifing from them. Part II. Containing the Nature and Kinds I of INFINITES, their Arith ME TICK and Uses ^ together with the Philofophick Prin- ciples oi Revealed Religion,. By George Cheyne, M. D* andF.R.S. I LONDON: Printed for George Strahan, at the Golden Ball in Cornh'tll^ over againft the Royal Exchange, Mdccxxv. Mi*iakBM> (3 19 " r r ■ •1! 11 J',*..- .-4 I i| I. I To His G R A C E "III o N, DUKE of ROXBURGH, Marquefs of Bowmont and Cepford^ Earl of Kelfo^ Vifcount of Broxmouth^ Baron Ker of Cefsford and Cawrtoim^ Sic. Keeper of His M A J E S T Y's Great Seal in SCOTLAND. May it pleafe your Grace, ^ 7(?^ condescended to do me the Honour to Juffer Tour Name to be prefix d to thi former Edition of this Work : So 1 humbly hope^ oiir Grace will continue the fame mdnefs to this more full and correH A X one, 14424 •0 HFW'i'*' ^r^-"«'-'?qF?;5r Dedication. one. J fo deeply andjuftly honour Your Grace, thafy as Jam fure Tou do not exPe£ty Co I own 1 dare not befiovj the Compliments ufualin Addrejfes of this Kind. That Your Grace may li've an Example o/Tolid Virtue, iriTour high Rank here, and may he crowned with an exceeding Weight of Glory hereafter, is the earnefi Prayer of May it pleafe Your Grace, % Your Grace's moft oblig'd, Moft faithful, Moft humble Servant, « t 4 Philosophical PRINCIPLES Geo.Cheyne O F Natural Religion Part I Containing the ELEMENTS O F Natural Philofophy, And the PROOFS for Natural Religion, Arifing from them. Ctje'aCljirD (gptti on. Co?te(tcO ano (gnlaigta. By George Che yne, M- D- andF.R-S . L O WD O N: Printed for G. S t r a h a N- 1725- I i I THE PREFACE To the Firfi Part. } Had not given the World any fartlier Trouble with my poor Labours on fuch uncertain and intricate Subjeds as are here treated o^ had I not been often foUcited to give Or- ders for another Edition of this Work, for the Ufe of the younger Students of Thilofophyy who while they were taught the moft probable Account of the appearances of Nature from the Modern Difcoveries, might there- by have the Principles of Natural Religion infenfibly inftilled into them at the fame time. This, with the Confent and Approbation of thofe, A 4. whole if The Preface. The Preface. |f ■I • i whofe Advice will be always facred widi me, were the principal Motives to this £ditiori; and .while it was un^ der Hands, 1 was inclined to have it as corredt and full, as the Animad- verfions and Corrections of thofe Friendsy who were capable and wil- ling to undertake them ; my own low Abilities, uncertain Health, and neceflary Advocations wou'd peonit. I had feen the Obfervations and Corredions, the late ingenious and learned T>[. Gregory, Savittan Profejfor of fiAftronomy, zi Oxford, had made on the former Edition of this Parr. I had fome Remarks from the re've- rend and learned Mr. John Craig ; as alfo fome very judicious Reflections from a Gentleman at Cambridge who conceals his Namd Thefe 1 freely ufed, with the beft Judgment and utmoft Application I was capa- ble of, to make the Corre(5l:ions and Emcn* Emendations of this Part now againr Publifhed. As to the Additions, be- fides what my own Refledions fug- efted, the principal ones were taken .Tom the fecond Editions of Sir Ifaac JSlezvtons ( that great Inventor and Improver of wo ft of our Modern Phi- lofoply and Geometrj ) his Of ticks and Mathematical Principles of Phtlojo- phy-, Mr. Cotes, (the learned Tlu- mian Profejfor ofjiftronomj at Cam- bridge ) his Preface to that Edition j the ^reverend and learned Mr. Der-^ ham's two late Pieces ; the Philosophi- cal Transactions, and the Memoirs of% the Academy Royal at Paris. I intend- ed to have had thefe Alterations and Additions printed by themfelves, for the Benefit of thofe who had the firft Edition, but I found it was imprac- ticable. I am very fenfible, the beft Ac- counts of the Appearances of Nature (in ^♦11 '■\ The Preface. ( in any finglc Inftance how minute or fimple foever ) hiiman Penetra- tion can reach, comes infinitely fliort of its Reality, an^ internal Conftitu- lion ; for, who caitfearch out the AU mighty, or his Works to Perfeaion ? Some of the grofler Out-lines and prominent Lineaments of Nature, are as near as is allowed to Mortals to approach. But diis I ^hink I may venture to fay, that jitheifm, may be eternally confounded, by the molt diftant Approaches to the tme Cau- ic^ of natural Appearances. And diat ^if the Modern Philofophy demon- ftrates nothing elfe, yet it infallibly proves nAthetJm to be the moft grols Ignorance. f*)!? Jl a 4 JCt yarn gMjgf^'y^ ' l ^^ LIBRARY. Q^^ E N T S, O rl A !• !• Of the Phy fical Laws of Nature. ARticfe I. The Iiitroduaion. Pag. i § 2. An Explicaticn of the Setife wherein Nature and its Laws are here taken, p. 2 $ 3. Tlb^ Opinions cf fome Philofophers about Nature and its Laws, confider'dy and the J^niftry o/fubordinate Spirits co^m'd. p. 3 &feq. § 4. The Scheme of Nature according to the ;«o^er» Philofophy, P* 5 Of the Pbyfical Laws of Nature, p. 7 & feq. § 5. Ti>^ firft Law of Nature, p. 7 \ 6. A Demonftration of the firft Law cf Na- ture, P* 7 $ 7. An Explication and Demonftration of the Vis inertiJC, in Bodies, p. 8. § 8. That Bodies cfl« wmkr move, nor alter the Dirediion of their Motion of themfelves, ^'^°' § 9. That ,:,; * *l 1 I The CONTENTS. § 9. Thqt a Body cannot move in a Curve Line cf it felf, ibid. § 1 o. That the coeleftial Bodies, do not mo've of themfelves, in their Orbits, p. 1 1 § 1 1. That neither Motion nor Reft, i. e. that neither of thefe particularly, is effential to ' Matter, [bid. § I a. 7i?J^ Necejfity of a Vacuum det/mftrated, a priori & pofteriori, p. 1 2 & feq. § IS. The fecond Law cf Nature, with its Demonftration, p; 15 § 14. The hnpojfibility of a perpetual Motion, demonftrated on the modern Scheme of Na- ture, p. 16 & feq. §15. Tee third Law of Nature with its De- ?iionftration, p, jg/ ^ 16. The Method ^compounding and refol- ving Motions, demonftrated, p. 20 § I J. Tie Proportion cf an obhque to a per- pendicular Impulfe, demonftrated, p. 2 1 Ibid. The Proportions of three Forces drawing I in three different Dire(aions in ^quihbrio. 23 Ibid. A Rule to diftinguift) Mechanifm from what is not fo, according to the modern Philofophy, p. 24 CHAP. The C O N TENTS. CHAP. II. Of Attraaion or Gravitation in Bo- dies, and an Account of fome ot the Appearances of Nature trom diis Principle, and thefe Laws now eftablifh'd. i can be retained in then Orbits, p.^J fs 19. Des Cartes, his Hypothefis fout je ^ formation of the Uni-verje, and the Caufe^ of iibf coeleftial Motions, . ^•'^, ,Jf„t § 20. This Hypotljefis is confuted ^at Urge^^ & 21. Ur.Leihmtz's Opinion about the i^y^es of the coeleftial Motions, ^ . P- 3^ «^^J & 22. T/j/x Hypothefis not fufficient, nor Jatts- 6 2I Tk Omion of fome other Philpfophers ^ 2rn the ^Caufes if Gravity, confiderdand veiled P- 35 «.leq. ^ 24. That fk Principle of Attraaion » f/j« ^ moft probable Caufe of the caleflial Motions Ibid. That the Gravitation of Bodies, imot a Principle effential to Matter, ^ P- 4© Ibid. V:. it's Diredion, is to make it a free-will'd Agent, ibid. Ibid. Allowing Matter a Self-motion, and an oblique Diredion, yet nothing but fluid or folid Inheres, could have been produced, p. 1 18 § 7. Allowing Matter a Self-exiftence, Self-mo- tion, and an oblique Uud^von^yet it could not have produced this Sjjftem ofThingSy ibid. $ 7. Voat Solidity or Cohelionj could never have arifen from one or all of thefe Properties^ p. 1 19 $ 8 There are fever at Appearances in Nature^ in* confijient withy and unaccountable jrom nieer Mechanifm, . p. 121 § 9. Allthe Coeleftial and Terreftrial Appearances that have been explained from the Principle of Attraftion, are unaccountable from meer Me- chanifm, p. 121 Ibid. An obvious Demonftration, from the Coe- leftial Appear ancesy that the Motions of thefe Bodies y could not proceed from meer Mecha- nifm, P- 123 § lo.The ProduSIion of Animals above the Power of Mechanifm, p. 124 Ibid. Animals demonfiratedy to be perpetua mo- bilia, atid therefore above the Power 0/ Me- chanifm, p. 12 J Ibid. That the different Organs in Animals are relatively infinite, and therefore above the ' Power 0/ Mechanifm. p. 126 Ibid. That in the Production of Animals, there was a Necefpty^ that all the Parts ( liquid and folid) The CONTENTS. folid) fbould have been formed at the fame in- fianty and therefore the Produif ion of Animals is above the Power of Mechanifm, p. 129 fin. The {pontaneous motions of the fenfitive Tribesy above the Power of Mechanifm, P- 132 Ibid. A Demonfiration of fornething above the Power of Mechanifm in Brutes y p. 13 j 5 11. The voluntary Motions of rational Crea^ tures, above the Power of Mechanifm, ibid. Ibid. How the voluntary and involuntary Fundi- ons of Animals, may be perform' dy p. 1 34 §13. Freedom and Liberty, inconjijlent with Mechanifm, p. 138 Ibid. Several Demonftrations of the Freedom and Liberty 0/ rational Creatures y p. 139 Ibid. The true Definition and Nature of Liberty^ p. 141 CHAP. IV- Of the eternal Produdiion and Dura^ .tion of the prefent State of things. § I. 'T^H E Ariftotelian Hypothefis of the Ori^ -^ gination of the Univerfey p. i/^i 5 2. 7 hat the Univerfe could not have been from all Eternity of it fetfy becaufe it requires an extrifinc Vimcu^lQyforitsprejent Subfiftence^ p. 1 44 a 2 § J. The C O N T E N T S. § 3. T})at all Things in this Univerfe, have an End, Ofeor Defign, which imply Contrivance and Creation, and not Self-exiftence, ib 1. Ibid. That nothing is fupernumerary or uf«. eft but wasforfome wife Furpofes^ which imports Defign, and confequently Creation, and not Self-exiftent, p. 14*7 § 4. TA^^ Animals could not have been from all Eternity, for the Reafon alledged in the two fortner Se^ions, ibid. Ibid. Some Reafons tojhewy that this prefent (late cf things naturally tends to Decay and Diflolu- tion, . p. 149 § 5. That the Quantity of Fluids in all the Planets, had been conftantly decreafmg^ and confequently had the World been frc?n all Eter- nity, there bad been no Fluids extent in our Syftem at prefent^ even fuppofmg the confiant SSipply from the Comets, ibid. ^ 6. Thatfwce the Heat, Light ^;?i Bulk of the Sun ana fix'd-Stars, conftantlj decreafe^ had the World been from all Eternity^ they had been aU extinguijhed e'er now^ p- x 5 1 Ibid. T}je Wafte oj the Sun V Heat and Light ^ by the approach if Comets ; and their ufe^ for . rekindling extinil ^xt-SizTSy P- 152 § 7. That the Coeleftial bodies do not move in altogether void or empty Spaces, but fuch as make fame very fmall refiftances to their M<7- tionsy which had the World I a ft ed from all E- ternity had quite dejiroyed the Motions of thofe ^ Bodies, p. 153. i^.Tbe The C O N T E N T S. k 8. The real, tho infenfible Ganges happening to the coeleftial Bodies, by their Anions upon one another, muft at laft quite change the prefent Face of Things, p* 15^ Ibid. That the Nature of material Bodies is to change afid alter their Figure, Bulks and Mo- tions, P- i^^ Ibid.Tib^t there are fnany Siifpiaons cf great Changes having happened to the material World, which is unaccountable from any other Philofophy, but that of ChnHimity, p., 162 § 10. Since the material World is finite m its Extent, the coeliftial Bodies had been all amp fed in the Center of the material World, by their Attraftion upon one another^ had the World been from all Eternity, P- 1^3 Ibid. A Demonftration of the limited Nature^ and Finitude of the material World, p. 165 § II. Had the World been from all Eternity,' the M of every Species, of Animals, 7w^/i have been infinitely big, ^ 12. Bad the "WoM lofted from all Eternity; Arts and Sciences, and particularly Mathc- maticks, had arrived to a greater Degree of of Perfection than they have attained, p. 170 § 13. Had the Number of any generated thing on this Glohe,either conftantly increased or decreas d in any finite number of Tears how great foever be any finite number how fmall foever, then thisWorld could not have been from all Eternity, p. 173 k 14. That this World mufl have been created by ^ a 3 »^^ The C O N T E N T S. The CONTENTS. r > the fupreme Being, when it was bis Plea- Ibid. The Nature of Self-exiftence, and what it implies in its pofitive Icka, v-i Jlj. jfx i« V • of the Exiftencc of a Deity. $ 1. 'T'H E Jntrodalfiea, p. 1 78 5 2. ■* Tbflf d// fiv Argument cf the freceeding Chapter, are fo many Demonftrationy cf the Exiftence o/jo/wf fupreme Power, p. 180 $ 3. Ihat the Exiftencc of Matter, ii a plain proof of the Being of a God, p. 182 5 4. Tloat the pefent State of Things, mufl of necejjftty have been formed by different Laws and Principles, from what they are now go- iienid by, and therefore tnuft have been prodtt- Cf^ ^ an Intelligent Being, p. 184 $ yfbat not only thejirft Formation awrf Arrange- ment of the Great Bodies of the Univeife j But alfo their firfi Impulfes along r;b^ Tangent cf their Orbits, did require the power cf an Almighty Being, p. 186 $ %6,That not only the Formation, and firfi Im- pulfes in right Lines, of the Great Bodies cf the Univerfe did require the Tower of Omni- potence, but aljo their Centripetal Energy, did J didy and does conjlantly require a Power above Matter, that is a divine Influx, p. 187 $ 7. That the Exiftence of Animals, neceffanly in- fers the Exiftence of d Deity, p. 188 $ 8. That the fpontaneous Motions of irrational, and the voluntary Motions of rational Crea- tures, their Freedom and Liberty, and all ■ the Appearances of Nature, above the Powers of Mechanifm, arefo many Proofs of the Be- ing of a God, , ,K I fi The Prefervation of the Being, and the t acui- ties of Things, neceffarily requires the Power, andconiequently the Exiftence of a Deity, p 190 Ibid. Voe true Nature and Origin 0] the Being, Prefervation and Immortality of Creatures, p. 191 ^lo.The Argument for the Exigence of a Deity, from the Wifdom and Meliority of the Crea- tion is that which has the nobleft Efjed on the minds ofmoft Mm, ^^P' .^^"^ fi II. ^ General View of the works of Creation, and a Reprefentation of the whole Syftem of Things, fhewing how tkCoeleftial Bodies are ranged through the univerfal Space, p. 1 9 5 5 12. Tk Numbers that reprefent the Periods, Diameters, Diftances, Gravities, Bulks and Quantities of Matter, in thrfe oj the Coekftial Bodies, which have afforded means for deter- mining the fame, from the latefi objervmms; p. 197 (iix.A Reflexion on the Beauty, Order, Sm.- ^ a 4 pli'^ity* The CONTENTS. I' $ $ 5 5 plicity and Concinnity, of this neat and comfa^i Syftem of Things: p. 201 14. Ihe Nature of the Sun, li^ Kange, Or. der, and Viffitudes of Seafom, the Diftances and Motions of the celeftial Bodies, in our Planetary 5yftem. P* 205 15. Bf Analogy and 'Refemblance of the Planets to our Earth, and of their Satellits to our Moon, demonflrated, with their Ufes, the End 0/ KteV Creation^ their Periods and Motions, p. 208 1 5. The Motions and Irregularities of the Moon, arifing from the Adions of the Sun and tarth, p. 2 1 1 17- Of the Nature, Diftance, d«^ Light of ;|ffixt Stars, p%' Ibid. Mr. DerhamV ConjeSiure about the ap- pearing and difafpearing fixt Stars, confi- 18. TJ^ Nature of Comets, r;&^ Laws of their Motiom, the Caufe and Magnitude of rfe«r Atmofphere and Tails, with their Ends andyks, mfome Inflances of latter Comets illuflrated, p.2i7&feq. 19' /i Demonftration of the Beauty, Wil- dom, and Meliority, of this our Planetary Syftem, p. 221 Ibid. From the conftant Proportion, between the Times of the periodical Revolutions of all t'-^ releftial Bodies, and their middle Di- .Ibid. § $ The C O N T E N T S. Ibid, from the fame Principle^ viz. that qf Gra- yitation, and one Condition thereof^ producing the conftant Motions of all the cxleftial Bo- dies, p. 1 22 Ibid. From the conftant Proportion, between the ' Times and the Area's dejcrfl/d^ by a Ray from the Sun, ibid. Ibid. From the Diftances of the Planets, from the Sun in refpe^t of their Denfities, p. 224 Ibid . Fro7n the pitching upon that Proportion, which fuits the whole Syftem beft^ in an In- finity of others^ o*ver or under ^ which wotCd not have fitted the whole Syftem, Jbid. Fro?n their being in a conftant regular Pro-^ portion, in a fettled uniform Order^ when they might ha've been irregular, uncertainy and inconftant in all their Affedions. p. 229 $ 20. Some more particular Reflections upon the Meliority of the Fra??te and Conftitution of the cseleftial Bodies, ^ p. 231' Ibid. The incredible Number^ immenfe Diftancey the beautiful Di'verfity^ of the Magnitude of the fixt Stars, p. 232 5 21. The \Jk and Neceffity of the Sun to A- • nimals and Vegetables, the ?niferable State of thofe who are deprivd of his Influence^ his Motion about his own Axe, the Caufe and JSIeceJftty thereof y ibid. Ibid. i\ The CONTENTS. t Ibid. A Demonftration 0/ the Motion of the Earth, and the Stability of the Sun, the necef- fity and teafon therecf^ P* 235 $ 22. Ihe Ufeand Neceflity of the Moon, the dreadful Confequences of her not ha'ving been, to the Animals and Vegetables of our Earth, the Ufelefnels efmore Moons, p. 236 Ibid. The great Benefits arife to our Globe, from the Tides which are produced by the Moon, p. 238 Ibid. The Wiiaom, Contrivance, andVk of the Satillities cf Jupiter, to their Primary Pla- net, p. 240 Ibid, the Wifdom, Contrivance, and Ufe of the Satellities 0/ Saturn, to their Primary Pla- net, p. 241 $ 2 J. Some farther Obfervat'iom upon the Nature, Motions, and Ufes of the Comets, p. 244 $ 24. Tie Wifdom of the Contrivance ofotir Globe, the Emh, the Necejfity andUfeofits Revolution about its own Axe, whence the Alternation of Day and Night proceedsy the fatal Inconveniences of a petpetual Day, or Night, or of one half of the Tear being Day, the other Night, p. 296&feq. 5 25. Tibe Wifdom of the Combination (^the Diurnal Rotation, with the Annual Kevolu- tion of the Earth about the Sun, the Ufe and Necefftty of the Seafons of the Tear, the Dif- advantages of any one perpetual Seafon, or of jewet than we erqcrj^ p. 2 54. Ibid. Ibid. The Nature of Vegetation, and the Caufet of Fertility, r , r ^Vl^^ 6 16. The great Advantages of the prefent Obli- ciuity of the Equator to the Ediptick, the inconvenience of their Coincidence in the want of the Seafons of the Tear, and of the greater Degree of Heat in tbofe Places which want it mofi, r , • ?'j^l° ^ in The wondcrftd Wiidom of the «/cf Adjuft- nVent of the Diftance of the Earth, and the reft cf the nmets from the S\xr\i yP' ^% Ibid. The Advantages of the Oihkuhr figure o^ the Earth, , P- ^^4 5 28. The Nature, Extent, and many Advan- tages of our Atmofphere, its necejfity for Life and Vegetation, for the Support of our Ootids and Vapours for Rain and frejh Wa- ter, for failing our Ship and drying our Uarfbes, . ^'^^1 6 20. V^e Defign, and Advantages of our Moun- tains, that they are the indiipenfable condition of our frefh Water and Rivers, and give them thofe beautiful Turnings and Windings which makes them enrich fo man) Countries in their Courfe, ^ ._ P-27f Ibid. The Nature and Manner ofratjing Clouds and Vapours from the Sea, Lakes and mafliy Grounds, , ^_ ^ P- ?74 Ibid. That Mountains are the Nefts or Matrices of our Metals and Minerals. p. 278 6 20. The valt Ufe, Necejfity and Beauty^ our ' ^ fluids, 'i i The C O N T E N T S. II Fluids, tbeFewnefs of the primitive Fluids the great Diverfity and Advantages of their ipecifick Gravities, with the miverfal Con- dition of their Pteffme on the fides cfthe con- tatmmVeffeh, ^ ^g^ Ibid. TJ^ Caufeand Necefitj of the Law of their Preflure,d«/ aaturn, p ^gg CHAP. VI. The Proofs for the Being of a G O D arifing from the Contemplation of the Human Strudlure. § 33-QF ^/^ Animal Oecononiy, and of the i.k-1 r ¥^ff^'^^^ ^f^be Hypothefisc^ the FHUofophers to account for the Animal y^D- pearancefy p i4 ^^«fra/ F/Va; ,/ /^^ Animal Oeconomyt p. 25>5 & ^eq. ^ 34- $ 34, lib^ Manner and Caufe of Digeftion, and the Courfe of the Aliment, till it is rnix'd with the Bloody Ibid. 5 35. The Struduve of the Ghndsy the Hdtme^ Laws, and Manner oj Secretions ingeneraly the general Conditions necejfary for SecretionSy and an Account offome of the particular ones^p. 298 5 36. The Strufture and Ufe of the Lungs ac- cording to the modern Difcoveriesy with a Con]eMure of another Ufe of thewy not hither^ to obfen)edy to wit y for forming the hlood Globules, p. 307 5 37. The Stvu&uve of the Mukles as commonly recei'vedy with the Conjectures ofPhilofophers, about Mufcular Motion, and of the Nature of the Nerves y P- 3 1 3 $ 38. The 7}ioJi probable Caufe of all the Motions of the Fluids in an animal Body, the Structure and fever al Coats oj the Veffelsy p. 3 14 $ 3 9. Tl^)e Nature and Manner of Senfation in generaly and the true Manner of Generation and Production of all Animals and Vegetables^ with the Nature and Manner of Nutrition, p. 318 5 40. Some general Reflexions upon the Wifdom, andContri'vance of the animalStru(5ture5p.32 5 § 41. The wonderful Contrivance of the Skin and Scarfe-skin, with the Manner and Or ^slus of Feelingy and the admirably wife Adjufiment of this Senfe to the Bodies about uSy p* 3 2 5 § 42. Some furprizing Inftances of WMoniy in the The C O N T E N T S. The C O N T E N T S. i the Order and Dijpojition of the Mufcles, and the proportionating the Expences (?/animal Spi- rits to the labours we are obliged to undergo^ P' 329 § 43. Jnjlances d great Wifdom and Meliority in the Struaure of the Articulations and Strength of the Bones ; the noble and amaz- ing Fabrick of the Back-bone, and the won- derful Contrivance to obtain a greater Strength to the. Bonesy in proportion to their Weighty p. 334 5 44. The admirable Structure of the Brain and Nerves, the noble Fabrick of the Heart, the different lexture of this Organ in Animals not horn^ from what it becomes in thofe when born ; the great and wife End, and Necefity of this Diverfity, p. 340 § 45. The noble and divine Geometry in the Fa- brick of the Eye, the Necejfity and Advan- tages, the Nature and Manner (?/Vifion, with the wife Adjuflment for every Animals dis- cerning objcdsy in Proportion to their own Bulks and Sizes. The Inconveniences of a diff'erent Stru^ure^ with fome Reflections on the Eyes of particular Animals, p. 344 %^6.The wonderful Contrivance of the Ears, the great ufe and Necejfttjy with the Man- ner and Mechanifm o^ Hearing ; the nice Adjuft?nent of this Senfe^ to the Motions of Bodies about us, P* 354 $47* 5 47. The Contrivance and Ufe of the Valves in the Arteries and Veins, the great benefit of the Anaftomatofis of the Veffelsy the wif^ Contrivance in the Strulfure and Pofition of the Foetus in the Womby P- 357 $ 48. Some Reflections on the Fabric^ and wife Contrivance of the Organs of fome irrational Creaturesy with the Conclufion of this Chapter andfirft Party p. 35^ Thilofophtcal I \ i t I I ■^- ^ #^^^^p2^^8^.^S,^fg*^y^| ... J •I "I Philofophical Principles O F RELIGION PART I. !5 I C H A P. I. Of the Thyftcal Laws of Nature. HERE is nothing a more common Subjcft of Dit courfe than Nature and its La'-ji's i and yet, however Ufe has made thcfe Words familiar, there are few that agree in their Notions about them : The Rea- fon of which feems to be, that thcfe Terms imply Notions fo compounded, and fo far re- B movU |i 1&ftnofop!)tcai Wntipxts of IKtlrgion* 3 ■MmmA if mov'd from the knowledge of moft Men, that there arc fcarcc any that diftinftly conceive all the Simple Ideas that enter their Compofition j I fhall not pretend to fettle the Signification of thcfe Words in their utmoft extent (That being perhaps above the power of Human Faculties in this Lapfed eftate) it will be enough to my prc- fent purpofe, to give the Senfc I (hall apply to them in the following Difcourfc. % II. By Nature^ I underftand this vaft, if not infinite Machin of the Univerfe, the Perfeft and Wife Produftion of Almighty God, confift- ing of an infinite Number of lefler Machins, every one of which is adjufted by Weight and Meafure. By the Laws of Nature, I mean, thcfe Laws of Motion, by which natural Bodies are commonly govern'd in all their Aftions upon one another, and which they inviolably obferve in all the Change that happen in the natural State of things. But here we are to diftinguiHi between the Laws of Creation and thofe of No- turej for not only the great Bodies of this Uni- verfe, but the inferiour Machins thereof, were formed by a different Law from what they are now govern'd. For none of the Laws oi Motion or Narure now eftablifh'd, will any way ferve to account for the TroduBioUy Figure^ Size, Mo- tion or Number of the Great Bodies of the Uni- verfe, nor of their appendages, tho' they may help us a little to conceive their Appearances, now they are Created, and put in regular and beautiful ■•«■ beautiful Motions^ But this will be more dift- inftly explain d afterwards. Jl III. That there is no fuch thuig as an Uni- verfal Created Soul animating this vaft Syftcm according to Tlato, nor any Subjianiial Forms according to Arijlotle, nor any Omnifcicnt Radical Heat according to Hippocrates, nor any Tlaftick Virtue according to Scaliger, nor any Hylarchic Principle according to Henry Moor, is evident from the following Cori* fiderations5 i. Thefe (as they are now gene- rally underftood, tho' perhaps a juft and true Senfe might be put upon them) are meet Allegorical T^tms coined on purpofe to concearl their Author's Ignorance When fome Thilofo^ phers cou d not account for the appearances o^ Nature, they were fo far froiftowning any want of knowledge, that to keep up their Credit with the thoughtlefs and credulous part of Man- kind, they attributed thefe unaccountable Ef- feds, to unintelligible Beings of their own Contrivance, which neither had Foundation nor Exiftence in Nature : Biit whoever will glvt themfelvcs the leaft trouble to confider the Mat- ter, will plainly fee, that they really meant nothing by thofe amazing Terms, but to dif- 1 guife their own Ignorance* 2. Thefe deputed Beings (as they are commonly underftood) are derogatory from the Wifdom and power of the Author of Nature, who doubtlefs can govern B * •1 J^ H 4 Wiofopt)tcai pmxtii^its this Machin he cou'd create, by more direft and eafic Methods, than employing thefe fubfcrvi- cnt divinities. 3 . The Appearances themfelves, to falve which they were contrived, may be by more intelligible and lefs indired Principles accomited for, as in fome mcafure fhall be af- terwards fhown. And Beings are not to be multiply'd without a plain Necefllty. 4. Laftly, Thefe very Beings will not ferve the defign of their Creation, unlefs we endow 'em with Pow- ers and Faculties above the Dignity allow'd by their Authors^ to fuch fecondary Agents. I do not here intend, to infniuatc any thing againft the Miniftry of Angels^ or the Admi- niftration oi Subordinate Spirits in the AllWife\ Government of the World, and in the Works of his Providenq&: On the contrary, I think that more certain, than any thing in our Phi- lofophy, difcoverable by the meer ufe of Hu- man Faculties can be, fince even moft of thofe jippearances\jhiQhwt account for from our Phi- lofophick Principles, may for ought we arc ab- folutely certain to the contrary, be owing to them. But as we are not to have recourfe to their Agency, without plain Necefllty, fo the) were never mtended by the Inventers of thefe Secondary Agents I hzvc been now difproving: on the contrary, by thefe, as they are commonly underftood, are meant fome Lifelefs, Indepen- dent, Fanciful Powers, Principles, or Faculties imintelllgible in true Thilofophy, and incon- iiftcnt of lacUgcon. 5 fittcnt with reveal'd Religion, though perhaps an Explanation may be made of them congru^ ous to both. § IV. The Scheme of Nature which feems moft agreeable to the Wifdom of its Author, ac- cording to the modern Difcoveries, is ( fuppo- fmg the Sy^em of the Univerfe already created) that he has fettled Laws, and laid down Rules, conformable to which natural Bodies are go- vern d in their Anions upon .one another, and according to which, the Changes in the mate- rial part of this Syftem are brought about, which all Bodies inviolably obferve, and which of them- fclvesnaturallyaaing,they never tranfgrefs in the leaft degree, whilft God Almighty by his intimate Prefence, in, and with every fingle part of the Univerfe, preferves them in their Faculties and Operations. All the Integral Parts of Nature, have a beautiful Refemblance, Similitude^ and Analogy to one another, and to their Almighty Original, whofe images, more or lefs expreflive according to their feveral Orders and Gradati- ons, in the JV^/^ of Beings, they are 5 and they who are Mafters in the noble Art of juik Ana- logy, may from a tolerable Knowledge in any one of the Integral Parts of Nature, extend their Contemplations more fecurely to the whole or any other IntegralVzit lefs known. Thus this great Machine of the Univerfe has a Refem- blance to the lefler One of a humane Creaturei for, as in the laft, the vital Fundions are per- B 3 form'd I ^ftuofoptntat ^vnciViitB of latUgion* 1^ formed by general and conftant Laws 5 the Food is conceded, the Heart beats, the Blood circu- lates, the Lungs play, the Secretions are made by the Laws of Motion, and the conftant Rules oijiBion of the lefler Bodies upon one another 5 So the great Bodies in the feveral Syftems of the Univerfe, move in their Orbits^ turn about their AxeSj and ad upon one another ac- cording to the cftabliOi'd Laws of Motion, and the great Principles of Adivity, of thcfc greater Bodies upon one another. Again, as the fpiritual Part of the humane Com- p«tind, is intimately prefcnt with, prefides over, aduates and enlivens the whole and each Part of the Body, fo the Infinite Creator and Governour of the Univerfe is co-extended with infinity Space, is intimately prefent with every Ungle Point of its Dimenfions, prefides over the Whole and all its Parts, maintains their Being and their firft imprcft Energy. The Ana- l^ might be carried to many, and much more fublimc Speculations, but thefe are fufficient f6t my prefcnt Purpofe, which is to fliew in the following Sheets, according to my poor Abi- lities, that the beft and moft fatisfadory Ex- plications of the Appearances of Nature hitherto ctifcovcred, do all evince the neceflary Being andfpccial Trovidence of God Bleffed for ever . S Y. It is not my Defign here to explain all the particular L^jis of Motion, and of the Adi- cwisof Bodies upeni one another, nor cou'd it be be well done in fo narrow a Compafs as I have propofed to my felf 5 I ^all here only fet down [he General Laws of Nature. Which virtually include thefe others, and infer fuch Concluii- ons from 'cm as I find moftneccOary for clear- ing fome parts of the following Difcourles. L A W I. ALL Bodies pcrfevere in the fame State of Reft, or of moving forward in a ftrait Lmc, unlefs forc'd out of that State by fonie outward imprcft Violence, that is, all Bodies at reft will naturally, and of themfelves for ever continue in Reft, unlefs fome external Caule put 'em in Motion : And all Bodies m moti- on will naturally move forwards for ever in the fame, ftrait Line, unlefs they are ftopd by fome oppofite Force, or turn d out of their Courfe by fome differently direded Violence, g VI. To fticw how inviolably this Law is obfcrv'd by natural Agents, we need only con- fider it never has been obferv'd that any Body did of it felf bring it felf from Reft to Moti- on, nor that ever any Body in Motion brought it felf to Reft 5 Nor that ever any Body in Mo- tion, of it felf altered its Courfe, but that whe^.#ver fuch Changes happened, there were always evident Caufes. If Bodies chang d their places of themfelves, all Things wou d run in- ^ B4 ^^ r *" J 8 iai)!iofopi)rcai ia?mnptes to Confufion, nor wou'd there be any certain Means to regulate the Motions of the Univerfc. We are certain TrojeSlils wou'd for ever move on in the fame right Line, did not the Air, their own Gravity, or the Ruggcdnefs of the Plane, on which they move, flop their Motion 5 or did not fome Body with a different Direftion alter their Courfe. A Top whofe parts, by their Cohefion, hinder one anothers reftilincar Motions, wou'd never ceafe to turn round did not the Air gradually impair its Motion. Na- tural Bodies confift of a Mafs of Matter, which by it felf can never alter its State, and if Bodies are once at reft, they muft continue fo, unlefs fome new Force put 'em in Moti. on. If in Motion, the fame Energy will con- tinue 'em in Motion and drive 'cm forwards in the fame Direftions. ,^VII. Moreover, there is in Matter a pa (live Trmciple, which Sir Ifaac Newton very well cxprefles by the vis inertia, whereby Bodies refift to the utmoft of their Power, any change or alteration of their State, whatever it be, ci- ther of Reft, Motion, or its Direftion 5 And this Refiftance is always equal in the fame Body, and in different Bodies is proportional to the quantity of Matter they contain. There is required as much Force to flop a Body in Mo- tion, as is rcpuircd to put it in Motioi^ ind e contra; And therefore fin ce the fame Body equal- ly rcfilts the contrary equal Changes of its Statc^ Of lRhf0ion. State, this Refiftance will operate as power- fully to keep a Body in Motion, as to keep it at Reft, and confequently of it felf, it can ne- ver change its State of Reft, Motion, or Dire- ftion 5 for to change its Direftion, is the fame Thing as to move of it felf another Way. Mat- ter then of it felf is fo far indifferent to Mo- tion or Reft, that it is no more inclined to the one than to the other, and does no lefs refift a Change from Reft to Motion, than from Mo- rion to Reft. This vis inertia is no where more confpicuous than in the fudden Motion of a VefTel full of Liquor upon a horizontal Plane, at firft while the Veffel is moving along the Plane, the Liquor feems to move with a Dire- ftion contrary to that of the Veffel, the Water rifing on the hinder Side of the Veffel. Not that there is really any fuch Motion imprefs'd upon the Liquor, but that by this vis inertia^, the Water endeavouring to continue in its State of Reft, the Veffel can't immediately com- municate its Motion to it, by reafon of its Bulk and fluid States But the Liquor perfe- veres in its State of Reft, whilft the Veffel makes forwards and fo feems to move a con- trary way. But when once the Liquor has the Motion of the Veffel intirely communicated to it, and begins to move with a Velocity equal to that of the Veffel, if the Veffel be fuddenly ftop'd, the Liquor continues its Motion and dafhes over the fides of the Veffel. This 7af five A V -^1 I Jive Principle or vis inertia is eflential to Matter, becaufe it neitlier can be deprived of it, nor intended or remitted in the fame Body,, but is always proportional to the quantity of Matter Bodies contain. Corollary i. 5 VIII. Hence it is evident that no Particle of Matter, nor any Combination of Particles, that iSy no Body, can either move of them- felvcs, or of themfelves alter the Direftion of their Motion; Matter is not endow'd with Self-motion, nor with a Power to alter the Courfe in which it is put, it is meerly paflive and mull for ever of it felf continue in that State and that Courfe that it is fettled in 5 and if it can't move of it fclf, it can never alter its Courfe of it felf when in Motion, for to alter its Courfe of it felf, is only to move of it felf after a particular manner. Corollary 2. 5 IX. Hence it is Evident, that no Body put in Motion will naturally, and of it felf mov^ in a Curve Line. All Motion is naturally for- ?vard in the fame ftrait Line with the Diredion |>f the moving Force 5 but what ever moves in a Curve Line muft in every Point alter its Di- redion, and therefore naturally of it felf, no body can move in a Curve Line. Co- of ^tXx^im. 1 1 Corollary 3. 5 X. Hence the great Bodies of this Uni- verfe the TlanetSy their SatellitSy and the Co- mets do not naturally and of themfelves (tho* at firft put in Motion) move in their refpedive Orbits, which are Curve Lines returning in- to themfelves, but are kept in them by fome attractive Force, which if once fufpended, they wou d for ever run out in right Lines, and con- fequently the Motions of thefe Great Fodies in their Orbits do abfolutely depend upon this attraftive Force, whencefoever it arifes. Corollary 4. 5 XL Hence neither Motion nor Reft (I mean not one of *em particularly ) is eflential to Matter, /. e. Matter is indifferent as to either of thefe particularly, and does as much refift its being changed from Reft to Motion, as it does the being chang'd from Motion to Reft. And as any Force will imprint fome degree of Motion on a quiefcent Body, fo the fame de- gree of Force imprefs'd at the fame time with a contrary Direftion, will bring it to Reft again, but it is not neceflary to the Being of Matter that it be in Reft or Motion, for Matter will be ftill Matter in which ever of thefe States it be. In a Word, fmc^ the formerly mentioned paflive 11 ^i)iiofop|)tcal i^irncrples \'\ paflive Principle or vis inertU is eflential to Matter, it thereby becomes indifferent as to Motion or Reft, and is equally fufceptible of cither according as the cxtrinfic Force urges it. Corollary $. J XII. Hence the Necefllty of a Vacuum, or fpace diftinft from Matter, is clearly demon- Arable 5 for fince by their vis inertiSy all Bo- dies refift to the utmoft of their Power, any Change or Alteration of their State, whether of Motion or Reft 5 and fince the Refiftance in the fame Body is always equal, or the fame, and in different Bodies is proportionable to the Quantity of Matter they contain 5 and fince confcqucntly, if two Bodies containing equal Quantities of Matter, and moving with equal Celerities in contrary Direftions, fo that they impinge directly upon one another, will cer- tainly both reft or ftop at the Point of their Concourfe, as alfo fince itisdemonftrable, that two Bodies moving contrary wife with equal Celerities, and both refting at their meeting, are equally Heavy 5 it neceffarily follows, that two Bodies containing equal Quantities of Matter, arc equally Heavy, and therefore were there no Vacuities in Bodies, two Spheres of equal Diameters, fhould contain equal Quan- tities of Matter, and confequently be equally Heavy, i. e. two Spheres of equal HiameterSy one of ^aeligiott. M one of Gold, another of Wood, (hou d have the fame fpecifick Gravities, which being con- trary to Experience, there is a Neccllityof ad- mitting Vacuities in the latter Sphere to anlwer the Difference of their Gravities. It is true, it may be here anfwered, that one of the equal Bodies may be fuppos'd to be more forofe than the other, and the Pores to be per- vaded by a fubtle Fluid, which paillng freely through the Bodies, is not concern d in the Im- pulfe. ^And to obviate this Objeftion, and con- fequently to make this proof of the Neceflity of ^Vacuum amount to aDemonftration, S'lvlfaac Newton has Ihewn from many repeated Experi- ments by Tendiihms in Air, Water, and Mer- cury 5 and more exaftly by Experiments on hea- vy Bodies falling in Air, and Water j that the Refiftance of Fluid Bodies is always proportio- nal to their T>enfities, that is to the Quantities ofMatter they contain, or their Vires Inertia. The Refiftance in Jluids arifes from their greater Trefiing on the Fore, than Hind part of the Bo- dies moving in them; and this muft be always in all Fluids proportional to the Quantity of Matter they contain, which preffes on thefe fides, that is, x\\cKT>enfity. Bodies moving in Fluids prefs upon and excite a Motion in the Fluids in their paffage; and this Motion thus imprefled arifes from theexcefsof the Treftfure of the Fluid upon the fore-part, above that Tref- y«r^ on the hind-part of the moving Bodies; and this I •f i ^1 '^ 14 !^l)tiofop!jtcai ^mtiplts this cxcefs of Trejfure of Bodies in Fluids, will not only raifc a Motion in them, but will alfo ua on the Bodies themfelves, by retarding their Motion, according as it is greater or lefs, whence the Rejifiances of Fluids, arife i wherefore the Refifiames of Fluids, are as tlie Quantities of Matter they contain, or their ©^w/iV/Vj, which alone can make the Exccfs greater or leffer. It is true, there is a Reiiftance in Fluids which may arife from there Elafticity^ Glutimufnefsy and the Fridion of their Parts, &c. This Rejijlance maybe leffer and in a great meafure remov'd by the change of the Figure and Size of their Parts. But thefe Confiderations have no place in any of the Fluids of our Syftem, wherein Experiments have been made, it having been always found that their Rejtftances were proportional to their Denfities. So that no Subtilization^ T^tvifionoi parts, or Refining can alter their Refifi:anceSy thefe depending intirely on their Denfities or Vires inertia, that is, the Quantities of Matter they contains and the moft fubtile ^yEther would give the fame Refifiance to'z Projeftile, as Mercury y if the Denfity or Quantity of Matter were the fame in the firft as the laft : for that * being fuppofed, the Exccfs of the Preffure or Weight on the fore-part, above that on the hind-port of the Vroje6iile would be the fame in both, on which alone the Refiftances of both depend. Since it is weight alone, that is matter, that can produce Treffure in inanimate Bodies. Fide of 3Bleli5tott> ^5 Vide Newton. Schol. Vrop. XL. lib. 11. id. Edit. From all which it is plain that if Bodies be ever fo ^(Mrofe and fiird with Fluids ever fo Subtile^ yet if there be no Vacuities without Matter in- tirely, thefe y^^r^?/^ Bodies muft be equally heavy with the moft compad ones, fince the Fluids repuir'd to fill thefe Pores muft be equally hea- vy with the folid Body, fince both muft contain an equal Qiiantity of Matter if there be no Va^ tuitieSy all Fluids refifting, that is indeed weigh- ing, in proprotion to the Quantities of Matter they contain. If therefore there be no Vacuities^ all Bodies muft be equally heavy, which being contrary to Experience, there is a Neceflity of ad- mitting Vacuities^ to account for the different Weights of Bodies. L A ^ 11. TIE Changes made in the Mo- are always pro- % xiii.^ J^ tions of Bodies portional to the imprefs'd moving Force, and are produced in the fame Dircftion with that of the moving Force. Effefts are always proportionable to their adc' quate Caufcs, and if any Degree of Force pro- duce any Degree of Motion, a double Degree of the fame Force will produce a Double Degree of Motion, and a triple a triple, and fo on; and this Motion muft proceed in the fame Di- redtion I 6 plyiloiopf^im ^lintiplts of Beltgiott. 17 i • t reftion with that of the moving Force, fince from this only the Motion arifes j and becaufe by the former Law, Bodies in Motion cannot change their Dircftion of thcmfelves, fo that unlefs fome new Force alter its Courfe, the Bo- dy muft proceed in the fame Direftion with that of the moving Force. And if the Body was before in Motion, the Motion arifing from this imprefs'd Force if in the fame Diredion, does fo much increafe the former Motions if it has a contrary Diredion, it deftroys a part of the former Motion, equal to that which is im- prefs'dj when it has a Direftion oblique to that of the former Motion, it is cither added to, or fubftraded from the former Motion, according as the Motion arifing from a Compofition af thefe two, is determin'd. Corollary. % XIV. Hence it is evident, that in the pre- fcnt Conftitution of things, there can be no perpetual Motion. By a perpetual Motion, I mean an uninterrupted Communication of the fame degree of Motion from one part of Mat- ter to another in a Circle : not as Bodies put in Motion do for ever continue in the fame, but in fo far as they arc refitted or ftop'd by other Bodies, but a Circulation of the fame quantity of Motion, fo that it perpetually return undi- minUh'd upon the firft Mover. For by this Law Law, the Motion produc d is but proportiona- ble to the generating Force 5 and all Motions on this Globe being performed in a refitting Fluid, viz. the Air, a confidcrable quantity of the Motion mutt be fpent in the Communica- tion, on this medmmy and confequently it is im- poflible the fame Qiiantity of Motion fhould re- turn undiminifhed upon ih^faji Mover, which is neccflary toward a perpetual Motion. More- over, the Nature of Material Organs is fuch, that there is no avoiding a greater or letter de- gree of Friftion, though the Machin be form- ed according to the exafteft Principles oi Geo- metry and Mcchanicks, there being no perfed congruity nor exad fmoothncfs in Nature 5 the manner of the Cohefion of Bodies, the fniall proportion the folid Matters bears to the vacui- ties in 'em, and the Nature of the conttituent Particles of Bodies, not admitting the fame. Bc- fides, how very imperfed our mott finifhed Me- chanick Performances are, a very ordinary Mi- rr^y?^;> J' % 1: I. I I ! k * « I if.j Corollarj i. % XVI. If a Body ji^ be impeird by two different Forces, one in tlie Direftion A jB, with the Velocity M^ another in the Diredion AC, with the Velocity N, make AB to ACy zsM toN compleat theParaleiogram^5C2), the Diagonal of which is A ©. The Compofition of both thefe Forces will make the Body de- feribe the Diagonal AT>, and in the fame time as it would have defcribed either of the Sides; for becaufe the Force, whofe Velocity is N, ads in the Diredion AQ parallel to 52), it will not in the leaft hinder or deftroy the Ve- locity in the other Force, by which it tends to the Line BT>. Wherefore the Body will reach J52) in the fame time, whether the Force, whofe Velocity is iV, be imprefs'd or not, and there- fore in the end of this time, it miift be found fome- of meligion. II fomewhere in B ©, in like manner, the Force whofe Velocity is as My ads in the Diredion J By parallel to C2), and therefore will not hinder the Velocity in the other Force in pro- ceeding to C©, and the Body will reach C© in the fame time, whether the Force, whofe Ve- locity is My ad or not, and confequcntly, in the end of the fame time, it muft be fomewhere ill C2)r but it cannot be fouiid in B "D and C2) both, but at the Point ©,. therefore, &c. , Corollary ^.\ I % XVII. From thcfc La4s, and their hcccf- fary Confequcnecs, all the kulcs of Bodies af- ceiiding or defccnding in vcjrtical Lines, may be deduced, as alfo, the Rules of the Congrcflcs and Refledions of two Bcgies, as the Geometers have fhcwn. From the preceding Corollary, the Method of compounding and rcfolving Moti- ons in any given Diredions may be drawn, for Example, {fee the former Figure) the Compofi- tion of the dircd Force A'Dy of any oblique ones, fuch as AB and 52), as alfo the Refo- lution of the dircd Force, into any oblique ones, fuch as AB and B'Dy and likewife the ratio of an oblique Force to move a Body, to that of the fame Force coming with a perpen- dicular Diredion to move the fame Body i for Example, {fee the follow ingFigure) let an oblique Force, as A C be imprefs'd upon the Body E C 3 ia i f •' *"' . ai f^liiiofopl)irai fazmciples of aaeltgfon^ ^? in C, at the Point C ereft a perpendicular C ®, and from j4 let fall a perpendicular upon C 2), and another upon CB^ then by the former Co- rollary, the Force ^C may be rcfolved into the two Forces ^2) and ^5, of which only j4 B has any Energy to move the Body jEi where- fore the oblique Force as yf C is to the I'anic Force coming with a perpendicular Diredion, as j4B to y^C, or as the fine of the Angle of Incidence ^jB to the Radius ^C. The fa'me is true of the Energy of an oblique Stroke upon the Body E, to that of the fame ftriking per- pendicularly. From the fame preceding Corollary, it fol- lows that if a Body A be impelled or drawn by three different Forces in three different Di- tcdiomAB, AE, AC, fo that the Body yields ' to to none of 'em, but continues 'maqmlikiOythc^c three Powers are to one another as three right Lines drawn parallel to their Diredions, and terminated by their mutual Concourfes. l(A^ rcprefent the Force by which the Body A is im- peird from A to 5, then will the fame A'D rc- prefent the contrary equal Force, whereby it is impell'd from A to ©. But by the former Co- rollary a Force, as ^ © impelling from -^ to © is equipollent to two others, ading in theDire- ftions^C, AEy to which the other impelling from^to©,isas^©toy^C,and^£orC©, refpeftively. So likewife two Forces afting in the Dii^edions ACy AEy and being equipollent to the Force afling in the Direaions A'Dy from AtoT> will be to the Force ading according to theDiredionyf ©, from >^ to©, as AC, AE C 4 ^^ if] f f to jiT> i and therefore the Forces ading in the Dircdions ^C and j4E, and equipollent to the Force acting in the Direftion, ^"D are to this Force afting in the Diredion ^2), as j^C, AE^ otCT>tojiDy that is, if a Body be urg'd by three different equipollent Powers in the Dire- ctions^^, AC, A By thefc three Forces fliall be to one another as ADyAQ C2> refpedive- Jy, q. e. d. and this lingle Propofition is the Foundation of all the Mechanicks, as feveral GcGineten have exprefly fliown 5 fo that it is plain, thefe three Laws do virtually comprehend all the Rules of Mcchanifm, and confequently, if any appearance contradid thefe Laws, or their ncceffary Confcquenccs, it is not to be Mechanically accounted for. So then in our future Inquiries, we have nothing to do to fliow any thing is immechanical, or not according to the eftablifh'd Laws of Nature 5 but clearly to evince, that it contradids fome of thcfe Laws or GoroIlari(;s. Of melrgrom ^5 CHAP, CHAP. II. 0/ Attra^ion or Gravitation in Bodies^ and an Account of fome of the Appearances of Nature^ from this "Principle and thefe Laws now ejiablifJxd. 5 XVIII. TTT Aving thus explained the Laws X X ^hat uninterruped Nature con- ftantly purines in bringing about her Purpofes and EfFeds. I come in the next Place to apply thefe to the moft fimple, uniform and regular Appear- ances that have as yet been obferv'd ; and thefc are the Motions of the Celcftial Bodies. Many repeated Obfervations, and almoft every fingle Appearance of thefe Bodies, evidently demon- ftrate them to revolve in Curve Lines yZnA there- fore by the ift Law to be drawn out of their rcdilinear Courfe, by fome extrinfic Forc^ ad- ing on them. Let us then enquire how it comes about, that thefe Bodies do perfeverein their Motions, and do conftantly move round in the fame Trads, without making the leaft Deviation ? Now, that can happen but one of thefe two ways, viz. Either by the Force of fome Qeleftial Fluid (call'd a Vortex) which' carries 'em about, or by fome Retentive Central Force which hinders 'em from running out in ftrait Lines, when they are once put in Motion by ^6 f^t)tiofopI)iral 0?map{es by the Fingers of him who fram'd this marvel- lous Mac h in of a World J'XIX. In order to account for the Celeflial Appearances, 2>^jG?r/^j fuppofcs the Matter of this Univerfe to have been at firft divided by Almighty God, into innumerable little equal Parts, each endow'd with an equal Degree of Motion, both about its own proper C^w/^r, and feparately among themfclves, fo as to conftitute a! Fluid 5 as alfo that feveral Colledions of thefe Earts were endow'd with a Motion about dif- ferent Points (at equal Diftances) as common Centers J fo as to compofe different VorticeSy and that thefe Parts being made round by fuch in- teftinc Motions, did produce Globules of dif- ferent Magnitudes, which he calls the Matter ai his fecond Element i as alfo that the fmall Rafpings and Filings of the angular Points of thefe Globules driven violently many different Wa}'s, did makeup the Matter of \\\s firft Ele- ment i and feeina there would be more of this firft Element that was fufficicnt to fill the Vacui- ties between the Globules of the fecond Element, lit fuppofes that the remaining Part would be driven toward the Centers of the Vortices, by the circular Motion of thefe Globules, which did for that Reafon recede from it ; and being there amafs'd in a Sphere, would in the Center of every Vortex produce a Body like the Sum that the Sun being thus fram'd, and moving about its own Axe with the Motion of the reft of of aaeligiom 7 of the Matter of the Vortex, would neccflarily throw out fome Parts of its Matter through the Vacuities of the Globules of the fecond Ele- ment, which conftitute the VorteXy cfpccially at thefe Places which are diftant from its Toles, receiving by thefe Toles as much as it lofes about the Ectiptick, and by this would be able to- carry round with it thefe Globules which arc neareft-, with the greatcft Velocity, and the re- moter with a lefs y and that fo of ncccflity thefe Globules that arc ncareft the Center of the Sun would be Icaft, for were they greater or equals they would by reafon of their Velocity, have, a greater centifrugal Force, and therefore recede from the Center. Now fhould it happen that any of thefe Sun-like Bodies in the Centers of the feveral Vortices Ihould be fo incruftatcd and weakened, as to be carry'd about \n the Vortex of the true Sun, if it were of lefs Solidity, or lefs capable of Motion than the Globules, to- wards the Extremity of the folar Vortex, thea. it would dcfcend toward the Sun, till it met with Globules of the fame Solidity, and capable of the fame Degree of Motion with it, and being fixed there, it would for ever be carried, about by the Motion of the Vortex,, v^'ithoM^ either approaching to, or receding from the. Sun, and fo become a Tlanet. Suppofing this true then, we may imagine our Syftem to have been at firft divided into leveral Vortices, in the Center of which was a lucid fpherical Body, and 4 I I I 18 |^;j!iofopl)ical ^lintipUS and that fome of thcfe being gradually incm- ftatcd, were fwallow'd up by others, more powerful and bigger, till at laft they were all dcftroycd and carried away by the biggeft Solar Vertex^ except fome few that were thrown off in right Lines from one Vortex to another, and became Comets. Hence it appears according to ^isSyfteniy that the Tlanets that are neareft the Sun, Tiiz leaft folid, which is T>es Cartes's Rea- fons, why the Moon fhows always the fame Face to us, bccnufe that Hemiffhere that is oppofite to the Earthy is fomewhat more folid than the dthcr. As atfo that the Matter of the/r/ Ele^ menty which makes up the Body of the Snn^ moves with greater Velocity the Parts of the VbrteXy and the Bodies fwimming therein, that arc neareft it, than thofe that are remoter, #hich is the Reafon why the Tlanets next the Smiy finiih their Periods fooner than thofe that are more remote ; and that thefe Tlanets move about their own AxeSy becaufe they were Sun- likty Jucid, and revolving Bodies before. % XX. Now not to mention the many De- fers in the mechanical Produftion of thisiriia- ginar)' Sifiemy I fhall only take Notice of the known C^/^/W Appearances it contradifts 5 and the Abfurdities would follow, tho' we fliould allow the Author all that he would have grant- ed. And I . It is certain, that a Vortex produc'd by the Revolution of a Sphere^ about a given Axis^ would be propagated in injinituMj if no- thing of aaeligion. ^9 thing did hinder it 5 and feeing there muft be as many fuch Vortices as there are fixt Stars, one Vortex would neceflarily run into another, and every Particle would be afted by a Motion compounded of the Motions of all the Central Spheres, which is abfure, and contrary to that Conftancy and Limitation obfervable in the Cc- leftial Appearances. 2. Since the Motion of the Parts of the Vortices neareft the Center is fwifter than that of the more remote, they will prefs upon the exterior Parts, and thereby per- pctually communicate fome part of their Mo- tion to them, and therefore thefc interior Parts of the Vortex will be continually lofing fome part of their Motion, which never being re- ftored, thefc Parts muft gradually move ftower, till at laft the Motion is quite deftroy'd. 3. Ac- cording to this HypothefiSy each 'Tlanet is of the fame Denfity with the Parts of the Vortex in which it fwims, and is govern d by the fame Laws of Motion, and is, as it were, only con- creted Parts of the Vortex : Now the Times of the periodical Motion of Bodies, carry 'd about by a VorteXy are in a duplicate proportion of the Diftances from the Center, whereas the Squares of Times of the periodical Motions of the "Planets, are as the Cubes of the Diftances from the Center, and confequently the Tla- nets cannot be carry'd about by a Vortex, 4. If a Vortex run out in infinittmy then a Body carry'd round by it would certainly dcfcribe a perfed 30 01)ilofopl)ical 0;mciplcs of Beltgtott* 31 pcrfcd Circle, unlcfs fomething folid did hin- der it, and therefore, the greater Diftance there were between thcfe folid Bounds, or the lar- 'gcr the Bafon were which contains the Vortex, in rcfpeft of the Orbit of the Body carry'd about in it, the nearer would this Orbit ap. proach to a Circle, i. e. The Excentricity of the Planets ncareft the <$*«», would be lefs than that of thofc more remote, the contrary of which is true, for that of Mercury is greater than that of Saturn. Moreover, fince the Tlanets in this Vortex would neceflarily move in Orbits nearly iimilar to that of the Sides of the containing Bafon, it would follow, that the ^>&^//^ of all the Tlanets feen from the Sun, would be direfted towards the fame fixt Stars 5 but this too is contrary to Obfervation. Likewife the Matter of the Vortex (as of every Fluid) when bound up within ftrait Bounds, muft neceflarily move fafter than when enlarg'd in a wider Channel 5 /. e. The Sun feen from the Earth, muft fecm to move fafter in the beginning of Virgo, than in the beginning of Tifces, which contradids Experience. 5 . A Body carry'd about in a Vortex of the fame Denfity with it, would neceflarily defcribe a Circle to whofe Plane, the Axis of the central Body, which produces the Circula- tion of the Fluid, would be perpendicular 5 but there is not one Tlanet to the Plane of whofe Orbit the Sun's Axis is perpendicular. Laftly, The Comets have their Orbits, not only oblique, but but fometimes at right Angles with the Plane of the Ecliptick, fometimes theCourfe of thefc Comets^ is Diametrically oppofite to that of the SuUi they perfevere in their Motions without any change, they defcribe equal Area's by a Radius from the Sun in equal times, they enter into the Vortex of the Sun, all which is impof- fible, if the So/ar Vortex mov'd round with Force fufficient to carry thcfe vaft Bodies of the Tlanets along with it. % XXL This Hypothejts is fomewhat altered and mended by the famous Mr. Leibnitz, he accommodates it better to the Celeftial Appear- ances, and makes it agree more cxaftly to the Rules of Geometry. He firft of all fhows, that all Bodies which in a Fluid defcribe a Curve- Line, are mov'd by the Fluid, for of them- felves they wou'd defcribe right Lines, and no- thing but the Fluid concurs to turn them out of their way. He next fhows, that every Tlanet is carry'd about by a Motion compounded of two other Motions, vi:z. zn Harmonical Circu- lation of the carrying Fluid, and a Tarace?itrical Motion of accefs to, or recefs from the Sim. For underftanding thefe Terms, we muft obfcrvc that the T/anetsdcCcnhcJreas by a Radius from the Sun, proportional to their times. Now the Fluid that carries the Tlanets, muft of ncceflity circulate fo as to produce this efFed, which cannot be done otherwife, than by fuppofin^ ianamerablc conccntrical Orbs of exceeding thinnels it f of aaciigion. 5? thinnefs to make up the Vortex^ every one of which has its own proper way of Circulation, viz. thofe Orbs that are neareft the Sun circu- late faftcft, and the Velocities of the Circula- tions are every where reciprocally proportional to the Diflances of the refpeftive Orbs from the Sun^ which will neceflarily make the Tlanet in whatever part of Vortex it is, defcribe equal Area's in equal Times; for thefe Area's are in a compounded proportion of their Radii or Di- flances from the SuUy and a reciprocal propor- tion of the Arches or Lengths of the Circula- tions, which in this cafe will make a proportion of equality, and this Law of Circulation of the Vortex he calls Harmonical. The Paracentrical Motion is compounded of two others, viz. the Excujfory Impreffion of the Harmonical Circu- lation, whereby all Bodies moving in a Curve ^ endeavour to recede from the Center by the Tangent^ and the Attradion of the Sun or the Gravitation of the Tlanet toward it ; and this lAx. Leibnitz is of Opinion arifes from animpulfe communicated by the Circulating Fluid. Now llnce the Tlanet s move in Elliftick Orbits, in one of whofe/^r/ the Sun is, and by a Radius from the Sun defcribe equal Area's in equal Times, which no other Law of a Circulating Fluid, but the Harmonical Circulation can ac- count for, we muft find out a Law for the Ta- racentrical Motion, that may make the Orbits Elliftick. Tht Excujfory Impreffion of the Cir- culating culating Fluid, would throw off the Tlanet from the Center by the Tangent. Wherefore the At- tradion of the Sun^ or the Gravitation of the planets towards it, muft be fufficient to deftroy this Effed 5 and befides, to make them move in Elliptick Orbits, which cannot be brought about, unlefs this Attraction or Gravitation be reciprocally as the Squares of the Diftances from the Focus y which is the Sum of Leibnitz % Do- drine upon this Head. J XXII. But even this Account of the Cele- ftial Motions is both precarious and infuffici- ent, for thefe Realbns. i . The Comets, as was formerly faid, have their Orbits, fome of them very oblique, nay, fometimes at right Angles with the Zodiak, and fometimes the Courfesof thefe Comets are quite contrary to that of the Planets : Now the Comets defcribing about the Sun Area's, proportional to the times, muft be carry'd about by a Harmonically circulating Fluid, as well ^sx\\zTlanetSy and thus we fhould have Vortices contrary to Vortices, which is very abfurd. 2. This Suppofition is not only un- reafonable, but difagreeable to the uniform Simplicity of Nature 5 nor is there any thing in the Motions of the Heavenly Bodies fo difficult to explain, as this v txy Hy pot hejis, which is in- troduc'd to account for them. Eefides, 3. In equable Motion, the Times are always as the Spaces direaiy, and the Velocities reciprocally j but in a Circular Motion, the Spaces in one Re- D volution ; Every one may ea- illy fee, this is not like the uniform and fimple Meafures of Nature. Befldes, the Comets mo- ving forward in the Zodiak, pafs through all thcfe Chafms and Interftices, and notwithftand- ing, move in the fame manner, as if they were carried by a Fluid, circnlmn^, Harmonically ac- cording to fome uniform Law, neither do their Appearances fliew the leaft Sulpicion of thefc Interruptions. § XXIII. It being thus prov'd, that the Ce- Icftial Bodies do not revolve by the means of any of iReligion^ 35 any circulating Fluid, they muft be kept in their Orbits, by fome Jrtraffive Power in the Sun, or by fome gravitating Power in them to- wards him, which is the fame thing, fince it muft be mutual by the third Law. This Gra- vitating or Attrading Power of the great Bo- dies oftheUniverfe towards one another, fome Vhilofophers endeavour Mechanically to account for, from the Aftionof a Subtile Matter, which violently whirling round the Sun in general, the Earth and the reft of the "Planets in particular, and acquiring thereby a Power of receding from the Center, impels Bodies towards that Center about which the ftrongeft Circulation is made; or being driven with an immenfe Velocity in right Lines according to all poffible Direaions, impels the Body according to the Direftion of that part of this Subtile Fluid, which is leaft refifted by the interpofition of other Bodies. And thus, not only Bodies within the Sphere of the £^rr/&'s Aftivity are impell'd towards it, but alfo the Tlanets do gravitate towards the Sun, but without entering into the particular Manner of the Explication of Gravitation according to this Scheme, there be two or three Objcftions againft all the poflible Accounts of Gravity in particular, or Gravitation in general from the Circulation of a Subtile Matter, i. It is im- poflible from the firft Part of this Hypothejis, to account for Bodies gravitating towards a Point, for the Motion quaqua verfnm in a great Circle D z Pf V 'If ^T"» of Jaeiigion* 37 J of the Sphere, which is alledged to falve this Difficulty, is a Contradiclion to Nature, no fuch thing being either conceiveable or polllblc. 2. It is inipofllbie to explain whence the Cir- cular Motion of this fubtile Fluid comes, there muft be conceiv'd another fubtile Fluid moving after fome certain manner to produce the Mo- tion of that Fluid, which is the Caufe of Gra- vity, and fo on in infinitumy or elfe we muft admit its Motion without any Caufe, which is harder to conceive then Gravity it felf. 3. That Matter which is the Caufe of Gravity, or by whofe Motion it is produced in all the pollible Mechanical Explications thereof, muft be with- out Gravity which is abfurd. Matter being every where in reafon to be fuppos'd of the fame uni- form Nature, and its Gravity to be always pro- portional to the Quantity of its folid Mafs. For lince all the Bodies we can make Obfervations upon are heavy, as well as extended and impe- netrable, it is reafonable to conclude fo of all Bodies whatfoever, elfe all Univerfal Troferties in Philofophy muft be given up. And therefore it is Abfurd to fuppofe there are fome Portions of Matter without that Quality which every Portion of Matter we can make Obfervations on has. 4. Bodies from the Impulfe of a Fluid can only gravitate in proportion to their Surfa- ces, and not according to their Quantity of Matter, which is contrary to Experience 5 for We find all Bodies gravitate in proportion to their their Solidities, /. e. their Quantity of Matter 5 And tho' this Difficulty may be removed, by fuppofing Bodies to confift originally of Cylin' ^^ri of infinitely fmall 5^/^J, for on fuch a Sup- pofition, thefe Cylinders wou d be to one ano- ther as their Surfaces, their Bafeshzmg nothing and confequently, the Gravities of Bodies, which by the Adlion of this fubtile Fluid areas there Surfaces, woud be alfo as their Solidities, /. e. the Quantities of Matter they contain, fince the Surfaces of the original Particles of Bodies are a& their folid Contents Yet this is fo very hard a Toftulate, to repuire Bodies to be diverfi- fied, only by the Lengths of their primitive conftituent Cylinders y that I can t fee how it can poffibly account for all the varieties of Colours, Taftes and Smells, and other fenfible Qualities of Bodies which arife from the Diverfities of the Texture and Figure of their conftituent Parts. But that which in my Opinion, over- throws all fuch Mechanical Accounts, however artfully contrived, is that. 5. There feems to be neceffary toward a full Explication of the Appearances of Nature, feveral different Con- ditions of this Univerfal Law of Gravitation, which c2iwnothz Mechanically explain d, without fuppofmg different Syftems of this Fluid, to move after different Manners, and acording to different Laws, which will neither accord eafily together, nor feem like the Limitations and Sim- plicity of Nature. That there are different D 3 ^^^' SI t 58 ^i)aofopl)ical ^tintipits Conditions of the univcrfal Law of Gravitation, neceflfarily to be fuppofed, fccms evident from the Nature of Light, as Sir Ifaac Newton has explain'd it from certain Experiments ; and there are other Appearances in Nature, thatfeemto require Conditions different from that which governs the Motions of the Ccleftial Bodies, and caufes the Inflexions of the Light, as fliall be afterwards fhown. Now, to account Me- chanically for thefc different Conditions of the General Law ofGravitation, there muft of ne- ccffity be fuppos'd various and different Syftcms of this fubtile Fluid, which looks ? little odd, efpecially if we confider, that it is not as yet known how many and how different thcfe Sy- ftcms muft be fuppos'd, to account for all the various Conditions of this General Law, that may hereafter be difcovcred neceffary to ex- plain the various Appearances of Nature. 6. Laftly, this whole Affair is more Naturally and Simply to be accounted for from Principles now to be laid down. Corollary. J XXIV. From what has been faid it appears that the Attradion or Gravitation of Bodies to- ward one another, is not to be Mechanically ac- counted for, andiincc it has been likewifc fliown, that the Tlanets cannot continue their Motions in their Orbits, without the Suppofition of fuch of Beliffton 39 an Attraftion or Gravitation, it is evident, that this muft be a Principle imprefs'd on Matter by the Creator of the World ; it is a Principle no ways effential to Matter, fince it is the Source and the Origin of the Celeftial Motions, as Sir Ifaac Newton has demonftratcd. And by the firft Law of Nature and its Corollaries, nokmd of Motion is effential to Matter, and therefore Attraaion or Gravitation cannot be effential to it 5 it is not a Refult from the Nature of Mat- ter, becaufe the Efficacy of Matter is communi- cated by immediate Contaft, and it can by no means aft at a diftance 5 for we fee an Objctt, becaufe the Light reflected from thence ftrikes immediately upon our Organs of Vifion, we fmell, becaufe Parts of the odorous Body touch the Nerves of our Noftrils, and univerfally all the other natural Effefts of material Things arc perform'd by the meer Impulfe of one Body on another, whereas this Power of Gravitation afts at all Diftances, without any Medium ot Inftm- ment to convey it, and paffes as far as the Li- mits (if any fuch there are) of the Univerle. Andafts, not \:±tMechanical Cynics, zccotA- ing to the Quantity of the Surfaces of Bodies on which it afts, but in proportion to the Quan- tity of folid Matter which thefe Bodies contain. Befides, by the firft Law of Nature, Matter is entirely paffivc in its Nature, and can no more tend to, or draw other Bodies than it can move of it felf i Ukcwife fuppofing this Gravitation D 4 ^^ 40 ^i)ilt}(opl)im Wntiplts of Beligicn* 41 1 i"* fi • — « of the Parts of Matter toward one another de- ftroy'd, yet ftill Matter would be the fame ex- tended folid Subftance. Moreover, if there were but one indivifible Part of Matter in be- ing, it could not be faid to have this Property, it being a relative one, and having refpeft only to other Farts which it attradsj whereas Impe- jietrability or any other of the cflcntial Proper- ties of Matter continues with it, even when it becomes indivifible. On the other Hand, if the whole Quantity of Matter now in being, were amafsd io together, that there were nci- thcr Motion nor Vacuities in it, (neither of which Suppolitions imply a Contradidion j for if any two Particles of Matter can be fo com- paded as to admit no Vacuity between them, then it is no Contradiftion to fuppofe the whole aggregat of M atter fo amafs%znd we are demon- ftrably certain, Motion is not eflcntial to Mat- ter) then the whole Mafs would either be with- out this Quality oi Attramon, or this Quality would be abfolutely ufelefs or without EfFed, which is much the fame thing in an aftive Qua- lity, as this oi Attramon is, Lattly, as Mo^ tion is in fome Circumftances, the neceflary Effea of Gravity in Bodies, and in other Cir- cumftances muft have proceeded from an ori- ginal Impreflion, (as in the /n^>^//^ Motion of the Tlunets along their Tangents) and yet is of the fame abfolute Nature in both Cafes, and certainly, is not ^/d-^^i^/ fo Matter 5 io Attra- ction £tion or Gravitation is not ejfentialto M atter, but fecms rather an original Imprefs which continues in it, by virtue of the Omnipotent Adivity, in the divine Nature y of which it is a Copy oximage in the low Degree that is fuitable to a grofsCreature, and fo may now be reckoned among thcprimary Qualities of Matter^ without which, as it is now conftituted Matter cannot be, but did not Origi- nail/ belong to it as ^Materia prima.On all which Accounts, its highly probable that thisUniver- fal Force of Gravitation is the EfFed of the©/- vine Tower and Virtue originally imprefs'd on, and by that firft Energy continued in Matter, by which the Adivity and Operations of Materia! Agents are preferved. And this Power of Gra- vitation being thus imprefs'd on Matter, is one reafon of the Diftindion between the Laws of Creation and Nature y for tho' the Energy of that firft Impreflion docs ftill laft, and is the Source and Spring of the Uniformity and Continuance of the G'/^/^/ Motions, yet its not being efTen- tial to Matter, nor arifing from its Nature, is the Reafon why it ought not to be reckoned among thofe Laws which arife from the parti- cular Texture, Figure and Difpofition of Bodies, fuch as moft of the Laws of Nature or Motion are. The chief DitBculties that I can find have ftraitned Learned Men, in admitting this Principle of the Univerfal Law of the Gravi- tation of Bodies upon one another are, i . That Ithey cannot conceiye how this Principle can be Mechani-' 4^ i^l)Uofopljrfai i&iinciplCB of aaelisi'on 4? Mechanically accounted for ; and they think it UT^hilofophkal to zAmit any Principle in the Ex- plication of the Appearances of Nature which can't be thus accounted for. It is indeed in my Opinion certain, that this Principle cannot be Mechanically accounted for 5 fqr there is no other Mechanical Qzwiz conceivable, this Principle of the Gr^w/<«//^» of Bodies upon one another, can arifc from, but the Motion of fome fubtile Fluid, and were there no other Argument againft all poflible Explications of Gravitation arifing from the Motion of a fubtile^Fluid, but this one, viz. that thereby thefc Parts of Matter which are the Caufe of, or produce Gravitation, are upon this Suppofition, deftitute of Gravity 5 I fhou'd think it fufficient to prejudice any'inquifitive Man againft fuch Explications 5 for it's certain that Nature is uniform and confiftent with it felf, and wou'd not deprive one part of Matter of fo Cardinal a Property, with which fiie had cndow'd all the reft. The whole Foundation of Natural Thilofofhy, is Simplicity and Ana- logy, or a Simple, yet Beautiful Harmony, running through all Works of Nature in an uninterrupted Chain of Caufes and EfFefts, with proper Limitations of Circumftances : And if thefe Principles be fupcrfeded, or this Chain broken, we can exped nothing but Ab- furdities and Inconfiftenccs in Thilofophy. But even the admiffion of fuch an Hypothejis removes us but one Step further from Imme ch ante al Viva' ciples. ciples, for the Caufe of the Motion of this fubtile Fluid, which is the Caufe of Gravity, is it felf Immechanical. Nor has any Body ever pretended to afllgn any other Caufe of the Motion of this fubtile Fluid, but the Omnipotent Caufe of the Univerfe 5 and fince we muft of Neccfluy admit the Motion of this fubtile Fluid, which is the Caufe of Gravitation to be unaccountable without a Firji Caufe, why niay we not rather admit this FirJi Caufe to have im- prefs'd this Property in Matter, fmce that this Difficulty is the fame in both; and that befides, the firft Suppofition is burthen'd with fevcral Additional ones, to which the fecond is not liable. There has never been any Syftem of Natural Thilofophy offered to the World as yet, that does not require fome Toflulates that arc not to be accounted for Mechanically 5 the feweft any one pretends to, are the Exiftence of Mat- ter, the Impreflion of Redilinear Motions, and the prefervation of the Faculties of Natural Agents, which no Man has pretended to account for from Principles oiMechanifm 5 and the Im- prcffion of an attraBive Faculty upon Matter, is no harder Tojlulate than any of thefe 5 but fince it is Matter of Fad and Demonftration, that Matter is in pofTeflion of this Quality 5 for we daily fee, that the Earth draws to its Center all Bodies within itsAftivity, we muft allow of it, whether it be to be Mechanically accounted /or or not 5 and fince it is not to be accounted for I 44 !&l)tlofopftfcal ^lindpUS for from Mechanical Principles, as, I think, I have demonftratcd, we muft of Necellity refer it to the Power and Influence of the Firji Caufe of all Things. For Caiifes proceed in a continual ChaiUy from more complex to more fimple Ones, and at laft to the moft ilmple 5 and when we are arrived at that Caufe, we can go no farther, clfe that Caufe would not be the moft Simple 5 and this moft fimple Caufe cannot be Mechanically explained whatfoever it may be, clfe it could not be the moft Simple : And therefore fince we muft admit of Immechanical Caufcs, fince Gravity is undeniably the Property of all the Bodies we can make Obfervations upon, and is fufficient to account for the Af- fearances of all thofe Bodies that revolve about us, as Sir Ifaac Newton has fhewn, there can be no Reafon for rejeding it, tho' it cannot ht Mechanically Qyi^\2L\n*d. 2. Another Difficulty ingenious Men have in the Conception of this Quality in Matter, is, how it can aft at a Di- fiance without any Medittm to convey this Afti- on, as of neceflity it muft. Now, were there no other Difficulty of the like Nature in Philo- fophy but this one, it might ftumble judicious Pcrfons 5 but we know the Manner oiThinking and RefleBiony oi Remembring and Senfationy arc Things not eafily to be cxplain'd, and yet wc muft admit them. The Communication of Motion from one part of Matter to another, and even the firft Produftion of Matter and Motion, of laeligiott^ 45 Motion, are not to be accounted for, and yet there is no denying that fuch Things really are, when we are capable to explain how our Souls and our Bodies ad mutually upon one another, we may come to be able to conceive how Matter ads at a Diftance without any Medium 5 but till then, it is fufficient to know, that fuch a Qua- lity is adually lodged in Matter, and that it is the Caufe of all the Great and Uniform Appear- ances of Nature. There is no Contradidion in fuppofing that the fame EfFefts may arife from Caufes not altogether the fame, but that only can be the true Caufe from which the Effcd truly proceeded. Other imaginary or Hypothe- tical Caufes have no Place in true Philofophy, In ClockSy for Example, the Hand on the Dyal- Plate, may be moved by a Spring or Weight 5 but if a particular fVatch were propofed, he would fay nothing to the Purpofe, who (hould explain all its Motions by a Spring ; when upon looking within it, he might havefound aWeight perpetuating the Motion of the Machin, which yet he could not explain by Kulcsof Mechanifm, No wife and honcft Man, who throughly un- derftands the Matter, will offer to explain by Rules ofMechanifmy how this Syjlem of Things was produc d, nor how the Faculties of Mate- rial Organs are preferv'd, whence. they arofe, and what way they communicate their Aftions and Influences to one another i it will fuffice fuch, from the Prefent Appearances to invefti- gate 46Wiofopl)icai iazincipies of aaeiigtom 47 -. -V' 1^ gate the Powers and Forces of Nature, and from thcfe to account for future Obfervations and Appearances 5 if we admit an infinitely Wife and Tawerful Being to have made this World, there will be little Difficulty in allowing him to have imprefs'd on Matter what Property he pleafcd, and if we will not admit of fuch a Being, there are much greater and harder Diffi. culties in the Mechanical Explication of the Nature of Things to be furmounted, as fliall be afterwards fliown. No Body who is but tolerably acquainted with the moft probable Difcovcries in Natural Thilafophy^ can imagine thefe to reach any far- ther, than fome of the groffer Lineament Sy or more confpicuous 0«/-//Wxof the Works of the Almighty i fince he muft be very Ignorant, who can think to fcarch Him or his IVorks out, to any tolerable Degree of Terfemon. Simplicity and Harmony are the fiircft Marks that the Difcove- ries made are of the true Kind, and^»^/^^/, the beft Rule to make them by. This is To evident in f he Principle of JttraBion, that I fliall here, tho' not in its moft proper Place, obferve a few Hints tending that Way. God has moft cer- tainly implanted fomething Analogous to At- traBion, in the greateft Central Body of each Syftem towards the leffer ones of the fame j Or, a Principle of Gravitation in thefe leflcr ones towards the greateft Central one, and to- wards each others From hence, and from their their diredly imprefs'd Motions, all their comely , regular and uniform Revolutions, Appearances'and Adions upon one another fpring. Thus it is in the great Bodies of the Univerfe. Something Analogous to this is the Spring and firft Mover (at leaft ading in the Order of God and Nature it ought to be) of all the noble and regular Adions of fpiritual Beings. God being the fole fove- reign^felfexijlent and independent Being, when he made Creatures partakers of himfclf. Ima- ges, Emanations y Effluxes and Streams out of his own Abyfs of Being, could not but im- prefs upon their moft intimate Natures and Subftances, a Central Tendency toward Him- fclf, an Eflential Principal of Re-Union with himfelf 5 which in him is a Principle of At^ traEiion of them towards him. Analogous to this Principle now mentioned in the Great Bodies of the Univerfe. As well might we fuppofe an exquifite Artificer voluntarily pro- ducing a piece of Work which fhould be the Rcverfe of his own Idea : As well may the Ray be fuppofcd T>if[imilar to the Body of the Sun, or the Stream to the Fount ain- Head \ as that infinite Power and Perfedion (hould pro- duce a fpiritual Creature, that had a neccflary Tendency to fhun or fly away from him, or even be in a ftatc of Indiffcrency toward him. SelfexiftencezndinfiniteTower muft needs fub- jcd all Beings to it felf, and infinite Perfedi- on 48 1^1)ilofopl)tcai ^limipics of l^elrgion* 49 ■It t 1' 1 !1 on niuft do it fo, as muft be mpft congruous to the Nature of the Creatures it produces, in order to make them as happy as they can be made 5 and therefore God could not make fpiritual Creatures, but he muft implant the Principle of Reunion in them, in order to bring them back to himfelf, that is, to make them happy : This is the Origin of Natural Troi^itj and Confcience. It is true, this Princi- pie may be, and in moft adually is, buried under Matter and Senfuality 5 extinguifh'd, as it were, by the more powerful Attra6lions of prefent fenfible Objeas, the Allurements of Carnal Enjoyments, and the violent "Dijlra^ eHons of the Pleafures of this World 5 fo that it is not eafily perceived, but by thofe who have for fome time faithfully followed its Di- redtion and "Drawings. But it is no lefs an eflential Principle in ^fpiritual Creature^ tho' thus ftifled and opprefs'd, than the Rational Soul is of an Ideot, tho' its Operations and Evidence be hindred and obftruded thro' the inept Organfation of its Body. This Princi- ple of Re-union in fpiritual Beings, whenever difentangled, unfolded, attended to, and regu- larly follow'd, will as infallibly lead thefe to their proper Center of Light and Blifs, and unite them for ever with it, as the Sun's At- traSiion will bring about the Seafons and Changes of the Year. On the other hand, if ihis Principle have not its Energy in this Life, when whenever the Charms and Attractions of Senfe ceafe, the acquired Principle of T>iJJimilarity ^ muft repel thefe Beings with infinite Force from their Centre, fothat the Principle oi Re-union being fet free by Death, and difintangled, and afting conftantly, becaufe Eflential, muft drive thefe Beings towards God their Original Centre^ and the Principle oiT)iJJimilarity repelling them, or forcing him to repel them with infinite Vio- lence from him, muft of neceflity make them infinitely mifcrable. Thus the future Happi- ncfs or Mifery oi fpiritual Creatures^ depends on this Principle of Re-union^ as indeed their prefent does likewife 5 for whatever is in the Order of its Nature, that is, of God, its Ori- gin, muft be Happy, fince he is fo 5 and what- ever is in a violent or unnatural State, that is, in a State oppofite to God and Happinefs, muft be in Mifery. As the Planets difturb'd by no other Attra5iionSy but from their Central Orb of Light, and one another, revolve in comely Order and beautiful Harmony, Ihedding their benign Influences on one another : So fpirituat Creatures, following the "Drawings of the lu- minous Center of their Being, and giving them- felves up to the Diredion of their innate Prin- ciple of Re-union, enjoy the whole Felicity of their Natures in their prefent State, advance in Purity and Perfeftion, and in mutual Benevo- lence and good Will towards one anothei:. Por as Motion is the neceflary Confequencc of At- E trafiion of 3aeligton. traBion in Bodies that have nothing refitting them from without, fo Love and Benevolence towards their great Origin^ and towards one another, is the neceflary EfFeft of this Princi- ple oi Re-union in free Creatures, when unfolded. Asthe^/^«r^, and even the Tlanetsztcfmi' fied by the Sun, and in fome Senfe m^dcjimi- lar to, and converted into his Subftance, by being rais'd nearer to his glorious Body : So Jpiritual Creatures 2iiz yet more refined, fpiritua- lized, and made liker the T)etty\ the nearer they approach to the Fountain of Purity and Perfeftion, by faithfully following his Attra£ih ms : which too, like the Suns, are powerful and vigorous 5 infufe Light and Strength, tho' not fenfible. In a Word, as the Attra5iion of the Sun on the Planet Sy makes them firft move, and then defcribe regular Orbits^ fo this Divine At- traSiion in fpiritual Beings, animates the Will, and aftuates the AfFeftions, and thefe do all the reft that is to be done in this prefent State : And as the difcordant Attraction of fome wan- dring Comets wou d certainly diftrad and difor- der the Harmony of the Motions and Revolu- tions of the y/^»^^j, if they approaclVd too near them 5 fogrofs irregular carnal AfFedions, earth- ly and fenfual AttraBims admitted too nigh, difturb and deftroy the beautiful Progrefs of fpiritual Beings , towards the Centre and End of their Being. VideCz^.z. Part 2. i %. XXV. §* XXV. The great and primary Law then, imprinted by the Author of Nature upon all the Bodies of this Univerfc, is that every part of every Body atPrafts every p^rt of every o- ther Body 5 alnd the moft general Conditions of this Law are, that the Force by w^hich one part attrads another in different Diftances front it, is reciprocally as the Squares of thofe Di- ftances 5 and that at the fame Diftance, the Forc^ of the Attradion or Gravitation of one pa^t toward divers others, is as the Quantity of Matter they contain : By the Vittne and; Effi- cacy of this Law, the Tlanets muft perpetually move in Elliptick Orbits, if they meet with nIor€over,rinceitisdcmonftrated,(yr^^. z.lib. i. yr/»r. ThiL Newtoni.) that Bodies,which move in a Ciiri;^, on a Plane, and by a Line drawn from them to a Point, fixt, or however moved, ^dcfcribe about that Point Area's proportional to their times; are urged or drawn by a Force tending to, or whofe Diredion is toward that Point 5 and fmce by Aftronomical Obfcrvation it is certain, that the primary Tlanets about the iy«»,and thtfecondary Tlanets zhoutthc primary Ones, defcribe equal Areds in equal times. It is evident, that the Diredion of the Force, whereby the Tlanets revolve in their Orbits, is toward their Centers : and this Force may be very properly called ^//r^(J?w^ in refped of the Central Body ; and Centripetal, in refped of the revolving Body. Lattly, Since it is likewife dc- monftrated, {Coroll. 6. Trop. 4. Lik i.Trincip. ThiL Newtoni.) that if Bodies move equably in Cmcentrick Circles, and the Squares of their periodical Times be as the Cubes of their Di- ftancesfrom the common Center 5 or, if Bodies revolve in Orbits that arc pretty near Circles, and the AJ^ids of thcfe Orbits be fixt : then the Cw/r#/f/^ Forces of thofe Bodies will be reci- procally as the Squares of the Diftances. And that the One of thefe Cafes, or the Other, is Faa, is univerfally acknowledged by all Aftro- mmers: andconfequently the Centripetal forces of the Tlanets, are as the Squares of their Di- ftances. Now th^t we may have a general View, how how a Tlanet by the fame Law, can be made approach to, and recede from the Attra^tve Central Body, which feems the greateft Diffi- culty in this Cafe 5 let us confidcr the follow- ing Scheme, wherein let S reprefent the Sun. AoBs, the Orbit of a Planet B, defcending from B to A. Let the time of its Revolution be divided into equal Parts, and then they will be reprefented by the equal Area's which are fuppofed to be defcribed by the Line B S, drawn through the Body of the Tlanet B, to the Sun S in its feveral Stops 5 "V, t, s, r, A and E 3 thefe > I 54 I^DtloCiopiifcal |^;(tttctpies of aaeUgion> 55 I ^^i thcfe Area's will be the Triangles B Sv^v St^ tSs,s Sr,rSA. Now lince the Attratiion in S encrcafcs reciprocally as the Squares of the Diftances, the Velocities of the Tlanet in its dc?f<2ending towards the 45«», muft becncreafed by the encreafmg Central Force on it, which muft make the. Safes of the Triangles larger, that is, the Arches Bvy vtyts^sr^rAy muft fttll grow longer, as the Tlanet approaches nearer the Point A. When it is come thither, it would of it felf run out in the Tangent ACy make ASq equal to A Spy equal to AS r. Then in the time in which it defcribed the AreaASr^ it would, if the Q'/^/r^/Forcein ^J werefufpend- ed, defcribe ASq i but when the Central Force afts, it muft be drawn out o( A q into A p, and defcribe the Area A Spy equal to ASq in the fame time, and fo of all the other Area's, till it afccnd to B again, and that perpetually. In a Word, the greater Velocity at A than at 5, would carry the Tlanet much further out in the Tangent A Cy than in the Tangent B ©, by which the Centralfotcc adting, it would be carry'd fur- ther out in its Orbit in afcending from A, than in defccndingfrom^i and confequently, it muft approach to iS* in defcending from J5, and recede from S in afcending from -^. By Virtue of the feme Law, and of thefe Conditions, the Moon will for ever turn round the Earth, as the Earth doth round the SuMy and the Satellits xrf ^atmn and Jupitir lound thcin^ asalfb the Cor f^ets tnets will in vayohlongElliptick Orbits defcribe about the Sun equal Areas in equal times ; but becaufe the Stmy not only attrafts the Tlanets and CometSy but alfo thefe the Suny and like- wife the "Planets attraft one another, their Or- bits will be fomewhat irregular, and differ from tyi^SiEllipfes, which will be more fenfible in the Motions of the Moon, becaufe She is fo near to us 5 and this one Confideration well apply'd, will account for all the Irregularities hitherto obferv d in the Celeftial Appearances, as Sir Ifaac Newton has fhown j likewife, fuice a great part of this our Globe is covered over with Water, it is plain, that by the joint Force of the Attraftion of the Sun and Moony the Water that lyes direftly under them, will be rais'd above its ordinary Level, which will likewife happen if they are direftly in the oppofite part of our Globe, becaufe the remoter parts of the Water will be lefs attrafted than the nearer, and the Motions produced in the Waters by the Attraftion of thefe two Z//^w^/;//a5r/V^ can't be ob- ferv'd feparately, but their Forces make up a compound Motion, which at New and Full Moon is greateft, and leaft at the ^adratures, and thefe effeds are varioufly limited by the diffe- rent Diftances of thefe Luminaries from the Earth, their T>eclinations from the iameters, of equal Solidity, and confequently of equal fpecifick Gravities, or at leaft they muft not widely differ one from another in thefe Qualities, that the Fluid may be HomogeneouSy and of the fame uniform Na- ture i from thefe general Suppofirions, all the general Appearances may be eafily accounted for. ff. XXVII. Water feems to confift of fmall, fmooth, hard, porous, fpherical Particles of equal diameters y and equal fpecifick Gravities, which have between *em fome Spaces fo large, and ranged in fuch a manner, as to be previous on all of aaclimon^ 61 1 all Sides. Their Smoothnefs makes 'em Qip eafily upon one another 5 the Sphericity keeps 'em from touching one another in more Points than one, by both which, their Friftions in Qi- ding upon one another is rendered the leaft pofliblci theirHardnelsisthercafon why Wa- ter is incomprcflibic, when the Air lodg d in it is exhaufted. ^. XXVIII. The Torojity of* the Particles of Water (which is fo great, that a Ctibical mea- fure of Waters contains at leaft forty times more Pores than Parts 5 for Water is nineteen times lighter than Gold, and confequently nineteen times rarer than Gold i and Gold will by much preflure, let Water pafs through it, and fo may be fuppofcd to have more Pores than folid Parts) accounts not only for the different Spe- cifick Gravity between Water and other Fluids, fuch as Mercury 5 but aUb for its greater Tran- fparency than moft other Fluids, the Rays of Lii^ht finding an ealy admittance on all Hands through its pervious Pores, and it fuggefts the Reafon alfo why it is more eafily concreted into a folid Form than other Fluids are. Cold and Freezings feem to proceed from fome Salin Sub- ^ance floating in the Air 5 we fee that all Saks, but more eminently fome, mix;d with Ice, pro- digiouily encreafe the Eifcds and Force of Cold, we fee all Salin Bodies produce a Rigidity and StiflFnefs in the Parts of Bodies to which they arc apply'd, much like the Eft'*cds of Freezing ; . we ''I m I 1 6i f&l)aofop|)tcai ^^i^ciplcg wc know from Mr. Boyle's Hiftory ofColdy that Freezing increafes the Dimenfioiis both of So- lid and Fluid Bodies 5 Microfcopial Obfervatians inform us, that the Figures of fomc Salts, be- fore they flioot into MalFes, are thin double wedg'd-like Particles, which have abundance of Surfaces in refpe^J of their Solidity, which is the reafon why they fwim in Water when they are rais'd once, tho* they be fpecifically heavier. But this Effed may be more juftly attributed to the fame Caufe that is prefently to be Ihown to be the Caufe of Freezing, viz. to the fmall Points of the Salts getting into the Pores of the Particles of Water, whereby thefe Salts are fufpended in the Water. In Summer, the Heat of the Sun diflblves the falin Parti- cles into a Fluid, breaks off their flcnder Points, and by its Aftion, keeps 'em in a perpetual Motion, fo that they cannot (hoot into a folid Wedge, and confequently are not able to pro- duce the Appearances of CV^upon Bqflies 5 but in Winter they are lefs difturb'd, and more at liberty to approach one another j and by Ihoot- ing into thofe Chryftals^ (as we fee the Particles of artificial Salts do, when the Liquor is ex^ pos'd to the Air) which by both their Extre- mities, infinuating themfelves into the Pores of Particles of Water, make 'em cohere, and fix 'cm in a folid Form. The Dimenfions of freez d Bodies arc cncreas'd by the Infinuations of thefe Chryftal Wedges in their Pores, and the Particles Of 3Seligiom 63 Particles of congeal'd Water are kept at fomc diftance from one another, by the Figure of thefe ChryftalSj which in Freezing, infinuatc themfelves in their Pores 5 for as I have before faid, thefe Chryjlals are obferv'd to have the Form of a double Wedge, whofe Extremities are pointed and (lender, but its Middle broader and larger, fo that when the Extremities have infmuatcd themfelves into the Pores of two watery Particles, thefe Globules cannot come to touch, by reafon of the Largenefs of the Mid- dle of thefe Chryjlals, and fo thefe Particles in Freezing, are kept at greater Diftances from one another, than they were when in a fluid Form 5 and thus the Spaces between thefe fphe- rical Particles, become larger and wider than bc;fore, which is one Reafon why Ice becomes fpecifically lighter than Water. But befides this, there are many little Volumes of Air included at feveral Diftances, both in the Pores of the wa- tery Particles, and in the Interftices form'd by their fpherical Figures. Now by the Infinua- tion of thefe Chryftals, the Volumes of Air arc driv'n out of the watery Particles, and many of 'cm uniting form larger Volumes, which thereby have a greater Force to expand them- felves than when difperfed, and fo both enlarge the Dimenfions, and leffen the fpecifick Gra- vity of Water thus congeal'd into Ice. Hence wc may guefs at the matter, how Water im- pregnated with Salts, Earths or Sulphurs, which arc i 64 l^ftiiofopixcat ^tinciplts of aaeWgion* 65 are not cafily diffolviblc, may form irfclf into Metta/s, Mineral, Gems, and other Foji/s, the Parts of thcfe Mixtures, becoming a Cement to the Particles of Water, or getting into their Pores, change 'cm into thcfe different Sub- fiances. C&roilar/. Hence it is plain, that the Quantity of Wa- ter on this our Gloie does daily decreafe, feme part thereof being every Day turn'd into ^»/- »^/, Vegetable, Mineral, oiMetaltick Subflan- ces, which are not eafily diflblv'd into their component Parts again 5 for feparate a few Par- ticles of any Fluid, and faften them to a fo- lid Body, or keep 'cm afundcr from one ano- ther, and they arc no more fluid, to produce which, a confiderablc number of thefe Parti- cles are neceflarily required. %. XXIX. Mercury feems to confift of exceed- ing fmall, fmooth, folid, fpherical or j^i&^m- dical Particles j for fmce Mercury in ever fo fmall Quantities is abfoiutely opake, and lets none of the Rays of Light pafs 5 and fmce, whatever be the Caufe of Reflexion and Re- fradion. Light being Material, muft either make or find a Paflage through every refrad- In^ Medium ^ fince like wife it is probable, that Light does not penetrate through the folid Sub- ftance of the conftituent Particles of Fluids, but rather rather through their Pores and the Vacuities form'd by their Orbicular Figures, it's plain therefore, that the Particles of Mercury have very few Pores, and if they be Spherical, that their Diameters are not much greater than thole of the Particles of Light, for thefe Interftices are as the Cubes of the Diameters of the Globules, by whofe meeting they are form'd ^ and feeing Light cannot pafs through thefe In- terftices, it is plain, that the Diameters of the Corpufclcs o{ Mercury vmSi not be much greater than thofe of Light i and if thefe Corpufcles be SpheriodicaU or Oval, their fhorteft Diame- ters muft not be much greater than the Dia- meters of the Particles of Light, to form Paf- fages for it. The Solidity of the Particles whereof Mercury confifts, and the fmallnefs of the Interftices they leave between them, ac- counts for that wonderful Gravity of Mercury^ above other Fluids. %. XXX. Air feems to confift of Spires con- torted into fmall Spheres, through the Inter-p ftices of which, the Particles of Light may freely pafs, and this is the Reafon why it is fo light, the folid Subftance of the Spires being very fmall in proportion to the Spaces tiiey take iip 5 their being fpiral, accounts for the clafticrty of Airs their being fpherical Parti- cles which gives free Paflage to any Heteroge- neous Matter, accounts for Air's being compref- fible, asalfohow when comprefs'd it retains F i^s 66 ^l)rtofopJ)ical pzmciptcs of aaeitgton. 67 its fluidity, becaufc fpiral. Spheres, tlirough which another Matter freely pafles, when com- prelVcf, form themfelves into Spheriods^ or Fi- gures moft refenibling them. Tliis Account of the properties oiAir, may perhaps pleafe fome 5 but there is another, which to others feenis the more genuine 5 for, if Air be fuppos'd to con- fift of Imaii Particles, which endeavour to re- cede from one another, with a Force recifro- cally praportional to the Diiknces betwixt their Centers 5 all the Appearances oiAir may thence be accounted for $ for upon this Hyfothefis they will compofe an Elajtick Fluids whofe Denjity is proportional to its CompreJJlon^ as Sir Ifaac Newton has demonftrated j Vrop, 2 3 . ^ag. 270. zd Edit. The diameters of the Particles of Air feem to be greater than thofe of Water 5 and the diameters of the Particles of Water, greater than thofe of Mercury j and that of the Light y by far the leaft of all, as fhall be after- wards fliown. % XXXI. Other Fluids (bcfides that of the Light, under which Name I comprehend all that which paffes under the Name oi^yEtherial 01 Subtile Matter, whiqhifliall examine here- after) feem to be compounded of thefe Pri- mitive Fluids, viz. Water, Air, Mercury and Light 5 and of Particles of Salts, Earths, Suls phurs, and fuch like Ingredients, and the Va- rieties of fuch mixt Fluids may in the general be thus eftimated. i . Suppofing all other things alike. alike, cfpecially the Primitive Fluid, and the Figure of the parts of the Ingredient, the mixt Fluids will differ proportionably to the Mag- nitude of the parts of the folid Body, which mixes with the Fluid \ thus Water or Lymph mix'd with Globules of Flelh or Blood of a greater diameter, will make a different Li- quor from the fame Lymph, mix'd with Glo^ bules of Flefh or Blood of a Ick^.iameter. 2. Ca^ teris "Paribus, (cfpecially the Fluid, the Figure, and the Diameters of the mixing Ingredient being the fame,) the Liquor will differ propor- tionably to the Difference of the Firmnefs or Softnefs of the Parts of the mixing Ingredient ; thn^ Mercury mix d with Globules of T>iamond, would make a different Fluid from Mercury mix'd with Globules of Silver or Brafs. 3 . All other things being fuppos'd the fame, the Fluid will differ proportionably to the Difference of the fpecifick Gravities of the Particles of the mixing Ingredients ; thus, a mixture of Gold and Mercury will make a different Liquor from that of Mercury and Lead, the Difference of the fpecifickGravijiies being here only confide^ red. 4. AH other things being fuppos'd the fame, the Liquor will differ according to the different Degrees of the Cohefion of the folid Parts among themfelves 5 thus, Mercury mix d with little fpherical Magnets, will make a dif-r fcrent mixture from that of Mercury mixt with little Spheres of Lead 01 Iron. And thefe feem F 2 to .i \ I 68 tdl)tiofopt)ira! ^limiyits to be the ^ritmgenial Differences of mixt Fluids 5 now, not only all thefe may be dif- ferently combin'd with one another, and with the four Trimitive Fluids, but alfo the Figures of the folid Parts in the Mixture may be infi- nitely diverfified, (whereas we have hitherto only fuppos'd all the mixing Solids fpherical) which will make an infinitely infinite Variety of mixt Liquors. J XXXII. That Light is a Body, or a ma- terial Subftance, feems to be evident from thefe Confidcrations. i. It is progrefllvc, and re- quires a determined time to go from one Place to another, and is not propagated in an Inftant, as is plain from Mr. Rotnefs Reafonings upon the Eclipfes of the Satellits of JujpiUr y{v/hich are confirm'd by the Obfervations of other jiftrmamers) whereby he demonftrates, that Light requires about ten Minutes to come from the Sun to us. 2. It may be ftopt or refifled in its Paflage from one Place to another, by the Intcrpofition of an opake Body, as other Fluids are ftopt in their Courfes by the Oppo- fition of any folid Body. 3. It may be con- gregated within a narrower, or fcattered thro' a larger Space, as is evident from rcflefting Specula^ and rcfrafting Burning-Glaffes. 4. It may be reflefted, and the Determination of its Motion changed like other Bodies, and it obferves the fame Law in its Reflexions that other Bodies do, viz. the Angle of Reflexion is of Beltgton^ 69 is always equal to the Angle of Incidence. 5. It may be put out of its Courfe more or lefs, ac- cording to the Nature of the Medium through which it paflTes. 6. It ads upon the Organs of Animals, and upon all other Bodies, as other fluid Subftances do, by ftriking upon them with a determin'd Force, by communicating a certain Degree of Motion to them, by fepa- rating their component Parts, and putting them in Motion i all thefe EfFeds we daily fee. 7. It may be confin'd and fhut up in determined Spa^ ces like other Fluids. The Light of the Sun will warm and heat other folid and fluid Bo- dies, which EfFeds, continue when their Cauic is removed 5 the Parts of Light are yearly im- prifon d in Fruits, Plants, and other Vegeta- bles, as we fee by the Spirits and warm jui- ces they afford. 8. Laftly, The Parts of Light are endow'd with various Original Colours, fome are Red, others Blue, others Tellow, and fome Green, as Sir Ifaac Newton has demonftrated, and may be feen by a Trifm apply 'd to the Hole of a darken'd Room, through which the Sun fhines. Now all thefe are the Properties of Bodies, and can belong to nothing but Mate- rial Subftances. § XXXIIL That the Particles of Light are extremely little or fmall, we may conclude from thence, that they pafs through almoft all Bodies that are pervious, fuch as ChryfiaLs, Glajfes, feveral Gems, and almoft all Fluids but F 3 Mercury \ h't)^ i!7*l I .>; H i»— 1 r ifo^W Mil of melfgfon 7» Mercury } and that it freely paffcs where no other Fluid, how thin foc\'cr, can enter, and yet, no Eye, however afliftcd, has been able to difcovcr or diftinguifh the parts 'of the grof- feft Fluid. But what moft of all demonftratcs their fmallnefs, is, that Light may be propa- gated from iimrancrable different Luminms Bo- dies, without any confidcrable -oppofition to «onc another; fuppole a Plate. of Mettal (ha* iring at the top the fmalleft Hole can be made) were ereftcd perfendicidarty upon a Horizontal 'Platte, and about it were fet innumerable lu- fliinoHs Objcds of about the fame height with the Plate, at an ordinary Diftance from it, the Light proceeding from every one of thofe Ob- )e^s, will be propagated through this fmall Hole, without interfering. This will appear by applyii^adarkObjeft in a ftraight Line againft ^t^ Luminous Body, for the Light of this Body will through the Hole be receiv'd upon the dark Body : Now it is inripoflible that fo many ^lifferent Streams ef Light cou'd be tranfmitted through fo fmall a Hole, were not the Parti- 'dcs of Light extremely fmall. Add to this, that were not the Particles of Light extremely little, being extremely fwift, (/'. e. more than a Million of times fwifrer than a Cannon- Builet, continuing in its greateft Velocity, as (hail be prefently fhown) they wou'd peircc all kinds of folid Bodies with almoft as great Facility as they do Vacuities, whereas we fee Light re- gularly eularly refledcd from fome Bodies. More- over, we find that innumerable different Spheres of Light within our Horizon, may be propaga- ted from their feveral luminous Centers, with- out interfering. How many Millions of Can- dles and Flambeaux may we fee fending out their Tides of Light, without clafhing upon one another, which argues both the Smallnefs of the Parts of Light, and the Largenefs of the void Interftices between the Particles ot Air and other Bodies. . ^. XXXIV. How extremely fwift the Parti- cles of Light are, we may gather from the forementioned Experiment of Mr. Romer's, whereby he demonftratcs, that the Streams of Light pafs from the Sun to our Earth in about ten Minutes 5 and Hugens in his Cofmotheoros, has prov'd, that a Bullet continuing in the Ve- locity with which it leaves the MuQe of the Cannon, wou'd require twenty five Years to pafs from us to the Sun : Now the Fia Ter- curfa being the fame in both, the Velocities will be reciprocally as the times, /. e. the Ve- locity of Light will be to that of a Cannon- Bullet, perfifting in its gteateft fwiftnefs, as twenty five Years is to ten Minutes; or as 1 J 14700 to one Troxime, fo that Velo- city, with which the Particles of Light pafs, will be more than a Million of times, fwiftet than a Cannon-Bullet, Moreover, the Diftance betwixt the Sun and us, is at leaft i 2000 'Dia- F 4 meters 4 {I 7^ 1&liilofopl)icai mtnar)\ts of l^cligiott^ 73 wr^r^ri of the Earth, bur allowing it to be only I Gooo DmmeterSy the Light runs a thoufand diameters in a Minute, or fix teen and half Dia- meters of the Earth in a Second, or beating of an Artery, that is more than iiooooo Toifes^ fince the "Diameter oUhc Earth contains 2865 French Leagues y and every League contains 2282 Toifes, according to the Numbers of Mr. Ticard. But Sound goes but about 180 Toifes in a Second, wherefore Light is about fix hundred thoufand times more fwift than Sound. Likcwife, fince the Eanh's middle "Diameter is 7H^ Miles, each of which contains 5000 Peet5 and fince Light goes in a Second, or in a Pulfe of an Artery, fixteen and a hzliDiame- ters of the Earth, it is plain, that in every Se- cond it runs at lead a hundred and thirty thou- fand Miles, which is a prodigious and almoft an incredible Space in fo fliort a time. But the extraordinary Eifcds of Light and Heat, fccm to require all this 5 we fee how powerfully it ads (being congregated) upon the moft com- paft folid Bodies, and we never perceive any diminution of its Force arifing from an abate- ment of its Velocity. § XXXV. The Sun and fixt Stars feem to be huge, denfc Bodies (like the Earth or T la- nets) heated to an extraordinary Degree, and their Heat probably may be preferv'd by the greatnefs of their Bodies, and the mutual Adion and Re-aftion between their Parts, and the NLight Light which they emit 5 and their Parts arc kept from fumeing away by their Fixity y and alio by vaft Weight and Denfit'y of the Atmof- pheres incumbent upon them, and powerfully comprelling them, and condenfing the Vapours and Exhalations which arife from them. The beft Image we can frame to our felvcs of the SuHy is to conceive the Body of the Sun^ and the Fhtid of Light feparated and apart, (and it is highly probable they may be adually fepa- rated, and the firft intirely drain'd of the lat- ter) the Sunt\iZi\ will be like a great Earth, only more den fe, compad, and folid. The Fluid of Eighty like that of Water or Airy but infinitely more fubtle, adive, and of finer Parts 5 and that (in compounding them again) the firft has been faturated with, or quite fwallow'd up in the lat- ter, by which the Parts of the firft has been put in ftrong, quick and vehement Vibrations.When the Sun znAfixt Stars are thus diflblv'd and drench'd in this Fluid, the Li^ht will be emit- ted from them by the vibrating Motion of their Parts, after the Manner we fee Iron, when heated to fuch a Degree, as to be juft going into Fufion, by the vibrating Motion of its Parts, fend forth with Force and Violence, copious Streams of liquid Fire all around : great Bodies preferve their Heat longeft, and that perhaps in proportion to their Diameters.. Sir Ifaac Newton has made it probable, that the Comet which appeared in 1 680, by approach- Mi « ing 74 1^!irtof0 plHcat mncmts of mtligioa 75 ing to the Sun in its Terihc4ium^ acquired fuch a Degree of Heat, as to be 50000 Years a cool- ing, whence we may guefs, that fuppofing the Sun and fixt Stars to be only Calle£lions of dcnfc and folid Matter like the Tlanets, heated to a very intenfe Degree, they may be many Milli- ons of Years without lofing any confiderablc part of their Heat. Ajhanomers iiave obferv'd a clofe, compaft and large Atmofphere about die Sun^ and there is no doubt to be made, that its Body is of the fame Nature with the other material Parts of this Univerfe, excepting what Alterations its vehement Heat may pro- duce, and conicquently, its highly probable, that the Sun and/;f/ Stars are only T/anet Aikc Bodies, vehemently heated. §. XXXVI. £(kiies and Li^ht, ad mutually npon one another, /. e. Bodies aft upon Light, in emitting reflcaing, refrading and bending its Rays, and Light upon BoiiieSy in heating them, and putting their Parts in a vibrating Motion, wherein Heat confifts, according to Sir Ifaac Newton's Difcoveries. If we fuppofc thzt Bodies ad: upon Light , by attrading it in Lines perpendicular to their Surfaces, /. e. fup- pofing two fimilar Mediums diftinguifhed by TarallelLmcs^ and that a Ray in its Paflage out of the one through the other, is urged perpen- dicularfy towards either Plane, by any Force, which at given Diftances from the Plane, is of given Quantities 5 then whatever Incli%»rtons the the Rays have to the Plane of Incidence, the Sine of the Angle of Incidence of every Ray confidered apart, fliall have to the Sine of the An^le of Ref ration a conftant ratto : In the fol- iowimr Scheme, let the fimilai; Mediums h^ dij ftin^rni'd by the two Parallel Lines A a and B b, which arc fuppos'd to define a Medium dif^ ferent from the other two. Let this Medium be divided by parallel pointed Lines Cc,^d, Ee^ Ffy into fimilar Planes. Let G //be the inci- dent Ray. And fuppofe the refra^ing Medium A a, B b, begins to aft upon it, either when it enters into it at H, or at fome certain Diftancc from it on the one fide, and ends at acertam Diftancc I TT! ';j.T;i»L.p[B 76 i^J)»tofopJj!cal ^zrnrrplcs of Belgian* 77 Diftancc from it on the other; and that at all Places between thefe two Limits, the refralting PJane afts upon the Ray in Lines whofe Di- redion '\s perpendicular to that Plane ; and that the Aftions upon the Ray at equal Diftanccs from the rcfrading Plane, be equal } and at unequal ones, cither equal or unequal at any Rate whatever. If the Impulfc of the refra£t- ing Medium AaBbovi the incident Ray G H be uniform, that is, at every Divifion of the re- framing Medium, Cc^Dd, Ee,Ff, be equal, then, according to GaliUus'sTroblem, x}\t inci- dent Ray G H, will dcfcribe in the rrfraBing Medium, the Tarabolick Curve G I, and be re- fracted into / K. Take J H, equal to F N, and creft the Perpendiculars G^, K N on the Pa- rallel Planes y^a and Bb, and the Sine of the Angle oflncidenccGy/, and ATiVthe Sine of the Angle of Reflexion, (hall be in a conftant Ratio in.all the Incidences of the Ray G H, as Sir Ifaac Newton has dcmonftrated in Trap. g^.Tage 303 . andy^tf. Trincip. Thil. id Edit, and Trop. 6. Tag.Latin Ed. Optic. And if the Impuife be un- equal on the Ray Gi/at the feveral Divifions of the refraeting Medium Cc, 7) d, E e, Ff, yet fince it mufl: be uniform through every iin- gle Divifion, if thefe be fuppos'd infinitely lit- tle and many, the Propofition will ftill hold true, whatever be the Law of the Attraftion of the Ray, provided its Diredion be Perpen- dicular to the Plane of the refraifing Medium and and equal, at equal Diftanccs from it. And fince by the zd Corollary of the 3d Law of Na- ture, the oblique Force of the incident Ray G H, may be divided into the two Forces G A and AH, and of the refraBed Ray IK, into KNitidlNi it is evident, that the Velocity of the Ray before its Incidence, is to its Velo- city after it Emerges 5 as the Sifte o£ Emergence KN, to the Sine oi Incidence, G A. And it the Velocity of the Ray before its Incidence be great- er than afterwards, that is, if the Obliquity of the Incident Ray be very Great, in refpcft of that of the RefraBion when it has enter'd the Re- framing Medium A a B b, then the Tarabolick Line will turn back toward the Plane of Inci- deiKe ; becaufe, in that Cafe, the Sine of Emer- gence will grow larger and larger, till it be- come equal to the Radius, and then the Ray muft return fomewhere at i\/in the Tarabolick Line AHmhL. Take ha equal to HA, and crea the Perpendicular a L, and it fhall be equal toy^G,that isthe Sh\e. of Incidence ^^W be equal to the Sine of Reflexion, as Sit Ifaac Ne-jt;ton has prov'd in the forecitcd Place of his Prm- ciple. Now fince it is matter of Faft and Ex- periment, that the Sines of the Angles of Inci- dence, and RefraBion of all Rays of whatever Nature, obfervc a conftant ratio, and that the Angles of Reflexion and Incidence are equal ; it is therefore on the other hand true, that the Rays of Light are thus urged by the RefraBing ' ** Media, 78 f»t)aofopi)^ral l^irncipieg Medidy and their Velocity thus abated by re^ fieBing ones, fo that it is evident, Refra£iian and RejkBion proceed from one and the fame PrincifJe, afting differently in different Cir- cumftances, that is, when the Obliquity of the Incident Ray is great, and the Refrahive Power of the Medium is alfo confiderablc, the Ray will be refleri;«irr.. Colours arue from a certain mixture of thefe. 15. i«iat the Colours of Natural Bodies depend upon the different DenfiUy of their fmali Parts, and thereby theu fitnefs to teflca Light of one G 4* If i ,1 88 faDtiofopDtcai Wncipits Colour and tranfmit that of others. 1 6. That fcveral forts of Rays make Vibrations of fcveral bigncfles, which according to their bigneflcs excite Senfations of feverai Colours much after the fame manner, that the Vibrations of the Air according to their feverai bignefles excite Sen- fations of feverai Sounds. 17. That the Har- mony and T>ifcord of Colours arife from the Proportions of the Vibration propagated thro' the Fibres of the Optick Nerves intothc Brain, as the Harmony and Difcord of Sounds arifcs from the Proportions of the Vibrations of the Air, Corollary. From what has been faid of the Nature of the Sun, and its Lights it is evident, that the Quantity of Heat and Light in the Sun doth daily dccreafe 5 like other vehemently hot Bo- dies it muft gradually cool 5 as alfo, by its Emijffion of fo.many Millions of Rays perpe- tually, quite round its Body, upon all the Tla- nets within its Syftem, which do not return, both its Bulk and Heat muft be diminiflied. It is not improbable that all the virtual Heat in the Juices of Vegetables, Metals and Mi- nerals, may be owing to the Aftion of/the im- prifoned Rays in 'em : the Produftion of Afti- mals in tht originary way, requires a certain Degree of Warmth, which proceeds from the Sun'% Influence. Some Bodies do ftifle and fufFo- of 3Relig Oceans of Rays, without any fenfiblc Diminution : But this can furprize no Body who confiders that Matter is infinitely divifiblcj for it is poffible to aflign in Numbers, a Quantity, whereof a Lody as big as the Sun may conftantly, for any finite Number of Years emit Oceans, and yet the. Sum of them all may not be greater than a cubical Inch, or even a Grain of Sand. §XU. We have akcady obferv'd, that the moft general Condition of the Univerfa/ Laii> of Gravitation in Bodies, was, that at the fame Diftancc from the Center of the attraftin? u "'c ^°!*'" "^'"^ gravitate in proportion to their Solidity, and at different Diftances, reci- frocaUy as the Squares of thofc Diftances j but this Condition may not be fo general, as alto- gether to exclude others : The way to know how this Umverfal Law is diverfify'd, in the dittcrent Bodies, is to obfervc what Lines Bo- dies in their Motions or Anions upon one ano- ther delcnbc, or what the EfFefts ofthefe Mo- tions and Anions are $ and then to invcftigatc what Conditions of the Univerfal Law of Gra- vitation will make Bodies defcribc thcfe Lines or produce thefc EfFeds. Thus if any of the rrmary or Secondary Tlanets did defcribc per- fca Circles or EUiffes about the Sun, or a ^rmarj'JPlanet phccd in the Center, the Con- dition of the Univerfa/ Law in thcfc would be, that of ^aeltg^oit. 9? that the attractive Force at different Diftances from the Center, would be as thefe Diftances direaiy. If they dcfcribed a ^Parabola, by fup- pofing the attraBive Force at an infinite Di- ftancc* or an Hyperbola, by changing the Cen- tripetal'xwto ^Centrifugal Force -, then the Con- dition of the Univerfd Larju would be, that the Force were always equable, and the fame at all Diftances in the firft Cafe, and as the Diftances direBly in the fccond, as Sir Ifaac Newton has denionftratcd, 'Prop. ii. Lib. I. Wc find, as has been infuuiatcd in the preceding Sefti- ons, That the Rays of Light in pafling tluo' different Media, arc attrafted perpendicularly, to cither the Plane of Incidence or Reflexion ; fo that the Force of Attraftion is always the fame, at equal Diftances from the fame Plane. We fee that the Parts of Air fliun or fly from one another, inftead of tending to one another ; fo that in accounting for the Appearances of Na- ture from the Univerfal Law of Gravitation, we are not ty'd to one fingle Condition, but may have recourfe to others, as the Nature and Neceflity of the Appearances fcem to require ; for the whole Difticulty of Thilofophy feems to lie in invcftii'ating the Powers and Forces of Nature, frotn the Appearances of the Mo- tions given, and then from thefe Powers to account for all the reft. J XLII. The obvious Appearances of cohe- ring Bodies are thus : Two very fmooth, wcll- poliflied I 1*11^ I i I 9 poliflied plain Bodies, put together, will firm* ly cohere, even in an cxhaufted Receiver i which (liows evidently that then: Cohejim is owing, neither to the Gravity, nor to any other Property of the Air; Saline Particles, when at a proper Diftance, and at freedom, will fhoot and unite into Clufters of thcnj- felves : All faline, cryftalline, and moft mine- ral Bodies, break in very fmooth and plain, or at leaft congruent Surfaces ; and univcrlally al- moft all hard and very compaft Bodies, breafc with Surfaces, which immediately upon the Separation, appear whitifli, which is an Evi- dence that tho' the Surfaces be very fmall, yet they are very fmooth and polifii'd, for only in- numerable little polifh'd Surfaces are fit to re- fled plentifully all kinds of Rays, whereby white Colours arc produc'd. Now thefe Ap- pearances of cohering Bodies, do naturally lead us to imagine, that one neceflary Condition toward Cohefim^ is the Plainnefs, or at leaft Congruity ot cohering Surfaces, and this feems neceflary to exclude any Fluid from lying be- tween cohering Bodies 5 for thefe Bodies can- not be faid to cohere^ or be continued, betwixt whofe cohering Surfaces, in all their Points a Fluid may infinuatc it felf. The Plainnefs and fmoothnefs of the cohering Surfaces, will make more Points come into Contaff, than when they arc rough and irregular. For whatever Caufc Cohejion arifes from, if we fuppofe that Caufc to ot aRelifiton. 9$ to aft moft ftrongly at the Conta^i, the more Points of the cohering Bodies come into Lon-^ taB the firmer the Cohejion will be 5 and tho* exad Congruity in Curve Surfaces, will bring as many Points into ContaB as plain Surfaces will, yet Curvity not being the fimplcft, nor moft expeditious Method of producmg this .Effcft, neither agreeable to Nature (who a - ways brings about all her Effecls the fhorteft and eafieft way) it feems evident, that the plainnefs and fmoothnefs of Surfaces, is one Condition of Cohefion, and that thofe Atoms that are terminated with plain Surfaces, will iaeteris partibus) produce Bodies of the firmcft Cohefion. This will appear more evident irom the contrary Qiiality in the conftituent Par- tides of Fluids : For we have Ihown before, that one neceflary Condition of Fluidity, is the Curvity of the Surfaces of the conftituent Par- ticles of Fluids, whereby their Cohefion is very fmall, in refpeft of the Cohefion of thofe Par- ticles that are terminated with plain Surfaces, and their Gravity always exceeds the Force of their Cohefion, fo that from both thefe Caufes, they eafily flip and move one upon another. We may then fuppofe, that fonie of the Tn- mary Atoms of which Bodies are conftituted, are terminated with plain Surfaces on all fides, which will produce Bodies of the firmcft Co- hefion 5 others are partly terminated with plain, and partly with curve Surfaces, which will ^ produce ill d. I 1 96 fBDiiofopDtcal mndpits of aaeligiott^ 97 produce Bodies of a mean Cohefiom others again are intircly terminated with €urt)e Surfa- ces, which will produce Fluids, and between thofe intirely plain, and intirely curve, there arc infinite Combinations of plain and curve Sur- faces, which will account for all the various Degrees of Cohejion in Bodies, in refpeft of their Figures. But tho' this fmoothnefs and* plainnefs in the Surfaces of cohering Bodies, will bring moft Points into Contaciy yet this will not hinder them from being feparated by any Force, how fmall foevcr $ and fince we are certain, that cohering Bodies require a deter- mined Force to feparate them, there wants ftill a Cement y as it were, to hinder them from be- ing eafily feparated when join'd. Now this can be deriv'd from nothing in Nature, but that UniverfalLaw of Attradion, whereby all the Parts of Matter endeavour to embrace one another, and cannot be feparated but by a Force fupcrior to that by which they attraft one another 5 let us then enquire what Condi- tion of the UniverfalLaw will moft fitly an- fwcr the Appearances of Cohejion. %. XLIII. On the Center A, and at the Di- ftance^2>, let a Circle bedefcrib'd, to whofe Plane at A, let P ^ be perpendicular, and P be a Particle of Matter, attraded by all the Particles of this Circle, in any Condition of the Univerfal Law^ from ?, to any Point in the the Radius of the Circle draw T £, in the right Line y A, take ? F=T £, and at F draw FK parallel to AT>, of fuch a length as may reprcfent the Force wl>creby the Particle t at- trafts the Body ?, and let LKIht the Curve which the Point K thus conftantly circumftan- tiatcd generates : Sir Ifaac Newton has demon- ftrated. Tag. 196. "Prop. 90. Lib. I. Trtnctp. Thil. Mathem. zdEdit. that the Force whereby the whole Circle, upon the Radius A Dy at- jj tracts *! \k ^ ' i 98 !a|)f^^«''/^of the W^^'^' with its ^r/^*/:'^^ ^^„^vS the Arc © H (whofe Center is T, and wtxoie 5!^7«c ir^'D-y^=«« •) will co-incide with Raatusisru — •^'"~ Vr ^a w^ Twill co- ^2), and confequendy^Land i^JwUl co tncide,andthereforey^X^HlZ.=^ X« ""iV „ = I and y A=a, let ^ H be called/, then VH=x=aJry- And the Ajtraftmoi the Circle upon th7c.r/«/r/. VAxAHIL If„=2.and'p!J=^,thcnthe^r^^^H/L will be «/.r. f^^« I«>>^ (the meaning of which Ixpreffion (hall be afterwards ^'^PJ-- V/l thereforethe Attraftion will be T ^^f"^^ = multiply'd into more than Infinite i from whence it appears, that the Force of the ^Z^^^- aion in this Cafe, when 'PA = o, is greater than that in the former Cafe, where »=i. and TA = o. H i If '^ loo |ai)flofopt)ical Wntiplts m If » = 3 and Tji = oct there the ^rea AHIL will be nothing, and confequentiy the AttfaStion == TA x AHIL = oo x= i . And hence it appears that in this Cafe, if T A = o, the Attraiiion will be greater than whpn jP A = cxDjforof two Produfts,;having the fameMuI- tiplicator, that is the greater which has the grea- ter Multiplicand, fo that if A denote the At^ traBiony when !P A=o and a the Attra6iion^ when y ^ = oo, I fay, that A Is to a^ As a grea- ter than infinite is to infinite, contrary to what happened in the firft Cafe, where w = i , for the AttfaBtm in that Cafe was the fame both when 5P A was equal to o and to oo^ viz. i . If » = 2 and T A=iay then as formerly A H being call'd^, the AtttaBion =TAy. AHIL ~ I ^ jL.y^ -1' 4.^-!, ire If »^ = 3 and y ^ = £?, then AHIL will be more than infinite, but AHIL'm this third Cafe will be greater than AHIL in the fe- cond Cafe, and confequentiy the Force of the Attra6tion\^htnV A— o in both Cafes, will be greater in this Cafe than in the fecond Cafe, for the reafon now mentioned, viz. becaufe y^=:^ is a common Multiplicator in both, and AHIL in this Cafe is greater than AHIL in the fecond. l£m=^ zndTA= oo^thcn, zshcforc^ A HIL will b^ equal to nothing, and confequentiy the Attraiiion will be oo xo=i. If of Beligiott lOI ' If i« = 3 and y ^ = ^, then the Attramon f sr i^y^ ^ 4- will be equal to ^— - + ^, — 2^5 ^ sy^ i^, e^c. After this manner, the pLrcc o Ahe Attramon of the circular Tlane in an afllgnable cafe of tlje 'P'>^'''^l^ll^^^ ftancey £, and at any affignable Diftance ot the C<;r/»/f/^ from the Plane. . Prom thefe Calculations it is evident, that the FoTce of the Jma^on of the Plane upon theSrr«/?l ^^'hcn the Diftance is nothing, or when the Plane and the Corpufcle come in- to antaZ increafes when the lowers of ^c^ Diftince » increafe; thus when«=2, and y ^ = . the Force of the JttraBm^s greate thfn when n = x and TJ = o, ^f^^^^^^J'J^^'^, hi-her As alfo 'tis clear from thefe C^/f»/^^^- «i that the Force of the Amazon 'of the pTane upon the Corpufcle, at the fame finite S ftanccs decreafes fafter, or at a greater rate when the Vowersoi the Diftances arc high, than :':" ty are lower, or whei. « is a greyer Number, than when it is lefs ; thus ^ the fame finite Diftances. the Force of the ^«^^ T r"f ?rra7d7ot oterwier; than when » = i, or 2, ana lu v' the Difference between n in one Cafe and in the other, is yet greater. i f\ H 3 Laftly, Laftly, Suppofe the attraftcd Particle jP and T AH ah and ? O to be the Afymptotes of the Hyperboldy whofe Ordinates are proportional to the AttraSlion of a Particle at their refpedivc LJt ■'■4 •tl Diftanccs from 5P, then if the Attraiiion be re- ciprocally as the Diftanccs, having defcrib'd the common Hjferkh ilILy whofc Ordi- nates t5?^ V^*' of 3ReUsiott< lO^ ^ r .,^1 tr. _-L- the AttraEiion of a nates y^ L arc equal to ^-^ ttie ^» r Circle whofc Radius is^^.J^UJ^^^^^^^^^^^ being made ^^"^^^^^1?^^;^,"^ ? ^, the Attra- is plac'dat an infinite l^"^"'^^i^ *'. ^u;. /-.r. ^;L will \.^ahil^'PA. But m this Cafe a dq ^i,_Z— L=o,yyhcvdozc ah il^al><.ah- JL-y.ah, and the Attramon is ah, that is o, or r.fifiitely lefs than at any finite Diftance. Likc- wTfc when TA is infinitely ^ttk, the Sj^ace AHIL is infinitely lefs than AHy.AL,t.e. than — i fo that the Attraction which is as >* F/ ?r V *? ^ will be infinitely lefs than AH, i^i'::lto. u «m be o^^-^««s« is biggeft when AHIL= -^^q Again, let kmKMbz^ Curve whofe Or- dinates ^Mare equal to ^^, then the ^f- ^r^^i.»of a Particle being rfpr^'^fy^'^l Snuares of the Diftanccs the Force of the Cir Squares or tn jHKMy. T A : So ttt'comVarifgli^^^^^^^^^ of.^jrr.^^-^ ogetherthe W/«. of the Circle v^JD being given, and the Diftance ^^ the fame in both Cafes, they will be as the S^zcts AH II, and H 4 < ■4 ,r-iw i 04 l^Drtofopfttcai pzmcipies AHKM, which when the Diftance is infinite is, as the Ordinatcs h i and i& *,/.?. as ^^ I and y^» or as y /? to r, that is, as infinite to finite. And when the Diftance as o, it is as o to I . In the fame manner, if the Attradiion be reciprocally as the Cubes of the Diftanccs, at the Contadl the Force will be infinitely greater, than when the AttraEiion decrcafcs as the Squares. If it decreafes in a ^uadruplicat Proportion of the Diftances, the Force at Con- taft will be infinitely greater, than when it decreafes as the Cubes, and fo on. So that if n be taken fucceflively, as i, 2, 3, 4, ^c. the corrclponding Forces at Contaft will be as o. 1 . 00 . 00 % ^c. And if we fliould compare the fame Forces at an infinite Diftance, they would be o. o'. o'. o*. ^c. Now to apply this to the Cohejim of Bodies : *Tis certain that the firft Condition {viz. when the AttraBion is reciprocally as the Diftance between the attra£iing Bodies) cannot obtain in the Cohejion of Bodies j for the Difference between the Force, when the Bodies are in ContaB, and when they are at fome Diftance from one another, in this cafe is fo fmall, as does not anfwer the Appearances : for we find that the Force whereby Bodies cohere, is very much greater, when they come to immediate ContaSi of meltfitott. 105 Contaa, than when they are at ever fo fmall a finite Diftance from one another. In the fecond Condition of the Umverfal Law of Gravitation, {viz. when the Force is reciprocally as the Squares of the Diftance) the Difference of the Force of Cohefion, between Bodies at immediate ContaB, and of the fame, at fome Diftance from one another, is greater than in the former Cafe ; but not fufficient to account for this Difference obfervable m the manner of the Cohefion of Bodies. But if it were poflible to gather by Experiment, the proportion of the decreafe of this Force, m co- herintr Bodies, to the fame, at fome detcrmin d Diftances from one another, that would give the Condition of the Univerfal Law. hnt it will be very difficult to make fuch txperi- ments, becaufe the Fluids which furround Bo- dies, upon the Surface of our Globe, get in be- tween the Surfaces of Bodies when they are at any Diftance, greater than the 'Diameters of the conftituent Particles of thefe Fluids, ^id fo by their lateral Preflures, deftroy the Efficacy ot the Force whereby Bodies cohere; thus the Particles of Light, and of Air, get in between the Surfaces of Bodies, remov-d at almoft an infenfible Diftance from one another, ind fee- ing Light and Bodies aft mutually upon one another, and that the Particles of Air endea- vour to recede from one another, they render the Efficacy of the Force of AttraBion, whereby % .^1 » io6 0!)aofopi)icat mmmts whereby Bodies cohere, altogether infenfible at any Diftances from one another, greater than are the diameters of the Particles of thefe FJu- ids; and a Diftancc equal to the 'Diameters of fuch fubtile Fluids, is too fmall to be diftinguifh'd by our Senfes, howfocvcr ailifted. After all It fecms pretty difficult, to conceive all the' Varieties oiCohefion in Bodies, from that one Prmciple of Attramon, and the Plainnefs of Congruity of Surfaces. For there is no one Law of Gravitation comprehended in \ (=y) which will beget a Curve IKL M, that will an- fwer both thefe Conditions, o x AHIL = to fomething, zndT Ax AHIL = to nothing 5 which It feems it muft do to explain Cobefion. Eclidcs, It would agree much better with the Simplicity of Nature, if the general Law where n=2, which obtains In the Celcftial Bodies, could be made agree with the Appearances of CoifefioTi It is not impoffible, that the Attra- dtion, which at contaft in this laft mentioned Cafe, IS I or finite, at any Diftance whatfo- cver that human Experiments can determine or obferve, may be fo entirely dcftroyed by the Interpofition of foreign Fluids (that are not fubjcfted to any of our Experiments in ex- hauftmg, fuch as is Light, and perhaps a yet more fubtile Fluid. p-iJ. pag. ultim. zd Edit. Frtnctp. Newtoni.) afling in a contrary Dircai- on, as to leave no remaining Force in it : Or, perhaps Of laoistotu 107 perhaps the Figures of the conftitu nt Pam- 5les of Bodies are to be confidered i" /he ^^^ fair oiCohefim, as well as the l.^^ oiAttra- mon, to give a fatisfying Account of it. cTxLlV. Cohefion in general, being fuppos d aft!r fome fuch manner as h^« ^een exphin d it is no hard matter to underftand J^^/^^; whch feems to aiife from the fan^ yr/««/./.. of fmooth and plain Surfaces and of fome one o more of the mention'd Conditions of die GeZralLawofAttramon.lnhcn^yr^zelftc'i iod es, wc find the Convex fide exceedingly ft°etcW,lnfomuch, that by frequent and long continued Bendings, there become v« i¥- fures in theout-fide, which no doubt were there before or in the firft Bendings, tho' not fo hr°e,%sto be vifible, as alfo we fee the Con- .%'fide, mightily contrafted, or ^ts Parts for- cibly prefs'd together, fo as to run into Folds Tilt Convexities, on the in-fide: the fame Sing happens, when two elafiick Globpot BaUs ftrike againft one another, only the Ce;«- S" fides, are'turnd in towards their Centers; the Matter being thus, let us fuppole that two very fmooth and plain fquare Surfaces, arc ^in'd together, fo that each Particle in thefe Planes attrafts another, by fome one or other of theConditionsof the General Law of Attra- aion i if thefe Planes, by any external Force, were fo feparated, as to move upon a common fide of the Congruent fquarcs as an Axts, and TST*:^'" R 108 #Daofop!jtcal Wncmts that no foreign Fluid cndov/d with a disioin- wg Force (fuch as ^/r and Z/^>&/ are) cou'd in- tcrpofe to hinder their Aftion : it is certain that the external Force which thus fcparatcd thele Planes, ceafingtoaft, the attraffive force would immediately bring thcfe Planes together agam ; and if thefc Planes were feparated by z parallel Motion, if the Diftance were fo ImalJ, that no foreign Fluid could get in to hmdcr their Aftion, if the feparating Force ccasd, t\it attraBing Force would aftand brin» cm together again ; and in both Cafes, with a Force which may be eafily gathered from the Condition of the Law of Attraaim, and In^r A'"f /.'''"^^ ^^'""' being given. Now an Elafttck Bodies in their Aftions upon one another, changing their Figures, mull of nc- celUty have fome of their Parts in thefc Afti- ons, fcparatcd by a Parallel ot a circular Mo- tion about an Axis-, or by a Motion afttr iome manner compounded of both thefe, (for It is no matter after what manner they are dif- joincd provided they be not feparated fo far, as to admit any foreign Fluid to enter, which inay deftroy the efficacy of the Force, whereby thefc Particles attra6t one another). If we then Juppofcthe Surfaces of the Parts of the Elaflick Eodies, plain and fmooth, and that they «?- traOont another after fome one or other Con- dition of the Umverfal Law ; being feparated by a foreign Force, they muft (when that Force ceafes) of meltgion> 109 eeafcs) join together again with a ««a»";?^S;.f of Force (which is tobeeftimatedfromtheDi- ftance and Condition of the Univerfal Law be- ing given) and fo will produce all the J^pearan- ces of Elaflick Bodies. It nuy be objeded, that it does not appeat from this Account of EUfticity, how a Spnng Ihould grow ftronger the more it is bent, iuKC in that cafe, the Fijfures being ^^.^^e wider, the attraftive Force ought to be leflen d, and con- fequently the Power of i^#^.^-«^^^^^^^^^^^^^^^ fo too. All I can fay to th* is, that theie is a proper arrangement of the Parts to be brought loIinElaftick Bodies, which may m fome meafurebe more readily obtam'd or facilitated Z ufej as we fee Watches go more regularly, fmoothly and exaftly after they have been usd for fome time 5 and it is pretty certam, that Elafiick Bodies, upon this account., may ma more readily into their Adions, when the Parts Ty ufe are form'd and fix'd in the Situation moft proper for this purpolc, which at firft "they may not fo pcrfcdly be, by rcaton of the folidity and firmnefs of the Pa«s of moft Elafikk Bodies : To confirm th s, we lee Springs by too long ulage, when the Parts arc too much worn out, and the Chaps and Fil- fures become too large and vifiblc, decay and lofe their Power of ReftiMion, like other Or- eanical Bodies, which Time and too long ulc wear out and render ufclcfs for their intended purpoles. 1 1 o |&!)iiofopl)ireBion to one another, it is pof- fible to form this prefent State of things. Wc have prov'd, J XL of the preceding Chapter, that Motion is no more ejfential to Matter than Reft 5 that of itfelf it can never bring itfelf into Motion ; that it would for ever continue in the State it is put in, and^ if it was from all Eternity at Reft, it would continue fo for ever; if in Motion, it would for ever move on. Now this being the Cafe, it would have been a great advantage to their Opinion, could they have fhown whence this Motion did at firft proceed 5 fuice it is fuppos'd there is nothing befide unadive Matter itfelf to produce it. Whatever can be fuppos'd to put Matter in Motion, may at the lame time, and with the fame eafe, be fuppos'd to have direfted the feveral Parts thereof to the Places they are now in, i. ^. to have produc'd this prefent State of things. No Body can thing Motion effential to Matter , who fee any Part thereof at reft ; for what is effential to any thing, that thing can never be without it. But fome ThilofopherSy and thofe of great Name too, have aflerted, that no part of Matter, ever was nor can be I at 1 '1 II m^Bm 1 14 f&IjiiDlbpl^ical Wndpltii at abfolutc reft. For, fay they, Motion is a Quantity, and may be divided in infinitum as well as other Quantities, and a Body may be movmg any finite time, and yet never fenlibly change its relative Place 5 for the Space is as the Velocity, and if the Velocity be very fmall, the Space it moves through is fo likewife : And they alledgc, that thofc Bodies which feem to be at reft, are only alternately mov- ing very (lowly to and from the termination of the Motion, or the Obftacle. To this I an- fwer, that tho' it may be very true, that no- thing in this Univerfc is adually at abfolute reft, but that every thing is in fome degree of Motion 5 yet that abfolute Reft in Bodies is not impoflible, is clear from hence, that it implies no Contradidion : A Sphere in a Va- cuity (hould be prefs'd by two other equal Spheres, with equal Forces and contrary Di* ledions, from which preflure the intermediate Sphere would be at abfalute reft ; wherefore, if it is not abfurd a Body fliould be at abfolute refty it is impoffiblc Motion fhould be ejfentid to Matter. There is another Argument, which to me fecms very conclufive againft Motion's bcingf^w//^/ to Matter, and that is, from the infinite pofllble Varities of its Direftionsj lay- ing afide the confideration of all other Bodies, or fuppofing a Body moving in vacuo^ it muft move in one certain Direction. Now what is it that determines it to this DireBion rather than Of Beiicriom *i5 than to any other of the infinite Variety ? no Reafon can poflibly be afligned, why it fliould move rather in this than in any other of the infinite number of Direftions. And it cannot poflibly move in more than one of cm at once, and therefore it will of itfelf move in none of 'cm, L e. it will not of it felf move at all, and confequently. Motion is not ejjential to Matter. For in the Faculties of natural Things, which are not endow'd with Free-will, where there is an infinite variety of Choice, and no pofllble Reafon to determine any one Way, there can be no Choice made at all. From all which it is plain, that allowing the Abettors of this Thilofophy their Void and their AtomSy yet nothing could be produced for Want of Mo- tion, it not being effential to Matter, as has been proved, and there being nothing elfe to produce it. ^ V. But allowing Matter to htfelf-exiftent and felf-movingy I would know whence came this Obliquity oiDireBiony which ihzy gratui- toufiytack to Matter; this is to afcribe Will and Choice to thefe Particles, and to alledge, that they are capable of refolving what way they will go. The Contrivers of this Scheme faw •wifely enough, that granting thefe Atoms to be felf-movingy yet nothing would follow but an eternal wandering in Lines /^^r^//^/ to one ano- ther, without any other effeft 5 and therefore Ihcy added, that thefe Particles moved with I z dif. i I I i 6 laiittofoofttcai Wntiplts different ablique T)treEiions to one another, by which means they would meet, and juftle, and rcfleft, innumerable different Ways. But does not every Body fee, that it is as eafie and as intelligible to fuppofe this World already in Being, as to fuppofe thefe Particles endowed with this obliquely direftcd Motion, the Caufc of the one being no lefs accountable from their Principles than the other. We fee all Motions now perform'd in the lame Diredion with that of the moving Force, and all Motions produ- ced by the fame adequate Caufe have the fame ^ireBims i and confequently, if the Motion of thefe Atoms arifcs from thcmfelvcs, they muft all follow the fame Tiire^tions % i.e. they muft all move in parallel Lines 5 and confequently, they could never meet in order to produce any regular Effca. It is furprizing we fhould not find that Matter or Bodies now can alter their Diredionsj and yet, according to the Opinion of. thefe Men infinite Ages by-paft, they have mov'd as they lifted. Why do they not fo ftilij Since (according to their own Suppofition) nothing has happened to alter their Nature, or the manner of their Motions ever iincc 5 it is altogether unaccountable why Matter fliould move in one DireBion rather than another, upon any other account, but the ^ireBion of the imprefs'd Force 5 and all that's alledg'd on this Head by the Favourers of this Scheme, is zkogcthci precarious and abfurj. S VI. But Of IReligioiu 117 I § VI. But allowing thele Atoms to be felf- exijienty felf-movin^, and obliquely direded, yet 'tis ftill inconceivable how they lliould pro- duce a World. For tiicfe Atoms could not move all with the fame degree of Obliquity to one another, for that would be making 'em all converge to a Point, and fo nothing but one great folid Sphere could be produced, if they happened to unite after their meeting : And if they again refleded from one another, they would produce a fluid Sphere, their reftili- near Motioirs turning into circular ones, or otherwile would wander on in right Lines as be- fore. And to make fome converge to one Point, others to another, is to fay, thefe Atoms were intelligent free Beings, which could chufe the Courfe they would go in. We have a very powerful Proof of the infufficiency of thefe Atoms, tho' endow'd with their obliquity of DireEtion to produce any thing; in the Rays of the Sun 5 which, as was before prov'd, are very fmall Parts of Matter, by the interpofiti- on of the Surfaces of rcflcding Bodies diffe- rently fituated, obtaining all poflible varities of Obliquity ; and yet thefe produce no regu- lar *yy/^«/J of Bodies, tho' they move and pro- bably juftle and interfere all imaginable ways. As I have juft now faid, thofe only whofc "D/- regions converge to a Point, could meet to produce any real Body, and even the Body which would be produc'd would only be ^fphe- I 3 rical I . M \ f ] 1 1 8 #Daofop|)ical |^?inctples rical one. So that out of all their Motions, only Spheres of different Magnitudes could be form'd, which how fmall a Part this is of the infinite variety of Bodies in this Univerfc, I leave the Reader to confidcr. The Truth of the Matter is, if Bodied were fe/fmovingy they could move what way they pleafed, and flop when and where they pleafed 5 i. e. they would be free-wiird EleBive Agents. % Vll. Again, allowing thefe Atams to be feifexiftentyf elf -moving^ and obliquely direded, yet I would gladly know, how from thence this Univerfe could be fram'd. It is not enough to fay barely thefe Atoms ^ thus difpos'd, would at laft fettle into this State of things, unlefs it be fhewn by what particular Motions ^ T>ireBions and RefieBionSy the principal Bodies of this Univerfe were fram'd. To (hew a thing pof- lible to be done^ we muft tell how, what way, and by what Laws it may be done. For un- lefs we defcend to Particulars, we are never certain it can be fo ; and 'tis as probable (till the contf ary be evinc'd, in fome Particulars at Jcaft) it may not be fo. Generals are always to be fufpefted 5 a Contradiftion may be dif- covered in the particular Explications of an Appearance that was not taken Notice of in the general Scheme i as indeed it happens in every mdividual Inftance of this preient Subjeft hi^ therto attempted. I (hall not ask of thofe who defend this Scheme^ a particular account of > aiitn i i i iii i ii '^^^^^S^ of laeustott^ 119 of the Mechanifm of every individual Appear- ance in our Syftem, for tliat indeed were end- Icfs : But if any one can tell by what Laws of Mechanifm, any one Animal or Vegetable was produc'd, or from what mcchanick Principles the Planets defcribe Elliptkk Orbits, I fhail for the fake of thefe allow their whole Scheme to be true. We all know how wretchedly 'Des Cartes (the ableft "Patron that ever this Opinion had) has blunder'd on thefe Heads, and his Fol- lowers have not mended the matter much. Ir is furprizinj? to think how any reafonable Man could believe this Univerfe to have been produc'd by Matter and Motion, when as yet no Man that ever liv'd, from thefe Principles alone, can tell bv what Mechanifm the moft contemptible of the Celepialoz terreflrialV>o- dies could be produc'd ; and yet to be fully fatisfy'd of the Truth of this Hypothejis, a Man muft underftand the particular Mechanifm of the whole Sfftent of Things, and of every in- dividual Appearance. % VII. Thefe Atoms arc fuppos'd mfrangtbley extremely compafted and hard (as indeed the Icaft Parts of Matter muft neceflarily be) which compaStednefs and hardnefs is a demonftration, that nothing could be produc'd by 'em, fmcc being fo, they could never come to cohere, in order to produce folid Bodies. The only to- lerable account of Cobejion in fuch like Parti- I 4 clcs I J.'^V tv If any of the Thilofopkers fhould (bewus fuch an Appearance, nay, if they would b'uttellus (without running upon Contradi- aions) how fuch a Machine m\ 131 if from this Power he be able to form the Idea of the Generation of an Animal, It is doing Pennance, to read the wretched Accounts of the wifeft and moft learned Thilofophers on this Head : To obferve, how in every ftep they contradid the known Laws of Motion 5 and indeed, the manner after which they would have 'em generated, is as much above the Power and beyond the Laws of Mechanifm, as the true and genuine Manner and Method of their Produdion is. From all thefe Confiderations it is evident, that an Animal cannot be produ- ced mechanically 5 it is too hard a Problem to be folv'd from fo few data as Matter and Mo- tion; for indeed, could this one be once folv'd by any of the Thilofophers, we (hould be eafily fatisfy'd of the reft 5 tho' Plants, and all theve- getable Kingdom be liable to the fame Diffi- culties, and furnidi us with the fame Objedi- onsj for they are indeed only Animals of a lower Rank. And could it be once prov'd, either by T^emonftration, or by Matter ofFaB, that a Plant or an Animal can be produc'd by Mechanifm, i. e. Nature, or the Laws of Mo- tion, the thoughtful parts of Mankind would be eafily tempted to believe, that iince the better part was produc'd by Mechanifm, the meaner, /. e. all the reft of this vifible World, might have been form'd the fame way. So that it is aMatterofthegrcatcft Confequencc, that we have demonftrated, that neither Ani- K 2 mals f f I ^1 f0!)ilo(op|)tcat ld;nnnpie5 ^ mals nor Vegetables ^an,be produc'd Mechanic cally. There arc m^ny other Arguments which I can produce, to prove the fame Propofition, which the Language I write in will not permit me to fet forth. 5 XL The Spontaneous Motioni^of the fenfl- tivc part of this Syftem^ is an eternal Contra- didion to the Laws of Mechanifm. We have fufficicntly fliewn, that neither Spontaneous (not indeed any) Motion j^cfl'cntial to Matters it is determined to one Pircdion (while in Mo- tion) which it can no more alter than move of itfclf. This our Scnfes may daily inform us of: The Bali goes on in the Diredion of the Stick, or of theBody of the Piece out of which it is fhot 5 the Arrow in that given it by the Bo wiring 5 and the Hand of the DiaKPlate in that given it by the Wheels 5 and thai necef- farily and conftantly, if not forced out of the fame by fome foreign Violence : But all Senji- tive Animals have % felf-motion^ can turn and wind, move thro' all the Points of the Com- pafs, go back and forward, as their Occafions require, or Inclination prompts 'cm. It's true, fome of our Modern ThHofojphershsiVczffznzd, that the Brute-Creation are only Pieces of Clock- work, and all their Motions are as neceffarily determin'd as that of the Hand on the Dial-platej but this Affertion is altogether precarious, and maybe deny'd aseafily asit'salledg'd.Befides, the Demonftrations apriori I have juft now brought to Of JBleugion ^^V to evince the contrary, the Obfervation and Experience of all Mankind contradids it 5 the docility and Sagacity of fome Animals demon- ftrate the contrary, and fome Brute- Animals fhew more Indications of it than fome of the Race of Mankind on whom they bcftow it. What more evident Vrook of zfpontaneous Mo- tions could thefc poor Creatures give than they do, if they were really fuppos'd to be endow'd with it ? Nothing but a Senfation in our felves of the Principle oi their Adions could create clearer Evidences of a Jpontaneous Motion. Be- iides, it is altogether impoflible to account for the far greater part of their Adions and Mo- tions from Mechanifniy as we have in the pre- ceding Propofitions fhewn at large. And we fliould be ftrangcly furpriz'd, if by any Com- bination of material Organs, we fliould pro- duce the fmallcft part of their Adions and Paf- fions. Wherefore, fince the fenfitive World is endow'd with fpontaneoul Motions, and fince this is far beyond and above the Powers of Matter, it is evident this Univerfc could not have been produced Mechanically. 5' XII. The Voluntary Motions of Rational Creatures are altogether unaccountable from the Laws of Mechanifm. Mufcular Motion is perform'd much after fuch a manner as this: (If the moft probable of our Modern Conje- dures in this Matter have any Certainty in them) the Mufcles are Bundles of Fibres, which K 3 being \ 1 I 1 34 #|)tlofopl)ical |d?tnnpleg being clofcly compaacd at both ends, terminate in their two Tendons^ each of which is inferted into fome one fix'd part of the Body or other : Every one of thcfe Fibres confifts of a prodi- gious number of leffer Fibres, or Fibrils, which arc fo many very {lender elaftick Canals bound about by fmall tranfverfe parallel or Spiral Threads, which divide thefe hollow Fibrils mto fo many elaftickQ/^J or VeficuU.^s if a Gut were vfA at equal Diftances.* Into every one of thefc VeficuUj an Artery, Vein, and Nerve enter ; the two firft to bring and carry back the Blood, the latter to carry thither likewife its proper Fipd or Spirit 5 which mixing in ihcVeJicuU with the Blood, produces a Rarefaction (the manner how, for avoiding Difputes, I fhall forbear at prefent to determin) whereby thefe VeJicuU are diftended, and their Longitudinal T)iameters (from Knot to Knot) ftraitned, and fo the length of the whole Mufcle fliortned. The Nerves arc the fecretary Duds ot" the glandulous Subftancc of the Brain, and confequently, are much of the fame Nature with the othcrExcretaries of the Body, which are nothing but fmall flender flips of the Arteries, for deriving an appropriated Juice Or Spirit from the Blood. Wherefore, fince the nervous Juice or Spirit is form'd out of the Blood, and fince the Nerves arc very fmall arterial Tubes this Spirit very probably muft move in thefc Nerves after the fame manner the Blood does in the Arteries, only with this difference, that it moves af aaeltgton. moves abundantly more flow (its Velocity being abated, either by the many Circumvolu- tions of the Artery in the Gland, which is the Oriain of the Nerve, or by the refiftance the Tuic'e meets with in the flender Pipe of the "Kerve it fclf. ) If the Circulation of the Blood be admitted, and all the Juices of the Body be allow'd to be deriv'd from it, 'tis impoffible that any of thefe Juices fliould ftagnate in their Veffels longer than till they be fiird ; and there- fore, the nervous Juice in its Chanals is pro- pell'd after the fame manner and by the lame Mechanifm the Blood is urg'd forward in the Arteries. Now in the Mufclcs of mvoluntary Motion, fuch as the Heart, the Lungs, the Sto- mach and Guts, and the mulcular Coats of the Veffels, this nervous Juice or Spirit is conftantly derived by a MechanicalNcceffity . In the Heart, while the j^uricles are full of Blood, they arc diftended, and the influence of the nervous Jui- ces into there Mufclesthereby flop'd j but when once this Blood begins to flow into the Fentn- ties, the refiftance arifing from the diftenfion ot the Auricles to the influx of the nervous Juice is taken off, and fo it flows into the mufculat Subflance of the AuricleSy and thereby they arc contraded while the Ventricles are diftended, and the influx of the nervous Juice into their Mufdcs is thereby ftop'd, till the Blood be de- riv'd into the Aorta, and the Impediment from this diftenfion to the influx of the nervous K 4 J"*^* I' <»■ ■ HJ ' > J II I* iP Wlofopljical pzincipies of laeltgtoiu '37 Juice be taken off, and fo the Ventricles come into Contraftion^ which hinders the Blood from running any more into tlie Ventricles from the Auricles, and then the Auricles are again fil- led: Andthus, byaMr^^r/zr^/Neceflity, they zQi alternately, the Auricles md Ventricles being as it were Antagonijls to one another 5 fo as that while thcfe are diftended thofe are contrafted, the diftcnfion of the firft permitting the influ- cnceof the nervous Juices into the latter; and fo on the other hand. After the fame manner are the mufcular Coats of the Blood-Vcflcis, and of the Coats of the other Veffels contain- ing Liquors deriv'd from the Blood, alternate- ^ contraded and dilated 5 for by the Contra- dion of the Heart the Blood is thrown into the Arteries, which diftends them, and fo the influence of the nervous Juice into their Muf- cular Coat is hindered 5 but when the Blood is by the impetus it has conceived, derived into the Veins, this impediment is taken off, and the Mufcular Coats of the Arteries then aft, the Membranous by the ir Elafticity concurr in g. In the Lungs the Gravity of the Atmofphere forces the Air into the fmall orbicular Veficles there- of, and dilates the Cavity of the Breaftj where- by the preffure of its fides upon them, and the Kcrvcs that aft in this Fundion is taken off, and fo the Mufclesof the T>iaphragm and the pther concurring ones are at freedom to ad, arid to diftend the Cavity of the Thorax, till the \ the preffure of the fides of the Breaft become too ftrong for thefe oppofite combin'd dilating Caufes; and then by their own Gravity, and the elaftick Force of the Ribs, they fall down and comprcfs the Lungs, and fhut up the Emif faries of the Nerves. So likewife in the Sto- mach and Guts, yij\itnt\\z Longitudinal Mufcu- lar Fibres are in Aftion, the Tranfverfe and Spi- ral ones are relax d by the prefiUre of the aft- ing Fibres upon the Emiffaries of the Nerves of the relax'd ones ; and fo on the other hand, when thofe are relax'd thefe are in adion, and univerfally in all the involuntary Motions there is a Mechanical Neceffity for the derivation of the nervous Juices into the Mufcles employ 'd in thcfe Motions. But in voluntary Motions there neither is nor can be any fuch Mechanical Neceffity, it being a plain Contradidion to their Nature ; and therefore voluntary Motion is quite contrary to the Laws of Mechanifm ; we can move our Hands and Feet how and when WQ pleafe in an inflJant, we can bend and unbend em as we will 5 there is no Mechanical Caufe imaginable to force this nervous Juice in- to the Mufcles of voluntary Motion, and no Motion can follow unlefs this Juice be deriv'd; as is plain from hence, that cutting the Nerves that ferve any Mufcle, tho' all other things continue the fame, yet no Motion will follow. And the only Conception we can form of vo- luntary Motions is, that the Mind, like a skil- ful ^ii i I (I I I I I 138 f>|)iiefopljtcal |&?mnpleg fill Mfiftcian^ ftrikes upon that Nerve which con- veys Animal Spirit^tothe Mufclcto be contra- ded, and adds a greater Force than the natu- ral to the nervous Juice 5 whereby it opens its Paflagc into the Veficles of which the Mufcu- lar Fibres confift, which it could not have done by its natural Power. But this Adion of the Mind or Will upon thefe Animal Spirits, being altogether anaccountable from the Laws of Mo- tion, it is plain, that voluntary Motion is al- together Immechankal : And indeed, were it Mechanical it co\i\d not be Voluntary 5 for what- ever ads Mechanically J ads conftantly and nc- ceflarily, and fo cannot ad voluntarily. 5 XIII. That Freedom and Liberty of choo- fing or refilling which we find in ourfelves, is altogether inconfiftent with Mechanifm. Some Men indeed deny that we have any Free-will at all 5 but thefe need only examine their own Con- fcienccs to be convinced of their miftake; they will find, that even when their Reafon would determine 'em to do fuch a thing, they have in their Power to forbear it, or to do the contra- ryj they can rife or fit ftill, go backward or forward, to (hew their own Fr^^^^r j they can chufe the Time and Place, the Degrees and Circumftances of all thefe Adions that are cal- led Free. It's true, fomc of our natural Adi- ons are neccflfary, but thefe whidwre common- ly call'd voluntary Adions, arc as much free as the nature of things will permit them. Their Of Beliijiott. 1^9 Their Power being limited. I would gladly know, what grcztci Indications of Freedom they could wi(h to have, than they now have. The Paffions of Mankind (which in moft determin their Adions) are indeed violent, but they have it in their Power to fufpend for fome time the fatisfying of them 5 which fliews, they arc not neceflariiy determin'd toward their Satisfa- dion 5 for the Adion of neceffary Agents can only be fufpended by a Miracle, Let us fup- pofe, that Man, in a perfed (late of Health, is free, and has a Power oi Election : The only In- dications he could give of this Freedom are, by doing the contrary, where there are weighty and folid Reafons for doing fuch a thing 5 or by making an EleBion among many things, when there is no imaginable Reafon to deter- min him more to one than another 5 or to be able to fufpend the efFed of natural Adions, when without thisinterpofition they would Me- chanically operate. Now it's certain that we arc; capable of giving all thefe Indications ^ to fhew our Freedom : We have it in our Power to hurt or even dettroy our felves, tho' there be the bcft Reafons in the World to hinder us from fo doing, we can take out the one and not the other, in two or more of the fame things in all Circumftances alike: Tho' Respiration be icck- onedan involuntary Adion, and tho' it is cer- tainly ^crform'dmechanically and uniformly, yet wc have it in our Power to keep in our Breaths, an4 - II ii I 1 40 #ijilof;op|>icai Wntiplt'J of MtiiQiOtt. H"^ and to fulpcnd th^ efficacy of this natural Fun- Biim for feme time ; and thi3 Teems to be one of the moft evident Indications oi Frcedort that ^an poflibly be defircd : For tho' in other Cafes it may be alledg'd, that it is the fubtile and /i»- ferceptiifle manner after which wc arc determi- ned, that makes any of our Adions feem free, yet in this Inftancc that Objedion can have no place J for if we are determin'd ever fo imper* €€ftiblyy it is by the Neceffity of Nature we are determin'd. Now it is abfurd to think, that Nature fliould determine any natural FunBion to be perform'd regularly and conftantly the fame way, and that by Mechanical Laws, and at the fame time determine this Function to be irregularly and uncertainly fufpended. On the other hand, if we are neceffarily determin'd in all our Aftions, and if we have no Freedom, it is abfolutely impoflible we (hould make any Eledion among things in all Circumftances alike 5 for if wc are determin'd, it can only be from the things themfelves without us, for all things within us are, upon this Hypothefisj to be fuppos'd to move uniformly and Mecha- nically. Now where the things without us arc in all Circumftances alike, wecan never be de- termin'd to any one of 'em by themfelves; and therefore were we not free, we could neveif make an Eledion among things altogctheralike^ By things altogether alike, I mean fuch as are alike as to all the Circumftances necefl'ary to con- conftitttte them the things requir'd. Thus two Farthings .are altogether alike, tho' they may difFpr.in fome fmall Circumftances that do liot concern the EJfence of that Species of Coin. Thus i> 3> 5> 9> ^re equally odd Numbers, and 2, 4, 6, 8, are equally even Numbers, and if 'twere proposed to affign an^ven or odd Number, there are infinitely many which are equally fuchi The fame thinp' happens in the Anlwers to all thcfe Troblemf^ which are call'd indetermin*d% and in afligning one of the Anfwers to any fuch ^rablemSj there is nothing in their Nature that can poffibly determine us,the Conditions of the Problem being had refped to 5 and therefore fuch things as thcfe are only pitch'd upon by the energy of our Wills or Freedom. In a wordi Freedom confifts not in doing any thing, orevcry thing, for thus even the Supreme Being is not free, it being impoflible for Him to do Evil \ •but in varying and diverfifying infinitely different ways, the Manner and Circumftances of what jnay be done, and chufing without conftraint, or irom any Motive foreign to the Party chufing. Butno Arguments will make a Man confefshe feels, if he be obftinately refolv'd not to confefs it! now liberty is athing felt, and is only to be found by ^ RejieBion on bur felvcs and our Adions 5 but there is one Argument which Will always have weight with the wiler and better part of Mankinds and that is, that without Free-will, Virtue and Vice, Jnftice andlnjuftice are only bare ■ -1 III 142 0!)iiofopl)rcal Wntiplts I i 1 bare Words. Now if Rational Creatures be free, as moft certainly they are, this Freedom is i plain downright Contradiftion to Mechantfik^ for Mechani/mprodviccs all its EfFcds ncccffarily. C H 4 R IV. Of the Eternal TroduBim and Duration tjif this frefent State of things. § I- TTAving, I think, fufficiently flicwn X 1 the Inconfiftcncy and Impoffibility of the Epicurean Scheme. I come to the feconft Opinion about the Origaiion of the Univerfe 5 which in few Words tells us very pofitivcly:; That this prefent ftate of Things has been from all Eternity of itfclf. To as we now « behold it 5 and that any Changes that have happened therein, have proceeded from the Laws of Mechanifm that now obtaih « in the World. " This Scheme coniifts prin- dpally of thefe two Parts, i. That this World has been for ever in the State we now behold it, 2. That it has been fo for everoi itfclf, independent of any other Caufc. This Opinion is commonly, but falfly afcrib'd to ^riftotky not as its firft Braacher, but as its tWcft Tatrm. But tho* Ariftotle held the firft part of it, viz. That the World was from all Eternity, as we now behold it, yet he did not tlliiik it was fo of itfelf% and there is a vcuy great tt it it cc of mel!3ioit» 14-a i great difference betwixt allowing this prefent S^yjlem of the Univerfe to have been created from all Eternity by an Omnipotent Caufe, and believ- ing it to have been for ever of it felf without my Cau/e. My Defign in the following Dif- couirfe, is not to difputc againft any Scheme of thofc who admit the Exiftcnce of a T>eity i i intend only to fliew. That this prefent ftate iof things could not have been from all Eternity, neither of it felf, nor without the frequent and particular intcrpofition of a %)ivine Towir, and to make it plain, that naturally, and of it felf, it tends to T>iJfolution: Tho'in the mean time, it is not to be doubted, but that that Almighty ^ower which could create, this beautiful Syftem of things, can prcfervc it in being, as long as He pleafcs. % II. That this Univerfe could never have been from all Eternity of it felf, in the prefent Condition it now is, is evident from hence, that it requires an ixtrinjick Trinciple for its fub' lifting in its prefent Condition. If one (hould fee a Piece of Clock-work, pointing out the Di- Vifions of Time exadly and regularly, heipight have fome Difficulties about the manner of its Produftion ; hut if he fhoqld fee or learn^ that it required fome Foreign Affiftance to keep it going, that its Morion depended upon fome Principle without it felf, that it requir'd wind- ing up of the Spring or Weights, he would be foon fatisfy'd it could not have been from all Eternity I 'Vf 44 ^motoyi^icai Wncipm g* . Etemitj of it felf in the ftate he then ,behel4 it. Now this is the very Condition of the Earth, the Moon, and T/aneU,^d of all the Cekfiial znd Terrejirial Af^t^nccs: Their Motions and Anions depend upon a Principle quite extrinfick to Matter, which* arifes from none of its Powers or Properties, as his* I^en Ihown in the former Chapter. The Power which produces and preferves their MotiodQ fprings from fomcthing without thetilfcf^esj and if this Power werefuipended or withdrawn; they would immediately ftop, and their Mo- tions would be deftroy'd, and th^y* would he^ come a lifelefs unaftive heap of Matter. And this Power is nothing elfe but that univcrfal Law of Gravitation, which annates the whole Frame of all the Sjftems of Bodies, which pro- ceeds from a Source both independent df, ^nd diftinft from Matter and air its Fa(fulties* Wherefore, it is altogether impoffible this pre- fent ftate of things fliould have been fronr al t Eternity of it felf, fince at prefent it cannot fub- iift in a regular and beautiful SyfteWj withoutf the perpetual influence of fome fupcrior and extrinfick Power. JUL When one tjiing depends upon another thing, as its Caufe ^ as alfo, when oh^ thing is ncceflarily requir'd for the fxiftence or Prefer- vation of another thing, thcfe can hardly be fuppos'd to have been from all Eternity of them- felvesi but much more likely feem to itnply Coiin- f of aaeugiott^ H5 CounfelandDefign, and confequently, to flow from the Wifdomand Power of fome Intelligent Being : For Selfexiftence ncceflarily implies In- dependency, as to Exiftence on any other thing, cither as Caufe or as Etfedj (I mean only of thofc things which ate about us, n)iz. the vifi- blc things of this World, which have but Qua- lities botli finite in Number and Degree j and confequently, have ajfigndhle relations to, and dependences upon one another 5 for it is other- wife in the Immenfe Being, in refped of his Creatures, which can have no proportion to Him, and He no dependance on them) and when a thing depends upon another thing as its Caufe, this implies, that the firft thing cxifts that the fecond may exift j which fuppo- fes Dcfign and Contrivance, and confequently is a fign of Produdion or Creation, and not of the Self-exiftence of thefe things. Likewife, when a thing is neceflarily •requir'd for the Ex- iftence or Prefervation of another, it plainly implies, that the firft thing exifts that the fe- cond may exift 5 which likewife fuppofcs "Defign and Contrivance, and confequently, can be no fign of Selfexiftence in thefe things. Now is there any thing more plain, than that moft o£ the things in this our Syftem are neceflary or ufeful towards the Being or Prefervation of Mankind ? Remove the ^un from us, ot us from the Sun, the Earth could bring forth no Fruits for our Supports take away the Mpon^ the L Seas I> 1 I 46 TOilofopDtcai mimms Seas would ftagnatc and the Fifli be dcftroy'd j level our Mountains we (hould have no frefli Waters 5 dcftroy our Atmafphere, or the Air's Bafticity, we (hould fwell like poifon'd Rats. Do not thefe, and a thoufand other Inftances I could alledge, demonftrate, that all the Be- ings of this Univerfe exift as the neceflary Ef- feft, or for the Exiftence or Prefervation of other Beings, and confequently, imply Cantri- VMce and Dejigm which is a moft evident fign, that all thefe things have been produced, and arc not Self-exiftent. If a wild Scythian or In- dian, who never faw a Houfe in his Life, fliould meet with a noble Talace, neatly finifli'd and finely furnifli'd, and about it fhould find Crea- tures that could not fubfift without fuch a Convenience, and fiiould plainly difcover, that the Accommodations and Conveniences of this Building were exaftly fuited, in every Circum- ftancc to the Wants and Neceflities of thefe Creatures 5 I think h*e would have no difficulty in concluding, that this Houfe was built by fome \fi(cArchiteB for the Convenience of thefe Creatures, he would certainly never dream, tliat it had for ever been there of itfelf fo as he then beheld it. Now this is the very Cafe betwixt us, and the Syftem of things about us : They have aU relations and regards to us in our prefent ftate, and to one another j there is a regular Subordination and Subfcrviency apiong all the Parts, they all confpire to great and 1 \ of aReiigrom I 47 and beneficial Ends : In a word. There is not fo much as a fupernumcrary, fupcrfluous or ufe- Jcfs Atom m the whole great and complicated Machine oi the Univerfe j every Age difcover- mg new /»«/ Caufes, and every the leaft Ob- )C&. difplaying fome new Utility or Beauty, to thofe whofeekout the Works of the Lord, and take pleafure therein: So that it is impoifible, that thofe who with due Preparation apply themfelves to them fliould ever think they could be of themfelves, or did not owe their Beino- to an All-wife and All-powerful Original. Not that the whole Syfiem of the Univerfe was con-" trived for the Race of Mankind alone j but that fince their Utility and Conveniency being fo plainly and fully confulted, in their pre- fent ftate, there can remain no doubt, that the whole Syfiem of Beings has been equally pro- vided for in this wonderful Contrivance, % IV. That Animals could not have been from all Eternity is plain, for both the Reafons alledg'd in the two former Sections. For, firft. Their Produftion and Exiftence depend upon Principles quite extrinfick from,' and indepen- dent of themfelves, I mean of their Material part. I have formerly flaown, that they can neither fubfift, nor be produc'd by the Powers of Mechanifm ; but for both require the con- ftant influence of a Principle, even different from that which governs the inanimated part of the Univerfe, viz. Gravitation. Now all that L 2 is n% )dI)fUHO)$tcal #7mcipics t is obfervable in this World (according to this Scheme) is Matter and Motion (for if wc once allow a Power diftinft from thcfe, we ruin this Hjp&thejis 5 for we do not then know how far the influence of this Power may reach, as to the Produftion and Prefervation of the pre- fcnt ftate of things.) But the Production and Prefervation of Animals is above the Powers of Matter, as has been formerly fhownj and there- fore, fince they depend upon a Principle di- llinft from, and independent of the Laws of Mechanifm^ and need a continual influence of fomc Principle, diftind from Matter and its Properties, they could not have been for ever of themfelves. Secondly, All the feveral Parts and Organs of the Animal Body, are fo pru- dently adapted to the Benefit of the whole Com- pojitumy as plainly implies Defign and Contri- vance, that itisimpofliblcto confiderthis, and imagin they have been Self-exiftent. How wifely arc the Bones articulated? How prudent- ly the Mufcles contriv'd, and how convenient- ly faftned to the feveral Places of the Body to produce the ncceflary Motions? With ^ what Judgment arc the Arteries^ Veins and Nerves ranged ? With what Wifdom are their Fluids difpos'd in their proper Velfels? How care- fully is the Propagation of the Species provided for, according to feveral Circumftances arifing from the particular Climate and Element each Animal 'xsQovifir^'dtOy and how juftly is every Par- ot meitgtott^ 149 f Particular adapted for the benefit of the whole Compound? I (hall have occafion to purfue thefe Inflrances farther hereafter 5 but any Body who is ever fo little acquainted with the Jim- £lure pf an Animal^ cannot but difcover evident Footrfeps of Tiejign and Contrivance in it, and therefore Animals cannot be Self-exifl:ent.Thefe, tvith the preceding Confiderations on this Head, make ^i,t, very improbable, if not impoflible, the present fl:ate of things fliould have been for ever of themfelves, without an Omnipotent and Omnifcient Original. I come in the next place to thofe Confiderations that feem to imply. That this prefent ftate of things is naturally, arid of it felf, tending to Decay and Diflbluti- on; and confequcntly, that it mufl: of Necef- fity have had a Beginning. § V. It has been formerly fliown, in Section XX VIII. of the preceding Chapter, and its Co- rollary, that fome part of the Nourifliment of Animals and Vegetables^ and the greateft part required to the Produdion of Minerals and Metals is a watry Fluid, impregnated with fome other Body, which, by proper Operati- ons upon this Fluid, is chang'd into a folid Form, of which but a very fmall part is ever refolv'd into Water again, whereby the quan- tity of Water on this our Globe is daily im- pair'd and diminifh'd ; whercf(5rc, if the World had laftcd from all Eternity in the State it now is, we had long fince wanted both fait and frclli Aj ■it ■ 1 5Q i^HilofopDicat Wncipit& ftcfli Water. This Decreafe of watry Fluids on our Globe is fo confidcrablc, that Sir Ifaac Mewtm makes one ufe of Comet s^ in regard to lis, to be to fupply the Earth and/other Via- mts with proper Materials for this purpofe: For as the Sea is abfolutcly necefl'ary for the prefent State and Condition of our Globe, that from it, by the Suri% Heat, Vapours may be fo plentifully rais'd, that being collefted in-f fo Clouds, they may fall into Rains, fo as to water and nourifli the Earth, for the Procrea-* tion of Vegetables of all kinds : Or being con- denfed on the cooler Tops of Mountains, may fall through their Chinks into Bafons and Rc- fervatbries, form'd by their hollow and open Texture, and thence into Rivulets and Rivers. So likewife for the Supply and Prefen'ation of the Sea^ and other Fluids in the Tlanets^ the Comets feem requifite, from whofe condens'd Exhalations and Vapours, whatever Liquor is fpent on Vegetation and Putrefaaion, may be fupply'd and rcftor'dj for all the Vegetables are nourifh'd conftantly by almoft Liquids on- ly, and from putrify'd Liquors there is a Slime conftantly falling : Hence the Quantity and Bulk of dry Earth is continually increaiing, and the Fluids, if they were not fupply'd elfe- where would perpetually decreafe, and at laft fail. Now wh«refoevcr the Decreafe of the Fluids be fix'd, whether in the Tlanets or C^- iwr/x, it's plain they do dcaeafe in this oujt of Beligion* ^5* i 1 f Syftem, and confequently, had the World lafted from all Eternity, they muft have fail'd e'rc now j for had the Tlanets wanted a regular Supply, fincc it is evident they have their Fluids conti- nually turn'd into dry Earth by Vegetation and Putrefaaion, had the World lafted from all Eternity, they had been more parch'd and dry than the Defarts of Arabia 'ere this time. But fuppofing their Supply regular from the Comets, and let thefe Comets be as many as you pleale, lefs than infinite, yetftill, had the World lafted from all Eternity, thefe Comets muft have been drain'd of all their Fluids, had they been nothing but Globes of Water, whereas we know they arc Mafles of folid dry Matter, like thcTlanets, with large grofs Jtmofpheres : So that it's evi- dent, the liquid Subftance in this our Syftem of Bodies is continually decreafmg; which feems to imply, that this prefent ftate of things is not fo contriv'd as to laft for ever, and fo could not have been for ever. g VI. It has been prov'd likewife in the pre- ceding C/^^/ffr, That tht Light oixhc Sun docs daily decreafe, and that the Body of the Sun docs continually grow cooler ; the fame may be faid of the fix'd Stars: Now had the Sun zad fix'd Stars been fro.m all Eternity, we fhould have been reduc'd long before this time to a ftatc of utter Darknefs. We arc very certain, that the Rays of the Sun arc imprifon'd in out *Plmtstind Vegetables, in our Metals and Mtne- L 4 rals. y r ' 1 5P f^DtiofopDtcat Wntipit& frclh Water. This Decreafe of watry Fluids 0B our Globe is To coniiderable, that Sir Ifaac Jttewtt^n makes one ufc of Comets, in regard to lis, to be to fupply the Earth and/other Tla- jHeis with proper Materials for ttiis purpofe: ' ]Por as the Sea is abfolutely neceffary for the prcfcnt State and Condition of our Globe, that from it, by the Sun*s Heat, Vapours may be fo plentifully rais'd, that being collefted in-^ fo Clouds, they may fall into Rains, fo as to water and nourifli the Earth, for the Procrea-? lion of Vegetables of all kinds : Or being con- denfed on the cooler Tops of Mountains, may fall through their Chinks into Bafons and Re- fervatbries, form'd by their hollow and open Texture, and thence into Rivulets and Rivers. So likewife for the Supply and Prefervation of the Sea^ and other Fluids in the Tlanets, the Comets feem requifite, from whofe condens'd Exhalations and Vapours, whatever Liquor is Ipent on Vegetation and Putrefaftion, may be fupply'd and reftor'dj for all the Vegetables are nourifli'd conftantly by almoft Liquids on- ly, and from putrify'd Liquors there is a Slime conftantly falling : Hence the Quantity and Bulk of dry Earth is continually increafing, and the Fluids, if they were not fupply'd elfe- where would perpetually decreafe, and at laft fail. Now whtrefoevcr the Decreafe of the Fluids be fix'd, whether in the Tlanets or C^- mts^ it's plain they do decreafe in this our of taeltgtom ^5^ 7t-#^ Syftem, and confequently, had the World lafted from all Eternity, they muft have fail'd c're now j for had the ^Planets wanted a regular Supply, fince it is evident they have their Fluids conti- nually turn'd into dry Earth by Vegetation and Putrefaftion, had the World lafted from all Eternity, they had been more parch'd and dry than the Defarts of Arabia 'ere this time. But fuppofing their Supply regular from the Comets, and let thefe Comets be as many as you pleafe, lefs than infinite, yetftill, had the World lafted from all Eternity, thefe Comets muft have been drain'd of all their Fluids, had they been nothing but Globes of Water, whereas we know they arcMafles of folid dry Matter, like th.i.'PlanetSy with large grofs Atmofpheres : So that it's evi- dent, the liquid Subftance in this our Syjfem of Bodies is continually decreafing; which feems to imply, that this prefent ftate of things is not fo contriv'd as to laft for ever, and fo could not have been for ever. § VI. It has been prov'd likewife in the pre- ceding Cz&^/'/'fr, That the L/^^/ of the .yaw does daily decreafe, and that the Body of the Sm does continually grow cooler ; the fame may be faid of the fix' d Stars: Now had the Sun zndfixd Stars been frqm all Eternity, we Ihould have been reduc'd long before this time to a ftate of utter Darknefs. We are very C€rtain, that the Rays of the Sun are imprifon'd in out y/«Bf jand Vegetables, in our Metals and Mine- L 4 '■^•'' y \. ^■^T^i i5^lWofopl)l(»li»10»fl!Cf Bodies IJpon Light ; and fpmc p^t of them by thor Separation from others, and their being 4mpri. fon'd in thefc Subftances^ an^ jhe Aftion of Bodies upon Light, are for eycr hindcr'4 from returning to the Body of the JW^j^qigcmfiip- pofing It were poffible, th|tt any Ray$cmiircd from that Luminous G^^^ could retuin. thither again, which is not very probable, they bcang projeded with fuch a Force and Vcloeity, and rctain'd by the AtttaElum of Bodies, where any oppofe their Courfe, and proceeding for ever in their ReBilinear Diredion, where no Bodies obftrud them. We are certain likewife, that the Fmnfain of our Heat daily impairs j that the vaft Body of the Sun is perpetually a-leffen- ing and a-cooling; not only by the fuming away of his Parts, but by the nearer Approach and ftronger Adion otCamets in their Terihelia^ ^hich carry off great Portions of his Heat and Subftance. It is very probable, that thcfe Specks and Clouds which appear gnd. difappqar on the Face of the Sun, are Vapqqr^ which fume away, and fill the Spaces through which the TlaneSs liiove,or ^TcattraBedby thdt Atmofpkeres j and. the Comets, by their fo near approach to the Sun^Xozs to ^nXQxmoUsJtmQfpher,e^:mxi&^. without all doubt, carrj^ pff confiderable Por- donsof this Subftance 5 infomuch, that Sir ^iw- Newton is of Opinion, that thele Comets may at Jaft fall into his Body, to rekindle and iiip* ply ply thi Wafte : and that thofe/ArW Stars that have difapptar'd, and now appear, may be Cticbi\i)s»Suns, rekindled by the Approach of a Comie9y')VL{t returning by the fiery Spoils of the Jii». Andtho* thcfe EfFedsbe not focon- fidcratete,^ as to become fenfible in three or four ihoii&nd Years (tho' if ancient Hiftorics be true, this abatement and diminution of the Light' and Heat has not been infenfible) yet, in an« infinity of Ages (this diminution being ftiii fomewhat) the Sun hath been reduced to the Heat and Light of a Taper long 'ere this time 5 and we had been involved in a more than Cimmerian Darknefs. But fince we ob- ferve no fuch EfFeft as this, it is plain the World has not lafted from all Eternity. % VIL But that which does infallibly de- monftrate, that this prefent ftatc of things both had a beginning, and that of thcmfelves they muft have an end, is. That our Earth, the planets, the Sun zndfxd Stars do not mdve in Spaces altogether void, but in fuch that do make at leaft fome refiftance to their Motions, I have fliewn in the preceding Chapter ^ that the Rcafon why, for example, the Tlanets move about the Sun is, that the Body of the Sun at- trads thefe Tlanets, and likewife thefe ^Planets attrad the i$W» 5 and that (fince the y/^»^^j de- fcribe Elliptick Orbits about the Sun) the at- traSive Force of the Sun upon the Tlanets is re- ci^ocaUy, as the Squares of the different di- ftances ^. |l ' " '■ 1 54 f^ttofop^al |a?mciples ces of the EiUftkk Orbit from the Suns Cen- ter in its fffus. But that befides, thefe T/anets were driven at firft, or at the beginning of their JMotion (to (peak fo) by a Force whofeDirc- ftion made an Angle with the attradive Force 5 or that at the very fame time the attradive Force of the Sun exerted it fclf on thefe Tla^ netSy they were pufli'd along in right Lines, by a Force whofe Direction was in fome man- ner or other inclin'd to that of the Direftioit of the attradive Force of the Sun, otherwife they could never have revolv'd in Orbits. • So that it's evident, the Motion of the Planets about the Sun^ is compounded of two different Motions in two different Direftions, cither of which being deftroy'd, the Vlanets muft have fall'n into the Sun^ or ftray'd for ever in right Lines 5 and tho' the reliftance of the Medium cannot alter the Centripetal Motion, (fo I call that whereby the Vianet tends towards the Smi^ yet if there be any refiftancc in the Medium through which the Planets pafs, the projeHil Motion (fo I call the other) muft decreafe and (in an infinity of Ages) be deftroy'd. Sir Ifaac Newton has indeed demonftrated, that the €e^ kftial Spaces thro' which the Tlanetary and Co- fmtary Globes do move, muft be void of all grofs material Fluids, which might make any fenfible refiftance to them : For fince all Fluids refift according to their Denfities, or in propor- tion to the Matter they contain, as has been akcady of Heltgton. 155 . fi already mentionU: And fince no fenfible refi- ftancc has been obferved to the Motion of the planets and Comet s, but that they freely move through the Mundane Space, on all Hands, and in every Point of the Compafs, without any fenfible diminution of their Motion, of neccf- fity the Spaces muft be void of all grofs and fenfible Fluids : Yet in the prefent Argument, utilefs thefe Celejlial Spzccs could be demonftra- ted to be abfolutely and Metaphyfically void, in an infinity of Ages, fome even fenfible Refi- ftancc muft have been made to their Moti- ons. I readily grant, that the prefent Frame of things is fo wifely contriv'd, that they may continue in their prefent Order, and obtain their appointed Ends for fome thoufands of Years, without any fenfible Alterations, and that their Ufcfulnefs and Advantages do not depend on indivifible Points. But when in- finite Duration is the Queftion, the Argument is confiderably, if not infinitely alter'd. There are many BLeafons for fufpeding the Celeftial Spaces, through which the Tlanets and Comets move, not to be abfolutely void. Light is a Fluid, as has been demonftrated, and pafles from tht fix' d Stars to us, and from us to them, and through all the feveral Syftems. The Sun^ very probably, throws out fome part of his Clouds and ^/;»(?/^^^r^ onxhzTlanets 5 the At-- mofpheres of the Tlanets are elaftick, and tho' dpubtlefs very rare at great Diftances from the \ ( 9 * II 1 > i 156 ^Ulf^if^^^i Wtttipits the Surfaces of their Globes 1 fo as that a Sphere df Ak of an Inch diameter, of the lame Denfi- ty as it is at the Surface of the Earth, if 'twere e3qpanded as much as the Air is at the height of a femdiameter of the Earth, would much more than fill all the Sphere within the Orbit of Ssium: Yet ftill being elaftick, they may tranfmit fomc thin Vapours into one another, as very probably they do, by all their (not al- together infenfiblc) Aftions on the Animals on our Globe. The C&mets fends Steams and Va- pours from their Tails, fufficient to fupply the £xpences of the Fluids in the TlanetSj as has been juft now mentioned. All of them, Planets and CametSj have fome fccret Influences and Aitions upon one another, even different from the bare Adion of their AtiraBims 5 all which piakt it very probable, if not demonftr^ble, that thefe Mundane Spaces arc not abfolutcly devoid of fome extremely thin and rare Fluid, whofe Aftion, tho' not fenfible in any finite time, muft have been fufficient, in an infinity of Ages, to have dcftroy'd the projeBH Moti- on; and confequcntly, long 'ere now all the ^imets and C&mets had been broiling in the Sutiy had the World lafted from all Eternity , which not having happened, it's plain this prefent ftate of things has not lafted from zWEtefnitf, in the Order we now behold it. S VIIL The real, tho* infenfiblc Changes and Variations that happen to the Ctlefiml Bo- dies '83 mMmim ^f Of BeUsfom 157 die$ in this our iSy7^^«i, in refped to one ano- ther, in their Motions, Bulks, and natural At- tra(iicns^ amount to a convincing Proof, that the prefent ftate of things was not intended to laft for ever, and confequcntly, could not have been from all Eternity. The Regular Defcrip- tion of equal Areas in equal Times in the Moon j (on which all the Philofophy of her Motions and Appearances depend) is fomewhat diftur- bed by the Adion of the Sun s befides innu- merable other Variations in her Theory y which have not all as yet been intirely coUefted or adjufted : All which pretty nearly happen to the SateliitSy with refped to their primary T/a- nets: Jupiter and Saturn diftutbing each others Motions near their Conjunftions 5 and thefe two greater ones difturbing the Motions of the lelTer, Mercury, Venus y the Earth, zwdMars-y fo that their Aphelia are continually changing in a progreffive Motion forward. The reafon why the Comets move not in the Zodiack as the Tlanets do, is, that in their Aphelia they may be at the greateft Diftances from one aQOther, and confequcntly, may difturb one another's Motions the leaft that may be, by their rxixxtyxiAAttraBioniS i not withftanding which they (o far difturb one another's Motions, as fcarce ever to return in the fame Orbit, or in the fame periodical time exaftly. That the Motions of the Tlanets are, or may be diftur- bed by the Comets, in their return into the Tlanetary 58 0Du- ration, in the Condition we now behold em, and confequcntly, that they could not have been for ever as they now be. J IX. I have obferv'd in the former Chapter, That the beft Image or Idea we could frame of the Syftems of the Univerfe was, as of a no^ ble and immenfe Machine, form'd upon the ftrid- eft Principles of a "Divine Geometry, the Whole, and its feveral Parts adjufted by Number,* Weight and Meafure, all confpiring towards, and regularly attaining fome great and magni^ ficent Ends, whole Springs are an immaterial Prmciple (if I may fo call that of Gravitation) which animates the whole and all its Parts ; an Original Imprefs, or a conftant efflux from the Divine Energy, which enables the whole, and i£o |»i)tlofopl) and it's as certain, that they do not tevolve about any common Center or Cen- ters, fince they have been obferv'd never to have Varied their Situations or Diftances from each other. Now if they be finite \xi Number, the terminating Bodies of the ma- terial Part of the World muftbe all free froiri Attradions towards the void Part, and fa muft be all approaching towards the common Ctnter of Gravity of the whole , and had the Frame of the World been eternal, they had long 'ere now all of 'em met there. Space indeed may be infinite in its Extent, but there is no imaginable Reafon to believe the Number of tKe fixd $firs is in6fff% fi:6i the ttmtmtt V 1 64 I^Dilofopl^icai |&?mcipleg material Part of the Univerfe boundlefs, fince we have very good Reafon to believe, that the folid Subftance has a very fmall Proportion to the Vacuities interfpers*d even in our SyJIem^ and that the Matter of this Univerfe is almoft nothing in refpeft of the containing Space, as has been infinuated in the former Chapter. For fince Space is infinite (as I fhall hereafter demonftrate) and fince there*s a Necefllty of admitting of aftual Vacuities, as I have formerly fhown, it*s plain, Matter cannot be infinite in its Extent, fince thereby it is not equal to Space. I very much doubt, whether one real and true Infinite, in its proper and ftrift Senfe, can be greater than another j the fe- veral Parts of Relatives or Creaturely In* finites (fo I call thofe that are generated by an uniform, convergent, or divergent Series, vide Chap. i. Fart 2.) may have finite Pro- portions to one another, but true Infinite muft be One only, to which nothing elfe can be equal. Space is infinite, as being the Place (to fpeak fo) of the Divine Ubi- qiiitjj and having fome Connexion with the true, fole, and proper Infinite ^ but Matter, if it be infinite, muft either be fo by the Neceflity of its own l^ature, or by the Will of the Creator. Not by the Ne- ceflity of its own Nature, becaufe then it muft be everywhere , which being already demonftrated falfe, it's impoflible it fliauld he infinite by the Neceffity of its own Na- ture : of SleUston^ 165 ture: For if it be true, that Matter is not every where, it is poflible it might be no where , that is, it*s poflible it fhould not be at all i and confequently, it is impoflible it fliould be infinite by the Necefllty of its own Nature. Not by the Will of the Crea- tor -, for then a Creature might be equal to its Creator, fince the jufteft Image we can form to our felves of the Creator^ is Perfeftion, apply'd to abfolute Infinitude ; and if abfolute Infinitude could be apply'd to a Creature, then, no doubt, Perfeftion might be alfo •, fo that then an infinitely perfeft Creature might be poflible, that is, there might be two or more infinitely Per- fefts, which is a Contradidion. Befides, could Matter be infinite, being of thofe Kinds of Infinites that l)ave three Dimen- fions ^ by the Analogy afid Simplicity con- ftantly obferv'd by Nature in like Cafes, it muft be fimilar, and equal to the other adual Infinite, to wit. Space. Laftly, Mat- ter is limited, in its own Nature, capable of aftual Limitations and Divifions, and feems properly defign'd for the Limits of Space, which is, in its own Nature, unli- mited •, and confequently. Matter feems not at all defign'd to be infinite in its Ex- tent. Now, if Matter be notadually infi- nite, in a proper Senfe, fince Space is fo, and fince the fixd Stars are limited in their Bulks and Sizes, it is impoflible they fliould t»p infinite in their Number , for when the M 3 Sut^ 66 ^l^iltOtp^^ Sura is finite, and each (ingle Part or Dt* yifion of the Sum is finite, the Sum of the whole of fuch Parts ca-nnot be infinite. i| IS true, we can affign no Reafon for a limi- ted finite Number of fix d Stnps^ and it is not impoflible, but that their Number may be as great as Created finite Muter can amount to, fiince alt the Works of God are immenfc, and worthy of Him who is Om- nipotent. But ftill they cannot amount tQ real and proper Infinity in Number, fince Ifatter feems.not capable, in its own Na- ture, tQ be infinite, but defignM for the Bounds and Limits of infinite Space^ and the Conveniency of the material groffer Part of animated Beings, who feem not to be infinite in their Number. Now if the fixd Stars be finite in their Number, or the material Part of this Univerfe limited in its extent, the Bodies, as the Limits of the material Part, being quite free from Jttra^ Bions upon the Side toward the infinite ^ $pace, muft yield to the attraSing Force * of the Bodies toward the common Center of gravity of the material Part, and the Boun- daries yielding, the Bodies next them muft do fo likewife, and fo on even to the Cen- ter i for nothing but an equal AttraBion pn all Hands, can keep the fix^d Stars con- ftant in their Places, and nothing but an infinite Number rangM up and down the infinite Space can be fufficient for this j Dtrherefore, fincc it has been evidently de- monftrated. of ]aeH0iott> 167 monftrated, that the material Part of this Univerfe is finite in its Extent, if the World had lafted from all Etertiiiy, the whole Matter of this Univerfe had been long before this Time amafs'd in the common Center of Gravity^ and had there made^a lifelefs Heap ^ which not having happened, it's plain this World has not lafted from all Eternity^ nor can of it felf continue to all Eternity. And it's not unlikely that the vaft, if not immenfe Diftances of the fix'd Stars from us and one another, has been delign'd to retard this EfFeft, as long as the Defigns of Providence may require. § XI. In the former Part of this Chapter^ J have demonftrated the Impoflibility of the Mechanical Produdion of Jnimals2inA Vege- tables ^ and 1 (hall have Occafion in the fol- lowing Chapter to make it evident, that every generated Animal is produc'd from a pre-exiftent Animalcid of the fame Species^ and that every Vegetable arifes from a fmall Plant of the fame Kind. And it is impofl^- ble it can be otherwife, upon our Adver- fary's Scheme of admitting nothing but Mat- ter and Motion ^ for if Animals and Vege- tables cannot be produc'd from thefe (and i have clearly prov'd they cannot) they muft of neceffity have been from all Eterni- ty •, and confequently, that all the Ant- fnaU and Vegetables that have exifted, or Ihall exift, have adually been all inr eluded in the firft of every Species: Or, M 4 which 158 mynoiop^itai ^imipitB I which IS the fame Thing, that pitching up. on any one Individual of either Kind, now cxjftent, that all the Jnimals or Veietables that proceed from it, were included in itj and It, With all thefe, was included in that one from which it proceeded, and fo on in- hnntly backwards ^ and confequently, fincc there is no new Produdion, all that are, or ever have been of that Species, were once aftually together included in one infinitely remote, from this now pitchM upon: and that any finitely or infinitely diftant Time Of they have fo long exifted) from their Generation or Produdion, all the Animals included m the firft of every Species were there moving and living Animakulsy and all Yegetahles included in the firft of every Kind, were there aftually growing and in- creafing fmall Plants. Now, fince every Animal and Vegetable has been prov'd to confift of Organs in Number infinite (tho' if the Orgatis of Animals be only finite in Number, it will as eff;:(ftually ferve our pre- fentPurpofe) it is abfolutely impoffible,any of tliQ Species of Animals or Vegetables fhould have exifted from all Eternity^ for then their Number muft hive been infinitely many, and the AmmalctdsznA fmall Plants, being Organical Bodies, and confiding of Parts, and thofe infinitely many too, and being all included in the firft of every Species, or thofe infinitely diftant from the •prefent Individuals ^ thefe firft ones of every Species Of laeligion. 169 species muftof Neceflity have been infinitely big; for infinitely many Organical Bodies, how fmall foever, amafs'd together in one Body, muft make that Body infinitely big. It's true, that tho* an Animal or ?lant con- fifts of an infinite Number of Organical Parts, yet their Sum, or the Animal or Plant is but of a finite Magnitude, either becaufe the laft Orgayis are infinitely fmall (as they really feem to be) or that infinite here is on- ly meant in a general, or lefs rigorous Senfc, for indefinite, or fo many that we cannot diftinftly conceive their Number, or give a Reafon for their Limits : But feeing thefe Animalculs, or Seed-Plants^ in this Cafe muft be finite, as confifting of Parts, tho' infinite- ly fmall, yet infinitely many in the firft Suppofition, and ot a finite Number of finite Parts in the fecond Suppofition: Confequent- ly, had the World lafted from M Eternity^ the firft of every Species muft have been in- finitely big: So that unlcfs we could admit the firft of every Species of Animals and Vegetables to be infinitely big (and how ab- furd fuch an Hypothefs is, [ leave the Reader to judge) it is abfolutely impoflible, that Animals and Vegetables fliould have been from all Eternity ;, neither can I fee how this Argument can be evaded, if we admit all Animals and Vegetables to proceed from pre- exiftent fmall Individuals of the fame Spe- cies^ included in the firft of each kind. And it IS impoflible this can be otherwife, upon ou^ '^'ii 179 MiloU^P¥t^l ^lintipm pur Adverfanes Scheme, if the Mechanical ProdufliQn of tliefe be iinpoflible, which I think I have clearly demonftrated. f XII. Had the World laftedfrom allEter- mtjzs it now is, it is altogether impoflible, but that Arts and Sciences inuft have been brought to a far greater Perfcdion than they have as yet attain'd. Let us take, for In- ilan^e, the Mathematkks : It is certain this Science has been more improv'd within thef$ two hundred Years, than in all the Tune paft before that, fince we have any Records ^ and two or three hundred Years inpre, going on at the Rate of thofe lad paft, may carry 'era to a Height which we cannot BOW iiQagine. Nqw it is altogether impof- fiWe the Improvewients already made fliould be loft, feeing they contain Things fo abfo- lutely neceilary to the Accommodations of Mankind ^ they will as foon forget the Ufe ^Houfcs and Cloaths, as the Advantages tq t>je reapM from this Sciences ^ wherefore, had .fbe World Etexnally been, this Science had bee^ brought to its utmoft Perfedion long 'ere now. It may be alledg'd, that Inrntda- $ms^ Deluges^ Wars and Peftilence might liave deftroyM all the former Improvements, und then we fliould have been left to begin gnew. As for Deluges it is impoflible th^ey Ibou Id have been Univerfal, /.^.Naturally and Mechannically impofliblci for the only Fbtlofophical Account of an Univerfal De- kige hitherto afTign'd, viz. tl?at of Mr. Whi- /}on\ Of Belifftm 1 11 fion\ depends intirely upon the Principle^ of Gravitatmi, which have been prov'd xiQK to be Mechanical^ in the Senfe us'd by oui; Adverfaries ^ and fince there could b^ hq JJmverfal Deluge natixrsilly^ (and to allow ^ iPrinciple above Nature, or the eftablilV4 Laws of Mechanifm^ is to yield the Cauf^) particular Inundations could never have been fufficient to have obliterated the Remains of Sciences, particularly of this one, which )by Infcriptions on Medals, by the Ruins of Jrchitedure, by Pillars^ Inftrnments, Qn4 Machines, might have been preferved in (Je? fpite of every thing but an Univerfal Cour flagration. Befides, it's meerly precaripu^j to fay there have been Deluges that h^v^ done any confiderable Damage to the who|? Rationil Creation, and may be den3^'d with the fame Reafon it is affirm'd, fince it is cey? tain we have heard of none of any confiT derable Confequence. It's true, there hap? pen'd an Univerfal Deluge in NoaFs Days ; but befides, as I formerly fa id, that this wm not brought about naturally, we know npt^ if this and the other Sciences had arriv'd at any great Perfection before this Deluge hap- penM. So that we are not certain, if th^ Perfedion of Arts and Sciences has been much retarded upon this Account. Wars and Peftilences, it's true, have been and may be, but thofe do not happen univerfal- ly over the whole World at the fame Time; and there are always fome G)untries and many 17^ |^Dtto fop|)tcal 0?mct plcjg immmmmmmmi^^^ ■ ' ■ many particular Perfons who cfcape •, fo thit it*s impoffible thefe Things could have obliterated all the i Remains of Arts and Sciences. I believe it almoft impoflible by tny Me^ns, except AnnihllatWHy or a gene- ral Confligration, fo to deface the Memory and Remains of all our modern Improve- ments, that fome of 'em fhould not laft at leaft ten thoufand Years to come •, and yet it*s certain we have no evident Footfteps of Improi'ements older than three or four thoufand Years. In (hort, this Argument Iiolds good againft every Thing but Univer- fal Deluges-^ and to admit or fuppofe any fuch to have been, is to yield the Caufe, fince its impoffible to explain fuch by the Laws of Mechanifm^ or to account for them byMatter and Motion, asThings are now fet- tled ; and to quit thefe, or to allow any thing to have happened contrary to *em, is to admit Powers fuperior to them, which, for ought we know, might have produced that which they can now fo powerfully al- ter. And tho* Arts and Sciences may have been at a ftand for many Ages in fome Countries, yet that is nothing to the whole Globe. For fince that Principle which prompts fome Men to improve Arts or Sciences they are inclin'd to, fprings natu-* rally in their Minds, according to the Scheme of our Adverfaries, and is neither imprinted upon them, nor were the Things thcfmfelves reveal'd to them by any fuperior Beings •, cf meltfiicn^ 173 Beings i this Principle, in an infinity of Ages, without any UniverfalDdug^e^ or even any particular one of any great Extent, muft of Neceflity have brought Arts and Sciences^ and the other Accommodations of Life, to a much greater Perfeftion th^n we fee they have now attained. From all which, duly weigh'd, it's plain this World has not Eternally been as it is now. And indeed, the Accounts of our Improvements anfwer very well to the Time aflign'd by Mofes for the Creation of the World. J XIII. If the Number of any generated Thing, which we behold on this Globe, does either increafe or diminifti continually, in any finite Number of Years how great foever, by any finite Number how fmall foever, then this World could not have been from all Eternity^'m the prefent State we now behold it. For had it increas'd in any fi- nite Number of Years how great foever, by any Number how fmall foever, long before this Time their Number had been infinite ; fothat this i^oor Mole-Hill of a Globe had not been able to contain 'em : And had they decreas'd, their Number had been none at all, i.e. the whole Race had been extin- guiftied. But fince neither of thefe has hap- pened, it's plain the prefent Stare of Things has not been for ever. It's not eafie to be- lieve, for Inftance, that the Race of Man- kind has been ebbing and flowing^ without confiderable Increafes or Diminutions, from all i; 174 |^l)flofop!)fefti 0? TTT governs this pfefent 5r/?^w ^/ Things. For fince this World could neither be produced by the cafual Concourfe of Atoms^ neithet- could have been from all Eternity it felf^^ as it has been fufficiently prov'd y and ^^tt that it now is no Body doubts, of Neceflity therefore it it)uft have been produced or created, fome Time or another, by forae pre-exifting Power. Now fince there is nothing elfe in being but this World, urtlefs vre admit that fupreme Power we are now fpeaking of •, and fince it could neither have been produced from th^ fortuitous Concourfe of Atoms ^ nor have been from all Eternity oi itfelf\ it inuft of Neceflity have been pro- duced by th^t fupreme Power ^ whofe Being we now inquire into. Since then this yii- preme Power^ of Neceflity muft have created this beautiful Sjflem of Things, and fince- exifling independently, he muft for ever be, and have been •, therefore that ^reat Power muft neceflarily now exift. All the Difficulty any rational Creature can have about the Exiftence of a Deity ^ is how to^ conceive his having for ever been of himfelf without a Beginning. Now if we could avoid this Difficulty, by faying, that this Syftem was produced by the cafual meeting of AtomSy or by alledging it to have for ever been of it felf, we might have fome flight Pretence for our Infidelity. But fince this Difficulty does equally lie againft all thefe three Suppofitions (for if the World has jbas been producM by the cafual Concourfe j^"Atom^, then a Void^ Atoms ^ and Motion^ have for even been, without a Beginning, of themfelves ^ if it has been from all Eter- nity of it felf as it \s, then the Cafe is plain, that we muft allow fomething to have been without a Beginning of it felf) wherefore I fay, fince the very fame Difficulty equally and unavoidably urges all the three Suppofi- tions •, is it not more reafonable and con- grous to allow that Being to have been for ever of it felf, without a Beginning, to whom we may afcribe, and who does ne- ceflarily poflefs all other fuitable Perfe- aions, rather than either of thofe^ others, which we know are neither endow'd with, nor capable of fuch eminent and tranfcenr dent Qualities? I will not fay with D^j Cartes, that becaufe in our Conception of a Being infinitely perfe0, there muft be in- cluded nece(fary Exiftence, that therefore fuch a Bemg muft of Neceffity aBually exift. But fare I am, fince our main Difficulty in the Conception of the Exiftence of a Being abfolutely perfeU, is his Neceflary-Exiftence, or his having for ever been of himfelf, without a Beginning, it is much more rea- fonable tofuppofe that Being to have for ever been of himfelf, who neceflarily pof- fefles all other fuitable Qi^alities, than thpfe who neither poflefs, nor are capable of any of*cra.' ^. J-r ,. Ii ' I E; i ill 1X2 l^ti^tofopiifeai ptimpm ^r^^ f III. The Exigence of yWrfWw is a phhl Hemonftratun of the Exiftence ef a Dtitt, I bcliev* no Body doubts, that thete now exjfts a Qjiantity offoliJMafs, out of which the celefiial and terreftrial Bodies xrttt form'd i and tho* perhaps in our moft foJid Bodies there be more Pores than Parts, or taon Vacuity than Solidity, yet there is flill efficient, not to perrait us to doubt of the Exiftence of Matter. Wherefore fince Matp «' no'"' a^ually is, whence or how came itfirft to bei It could never have been of W felf, fince we are certain, that itisde* ftitutc of all a$we Qualities whatfoever. And Self-Exijience, in its proper and pofi- tive hlea, feems to involve (befides having no Caufe for the Being of the Thing to which it is apply'd) fome other adive Qpa- Jmes, as Power and Knowledge, as I hav* already hinged. But we have already prov'd, that Matter cannot move of it felf, nor when put in Motion can it reft of itfilf nor of kjelf chzngt its Courfe, nor alter its Dire- ftion^it can neither change its Fi^ure^ nor Colour, nor Situation ; in u Word, it is enduM with ro Property but Inaftivity, which is a Negation. How abfurd is it then, to imagine it could have brought « y^y^ into Be- Wg, when it can do juft nothing of it felf f Tocooclude, could Mitter be Self-exiftent even in the Negative Senfe of the Word, it muft nepefTirily have been ^ and if iiecefla- fily. It ipu|J, from the Neceffity of its of l£leH0loti* mm f i n . mm 1 - ■ Beingt have been ever, and every where, that is, it muft be Eternal and Infinite j from which, ifs plain, that it muft have beea every where Uniform^ all Variety of Forms being a Contradidion, to Neceffity ^ it muft have alfo been immoveable, for had it nc* celTarily mov'd in any one Direftion, witk a determined Velocity, which being impot- able, it could not have movM at all \ for both thefe are fuch Contradidions to Sen(fe and Reafon, as none but an Atheifl caa fwallow. We may as reafonably imagine, that l^on entity fhould bring it felf to bor come a pofitive Being, as conceive it pofli^ bic, that Matter fhould, of it felf , for ever have been. Befides, admitting Matter to have been for ever of it felf, yet this will not folve half the Difficulties arifing in the Formation and Produftion of the prefent State of Things, as has been (hewn in th^ preceeding Chapter^ and (hall be now farther illuftrated. Whereas the admitting of aa infinitely Powerful and ?erfe9 Being to have for tfwr been, and to have created the felid Msfi^ and out of it to have framed this wonderful Syjiem of Things, contrads all the Difficulties of Nature into this one of his Exijlence, For as to the Difficulties of Creation, they vanifli quite before infinite Power ; for Power implies a Capacity to aft, and infinite Power a Capacity to ad every Thing,not involving a Contradiftion. Where- fore, fince Matter now adually 15, and yet VI . Of laeltgiom 185 Jpllfeirber could h^ve been fdr ever of it felf, tfiori had it for ever been, would that re^ iTiove the Difficuhies arifing in the Forma- 'ficvii of this prtUnt Sjjfem of Things, but, on the contrary, would: multiply 'em : Is it not -much more reafonable then, to admit an infinitely wife Being to have been for ^^vfhimfelfg Whereby all the Difficul- ties, in the conceiving th€S Manner of the Produftion of this Univerfe, do vanifli at once. ^ IV, It has been formerly fhewn, that this Univdrfe was not form 'd by the fame Laws it is now governed, and which, its fe- veral Parts in their Anions do now obey j arid therefore, of Neceflity there muft have been fome Power fuperiour to, and diftinft from that of Matter, which formM this Sj- ftem at firft, and prefcribM Laws for its Parts afterwards to obferve. We fee all the Chan- ges that now happen in thismaterial World^ are according to the Laws eftablifh*d in the frj} Chapter. But this Syftcm of Things could never have been brouQ;ht into its pre- fent Order, by the now eftablifti'd Laws of Nature (even admitting M rrrer to have been eternally exfpnt of n felf ) as I have abun- dantly fhewn in th/rr/?Ci?/7/??^r^ neither one, nor all c^f tbefe L:^ ws were fufficient to have feparate^ th.n thin and rare Fluid of htght, from tfafe other groff^r and more denfe ones, and am^ft'd it in' the 5;m and jiVW Stars'^ neither did the Laws of fpecifick Gravity Qbtaitti^in x\\t ^^yimmomn^ Situar 4. * pon tion of the inner Parts of our Earthy and the other Planets ^ nor in the Separation and Situation of the feveral Fluids thereof. By none of the known Laws of Motion was the Numhr, Magnitudes, or Diftances of the /x^^5^//rj determin*d. The Figure, Num- ber, Denfities, Gravitations upon one ano- ther. Situations and Order of the Planets adjufted. The Number, Diftances, and Mag- nitudes of the Satellites of Jupiter^ the Form and Bulk of the Anmdus of Saturn limited. In a Word, the whole Procefs of the Forma- tion of the celeftial and terreftrial World, as to their principal Parts' and Arangements, could be brought about by none of the Laws of Motion and Mechanifm, that now obtain in this fettled State of Things , or at moft,thefe Laws had but a fmall Share in their Produftion. Wherefore, fince this beau- tiful State of Things has not been for ever of itfelfl nor could be form'd by the Powers and Laws of Nature, it is plain, it has been producM by fomething fuperior to Matter and its Qualities : And confequently, by that fupreme Being, into whofe Exijlerue wc are now inquiring. And truly, from what has been here faid, and a great deal more of the fame Nature, alledg'd in tht firjf Chap- ter^ it is evident, we can have no Notion of the Formation of this prefent State of Things, other than what we have of a Planetary Clocks or any other complicated Machine^ form'd by the Han(J of a (kilful 4ruf j where tho' the Pules \%6 i&Diiotop|>ical 0nncipUg Rules of Motion, and Laws of Nature may «>btain, when it is adjuftcd and finiihed : The Parts of the Machine, their Figures, Sizes and Proportions, and the Conneftioa and fit- ting the whole, was brought about by vo- luntary Operations, different from, and fometimcs contrary to the Law of Nature and Motion, whereby it now fubfifts a re- gular Machine, «nd performs its intended Chjerations •, which neverthelefs, it is not of itfelf able to perpetuate, without frequent Interpofals of the fame voluntary Powers, and the Removal of thofe Obftruftions and Difturbances, Time, and the frail Nature of material Organs muft bring upon it. And tho* this, no doubt, be but an infinitely low and faint Refemblance of that noile and glo- rious Work, yet it is the beft and moft ad- equate our Imaj^inations, without running upon evident Contradiftions, can frame. § V. As the Formation and Difpofition of the ^reat Bodies of this Univerfe, did ne- ccfiarily require the Hand of a Being infi- nitely powerful-, folikewife did their firft Movement, and imprefs'd Motions, demand the Irapulfe of an Almighty Hand to fet them firft a-going. For fuppofing the ce- fctfitf/ Bodies already form'd, and rangd according to their feverai Diftances from one. another i yet without this Impulfe, they had continued unaftive, unmovmg Heaps of Matter. Now it has been already fcewn, that no Particle of ^^tte^, nor any Of ^Miqiotu Combination of Particles can move them* fclves, and therefore it was abfolutely ne- oclTarjr, that fomethingdiflEerent from them- felves (hould put them in a Motion, withsi due Velocity, along the Tangents of their fe- ll veral Orbits \ other wile they had for ever continued in the Places, and at the DiHiances they were at firft fet. Wherefore, fince it is certain, that thefe^^/ar/^fix Bo4ieshzvthttii rolling about thefe four or five thoufan4 Years ^ and (ince it hath been demonftrated, that they are not felf-moving, being folid Maffes of Mattif i fince it has likewise been (hewn, that they have beea fet a-going by fome powerfiil Hand \ and what Hand fuf* ficient for fuch a Work, but his w^o is infi* nite both in Strength and Skill ? and con- fcquently, he who did fo great andglori* ofis Things, muft neceflarily be. S VI. Not only the Formation Sind fir&Im^ pulfe of the great Bodies of this Univerfe, a- long the Tangent^ of their Orbits, but their Centripetal \m^M\{t%, whereby their Revolu- tions, or ^r^/Viwi^r Motions, are performed* did, and ftill do reouire a Power beyohd that of Matter and tne Laws of Nature, to the Prefervation of their Motion. Sir Ifaao Newton has demonftrated, that to the Mo* tion of any of the celeftial bodies in an Qr-r iff, there is neceflarily requir'd twolmpul- fes, one along the Tangent of the Orbit, ano* ther toward the Center, about which tha Bodv raoveSf The firft being once imprefs'd. npuMP- ^1 « S8 #Dilofopl)tcal ^mtiplts -does continually perfcveie, and needs no more to be renew'd, as is evident from the firft Law of Nature : The fecond continu- bHv draws the celeftial Body from its reSili- near Motion, and forces it into a curvilinear Orbit •, fo that it muft be repeated every Minute of Time. Now thtkjecondary Ira- pnKts arife from that Univerfal Principle of j^WtfSi^», whereby every Particle of Mat- ter^ and all the Bodies of this Univerfe tend toward one another ^ and by which the Sun, being the far greateft Body of this our Sy- fiern^ draws toward him the PlanetSy and Aey their own Sattellites.zni without which they would for ever wander in right Lines. But it has been demonftrated in the firjl Chapter, that this Principle, whereby the Re- volutions of thefe glorious Bodies are per- formM, is independent of the Laws of Me- ebanifntyZnA only accidental (no ways effen- tial) to Matter, but implanted therein by fome cxtrinfick Power, and confequently pncc it muft be repeated every Minute) «&uft be perpetuated in it by fome uninter- rupted Influence, or by the perfevering £i ner^y of the firft Imprefliom And feeing there is nothing in Nature but Matter, and the Powers thereof, unlefs we admit that fupreme Being for whofe Exiftence we con- ten^, therefore the Revolutions of the ce- lejiial Bodies, in their feveral Orbits, do ne- ceffarjly inf^r the Exiftence of a Deity. . J VII, Thq Ktif l&eitgtott; ^ Vlf. The Exiftence of Animals does h'e-•^ ceffarily inferthe£jf{/?^nr^of a Deity^ foxjtr has been demonftrated in tht former Chapter^ that all Animals are, in their own Natures, perpetua mohilia, that they have fome Princi-. pie above the Power of Matter that govetrii*' their Motions : It has been likewife fhewn, that tvery individual Plant 2nd Animal is a Machine of an infinite Number of Organs j that no Animal is, or can be produced or ge- nerated by the Force of Matter and Laws of Mechanifm, (that all Animals and Vegetables- that ever were, or fhall be, were all created, or form'd at once, as fliall be afterward ihewn) and that all thefe are abfolutely un- accountable from the Laws of Motion, and confequently, muft fpring from a Principle independent of, and altogether above the Powers and Properties of Matter. Now, whenever we forfake the Powers of Matter, and the Laws of Mechanifm, we neceflarily muft have Recourfe to the Exiftence of fome Power fuperior to, and independent of Mat- ter, and all its Laws and Properties, and confequently, to that infinitely perfeB Being, into whofe Exiftence we are now inquiring ; fince there is nothing befides Matter and its Properties in the World, unlefs we admit the Exiftence of thzt fupreme Being* J VIII. The fpontaneous Motions of irja- tional, and the voluntary Motions of rational Animals, the Freedom of Will, and Liberty of chufing or refufing in the latter -, and, in a Word, ririi hthe Apfmsranees ofNature,which tfe above Ac Powers of Mechanifm (which are infiumerahle) are fp many undeniable Proofs of the B^iwf of a God. For (ince this prefcnt Syftem of Things has not been from all Eumitfy of itfelf^ and (ince thefe areal? low*d to be above the Powers of Mechanifm^ they muft have been produced by fome Pow- er fuperior to thofe of Mechamfm. But no Power is fufficient for thofe, but his, wb0 atma does great and marvellous Things •, who adjufted all the Parts of this noble Fahick by Number, Weight, and Meafure ^ and there* fore he that brought about all thefe glori* out Things, He who alone does Wonders^ muft neccAarily^f. f IX. The Prefervation of the Being and Faculties, both of the animate and in# Thfi of SleUgiom 199 The Quantity of Matter in, and the Gravity of fuch of the heavenly Bodies (as afford Means for the determining the fame) at the fame D£- ftancefrom the Center of the Sun^ is as follows^ The Suns Jupiters Saturns The Earth's The Moons 66690 00060I C0028:J. 0000 1 oooooi4 The Diameters of the Snn and Planets. The Suns Saturns Jupiter's Mars's The Earth's • The Moon's Venus's Mercury's 494100 04392s 052522 002816 008202 ^ 002223 00494 I 002717^ Statute Miles each 5000 Paris Feet# The Diameter of the Celeftial Bodies in En- glijh Meafures. The Sun Mars The Moon Mercury The Earth Saturn Jupiter Diameter. 822138I 487s I 2175 I 2748 Y Englifli Miles. 7967 934SI I2o6S3j O4 Tke I ' ym 2r00 «— — —— —— ^ ^ 'The Weight of Bodies on the Surface of the Sun and Planets. On the Sur- face of The Sun jThe Earth Jupiter •The Moon Saturn ICOOO 012581 00804I C0630 00536 L Jhe Denfties of the Celejlial Bodies. The Moons The EartFs The Suns Jupiters Saturns 700 100 076 060 The Periodical Times of the Satellites of jupiter. 1 2 ■I d. 18 h. 28'!' 3 d. 15 h. 17'^ 3 4 7d. 3h. 5/4: 16 d. 18 h. 5'|. Ti& Jrom the Peri- odical Times. f- 5T78 -* I I L 5.57^ .2 fe/876. 8. -873. 14. 1^9- 14. 168. 24. 903 24. 96S Semidi^- meters of Jnfiuu Tbp Of saeUgiotit 201 The Periodical Times of the Satellites of Saturn. I 2 I d. 21 h. i8^ 31'^ 2 d. 16 h. 41'. 27'^ 3 4 4d. 13 h, 47'. i6'^ 15 d. 22 h. 41'. 11''. 5 79 d. 7 h- 53'- 57 // Ti?^ Dijlances of the Satellites from the Center of Saturn. 1234 5! Diameters of the Ring of ■^i\\\i\i2.y Saturn. The middle Dijlance of the Earth and Pla-^ nets compard with their Periodical Times. ■& y (f s $ 5 0bSL'°}9Hi98 512T20 152350 lOOOOO 72398 3858T. According to"^ thePeriodical S9T3806 5 201 16 152399 lOoooo 72333 38710. Terms J The Tif^^s of the Revolutions of the Sun and Planets about their Axes. The Sun in 25 Days The Earth in i Day The Moon in 2 9 Days Jupiter in 10 Hours Mars in 247 Hours Venus in 23 Hours.* J XIL What a beautiful Scene of Things have .we here ? How fimple, and yet how wonderful are the Works of Nature ? Such- like T^rr- 'i. !ii like are all the EfFeds of infinite Wifdom, her Foundations are plain and fimple, but her fuperfiruSttre^ various and wonderful. Her Caufes few, her EfFeds innumerable. Her Courfe the eafieft and fhorteft poflible, and her Means the feweft that can poflibly bring about her Ends. Let us but confult the Books of the old Afironomers^ and we will then have fufficient Ground to admire the frugal Simplicity of Nature, in this neat compaft Syjlent'^ we fliall fee there what forry, perplex'd Work they made, with their Cycles^ and Epicycles^ their carryings and Aquatingy their Concentrick and Excen- trick Circles, their Stations and Retrograda- tions^ their folid Orh^ and the perpetual Change of the Axe of Motion, in the ce- leftial Appearances : Such a ftrange ungea- metrical 2ini contradidory Syftem they made of the Heavens ^ whereas from thefe few plain and fimple Pofitions, all the Appea- rances of the Heavens^ are accounted for, with wonderful Confiftency and Facility. 5 XIV, The Sun being a huge Body of liquid Fire^ brought into Fufion by the Force of his Heat, and thereby fending out Oceans of that thin, adive Fluid, which is the Medium of Light, and the Caufe of all Heat, turns round his own Axe^ from Weft to Eaft in about twenty five Days j which arifes from his firft Being put into fuch a Circumgyration^ after his having beei) fea- ted in his Place. And there being little or no of laeltgtoa noRefiftance in his Region to retard his Mo- tion; it has continued ever fince, and will do, *till the Confummation of all Things 5 by Virtue of that firft imprefs*d Gyration^ and the firft Law of Nature. His Motion about his own Axe, has been difcover*d by Spots on his Surface, and his Fluidity, from his leffer Denfity, in Refped of fome of the folid Planets, (fome folid Bodies being more denfe than moft Fluids are) his Sphericity, and that all Bodies heated to fuch a De- gree, as the Sun muft neceffarily be, muft certainly be vitrify d ^ that is, muft continue in a Fluid State, as long as this violent Heat lafts. Befides, the Fountain being in Reafon to be fuppos'd of the fame Na- ture with the Streams, fince the Rays of Light ^rt moft certainly, a thin, rare, adive Fluid : Much of the fame Kind, with due Regard to the Circumftances, muft the Light iij the Bodjr of the Sun bej the greateft Difficulty, is to conceive how this Gloh of liquid Fire ftiould be able to pro- jed his Beams with fuchVelocity and Force, lb as to be able to diflblve every thing al- moft. That which may contribute to help our Imagination here, is what may be daily fccn at a Smithes Forge, when the Iron is fo much heated, as to run into Fujion, it fends out copioufly on all Hands, Streams of liquid Fire: All fulphureous Boim like- wife emit, and iffue out liquid Flames, 01 burning 1i III ' .1 •■ I. 1 ■ -- ■ I ,» 204 0Dttofop!jtcal !^?(ncipleg bmrning Smoak, which by Reafon of the greater Gravity of the Circumambient Atmo^ fphere^ is fx3rc'd upwards, but if there were no Atmofphere^ thefe Flames would be pro- jefted every way equall)^. Now, as Bodies aft upon Lighty by emitting, refrafting, and refleding it ^ fo Light afts on Bodies in heating them, and putting their Parts in a vibrating Motion, wherein Heat confifts. And when their Parts are thus heated, or put in Vibrations^ beyond a certain Degree, they emit Lights and fliine, and this Emif- fion is performed by the vibrating Motions of the Parts. So that fuppofing the Sun a great Body like our Earth, vehemently helted, thaf is, having its Parts fet in- to vehement Vibrations^ thefe Vibrations of the Parts of the Earth wou'd force- ably projed, and violently thruft forth immenfe Oceans of this fubtile Fluid on all Hands-, fo that as Light produces thefe Vibrations on the Parts of Bodies, thefe Vibrations in Bodies, are the Caufe of this Emiffion of Light on all Hands. Every fingle Particle in Bodies, when put in this vehement vibrating Motion, pro- pelling, in its Turn and Return of Fi- bration^ a Cylinder of Light, equal to its Sedion, tho' its Center, and the Sura of all the Particles of the heated Body urging fo many fuch Cylinders on all Hands, as is the Number of fuqh vibra- ting of BeUgibtt^ ting Particles. The greater Quantity of Matter, and larger Dimenfions of the Sun in Refpeft of the Planets, makes him fuffi- cient for all the Expenfes of Light, he liys out upon them, whereby his Bulk and Heat is conftantlydiminiftiing, as alfo,for drawing ail the reft of the Planets, and their Satellites towards him ; for, as has been formerly in- finuated, the Force of AttraSion of one Bo- dy upon feveral others, at the fame Diftance, is as their Majfes^ or Quantities of Matter: Wherefore, feeing the Sun contains a grea- ter Quantity of Matter by very far, than any of the Planets, the Sun muft neceflari- ly draw the Pla?iets with their Satellites to him 5 which wouM have unavoidably come to pafs, had not the Planets, at the Inftant they were feated in their Places, received an Impulfe, which drove *em along the Tan- gents of their Orbits , and had not thefe two Motions been fo exaftly counterpoised, that neither of them fliould over-power the 0- ther. Thefe with the fmall Refiftance they meet in their Courfes, and the Force of the Attraftion diminifhing, as the Squares of their Diftances increafe, has made 'em ever fince revolve in their Elliptick Orbits, in one of whofe Foci, the Sun is fituated : And whatJs hete faid of the Caufe of the Prima- Ty Planets Motions about the Sun, may be underftood of tht fecondary Planets Motions about the Primary ones. All the Planets re- volve I \ ' ', 1 !' »i ' I J ii' m ^ zo6 0tHto^i)tcal ^?ittcipleg voivc about the Sun in Elliptick Orbits^ or fuch as are not very far different from them ^ as alfo, moft of 'em turn round their own Axes from Weft to Eaft ; the Earth \n twen- ty-four Hours, about an Axe^ which is in- ciinM to the Plane of the Ecliptkk 661 De- grees : And in its Motion about the Sm, this Axe of the diurnal Rotation, obferves always a Parallelifm with itfelf i the Rcafon of which is evident, for if a Sphere move about ^n Axe, this^jir^ (there being no o- ther Motion fuppos'd in the Sphere) is im- moveable, while in the mean Time every Point in the Sphere defcribes a Circle about this Axe •, and therefore, if a Sphere move cither in a curve or ftrait Line, and at the fame Time, turn round its Axe^ the Axe (hall always continue /^/zr/t/W to that Line it was firft parellel to, for that Impreffion which perpetuates its Rotation upon its Axe^ and the Impulfe along the Tangent of its Orbits are two diftinft Motions, which ne- ver interfere, and fo each of them muft con- tinue the fame as if the other were not ^ fo that every Body turning about its Axe^ and at the fame Time defcribing a right or curve Line, muft of Neceffity retain its Axe pa- rallel to itfelf, if nothing elfe difturb it. hipiter^ likewife, Mars^ and Venus^ and our ^oon^ do alfo turn round their ^^x,* from Weft to Eaft, and would retain this P^- talUlifm^ if not difturb'd by foreign Vio- lence. of Ileltsion. ^F"^ 207 lence. The Satellites of Jupiter and 5tf- turn^ do likewife turn round their Axes^ as is evident from hence, that they, like our Moon^ turn conftantly the fame Face or D//it toward their primary Planets -, and it is not improbable, that the others in which we have not had the Occafion of obferv- ing the like, may alfo turn round their Axes •, that in a Revolution about the 5ww,. they may, in all their Parts, oftner than once, enjoy his Light and Heat ^ for it is from this Rotation of our Earth upon its Axis^ that we have the ViciJJitudes of Day and Night, and from the Parallelifm of the Axis to itfelf, in the Earth's Revolution about the Sun, and its being inclined to the Plane of the Ecliptick^ come the beau- tiful Seafons of the Year, Simmer and Win- ter^ Spring and Autumn, which are of fuch Comfort and Ufe to its Inhabitants. From the Opacity of the Moon and Planets^ and their SattelUtes, and the Obliquity of their Planes to the Plane of the EcUptick^ toge- ther with their diurnal and annual Mo- tions •, and fome of 'em revolving in Or- bits, within one another, their Phafes, th|j| appearing anddifappearing, their total ana partial Eclipfes arife. 5 XV. Since their Solidity arid Opacity^ the Similar Nature of their Or^irj, and their Satellitious Attendance, their Revolutions about the Sun^ and their Rotations about their ■iaB 2oS 0|^tlofopDim WntiT^lts i i^ their Jxes, their Gravitations and mutual Jttra3ions^ the Proportion of their Periods to their Diftances from the Center of Mo- tion, the equable Defcription of Areas in equal Times. Since, I fay, all thefe and many more Particulars areexadly the fame in our Earthy and the other Planets with their Satellites ^ it is not improbable, that they may be alike in other Things, and that they may have Inhabitants, both ra- tional and irrational, Plants and Vegeta- bles, Water and Fire analogous to, tho' not of the very fame Nature and Conftitution with ours j and fince our Ji:/ J Stars are ex- aftly of the fame Nature with our Sun, as ftiall be afterwards made; appear, it is very likely that they have Planets, and thefe planets have Satellites, and thefe Planets and Satellites have Inhabitants, rational and ir- rational. Plants and Vegetables, Water and Fire analogous to thofe in out Sj//lem. On thefe Suppodtions, which not only arc not abfurd or contradidory • bur on the con- trary, highly probable, as (hall be after- wards made appear more fully , what is noble and glorious Fahrick would pre- ftntf itfelf to our Imaginations? How is it poflible for any one who had this Idea of the Univerfe^ to think it pofli- ble, fuch a beautiful Syjlem cou'd have been produced without infinite Wifdom ? None but the Wilful or Obftinate, cou'd refifl Of Beltgion^ 209 refift fuch a powerful Impreflion of divine Power and Wifdom. On the other Hand, how is it poflible to conceive that, that immenfe Number of glorious and Sun-like Bodies ot the fix'd Stars, thofe vaji and huge Bodies of fome of the Planets (in re- fped of our Earth) with their noble At* tenJa?Jce, were made for no other Ufe but to twinkle on us in Winter Evenings, and by their Afpe&s to forbode what lit- tle Changes of Weather, or other piti- ful Accidents were to be expefted below, or to be peep'd at by fome poor paltry Fellows of Aftronomers > Or can any Body force himfelf to think, that all Ani- mals ^nd Plants, have been exhaufled in furnifliing out this poor Corner, while the other more glorious, great and noble Parts, are left deftitute and bare? Cer- tainly they muft have a great Opinion of themfelves, and of their own Habitation, who can think fo poorly of the reft of the Univerfe. It is true, from the great Refembhnce, and A?iaIogy, between the greater material JVorld^ and the lejfer one, of an Animal Body ^ and from this Hy- pothefis, of new Worlds^ and new Setts of Living Creatures, it is bearing hard, up- on the noble, and glorious CEconomy, of the Redemption of lapfed Creatures: By contining it to a dirty Mole-Hill of a An- gle Planet, fome pious and enlightened P Perfons, ■-•■ •■•'•• ■ 201 )a|)iiofopl)tcai Wntipits .j^ \' il Perfons, have taught, that as in an Jni- mal Body, the Brahiy the Heart, the Lnngs, the Liver, the Guts^ the Spleen^ and all the infinite Nftwhr of Conglobat and Con- glomerat Glands, had their feveral diftind: Ufes, for purifying, refining, and exal- ting, the necelfary Juices and Spirits^ or for fecerning, and throwing off, the noxi- ous ones-, and yet all this Complex and infinite Variety of noble and wonderfully contriv'd Organs, were defign'd folely for the Prefcrvation of one Animal and the Propagation of its Kind. So in the grea- ter material JVorld^ all that infinite Varie- ty of Stars, and Planets, might be for purifying and fubtilifing, conceding and preparing the Jflral Influences neceffiry for the Prefervatian, Propagation and comforta- ble Support of the i'everal Setts of Crea- tures inhabiting this fpoil'd, dtfac'd, and ruinous Globe of the Earth. Whatever may be in this, I fliall proceed in fuppo- fing, the Planets to be inhabited, and that the fix'd Stars have their Planets and In- habitants, yet they are not of the fame Nature and Conftitunon with thofe of 6m Globe, as is evident from the diffe- xent Degrees of Heat and Light they en- joy i as alfo from the different Viciili- tudes of their Day and Night, and the Sea fons of their Yean Mercih-y is three Times nearer the Si:n^ than we, and ca\\^ fcfjuently of laetigion. 21 I fequently enjoys nine Times as much Heat and Light, he never removing twenty ciglit Degrees from the vaft Body of Light* Venus enjoys twice as much Heat an^ Light, and her Motion about her Axa is performM in twenty three Hours, and fg her Day is but one Hour lefs than ours ^ flie has all the Pbafes of our Moon, apr pearing fometime's horn'd fometimes halv'd^- Mars has no Inclination in the Jxe of his Rotation to the Plane of his Orhit, and confequently enjoys a perpetu-:! Equinox^ but no Viflitudes of Seafons-, he receives but the third Part of our Light and Heat, Jupiter like wife enjoys a perpetual Equi- nox, and a Day of ten Hours, but rer ceives only the twenty fifth Part of our Heat, and Saturn but the Hundredth. J XVI. The Satellites of the feveral Play 7iets in^tv many and various Difturbances in their Motions from the Sun, as alfp, the Primary Planets fufFer like wife from the Forces of the Sun, and of the Secon- dary Planets. Thus the Moon (if a fled up- on only by the attraftive Force of the Earth) wou'd by a Ray from the Center of the Earth, defcribe equal Area^s in equal Times, wouM about the Earth in one of its Foci^ defcribe a perfeft Ellipfe of the fame Species conftantly, whofe Plane ,woad be immoveable, or always the fam,e, and vWfe Inclination to the Plane of the Edip- Nw MBap 212 0Dilo(bpt)icai ^^mcipUiSi of Eeltgiott »«5 ! !■ lia wouM never vary j but by the Aftion df the Sun upon the -Afo^n, all thefe Ef- fefts are difturbM, for fhe neither defcribes equal Areas in equal Times by a Raj from the Center of the Earth, but forae- what larger ones in her ConjunSioni and Qppofitions with the Sun than in her Qua- dratures. Neither is her Or^fr always ^^- afically the fame, nor is the Earth in any 0f the Foci of her Orbits-^ for they are more Curve about the Quadratures^ and lefs toward her Conjun3ions and Oppofi- tims : In every Revolution fhe defcribes a new Kind of Curve^ and both the Situa- tion of the Plane of her Orbit^ and its Inclination to the Plane of the Ecliptick, varies every Moment, and all thefe Un- certainties and Aberrations, are multiply'd by her nearer or remoter Diftances from the Sun^ befides a great many other Irre- gularities too tedious here to relate. Up- on the Account of all which, it has been fo very hard for AJironomers^ to reduce her Motions to rule, and to exprefs them in Numbers i and yet all thefe Irregularities are wonderfully accounted for, from the Adioft of the Sun and Earth upon her, upon the comraoft Suppofition of the Law of Attradion, even to a Nicety, beyond \lrhich, Obfervatiun cannot diftinguifh, as i$ evident from Sir Ifaac Ner^tan's Theory ^f the Mean, irfiich is a furprizing Con* firmation firmation of the Truth of that Principle. On the other Hand, the Force of the Sun^ but efpecially of the Moon, difturbs the Motion of the Earth, as is evident from our Tides, which do fo exaftly follow the Motions of the Moon, that he who knows the former, with fome few collateral Cir- cumftances, cannot be ignorant of the lat- ter ^ for when the Moon comes to the ver- tical Point of any Place, we haye a Tid^ there, as alfo on the Place diametri<:aUy op- pofite to it i this Tide is greater at the ConjunHions and Oppnfitions of the Moon tp the Sun, than at her Quadratures, and great- eft of all at the Equinoxes, efpecially if the Moon is then in her Perigeum, the Rea- fons of all which, J have fuggefted in th^ fecond Chapter. And what is here faid of the Earth, with Refped to the Mppu, may be with due Limitations underftood of any primary Planet, in Refpea: of its S4' ^ XVII. That the Jix*d Start are Bo- dies like our Sun, all the late Aftrommers agree • for it is plain they ftiine by their own Light, fince' it is altogether impoffi- ble, that the Light of the Snn, fhould be fent to them, and tranfraitted to us, fo as to make them appear fo lucid as we fee them. We fee how faintly in Refped of fome of the fix'd Stars, Saturn (hines for all his Bulk; and yet his Diftancc i* but U' ' ' » *l i ! « • I! ',, ^14 PWfJiopWta Wntmts a Point, in Refpeft of the neareft fix'd Star, from the Sura The Rays of the Sun would be lo diflipated before they reach'd fo re- mote an Objed, that the beft Eye of the World, cou'd not by ir, difcover them. Their Diftance is fo great, that the beft Telefcope^ ihftead of magnifying them above what they appear to the naked Eye (as they do any Objeft, rcmov'd by any men- furable Diftance, how great foever) does tonfiderably ielTen them, fo that they ap- pear like lucid Points. Befides, tho' we m ihis Globe, approach nearer them fome twenty four thoufand Diameters of the Earth, (or 188304000 Miles, allowing five thoufand Feet to the Mile) one Time of the Year than another, yet their Parallax is Icaite fenfible, if any at all ^ which could not be, if they were at any moderate Di- flance : By Mr. HugerCs Computation, the Diftance of the Sun from us, is to the Di- ftance of the neareft fix' J Star from us, as 1 to 27664 that IS (allowing the Diftance of the .9h» from us to be 12000 diameters ot theEirth, and a Diameter to be of 7846 Miles, according to the beft Calculations) the Diftance of the neareft fix'd Star from US, IS atlcaft, 2404520928000 Miles, which a Cannon Bullet, moving with the Velo- city It has, when parted from the Muz- zle of the Piece, wou'd fpend alinoft fe- ven hundred thoufand Years to go through. ^ Since of Religion. 215 Since then, both thefe are true, that they ftiine by their own Light, and that they are at fuch an immenfe Diftance from us, it is plain, they muft be Bodies like our Sun -^ which wou'd be evident, cou'd they be brought near us, or we near them, for ir is only the Diftance that creates our Douhr. Now, this being true, it is impoflible they ftiou'd be all in the Surface of the fame Sphere, fince our Sun, which is one of 'em, cannot be reduc'd to this Rule. Befides, their different Mag- nitudes, ftiew that they are at as im- inenfe Diftances from one another, as the neareft of 'era is from us. Let us but imagine ourfelves remov'd at an equal Diftance from the Sun, and fix'd Stars, we (hould then certainly perceive no Dif- ference between them •, for as to all the Planets, that we fee now attend the Sun, we ftiou'd not have the leaft Glimpfe of them i both becaufe their Light wou'd be too weak to affeft us, and becaufe all their Orbs wou'd be united in that one lucid Point of the Situ. In this Station, we fliould have no Occafion to imagine any Difference between one Star and ano- ther, but ftiould certainly conclude both Sun and fix'd Stars, of the fame Nature ^ and knowing the Nature of one, we fliou'd certainly conclude the fame of all the reft, vi&. that if one was a lucid Globe of P 4 liquid r, \] 2l6 t^DtlofopDieal mntms of ^eUgida ^l^ i' '1 1 1' i ' ^ ( liquid Fire, fo wou'd all the reft be, and that they were at immenfe Diftances from one another. If Mr. Derhatns Conjedure, about the appearing and difappearing Stars ( of ^ which there are many Inftances ob- ferv'd by Aflronomers) be true, to wit that they are Planets, belonging to fome of the neareft fix^d Stars -^ which become vifible, when they are in that Part of their Orbit, next to our Earth, and difap- pear when they remove, to that Part of their Orbit^ which is fartheft from us, I fay, were this Conjedure certain, as it is not improbable, then we had a certain Confirmation of the modern Theory of the ckleftial Bodies , but I am afraid', if the fix'd Stars adually had Planets, and they. Satellites, that at our Diftance, we cou'd hardly fee either. Since then, there are fevcral probable A rguments,(fome of which I hinted before) that they have attendant Planets, and no poflible one to evift the cotitrary* we may fafely conclude, that the jfxV Stars are fo hfiany Suns ita the Center of a Sjjhm of Planets and thfeir So- teUites. f XVIII. Befides thefe already men- tioned, thei-e is another Species of heavenly Bodies, caird Comets, which revolve about the Sun, in very oblong Elliptick Orbits, ap- proaching to ParaMick Curves. The Times of their Periodical Revolutions are very long, fince in three or four thoufand Years, we have not pofitively determined the Re- turns of above one or two •, however, it is certain, that like our Planets, they do move in a recurring Orbit \ that the Sun is in one of the Foci of this Orbit i that by a Ray from the Sun, they defcribc equal Arenas in equal Times ^ that the fame Law of Gravitation obtains in them, which does in the Planets ^ that their Pe- riodical Times are certain and invariable •, and that their Motions are regular, only their Courfe in their Orbits is not deter- mined one Way, but indifferently, fome of them move one Way, others another : They are alfo about the fame Bulk with the Planets, generally fpeaking ^ and like them are compad folid Bodies, but fur- rounded with a vaftly large thin Fluid, intermixd with feveral grolTer Particles, and compofing an irregular unequally dif- posM, and uncertainly agitated Mafs j which is caird its Atmofphere, whofe Via- meter is ten or fifteen Times as long as that of its Body. Befides which, it has a long lucid Train, which is raised in its Approach to the Sun, by the Heat thereof, and extends fbmetimes to four hundred thoufand Miles above its Body. It is al- ways oppbfite to the Sun, becaufe it is the thinner Part of its Atmojphere, extremely rarifyM by bis Rays ; and fo rare, that ia ^ ^ . ■ . tho 21 ^ mwop^itai micmti of Beltgioit 219 T^il accompanies n through irs Courfe per all its Planetary Regions, encreafins in 1^ Approach to the Suu, and lefTeninHn US Kecels, And, which is very (^b'erv-'ble as the r/7//j decreafe, the Atmofphere is en- larged, which happens in xhtiTReufs from tjie .S„« ; and as the 7>;/. cncreafe, the Atmofphere hK,n,, which happens in their Aaefs to the 5«;,, juft as it ftould be ac' warding to this Theory. 1 hefc Cov.ets fome- times come fo near the Sun^ ,s ro he heat-^ ^^ tQ fuch a Degree, that th ■- r.nnot be- ^,me cool again in man-.- ihoufands o£ I ears. Iheir Ja,h arf nro^.der at their Jecaufe, m thefr Ixof^ v-d Sn.ces the Vapours are marc .ind -T^orc r,,ifv'd'and ^ijated: And .;■ .h.c ncrp.tuj Rirefac- t^).n and Dilation, thtde V:;nours of the Jails of Cometi, nre Tpread 'nl difperfed ^irough our whole Sy(l,m • and fo are at- tiraded bythe Gravitation of th'e Planets ^nd mixd with their Atmofphere, as has' foen formerly fiiown ; and become a Sup- ^■^u m ^ continual decreafe of Fluids ^n the Planets, which is caufed by tha qontinual Confumption on Vegetation, and the Putrif,6lion of thefe Fluids. And as i^nong the ?/^mx, they are the Jeaft, yhich revolve in leaft Orbits, and neareft m Sun : 5q it is not unUljiely, ^hqfe Co- mets^ wets, which in their Aphelia come neareft the Sim, are of the leffer Sort, that by their AttraBions, they may not difturb the Sun too much. It is not improbable, that fome of thefe Comets have vifited our pla- netary Regions oftner than once. The Co- wet that appear'd in 1667, and that in 1682, had both, by Computation, pretty near the fame Orbit, the fame Aphelia and Periphelia, and the fame Inclination of the Tlane of their Orl'its to the Plane of the Ecliptick : And confequently, it is not im- probable, that they were both one and the fame Comet. And therefore, the Time of its Revolution is about 75 Years. The reft of the Comets take up a longer Time in their Revolutions, and afcend higher from OUT Syftem. Befides, the Comets, by reafon of their great Number, the great Diftance of their Aphelia from the Sun, and confequently their long Stay, and flow Motion in thefe Aphelia, muft di- fturb one another by their mutual Gravi- tations : And therefore, their Eccentricities, and the Times of their Revolutions, mutt fometimes be encreas'd and fometimes lef- fen'd i and confequently, it is not to be expefted they ftiould conftantly return in the fame Orbits, and in the fame Periodi- cal Times exadly : It is enough, the Changes be not greater than may be ex- pefted from fuch Caufes i and from hence we } 220 l&t)ttofop|)(cai ^mams we may obferve the Reafon, why the Co- pufts arc not contain'd in the Zodiac, as the Planets are ; but dired their Courfes differently, on all Hands, and through all the Regions of the Heavens j and that is, that in their Aphelia, where they move the floweft, they may be at the greateft Piftances from one another, and fo attraS and difturb one another the leaft that .may be. The Comet that appear'd in 1680, approach'd the Sun nearer than a fixth Part of his Diameter : And by Reafon of that Comet's great Velocity, at fo near a Diftance, »nd the fomewhat Denfity of the Stm's Jtmofphere, it muft have fuf- fcr d fome Refiftance to its Motion there- by ^ and fo muft have been fomewhat re- tarded, and muft have approach'd fome- what nearer the Sun ; fo that in every Revolution, approaching nearer and near- er the Sun, this Comet muft at laft drop into the 5»«'s Body: As alfo this Comet may in his Aphelium, where be moves the floweft, be retarded by the Attraftioii of other Comets ^ and thereby, in his Re- turn, be fwallow'd up of the Sun. Af- ter the fame Manner, the fixed Stars, which by little and little expire in Light and Vapours, and fo are extinguifli'd, may be rekindled by Comets falling into them, and being recruited by this new Fewel, be' accounted new Stars. If they be not Pla- nets, of laelistoa 2tl nets, accompanying the ueareft fixed Stars, as Mr. Derham conjeaures. . § XIX. Thus I have given a Ihort View of this Syftem of Things, as it is at pre- fent ; and I am of 'Opinion, it is nearer the Truth than the antient Theories. And now let any one ferioufly refled upon the Vaftnefs, Magnificence, Beauty, Order, z^ Symmetry of this Scheme, and try if he cm think it the EfFed of Chance •, or if he can fo much as doubt, that fome inti- nitely wife and powerful Archite9 has rear'd this noble Fabrick. But to drive the Argument farther, let us enquire a httie into the particular and obvious Defigns and Contrivances of this Divine Architea. And ift. It is plain from what has been (hewn, that the univerfal Principle of At- traBion or Gravitation, obtains in all the Great Bodies of this Univerfe ^ and that the Motions of all the Plajiets, their Stf-. tellites and the Comets, are govern'd by one Condition thereof, viz. that the Force thereof, at different Diftances from the Center of Attradion, is reciprocally as the Squares of thefe Diftances. Now, is it at all probable, that fo univerfal a Law, fo powerful a Principle, and fo conftant a Rule (hould be owing to Chance > If one with 10000 Dice, (hould throw 50CO Sifes, once or twice, or even icco Sifes, orice and again, we might poflibly fay, he did Air 5^ •■•f 222 j^WbpJicai Wncmts of l^eiigtotti .j^ 223 It, it by Chance • but if, with almoft an in- finite Number of Dice, he fhouJd alwav*? without failing, throw the fame Side m' them all we ftiould cectainJy conclude, he either did it by Art and Ontrivance, or that thefe Dice could turn up on no other Side. Now, I have demonftrated, that Gravitation is not efiential to Matter, and 10 It might have been without it •, and yet all the Bodies of the Univerfe, fo far as we can difcover, are endowed' with this Principle, and obferve this one Condition of it i and therefore, both were defign'# by him who laid the Foundations of the World. 2dly, it is worth our Obfervation to take Notice, how conftant and beautiful a Proportion, the Times of the Revolu- tions of all the Phjiets, and their Satellites, Iceep to their middle Dijlances -^ for univer- fally, in all the Revolutions of the Pla- nets about the Sim, and of the fecondary Planets about the primary ones, the perio- dical Times is in a Sefquiaker Proportion to the middle Biftances , or the Cubes of the middle Diftances, from the Center of their Motions, are in all of them {Planets and Satellites) as the Squares of the periodical Revolutions. gdly, All the Planets and Comets by Rays from the Sun, and all the Satellites^ by Rays from their primary Pla- nets, defcribe^equal Area's in equal Times, /,/, th^ 4rea\s defcriby, are always pro- fortigml portioned .the Times pretty nearly; Sd that wbei y approach to the Center of their Mot; 1, they move fafter, and when they reced. from it, flov/er •, fo as to totii^ penfite lUcir Nearnefs by their Swiftnef^^ and their Diftance by their Slownefs: Al- ways making up equal Area's in eqtial Times. Thefe two fo tmiverfal^ and id re^nlar AfRdions, of the Motions of the Cetefti^l Bodies, are not only difcoverable by Obfervation, but are the neceiTary Ef- fed of the Law of Gravitation, juft now mentioned to be the Principle of the hea- venly Motions. Can any Body now, whd conliders how many Things are concurring to and depending upon thefe beautiftil h' ^rtions, ^lod regular EflFeds, fo raucH as jace Queftion whether they are the ProJud of infinite Wifdom ? Certainly nothing lefs could be fufficient, to make the Lofnputation, .:djuft the Forces, and de^ termine the Ppwcrs^ necelfary towards the Prud'jaion of fuch exaft and regular j^" fetls. 4th ly. All the Planets are fo wifely fituated, in refpecl of the Sun, that the denfer Planet is ftill neareft him, and the lefs denfe is farther removed from him^ and the. leaft denfe of all, is the moft remote. Now, can any Body think this wasr fo order'd without Deftgn ? No cer- tainly, it is fo obvious, no Body can mif^ 0f it ; f<>r it is plainy the more denfe Mai- ' .. ief i mmmmmm^mmfsmmm i ofSUUston 2X$ I* ') tcr requires a greater Degree of Heat, to fit it for natural Produftions ; and the lefs denfe needs only a lefTer Degree of Heat, for the fame End* And confequently, their Diftances were adjufted for this very Reafon ^ and this by the by, is a Pre- fumption for the Planets being inhabited, fince, according to their Denfities, they ire fitted with Degrees of Heat neceflary for natural Produftions : Now this Adjuft- mcnt, and thefe natural Produdions were ufelefs, if there were no Creatures to en- joy the Benefit of *em ^ and we all know that Nature has done nothing in vain. And therefore, fince thefe Accommodations arc provided for Living Creatures, there are fuch probably to enjoy 'em. 5thly, The Velocity of the Planets Motions, is fo adjufted in refpeft of the Swn, and the Ve- Imty of the Satellites^ in refpeft of their primary Planets^ that the Planet which is neareft the Snn^ moves fafteft ^ and that more remote, lefs faft^ and the fartheft, floweft of 2II. And fo in the Satellites ^ the neareft to the primary Planets, moves quickeft ^ and the remoteft, floweft. For fince the Centripetal Forces are reciprocally, as the Squares of the Diftances from the Center, and the Celerities in that Cafe, re- ciprocally, as the fquare Roots of the Di- ftances from the Center j and fince the fquare Root of the remoter Diftance is greater greater than the fquare Root of the nearer, therefore the Velocity of the nearer, ifr greater than that of the remoter. Now, this is a wife Contrivance of the Author of JJature -, for fince the nearer Planet enjoys more of the Heat of the Sun than the re- moter, it was fit the Viciflitudes of the Seafons fliould be quicker, that anfwering beft the Ends of Natural Produftions , for fince their Diftances are leaft, and their Velocities grcateft, that are next the Sun^ their Periods muft be fliorteft j and fince they all move about their Axes^ moft, if not all of them, making thereby fome An^le or other with the Plane of their Oibit, they muft admit of variety of Sea- fons i and where the Heat is greateft, there, for the Conveniency of Natural Produftion, it was neceflary the Seafons fliould be fliorteft •, where the Heat is leaft, there the Seafons fliould be longcft: Now, all thefe Effefts are taken Care of, by this adjufting of the Velocity to the Diftance, And what is here faid of the Seafons, in Refped of the Planets, may be underftood of the Satellites Influences, from their primary Planets •, for, whatever Effefts the primary Planets produce on the fecondary ones, it is doubtlefs moft con- venient the Viciflitudes thereof fliould be quickeft in the neareft, and floweft in the remoteft Satellites* And this, as well as O the XV] r i. tiie former, is a flirewd Prefumption o( fike Planets being inhabited ; for all this |)cautifal Contrivance is loft, if there h^ Ad Inhabitant in the CeUjlial Bodies, to eiijoy the Benefit of it. 6thly, All th« Plsnets defcribe about the Sun^ in one of their Foci, EUiptkk Orbits^ of one Species Qf another ^ and all the SatelUm defcribe about their Primary Planets in one of theif fWi, Elliptici Orhts alfo ^ and the Planes 0f all the Orbits do very nearly coincide with one another, and with the Plane of tfie Ecliptick* That the Planets defcribe W^tkk Orbits about the Sun^ there is n^ manner of Doubt now among Jftronomerst And though they fay, that the Orbits of the Satellites are not exaftly elliptical 5 yet ^at is from neceflary Caufes, and is nol ©wing to Ghance, but to the already efta-- Uifli'd Laws of the Univerfe ^ yet ftill dieir Orbits arc nearer Ellipfes than any other Geometrical Curves^ and may be re- duced to thefe i and that the Planes of the Orbits of the Pla?iets coincide with the Plane of the Ecliptick, and with one ^Bother nearly, is Matter of Obfervation. Now is it imaginable, this beautiful and conftant Order of thefe three Things, of Elliptick Orbits^ the* Situation of the Sun in the one of the Fociy a^nd the Coinci- dence of the Planes of the Orbits with that of the EcUptick^ could have been the EiFeft Of ISeligiom IZ I Effeft of Chance and Cafualty > Or that it was without Defign or Counfel ? Na* certainly, for the Advantages thereby ari- fing to our Earth in particular, are evi- dent •, for thereby, the colder and more- Northern Places of our Globe, are brought fame Hundreds of Thoufand Miles nearet the Sun in Winter than in Summer j which cannot but be of fome fmall Ufa to thofe Places, that by the natural Courfe of the Earth, are deprived of the benign Influence of the Sun at that Seafon. Now this Benefit would be conftant, if' the Place of the Periphelium did not change j but fince that is not conftant, the other is not durable, but temporary. But this now to be taken Notice Queftion if thefe Irregu- Part of the firft Contri- vance of this Univerfe. Now, though in the reft of the Planets^ the Situation of {\\t\x Periphelia is not the fame •, yet no- thing is to be concluded from thence, a- g:iinft this Argument, fince we know not the t^ature of their Inhabitants, nor of their natural Produftions : But this we may conclude, fince it is of notable Ufe to one of the Platrets^ it cannot be amifs to any of them, they agreeing in moft Things : But whatever be the Defign there- of, yet the- conftant Order of thefe Things arc a fufficieot Proof that they were not d 2 cafuai. Change is not of, fince it is a larities were a l This, not dtely fSeir dp fercnt apparent Magrikudi^s, brft Hkewifd the Number of thofe of the firft afnd fe- cond Rate, does evince- For, ii^6n the Suppofition, that cVety /y^ S^ar \^ mt^ our 5fin, and governs ia a Portion of Afe#- ian Space, equal to our Syfl^, thefi there muft be only as many fixed Starj^ of the ftrft Magnitude, as tl^re' are SyfietHs tft^ an ftand ifound ours : But there are but about twelve or thirtefeti* Spheres fliat catt ftand found a middle oM, ecjirfl^to them 5, and fo many ar^ the Stars of the firft Mag- nitude. Again, if we examine how i^any Spheres C3!l ftand round Khis firft Range ()f Sph^es, we will find thetr Number be^ twixt fotty eight ctnA fifty t#o, and f11 the various Motions and Appearances or the CeleJIial Bodies. Thus then this great and glorious Body is fixed, like a power- ful and a kindly ^ Monarch on his Throne^ diftributing Light, Warmth, and Life in plentiful EfFufion, to all his furrounding Vafals, and that fo equally, that the near- eft have not too much, nor the rcmoteft too little. Thefe are fuch great, fuch wife Ends, as clearly fpeak the Omnipotence and Omnifcience of their Author. Moreover, let us confider, with how much Artfulncfs hi^ Bulk and Situation, in Refpeft of the ?la^ ms, is contrived, to have juft Qiiantity enough of Matter to draw round him thefe Maffy Bodies, and their Satellites, fo various ^- in ♦ « i\ ■«»M«BH|i» ^Dilofopttcat 0?incip!eg of 3aeU0ton ML, 37 hill in their Bulks and Diftances from him ^ an^ tliat in regular and uniform Orbits, How exaftiy his Body is rounded, how fully it has been faturated with the Fluid of Light, to be able to laft fo many Years without any fenfible Diminution, tho' there itc conftant Emanations thereof upon his Attendants. As for his Rotation about his own Axe, it is no doubt likewife, for wife Ends and Purpofes, perhaps it may be for the better propagating, and emitting this Fluid of Light, through the Planetarj Re- rnkns^ or for helping forward the Revolu- lons of the Flanets \n their Orbits round about him* Ji JXXII. We can no otherwife gather the Ufefulnefs of the feconJary Planets, to their pmmrj ones, but by fuppoGng the reft may reap refpeSivelj, fome Thing analogus, to the Benefits we of the Earth receive from OUT 'Moon, which are ift, the fupplying of the Sun in the Night Time, for at leaft three Fourths of the Year. Now, how comfortable and delightful a Thing this is, Travellers and Voyagers can beft tell, Cw- fiojity, Jmhition, znd Luxury, if not fome- times Necejjtty, have now made it unavoid- able, that fome Part of Mankind (hould be travelling by Land or Sea , in the Night Seaions , how pleafant then, and joyfol aThing is it, to have a Light held US forth from Heaven^ not only to guide 0»r our Steps, but to direft us in our Courfe; and to point out to us, how our Time wear^ out ? For a very little Experience, makes us reap both thefe laft Advantages from the Prefence and Motion of the Mcon^ 5dly, She raifes our Ttdes^ twice in twenty four Hours, which how abfolutely neccl- fary that is toward the Subfiftance of Ani^ mats and Vegetables, we (hall now fliew. Every Body knows that a Lake or Loch^ that has no frefti Water running into it, will by the Heat of a few Months, and its Stagnation, turn into a ftinking rotten fuJdle, fending forth naufeous and poyfo- nous Steams •, for tho* I do not think, the conftituens Particles of Water themfelves, are alter'd by this Stagnation, yet no Wa- ter is abfolutely pure, but contains a grea- ter Quantity of Fleftiy, Bony, Earthy, Sa- lin, Metallick, and Vegetable Particles, than of pure Element:^ and it is upon thefe, the Heat operates, by diffolving their Union, and combining them in new Forms, and feparating thefe Salin, Sulphurous, and other noxious Particles which produce this Effeft. Now though there be many thou- fands of frelh Water Rivers, daily run- ning into the Sea, yet they are very inconfiderable in Refpeft of the vajl Ocean of Salt Water, and wouM by no Means hin- der its Stagnation, and confequently, its Corruption and Stinking. But admit the Ocean mm I ij8 0]^(lo(bpl)icitt |&?incipleg Ocean once ftagnated, and then the firft £|Fed woti'd be^ that all the Places toward liie Siioffes, wou*d be firft wrought upon by tfce Adion of the Sun, and turned to a MiWphitis, and then by Degrees it wou'd get £ifther, 'till the whole were become more ianeful and pojfanous than the Lake 6f So- akm and Gomorrha j whereby the Fifljes wouid be firft deftroy'd, and by the nox- icMis Steams thence arifing, afterwards the H0MS and Ammals ; whereas by this Adion of the Moon^ the Waters are lifted up in a Heap, as it were, and then let fall again j whereby the Waters near the Shores, are QMlftantly fecur'd from Stagnation and Cor- ruption, and the beginning Malady ftifled. This perpetual Change of new Water on the Shores, keeping any one Portion there- of, too ihort a Time, exposed to the Heat of the&m, to have its Mixture corrupted^ Now, what a noble Contrivance have we here! By appointing ^n Auendant to our Earthy all the Vegetables and Animak are preferv'd from certain Deftruftion j (but 1 am of Opinion, that to the full Effed of this wife Defign, the Salt of the Sea does very much contribute , for as I have faid before, and may obferve afterward, the fxiinted flender Particles of the Salt ftick the Parts of Bodies fo together, that the Particles of Heat cannot fo eafily tear *em afundcr j and it is FaS^ and Obfervation, that there tA Helisicm. 239 there arc many fa line Rocks and Mountain! difpers'd over the Foundations of the great Ocean.^ Befides this, how many Convenien- ces for our Navigation, in Rivers and Har- bours, does this Ebbing and Flowing of the Sed afford > No Body that confiders them, can ccafe from Wonder, or can coa^ tinue'jn Unbelief. And here perhaps it will not be amifs to confider, that if out 2arth had any more than one Moon attend* ingit, that we ihouM receive more Damage than Advantage from it ^ for tho' perhaps thereby our Light in the Night (provided (he were of any Bulk, or at at any Diftance near to that of our prefent Moon) might be augmented, yet at tht ConjunSions nnA Oppofitions with one another, and with the. &i», we ftiou'd have Tides that wou'd raifc the Waters over too much of our dry Land^ and in their Quadratures^ we lhou*d have no Tide at all. in fhort, if our Moon were' bigger or nearer the Earth, or if we had more than one, at any tolerable Diftance from us, we (houM be every now and then in Hazard of being drowned j and if oui? prefent Moon were lefs, or at a greater Di- ftance, or if there were none at all, we fhouM be in Hazard of being ftifled by the noxious Steams arifing from iht Ocean^ which wou*d ftagnate more than it now does. From all which it's evident, how wifely our Satellite has been contrived for our ; I ^jintipUS i ll ■ ■ ■ -*- of XUUgiom 241 i ' t ■ iMir Purpofcs. As for the numtrous Atten- dants of Jupiter and Saturn, they muft be icafonably expefted to fit the NecefTities of the Inhabitants of thefe Planets, fince our Moon fuits us fo well# As to Jupiter, confidering his Bulk and Diftance from the Smn^ being near 400 times bigger than our Earth, and receiving but a twenty-fifth Pirt of our Heat, in wh^t a difttial State of Cold, and Darknefs efpecially, wou d he be in ? Were it not for his Moons or Sa- tellites, aiid for his Rotation about his Jxe, in about Ten Hours: Whereby the lit- tle Vigour of his Light and Heat, is com- Iienfated, by its quick Returns. His Satel- Bes being each of them as big as our Earth, and refleding in upon Him fo ftrong, brilk, and vivid a Light as they do : And their MroGhitions being fo ad jutted, as may be feen in the Table of them in the Befriningof this Chapter : It thereby happens, that fcarce any Part of this Planet is any Time with- out the Prefence and Influence of fome one or more of thefe friendly Attendants. &> that by this numerous Retinue, their firong Light, the encreafing Periods of their Revolutions, as they are diftant from him, and his quick Motion about his^^Ar^ his Light and Heat are wonderfully en- crcas'd, from what they wouM be without thefe Contrivances and Adjuftments. But that which is the fineft Contrivance of alK in in thefe Satellites is (as Mr. Derham has ob- fcrv'd) in their Latitudes, or their Eva- gation towards Jupiter s Poles> the Lati- tude ot the innermoft being -f of Jupiter's Diameter, of the next 4, the third \ and the laft going beyond Jupiter % Poles, one third Part of his Diameter: And as their Latitudes differ according to their Diftances, and Periods, fo they change their Lati* tudes in (horter or longer Times, according to their lefler or greater Latitudes-^ fome making their Progrefs towards his Poles one Way, whilft fome are wandering the other, fome flaying there a longer Time, and fome a leffer and a leffer Time, by which quadruple Variety, thofe large Trads towards the polar Parts of this huge Planet^ have a conftant and yet various Share in the Light, and kindly Influences of thefe four Moons,\nA are fcarce ever deprived of one ot other of them. As to Saturn as he is yet farther from the Sun, than Jupiter, and has but the hundredth Part of out Heat, he is accordingly provided with more Satellites (at leaft five it not more) adjufted much after the fame Man- lier, artd appointed for the fame Ends and Purpofes with thofe of Jupiter, we have now dcfcribM. But he has ftill a farther Provifion made for him, and that is his Ring the moil fuprizing and Angular Appearance in all the Celejiial Regions : R Its Ill I Its fize is prodigious, being more thaq twice as broad in Diameter^ than Saturn is ! And the Breadth of the Ring it felf about a fourth Fart of Saturn s Diameter : And its Diftance from his Body^ about the fame Length, whereby the Sun% Heat and Light has a free Admittance between the flanet and its Ring^ while other Heat and Light is at the fame Time reflcdcd in up- on'ir, by this Ring. Its Thicknefs is fcarce perceivable, which prevents its throwing any great Shadow on Saturn. But its Smoothnefs and refleding Faculty, is very confiderable, as is evident from, the ex- ceeding Brightnefs and Illuftration it re- verberates on its Vianet: So that it feem.s not unlikely, that it may be a Kind of fpecular Contrivance, for reflefting Heat and Light on its central Sovereign, in his great Diftance from tKe Source of Light and Heat. And very probably Sa- turns Period, on his Jxe^ or diurnal Ro- tation, may be pretty quick, and his In- clination to the Plane of his Ring^ or Plane of his Orbit pretty large, as it is in Jupi- ter^ to make all thefe wife Provifions and Accommodation perfeft and compleat. But farther we may obferve one fignal Inftance ©f Wifdtm and Contrivance^ in placing the Heavenly Bodies at fuch a Diftance from each other, and efpecially the greateft at the greatcf Diftance j far had they been fituatea fitiiated much nearer to oriq another, they; woqld have.paus'^ prodigious Difordei's^ir^ very* different Manners ; apd in Particulajj;^ fuch deft ru6l:iy^^ Tides ^ wherever there w^a *%* any Qiiantity of Fluids, or^ great Oceani, that neither .^;?m^/j not, ^eget able s wo^\^ have been able to fuftaiji their Futry^'ir which by.this prudent phoing the lUa- venly Bodies^ M f^ch a Diftance from ,p^C apother, are intirely prevented. 341}%: From our Mpon the EcUffes cdXWA by lie^ Name proceed, :w|iich is of exceeding UCe|^ in Ifavigationn^ for by theraj:lie.Diflrerencqf[, of Meridians^ and the Longitudes of Pla^cS* are determinU Of the fame IJfe ai^.e th^. Ectipfes of the 5m7i, and *of tlie Satellite^ of the otheir flanets ^ which laft being fo^ ^Ffquent, are of wonderful, Affiftance, tog-Diys \ for \% were abfolutely impoflibic, that any Thing (that has l^ife, fliould rcfift fuch a Degree of Heat, It's true, there arc fome Peopjp live under the £quator , yet they have but an uncom- fortable Time on't, though they are fup- piyd with conftant Breezes, and Trade- Winds, arifing from the Earth's Rotation about her Axis^ and prodigious Quanti- ties of Rain, falling by the Plenty of Va- pours, raifed by the Day*s Heat,' and let fall by the fupervening Cold in the Night, having as long a Night as they have a Day, which is a mighty Relief j the continued uninterrupted Adion of the Sun^ being by much a far harder Part, than the Degree of the Heat at ftated Seafons. And as for the foles^ we have very certain Informa- tion^ that few, if any at all, inhabit near tliefa# The extreme Degrees of Heat and Cold ^it happen there, being incQnjiiatt- ble with an Animal Life. But that which makes the Cafe much woffe than in anf Part of our Globe ^ upon this Suppofition, is, that the Rays of the Sun would be both direft, and there could be no Rains nor Winds, becaufe it is the Cooling of the Air, that is the Caufe of both ; which by no Means could happen in our Cafe, etery fucceeding Hour heating the Air to a greater Degree than the former. Add tO all thefe, that our Seas^ even notwith* (landing our Tides, would either be ex- haled, or turn'd into Defarts of Salt, and fo, not only our Fiflies would be dcftroy'd, but we could have no frefli Waters, feeing we could have no cool Air to fend them down : If we had any ?lants or Vegetables^ they would be but of one particular Kind, w«. thofe which require the greateft De- grees of Heat : But it is demonftrable we fliould have Occafion for none ; for any Body, who underftands the Animal CEcono* my, will eafily fee, that no Animal, fuch as 'we have on our Globe now, could bear fuch an exceffive and uninterrupted De- gree of Heat. Upon all which Accounts it is very plain, that the prefent Rotation of the Earth about her Axe, is one of the mod (ignal Inftances of Wifdom and Con- trivance, that can be imagined. § XXV. Next let us combine this Diur- nal Rotation of the Earth about its own A-Xe^ ill a54 1^i)ilofopl^tcal ^tintipm ^^, with the Annual Revolution of the fame about the Sun^ and the Farallelifm of ihtAxe of the Djumal Rotation with itfelf : And from thence we (hall have the beau- tiful Seafons of the Year ^ Seed-Time and Harveft, Summer and Winter ^ the com- fortable Viciffitudes of colder and warmer periods, of Snow and Rain, Winds and (ialms, of ftiorter Days and longer Nights, aijcl again, of -longer Days and Ihorter Sghts i and bf all thofe delightful Chan- gs, which are fo Pleafant, Comfortable,yela, and Neceflary in our prefent Circumftances.: If the Earth had only turn'd aboiit her own Jl^e^ once in twenty four Hours, then all pnt ,ViciJpt7{Jes would have been of Days, aiid' Nights ^ which by no Means would ^aye been fufficient for Vegetation. If the Earth had made a Period about the Sun once in the Year, without any Rotation^ we (hould have had but one long Day, and another equal Night i which, as I have ftiewn, would not have agreed, neither with Life, Dor Vegetation. If both thefe had been united without the third of the ParaUeliJ}n of the Axe of the Diurnal Rotation to it- felf, we might have had Days and Nights, but our other Seafons would have been uncertain, and in fomc Places none at all •, and fo the Effeft of the Annual Revolu- tion would have been deftroy'd in fomc Meafure. But by this wife Conjundion of Of Bieltgion^ ^$s all thefe three Modifications, we enjpy our Seafons, and the other confequent Changes of the Tear, which are of f<^ great Ufe to us j for, had we enjoy'd ii% coiiftant uniform Seafon all the Year rounds fuppofe of Summer Weather, then our Ground had been exhaufted, and worn out by conftant bringing forth of Veget^t hlesy and would have run into Weeds, and thofe other Plants that require the leaft rich Soil, and moft Heat only j fo that \n a few Years, the Earth would have been reduced into a Wildernefs of needlefs Herbs ; for toward the Produftion of the more ufeful Plants, there is required (befides a certain Degree of Heat and Moifture) a LixiviaU Nitrous^ or Urinous Salty which keeps the Mold loofe (for receiving the moift Air, and for the Entry of that Heat and Moifture.) For tho' Salts confolidate Water, which confifts of folid porous Parts, whereby their Particles are ftuck to- gether, yet they keep the Parts of Mold, or Sandy Clay ( which has little or no Water) afunder, and loofe, by the fame very Reafon v for their Particles not alloW'- ing them Entry into themfelves, they get betwixt them, and firft feparate their U- nion, and then keep them from coming together •, and perhaps both forward the Motion of the Liquors in the Vegetabk Channels (which are certainly endowed ^r^jvm^ w 5($ |»ft(!ofopDicm |»)incipleg of i&eUgion^ 257 "« With fotne Degree of Elaftkk), and capa- We of being ftiraiilatcd, as it evident in younger Twigs and Bratichcs, as well as dmmd ones) and endows the? juiced with the Qualities the fUnt requires* Now thcTe are either quite eihaufted, ot dc^ ftrovM by conftant Growth and Fegetation. We fee the beft Ground wears put in a ^w Years, and turns into wild ufelefs Weeds •, and all the Materials ^or enrich- ing Ground, are gathered from Places de- barrM from the Aftion 0^ the Surt, atid the Expenccs of Vegetation, but e*posM to the Air, and Weather, whef eby they are impregnated with this Nitrous or othet Saks / Such are old Turf, new Mold, the Dung and Excrements of Animals^ ot thole Things which abound with Lmval Saks i fuch are burnt Wood, burnt Turf, Stubbie, and the like. Now all thefe, irould by a Ihort Time's uninterrupted Ve- ffitation have been quite fpcrtt* Add to thefe, that in a perpetual Summer, there would not fall fufRcient Quantities of Rain, to moiften and foftett the Mold to that Degree, that it is neccffary for con- fbiit Vegetation •, for we find there is twice or thrice as much Rain falls in the Wmur ix Months, from September to Aprils than hx the Summer fix Months j and yet all l!his li but fufficient for one fix Months feietatitn. • Moreover, even the AmmaU them- themfelves, could not conveniently. bear a perpetual Summer-^ for we find now, that the Cold of the Winter, by flopping the Pores of the fenfible Perfpiration, keeps the Warmth more within, whereby there IS a greater Quantity of Spirits generated, the Blood is lefs rarify*d, the natural Fun* aions are more ftrong, .ind performed with more Vigour, the Digeftion is better, the fenfible Excretions more natural, and lefs violent, and the Crudities of the preceding 'Summer are fettled and digefted, I mean; in healthful and found Animals, (for the Cafe is quite other wife in Valetudinary ones,, as of Neceflity it muft be), .and in a mode- rate and not oVer tedious Winter , where^. as in Summer the Blood is more rarify'dj the Spirits more exhaufted, the fenfible ferfpirations more violent, . and lefs natu- ral, the Digeftion worfe, and all the Gon-> coclions lefs tjioroughly perform*d. So: that it is evident we could bear neitheu. of thefe States perpetually, the Change ofi the one being abfolutely neceflary to qiia-l lify the Errors and Extreams of the other. If we had a petpetual Summer, we fhould' be reduced to meer Skeletons ^ if a perpe* tual Winter^ we (hould turn Dull, unaftiv© Drones. Now, perhaps, againft all thefe it may be objefted, that there are rational Creatures, who inhabit this GM^ of ours, who are perpetually in both thefe. Ex- S treamsi ifcaiM $6 ^ftitofopftical t^itncipleg of laeltston. M7 with fome Degree of Etaftiek^, and capa- ble of being ftimulated, as is evident in younget Twigs and Bratiches, as well as Animal ones) and endows the Juices with the Qualities the Plant requites* Now thcfc are eitheif quite exhauftcd, ot dc- ftrovM by conftant Growth and Vegitation. We fee the beft Ground weats put in a ^w Years, and turns into wild ufelefs Weeds i and all the Materials for enrich- ing Ground, are gathered from Places de- barxM from the Adion of the Sun, afad the Expenccs of Vegetation, but expos d to the Air, and Weather whefeby they are impregnated with this mrous or other Saks : Such are old Turf, neW Mold, the Dung and Excrements of Animals, ot thole Things which abound with Uxival Salts V fuch are burnt Wood, burnt Turf, Stubble, and the like. Now all thefe, would by a fliort Time's uninterrupted Fe- getation have been quite fpertt* Add to thefe, that in a perpetual Summer, there would not fall fufticient Quantities of Raio, to moiften and foftetl the Mold to that Degree, that it is ncceffary for con* Aant Vegetation , for we find there is twice or thrice as much Rain falls in the mnUr ix Months, from September to April, than k the Summer fix Months j and yet all this is but fufficient for one fix Months fegetaticn. * Moreover, etili the Animah them- themfelves, could not conveniently bear a perpetual Summer ; for we find now, that the Cold of the Winter, by flopping the Pores of the fenfible Perfpiration, keeps the Warmth more within, whereby there IS a greater Qjaantity of Spirits generated, the Blood is lefs rarify'd, the natural Fun- dions are more ftrong, .ind performed with more Vigour, the Digeftion is better, the fenfible Excretions more natural, and lefs violent, and the Crudities of the preceding dimmer are fettled and digefted, I mean, in healthful and found Animals, (for the Cafe is quite otherwife in Valetudinary onas^ as of Neceflity it muft be) and in a mode- rate and not oVer tedious Winter -^ where- as in Summer the Blood is more rarify'd/ the Spirits more exhaufted, the fenfible ferfpirations more violent, and lefs natu- ral, the Digeftion worfe, and all the Con-> coftions lefs thoroughly perform*d. So- that it is evident we could bear neither^ of thefe States perpetually, the Change of* the one being abfolutely neceflary to qua-, lify the Errors and Extreams of the other. If we had a perpetual Summer, we fhouH Skeletons \ if a perpe be reduced to meer tual Winter^ we (hould turn Dull, unaftive Drones. Now, perhaps, againft all thefe it may be objected, that there are rational Creatures, who inhabit this Globe of ours, who are perpetually in both thefe. Ex- : S treams^ Ifi I # »!l 58 ^DilofopDtcal f^^incipus treams, and yet are found to be not at all difposM, as I pretend they wou'd be. To this I mfwer, that though, as to the Prefehce or Abfence of the Sun, they may be much the fame, as I fuppofe, yet, there are other concurring Circumftances, which arife from the Vicijfitudes of the Seafons in tfte other Parts of the Globe, which alters tlie Gafe quite , for there are conftant Seafons of Rain, in the more Southern Countries, which fall for fome confiderble Time, that both hinders the perpetual Ve- gelation, foftens the Mold, and fattens it for the next Crop \ there are Clouds of Snow and Rain, impregnated with thefe nitrous Salts^ which are driven ( by the Force of the Winds) from colder into thefe hotter Countries, and there falling, do enrich the Ground. Befides that, even the Clouds, raisM from thefe hotter Coun- tries themfelves, when diftillM into Rain, ate fufficient f6r this End •, for as I have fkid before, the Air every where is full of fuci^ Saks^ as is known by Experiment. Let any one confult Varenius^ and he will Be' fatisfyM that thefe Southern Countries have Winters, though not of Snow, yet what is abundantly fufficient to ftop the perpetual Vegetation^ to moiften, foften, and fatten the Mold, and to cool the Blood, and other Fluids of the Animals. Now, the principal Thing that makes this foetical State of ^ligtOlU MUiM 2^9 State of a perpetual Summer, unfit for the prefent Conftitution of the Animals and Vegetables, is, that in fuch a State (either arifing from only a Diurnal Rotation, with- out an Annual, or an Annual without a Diurnal) there would not be that Variety of Rains and cool Breezes, nor coriftant and Trade-Winds, nor overflowing Rivers^ and fuch like Circum (lances, which are the Effed of this combining thefe two Mo- tions together. I need not fliew the In- conveniencies of a perpetual Winter, every Body is fufficiently fenfible, that upon fucfe a Suppofition, we (hould have neither Ve- getable nor Animal in a very fliort Time j efpecially of any confiderable Ufe, or Va^ lue, fuch as require a Summer's Heat fpr their Growth ^ and as for Spring and Au- tumn, they are not fo much diftinft Seafons from the two former, as gentle Gradations and eafy Steps, whereby the one Aides in- to the other, through the intermediate Degrees. From all which it is evident, how wifely thefe three fo different Modi- fications, have been linked together, for the Benefit of the Inhabitants of this Globe;, for by thefe, we have fufficient Heat m Summer^ to ripen the Fruits that are the Produft of every refpedive Climate , and we are furnilh*d with Reafon, and made capable of Induftry, to transfer the Pro- duds of one Country to another 3 we hayp S 2 jRaia TuBrT> q^*p»^Hy I U :■ M f! 60 )^Dilo(opt)tcai i^^nciplefii of Sleltgion 261 I! Rain and cooling Breezes in the fVinter, of thofe Countries where Heat is not wanting, to cool, foften, and enrich the Moid, and to ftop conltant Fegetation j and we have Froft arid Snow in others, where the Heat is not to fpare, to lock up the Mold from being walh'd away, and to keep in either the natural, or adventitious Heats, 'till the Time that all Circumftances concur, to have the Produft of the Ground brought to its Vegetations, % XXVI. Come we now to confider the Obliquity of the Plane of the Ediptick to that of the .Equator, or of the Axe of the Diurnal Rotation, to the Plane of the an- nual Orbit of the Earth, which makes an Angle of 66 k Degrees. I have already ihewn, that if the Equator and Ediptick had coincided, it would have render'd the annual Revolution of the Earth quite ufe- lefs ^ for if the Earth had mov'd about its own Axe, and this Axe had been at Right- Angles with the Plane of the Ediptick, the fame Appearances as to the VtciJJitudes of Day and Night, had happen'd, whether the Earth had mov'd round the Sun, or not j and the Alterations of Seafons, and all the Confequences thereon depending, had not been at all j and what a Hin- drance this would have been to Life and Vegetation, I have already (hewn. l^efides that in the Torrid Zone the Heat would have have been intollerable, and not to have ' been endur'd ^ and in the frigid Zones^ the Cold would have deftroy'd both Am- mals and Vegetables •, and even in the Tem- perate Climates, the one Half of -era .wou d have made but a very comfortlefe Habita- tion, for fuch Creatures as we now are j fo that but only the other Half would have been any ways a tolenble Seat for rational Creatures, and five Sixths at lealt of the whole Globe, would have been render'd ufelefs. But Got», who is wiler than Man, has contriv'd the Matter much better ^ for by this prefent Obliquity of the Ediptick to the Equator, we reap one very confiderable Advantage, which is takeii Notice of by my very learned and ingenjouf Friend Dr. John Keill, and that is, that we beyond the forty fifth Degree of Latitude and v^ho confequently have the greatdt need of the Suns Heat, have more of it, take the whole Year about, than if the km had moved continually in the Equator \ and they that live in the T'*"''"'^'' '2'o»^ and the adjicent Places, even to the Latitude of forty five Degrees, who are rather too much expofed to the Heat of the Sun, than too little, have by thcfe Means lefs of his Hear, than they would have had, had the Earth obferv'd a right Pofition. To thefe add, that fince this Globe of 04rs has been defign'd for a Habitation of S3 rational z6i pi)iio(op|)tcai ^^ittctpiejQi of BeUfiion. 263 !■ \ Hi ratiotial nnd irrational Creatures, of vari- ous Tempersy Conftitutions^ and Difpojitions ^ 3tld for VegHahles of different Matures and Virtues, requiring different Degrees of Heat and Nourillimcnt, to ripen, and bring them to Perfeftion, (to fhew the manifold Wifdom of the Author of Nature^ in the Variety of every Thing:) And fince we find the prefent Heat of the TorriJ Zones very well fitted for all the Kinds of Jni- mals and Vegetables that inhabit and grow there , the Colcf of the Frigid Zones very tolerable to the Inhabitants \nA ProduSions of thefe Places, and the Temper of the intermediate oqes, fuited to theirs ^ thofe Animals that cinnot tranfport themfelves, and the Vegetables that require a greater Degree of Heat, not having too much 5 and the like Animals and Vegetables that can fufFer Cold, not having too little Heat ^ and the rational Creatures being endow'd with Reafon and Means to tranfport them- felves where they live moft at Eafe : And fince it was impoflible to have accomodated all thefe fo various and different Animals and Vegetables in a Place of an equable and uniform (or in one and the fame) Climate^ it is evident, that the prefent Situation of the Axe of the Earth to the Plane of the Bctrptick, is the beft (of that infinite Va- riety pofiible) that could be, for our pre- fent Circumftances j for by any other very 2 confiderable confiderable Alteration, all or mofl of the mentioriM Advantages would be loft. For all which Reafons, we can never fufficient- ly admire the Wifdom of the Author of J!ature^ who has provided fo liberally and prudently for his Creatures. 5 XXVH. The fame divine Wifdom is cotifpicuous in the Situation of the Earth in refped of the Sun ^ for had the Di- ftance between the Earth and the Sun^ been the fame with the Diftance between Mercury and the Sun, i. e. were we brought three times nearer the Sun than we are, or the Sun brought three times nearer us than he is, our Ground in Winter would have been hotter than a red hot Iron, and what a Condition we fliould have been in then, we may eafily guefs. On the other Hand, had the Sun been remov'd from us, or we from the Sun, to the Diftance Jupi- ter or Saturn are removed, our hotteft Sum- mers Day, had not afforded fo much Heat, as thofe that now live under the very Polar Star (if any fuch there be) of our Globe, feel in the Midft of Winter. Are not we then very wifely provided for, who are put in fuch Mediocrity, between thefe two extrcam Diftances ^ that neither our Heat nor Cold is fo violent, but that we may either endure them, or with a little Indu- ftry fence our felves againft their Injuries ? Again, as to the Figure of our Earth, w^ S 4 ara K ^*4>t^*-4 Wm 264 t^Dilo(bp|)tcal l^nnctples are certain, from its Shadow in the Eclrp- fes of tht Moon^ ^nd a great many other experimental Obfervations, that it is Sphe- rical, Spheraldical^ or Orbictdar^ bating the Inequalities the Mountains make : And this Figure is a wife and beneficial Contri- vance, not only as it is the moft Capacious, and renders all the Parts of its Surface equidiftant from its Center of Magnitude, and alfo from its Center of Gravity pret- ty nearly, whereby the Equability of its Emathn about its Jxe^ and of its Circum- volmion in its Orbit, is preferv'd, and all the Motions on its Surface in all its Parts, are rendered Uniform and Similar. But alfo, as the Ingenious and Reverend Mr. Derham has obferv'd : ift, Becaufe this Figure is the fittefl of any, for a regular and gradual Reception and Surrendry of Light and Heat ^ both thefe being admit- ted, and given off, by more flow, creep- ing, and infenfible Degrees, than they could be, were the Earth of a Figure roadie of plain Sides, or any other Figure whatfoever. jdly, Becaufe this Figure is the Jitteft for a regular and equal Diftri- bution pf the Waters i which being a hea- vy Body, would fall more unequally to- wards fome one Side or other, were the Earth of a Figure made up of equal or unequal Plains, gdly, Becaufe this Figure is the moft proper "for an uniform and {. r equal of laeltjston^ 265 equal Diftribution of the Winds, and the other Motions of our Atmofphere ^ for we find, that large Mountains, Bays^ Capes ^ and Headlands, alter and difturb, in fome Meafure, the uniform Propagation of the Wmds, even of the general and conftant Trade Winds 5 and if the Earth were of a Multiangular Figure, the Advantages ari- iing from regular Winds, and Fannings of the Air, would be difturb'd and de- ftroy'd to a much higher Degree. Now thefe are fome few of the Advantages of an Orbicular Figure in general 5 but as to the prolate Spheroidical Figure in particu- lar, though it be the necelTary Refult of the Earth's Rotation about its own Axe^ and the Fluidity of its fuperficial Parts, at the Commencement of this Rotation ; yet it alfo is very convenient for us. By the Earth's Motions about its Axe^ the Parts endeavour to recede from the fame Axe, as much as they poflibly can, by a centrifugal Force, arifing from the circular Motion i and therefore, if the Matter of any of the Heavenly Bodies was fluid, at the Commencement of this Circular Mo- tion, it would neceffarily have rifen from the Voles, and accumulated at the Equator^ and fo induced a Spheroidical Figure on the planet's Body, generated by the Circumvo- lution of an Ellipfe about its lefler Diameter^ Now, fince it is evident to our Sight, af- * ' " fitted ■ 1 H 4 t66 i^DiloCopft^cai 0?tnc(pleg fifted with a good Tele/cope^ particularly ia Jupiter^ that the Diameter at the £yw^- $of^ is longer than that at the Pales •, and ince Sir Ifaac Newton has dernonftrated, that the Earth is at leaft feventeen Miles higher at the Equator than at the Poles^ and fince many repeated Experiments on the Lengths of Pendulums in different La- titudes have confirm'd the fame ^ it*s plain, that at the Commencement of the diurnal Rotation, the Surface of the Planets has been covered with a Fluid 5 which gives an Account why, at every forty or fifty Fathoms below the Surface of our Earthy we never mifs of Water. It is likewife evident, from this Figure of the Body of the Planets^ that the Surface of the tem- perate Climates is larger than it would have been, had the Globe of our Earthy or of the Planets^ been either fpberical^ or ob- Imgljt fpheroidical*j fo that the Advantage nf this Figure is very confiderable •, the Sirfaees of the Polar Regions^ which by Reafon erf the oblique Incidence of the Rays of the Sun upon them, are colder, and lefs convenient fur the Habitation of Jtmrnalsj and the Produftion of the no- bler Sort of Vegetables^ are hereby con- fiderably lefien'd, and the Surfaces or Space about the temperate Zones^ which are moft comfortable and ufeful, are there- by coafiderably enlarged. The fame Fi- gure of SlelijStom 267 gure obtains not only in the Earthy and the reft of the Planets^ and their Satellites but likewife in the Sun^ and univerfally in every fluid Body revolving about an Axe. J XXVIII. Having (hewn fome of the Advantages arifing from the feveral Mo- tions of the Earthy and the Combination of thefe, which are common to the other Planets^ I come now briefly to confider, thofe that poflibly may be more particular- ly belonging to our Globe^ and are not the immediate Confcquence of its Motions j and the firft in Order is our Atmofphere^ of fuch Neceffity toward the Subfiftence of Animals^ and the Growth of Vegetables^ that neither could fubfift any confidera- ble Time without it. This Atmofphere is a thin elaftick Fluid, intermixed with Par- ticles of different Natures^ furrounding our Globe to the Heighth, of about forty or forty five Miles. The Nature and Pro- perties of this Fluid, I have in fome Mea- fure ftiewn already. But fome of its Ufes I fhall now point out, and firft as to 3^- getation^ Dr. Grew and Malpighi have (hewn, that it is a Principle concurrent therein 5 and by Experiments on Seeds fown in Earth and put in an exhaufted Receiver^ it has been provM that no Vegetation can fucceed without it , what makes it fo ne- ceflary feems to be becaufe it being more eafily 6g i^DUDfopDtcal l^^tnctpleiS of ileliston^ 269 cafily rarify'd, and heated by the ASion of the Sun, than other more com pi ft, heavy, and hkfpringy Fluids, is fitter to promote the Afcent of Juices in the flender Chan- nels of Vegetables ^ and there being no Fluid without a confiderable Portion there- of» lodg'd up and down among its Parts, the firtt Impulfe of the Juices upwards, does thence arife. As alfo becaufe of it§ adive, fpringy and fubtile Nature, it ra- Tifies, aftuates and refines the more fizy Vegetable Juices to promote their Circula- tion, and performs Fundions on them. Ana- logous to that it does on the animal Fluids. l4ext as to Animal^, it is well known, that they could live but a few Minutes with- out this elapck Fluid, and probably that which fo fuddenjiy kills thunder- ftruck Anitnahy is the quick and violent Rarefa- dion of the Air about them •, for the Liings of all fuch, upon opening, are found quite deftitute of Air, and the Sides of their Veficles quite clappM together.^ It's certain, that the Blood i5 fent from* the right Ventricle of the Heart to the Lungs, and if the Veficles thereof be not diflen- ded or blown up, by the Air, the Qr- ctdation mufl flop there, and the Animal perifh, and both for the Comminution of the Particles of ;he Blood, that they may more eafily pafs through the G//?//A^'7 and terminitine Vcirels, and for the Propa- gition gation thereof in the wider ones, there is neceflfarily required a Fluid of a deter- minate Gravity, and Elafticity. We have ^s great Difficulty of Breathing, in a thin (as is evident from the Difficulty of Breath- ing on the Tops of high Mountains, and from Experiments on Animals in nearly exhauftecl Receivers^ as in a thick Air ; and even in Fijldes, where the Water in fome Mcafure fupplies the Want of Air; yet if you draw out all the Bubbles of Air, which are always found in Wate^ they will languifh and die^ and in great Frofls, if the Ice be not broken to ad- mit frefh Air, the Fif) in Lochs and ?onds will languifh and die;> not to mention here their Swrntmng- Bladders ^ which are fo necefTary to them, and communicates with the Air in their Gills, So that even to them, a certain Portion of this elajlick Fluid, isneceifiry. Now how well is this Fluid fitted for the Generality of the In- habitants of this Globe ! It being neither too heavy, nor too light, neither too much, nor too little Elaflick, for the Ufes of Re- fpiration. Another Advantage we reap by our Atrimfphere^ is, that by it our Clouds and Vapours are fupported, without which "we (hould neither have frefti Water, nor Snow, nor Rain, nor any of thofe Things, which moiften and enrich our Soil, and make it fit for Vegetation. For though it be \. 70 )dDilo(bpl)tcal 0;tnciples; of laeligion. *7^ T)c the Sw/i that rarifies the Water, and makes it take its firft Flight in Vapours and Steams ^ yet it's by the Jtmofphere, its Progrefsis continued to the upper Regions, and fupported when it is there, to be af- terwards formed into Snow, or Hail, or Rain, or carry *d into other Regions, whofe Soil does want it more. Every Body knows, that if there were no Atmofphere^ but a perfed Void^ around the Earthy the Aftion of the 5«», would not be able to raife the Vapours above a few Feet from its Surface ^ and that it's only the At.mofphere\ being fpecifiallj^ heavier, than thefe Vapours, that buoys them up in the Air, by its greater Tendency toward the Center. Now then, if there were no Atmofphere, the Va- pours could rife to no fufficient Heigh th, and fo could never be cool'd fufficiently, fo as to be form'd into Snow, or Rain ^ for at a fraall Diftance from the Earth's Surface, the reflefted Rays of the Sitn, make the Places fo warm, that no Vapour could be turn'd into Snow, or Rain, there ^ for it's the Coldnefs of the upper Regions, (being de- ftitute of thefe reflefted Rays) and the Length of their Defcent, that forms thefe Clouds znd Vapours into Snow, and Rain, whenever the fupporting Atmofphere be* comes lighter, than thefe accumlated Va- pours^ they fall down with the Temper pi Heat or Cold, thej had in the upper Regions^ Re^ions^ and fo become Snow, or Rain ac* cordingly. So that it's plain, it^ our At^ fnofphere that is one of the principal Means of our Dews, and Rains, and all the Blcf* fings^ that follow upon thefe. A third Advantage of our Atmofphere is, our Bre^^^ %es and our Winds^ which carry out Ships upon the Sea^ and purify our Air, from noxious Steams, which (with the Concurrence of the Suri) melt our Snows, and dry our Ground when over-moiften'd ) and ferve for fo many other Purpofes, for the Accommodation of Humane Life. Wind is nothing but a violent Motion of the Air, produced principally by its Rarefa- ftion, more in one Place than another, by; the Suns Beams, the AttraSions of the Moon^ and the Combinations of the EartW% Motions. Without our Atmofphere^ we fliould have no more Wind above, than under Ground, and fo be deprived of all the Benefits arifing thence, Laftly, Our Atmofphere is the Vehicle and Medium of Sound, that Senfe wliich moftly diftin- guifties us from Fif^es^ and the inferior Sort of InfeHs. Sound is nothing but a Modulation or Percujjion of the Air, com* municated by an Impulfe, from the vibra- ting fonorous Body, and propagated in Vn* dulati07iSf through the Fluid of the Atmo- sphere^ every Way round. Without our Air we (hould not be able to hear the Report; z-jz t^DilofopDical 0;inciples of ]aeltston« |i n Report of a thoufand Pieces of Ordinance, difcharg'd at the fmalleft Diftance, as is evident from the Experiments on Sounds in exhaufted Receivers. We (hould have no fuch Thing as Languages or Mufak, and what a comfortlefs State this would be, I leave th© Reader to judge. Add to all thefe, that it is to our Atmofphere the Beauty, Variety of Colours, and Figures, which are painted on the Skies, the Light- fomncfs of our Air, and the Twilight are owing. By it the Day is protrafted, and the Night (hortned, and in thefe Places moft, which waiit thofe moft. By the JiefraBions of our Atmofphere^ the Sun rifes fooner, and fets later in Appearance, and with its beneficial Confequences, even a Month fooner in fome Places than it would otherwife: And the Land and Moun- tains, appear fooner to the weary wan- dering Sailor. Thefe arc great and noble Advantages to the Inhabitants of this Globe, as they bed can tell, who by Accidents are fometimes deprived of them. From all which it's very plain that there was Counfel and Defign in the Contrivance and Pro- duftion of our Atmofphere. gXXIX. The next Thing in Order to te confiderM is, our Mountains^ without which it were aim oft impoflible for Ani- maU to fubfift, or Vegetables to grow, they being one of the principal concurrent Caufes toward toward the Produftion of our frefli Wa- ter Rivers. It has been (hewn from Gal- culition, by feveral Perforis, and parti- cularly the ingenious and learned Profef- for of Geometry at Oxford^ Dr. Ed. Halley^ that the Sun raifes Vaoours from the Sur- face of the Sea, in a Year, fufficieiit to fupply all the Rivers with frefh Water for that TimCi Now thefe Vapour^ bein^ tais'd (the Sun afting upon the Surface .of the Sea, as a Fire under an Alembick^ by farifying the fame, it makes the lighteft^ i.e. the freffieft Portions thereof, to rife with it firft ^ arid it rarifies the Water by the Infinuation of its aftive Particles among the porous Parts thereof, whereby they are put in a violent Motion innumerable different Ways, and fo are expanded by the compound Fluid of Heat and Air, or hot Air, which carries up with its every little Volu?n^ a Coi)er of the more glutin- ous Fluid of Water which becomes a lit- tle Bubble of hot Air inclofed within at Shell of Water, whereof a great Numbef conftitutes a Vapour, which beirig thu§ form'd into little Bubbles of larger Di- menfions than they formerly had, by the inteftine Motion faifed by the ,Heat ori the Air and Water, which makes their Parts turn round their Centers of Gravi- ty^ and fo to poflefiS moie Spate, arid like- Wife to? ffy iioiTi one ahotlief,' and by 't thefe 274 0Dilofoptltcal ^intiplts of Xleliston* 275 thefe Means being become fpecifically ligh- ter, they are buoy'd up by the weightier Atmefphete) and tfiat this is pretty nearly the Fad, in the Produftion of Vaptnm, 'may be evident to any one who Will view thefe Vapours raifed from common Wa- ter, by a culinary Fire with a Microfcope, through a Beam of the Sun^ which will prefently be feen to be innumerable lit- tle Bubbles of Water, of different Magni- tudes according to the different Force of the Heat in blowing them up. A fmall Heat throws off but few Vapours, and fmall Bubbles, a greater Heat, groffer, kr- ger, aitd more numerous Globules. And a very great Heat, fo weighty, large, and many Veficles^ that the Air is not able to f eceive and buoy them up, and fo produces a boyling in the Water. And every one knows that cold folid Bodies, intercepting Vapours, will condenfe them info Moi- fture, watery Drops, and Water. From all which it is evident that Vapours may be raifed by the Sun in fuch Quantities, as is fufficient to make Clouds, which reft- ing in thofe Places, where the Air is of equal Gravity with them, are carry'd up and down the Atmofphere^ by the Courfe of that Air, 'till they at laft hit againft the Sides of the more eminent and Monn" tanous Places, of the Globe^ and by this Concuflioa are condenfed, and thus be- come come heavier than the Air they fwom in, and fo gleet down the rocky Caverns of thefe Mountabis^ whofe inner Parts being hollow, and ftony, afford them a Bafon^ 'till they are accumulated in fufficient Qjjantities to break out at the firft Crany j whence they defcend into the Plains, and feveral of them uniting, form Rivulets, and many of thefe Rivers j fo that it is evident the great Benefit of thefe Emi- nences is not, that by the Shock thefe Vapours get in their Courfe from them, they are condensed, fo as to be precipita- ted thereby through the Chinks of the Rocks, but that afterwards in their Bow- els they are prefervM, 'till they be of fuf- ficient Quantity to form Rivulets, and then Rivers ^ for doubtlefs our Vapours would fall in Rain, and Dew, though there were no Mountains^ but then they would fall equally, over confiderable Places of the Qlobe at once, and fo would be fuck'd up in the Ground, or make an univerfal Pud- dle ^ whereas by thefe Mountains, they are perpetually almoft, (at leaft a Nights) pou- ring down in fome particular Places, and there treafuring up, for a conftant Sup- ply to the Rivers. Not that other Caufes may not concur toward the Produftion of Fountains, Rivers, and frefli Water, be- fides the raifing of Vapours by the Heat of the Sun, to defcend in Rains^ Mip^ T 2 and ifa ■!<■ Hi- ll ^ |M i«»*. f r»* B76 |^Dfl0fi)|^teal f^mUpletf ind Dews. They might be raifed from the Sea by Subterraneous Heats, and percolated from their SaltnefSj by being ftrainM thro' Marths and Layers of Minerals of diffe- rent Natures ^ but it is not eafy to con- ceive, how any {training can bring fait liVater to that Degree of Freflinefs, our Rain, and Snow Water is. brought. All the artificial Strainings, tho* never fo of- ten repeated, and through whatfoever Kind of Sands or Earths, hitherto difcover'd and inade ufe of, ftill leave a BrakiJJmefs in fait Water, that makes it unfit for Jfrnw^/ZUfesi neither does there appear any Kind of natural Operation, fufficient for this Pur- pofe, but this natural Sublimation and Di- filiation of Vapours into Dews, Mifts^ and Rains^ which makes it very probaole that this is the principal Efficient in the Pro ^udion of Rivers and Fountains. As to tlie Perpetuity, and Equability of fome Foun- tains, where there are no confiderable Mountains over and above what is to be expefted from the uncertain and unequal failing of Rains^ Mijls, or Dews^ nothing can be concluded from thence, unlefs the Extent and Capacity of the Refervoirs of failing Rains in the Bowels of the Earth were certainly known. For the frefli Wa- ter may be conveyed to fo great a Diftance, and in fuch a Quantity, and to fo great a 0eptb, by the Situation of the internal Gha- »7? Chanels, as may be fufficient to raife ij in larger Streams, than any Fountain Head as yet known, can fend out j and the Deptli and Diftance of the Bafon may hinder it from fending out Senfibly, more Water -at one Time than another. Tho' if the Quan-^ tity were precifely the fame at all Times, in thefe perennial Fountains, the Difficulty would be greater. However, whatfoever the Origin of Fountains may -be, ftill Hills are the Refervoirs in this great Work. An^ other very confiderable Ufe of thefe Ktlhy and Eminences^ is the Determination of thefe Rivers •, tor tho* there had been Ri- vers without Mountains, (which is hardly poffible) yet in that Cafe the Rivers coul4 only have run in a ftraight Line, if they had run at all j whereas, by thefe Eminen- ces, plac'd up and down the Glohe, the Rivers make innumerable beautifying Turn-^ ings and Windings, whereby they enrich, fatten and water the Soil of feveral diite- rent Countries in one Courfe, make the Tranfportations and Carriage over Lands more eafy and manageable, and at laft dif- embogue in feveral Mouths into the Sea 5 where, by the Affiftance of the Tides, they form Harbours and Ports, for the Conveni- ence of Shipping and Navigation, All thefe Advantages we have by our Mountains ^ foi tho' from other Caufes, we might poffibljr be fupplY*d with frefti Water Springs, (tho ^^ ^ T 3 Nature ♦i: m I ■^' «*• » 7^ t^DaoCoptitcal l^^incipUiSi Nature feldom is Luxuriant in Diverfity of Caufes) yet without our Mountains we could never have Rivers, nor could thefc Rivers have fuch delightful Turnings, nor thofe ufeful Falls, which gives them an Irs- petuofity that may be improv'd to fo many delightful as well as profitable Ufes. Laft- !y. If we confider what thefe Hills in their own Nature and Caufe are, we fhall plain- ly, perceive their Neceffity and Ufe : A Hill, is nothing but the l^eji of fome Mettal or Mineral, either of Stone, Iron, Tin, Cop' fgr, or fuch like lower Vegetables : Thefe Mettals and Minerals, by a plaftick Virtue proper to therafelves, and the Efficacy of fubterranean Heat and Fires, converting the adjacent Earths into their Subftance, do encreafe and grow, as truly as Animals ox Vegetables, and requiring free Paffage both for Air and Water to affift in their For- mation j by their Growth, and the Heat of the fubterranean Fires, raife and pufti upward the Surface of the Earth accor- ding to the Neceffity of their Nature, and the Qixantity of the Metalllck or Mineral JScd, I do not fay that all Mountains owe their Origin to fuch Caufes, fubterraneotis Fires have thrown up Mountains of Mine- ral and Metallick Beds, already form'd j the &a and Tides have thrown up Banks and Bays of Stone and Sand-, Currents and Stjaiaras in proper. Situations, meeting and jufiling of EeUgioti^ »79 kftling have forra*d Eminences (rf diffe- rent Sizes and Matter : And Art a«d hu- mane Induftry has raifed fome. But ge- nerally and for the inoft Part, all the emi- nent Mountains are found to be Nefts, and Beds of Minerals and Mettals, which have large hollow Cavities, for Water and Air, and whenever they have been digg d into, thefe have been found in them, with all the Appearances of fome Parts of them a forming and growing in a Manner proper to them, and analogous to the Vegetation ot Plants. The Manner how they are pro- duc'd is not here neceffary to be enquir d into, but that Mettals and Minerals are enj- ereafed and do grow is paft all Doubt, and is confirm'd by all Miner's and Diggers : And that there may be fubterraneous Heats fufficient to raife them into Hills and Moun- tains, is evident from fome, fo form'd near Vulcano's and burning Mountains : And the Force and Violence with which theie burn, and throw out fuch Maffes of pny^ fulphurous, and earthly Matter. From ail which it is evident our Mountains are as neceffary as our Mettals ann Minerals are. I do not mention here their Ufe and Ad- vantage for the Produftion, Shelter, and Nouriffiraent of fome Sorts Vegetables and Animals which could not grow or live lo well any where elfe. But from the whole, we may fee of what Advantage thefe un- . T 4 fightiy ft I #IP tmmim»mm ^ghtly Moles (as fome thought them) are po the Accomnaodations and even Necefli- ties of Living. § XXX. Next come our Fluids to be ponfider^d, without which we could never have been, feeing they are a very effential prt of us.: That which I (hall principally tal^e Notice of, is, ift, The fewnefs qf the pri^inal and primary Fluids, in refped of that vaft Number of compounded ones, which are, indeed, numberlefs. The pri- mary ones hitherto certainly known, are only fpur, vi^. Air^ Water ^ Mercury^ and lAght -, three of which are but feldom much compounded with others ^ fo that it |s Water alone, or Lymph^ that is the Bajls of all our Mixtures j arid it is the Parts of folid Bodies floating in this Fluid, that produces all our delightful and ufeful Varieties of Liquors ^ fo frugal is Nature in Principles, and fo fruitful and various in Effed and Compofitions. 2dly, The great Difference between the fpecifick Gravities of our Fluids, Mercury being about eight Tlioufand Times heavier than Air. Now, iK>t to mention the many Ufes of this laft Fluid in Artificers Works, had Air been as heavy as Mercury^ it had. been altoge- ther ufelefs in Refpiration 5 on the con- trary, it had choak'd us immediately- and md there not been a Fluid of the fame Weight with Mercury, i. e. a Colleftiofi of 2 exceeding ^T of ^t^%im* ^m 2E1 iwtnf exceeding fmall, vaftly heavy Spherules^ in the prefent Circumftances of Mankind^ I do not know what a great Part of the World would have done. For the Lewd- nefs and Debauchery of Mankind, has brought a great many Difeafes to that De^ gree of Malignity, that I fcarce fee how a thorough Cure could be made of them, without this Fluid , for it is certain, when^ ever any Diftemper arifes from an Ol> ftruftion of the Blood- Veffels, wherein the Blood and its VelTels are chiefly concern'^ (for in Nervous Cafes, I am fatisfy'd it i$ pernicious, in great Quantities efpecially) that this Fluid, if not abfolutely necelfary, is extremely beneficial ^ for nothing has fufficient Force to take away this Obftufti- on, and to feparate the Globules from onQ another, in the extreme capillary VefTels, but a little weighty Sphere^ fuch as the Particles of Mercury certainly are. Now, by this Difference of the Spectfick Gravity of the Fluids, a Remedy is provided for all thefe Maladies, which I am fatisfy'd are more than two or three. But that which is mod wonderful in thefe Fluids is, gdly. The univerfal Condition of the Diredion of their ?re(fure upon the Sides of the coa* taining VefTel •, for in all Fluids of what- foever Kind or Nature, this ?reffure is com- municated in Lines perpendicular to the Sides of the containing VeffcL Now, this Property v :) '4 .«4 Property of Fluids, which is fo beautiful and uniform, is the neceffary Confequencc of the Spherieity of their conftituent Par- ticles i for fince, by the third Law of Na- ture,- ReaSion or Repulje is always equal and contrary to ImpuHe or Ajftion, in the fame Direftion, confequently the Sides of the containing VeflTel prelTes the contained Fluid, as much as the contained Fluid pref- fes the Sides of the containing VefTel ^ and this Prejfure of the Sides of the containing Vcflel, is direfted in the fame Right Line with that of the contained Fluid, but is contrary to it. Now, feeing a R^^ht Plane can only touch a Sphere in a Point, and can prefs it in a Direftion thro* that Point of Contaft; if this Direftion thro' the Point of ContaS, do not likewife pafs thro' the Center of the Sphere^ the Sphere will necelTarily revolve upon a Plane^ 'till the Direftion of its prejfure from the Point of CmtaBf pafs through the Center of the iSphere\ juft fo likewife, if a Plane prefs two Spheres in the fame Diredion, the Line of this Direftion will necefTarily pafs thro* both their Centers. And fo if there be any Number oi Spheres whatever, prefs'd by a Plane in the fame Diredion, the Line of this Direiftion will neceffarily pafs thro* all their Centers. But a Line thro* the Center of a Sphere from the Point of Con- tad, is perpendiadar to the Tangent Plane ^ and m* Of Beltgtotu 283 and fince this is the Diredion of the pref- pure of the Plane upon the Spheres^ it is alfo the Diredion of the prejfure of the Spheres upon the Plane. Since alfo the Particles of Fluids are Spherical^ or nearly approach- ing thereto, and fince they are fuppos'd exceeding fmall, as alfo fince curve Surfa- ces are compounded of an infinite Num- ber of little plain Surfaces ^ it is univer- fally true, that all Fluids, of what Nature foever, prefs the Sides of the containing; Veifels, in a Direftion perpendicular thereto. And on the other Hand, fince by Experience it is found true, that Fluids do prefs the Sides of the containing Veffels, in a Di- reftion perpendicular thereto ; *tis certain that the Particles of all Fluids zxt Spherical^ or nearly approaching thereto •, fo that this is now no more Hypothejis^ but Demon- Jlration. Now, could any Thing but the Fingers and Almighty Power of God, have rounded thofe infinite Numbers of fmall Particles, whereof Fluids confifl: ? Or could any Thing but his Wifdom^ have affign*d them their true Dimenfions, their exaft Wpights, apd required Solidities? We (hall 3II0W him to continue in his Infidelity^ who can demonfirate by what Laws of Mechanifm all the Particles of Water were turn*d of the fame Diameter ^ Solidity, and Weight i and thofe of Air, Mercury^ an4 l^ij^hty turn*d all of different Diameters^ So- lidities, \\ ^S«r -v;^-^ i%4 0Ditotoptiical |^?tnct pie]9( liditiqs, and Weij^hts from one another -, fj^t all of the fame Diameters^ Solidities, »nd Weights among themfelves. 5 XXXI. What a noble Reprefentatlon of the Divine Wifdom does our Fluid of light aflFord us ! How wonderfully are its Parts framM ! And with what a prodigious Velocity are they fent from the Body of the §un ! Its Subtilty is almoft beyond Imagi- nation, no Pore fo fmall as to exclude it 5^ no Stream of it fo great, but may be con- gregated almoft into a fingle Point ^ no Sur- ftce fo finely polifh*d, as not to fcatter al- moft one Half of it •, its Rays traverfe thro' qm another. Millions of different Ways, without iaterfering ev*n in the ftraiteft Paf- fages : In a Word, we are not able to com- ?>tehend nor imagine a Number fufficiently mall, to cxprefs its Subtility j in every Pulfe of an Artery^ it runs fome hundred md thirty Thotifand Miles ^ what an ama- aing and unconceivable Velocity muft this be ! nothing but the Aftion of the Mind, c?in any ways reprefent it : And then, what a beautiful Idea of this Fluid, do Sir Ifaac ^fkwfans later Difcoveries prefent us with ; every Ray is endowM with its own Colour^ 9nd its different Degree of Refrangikility and tieftexibility. One Ray is Violet^ ano- Aer Indiga^ a third Blue^ a fourth Green^ a ifth Tell0i»^ a fixth Orange^ and the laft Jtci/« And thefe are the primary and origi- nal .Km II * it! of meitoion. nal Coloursy and from the Mixture of the(fe, ail the intermediate ones proceed, and White from an equable Mixture of the whole i Black, on the contrary, from the fmall Qiiantity of any of them being refleaed i oT, all of them in a great Meafure being fufFocated. So that now it is not Bodies that are colour'd, but the Liiht that falls upon them j and their Colours arife from their Aptitude, to refleft Rays of one Cd- lour, and tranfmit all thofe of another. Their prominent little Parts, upon their Surfaces, according to their different De- grees of Denjity and Thhinefs, are apt to re- fleA back upon our Organs^ Rays of one Colour, and of one Degree of Refrangibihr ty and Keflexibility, and to let others pats through their Pores ^ and this one Colour too, is lefs or more intenfe, according as their prominent Parts are of different Ven- fates, or are thicker or thinner. For the firfl Degrees of Intenfenefs, in all the pri- maty Colours, feem to arife from fome de- termined Degrees of Denjtty and Thimefs v and the fubfequent Degrees, from the other different Degrees of Denfity, or Thicknefs, or Thinnefs, of the prominent little Parts of the Surfaces of Bodies. Light afts upon Bodies, by heating, diflblving, and putting their Parts in a vibrating Motion ; as alfo. Bodies aft upon Light, in drawing its Parts to them, and that irt Lines perpendicular to thei< i If f A 'J ■ 2U l&ftilpfopDicai 0?incipleg their Surfaces. All the differently reflexibk Lights obferves this one Law, That all the different Jngles of Incidences are refpeftive- lir equal to the Jngles of Reflexion , and all the differently Refrangible Rays of Light, obferve one Law likewife, viz. That in all the Obliquities of the fame Ray, to the Plane of Incidence^ the Sines of the Jngles of h- ddence^ are to the Sines of the Jngles of RefraSian in a conftant Ratio ^ and both thcfe Properties proceed from one and the fame Principle, ading in different Circura- ftances, viz. that Bodies attraft Light in Lines perpendicular to their Surfaces j and that this Attradion is equal in all the Inci- dences and Refra8ions at equal Diflances from the fame Vlane^ and the reflei^ed R^ys are turnM back before they arrive at the refle3ing Plane : For if the refleSling Plane have luch a Force of JttraHion^ that be- fore the Ray arrives at it, it has already made the Sine of the Jnile of Incidence equal to the Radius^ the Ray muft refleft, and not enter into the refiefting Plane at all ; if a leifer Degree of JttraSion^ then muft it enter the Body of the Plane, and proceed in the Line, that its direft impulfe^ together with the Degree of Jttra8ion in the vefraBing Body, neceflarily generates. And as there may be different Degrees of JttraUion in Bodies, which produce their different Degrees of ElaflicHy and Cohejion, fo of Ileltsion^ z87 fo there muft be different Degrees of Jt- traSton in Mediums fuppofed, to account foe their different Porvers, in bringing the re- frabed Rays nearer to, or farther from, the Perpendicular •, for it is well known, all Medium have not the fame refraHive Vir- tue. Now, what a beautiful, uniform, and fill] pie Theory of Light is here ! This is fo very like the fruq^al Simplicity, and yet the mini fold Variety of Nature, that one would be almoft tempted to believe it true, were there no Demonflration and Experiment to confirm the Truth of it. I might likewife fhew here the Art and Contrivance of Na- ture in the Produftion of the Cohefion of Bodies. But having been pretty copious on this Subjeft already, I ftiall only fuggeft one very remarkable Inftance of the won- derful Contrivance and Wifdom of Nature, in the Propagation of Light^ viz. That a Ray of Light, in pafling from a luminous Point, through two differently refraining Mediums, to illuminate a given Point, fpends the leattTime (the refrading Powers of the feveral Mediums conliderM) poflible; and confequently, when a Ray paffes but through one and the fame Medium, i.e. when a Ray paffes from a luminous Point, to reficd upon a given Point, it takes the Ihorteft Way poflible. This the Geometers have demonftrated, and particularly, Mr. Hugens in his Treatife of Light, very ele- gantly Tsrc ■adai idO^ 88 ^l^iMtip^itai ^ntipUS tantly Page 46 and ^t. Now I appeal to tne Reader, how increJutous foever, if this be not ati Inftance of Counfel and Defi^n ? Is not this like the Methods of Fruderue and Wifdom^ which will not fpeftd liiorc Time on a Thing, than juft what i^ riecef- fary to do the Bufinefs •, which will not go about, but take the fliorteft Courfe poifible, that will bring it to the Place defign'd ? He that can refift fuch pregnant and power- ful Inftances of Divine Wifdom, will never be convinc'd. J XXXII. I (hould next proceed to fliev^ the Wonders in the Bowels oi cur Earth -^ but there our Difcoveries ate fo few, and 6ur Accounts of this Matter fo lame, that little to be reckoned certain, can be deter- mine about thefe Inner Regions. Some have concluded that there muft of Necefli- ty be a Central Heat, becaufe they hw that Springs run fafter in Froft and Snow, than in hot Weather •, but that might proceed from fome of the other more narrow out- lets of this Bafons being ftoppM by the Froft i and the Vapours that the Sun raifes thence, being kept in. Others have thought, 'that within this outer Cruft of Earth, there muft be a pifcontinuhy^ for fome^ con- fiderable Diftance, quite round j and that there was fucceeding this, a large Sphere^ moving after a certain Manner, to account for the Variation of the Magnet ^ what Truth •..-.• ,1 288 f^^itofop^icai I^Mncipleg §antly P/t^^ 40 and d^i. Now I appeal to be Reader, how incredittous foever, if this lie not an Inftance of Counfel and Dejizn .«? Is not this like the Methods of Prudence and Wifdom^ which will not fpeftd more Time on a Thing, than juft what is tlecef- fary to do the Bufinefs , which will not go about, but take the (horteft Courfe poifible, that will bring it to the Phce defign'd ? He that can refift fuch pregnant and power- ful Inftances of Divine Wifdom, will never be convinced. 5 XXXII. I fhould next proceed to flie\^ the Wonders in the Bowels of cur Earth \ but there our Difcoveries are fo few, and our Accounts of this Matter fo lame, that little to be reckoned certain, can be deter- mined about thefe Inner Regions^ Some have concluded that there mufl: of Necefli- ty be a Central Heat, becaufe they faw that Springs run fafter in Froft and Snaw, than in hot Weather -, but that might proceed from fome of the other more narrow out- lets of this Bafons being ftoppM by the Froft ^ and the Vapours that the Sun raifes thence, being kept in. Others have thought, "that within this outer Cruft of Earth, there muft be a Dif continuity^ for fome^ con- fiderable Diftance, quite round j and that there was fucceeding this, a large Sphere^ moving after a certain Manner, to account for the Variation of the Magnet j what Tfuth Of lEUltgiom t >iirf zgjr Truth may be in that, we muft leave td Time and future Obfervations to determinCf But the Magnet in itfelf is a beautiful In- ftance of the Power and Contj;ivance of thd Author of Nature, of the Reality o( Jttrac tion in general in Bodies, and that different from their Gravities, and of their impercep- tible Influences upoii one another. For xh\i wonderful FoJJil not only attrafts and repels Iron^ and all Chalibeat Compounds, and all other Minerals of the fame Nature with it felf, according to their different Situations in refpeft of its Poles :. But when Iron ii duly impregnated with the Virtues it com- municates, and properly managed, its Ex- tremities at fometimes points diredly North and Souths and thence varies both in the fame and in different Places of the Globe^ in regular and uniform Figures, towards Baft and Wejl^ according to the Syjlem oi thefe Variations difcover'd by the Leartied and Ingenious Dr. Halley. And very proba- bly, as the common Horizontal Needle iS continually varying towards Eafl and WeJ}^ fo the dipping or inclining Needle is vary* ing up and down, towards or fromwards the Zenith, according to the Sufpicions oi the Learned and Reverend Mr. Derham, anci poflibly in a regular and uniform Syjiem j and there may be other beautiful and re- gular Qualities not )^et difcover'd in it, all thcfc menuon'd being fpund out withiii U left tr < i") l^'V lefs than 5€0 Years. There is a Ring about S^turn^ whith moves differently from his Body, that fon^ewhat favours this Suppo- fitipn of Interior Orbs y bat I cannot come into the Opinioft, that this Annulns maybe fbme Remains of the Ruins of a Cruft that's fallen in upon the Body of the Planet 5 be- caufe this Ring appears to be regular and uniform, of an equal Breadth quite round, and at an equal Diftance from the Body of the Planet: Befides, it is fcarcely probable, ttiat thefe Planets, which, like ours, may be defign'd for the Habitation of fome Sort of Jnmals^ Ihould be fo ruinous as this Suppofition would make that Planet to be. tf it be true, that all the Bodies of thp Uni- verfe attraS one another -^ and if it be very fcrobable, from the Benefits of our Moon to the Earth, that fuch like and analogical Advantages, of raifing Tides in the Fluids, reflefting Light in the Night Seafons, and emitting other Influences for Life and Ve- getation, accrue to the Planets from their SatetlHes and other Appendages -, then *tis very plain, that whenever a lefler Body (however figur'd) attends the Motions or, and revolves with, a greater, that lefter Body is defign'd by its Attra3hn and In- fluences fo procJuce fome EfFeft, that is the Confequencc of this AttraSion, and thefe Influences. Thus it is plain, out Moon was 4efign'd*l6 faife our T/^^, and regular "Wind?, of Ileliston. 291 Winds, to enlighten our Nights, arid to difturb the Motions of our Earth, forPur- pofes that poflibly we may, or may never, come to difcover j and fo. the Satellites ox Jupiter and Saturn, were defign'd to attraft their Fluids, and to enlighten their Nights, or diforder the Motions of their refpeftive Planets, or to produce fome EfFeft (:onfer quent upon Attradion ; and I have fug- gefted before, that the Multitude of the Satellites of thefe Panets, may ferve in their vaft Diflance from the Sun, to hinder their Fluids (by frequent and various Diflurban- ces) from freezing ; and to enlighten their long and tedious Nights ^ and the greater Number of the Satellites of Saturn than Ju- piter, feems to favour this Conjefture. Now this Annulus may poflTibly ferve fome fuch Purpofe as this, fince it moves differently from the Body it felf. But all tbefe^a^re but Conjedures •, and as fuch I leave 'em/ It is probable, that Earthquakes and Vulca- noes proceed from fome Motion arid Mix- ture of different Particles within the Body of the Earth ^ for as to a Central Globe of tilt, it is not eafiiy to be conceived how it can fubfift without Air or Fuel, or without confuming the contiguous Parts pf the Globe -, and if it had either Air or Fuel, it mufl make a greater Havock than any Hi* ftory mentions. . Befides that, it cannot well confift with thefe raeritrori'd interior V H Orbi^ \\ \A mmm ■■i ii ■I ■ -mmiUSm :,»! '} 4 2 9 r l&ftilof opl)itai ^^mtipleai Or^x, without confounding their regular Motions : All the Appearances of Nature, which feem to require it, may be more m- turallj' folved by the Fermentation of diffe- rent Steartis arid Vapours, wjthin the Cavi- ty of the Earth. Thefe Vulcanoes, and fiery Eruptions, never happen but where Sulphur and Iron are copioufly found, which i^e are certain may produce Heat afid Flamed, when duly mix'd and ferment- ed, any where : And it's obfervable, that there are fcarcely any Countries much an- noy'd with Earthquakes, that have not 6fie of thtkjierj Vents ^ which (hows, that thefe Vnlcanoes are the necelFjry Confe- quences, and the Tunnels of the fermenting Vapours in the Bowels of the Earthy and not Chimneys to the Central Heat : AnJ this, by the Way, is a bountiful Contri- vance in Nature, to lelFen and evapofate thefe tumultuous Steams, which otherwife might make much greater Havock thafl now they do. Earthquakes and Vulcanoes in the Earth, being the fame that Thunder and Lightning are in the Air, and from the fame Caufes : It is likewife probable, that its Strata are not of fuch Gravities, as a regular Subfidence according to the Laws of Gravitation of Bodies would re- quire i which fhews, it has not been com- pounded by thefe Laws. It is certain, that wc have frefh Water at any confidcraWe Depth, of Sleltgton 93 Depth, in moft Places diftant from the Sea-^ which (hows how uniformly and equally this fo abfolutely neceffary Fluid has been diftributed for the Benefit of the Inhabi- tants of this Globe -, we have from its Bowels, all thofe Metals and Minerals, witH all their Varieties, which are of fo much Ufe for the Accommodations of Life, and the Subfervience of Medicine •, from the Depth of the Sea, and the Borx>els of the Earth, we have ail our natural Salts, which do us fo great and manifold Services. If any one had but Occafion to look over the Variety of beautiful Figures, and Colours oi Shells, Petri faHions, Ores, Minerals, and Stones, and other" natural Curiofities, (of which, the nobleft and largeft Colledion poflibly now extant, is to be feen in the Poffeflion of the Induftrious and Learned dr. Sloane) he could not but admire the manifold Wifdom of the Author of Nature. This were a very large and copious Field, and would afford very demonjlrattve Inftan- ces of Counfel and Contrivance. But I have- fo many other Things to fuggeft on the Head I am about, th^t I mqft cpnt?nt my felf with Generals^ 1 U3 CHAP. it^ »» ^rx^^WW^^^^^ ^94 )^Dao(opMcal i^^tncipiesi of Beligibtt 295 G H A p. VL The Proofs for the Being of ■ a God, arifing from the Contemplation of the Hu- mane StruBure. S XXXIII.r TAving dwelt fo long upon I. JL the inanimate Part of this Syflem of Things, I come now to confidcr the Animal Kingdom ^ that noble and ma- nifeji Reprefentation of the Power and Wif- 4om of the Juthor of Mature, One of De- tnocritus or Des Cartes'5 Difciples, may pet- haps undertake to give fome faint and ira- perfed Kind of Explication of the Cekjiial Appearances, froni their Principles, though how wretched their Accounts of this Mat- ter are, we have in fome Meafure al- ready ftiewn. But when they come to a plant, or Animal, they are perfedly at a Lofs, they can produce nothing coherent, or of a Piece •, their Schemes then, are like the EfFeds of the cafual Concourfe of Atoms, an odd inconfiftent Mixture of Thiiigs, that has neither Form, nor Beauty. For every part of thefe, is fo exadly adapted to fome ^ ' . ' wife wife Defign ^ ev'ry thing is fo fitted, to its own proper Ufe j and thefe Ufes are fo ina- nifeft and evident, that they clearly argue an infinite Wifdom, an cxaft and exqu^fite Knowledge in the Laws of a Divine Geo- metry and Htfrwtfw^infinitely fuperior toour low Figures and Numbers, that nothing is fufficient for, but a Being abfolutely per- feS. I (hall here, as I did in the Cleftial nilofophy, give fome general Scheme of the Animal Fabrick, and CEconomy^ and (hall confine my Speculations, to the Hu- mnt Stru3ure, as being the moft perfeft we are acquainted with, and which being fully underftood, the reft will eafily fol- low. I Ihall begin with the Procefs of the Aliment and the Circulation of the Blood. , . /I j- fi XXXIV. The Meat being grotty di- vided by the Teeth, and foftned by the Saliva, is through the Gulkt, by the Con- ftriaion of its Fibres, thruft into the Sto- mach i where being fwell'd and farther foft- ned by the Succus of its Glands, and the Liquors taken in, by the perpetual Motion of the Coats of the Stomach agamlt one another, the MufcUs of theifcfi^n/and^*- domen employ'd in Refpiration, and poflibly from other Caufes, never to be known, its Parts arc broken, and their intimate LohC' fions diffolv'd. And by this Prejfure of the Sides of x\i/f/ Explication of the Separa- tion of one Liquor from another in an Ammal Body: All I have hitherto feen on the Head, being either too general of too precarious i But fomething like thefc three Conditions, (eeras to enter into this Difquifition ; ift. The different Diameter of the Orifice of thefe Secretory Dufts, where- by Particles of a Diameter^ greater than that of this Dud, are excluded, adly. The dif- ferent Angle^ which this Duft makes, with the Trunk of the Artery:, for it is already demonftrated, that all Fluids prefs the Sides of the containing Veffel, and that in aDireftion/>^r/>^^/i^fi//7rto thefe Sides j and thi^ is evident in the Pulfafwn of the Jr- Urks^ fince it is to that Prejfure, this Pul- pftm is owing. It is likewife evident that the Blood is urg*d forward by the Force of the Heart, fo that the Motion of &- imkn muft be compounded of both thefe Motions* Now tho' this lateral prejfure^ is gie^ter, when the Veheity of the longitudi- ml Motion k Co, yet it is not in the Pro- portion of l^elisiottt 301 portion of this Felocity ^ for this preffure « always fomewhat even,, when the Fluid id at reft, and is then in Proportion to the Spd'^ cifick Gravity of the Fluid, nothing elfe being in this Fluid to produce thhprejfure^ atid in a Fluid urg*d by a Longitudinal Dl* teftion, as the Blood in the Arteries^ this lateral prejpure^ is in a compound Propo- lion of both , whence it is evident, that if two Particles of equal Diameters^ but Of unequal jf^mjf^'i Gravities, arrive with the fame Velocity, at an Orifice capable of ad- mitting either of them, yet they will not both pafs, becaufe their Motion of DireSion is different : So that this Diverfity in the Angles thefe Secretory Duds make with the Trunk of the Artery, feems altogether lie* ceffary to account for the poffible Diver- fities of fecern'd Fluids, even admitting that Diameters^ and Figures, to be the faine# For it is not to be doubted, that the Blood is d.'^Heterogeneous Fluid, and contains Parts of different Specifick Gravities, different Cohefions, and of different Denfities \ and the feparated Fluid muft be nearly Honto-' meoiis to perform the uniform Functions of Life. 3dly, The different Velocities, with which the Blood arrives at the Orifices of thefe Secretory BttBs \ for fince the Secretions are made in Form of a Fluid, there is no poffible Reafon can be afiign'd, why fome Animals of the fame Specie? ate of a foft, looic 3ot |&||itofopl)tfal l^?tncipics loofe Texture, and Union of folid Parts and why one Part of the Body is of 3 tender loofe, eafily feparablc Texture ^ othersof an harder, firmer, and more clofe Cohcfion, but this different Velocity of the Blood, at the Orifices of the feparatory Duds- And though the Diverfity of the Diameters of thefe Duds, is certainly that which is of greater Moment in this Affair of Secretion-y yet it is impolTibJe to account for the Similaritj of the fecerned fluids from fo Heterogeneous a Fluid, as the Blood is, from this alone. For fuppofe, (as my worthy and learned Friend Dr. Cockburn has very juftly reafoned) the Diameters of the Particles of Urtn^ Gall and Semen, to be as I, 2, 3. The Diameters of the Secre- eretory Dufts,of the Kidneys^ Liver^ and Tefli- cfej, muftbe in the fame Proportions. Now tho'upon this Suppofition of only different Diameters^ the Particles of Gall and Semen cannot be feparated in the 'Kidneys^ yet the Particles oi Urine and Gall may be fe- parated by the Excretory Duds of the Tejli- eles'y the Diameters of the Particles of the Fluids, being by Suppofition, lefs than that of the Diameter of the Excretory Dufts of' the Tefticles. So that upon this Suppofi- tion of only difFerentDi^a#«^f^rj,it is impomble to account, for the Homogenity or Simitari- ty of the y^^r^rw^rf Liquors : For all the Par- ticles, of whatever Kind, that are lefs than th€ »»m Of meligion 303 the Diameter of the Secretory Duft, muft be indifferently feparated there, l^utri- tton may be perform'd by a Secretory Duct, arifing from the terminating Artery, which carries a fuitable Portion of the Blood to every Part to be nourifh'd, fo that every Point in the Body, muft be the Termina- tion of a Secretory Duft, through which a proper Part of the Blood is brought. The Blood in its Circulation, being carry*d mto the Cavity of the Skull^ in the Branches of Carotid and Cervical Arteries, thefe are di- vided into innumerable Ramifications, io as to become extremely fmall : Their laft Extremities after the Manner now de- fcrib'd, form a little Gland (all thefe little Glands together make the Cortical Part of the Brain) terminating in two little Veffels, one for carrying back as a Vein, the grojTet Part of the Blood ^ another as an Emijffary Veffel to each of thefe Glands, diftributing throughout the whole Syjlem, the more pure, refin'd, and fubtile Part of the Blood, (as is fuppos'd) which is then call d the Anintal Spirits. All thefe little Emiffaries^ united together at their Origin (the Cortical Part of the Brain) make that Subftance, which is caird the Medullar Part •, being a Bundle of very fmall, thread-like Chanels, or Fibres, forae of which are carry 'd thro their propef Cavities, in the Skull, for the Ufe of the Onans of Senfation j the reft through • f, !04 )$f)ilofQpl)tcal ^tintivlts <^ • . ■ -III •> ■ ■ ■ . ._._ _ tlirough the Cavity of the Spine^ to be Ijftribdted at proper Places, through the fgft of the S^ftem. h is not impoflible but tliefe 'Emijfary VcfTels of the fmall Glands^ i^htttof tht Cortical Part of the Brain cgnfifts, may contaia a Liquor, and that this Liquor may be the more refin'd, and Ipbtile Part of the Blood , efpecially if 'are refled that Nature does nothing in fain, and that thefe Glands differing fcarce- ly at all from thofe others, which we certainly know feparate proper Liquors, but in the Length of their Emijfary Vef- fels (the Neceflity of which in the pre- fent Cafe is felf-evident)and that the Blood- Veffels, being fent in fuch Numbers in- to the Brain, and in a much greater Pro- portion, than to any other Part of like Pinienfion, and being there formM into the mentioned Glands ^ and thefe Glands fending out thefe fmall Emtjfary Veffels, §vcr the whole Sy^em. It is not impofli- |)le I fay, that thefe may carry a fuitablc i^kuor. For ift, alraoft the whole Mafs sf piood, in a little Time is brought to this Cortical Part of the Brain : (The mod fujbtile, moft fpirituous, lighted, and moft Oioyeable Part of the Blood, afcending jby the Carotid and Cervical Arteries \ the iroffer, heavier and leaft aftive, defcending toward the lower Parts, by Reafon of tfj§ Sifuation ^ jnd the ^vtm^ fpecifck Gra- vity of saeltgtott 305 vity of thefe laft Parts of the Blood. ^ Qdly, In the Medullar Part of the Brain is often found on DilTedion, a thin, whey- like Subftance, which Fire hardly thickens* gdly, The Nerves are equally diftributed all over the Body, are abfolutely neceflary toward all Motion, natural and voluntary, and 4thly, They are the Specifick Organf] of Senfibility. All which feem to impjy, that they are the containing Chanels of fome Liquor ^ and then poflibly this Li-. quor may be fomething a-kin, or analo- gous to thok Spirits we gather from ani-, mal Subftances, by Heat in an Alemhick :. Such as are Spirits of Sal Armoniack^ Hartf- horn^ Raw Silk^ or Humane Skulls ^ and what renders this Conjefture more proba-« ble, is the not altogether diflimilar Ap- paratus in forming thefe animal Spirits in the Brain, from that of drawing thofe others in an Alemhick by Fire ^ and the wonderful prefent Efficacy thefe laft have on the firft , and that both ^ are equally unalterable by Heat, and incapable of Burning/ But then, if we confider on the other Hand, that thefe nervous B^ bres ferve equally, and adminifter unta Nutrition, local Motion, and Senfatioi^ j this laft Funftion feenis ^fltirely oppofit^ to the Nature of a Fluid, neceiiarily aflt^ ing in the', other two Funftions, fron^ within to without, and in thisf iaft^ fron^ X withouj J-O-I 504 i^lftiiofopl^tcal )^;tincipleiS of iaeligiom 305 through the Cavity of the Spine^ to be ^jftributed at proper Places, through the fgft of tht Syftem. It is not impoflible but tbefe Smijfarj VcfTels of the fmail Glands, whereof the Cortical Part of the Brain cgnfifts, may contain a Liqupr, and that this Liquor may be the more refin'd, and fubtile Part of the Blood ^ efpecially if we reiieft that Nature does nothing in vaiij, and that thefe Glands differing fcarce- ly at all from thofe others, which we certainly know feparate proper Liquors, but in the Length of their Emijfary Vef- fels (the Neceflity of which in the pre- fent Cafe is felf-evident)and that the Blood- Veffels, being fent in fuch Numbers in- tQ the Brain, and in a much greater Pro- lortion, than to any other Part of like fimenfion, and being there form'd into the meiitionM Glands^ and thefe Glands fending out thefe fmall Emijfarj Veffels, §Vpr th€ whole Syftetn. It is not impofli- Ible I fay, that tbefe may carry a fuitablc l^iguor. For ift, alraoft the whole Mafs ©f Blood, in a little Time is brought to this Cortical Part of the Brain : (The mod jTubtile, raoft fpirituous, lighted, and moft nioyeable Part pf the Blood, afcending by the Carotid and Cervical Arteries j the groflfer, heavier and leaft aftive, defcending fQWard the lower Parts, by Reafon of tb§ SiWatjipn j jnd th5 ^tcnct fpecifck Gra- vity vity of thefe kft Parts of the Blood. ^ Qdly, In the Medullar Part of the Brain is often found on DiflTeftion, a thin, whey- like Subftance, which Fire hardly thickens^ ^dly, The Nerves are equally diftributed^ all over the Body, are abfolutely neceflary toward all Motion, natural and voluntary, and 4thly, They are the Specifick Organfi of Senfibility. All which feem to irapjy, that they are the containing. Chanels of fome Liquor ^ and then poflibly this Li-. quor may be fomething a-kin, or analp^ l^r/j to thofe Spirits we gather from ani- mal Subftances, by Heat in an Jkmhick :. Such as are Spirits of Sal Armoniack^ Hartf" hoTHy Raw Silk, or Humane Skulls ^ and what renders this Conjefture more proba-^ Me, is the not altogether diflimilar Jp^ paratus in forming thefe animal Spirits ivk the Brain, from that of drawing thofe others in an Alembick by Fire ^ and the wonderful prefent Efficacy thefe laft have on the firft ^ and that both ^ are equally unalterable by Heat, and incapable ot Burning. But then, if we confider pn the other ]Hand, that thefe nervous J^^'^ hres f^rve equally, and adminifter^^umcf Nutrition, local Motion, and Senfatjofj j this laft Funftion feems ^fttirely oppofitQ to the Nature of a Fluid, lieceffarily aft^ in^ in ihe,\pther two F!i?ftions, fron:| within tQ 'without, and in thi^ laft, froiq X vi^ithouj t without to within. Add t6 this, that this licrvous Fluid has never been difcoverM ii live Animals by the Senfes, however afj&fted •, nor its Neceffity evided by any cogent Experiment ; and that Leuven- Mfeck's Experiments make the Fibres, or die laft Chanels of this Fluid, fo infinite- ly flender, fmall, and fpungy, that confi- defring the Refiftances from the Sides of AeVeffel in fmall Tubes, it feems abfo- lutely impoffible any Fluid (fuch as we IiaVe an Idea of) could move with Velo- city to anfwer the Appearances ; fo that after all, it feems pretty difficult to com« o any certain Conclufion on either Side. iik either the Fihes contain a pretty con- fiftent Fluid, whereof they are constantly fiill, and then the leaft Drop forced into Hie one Extremity, will drive out as much at the other, and that inftantaneoufly •, or thefe Fihes are folid, and not pervious ; and fome infinitely fubtle Spirit pervades them with as much Facility as it would iHe mod: pervious Tubes j either of which Suppofitions will account for the Ap- pearances in a grofs and general Manner, which is all we can pretend to in fuch cohjcftural Cafes. By the Motion of the Jffiwr^t, through the Bmulgent Branches, the Blood is brought to the Kidneys^ and is there freed of its &rii*f, by their little GUfidsp and is received into the fmall Be- itetorj onRrliffiom 307 t cretory DaSs of thefe Glands^ to be carr ry*d into the Pehhy and thence, by prc^ per Tukes, into the Bladder. Much after the fame Manner are their proper Fluids feparated from the Blood in the Liver^ Sweetbread^ Teftkles, and the other Cn- Mate and Co?i^lomerate Glands of the Body, fo that it is needlefs to infift on thefe. § XXXVI. The Lungs are composM of ati infinite Number of little Lohs^ of dif- ferent Figures and Magnitudes, but fo joined, as to leave but fmall Vacuities be- tweeen them. Each Lobe confifts of an Infinity of fmall fpherical or oval Veficles, form'd by the Coats of the fmall Branch- es of the Trachea -, fo that they may be confider*d (when blown up) as fo many fine Tubes^ ending in little hollow Spheres or Spheroids ^ upon the Sides of the Veft- clesy the Blood- VefTels in a fine Network are^fpread. Now, before the Fcetus is brought to Light, thefe Feficles lie flat upon one another, and by their Preffure upon the Blood-Veffels, hinder its Pro- grefs through them , but as foon as this Foetus enjoys the Benefit of the Air, by its Weight and elaftkk Force, this Air ruflies through the Pipes of the Trachea into thefe Feftcles, and blows them up, where- by they (land ered upon the Trunks of thefe little Wind-pipes, and give a free Paf- X 2 fage i So8 0DiiofopDicai ^^nnciples of ^elision 309 fage to the Blood through thefe VelFels, fpread upon their Sides. And when by the Weight of the Thorax, and the Adion of the Mufcles thereof, with thofe of the Abdomen and Midriff, this ebftick Fluid is thruft out of the Veftcles, through the Tra- chea in Expiration ; thefe Veficles preffing Sgainft one another, and the ela flick Fluid afting upon the Sides of them, and confe. quently on the Blood- Veflels fpread there- on, feparate the Globules of the Blood, which had Room and Liberty to unite in the wider Chanels of the Veins j and this Separation of thefe Globules of the Blood, from one to another, renders it more capa- ble to circulate in the more narrow Paffage* of the Capillary VeiTels, divides and fubtil- lizes the groffer Parts of the Chj/le, gives a Scarlet Colour, Fluidity, and Energy, to the grofs, grumous, and ftagnated Venous Blood. But, if I be not very much mifta- ken, there is ftill another Ufe of this natu- ral FunSion behind, and that is to form thefe elaftick Globules of which the Blood principally confifts. It is Matter of Fad and Obfervation, that the Blood confifts of a Lymph, which is the common Vehicle^ fe- veral Salts, Ramenta of a thick Confiftence, made up of fmall Particles of carneous and vegetable Fibres from the Food, (which is probably the unform'd Part of the Chyle and Aliment) arad thefe red Globules, of which which we are now fpeaking ^ but forae- tiines they are of different Colours, as White, Blue, and Furple ; . thefe any Body may difcover with an ordinary Mtcrofcope.. Now, it is certain, that thefe Globules may be burft, as in Obftruaions •, or may be allexhaufted, as in vioXtni Haemorrhages -^ and yet be all recover'd, and recruited azdn 1 wherefore it is of Neceflity, that thefe GlobuUs muft be form'd fomewhere in the Body from the Chyle, And fince it is certain that they are not folid ? articles both by ocular Infpeftion and Touch, and by the Neceflity they are under to chaiige their Figures into oblong Spheroids, xri the cmllary Veffels, as alfo from their Colour, and that Acids do aftually deftroy their I Figures, and coagulate thefe Globules^ it • is not improbable, they may be little bub- ' bles, blown from the vifcid Part ot the Chyle, by the Force of fome more fubtile tlallick Aura, Now no Place in the Body, but the Lungs, can fo conveniently attord this elaftick Fluid ; and this may be the Reafon why theCy^ enters into the Veins ; and thefe too only, which are jult re^ turning immediately to the Heart, to oe fent into the Lungs. For fince, in out grofs Element of Air, there is conftantly lodged a finer elapck Fluid, which is_the principal Agent in all the fubtil Effefts eommonly afcribed to the other, though X 3 *"^ i tmft 310 jajjilofopliical ^a^incipies the grofTer Element cannot, yet this finer Fluid, by that vaft Force ufed in Expira- tion, may be thruft in, through the Sides of thefe Veftcles, to the Blood- VeflTels j and feeing thefe Blood Globules muft be gene- rated foraewhere, and fince there is no Part in tke Body this fubtil elaftick Fluid can fo conveniently be fqueez'd with fufficient Force, to get through the Sides of the Blood-Veflels, bat in the Lungs j it feems not unlikely that thefe Globttles are forra'd there after this Manrier : The vifcous Part of the Chyle being by the ihorteft and fafeft Courfe poffible, brought into the returning P?rt of the Blood, is feat from the right rentricle of the Heart to the Lung*, and is fpread upon the Sides of the Veficlet thereof, in little fine Tubes, this fine ela- fiick Fluid being fqueez'd iti the Aft of Expiration, thro* a Pore, continu'd thro' the Vejicle of the Lungs, and the Side of the Blood- VefTels is forc'd into the vifcous f^Tt of the Ciyle, which is running by in the Setim, and by its perpendicular Pre(fure Bpon the Sides of that Cavity it forms, produces a fmall little Bubble of a certain Magnitude, and Thicknefs of Shell, from whence it hafe its Colour, and by the Force df.the fucceeding Fluid, this little Bubble IS broken olF from tbie Fore, and car^'d iXov^ the Artery, and the Cobefum of the f^rw pi fbe SlicJl cif this BubMe, being greater $f iUligfOtt^ 3'« greater than the Force from without, where- bv the thin Serum afts upon it, it is pre- ferv'd in its Figure in all the various Mo- tions of the compound Fluid of the Blood ; and if it happen that thefe little BubbUs (hould be burft, (as they moft certamly^are bv a Thoufand Caufes) whenever they come to the Lungs, they are new form d aeain, whereby the circulation \s fender d conftant and uniform. For (hould thefe Globules be all deftroy'd, ther^ muft of Neceffity arife a general Obftruftion in all the Capillary Arteries. The Manner of this Produftion of the little Bubbks m the Blood, hy tht elaftick Fluid fofcd through the Sides of the Vejicles^nd. Blood- Veffels in the Lungs, is fo obvious, that I ftiall infift no farlher upon it, fince every Body may fee an Inftance of the fame Nature, in mixing Oil with Vinegar 3 the Subftance of which Mixture, when view d but witl^ an ordinary Microfcope, appears to be no- hing but an /»^''A °f ^"^^^f J "he Bubbles, form'd by the Imtnf on of the Air and Vinegar into little Shells of Oil. Sit from thi! Principle, fome of the de- fpair'd-of Appearances in the Animal Ob^- '^r l*Jir?n7^"'R^"'''^u''?"*'? theEffefts thence mng. But n being both foreign to my Defign and unfit for the Limits I have prefcnbed to ray felf, to deduce Ccrollaries anhng from a Conjefture only : I fhaJl therefore proceed to reprefent fome others £/! »^ "^"""^^ ^"^^"^ ^^^ FmSions, in the beft Manner I am able. r ? ■^^^^^^- A ^H'^l^ is a bundle of Fe- fuular Threads, or of folid Filaments, in- S. r 'i? °"^ common Membrane, one of i(rhofe Extremities is faflen'd to an im- mt)veabJe, the other to a moveable Part of the Body i which by the Inflation of the ^^f/^x, or fwellmg and hardening of thefe pigments, are brought nearer one anotlrer. ahd fo become the proper Organs of Mo- tion. When ^Mufcle, by boyling. waft- ing, and cleaning, is duly prepar'd, the Texture of thefe veficular Threads, or fo- iid filaments, become more evident and Jerfpicuous. If the laft Fibres of Murdes be vejtcular, then probably they may not l?e unlike a ftring of hollow Beads; and may be originally hdllow Tubes, ftraitly ty d together by tranfverfe Filaments, fo as to form thefe little Bladders ; with which, [mall Branches of Blood- VefTels are fo in- terwoven, as that the Mouth of a little f/??'^ 'xy /^"""^^ g'P" ^"f° the Cavity of thefe F-eJlcles .- Both which, are fo ab- foiutely neceiTary to the Adion of a Muf- Of SleU0ioa ihjjjii|^ m cle, that either being ty'd or cut, at thd entry of it, no Adion or Motion can eh*. fue* , - If Mufcnlar Fibrils be Veficular, then weS may reafonably fuppofe, all the Carneous Fibres, which are neceflarily required for Motion, to be Vt^ficular, after the Manner I have now defcribed thera •, and that thft 'Nervous fibres^ are Cylindrical Tubes, for conveying the Nervous Juices. The twd Extremities of the Mufcle which are called Tendinous, were generally thought to be the Ends of the Carneous Fibres more clofely compared, fo as to admit but few Blood-Veflels, or nervous Chanels. But Mr. Leuvenhoeck, by his later Obfervations on them, feems to think them of a diffe- rent Subftance from, and to be difconti- nued with, the Belly^ or flefliy Part of the Mufcle. If the tnufcular Fibrils be Vefi- cular, (as I have faid) then the Ufe of their veficular Cells, may be for receiving the Arterial and Nervous Juices, that by their Aftion upon one another, they may be fweird fome how, fo as to (horten the Length of every Fibril, and confequently to bring the Extremities of the Mufcle near one another, which is the proper Aftion of the Mufcle. But whether the fwelling of the Veficles be owing to an Ex- plofion ^ to an inftantaneous Fermentation 9 to the greater AttraSion of the Nervous Fluid 114 !^PoCopDic$r^inc(pl0S! Fluid on the Blood Globules, than thofe have upon one another ; or to the mere mechanical Adion and Preffure of the Ner- vous Juice on the qrterial Blood already fillins the Vejicle. Or laftly, whether the Bhriis are not iq themfelves folid, (and not Tubular Filaments) contraded by a fubtil Spirit pervading their folid Parts, whofe Law and A^ion, is, or is never to bt determined, I will not take upon me to decide. But if I conjefture right, the Nature of LiTir, Lkht^ and animal Motion^ Wfii be an eternil Reproach to Mecha^ mip, and Humane Invention. The fu reft Method to arrive at any Certainty, in fuch intficate and obfcure Subjeds as fome of til^e Animal Fundions are, is to go no iiniier than Anatomy and Occular Infpefti- en will direft us ; and fince it is not as yet pofitively demonftrated whether the Miwud Spirits be a Fluid contain'd in the ^mtmus and Membranous Fibrils, as hol- low Tubes, or if they are only a ftikile Spirit or Aura pervading thefe, as folid Fi- laments, Nor whether the laft and fmall- fft Mofcular Fibres be veficular or not, I cannot fee fufficient Materials, to found any juft Explication of this Animal FunC'* tion upon. f XXXVIII, The Fluids of the Body lire principally propeil'd, by the Adion irf the Heart, and the eUftick Force of the Fihm «f XleUgtmu Hi fibres of the containing VelTels. Now the Heart is a Mufcle^ like other Mufclet^ confifting of feveral Orders of fleftiy Fibres^ of different Diredions 5 it has two little f,ars and as many Ventricles^ which are Cavities for receiving or holding the Blood, as it comes from the feveral Veffels, or is to be driven to different Places. The fibres of this Mufcle, ad as thofe of other Mufil^s may be fuppos'd to do, for by the winding and fpiral Diredion of its feveral Orders of Fibres, the Cavities of th^ Ears aiid Ventricles are leffenM or conftring'd. And it is obfervable that all the Mufcular fibres of the Coats of the Veffels, ad af* ter a different Manner from the Nervous or Membranous Coats, the firft feem to ^d by the Affiftance of fome foreign Fluid, Spirit^ or Principle. But the Membranous Coats, mceriy by their own Elaftici^^ being ftretch'd firft by external Violence. Thus the Sides of all Membranes are bent or prefsM outward by fome included Fluid, but reftore themfelves by their own na^ tural Elafticity •, whereas, whenever a Coat contifts of Fibres of whatever kind, eaD- cepting thofe for Sensation or tkitrition^ it is a fure Indication that this Coat ads as a Mufcle i for Nature does nothing in vain, and would never have dinftinguiftiM a Coat into Fibres, but for Mufcular Adion, when a continued Membr-anoiis^ or Tendinous one, J' /■ Cine, is more capable of afting by its own ^afticity. So that the Nature of the Coats, and of their conftituent Fibres of the Cha- nels, being known, together with the Range and Direftion of thefe Fibres^ it is eafy to know the Manner of their operating ttpon the included Fluid. The Coats of tlie Gullet are three ^ the outermoft Mem- ktanmis, the fecond flelhy and Mufcular, turning obliquely from the upperraoft End tf the CEfopbagus to the Stomach ^ the third is tendinous and mufcular, of white flender Fibres diverfely interwoven. The ^(i^machhdL% four Coats, the innermoft is Carpet-like, of white fliort tendinous fi- Iffjr ftanding perpendicular upon the next Caat, which isnervaus and extremely fen- fibk i the third is flefliy and Mufcular, of fttaight and circular Fibres-, the fourth, Membranous from the Peritonmm. The Quts confift of three Coats, the innermoft h of the fame Nature with that of the ianermoft of the Stomachy the fecond is ef two Orders of Mufcular Fibres, Lon- ^mdind and Spiral^ the third is common SQcl membranous, arifing likewife from the 9mion£um^ The Nerves, as I have be- fore faid, are a Bundle of fine, fmall,and flencier Pipes, or Threads, wherein the Animal Spirits, or fomething Analogous to what is caird by that Name, are trca- focM U|> for the Expeaccs of Motion and Senfa^ of laeligtoa 3>7 -•aa SenCation \ they arife from the Glands of the cinerhioits Part of the Brain, and aft terminated in all the Points of the Body % ten Pair defcend immediately through pro' per Holes of the Skill, and ferve the ad- iacent Parts, and particularly the Organi of four of the Senfes ^ the reft in a large Bundle, are let down by the Cavity 6t the Vertebra, and at fit Places are feftt forth to aftuate the feveral inferior Part* of the Body. The Arteries have three Coats, the outermoft is a fine Web of •Serves and Blood-Veffels, for the Nourijh- ment of thefe other Coats, and for thS Mufcular AH'ton of the intermediate one, which is made up of feveral /rtfttf of Sfi- ral Mufcular Fibres, according to the Bi|» nefs of the Artery. The third is a cldlfi tranfparent Membrane very ftrong and Coltt- paft, to keep in the Blood, which otheU- wife upon the Dilation of the Artery^ wou'd tear the Mufcular Fibres afundef. The Veins have the fame Coats with the Arteries, only the Mufcular Spiral Fibrei are thinner, becaufe of the leffer Force of the Blood againft the Sides of the di- verging Veins, than thofe ot the converg- ing Arteries. From this general Account of^he Strufture of the Veffels, their Aftions upon the inciofed Fluid may be eafily underftood, the ftioft ereded Fibres ferve for the Attrition of the Aliment, and tot . a ftraitninj; I ftraitning the Cavity of the Guts and Sto- m0cb ; the oUique Fibres^ which make but few Turns, ferve to propagate gently the included Fluid, the Longitudinal ones to move the Veffel, and the included Fluid, up or down in a Direftion parallel to its Length, by encreafing this Dimenfion, and thereby leffening the other, i. e. the tranf- verfe Diameter -, the Spiral ones by fquer z- ing it tranfverfely, and fo encreafing it in Length or leffening it in Breadth. Thus the Blood being pu(h*d by the Contradion i»f the Heart into the Arteries, diftends their Coats along their whole Length, 'till rise Force of the natural Elafticity of the Membranous Coat, be equal to the Forc^ rfthis Iinpulfe ^ then that Elaflicity of this Coat beginning to aft, at the fame Time tiic nervous Juice, or Spirit is derived thro* the Nerves by this Dilation of the fmall Jktiems^^ among the Originating Nerves in the Brain, and fo brings the Mufcular Fi- hes into Adion. And both thefe Forces lf*ing at once, propel the Blood in a continued Stream, through the uninter- OTpted Chanels of the Feins and Arteries. And the Irapulfe of the Heart, propaga- ted only by the Membranous Coat, is that Wbich when felt, is callM uljilfe or PmU fstion of the Artery, ^ XXXIX. All Senfation h perform *d by the immediate Aftion of the finer and motp fluid Of ^Higion^ v^ fluid Parts of Bodies, upon the Organs^of Senfe •, the Impulfe communicated by theft fubtile Parts of Bodies, upon the Organs fitly difposM, is through them tranfmitted to the Nerves, appropriated and contrived for fuch a Senfe, and through them, to the Brain. Thus in Vijlon, the Light re* fledcd from the Surfaces of Bodies, is tranf- mitted through the Humours of the Eye, and congregated upon the Retina^ in the fame Manner it was refledcd from the Body 5 and thereby an Impulfe, modify*d after a certain Manner, ftrikes the Fila* ments of the Optick Nerves, which convey this Impulfe to the Brain. In Hearing, the Sound after diverfe Modifications, in its Paflage through the Meatus ^ Aitditorius^ ftrikes on the Tympanum, which moving the Bones of the Barrel, and they the in- closed Air of the Labyrinth, the Auditory Verves there, are mov'd after the fame Manner they would have been, had the common Air aSed upon them, with the Advantage of a better qualifyM and gentler Impulfe than they could have had other* wife. In Smelling, Tajling, and Touching^ the Effluvia and more fubtile Parts of Ba- dJes, aft immediately upon the Nerves thc^^ felves, and they communicate this Aftion to the Brain: So that in fome Manner, «U Senfation is nothing but Touching, feveral Ways-di verflfy'd. Generation is nothing but Acretioup t Acr^ian^ for it is beyond all Doubt, that gll Generation is from a preceding little Jni- mal lodgM in the Male. I have demon- llrated the Mechanical Produdion of Ani- wals, to be impoflible and unconceivable- there is nothing in an Animal but an bififiil n of branching and winding Chanels, and their contain'd Fluids ^ and noDifpo- lition or Arrangement of either, can pro- duce an Animal, fince all the Parts muft be formed together, in order to make a gompleat Animalcul ^ for it is not in Ani- mals as in Houfes, or any other humane Performances, where the Parts can fubfift f^parately, and be fram'd one after ano- tlier, but towards an Animal, the whole integral Parts at leaft muft have been formed at once : Since we are very fenfible there is not one noble Part, that an Animal can |)e without, but with the immediate Dan- ger of the whole Compound. And to have the ^mwif/ com pleat and perfed in its Kind, there is not a fingle Veffel or Orian, how inconfiderable foever, that muft not have been compleatly form'd and fitted up, all and fundry, at one and the fame Inftant of Time.fince the Circulation of the Fluids, and the natural Fundions of the whole, do in p higher or lower Degree, depend on the In- tegrity and Perfedion of each fingle Part. We find fome little Bubbles^ or Blood Glo- ktiles^ may be form'd put of the Chjle in the of Belinton^ jii the Veffeis, and one kind of Liquor may be feparated from another, out of the Blood in the Glands^ and thefe are allthePro- duftions an Animal is capable of, which can- never reach to that wonderful Number, and Difpofition of Parts, an Animal eonfifts of. Now, fince there is no Neceffity to think God almighty is confin'd to a new Creation, in ev'ry Generation of an Animal^ and that thefe Animals themfelves are confpicuous in all male Seeds hitherto examined, it is plain that they muft have been all created at once^ and lodgM in the Loyns of the Ori- ginal Pairs of all the Species of Animals. Likewife the Fluids, if they did not move in the Channels oi thefe fmall Animals^ wou'd corrupt and deftroy tlieir containing Veffeis. It's evident then that they muft circulate after a Manner proper to them- felves ; tho' doubtlefs the Velocity of their Motions is perfedly accommodated to the finallnefs of their Bulk^ and the flendernefs of their folid Parts ; we fee an Image of this flow and low Kind of Life in Swallows^ In- feUs^Vipers^^nA other Reptiles m the Win- ter, and in almoft all younger Species oi K- nimals; and even in adult Animals of the ra- tional Kind, a nervous Diftemper has con- tinued them long alive, in a kind of a lethar- gick Drowfmefs without Food or Motion; and without the common Expences of Life; y But- jii |^!)he inanimate Produdtions of Na- ture, that a weak Eye may difcover the vaft vaft Difference. Wherefore of unavoidable Neceffity, he that formed the Eye mufthm- felffee, and he that made the Earmuflhm- Whear, and he that endued Man with Wdom muji himfelf mderftand- and he Sat contriv'd fo wonderfully and wrfely and forra'd fo juftly and exadly, all Thmgs both animate and inanimate, ipuft needs, ^'If /proceed to make fome Refleaions ution the particular Inftances of C.««/./ and Wifdom in the animal Fabrick. 6 XLI. The Skin with its Parps is what offers it felf firft ; the Scarf-shn being up- permoft, is compos'd of feveral Lays of fmal S/ which cover one another mo e or feff or' iS thicker., according as it is thicker n one Part of the Body than another ■ between thefe Scales the excretory Duds ot JhSry GW. of the true Skin open, tiJ^ reckons, that about one Cuticu- , Vr Scale 5O0 fuch Duas may lie,andtliat a Grain of Sand will cover =SO of thefe Kr^u, fo that one grain qf Sand w»ll cover Now what a prodigiPXis Numbei ot lua Glands muft there be on '^'^^^ ^^^^^l^^l whole Body I Intpev^ry ^^'^^f^^^lXL an ArtPrN Vein and Uerve do enter lotnai we mly-^gS how prodigious the Number d'OrlL/in an Animal Body muft be, from Y 3 * * 3^^ Wtofopfticai i^tinapies ^hcfe that are vifible to the Eye affifted with an ordinary Micro/cope. Thefe G/ands fe- cem the Sweat and infenfible Perfpiration. And of necefljty they muft be many, fmce SanBorius obferyes, that through them fifl teen Ounces weight of a Fluid paffes in 24 Hours. Next under the Scarf-skin are the Ta- pilla 'Pyramidalesyiniinitf: like wife in Num- ber ; they are the Extremities of the Nerves of the Siin, and ferve more immediately for the Senfe of Feelim, to convey the Impulfe received, along the Nerves to the Brain. A- bout thefe, the Nerves and other Veffels make a fine fFei>, all cover'd over with a mucous Subftance, to moiften the^tTaplU Tyrami- dales ; and then under this the mi/iarj Glands themfelves are plac'd^ protruding their /?- cretory Duds to the Surface of the Scarf- shn; upon which there are many parallel Lines, and, thefe interfefted by others, and in each Interfedion a Hair is planted. In the Summer the Skin is thinner and fofter, m Winter more compaft and hard, by rea- fon ot the Heat and Cold of thefe different Seafons. The Scales of which the Scarf-skin n compos d are defign'd to fence the Orifi. ces of thefecretory Duds of the miliary Glands,and to hinder Objefts from making too pamful andexquifite an Imprelfion on the Nerves and to skreen them from external In- juries J the Skin it felfis defign'd to wrap up the of 5acii5ton. ti;r^e Body, to fuftain a^d to keep the faPilUTyramidalesmthtnJhccs,andt,c Jiary Glands from being di^'-der-d, to ic ceive the Impreffions of ^xteri^l Ob^vfts, and to b: the Organ of the Senfe o^Touch ,„g and Feeling^ Now what can be more iaderfurty contrivM than this ex, ei im Pa^t^ Glands hid beea few and large, then tU Intervals had been without any ^f^J. Feeling, and fo might have be- ^^/-^ ^^ without our Knowledge, to tli-iJam,c the whole; and -thefe ^"^^^7^^^^^ '^^f,S been fi-eed from the ^^f °'^^'^^^^t . v tS are here thrown out. of tl^e Body by thele Glands; but by their mfimte N""^be '.f !^ Point and Atom of the ^f.^,f .f ^^Vmoft ken care of. But that which is Y.-t J"^ ^ '^nderful, is the apt P-POnrs'arl t Senfe of Feeling, to the At^ions and im nulfes ofthe Bodies among wluch we live. To' hS our infe of M«| been t^n^r twenty times as >xquifite ^,^1." ;„^f »,^ " {houMhavebeeainpeiTetualToumnt ev ly Hair had been a Ragger, the touch (J a Feather, or of the ^l'^'^,,''^ X.vhaTd made us cry out, we fliou'd not nave dai a Save appLch'd our Cloaths ovourBeds n ftort, we had livM in perpetual Mitery , and had it been as many times duller o^ more callous than it is, our tendereft Pai.ts fl r' and might have been torn away or con- lum d, without our Knowledge or Concern Whereas by this nice adjuftment of the Senfe Roi^r -^ "? '^ ^"'P"^^^'' ««d Aftions of Bodies round us, we can live in Indolence 5?i? i'^^.P'ft^'-bance of the effluviajnd Aaiojfs ot little Bodies that are neceM? in Motion ; and we feel fenfibly enough! our Fat- ?' ^"'^ J^azarding the Ruin Xw '^- r^"^ univerfilly indeed in all ^«/^^/. whatfoever, this Seife is adapted I^h.vr- *^*''C""Vftances wherein they live. W^uVtCv^^^ InW ofCWi/and iff. So^K Formation of the Parts. And n«l T ^ noticing, that this Senfe o(Fee. t'ng is rendred more exquifite and fenfible ormore dull and imperceptible as it ismoS the '^'^/i?/ which compofe the JV«r/:j>fi» and S J V ? i"P°"..'> ^°«hs of the/«- wh^Jh . P ^ ^ '"'^'^'^ ^^"'^ ^s forc'd out, which there drying and hardening, become M^utL of .^ and therefore theoftnerthe or the nft^r y^?^'^,^'-^ PrefsM upon, u i??*^^ °* '^*^^e '^^«^«?-r are Ibrm'd anS the Skin becomes the thicker, S fo a T^ hujnefs mrmmmm Of aaeitcnott. 52^9 loufnefs gtows upon it. And confequently, the more moderately we ufe the Pleafures of Senfe, the more lively and fenfible they are, and the more immoderately we ufe thefe Pleafures, the left they are fo ; which is a wonderful wife Contrivance of the Author of Nature ; for were it other- wife, fo diftraded is the moft Part of Mankind, that they would certainly deftroy themfelves, fince we fee where there is both Sin and prefent Punifliment, they are not kept from Exceffes that way. § XLII. Having already fliewn the won- derful yet fimple Structure o( tliQ Mu/clesy I have little more to add upon that Head. For tho^ ev^ry fmgle Mufcle , of which there are about 446 in a human Body, either in its Figure^ Situation or Infertion has fomething that fpeaks T^efign and Coun-^ til ; yet feeing Borelli has written a whole Book to fhew this, and to inftance in all the Particulars, were to tranfcribe it, or to write, a whole ^yfiem of Myologie^ I fhall refer my Reader for his full Satisfaction in this Affair, to that learned and furpri- fing Book ^e motu Animaliumj and fliall only fuggeft a few Inftances. i. Then the Manner of the Difpofition of the Mufclesi of the Fingers and Toes^ is admirable. We know that for the ' Ufes of Life, thefe Mufcles Ijo f&ljflofopljical f&rKficiples of Bfliston. 331 Mufcles were to be ftrong and large, that they might be fufficient for the various and forceable Motions of thefe Organs \ now had they been fituated near or about thefe Parts, they wou'd have altogether dir fturbM their Motions^ and made thefe Pla- ces foft and fpongy, and confequently un- fit for grafping and going : And to avoid this, the infinitely wife Author of Nature^ has plac'd them at a confiderable Diftance from thefe Organs \ and that ev^n there, they might not in beqding the Arm or Leg^ rife up and fill thofe Places with their Bodies or Tendons^ he has tyM them to the Bones by annular Ligaments ; and alfo that one Tendon might not be interrupted in its Courfe by another, he has flit fome, that others might pafs through them undifturb'd. This IS fucn a wonderful Inftance of Wildom and Defign, that none can pafs it over with- out Admiration. 2. It is very obfervable that in mufcular lAoXAoii the Expence of animal Sprits is not in Proportion to the Labour the Animal is at. Mr. Bernoulli in that curious Meditation about mufcular Motion, printed in the ABaLiffia 1694, has demonflrated (for whatever be in liis The- ery^ yet there is certainty enough in his general Conftrudion of a Mufcle, to bear out this Obfervation) that the Expences of animal Sprits are in a much lefs Prppor- tion, tion, than the elevated Weights ; for fuppo- fing the animal Spirits expended, to be as 8, then a Weight four Times as great, as when they are but as 5, may be lifted. So that when the animal Sprits are but as 5 to 8, the Weight fuftain'd by 'em fhall be as I to 4. And the like of tlie other Propor- tions of the animal Sprits ; efpecially the Difference becomes moft fenfible between thefe animal Sprits and the fuftain'd Weights, when thefe Sprits are expended in great- eft Quantities. Now what a wonderful wife Contrivance and Compendium of Na- ture is this ? Here in great Labour, the ani- mal Sprit s^vA\id\ are the Life of the Blood, ^jDhich is it felf the Life of the Animal^ are fav'd as much as is poffible ; fo that a Man who is obliged to hard Labour, is not re- duced to the Neceffity of having twice or four Times as much Viduals, as one that is under no Neceffity to Work. We all know that the Spirits are the moft precious things in all the animal Body^ by which we move, and our Blood circulates^ i.e. we live ; by which all the Pleafures of Life are relifhed, and all Senfatton perform'd, by which w^ have that Livelinefs and Agiiity, that Chearfulnefs and Tranquility, that aftuates all our Enjoyments ; and without which, we are languid, and dull, unaftive, and thoughtlefs. Now this, fo neceflary and ufe- 33^ ^t^micai ^tmviis of aaeltgton* 335 yfeful a Subftance, was to be lav'd by all Means poflible, and agreeable to the Necef- fities of Life, and we fee the wife Author of Nature has taken wonderful Care, that no Expences fhou'd be made therein that couM be avoided. 3. What a ftrange va- riety of Motions are our Organs capable of ? There is no poffible one, that might be ufefiil to us that we want, and how wonderful is the whole Machin adjufted ? For our ereft Motion, the Center of Gra- vity is fo difpos'd, as to fall, by a Line drawn from it to the Center of the Earthy always in fome Part of the Tarallelogram form'd by the outer Sides of our Feet, and two Lines drawn by our Toes and Heels, by which Means we are kept from tumb- ling : And if at any Time we chance to throw this Line without that Space, and fo be in hazard of falling, our Arms, and the various Motions of our Head and Breaft im- mediately bring it back within that Space. Thofe Animals J, that are defign'd for flying or fwimming on the Surface of the Water, have all their ftrongefl: Mufcks upon their Breafts, whereby they are kept in the fitteft Pofture for iwimming or flying, the Center &f Gravity being fo difpoled, as they are thereby enabled very eafily to keep their Heads above Water. And in thofe Animais that live within the Surface of the Waters, there there is a Bladder fiU'd with Air, which has a®«i? open to the outward Air on the Surface of the Water, whofe Orifice is en- dowed w ith a mufcular Sfhindter^ by which they let out and take in the Air^ to render them Jpecifically lighter or heavier, than the Fluid they fwim in, and fo fink or emerge as their Occafions prompt them, or as they pafs to a ffecifical lighter or heavier Ek- ment ; for by taking in more Air^ they be- come lighter than they were, and fo necef- farily emerge, and letting out Ibme, they become heavier, and fo fink. And it has been oblerved, that Fifties have got up to the Surface of the Water meerly to change and alter the fpecifick Gravity of this Air. And this Bladder is commonly full of Air^ which is under fome Degree of Condenfati- on, from the Trejfure of the mufcular Sides thereof; fuch to wit, as renders them in an Mqiitltbrttim without any Pain, with that Kind of Fluid they live mod: in, and they commonly alter their Equilibrium^ by the ComprefTion or Expanfion of this Bladder, which being cut out, the Fifli ever after^ either fwims on the Surface or finks to the Bottom. Birds and Fowls that fleep, rett- ing one Foot to cafe the other, naturally lay their Heads under their Wings, that fo the Center of the Gravity of their whole Body, may fall upon the Foot they Hand on, and I V •:J IJ4 I^DilofopDicai i&?mnples and the Anmalh^ preiervM from overturn- ing ; and thofe Fowls tJiat fleep fo on the fmall Branches of Trees, incline a little backwards, that their Claws by the Gravi- ty of their Body, without any mufcular Contraftion, may grafp the Branch more ftrongly. Thefe are wonderful Inftances of divine Wifdom and Trovidence ; but thofe who pleafe to confult that noble Work of Borelli\ ^i^ find to their Satisfaftion, a thoufand fuch Inftances, relating to this Head alone of mufcular Motion. § XLIIT. The Bones confift of hard com- pafted i^r^r^x, ty'd together h^ tranfucrfe ones, after the Manner of the Mufcles-^xhty are nouriftied by Blood Velfels, which enter their Subftance at feveral Places, which up- on the compleat Growth of thefe Bvnes^ are fo ftraightned as to admit only what is fuf- ficient to repair their Decays. All the con- fiderably thick Bones are either hollow or fpongious, and both Sorts contain an alea- ginous Subftance preferv'd in little Veficles^ which by the Heat of the Body is exhal'd through the porous Subftance ofthefe5iametert are ; fo that a hollow Bone of a double ©i- ameter^ to a dole one of the fame Number of Fibres^ is as 2 to i , or the firft is twice as ftrong as the fecond. This is moft con- foicuous in thofe Animalsthzt are form'd to ify ; it is wonderfiil, how light and yet how ftnbng the Quills of their Feathers and their Bones are, and this wonderful wife End Cou'd no otherways be obtain'd but by this Contrivance. Borelli hath fhewn that thefe Bones ax"e fo many VeBes^ of which the Center of the Articulation is the Fulcrum ; the Tendons are the Rofes^ by which the Vires Motivd of the Mufcles elevate, and move any Weight, or overcome any Refi- flience. There is a wonderful, and cxadly nice Geometry ufed by Nature in the Figure, Connexion, Order, and Motions of thefe Tiilars of iaeltston. 337 Tillars of the Body, and of their Cover the Mufcles: it were alone a fufficient Work, to Ihew all the Neceftties, the vfi^t Contri- vances and prudent Adaptions of thele a.d- mirable Machines for the Benefit of the whole. I ihall Inftance only in two or three Particulars, and then proceed, i. Then, what can be more wonderfully contnv d than the Back-bone, had it been all ot one entire i?o»?, \s\xk\.o\iX. Articulations, sn^zo^ d not have flopM or turned, but have gone tor- ward like a Poft or Pillar ; had it been com- posM of a few Bones only, then xJci^Arttcu- lations of thefe Bones in bending our Backs, muft have made a large Angle upon their m- nermoft Edges, and fo the ffind Marrow, which fends Kerves to all the interior Parts of the Body, had been in hazard ot being bruisM at every ftooping ; and confequently all the inferior Parts, had been in perpetual hazard of being deprived of the Inltruments of their Motions ; befides that the whole wou'd not have been pliable, for the vari- ous Poftures we have occafion to put our felves in. If it had confilled oU^x^xo^x% Bones without intervening Cartilages, we ftou d have had no more Benefit by it, than itittiaa been entire without Articulations^ or had thefe Articulations been after the manner ot fome others of the Bones, we had not been capable of thefe Varieties of Motions that we now are, if each Vertebra had had its o%vn ' rj pro* H «■• iiLi ^36 ^f^MfXj^M^mtipitS of Motion mi^ht not require too great an Expence of Spirits, to move them, and that the mechanical Machin might not become a Burthen to themfelves j now the wife Au- thor of Natufe has wonderfuHy provided for this, for he has made 'em lignt, by eva- cuating their middle Subftance, and yet tliey are ftronger by very fer, than if tney had compos'd one folid Cylinder ; for Galileo has demonftrated, that of two Bones of equal Lengths^ and of equal Number of JKtbres i the Strength of the one is the Strength of the other, as their 'Diametert are ; fo that a hollow Bone of a double "Di- ameter^ to a clofe one of the fame Number of Fibres, is as 2 to i , or the firft is twice as ftrong as the fecond. This is moft con- Ibicuous in thofe Animalsthsx. are form'd to fly ; it is wonderful, how light and yet how ftrbng the Quills of their Feathers and their Bones are, and this wonderful wife End Cou'd no otherways be obtain'd but by this Contrivance. Borelli liath fhewn that thefe Bones are fo many VeHes, of which the Center of the Articulation is the Fulcrum ; the Tendons are the Rofes, by which the Vires Motiva of the Mufcles elevate, and move any Weight, or overcome any Refi- ftence. There is a wonderful, and exaftly nice Geometry ufed by Nature in the Figure, Goimexion, Order, and Motions of thefe Tiilars of iaeltston« 337 Millars of the Body, and of their Cover the Mufcles ; it were alone a fufficient Work, to fhew all the Necejfuies, the wife 0«fr/- vances and prudeiit Adaptons of thefe ad- mirable Machines for the Benefit of the whole. I Ihall Inftance only in two or three Particulars, and then proceed, i. Then, what can be more wonderfully contcivd than the Back-bone^ had it been all of one entire Bone^ without Articulations^ we cou d not have flopM or turned, but have gone for- ward like a Poft or Pillar ; had it been com- posM of a few Bones only, then the^^^- lations of thefe Bones in bending our Backs, muft have made a large Angle upon their m- nermoft Edges, and fo the ffinal Marrow, which fends Kerves to all the interior Farts of the Body, had been in hazard of being bruisM at every {looping-, and confequently all the inferior Parts, had been m perpetual hazard of being depriv'd of the Inftruments of their Motions ; befides that the whole wou'd not have been pliable, for the vari- ous Poftures we have occafion to put our felves in. If it had confuted of various^ow w without intervening Cartilages, we ftiou d have had no more Benefit by it, than ifittiaa been entire without Articulattons^ or had thefe Articulations been after the manner of fome others of the £(7«^J, we load not been capable of thefe Varieties of Motions that we now are, if each Verubra had had its own ? 3 8 l^ftiloiopiiicai f0?it\apie5 of Beltgon a* 55? proper Carttlage, the Articulations might have been eafily disjointed. So that we fee the Contrivance ot tliis Hulk as it were, of tlie Body IS the belt that can be imagin'd ; for by thefe many and fmall Articukttons upon fomewhat plain and fmooth Surfeces, ty'd by a common Cartilage^ the Back, for the Secu- rity.ot that iV/,?^a//^r> Subftance, that runs down Its Cavity^ is bent after the manner of the Catenarian Curve, by which it obtains lif" ^*''^''^«''^ that is fafcft for the included Marrow, and brings the greateft degree of hrmnefs; the oblique Procelfes of each Superi- or and Inferior Fj-^ about which the Tendons pafs, at fome diftance from the Center of the Ar- ticulation^ whereby the direftion of the Motion of thefe Tendons^ are remov'd al- ways at the fame diftance fromtlie Center of Motion, of the Articulation. The feme A r- tifice is usM in the Knee^ by means of the Tatella^^ thefe are wife and noble Ends, which the Wit of Men cou'd not have thought of, had they not obierv'd them. §. XLIV. How wonderfully is the Brain contrived, how carefully andftronglyis that Fiflcipal Organ of the Bod v, fenc'd from ex- ternal Injuries, by a thick Wall of hard Bone^ and two very clofeand com^zd: Membranes? What an infinite Multitude oi Glands, are in the cortical Part, and of beginning Nerves in the Melular part, a hundred of which do not exceed one fingle Hair? How commodi- oufly are the Nerves, that ferve for four of th^Senfes, and all the Parts of the Superior Regions, fent out the ihorteft and fafeft ways through proper Holes in the Head ? And thofe lerve the inferior Re2}ons of the Body^ " '^'' y'd down in a bony Channel. Audit is ' y remarkable^ that the Veins do not pafs - , at the fame Holes the Arteries enter; for ^f)ilofopl)ical jdcmapieg 34^ for if they did, then upon any violent Moti- on of the Blood, or any greater Quantity thereof than ordinary, lodg'd in the Arteries their 'Dilatation and Sulfation wou d com- prefsthe Veins again ft the bony fides of their PalTage, and fo occafion a Stagnation and Extravafation of the Blood in the Brain, to the deftrudion of the whole Machm ; which bv thefe m^vint Enteries 2inA Exits oithQiQ Veffels is prevented. Thefe Veins alfo do not run along by the fides of the Arteries m the Brain, as they do thro' all the reftot the Body, which is alfo another wife Contrivance of Nature; for the Arteries here, were by tlieir ^Dilatation to prefs out their Juice or Spirit from the Nerves, into the Mufcles ot involmtarylAonon, which wou d have been hindred if the Veins had always gone a ong with the Arteries; for thefe Ff/«J wou d have receiv'd the impulfe of the ^r?^r/fj and there- by in fome Meafure kept it from the ^^rwj. Next how ftrongly is the Heart built, and with what a force does it fqueeze out the Blood into the Arteries ; Bore Ui reckons it equal to the force of 3000 Pound Weight, and that 2 50 Pound Weight of Blood, pafles thro the Heart ev'ry Houre. How varioufly and eftbaually for its end, are its niufcular J^t- bres arrang'd, and with what Judgment are its Columns and Furrcavs difpos d, for the clofer Contraftion of its Ventricles\ its point is turn'd a little toward the lett Iide Z 3 for the more eafy afcent of the refluent Blood m the Cava, for thereby like a reclining in- verted SfJ>bo», the left /turicU becomes low- er than the rigfit. All the Auricles md Ven- tricles have Valves, whereby the Blood has a Paflage to its true courfe forward, but is hindred from returning the lame way ; which woird frequenrly happen, upon the equal treffure of the Blood on all Hands, and the Refiflrence of the fides of the Velfcls, to the Ruin of the Animal; which Inconvenience is mtirely prevented, by this prudent Con- trivance and Situation of the Valves. And ev n the Figure of the Valves themfelves in the fevei-al dilFerent Places, is for wife Ends and Purpofes. But that which is moft won- derful in chis AlEiir, is the different Structure oi the Heart m the F^etus, from that of the lame in adult Pcrlons. In the Heart of the ^tetus, ,ufr oppofite to the Mouth of the Ca- va afcendens, there is a Hole from the Cava that opens mto the ^vtf Tulmonalis, and is ^11 d the Foramen Ovela-, there islikewifea IJliage, which i-uns from the Trunk of the Aorta to the Trunk of Arteria Pulmonis. Now the Blood which is received by the Tla- centa from the Mother, is by the um^cal ftn^?h ''?''"'2 ^y\Canal, which goes ftrait from the rr»»>^ of the one, to the rr//«>^ of the other, by the Cava it is thrown throush tht foramen Ovale, into ?!ie VenaPulmoL lis, of l^.eltfTion 34-5 /l^T^^dUdT^es it to the left ^^f^f^°f the Heart, by which it is fqueez d mto the Jorta, tobedifpers'dovertheBody. The Blood that comes from the fufer'or Parts oi the Body, is diverted by xhelfthmus of the Cava from the foramen Ovale, and tallsmto theuzhtVentricle, which throws it into the Artefia Tulmonalis, kom whence by die communicating Canal, it is ^^S^^^^^^^l^' ried into the Aorta ; fo that the Blood that omes from the Cava ^^^-^^ Pfjw^J throu<-h the right Ventricle, whilft that whch comes''fromthe'D./m.^.«x, paffesonly thro fhe left Ventricle The Reafon of which PaSs is becaufe the Blood in the/^^«^ foSfnot go thro' the Lungs, the. Vefck^ bv their compreffureupon theBlood Vellels, Sftruaing tL Courfe ; neither indeed did the Blood need to pafs through the X.««i/^ the F^tus being nourimed from, the Mother whofe Fluids had already '^eceiv^'' .^^\' f . Advantages that itcou'd reap fr^^J^^he A^; in her Lungs ; but when it comes into the Atr andTs no longer nourilhed from the Blood of die Mother, this ^r./«r. is taken off from^ he Blood Veffels, by the ^f^^J^^^J^^fl Lums after the manner already explain a. An?fo finding a free Pailkge through the Umil h runf no more by the communica - ing Canal: And fo that dries up ; and by the cf rrent in the Pulmonary Vem, theK./^ of the foramen Ovale is Ihut, fo that the 344jWofopl)tcal l^ttnaples of BeWgton. 345 Blood can no more pafs that way from the Cava. Now how wifely are thele different Channels for the Blood coniriv'd, for the different neceflities of the Fmus^ before and after its Birth ! This is a plain Indication of fore-knowledge, and fuch an one as nothing but Omnifcience, is fuificient for. And this is certainly one of the moll: convincing Proofs of 'Defign and Counfel^ that can poffibiy be wifh'd tor; for to provide for an Event, that in the natural Courfe of things, muft happen a long time after^ is an infallible evidence, that the thing was forefeen, and the Pro- vifion defign'd, by fome intelligent Being. But this IS not the only Inftance of a Tre- caution^ for it is evident, all the feveral Steps of the Growth and Vegetation both oi Ani. tnals and Tlants, have been forefeen, and fore-defign'd, by the \v\{q Author of Nature ; feong, diiferent Provifions are made^ and different Circumflances adjufted, for thefe various Periods of their Lives. ^ §. XLV. What a noble piece of Geometry IS manifefted in the Fabrkk of the Eye and the manner of ^//i"^ were plac'd, wecou\i not diftinftly perceive them that fhou'd be fituated towards the fides of our Body, and fo couM not guard our felves from the Dan- gers thence arifing. Befides, w^e couM not difl:inguifli the Diftance of Objefts by one Eye^ for our tu^o Ejes are like two different Stations in Longtmetry^ by the Affiftance of which, the diftance between two Objefts is meafured. As alfo, when one Eye is acciden- tally rendred ufelels, we enjoy the Bleflings of this fo neceflary a Senfe, by the Benefit of the other. It is obfervable that the Figure of the Chryftallin Humour of Fifhes, is a great deal nearer to a Sphere ^ than that of Land Animals^ and that becaufe of the different refi-aftive Virtue of Water from Air, for that convexity which wou'd unite the Rays of Light coming through Air^ will not u- nite the fame fo perfedly at a Point, in the lame diftance, coming through Water. In thofe Animals that gather their Food from the Ground, the Vtipill is Oval or Ellepi- cal^ the greateft "Diameter going tranfverf- ly from fide to fide ; in thole that feek their Food on higher Places, its greateft Diameter goes from the top of the Head towards the TSttt jperfendicukrly^ thefe two different Fi- gures being wonderfully fitted to the diffe- rent necefFities of thefe ^;^i;»^/x. Thofe living Creatures Creatures that by their Figure^ and for other Reafons, have no Motions of their Neck, have aClufterof Hemiffherical Eyeballs which fend in the Piftures of Objefts all around them; and thofe that feek their Food in the dark> have their Retina coloured white, which reflefts the Light and enables them to fee beft in the leaft Light ; thefe are wonderful and furpriz ing Inftances, of Forefight and Councilm that Being that fram'd thefe Organs-^ but that which to me is moft furprifing iu this Affair, is that in all Animals, whofe Or- gans are found; they fhou'd have been fo nicely framed in all the infinite poffible Vari- eties over and under^ as to reprefent Objeft at a due Diftance, of that Magnitude that has the jufteft Proportion and trueft Analo- gy, to the Magnitude of each particular Ani- mal. What the real Magnitudes of Bodies are, I doubt no Body can juftly tell, nor were it of any ufe to us to know, fince their ^^^z- /^^if^/ Magnitudes to the Magnitude of our Bodies, is all that we have any Concern about. Thus taking our own Hand, Foot, or Height for our Standard J all things about usarerepre- fented in a conftant uniform Proportion to thefe, fo that we are thereby informed of that Diftance and Magnitude of Obiefts that is moft natural and familiar to us, and is alfo moft ne- celfary for our Security and Prefer vation : And the lame is true of every other Animal fmall, or great, thus t^kt^in Elefhant^^ Man j and a Mite, 1/ 354 1^l)iiofopl)tcai ^mtipits MitCy and prefent the fame Objeft to them all three, and it fliall appear, not of the fame Magnitude.to them, but in a Magnitude m Ibme Sort, reciprocally proportional to their own Bulks, that is, to the Elephant, lefs than to the Man, and to the Mite, much greater than to either, and thisof Neceifity from the different Magnitudes, and Fabrick of their Nerves and vifual Organs ; and for the Ne- ceflity of their Prefervation, and feeking their Food. Now we know from the Latvs of Ofticks^ that had the Retina been removal farther from^ or brought nearer the ChryjU allin Humour, or (keeping the Retina at the lame Diftance from that Humour) had it confifted of two Segments of a lefs or greater Sfhere^ the vifion had been indiftinO: or none at all; or had the Diftance been fitted exaftly in the Focus of the Chryfiallin^ but had it confifted of Segments of Spheres j lefs or greater, than thofe of our chryfiallin Humour that are at prefent^ we had leen Objefts ev'n at a due Diftance, either bigger or lefs than we now behold them, which wouM have ex- posM us to a thoufand dangerous Miftakes ; for Example, the Precipice that perhaps was not many Feet from us, might have appeared at fome Paces Diftance^ and we have tumbled ^own^ ere we are aware^ or the Atom that we now fcarce take Notice of^ wou'd have covered all our View, and hindred us from taking in any other Objed ; in a Word, befides that of IBleKgion. 353 thus we Ihou'd not have difcovered that Mag- nitude of Objeas, which has the moft proper and fit Analogy to us, which woud have had a Thoufand fatal Confequences, had oui:Eycs magnified Objeft, any thing confiderably, we cou'd have feen but a very fmall part.of them at once, and Twenty dangerous things might have been in our ways, which we cou d not have difcovered, but by a great deal of Pains ; fo that our progreflive Motions, muft .have been fiower than thofe of Repils, and .then ev'ry little Particle, likewife, wou'd have been able to have damn d up, and obftruded our Sight; and had our Eyes diminilhed Objcds confiderably, we cou d have feen them but faintly and indiftindly, all minute Bodies woud have vanifhed, and we, might have been dc- ftroy'd by thofe which we thought at a di- ftance. In one Wotd, .tlicrf are infinities of different Ways, our Eyes might have pofllbly been fo.rm;d, none of which could have brought with it, the Advantages the prefent Strudure does. Can there be a more pregnant and convincing Evidence of the Being of an infinite- ly wife Power, who out of the infinite poffible Varieties, of difadvantagious Fabricks of this Organ^ ha3 fingled out that only one, thatwa^ beft; he certainly defervcs not to enjoy the Blefllngs of his Eye-Sight, whofe Mind is fp depraved, as not to acknowledge the Bounty and Wifdom of the Author of his Nature, in the ravijhing and ajtonifhing Strufturc of thi$ noble Or^^». A a J. XLVI- 3 54 l^llUof opt)ttai i0;{map/r^,) whofe Bafe is t\\^fufreme and abfolute Infinite, the Origin of the Be- ing and Faculties of all created Things ; and its Body^ is the whole Syjiem of Creatures, from the hi^ht^ Jpiritnallntelligence ; def- cending in a perpetual Subordination, and continual Scale^ down to brute Matter ; or if there be any Creature lower than this. It is true, in this Metafhor or Refemblance, the Bafe is to be fuppoCcd at zn ab/o/ute/y tnfimte Diftance, from the Body of the Cone^ (as the Sun, whofe Rays define the dark Coneoi the Earth's Shadow, is diftant from the Earth,) But tlien, as all the Se£tions in in a Cone, parallel to the Bafe, are fimilar to the Bafe, and to each other. So in this fer^ petual Scale of Creatures, confidered in one View, together wkh their Creator, every Species and Set of Creatures is fimilar to the Bafe, and to every other Sfecies and Set of Creatures, from the highefl: to the lowefl:,^ ;. e. every Secies and Set of Creatures oi a higher Order, has the great Lineaments^ and prominent 0ut4mes of their Bafe, x\\^ Orio-in of all Being and Perfeftions, more ftrongly, clearly, and largely reprefented and exprefsM on, and by them^ and every Species and Set of Creatures of a lower Or- der has the fame Lineaments and Charac- ters reprefented and exprelVd on, and by them, but in a more weak, more faint, and more contrafted Manner. And fince Life, ABivity-j and Fecundity, are among the moft un'iverfal, primitive^ and original Qualities of the Bafe, the Source, and Ori- gin of all Being and Perfeftions : So every Species of Creatures and each Individual of every Species, muft in a higher or lower Degree, according to their Rank in the Scale of Exifl:ence, partake of thofe/r/»?/V/t;^ and original Qualities. If this Trinciple, and Foundation, thus (hadow'd out, may be al- lowed me^ and fure methinks it is evident; from the Nature of Things a Triori, from all Experiments and Obfervations hitherto A 3 made . 4. m The Pr E F A c E; f f« Tht Preface; "p made on our material j>/m of Things a Toftenori, and even from.the moft genuine and fimple Refleftions of our Minds within ourfelves. Then it will follow^ I. That there is a perpetual Analosj (phyfical not mathematical) running on in a Chain, thro' the whole Syftem of Creatures up to their Creator. ' •r?; '^^'^ the Vifible are Images of the In- vifible, the Senfible of the Infenfible, the hOypcal of the Archiytipcal, the Crea- tttresoi the Creator, at an abfolutelv infi- mte Diftance. ^ III. That the Arguments from the Jttri. tutes of the Creator, to the Qualities of the Lreature, with due regard to the abfolutelv tfifimte Diftance, is juft and conclufive, ® vice versa. IV. That, a5 there are Ob^eSs intirely oppofite and dtffarata, fo there muft be faculties in intelligent Creatures, fuited to thofe different Obje6ls, difiering according to the Diverfity of the ObjeEts. ^aJ^^'^^ ^* ^^^'v^t^tion be the Principle • T^t^^^y in ^o^ie^ ' that of Re-umou with their Origin, muft by this analonkal Neceflity be the Principle of Adion in o^trits. ■■ y}' J)^^*»aterial Subflances are the fame ^ith jptrttual Siibftances, of the higher Or- ders, at an infinite Diftance, or tliat materi- * . at al Subftattees are ffrrituah Subftances ihfe- nitely condenfed or contraacd, fince in the Scale oi Exipnce, thefirft are fuppofed at an infinite Diftance from the Utter. VII. That there is fome Analogy between the Conftitution, Temperaments and Comi- plexions di Jpiritual Beings, and the known different Textures, Elements, and Faculties of material Subftances. These I think, as they are neceflary Gon- fequences from the preceeding Principle, fo Uiey are the main Pillars, and fome of the principal Propofitions- of this fecond Chap- ter, which, if underftood and granted, e- very Thing elfe will either be eafily re- ceived, or may be fafely rejeded, without any Hazard to the main Syftem. After aU, feeing my whole Intention) and Defign, in advancing and publifhing thefe Speculations:, was to beget in the Minds of Men, noble, generous, and mag- nificent Sentiments, of God and hts Works, that, thereby they might be more power- fully engaged, to love, adore, and ferve Him. To convince them of the "Degenera- cy and Corruption of the whole Race of Mankind ; of the NecelTity.of expanding and cultivating their fuperior Faculties, by a faithful Obedience to the divine :4ttraBi' on and ^Drawings in their Hearts; and thereby, of begetting in their Souls, Chari- A 4 ty. \\ yv i \ The Pre FA CE. The Pre f a c e. H \\ tyj or thtpttre Love of God^ and of all his Images in a proper Subordination : All which can by no other Means be brought about but by a careful copying after, and imitating the Model and ^Pattern the BLESSED JE- SUS has fet us in his Life and Doftrine. I fey, fince this was my whole End and Aim in advancing and publifhing thefe SpecuU. turns. If any Perfon fhall think fit to con- travert them, he may do it very fafely for me. For being fatisfied, in the Honefly and Simplicity of my Intentions, and of the \5\^ and Benefit thefe Speculations have been to my felf for thefe Ends and Purpofes I am firmly refolved, not to fpendmy Time m idle Difputes. If others differ with me about the Truth and Reality of thefe Spe- culations, or their ufefulnefs to, and influ- ence on the Ends propofed, or are not dif- pos d to rehfh or receive them, they mav fet them alone or rejeft them, it is equal to me. All I fhaU be ever prevail'd on to do, in fucli a Cafe (excepting always, in Cafe thofe who either are my lawful Supe riors, or whom I look on my {qH obliged in Gonfcience to obey, fhall command o- therwife,) fhaU be ; to amend, alter, or re- trad wliat 1 fhall be perfwaded is amifs in the tmur&Mditions of this Work if it fhall have any more. IIL The \\ III. The third Chapter is what the reve- rend and ingenious Mr. John Craig fent me about feven Years ago, when I defired him (being low in my Health, and otherwife en- gaged) to write me down his Thoughts on, correft or alter, what I had formerly pub- lifhed on this Head in the Jirji Edition of this Work, in order to a fecond Edition. I have altered or added nothingj but one Note before his Additions, and that in Italick Charafters. To conclude, if any Perfon, by either of the Parts of this Work, fhall be moved to adore, worlhip, or love the lovely and ado- ralfle Author of His Being, (who is wonder- ful in all his Works, and great in the leaf!:,) I fay, if any one fhall be wrought on there- by to love him more, or ferve him better, I fliall have the whole Reward of my La- bour, having intended it folely for his Glo- *ry and the Good of my fellow Creatures ; and having I hope, in the whole, and each fingle Part, as far as my Weaknefe and Corruption wou'd permit, difengaged my felf from "all finifler Ends, from all Fraud^ Malice, Vain-glory, and Hyfocrify. ii THE A^^44^^44^4^^W4^44^ifW*4^44^***^4^4444* v^mvi^sy^ ::;oNTENTS OF THE Second PART. The CONTENTS. C H A P. L Of the Nature and Kinds of Infinites, of fomc of their re%ea:ive Quali- ties, and of a new Aritlirnetick of Infinites. T' *' HE IntroduUion. page i Def. I. Quantity defined j and ex^ fkm'd. p^ ^' De£ II. Body defined and explained. ibid Def. III. TheTrinciple ^/Aftivity in Bodies, defined and exflain^d. p. 3. Def. IV. Spirit de^n'd and explained, p. 4 J J; P^ "Principle of Aaion in Spirits, defin d and explained. ibid Def. yi. The Nature of Finitude defined and explain d. p, r Def. yil. The Mature of Infinitude defined and explain'' d. Jbid SchoL Schol. The Nature of infinite ProgreAlons, defined and ex^lain^d. p. 6 D^. Vlll. Relatwe Infinitude, defined and explained. P- 7 Schol. The Divifon iot\\ingj and the JkPerior degree of rela- tive Nothing, to the inferior as relative Nothing is to Unity. p. 27 The Atithmetick of Infinites. p. 28 Prop. VII. That indefinite ^antities are properly neither finite nor infinite but between both. p- 29 Schol. ji farther Explication of the Nature and Limits a realise- monfiration of the Exifience and Attributes of the Author of Nature ^and oftheQuBVi^ ties The C O N T E N T a. The C O N T E N T & i» I mf ties of Things thereby difcovered. p. 3 o Lemma III. the Rules for infiitutinr this Analogy. p^ Prop. IX. That the m{\\i\&^ intelleaual «» mly comfetible to the divine Nature, p. 55 Coroll. IV. That univerfal Space is the^ na- tural Image of the divine Infinitude, ibid Coroll. V. That univerfal Space may be aptly called the Senfocium Divinitatis. ibid Coroll. VI. That anabfolutely infinite Crea- ture ^ is a Contradi6lion. P« S4 Schol. The Difference between^ Finite, re- lative Infinite, and abfolute Infinite, and the Limits of natural and phyfical Ef feSts. ibid Prop. XIII. Abfolute Infinite is the frecife and f refer Oppofite to abfolute No- thing, p. j5 Coroll. I. Since abfolute Nothing implies the utmoft Contradict ion to Reality j there- fore abfolute Infinite muji imply Necejfity of Being. , p. 57 Coroll. II. Therefore the abfolute Infinite,, mufi necejfarily be. p- 58 Prop. XIV. Finitude and Infinitude, when belonging to natural and created Things^ imply not Realities^ but Modes of Rea- lities, ibid Coroll. I. That the Modes of created T hings jwhen elevated to their Jimilar At- tributes ,_*V"*^ The C O N T E N T S. The C O N T E N T S. I •' tributes J m the fupreme Infinite^ are in hi^ Realities. p. j^ Corbll. IL That the Attributes of Power, Subfiftence, Sfc. are different in Nature ^ as well as "Degrees j in the fupreme Infi- nite, ^^wiwAtf^^^^ are in Great fires p. 6i Schol. That the Faculties belonging to the rational Soul, is compounded intelligent Bein^Sy are finite, but thofe belonging to their fupreme Spirit are infinite. p. 61 Prop. XV. That the Defire belonging to the fupreme Spirit in compounded intelligent Beings is infinite, and the moji cardinal Faculty of their fpiritual Tart. p. 67 Schol. Shewing how this may be conceived. _ „ p. 68 Coroll. I. That fmce the Defire is infinite Nothings but the fupreme Infinite can ade- quallyfill it. p. 5^ Coroll. IL Since the Defire, infinite in it felf can be only filPd with ^>&^ fupreme In- finite, itmuftthen be infinitely happy, p. 70 Prop. XVI. The whole Univerfitas Rerum ts comprehended under Faculty its ObjeSlj and the Senfation between them. ibid Prop. XVII. jin intelligent compounded Be- ingj is an Epitome or Image of the whole Univerfitas Rerum. p. 71 Coroll. I. From this^ all the Relations, and moral Duties of compounded intelligent Beings are to be deduced. p. 75 Coroll. Corol. II. From this the Nature of the component Tarts in thefe Beings^ and of the whole material Syltem is to be de* duced. p. 74 Coroll. III. Hence the Immortality of the fpiritual Tart of all the intelligent Be-^ ings and of the whole Individuals of Cr cap- tures ^ under one form or another is to be deduced. 75 Coroll, IV. That the Defire of the Soul to- wards its proper Objeii is^ as the infinite Space or void, to the divine Plenitude. p. 77 Schol. I. That as in the Univerfitas Rerum all may be comprehended under Faculty^ Objeft, and Senlation, fo in the material Syftem, we have Brute-Matter, Gravita- tion and the beautiful Appearances, and. in every fingle Body, we have Matter, Form J and Congruity. P- 78 Schol. II. An analogical Reprefentation of the ever blefled Trinity in Unity, from the Tropofitions foregoing^ in elevating the conftant Realities of Creatures to their arcliitypai Patterns, in the divine Nature. P- 7^ Prop. XVIII. That there muft befome Trin^ ciple of Aftion in intelligent Beings^ A- nalagous to that of Attradion ih Bodies j and that this can be nothing but that Trincipte of Re-union mth the Origine a of 4' 3t : T'' } r The C O N T E N T S. The C O N T E N T S. t« ; i tributes^ in the fupreme Infinite^ are in bitf$ Realities, ?• 59 Corbll. II. That the Attributes of Power, Subfiftence, &c. are different in Nature j as well as degrees ^ in the fupreme Infi- nite, yr^MiwA^a^^A^ are in Creatures p. 6i Schol. That the Faculties belonging to the rational Soul, is comfounde a intelligent Bein^s^ are finite, but thofe belonging to their fupreme Spirit are infinite. p. 62 Prop. XV. That the Defire belonging to the fupreme Spirit in compounded intelligent Beings is infinite, and the moft cardinal F^uky &f their Jpiritual Tart. p. ^7 Schol. Shewing how this may be , conceived, p. 68 Coroll. 1. That Jince the Defire is infinite Nothings but the fupreme Infinite can ade- qualhfillit. p. 5^ Coroll. 11. Smce the Defire, infinite in it felf can be onfyfilPd with ^/&^ fupreme In- finite, itmuftthen be infinitely happy, p. 70 Prop. XVI. The whole Univerfitas Remm ts comprehended under Faculty its ObjeB^ mid the Senfation between them. ibid Prop. XVII. An intelligent compounded Be- ingj is an Epitome or Image of the whole Univerfitas Rerum. p. 71 Coroll. 1. From this, all the Relations, and moral Duties of compounded intelligent Beings are to be deduced. p. 75 Coroll. Corol. II. From this the Nature of the component Tarts in thefe Beings^ and of the whole material Syltem is to be de^ duced. p. 74 Coroll. III. Hence the Immortality of the fpiritual Tart of all the intelligent Be- ings and of the whole Individuals ofCrea* iures^ under one form or another ts to be deduced • j^ Goroll, IV. That the Defire of the Soul to- wards its proper ObjeB is^ as the infinite Space or void, to the divine Plenitude. p. 77 Schol. I. That as in the Univerfitas Rerum all may be comprehended under Faculty^ Objeft, and Senlation, fo in the material Syftem, we have Brute-Matter, Gravita- tion and the beautiful Appearances, and. in every fingle Body, we have Matter, Form^ and Congruity. p. 78 Schol. II. An analogical Reprefentation of the ever blefTed Trinity in Unity, from the Tropofitions foregoing^ in elevating the ^ conjiant Realities of Creatures to their architypal Patterns, in the divine Nature. p^ jn Prop. XVIII. That there mufl be fame Trin^ ciple of Adion in intelligent Beings^ A- nalagous to that of AttratHon /* Bodies j and that this Can be nothing but that Trintipte of Re-union mth the Origine -TSTTSST^Sr The C O N T F N T S. The CONTENTS. ofibetr Beings. p g Coroll. I. Hence, the Source ^/natural Con- Icience and of all internal Motions in the Soul. gg Coroll. II. Hence, the Degeneracy, and Cor- ruption of Mankind is evident. p. 89 Coroll. III. Hence, the beautiful Analogy of Things ts to be deduced in fpiritual Sub- itances. Coroll IV. Hetice, the genuine Nature ^of moral Good and Evil is to be deduced. ^^^}rS^' 7-^^ Charity is the nece'ffary EffeBofthtsTrmciple ofRc-union.i-hen expanded and fet at Freedom. p. 92 Coroll. I. /r^«r^ Charity, is not founded on Rewards and Tunifhrnents. p. g? Coroll. II. Hence, the Service, Worfhip, ^S Homage, we owe to the fupreme Beins ts founded intirely ufon his own original Excelknctes and VerfcBions. p. gS frop. XX Charity, or the pure Love of ^od and of hts Images, in a proper Sub- ordmatton, is the end of the Law, and the confummate TerfeEiion ^/ Chriftianity. are anfwered. p ' ^'2:f¥'Il "^^ intelligent Beings, there fnufi be dtferent VzcuXu^s, fittel for the f^^eral Ranks of Beings in the Univerfi- CoroIL Coroll. I. Hence ^ the Re a fin why the whole MaUy is difi'mgiiijhed into Body, Soul, and Spirit, as alfi^ of the Law of the Mind, and of the Law in the Members. p. 105 CorolL I[. Hencejjince there are three Pre- dicaments of Beings there muji be three dtftinB Faculties in intelligent Creatures p. 106 CorolL III. Hence^ the true Nature and EX'* tent of the Corruption and Fall of the humane Race is to be deduced. p. 107 Prop. XXII. The rational Soul is not that Faculty in compounded intelligent Beings^ which in the Order of Nature^ is affro-^ friated for the fpiritual World, p. 108 Coroll L. Hence^ as the Light of the Sun is the Medium through which material Things are perceiv" djbthe effential Light of the fupreme Infinite, is the Medium through which his Nature and Attributes are to be underflood, p. 112 Coroll. 11. Hence ^ he who wouU Judge of divine Things by his natural Light, mufi be miftaken^ as one whowou*dt2i&LQ Sounds or hear Light. ibid Coroll. III. Hence J the Errors and Impieties of Spinofa ond Hobbes, and the Miflakes of Mr. Lock are to be difcovered. p. 113 Prop. XXIII. In the Analogy of Things, as the material World, is to univerfal Space a 2 The C O N T E N T S. ^^ Space, fo is the fpiritual World to the fn. preme Infinite. p ^^^ Coroll. I. Hence, material and fpiritual J-a^. Jtancesare both of them extended, p. „, toroll. II. Hence, Matter and Spirit are Omjitfy tn every other equality but in that of Extenfion. ;k: j Prop. XXIV. By the Analogy of Things a • ^i"^u, ""^ ^«e«ded, penetrable, acTive, mdivifible intelligent, Subjfance. p. i,8 Coroll. I. Hence a material Subjiance'ts an infinitely condenfed fpiritual J«M««f^ **»« vice versa. p ,,. Coroll. II. Hence, there mufl be fpiritual Subftances of all ^Degrees 'of Rarity and Denfity /« « ferfetual Scale. ^ , 33 ^r^^ « Schol. Generale. r-^^ Conclu/on. ill C H A V. TheCONT E NTS. —)—■——■— " "" " ' 1 Chap. III. Of the Ufe of Arithmetick of Infinites. ^ r-|— ^^^ Arithmetick of Infinites ^t^- X /yV / ... Prop. II To find the Sum IT? wb Jny^T;) rftrtJ^ ?trTn) 1^ c HAP. L Of the Nature and Kinds of Infi- nites. Of fbme of their refpec^ five Qualities ^ and of a JSlew jirithmetick of Infinites* H AT we may realbn, as cair-» tioufly as poflibly we can, a- bout Matters fo intricate, and fo far remov'd from the corn- mdn Way of Thinking, as the Nature and Qualities of Infi-^ nites, and the other SubjeiEts df this Chapter are ; we fhall begin with 'Definitions md Ax^ ioms^ and proceed to fome general Tropofiti-^ ^Sy demonftrated after the plaineft manner- B till 1 ^ mi ■^(9 nS^ i ^ T i c m pi ^ ^ f- ' 1 ■ 1 1 If* p \i till we obtain Trinciples to found our confe- quent Reafbnings on ; and then draw fuch Corollaries, from the feveral Parts, or from the whole, as arifing neceffarily from them, may be of ufe to afcertain fome Speculations advanced in the foregoing Treatife; or may otherwife help to conduft the Underftand- ing in thofe other Sciences^ where they may find a Place. definition L QUANTITY is what may be increased or diminiflied. Tho' this definition may not exhauft the metafhyfical Nature of ^antity y yet it points out that Quality in it, that is here chiefly regarded ; for evVy Quantity may be increas d or diminiflied, and that conti- nually, as ftiall be afterwards fliown T)efinition II. A BODY is an extended, impenetrable, paflive, divifible, unintelligent Subftance. T^hisT>efinition dlioy tho^ it exhauft not the internal Eflence and intimate Nature of Matter, yet it fums up its fenfible and moft conftant Qualities, by which it is dif- tinguifhed from every thing elfe» of ^tii^m. "'S'SSBSS^ definition VJ. The inherent Trincifte of Activity ^ in the great Bodies of the Univerfe, is Gravi* tation or fomething analogous thereto* Tho' I am perfectly tonvinced, from the Simplicity and Uniformity of the divine Nature, and of all his Works, that there is fome one great and univerfal Trincifle^ run- ning through the whole Syjiem of Creatures analogically^ and congruous to their relative Natures ; which is the iame in all Bodies great and fmall, and the Origin of all their natural Anions upon one another, with re- gard to their different Circumftances ; and that there is not a different Trinciple for the natural Actions of the lejfer Bodies from that which is the Trincifle of the natural Aftions of the greater Bodies of the Vnt^ verfe^ but one and the (ame Trinctfpe in both, afting differently in different Circumftances. Yet fince Gravitation^ or fomething analo-^ ^ous thereto, feems neceffary for accounting tor the conftant and regular Motions, and Anions upon one another, of th^ great Bo^ dies of the Univerfe ; Gravitation pr fome- thing analogous thereto muft be a neceffary Confequence in the greater Bodies of the Univerfe, of this more univerfal Principle, and the Orioin of the Adivity of Bodies. ' . B a "Defi^ laptofopincai mtviip\t& of aaeitstim« [■■I- I I: IDefimtion IV. A SPIRIT is an extended, penetra- ble, aaive, indivifible, intelligent Subftance. Body and Spirit are in ev ry other Qua- lity oppofite, except' in Extenjion; therefore as the toregoing^eji»itio» of Body fumms up Its fenfible and moft conihnt Qualities, fo to aflign the "Definition of Spirit, there was nothing to be done, but to joyn the oppofite Qualities of Body to that of Ex- tenfion or extended Subflance. definition V. The Trinciffe o£ Aetioa in fpiritual Sub- filtences is, or ought to be, tliat effential one of REUNION with the Or/>/» of their Being, imprefs'd on ev'ry Individual of this Rank of Creatures. The univerfal Trinciple of ARion, men- tioned m the third Definition, that runs through all the Syfiem of Creatures, muft analogtcally be carried through ev'ry Indivi- dual oi^trttual Beings, and can be nothing but this effential Principle of REUNION w^th the Origin of their Being, as Ihall be afterwards demonftrated at large. ^Definition VI. A finite ^antity is that, of which the Bounds or Limits, beyond which it cannot reach, are afilgnahle, Thu s a Line is finite, when both its Ex- tremities are given, or the Points which are its Limits, beyond which it cannot reach, are afiignable : An Area is finite, when its terminating Lines are afiignable ; a Solid is finite, when its terjninating Planes are af- fignable\ a Number is finite, when the Uni- ties (which are its Limits) of wliich it con- fifts, or the Bounds beyond which it cannot reach, are ajfignable. Definition VII. \r" An infinite ^antity (in its fimpleft Na- ture and lowell Degree) is that, fome one or more of the Limits or Bounds of which, beyond which it cannot reach, are not af- fignable. Thus 2iright Line^ one or both of whofe Extremities are not afflgnable^ or the Points beyond which it cannot reach, are not af^ fignable^ is an infinite right Line. An Area^ one or more of whofe terminating Lines are not ajfignable^ is an infinite Area ; a So- lid j one or more of whofe terminating Planes B 3 ^^e / n' ii miotti^^fm Wwtipits d 3acUQion< I' 4 * 'C are not aj/ignaile^ is an infinite Solid -^ a Number, increafing continually, whole laft Increafe is not affignable, or the Bounds, be- yond which it cannot reach, are not ajfigna^ tkj will at laft make an infinite Number. Scholium. An infinite Number may be fuppos'd to be generated by the perpetual Addition of a finite Number to it felt Thus i -f i ^ 1^ + i-f I, ^c. ^ + » = ',T. * T r^-.: f I W. And CO ,* is a relative Infimte, S 4 * il 8 lainiof opijtott mncipus of 3KeU9(dn« H Li- as It ftands related to the given Finite «, bv the perpetual Addition of which to it felf it Scholium. • ^^J^\ ^^T^ Relation, that relative Infi- nite ftands above a given Finite in afiendm, m the feme may another Quantity be fuppo- rJ° ?? K""^ " ^" defcending, in wliich Cafe, we Ihall have a relative infinitely sreat Quantity m afiending above the given Fi- nite ; and a relative infinitely litt^ Q^^siti. ty in defiendmg below it. So that relative S in ^,i? ^^^^ ^^^ ^ ^P^'y diftinguilb. ed in i-efcea of the given Finite, inti re- httvemfintteh, great, and relative infinite- hhttle For brevity fake, we Ihall call the firft relative Infinite, the fecond rell true Nothing, ^efinitiottTX.. and loweft Degree) is an infinitely little Quantitj' as it ftands related to a given Fimte, by the perpetual Subftraftion of Thus oi is a re/afive infinitely little (Quantity, as it ftands related to Ximij^^ by thp per* perpetual Subtraftion of which from it felf, it is generated ; that is ^i = i — i -f i — 1 -f I — I + I —I ^c. and ^ ^ is an infi- nitely little Quantity, as it ftands related to the given Finite a^ by the perpetual Subtra- ftion of wliich from it felf, it is generated ; that is^^=:^ — ^4" ^ — ^-f^ — ^ ^<^' definition X. An indefinite ^antity (in its fimpleft Na- ture and loweft degree) is fome mean Pro- portional, between Finite, and relative In- finite or relative Nothing. For, as in defcending fi-om i to o, we do not immediately flip from finite to relative Nothing, but muft neceflarily pafs through the intermediate Steps |, f , ^, 4- ^c. in Arith- metical Progreflions ; and in afcending from I to oo we muft pafs through the Steps be- tween both 2, 5, 4, 5, ®r. in the fame Kind of Progreflions. So in the Geometrical Vyo- greflions, in defcending from i to c, we muft pafs through thefe mean Proportionals^Vo Vo "^Vo ^c. and in the fame Progreflions, in afcen- ding from I to 00 , we muft pafs through the mean Proportionals ^^/ oo ^^ oo V cx>, ^c. and thefe we call Indefinites. Thus in Geo-- metryj if we cou'd imagine a Circle^ drawn upon the fumm of a finite right Line repre- fenting i, and an infinite right Line repre- fenting lO l^Dtlofopimal mtmims of EdtgCmu ii fenting 00 1^ as a diameter. A Perpendi cular erefted on the Point where thefe two Lines meet, reaching the Circumference wou'd reprefent the indefinite right Line implied by V'oo i. Let QO ftand for fuch iniefinite Qjiantities in general. Scholium^ Unity being the Cmpleft /«//5b there- fore coL 00 = Ly. but L 00=00 (as will be fGtn by the laft Chapter) therefore cjo X 00 =Ly. that is ^=irrLy. But i maybe the ^Logarithm of any finite Number, grea- ter tlW Unity, in the Scale of Proportionals 1°, a^V. a^. a4. S?r. therefor^ "^Voo i may be any jflidte Number greater tlian Unity.The fndefinite^oi the firft Degree, that is where- in the Number denominating the Root is an Integer, may be univerfally thus exprefs'd "iv^a="V^=i — 1~ _j I It ixm + i * ro ' m X 2 m , ixmTIx2m+i i. i xm-t-iX2m-fiX '' mxamxsm '^ mx 2 m x 3 m x SE + ^f. Now as 00 1=1 + 1 + 1 + }+i ^c. and o i=i-i + i--i+ 1— I, ^c. and "Voo I. are of the funpleft Nature, fo alfo are they of the loweft Degree. The fuperior Degrees being generated of 00 1, af- ter the fame Manner that 00 i is of i, tor if we add 00 I, perpetually to it felf, we {hall have a relative infttifely greaf Qn^nti- ty of the fimpleft Nature in its Kind, but of a higher Degree, viz. 00 1+ ~ 1+ 00 1 + + i + i + i + i+iCSff.+i + i + i + i + i®'^. eJf. =r (Since a perpetual Addition of any Quantity to it f elf, is equal to a Multi pbcati- onbyooi)ooiXi+i + i+H-i+i®^J= = ooX^a+a+a+a+ata~^. = 00 X 00 a— ooi a. After the fame manner 01=1-- 1 1: x-i + i-i ^c. If fubftraaed perpetually fro m it felf, it becomes o i--oi_+oi-;;Oit£f. _-;_i-|-i— i + T — I @f. — I— I -I- 1-;^ 7zir^r+ i-i+i-i+i-i^ — I— ,^,_i_j-'i__i ^c. + &c. == (fince a per- petual Subftraftion of a auantity from it lelt IS the fame with a Divifion by 00 ) _L:iJ V 12 0lbflo(bplbical Wmi^m of Beligiom ij I •f I— i-fi— I Sfr. 00 =r— zz:— X0=0Xl ~i a relative Nothing lefs than o, but of a fu- perior Degree; for as relative infinitely ar eat Numbers increafe in their Value, by be- ing raifed to fuperior Degrees, fo relative mfinitely little decreafe, becaufe the firft perpetually afcend from Finite, the latter defiend perpetually further from it. And thus all the Degrees, that finite Quantities admit of, may be form'd from relative In- finites and Nothings. And as we have Inde- finites °»Voo between i and Infinite in afien- dmg, and ^yfo between i and o, in defcen- ding, lo malogous to their Natures we have the fuperior Degrees ™ V°^ ° and "Vo" Na- ture m all thefe Cafes admitting of no Bounds nor Limits. definition XI, Abfoluteor SUPREME Infinite, in a pro- per Senfe, is one. Individual, admitting of neither Increafe, nor Diminution, or of any Operation that mathematical Quantity IS fubjeded to. ^ ^ Thi s will be better underilood afterwards. "Defi^ definition XIL Abfolute Nothing in a proper Senle is neither capable of increafing nor diminifh- ing, nor of any wife altering 2Xi^ Mathema- tical Quantity to which it is apply^d, but ftands in full oppofition to abfolute Infinite* Axioms. !• That which is greater or lefs than any polfible finite Quantity, how great or little Ibever, muft be a relative Infinite ^ Indefi^ nite^ or Nothingj and which of all thele Three, the given Quantity is, the State of the Cafe wiU always determine. Besides, Infinite j, Indefinite^ and No- things relatively confidered, we have no /- dea^s of Quantity, and the Definitions of thefe already given, applyM to the State of the Cafe under Confideration, will always determine which of thefe the Quantity aC- figned mufl be. II. Number being the fimpleft Meafure of Quantity, and a proper Unity being the Meafure of all Number^ a proper Unity is the Meafure of all Quantity. That Unity is the Meafure of all In- tegers is evident : And in Fradions, the ^denominator determines the proper Unity, whereof 14 ^^Mt^itSA^mctpltS df ISleUsion. 15 '-i whereof' the Numerator determines the Number. Whei-efore in the following Pro- pofitions inftead of Quantity, we fliaS fre- quently ufe its Meafure Number, to exprefs their Meaning and to demonftrate their Truth. Trofofittons. ■•1 I. ^antity maybe increased or diminifli'd in Infinitum. Case I. Th2X Quantity may be encreas'd in Infnitum, is dTident from hence, that fince it is certain, a finite Quantity may be added to a Finite, what may be once done, may be done amin and again, and confe- quently may be done any Number of Times, greater than any finite Number how great loever, that is by T^efinitian ^, and Axiom i. Quantity may be increased in Infinitum. Case 2. that^«^»^/ifjr may be dimini- fhed mlnfimtumi^ evident from hence, that out of ^ ^ ^ _ thegi- -^ "^ '^1^1 ^v'n'iiW ^^ ven Quantity AB^ by the Sixth Book of Euclid^ you may take out any given — n Part, and out of the Remainder, you may alfo take out any - Part, for the fame Rea- n fon that you can take it out of thefirft given Quantity AB, and fo on continually, and yet you Ihall never reach the Extremity 5, fuice the - Part is ftiU lefs than the whole » Remainder. That is^ you may take, out - Parts in a certain Proportion out of the given Quantity ^B perpetually, that is, the Quantity AB may be divided in Infimtum. q. e. d. Another 'Demonftration of both Cafes. The Incommenfurabil'tty of furd Quanti- ties to rational ones, as they are call'd, is a full Demonftration, that ^antity may be increased or diminilh'd in Infinitum. For i6 j^fttlgfop tKcal^rtrnftrteg S§V^"i?^ '^^ ^'^" ^2)='- Thin Is ^ to Z)^, as I to v'f . Take in the SiH^ ^©, apart y/ the leaft poSihkiawTM fm. parallel to AB and ^«j parallel to >4^* Since the Triangles ^^© an'd S arffi' milar ie« will ftill be tomlSTas^toJl' nite Number of Times haJarl^l P ^^ fv»^,i'^ u * , ^ ""^s, now great ibever fliou d be equal to mM. So that let 7^ turn, and AD mcreas'd mlnfnitum. q. e. d. of Ecligion. 17 Corollary L rtENCE it is evident, that to affign the ah/blutely greateft relative Infinite^ or th6 abfolutely leaft relative Nothing is a plain Contradiftion, feeing both thele are ftill ma- thematical Quantities (as is plain from T>ef. I. 4. ® 5 and fliall be afterwards further demonftrated) and fo by tWs Propofition, are capable of further Increafe or Diminuti- on s and fo the aflign'd can feither be the greateft nor leaft^ abft)lntelyi Corollary 11. Hence, and from ^ef. 4- 5sf ^ we niay difcover Wherein t\\tfpectfick Difference be- tween Finites and relative Infinites or No- things confifts : To wit, m the limited In- creale or Diminution of the former, and in the perpetuity of the Increafe or Diminuti- 6f the latter ; for as foon as the Increafe' or Diminution in thefe latter ftops, they be- come limited and affignable, and confequent- ly Finite^ and thereby, no Part of the defi- red Infinite. oro^- r- -(•■-••-'T»- 1 8 0])tioropt)tcal ^jincipleg Corollary III. Hence it appears, that an Infinite of ei- ther Sort is (as to all arithmetical Operati- ons on it, with due regard to the Perpetui- ty of its Increafe, or Diminution) of the Nature of an unknown (^antity in^^^^^^r^. For as in this, from the State of the Problem ^ we perform arithmetical Operations on it, as it were known, and thereby we fome- times do, and fometimes do not determine Its Value, but^y Approximation : So on this, we may perform the like Operations as up- on an unknown Quantity, with due regard to its particular Nature, and the State of the Trobkm^ and thereby often difcover the Jpecijick Genius of its Progreflion, which is always regular and harmonious^ 2is will be af- terwards leen. Tropofition II. Vnity divided by an infinite Numhr of Vnities makes the Quotient relative Nothing or 00 I = o. ^emonjtrat. od i ziri-f-i-f-i-f-i-f-i f£c. fer "Def. 4. ® oi = i — i + 1 _ i ^c. fer jD^/ 5. divide i, by i+i+i-f-i-f-i S?r. and by the common Operations of Algebra j you iliall have i-f-i-f.i-{-.|-}-.i^f.) i i+i— i+i ^c. z=^Q. q. e. d. I 'm' 'I r I — ' of Eelfgiott. Corollary I. Fkom hence it is evident, that l^^/zi^)' divi-» ded by relative Nothing is eqiial to 00 i . for I — 14-1 — i+i — I ®r.— o) I (i-Hi-f-i-H t-j^i (gc. = 00 i therefore 4^ = co . Corollary IL Hence alfo it follows, that 00 X o =r i* But this may be demonftr^ted otherwife thus^ ooi=i + i+i + i4-i ^c.fer. "Def. 4. Multiply both by and then it is, 60 0= f -H 01 +01 -Ho I ^c. z=z o X 1 +1 -Hi + 1 +1 _^^j but by Trop^ 1. 0= c5o* and i+i-Hi-hi ^c. r:r 00. therefore 00 X 0= r^ X 00= — = i q< e d» 00 Tropofition VHi As Finite in general is to relative Inp nite in general, fo is relatrve Nothing to Vnity. That is : 00 : i 0:1. "Demonpdt.Sy i. Corollary "Prop^ 2.4= „. Multiply B«hb,e.he„^^=». that is I =: 00 00* tlierefc«:e : 00 : 5 o : I. q. e. d. \ Coral- %^ 3 ^tO' ■Jt \ 20 I^Dilofopl^trai l^indples of meligton^ 21 Trofofition IV. , Relative Nothing is a real mathematical Quantity, and implies the leaft Part of the Finite, to which it is related or compared. . 'Demonflrat. This is evident from the Ge- neration oirelative Nothing^sB^tCd'tn *Def. 5. But to demonftrate the Propofition, with- cut regard to this Definition, let AH infi- nitely produced from A^ be divided into e- qual Parts AB, BC, CD, 'DE, (jye. So that an equal Jb Part * of Jr thisLine "^ i 1 I> E F I£ may denote any Number. Supoofmg^5-f , let * denote any Number, for Example x —^is, y=Ab^ then by tlie common Rules of Divifion I =-14-14-^4-?! Wr XT r ^ y—X y^y*^y3 V Now fuppofe B infinitely near to B, then y-X=Bb=i & L=L_but ;, ^ ;^ . i . * y — X ' ' * + ^ ^^ - tjy ®c/^ 4. that is x=i X rn + I + I e^f. therefore l^l+I-LL+i &c. But by Suppofition AB—x—i therefore 7='+'+' + ' + ' ^. =001. But by i. I' i Corollary i . Trojf j. ^_ ^ therefore ~ = V and i and.confequently x^o. But * being a real mathematical Quantity, by 'D^/. i.o. alfo muft be a real mathematical Quantity, and the leaft Part of Unity to which it ftands related or compared, q. e. d. Corollary I. . Since 00 afcends from the given Finite in the fame Manner that defcends below it, and fince is a real mathematical Qiiantity, fo alfo muft the <» be. And as is the leaft relatively below it in its own Order, lo is 00 the greateft relatively above it in its Order but both below and above thefe, we may kefcend or afcend in a higher Order or Degree, without Bounds pr Limits. Corollary II, When a Curve is faid to meet with its AJymftot^ and when in the common Hyper- bola we obtain the Area -L— - or in thp Example propofed we put y = x, in thefe and fuch like Cafes we mean only,Uiat in the firft Cafe the Ordinate is infinitely little, in the fecond, we mean the leaft Part of the Ahfcifs, and in the third that y and X muft ditfer only, by an infinitely little Part of y, or by x oaly ; and not taar C 3 thiy zz 01)tloropt)icai i^^tnoples; of aaeltston. 2.} they Are aijbkaefy eqaaly elfe there wou'd be no Divifion, and confequently no Quoti^ ent, as fhall be afterwards fliewn. Corollary III, Since by Corollary i, ^i'Prof. oo = -J- = 6?r. Since alfo — — =1 + 14-1 + 1+1 I -* I 6?r. as is evident from the common Rules 9f Divifion, feeing the two firft Terms on- ly eflfea the Quotient, (all the reft being but Repetitions of the feme Terms) and laftiy, feeing the fame Quotient is c^tain'd whether the Divifor bei — i or 1 — 1 + I — i+i — I ^c. the reiterated Multiplica- tion of the Quotient upon the Divifor, pro- ducing the fame Effea (in the actual Ope- ration of the Divifion) which foever of the Divifors we choofe, we may fafely put in common Cafes 1 — i or 2 — 2 pr a — a for 0^ Corollary IV, From hence, and Def. 4. we may difco- yer the true meaning of the Expreflion,\vhen 4t is (aid a ^antity is greater than Infinite j, or one hifintte is greater than another. In fhefe apd the like Expreffions 00 i = i + i -+.i4-i-»-i Sff. is always fupppfed the com- ^ Q^a ;/=. rd or Meafure, to which all others moti Standard or Nieamr^ being by Ax- are compared, proper ij/w'y ^ & 1 . Im 2. the common Meafure of f Qu^nt^ tv, and when a Quantity x is faid to t>e SWt^r tlian Infinite, the meaning is, Uiat k mav be an Infinite, greater than a. i . It mav DC oii ■> greater than and when 00 2 is laia lu u ^ «, T it is no more than to fay 2iameter will S2as2t& S& through this lDi.«..- J'r as ~S and its Content as c«3. q. e. d. ^ropfition VI. rnkthje Infinite has to «1>? '''"«'j,;j?^J' Infinites in general oo » = » + » "t" -<- «,. being i that is »» = fl«-^°^'"''= fuppofe the H^tto ot the relative ^ 1 « to « to be a finite Ratio - general oo » to », ••" " ' then 00 n =^vvhich is impofllble by 2 Co- ^ rolkry 0l?flofoptHmi ^imm ts rollary Trof, 3. wherefore fmce oann-^x : o by compofition of Ratio's, cou^n'n ' ' J • • u° ''"'='+ o is but I. therefore oo«-f-» isbutoc», or » a finite Quantity when compared with its relative Infinite a, i becomes o. q.e.d. • Corollary I. Hence, relative Infinite in general is to Mnf- 0. ^'"""'i'- '?^^''/ ^'^ ^° relative No- reiattyelnfimtein general, becomes rf/^^/W JVi»/A/«^:tliatisvco:0::i. tf "Demonftrat. ky th^ precedent Trofofit ion ?f rIh^'c * = " = • -^ • " «. and by converfion fto^ertfS/^A^'v'^'.t ?l^PP«fing then 2 V °t^-^f^^Q."^tity, Nothing but an in- finite Number of relative Nothing ovo\ ^"SX'S/' ^Y Corollary ,. i>Z!l ^* muft be ftilU, or a-a^a-a^-a-Ific, ?i^\l '.'1 ' ' '""^ ^y compofition of i?^. fin7e,il'-\"^\^^ = ^'+^^''- and «., Wherefore w : o ::,;<,, or wlien any Safon hvT'? (f'y.^ddition, (orbySub- Sfl^fin-^ Divif-on of Ratio's)) with r^/^. &^Sa e";!^'^^?"^' '' ^^^^^ relative mthtng q. e. d. The true Analog is this, 00 7/ of !Sleit9am< ^7 co« or »-|-»+»4- eJf./ ••.: » •• ''rf+tr ^-f.^-^ eif. butbecaufe a is fuppofedFmite, ^Tis the fame (in Cafes of Addition and Subtraaion) with p. But were j»^ 00 i, then *-,»+4-«+4- a t$c. won d_bea.— eo _f_ 00 — CO 4 - 00 — 00 ^. = 00 X 1 I -+- 1—1-4-1— r egf. — 00 X d =i I, and 00 »— oo»-hoo» — 00* ®f« = 00 ^='^' Corollary II. * • Put n equal to any Integer, then oo « -^ : ^ f ^ .« . ^«-i . . /I • 1 tor the I : 9, m • I : tf, but ^ : o"-* firft being reduced, becomes 00 :i : • * • -, and the fecond being reduced, becomes ; I : : * : I ;,and therefore when oo«-^ is to be added to, or fubtraaed from oc», it be- comes ; and when ^»» is to be add^ to, or fubtraaed from fl»~^ it becomes alfo <>, by Scholium Tfef. 6. and the Cafe is the lime when the interior Powers fuppofe oo»-S or. CO"-? ^c. are to be added to, or fubtraded from 00", or when o» is to be added to, op fubtraaed from the inferior Powers c>-- or on -5 ^c. in all fuch Cafes it is evident froni the precedent yrf?/. and its i. Corollary, that ppp-i op»--5 and o» become 0, SvJjO' ■I f I ^'1 Ji* u [^ i«^ ^Mttfitmi Wmpks Schclium. From thefe.yr -» Subttraftion. Soo-^scc— 300. loa CO— ^aoo=:y aoo. 6 nco — A,n co z=z 2 »oo. 500 — 7oo = — 200. 700^—5005 ~ 2 ooh_J_oQf — Sco^ — ^coP. 5 CO/' — -^oo;>=5^^^, 3^_7^5^^ ^ 00 — ^ = .^00. OOP — oqP-'i ~ coP. L^t q be an Integer, lefs than / then ooP — Multiplication. c^X3r:r3co. 00 xa^ #00 . 00 X 00 = 00^:00* X oo5 =00^, ^p^ oof = oc^•f. ^ 00 X ^ 00 = ^ ^ oo\ 3 eo 400 4' 00^ ^ oof 00 — 2 — Qo a d e* -}-• 00 2 . £_ 22 a 09 — 00 — h 3 5 15- ^ oo^rr 00 -^ ■ •— 00 -- -h 00 -00 , q ^ ^ ' ^ 5 15 OQ — — 00 — = OP : 00* - ^ rxoo^r* ^ q- ^/co^^oo^|^=^/-.oo 1) eq- ej q\ q^* 4 >^ 8 09 V .»5- Thofe who are ever fo little acquainted with the Jpecious Arithmetick^ will ealily underftand the Reafon and Truth of thef& Operations. 'Profojition VII. Indefinite ^antities are not properly ei- ther Finite or Infinite, but between both. 'Demonjirat. An indefinite Quantity is fom& mean Proportional, between finite and re- lative M ■-^. 'VM 1 i.ii- >t 30 I^Dr *''" "^^ ^" "«'l^er be Fi- nite (and this Manner of Reafoning will hold good of any other Indefinite whatfoever) nor Indefinite ; not Finite, elfe o- would be In- hnite, which is impoffible ; nor Infinite, for for the leaft poffible Infinite niuft be Infinite Finite^ *, and then if Vco be infinite, V vo =- and X* z=i —''= CO. which is alfo abfurd* Again if Voo be infinite, then is *° ^;;^(= ^00) = infinite, and J-^r= to its felatiye infinitely fmaU Part, or it?re- ktive Nothing =0, and fo coxo=«> x Vw =(v'oo zj=') to infinite. But by Corolla S'yn^^t'-'' V """i^'' ^^ ^"ft^cl of quation, it will be co X o = i = «, ^ 1-= /»/»/;^, by Suppofition ; and thi$ abff J^fi^jfe would become i, which is SehO' of ^SleUgion. 31 Scholium* Taking the Inftance of the indefin ite Quantity propofed Voo i=Vi+i-Hi+iyf' It's plain the Root of any given Number grows greater or lefs, as the Number expref- fine or denominating the Root is lefs or grea- ter: and in Voo I, its infinitely little Root or «>Voo I may be any finite Number greater than Unity, as has been already fhewn ; and its infinitely great Root or Vco 1 is infinite^ And between thefe lie all the Indefinites tlmt can be formed on i and 00 ; to wit V" ,• V* , 4V°° ^c. and none of thefe can be properly called either Finite or Infinite, but are in a perpetual Gradation towards either of thefe Extremes, as the Number that denominates^ the Root grows greater or lefs \ and thef never become aftually finite, but when the Number denominating the Root is aftuaHy infinite, nor adually infinite, but when the" Number denominating is 'Vnity. And be- tween thele two Limits^ they are neither aftually finite not infinite. Next to V 00 = 00 (in order of the fimpleft Indefinites,) is Vco = I -h-+-^ +-l+Tf«^''' ^^^^^''^' a 00 16 120 in (by the quick Increafe and Greatnefs of the fucceeding Terms) the laft becomes ^ in a few Number, fo to fpeak, of thefe Terms^ I ill 3^ l^htirtJipDtolg ii Terms, where the Series terminates, and fo tfteir bum Voo . becomes thereby lefs than *^r V^o VT^^T^TT-rCSf. we lee the Terms ot the Series converge yet feftcr, and wifl S'i !^f^~u rP ^^ '""'^^ ^e^s than /^V-'^"'! S*^ **^^« (even when they rife to fiaaional Exponents, whofe Numerators are greater than i, fuch as oo^. coi m^ ^c.-) ^TiArithmetickm^^ be formed, Vccwdl ingtotheExampIe laid down in the Scholium ot the precedent Propofition, with this ad- dition, that an Indefinite as ^p or// a multiplied by another Indefinite oo 7 gives ni^/S!i'^°°'L ^^^^^ ^^'^omes Infi. nite,when f ^+/ris = or )/ q And if an Indefinite as oo r be divided bv r ^ an Indefinite, as oo j the Quotient 00/ — J is Infinite, when qs — fr is = or < only Indefinite, when qs—^r^ps. as of l^eligiom 55 it ought to be according to the Aritlunetick ° N.'b^' That in expreffing an Indefinite by 00/ it is always fuppofed that the Number q Sfefs than /, for if ^ be either greater or equal to/ X. then co/ tho' it may be an Indefinite of tlie fuperior Degrees, yet it is always infinite in its Value. Trofojitign VIII. ^pace, or the Extenfion of the Univerfe, is a relative Infinite, but ot a higher Degree than tlie fimpleft relative Infinite 00 i. "Dcmonftrat. Every Ltmtt is the 1 ermi- nadon of two Diftances, one gorng forward, the other backward from the imiting ioint,- and were the Extenfion of the Univerfe li- mited, .^Umits wou'd terminate a Space, beyond thetc Umits, as wel as within the.^. That is, either the unlverlal ^/^^^ muft be tinlimited, and comWntly i^^n^^J ^^^f^^j^ muft be Space beyond the Lumts ot univer- fel Spacef whicl/ is abfurd. Again if the ExtenfioA of the Univerfe were l^f ^d^"/^ way, fo as to become finite, then ^ Sphere of a finite T>t^^eter might.be found equal to it. For the Cube ot a finite Side may be found equal to any finite Content whatfoe- Part II. D ^''' K 1 \ \ r, IviM T^rf f » where the Series terminates, and fo their Sum Voo . becomes thereby lefs than following Chapter, and in Voo (for wam- fe)rl+T-f---^f^.^^. we fee the TerSs ot the Series converge yet fefter, and win lo their Sum Voo will be much lefs tlian .« £ A-^"1 ^°' ^^^^ (^^^" wJ»en they rife to fraftional Exponents, whofe Numerators are greater than i furh oc > viaiui> CSf.) ^Artthmettckmz}j be formed, accord- mg to the Exampleiaid down in the Scholium of the precedent Propofition, with this ad- ditibn, that an Indefinite as l^f or/y^ q multiplied by another Indefinite « j gives tlie Produa 00 7 7 which becomes Infi- y.te,when ^x+/ris = or // q And if an Indefinite as oor be divided bv an indefinite, as oo7 the Quotient oo/ — J is Infinite, when qs—j^r is = ©r < {niV ^"n Jfi ^!"''^ T^^" ^ ^ -/ r = ^ and only Indefinite, when qs—^r>fs. as of i^eligion* 55 it ought to be according to the Aritlimetick "^ N.^bI' riut in expreffing an Indefinite by oo/ it is always fuppofed t^^he Number ^^ is lefs than/, for if ^ be either greater or equal to/ X. then co>"tho' it may be an Indefinite of the fuperior Degrees, yet it is always infinite in its Value. Tropjitipn VIII. Space, or the Extenfion of the Univerfe,' is a relative Infinite, but of a higher Degree than tlie fimpleft relative Infinite oo i. q)emonJirat. Every L/»?/Ms the 1 ermi- nation of two Diftances, one going forward, the other backward from the imiting fointi and were the Extenfion of the Univerfe h- mited, iiyt{^ Limits wou'd terminate a Space, beyond th^Umtts, as wel as within them. That is, either the univeral ^/^^^ muft be tmlimited, and coufequently /i^^f'te ^rf ere muft be Space beyond the Limits ot uniyer- Sl Spacef whicl/ is abfurd. Again if the ExteSlioA of the Univerfe were Iniiited any way, fo as to become finite, then ^ Sfhete Of a finite 'Diofneter might be found equal to it. For the Cube of a finite Side niay be found equal to any finite Content whatfoe- Pakt II. D ver, 4 L 34 l^})tloropi)teai ^imipus of mettslm 35 ver, as is well Sfhere equal of the Side of cube Root of 4 Radius to the pofe the whole verfe equal to known, and the Radius of a to tin's Cube is the TroduS the Cube^ multiplied into the - Tarts of the Ratio of the Ctrcumference. Let us fup- finite Extenfion of the Uni- the Sphere whofe Radius is ^ C AB. Let this Sphere be cut by a Tlane Z^ ri^^'j ".'' ^^"^'" from the Ele. ments ofEuchd, that to any given Point A a Tangent ^Cmay be drawn, of which on* y the Point ^ tails upon the CircS) the From whence it is evident, that there mufi be hxtenfion without this Circle, or the Sphere Sphere by the Seaion ot which it is genera- ted Since a TUne pafling through this Tanzent. and perpendicular to th^Jlane of this Circle, will only touch the Sphere in a Point • by which there will be an extended See remaining between th^Orctmfe- renvoi the Sfhere, and the touchtHgT lane, in all their Points excepting that one at A ; And fince this is true of every aj^gnable Ex- fenfion how great foever, lefs than Infinite, it h evident The Extenfion of the Umverfe I greater than majfgnable Extenfion, how prSt foever, that is, by Axiom i . it is r^- iZeflnfnite which is^J^f -- -^e^^ £ ?um oV infinite, and feeing this Infi- nite isTf tln-ee Dimenfions or as op i m HeUt, Breac'th, and Depth, therefore it SuftiaitsContentbeasooMhatis,ofa fuperior Degree to ooi. q-e.a. t> 2 Ghapj I I :( ,"5e.s9JfJ 3^ fpMofit^tm mndpltd of Religion. 37 Chap. II. Of the Philosophical Prin- ciples of revedd Religion. Lemma L TH E R E is in all the Works of Na- ture a Symmetry and Harmony, riin- njngonina perpetual ^;/^^^ (with pro: per Limitations arifing from the different Circumffances of the feveral Parts) through the whole and the Parts; or there is a rezu- lar Cmnexm, and uniform Troportion be- rween fimilar Caufes and Eifefts, a Congru. ity betwt^n the End and the Means. Kn ^^aT. ^"^f ^" the Faculty and its Afts, ui fn Z" ^^O'-S^f.^^d their intended Uks in the whole, and in the feveral Parts of dus Syftem of Thiiigs. "' meShrf r- '^"!"' i' "^^^^"^ fi-°ni innu- meiablelnltances already difcover'd and af- certain d. And every new Difcovery in the moll minute Part in the Works of \Tature carnes cdong with it a frclh T)cmonJhation ot tins Propo/itfon ; one niuft k ,.-4 Iv iV norant oi Thil^hy, and Mathem:^;Ss £ want a Cloud o: Wit.-.elTcs to th-s '^n th For Inftance, t\x^ fefquialtcr Tropo^tlo^ the the periodical Times of the Revolutions of the prmary Tlanets about the Sun ; and ot t\v/recundary Tlanets about t\v& prtmary Ones; to their middk Diftancesjxom the SumnA primary Tlanets refpeaiyely, gb- ^ tains univerfally. Their Magnitudes Gra- vities, Ttenjlties, and their Veloctttes in their Or^i^J^ in refped to, and about the Sun and the primary Tlanets, in the rta- nets. Comets, and Satellits, are m a regular and comely Proportion ; the fame.^^^S^^ the fame Law thereof, and the firm arEffeas of both, obtains through the whole materi- al Syfiem of Things. The Reflexions, In- fiexims, and RefraBions ot Light, are the fame in all the planetary and cometary Bo- dies and Regions ; as they are on our terref- trial Globe, witli due Regard to the differ- ent "Denfities ot the Mediums. The Circu- lation of the Fluids, the Manner and Organs of ReCpiration and Generation, are analogi- cally the fame, in Man, Brutes, and Vege- tables- with proper Limitations arifing trom the differing Circumftances of thefeGradati. ons of Animals. The^^«^r^/ Laws of Flu- ids, Elafticity and Gravity, obtain jn ani- mal and inanimate Tubes, but fo tar as they are alter'd in the tirft by collateral Caufes. The whole of Thilofophy and Mathematicks, is nothing but particular Inftances of this beautiful Analogy, and the precsedmg ghap- ^ Da ' ?er§ \ fi 38 i^Jniofoptricai mmpits diiFerent Circumftances of thefe Beings will Sli^Si ^/i*^ '^ \" ^^^ Demonftration, it Be^ng mfinttelyperfea, who contrived and Sn §-T^ «>{ Things; it is impoffible it fliou d be otherwife : A Being infinitely nlho, ; r •? ^'^''^ ^^^' muftneceffarily bring about fimiiar Ends by fimilar Means anH hiln^K 5°"^ ^^y P°^»ble; due Regard whole fr,rnL!°- ^ another, and to the ^S/;^ obtaining its propofed End. ©//- Sn7 nn v'^''^4*^'''^J» 2)^>^^, and the Proof? pnH tT °- ^'^^S^' ^'^ ^he furert teS .nH p ,^^^^t^°^s of Chance, Impo- his WolS' 1 ^t Man perfoVms all ^n^{^tjn^T)^>^^'^^'^ andMeafure, Sir i""'*' /i^(/2fc«f. Simplicity, and the moil confunmate Harmony, Trofortkn of aaeitston. ?9 and Regularity. And this in the following Pam of this treaties for Brevmes lake we fhaU call the ANALOGY OF THINGS. Lemma II. This ANALOGY OF THINGS duly inftitutcd is as certain a T>emonftraUon of Se ^S^i and JVifdmoi the Author of thefe Things, and of the Contriver of this litie.; nF thefe Things difcovered by this A- is of the Propofition propoled. * S)S«7? J. No Effea can be without its prope/caufe- a wife and ^f^I^t mull: be produced by a wife and intelligent Caufe andanm/«iW^^^/^. ^nA mfimtely c^n infiniteh 'wife znd Omnifaent LMie. r\SizX ce/tain and infallible Jxtops diat Iknow not if in all the Compals of human Knowledge, any othei^ca..e up o vlipfame Degree of Evidence. And lie can he no^roper'subjea of Whfophy or Ma. 'irS whJcWd ferioully deny^^^^^^^^ fince the whole Evidence o bodi tu.k Scr ences fuppofe the hrft ot the ^x«;m, and the reft are but like multiplying bo^ll, ^^^^^ of the fame Equation by the Jame Teims. fhlve already obferved, that the Wtjdom oi^ r) 4 • ' i an t^ffett, or Syftem of EfFefts, coiHifhTn OF T^ct a ^"'-'^^ ''^^ ANALOGY fci found i^^n'M^^'i"?'^ demonftrated to wnole, in every the moit mlm.r^ p-,// And in thefe Inftances of ^ ' 5 f^ " without Number, a^d witl In F f'^^r^' very new Sten in \^% ^^«1 out End . ( E- difcLerin^ Sih iJ^,'!^^^^^^^^ all thefe, I fay, do Sel,^'' ^f ^'^> theref4 therEfflts Tf ft ^^^'^^ ' n?"^ infer the ExiftenrP !.? »i 7^ ?^ necelTary Certainty dcnenrk ;, ^'^PO"tion ; fince its tween ^JT:^m.^t\5rrT''}'% this Analogy in genemi 'l fev i'%?"''^ °^ this X^f:%uTv ^'i"S^' ^covSid by certainly Sc]uSf;"oS"t£'-y, ^^ ^ any mathematical Demo^fi!-,? ^^'^^'^c?/, as Its Propofition M^li ■l'"'^ cor.ciiides poation, Mathemattcks and ^^i^- Of BeltQiotu 41 /of by J fo far as they are juft and genuine, are but Branches of this Analogy, Mathema- ticks are but this Analogy apply'd to Fi- gures and Numbers. Thilofophy^ properly To call'd, is but this Analogy apply'd to Bo- dies, or Syjiems of thefe ; or to the ab- ftrafted Natures of Things. Both flippofe the Truth and Neceffity of this Analogy^ without which they are but Jargon and Ro- vtance. An Inftance or two will make the whole Matter clear. Suppofe it were re- quired to lind the refraBed Ray^ when the refractive Towers of the two Mediums^ with the Inclination of the incident Ray^ on the incident TlanCj are given. Let us borrow a Corollary from this Analogy of Things, to wit, that the Diftance between any fix'*d Point in the Incident^ and ano- ther in the refracted Ray ^ {t\\t refra£live Powers of the two Mediums being regar- ded^) is the fhortell poffible ; and with this Corollary make an exad Computation ; we Ihall then find the r^/r^^^^ i?^^)/ precifely the fame with that found out, from other different Principles and Methods (fuppofe of Trigonometry^ where this Corollary has had no Place, as the Geometers have fliown, This fhyJicalDemonJtration of this particu- lar Property of Light, (to wit, that in all Incidences^ the Sine of the Angle of Inci- dence^ is to that oi Refradlion^ in a coniiant Ratio) 4^ i^l)iiofop()icai ^mams RatioJ arifing from this Analogy^ is as cer- ^^u ?r<^°f of the Exigence and Wifdom Attributes or TcrfeBions^ the only Thing he cou'd have to copy out. Corollary II. Hemce it is evident, that with proper Limitations arifing from the infinitely -infi- nite Diftance ; (fo to fpeak) between Finite and abfolutely Infinite we may reafon analo- gically from the Nature and Attribute of the fufreme intelligent Beings to tlie Nature and Properties of finite intelligent Beings ; and from thefe to thofe ; to wit, by fuppo- iing 48 *Opt)A^ of Beligion* 49 ling thefe laft Images, Piftures, and Repre- fentations at an infinite Diftance of the iiift. Trofojition X. A mathematical Point, and infinite Space / are the two Limits of natural or created Things, as to Qiiantity or Extenfion, in Af- cending or defcending from Finite. And neither of them is any Part or Multiple of the other. "Demonftrat. This is evident from Trof. 8-. for natural or material Things can have no more Dimenfions than three, and there- fore the biggeft Extreme in created Things, can rife no further by the Analogy of Things than to 00 raifed to the third Dimenfion. And fince infinite Space is as oo^, therefore Infinite Space is the biggeft Extreme, or Li- mit of natural Things alcending from Finite. And fince a mathematical Point is the Sur- fece (fo to fpeak) of the Extremity of a ma- thematical Line, which has but one Dimen- fion, it muft of Neceflity be the leaft Extreme in defcending from Finite : In a Word, we can rife no higher in natural and material Things than infinite S{>ace, fince that is the Locus Vniverfalis of all created Beings. ^ And we can defcend no lower than a mat he ^ matical Point, fince every Thing below it (if poiHble) cou'd have no Place at ali, or wou'd wouM be no where, that is, wouM be abfo- lute Nothing. And neither of them can be any Part or Multiple of the other, fince no Number of Points, no not even an infinite Number can make any real natural Quantity, not fo much as ^mathematicallAnty therefore ^c. q. e. d. Corollary I. Hence a mathematical "Pointd.nd univer-^ fal Space are true and genuine Oppofites in Nature, and in the Analogy of Things, and between thefe two lie all created finite Sub- fiftences. No natural Thing can be bigger than infinite Space^ and no natural Thing can be lefs than a mathematical Point, they differ the moft widely that natural Things poflibly can, and have nothing common but Entity^ and fo are true and genuine Oppo- fites. . Corollary IL Hence in x\\t Analogy of Things, Mattet cannot be infinite, in any Senfe of Infinite afcending firom Finite. For fince Matter is of thofe natural Things, that neceffarily re- quire all the three Dimenfions, were it infi- nite, by the Analogy of Things:, it wou'd neceflarily be as oo^, that is, it wou'd be e- qual to infinite Space ; but fince the Neceflity of a Vacuum has been defnonftrated in the firft Chapter of the firji Tart^ it cannot be Part II. E cquif 4 4^ l^fti!efepl)tcal|a?mrtplgg fing thefe laft Images, Piftures, and Repre- fentations at an infinite Diilance of the tirft- > Tr Op fit ion X. A mathematical Point, and infinite Space are the two Limits of natural or created Things, as to Qiiantity or Extenfion, in Af- cending or defending from Finite. And neither of them is any' Part or Multiple of the other. T)emonftrat, This is evident from Trop. 8". for natural or material Tilings can have no more Dimcnfions tlian three, and there- fore the biggeft Extreme in created Things, can rife no further by the Analogy of Things than to 00 raifed to the third Dimenfion. And fince infinite Space is as oo5, therefore infinite Space is the biggeft Extreme, or Li- mit of natural Things alcending from Finite. And fince a mathematical Point is the Sur- face (fo to ipeak) of the Extremity of a ma- thematical Line, whijli has but one Dimen- fion, it muft of Neceflity be the leaft Extreme in defcending from Finite : Li a Word, we can rife no higher in natural and material Things^thaniiifinite Space, fince that is the Locus Vmverfalis of all created Beings. And we can defcend i;o lower than a mathe- matical Point, fince every Thine; below it (if pofiible) couM have no Place at al:, or wou'd of Beitc^ton* 49 f % wou'd be no where, that is, wouM be abfo- lute Nothing. And neither of them can be any Part or Multiple of the other, fince no Number of Points, no not even an infinite Number can make any real natural Quantity, not fo much as ^mathematicalUvnty therefore ^c. q. e. d. Corollary I. Hence a mathematical TointdLVid univer^ fal Space are true and genuine Oppofites in Nature, and in the Analogy of Things, and between thefe two lie all created finite Sub- fifi:ences. No natural Thing can be bigger than infinite Space^ and no natural l^hing can be lefs than a mathematical Point, they differ the moft widely that natural Things poffibly can, and have nothing common but Entity^ and io are true and genuine Oppo- fites. Corollary IL Hence in \}l\^ Analogy of Things, Mattet cannot be infinite, in any Senfe of Infinite afcending fi-om Finite. For fince Matter is of thofe natural Things, -that necelTarily re- quire all the three Dimenfions, were it infi- nite, by the Analogy of Things^, it wou'd necelTarily be as cx>^, that is, it wouM be e- qual to infinite Space ; but fince the Neceflity of a Vacuum has been demonftrated in the firfl: Chapter of the firji Tarty it cannot be Part IL E cqu^f i \ 50 ii)!)tl(jfop!)its^ that are Curves ot the /e- condTower. TrojeBiles move in farabo- lick Lines, which are of the fame Order. The Curvature of the Surfa,ce oi all thece- leliial Bodies are of the comcal-fi£im-kmd. The Surfaces of Fluids, rifing in great or fmall Channels, are of the fame Rank. Na- ture admits but of three Dimenfions, and 1 know of no natural Effed that rifes higher than the third Power. Even the irrational Curves that Nature forms, in conduain^ rolid Bodies, and the Rays of Ltght (thro different refraBing Mediums) the fliorteft and eafieft Way : And in fome othei- of her Operations, fuch as the Cycloid Conclmd, Catenaria, Velaria, (.urva Elafimtatts Logarithmica, the Spral and the like, all of them are of the loweft Rank of their Order : And their Natures imply only Portions ot Curves, or of their Areas of the conical- CeBion-kind, the loweft Order of all Curves whatfoever. So true it is that Nature oer- petually brings about her Purpofes thejhof^ teft and fimf left JVay, and keeps conftant to this beautiful Analogy of Things. But fince Quantity may be ftill increafed, 00 may be Ibppoled to rife to higher Powers than oo3 m the intelledual Sfecies of Things, fuch as E 4 ^'^ p (.■'■is li 54 0i)dofopl)iaa l^^uidplesi of aaeltgton* 55 erne. Infinite Space is the Image of the divine Infinitude^ wherein as in a Picture of him (in whom all Things live, and move, and have their being) all created Things pre- fent and manifeft themfelves to the intuitive View of thtjiifreme Infinite^ and therefore in the Analogy of Things, infinite Space is to the fufreme Infinite ; what a human Senfi^rium may be fuppofed to be to Men. . CaroUary VI. An ab/blute infinite Creature is a Contra- diftion, becaufe abfiilute Infinite is me and individual^ by Corollary 2. of this. Scholium. One very remarkable Difference between Finite^ relative and abfi)lute Infinite is this- Fi^i^emay ftillbe increas'd by it felf, and yet continues its finite Nature, 'till the ls[umber of Additions be aftually Infinite. Relative Infinite may be increafed, not by Finite, but by it felf ^ and ftill continues its Nature, afirer infinitely-infinite Additions, without Bounds or Limits : For let it be ever fo often increased by it felf, it continues but relative Infinite. But abjolute Infinite can be increasM by nothing, not even by it feif, elfe it couM not be the abfolute or great- I \ greateft Infinite. In natural Things Fmtte, and relative Infinite never rife lugher than the third Power. The Comets and Tlanets move in Orbits, that are Curves of the Je- condTower. TrojeBHes move in farabo- lick Lines, which are of the feme Order. The Curvature of the Surface ot all the f^- Mial Bodies are of the comcal-feaion-kind. The Surfaces of Fluids^ rifing in great or fmall Channels, are of the fame Rank. Na- ture admits but of three Dimenfions, and 1 know of no natural Effed that rifes higher than the third Power. Even the trratmal Curves that Nature forms, in conducing folid Bodies, and the Rays of ^#Kthro different refraUing Mediums) the Ihortett and eafieft Way : And in fome othei- of her Operations, fuch as the Cycloid Conclmd, Catenaria, Velaria, Curva Elafticitatts, Lozarithmica, the Spiral and the like, a 1 ot them are of the loweft Rank of their Order ; And their Natures imply only Portions ot Curves, or of their Areas, of tht comcal- remon-kind, the loweft Order of all Curves whatfoever. So true it is that Nature oer- petually brings about her Purpofes thepor- teft andjimpkft Way, and keeps conftant to this beautiful Analogy of Things. But fmce Quantity may be ftill increafed, oo may be fuppofed to rife to higher Powers than oo^ in the intelledual Stecies of Things, fuch as E 4 are |;,:iT: 56 iaDaofo{A)tcai )a»tictpie£t are, 00 ^ 00 ^ co". oooo"*"^- Now tho' thefe Powers of 00 fuperior to co ? , can nave no Place in natural Things, or the material Syftem, yet are they the intelkSlu- alSfecies of created Things, and are in their refpeaive Orders, Images^ and Reprefenta^ tipns of their archityfal Ideas^ in the di- vine Mind, and Inftances of the unexhauC- tible Store of manifold Wifdom in the di- vine Nature. And as infinite Extenfion is the Ima^e in Nature of abfolute Infinite^ fo oo«>"*'-is the Image of the fame abfolute Infinite, in the intelleEiual Species of Thin^^s- And by the Analog of Things, relative No- thing, and relative Infinite are the intellec- tual Images oi abfolute Nothings and abfo- lute Inf'ttte, fo univerfeUy does this Analo- gy hold good. Tropjition XIII. Abfolute Infinite, in the Analogy of Things, IS the precife and proper Oppofite to abfolute Nothing. T>emcnjirat. This is plain from TroP, 12. and Its firft Corollary. For fince a mathe- matical Tomt is the precife and proper Op- pofite to univerfal Space, and fince in the Analogy ot Things, a mathematical Toint IS to mfintte Sface, ^.sabfolut'j Nothing is to abfolute Infinite: Therefore abfolute' Infi- nite =iw 1 of aaeltston. 57 nite is the precife and proper Oppofite to ab/b lute Nothing. Befides, abfolute Nothing and abfolute Infinite^ being the Limits of the ^niverfitas rerum omnium^ in afcend- ing or defcending from created finite Beings. They mufl: be precife and proper Oppofites, having nothing common but their being Entia and Limits, q. e. d. I* Corollary I. SiKCE abfolute Nothings in its pofitive Idea^ implies the utmofl: impoflibility of^ and the mofl: extreme Contradiftion to Reality or real Beings as it mofl: certainly does, for it is not poffible to conceive a greater Contradiftion to, or Impoffibility of Reality or real Being, than is imply'd in the pofitive Idea of abfolute Nothing or Non-entity^ beyond which there is no fur- ther defcending from Reality or Being. (It having no real Entity^ tho' it may be clafs'd, as to its negative Conception, in the Category of Entia rationis^ Therefore by the Analogy of Things j abfolute Infinite mufl: imply in its pofitive Idea^ and that neceitarily, the utmofl: Poflibility, and the mofl: extreme Neceffity of Reality or real Being. Corol- V 58 p(jMtf0m ^tmupUS Corollary II. Wherefore fince abfolute Nothing, in its pofitive Idea, implies the utmoft Contra- diaion to real Being, fince abfolute Infimte is the precife Oppofite to abfolute Nothing, fince alfo being Oppofite in every Thing (except as Entia and Lmtts, which do not efFeft the Realities in abfolute Infinitude, as to its pofitive Ided:) abfolute Infinitude muft imply in its pofitive Idea the utmoft Ne- ceffity of Reality, or real Being ; therefore of Neceflity the abfolute Infinite muft really Be, or the Being to which abfolute Infini- tude is only compatible, muft neceflanly exift. Trofofition XIV. Fmitude and Infinitude, when apply'd to natural and created Tilings, in their pofitive Ideas, imply not Realities, but the Modes of Realities. 'Demouftrat. Finitude, when apply d to natural or created Things, imports only in it's pofitive Idea the Proportions of the ife- veral Degrees of AffeBions, or Troferties of thefe Things to one another. Infinitude, the unboundednefs of thefe Degrees ot Af fcBions, or ^Properties. Finitude and Infini- tude ^ ^i i^mM ^* » ':^-%^' of aaecjston. 59 tude^ in themfelves^ -kbftraaed from a pro- per Subjed or Sub^anttve^ are incomplete Ideas in natural o^ created Things. Infi- nite ExtenfioHj mtmber^ T>uration^ Wif dom^ Knowledge J &c. are complete Ideas^ whereof thefe Realities are the Subje£ts or Subjtantives, and the Infinitude, the Efi- thet or Adjective .-^Wherefore Finitude and Infinitude in natural or created Things, be- ing but Adjuncts to Realities, in their pofi- tive Ideas, do not imply Realities^ but the Modes of Realities, q. e. d. Corollary I. Hence the Modes of natural or created Things are Realities j in the fupreme or abfolute Infinite ^ or the Modes of natural or created Things, when analogically eleva- ted to the fupreme, and abfolute Injinite^ are in him not Modes, but the utmoft Reali- ties. This i§ plain from the preceding Tro- pfition, and the 2d Corollary of the 13, Infinitude is but a ii/j- belonging to the rational Soul are likewife finite, but of a higher Rank of Finites than thofe Powers belonging to the Body. The Ima- gination can paint a larger Idea^ than the Eyes can fee, and the Memory lodge a greater Store of Images, than all the Senfes can pre- fent at one Time : And the Underftanding can combine and disjoin thefe, and compare them many different Ways : But flrill thefe Faculties are but finite in x}i\€vL Capacity. We can form no dilHnQ: Ideas of Millions of Millions^ of a multiangular Figure^ or any relative Infinite^ fmall or great : The Ima- gination feems not able to contain thefe ; there is no room on it, for fo large Pi- ftures. The Memory is the Repofitcry of the Images that have been framed on Thantajy^ and can go no further than it reaches ; nay feldom or never contains more than a fmall Part of thofe. Tlie Vnderjianding can work no T-^ \ ' 64 ^!)tlorop})tcal |^;tinaplesi M'lf * '■ih?*''' no further than thefe two afford Materials ; its Works being to coUate^ combine^ and garble J as it were, thefe Images and Ideas the Imagination and Memory prefent to it* All thefe are limited, as the Senfes are, tho' not quite fo ftraightly, becaufe the Vnder- ftanaing may varioufly combine thofe /- ^as they have convey'd to the Imaginati- m and memory ^ and fo increafe their Num- ber : And the Will liaving no fubjeO: Mat- ter to proceed upon, but as it is prepared by thefe prior Faculties, can go no further than thofe allow it^ The Underftanding may diverfify thefe as far as their Cotl binatkns will reach^ and the Will may pick and choofe among thefe, but fince it cannot create Objefts tor it felf to work on, it muft be limited to the Images and Ideas on the Imagination and in the Memory. The Will I mean, as it is the Faculty belonging to the rational Soul. All thefe Faculties feem to have been originally defign'd for Nothing but this material World J and the Syflem of Things about us. They help us to no Notion or Conception of^any Sort of Beings diftin£t from Matter^ but in fo far as Ana- logy will bear us out, and even as to ^ the material Worldy they feem fitted for little elfe, befides the grolfer, more general and more neceflary Knowledge of Things that are required for due Conveniency, Sub- fiflence, K of Eeligjom 63 fiftence, and fhew but fpme of the groffer Out 'lines of the real Natures of Things.- Every Thing that might violently entertain our Curiofity, or flatter our Vanity, as to the Knowledge of the Nature of Thingsy feems to have been induftrioufly conceard from us> and no Faculties to have been in- dulged us tor thefe Purpofes, leaft they fhouM have withdrawn us too ftrongly from Things of greater Moment to the End of our Being: Elfe infinite Wifdom and Power had contrivM them after a more perfefl: Manner, with a larger Capacity^ and a flronge]- Ener^ gy. As to the Faculties of the fufreme Sp- rit^ (which is a third Part of intelligent compounded Beino-s) they moft certahily are infinite in their Capacity and Energy^ I mean they may be enlarged and increafed without Bounds or Limits, which by 2)^/ 4- is to be relatively infinite. Not only the y/^j of thefe Faculties may be multiplied perpetually, but the Capacity and Energy oi thefe may be dilated and intended without Bounds or Limits. The "Perception, the "Dejires^ the Wilh (the Faculties belonging to the fupreme Spirit J are unlimited and boundlefs^ fitted and defignM for infinite Objeas. Hiefe indeed are the firil, prmct- pal, and original Faculties, belonging to all compounded intelligent Beings : By which they are made capable of communit^tmg Part IL F with "V I {'& ti^^ 64 ^^ibtlof opi)tml |^;tmdplesi ihi ■— — II I ' ' ' ' "■ no fiirther than thefe two afford Materials ; its Works being to collate^ combine^ and garble J as it were, thefe Images and Ideas the Imagtnatim and Memory prefent to it. All thefe are limited, as the Senfes are, tho^ not quite fo ftraightly, becaufe the Vnder- ftanaing may varioufly combine thofe /- deas they have convey'd to the Imaginatu on and memory^ and fo increafe their Num- ber : And the Will iiaving no fubjeft Mat- ter to proceed upon, but as it is prepared by thele prior Faculties, can go no further than thofe allow it^ The Underftanding may diverfify thefe as far as their Com^ iimtkns will reach, and the fFill may pick and choofe among thefe, but fince it cannot creaU Objefts tor it felf to work on, it muft be limited to the Images and Ideas on the Imagination and in the Memory. The fFill I mean, as it is the Faculty belonging to the rational Souk All thefe Faculties feem to have been originally defign'd for Nothing but this material Worlds and the Syftem of Tilings about us. They help us. to no Notion or Conception of any Sort of Beings diftinft from Matter ^ but in fo far as Ana- kgy will bear us out, and even as to the material Worlds they feem fitted for little elfe, befides the grolfer, more general and more necefTary Knowledge of Things that are required for due Conveniency, Sub- fiflence. •MMM^ of Eeligion. 65 fiftence, and fhew but fome of the groiTer Out 'lines of the real Natures of Things- Every Thing that might violently entertain our Curiofity, or flatter our Vanity, as to the Knowledge of the Nature of Thingsy feems to have been induflrioufly concealed from us> and no Faculties to have been in- dulged us for thefe Purpofes, leaft they fhouM have withdrawn us too ftrongly from Things of greater Moment to the End of our Being : Elfe infinite Wifdom and Power had contriv'd them after a more perfeft Manner, with a larger Capacity^ and a ftronger Ener- gy. As to the Faculties of the fafreme Sp- rit^ (which is a third Part of intelligent compounded Beinsrs) they mofl certainly are infinite in their Capacity and Energy. I mean they may be enlarged and increafed without Bounds or Limits, which by "Def. 4. is to be relatively infinite. Not only the yf^j of thefe Faculties may be multiplied perpetually, but the Capacity 2ind Energy of thefe may be dilated and intended without Bounds or Limits. The Tercepion, the "DeJ^res, the IVillj (the Faculties belonging to the fiipeme Sprit) are unlimited and boundlefs^ fitted and defignM for infinite Objects. Tliefc indeed are the firft, frtnct- pi, and original Faculties, belonging to all compounded intelligent Beings: By which they are made capable of communigLting Part XL F with / V » • 1 66 ia})rtofopl)tc^ i^^noples of lEleltston. 6j/ with the fuj^reme Infinite. And next in or- der of Nature to thsjufreme Sfirit^ is the rational Soulj-whQTQhy they are enabled to communicate with the material World: And to the Faculties of X^\\% fecondary Part of the Compofition, the SenfesoftheBodyare the Conduits^ and Conveyances, which make up the third and laft Part ot compounded intelligent Beings : In the due Subordination^ the perfea Harmony^ and perpetual Concord jof thefe Three, with each other, the Ter- feSlion of thefe Beings does confift : In their 'Difiord^ Confufion^ and Rebellion one againft the other, their 'Degeneracy^ Corrapion, and Fall. It can be no Difficulty to thofe who are acquainted with the Analogy of Things, to conceive how thefe feveral Parts of com- pounded inteUigent Beings are contain'd without Confufion or Contrariety in each o- ther ; in their primitive and uncorrupted State : When tliey confider, that in Water is contain'd Air, in that yEther, in that Light and perhaps in this laft, a more fubtle and rehn'd Sprtt ; and all thefe in perfed Har- mony^ and Concord. But to confider thefe a little more particularly. The Tercepion as it belongs to the fufreme Sprite muft of" Neceffity be ^faffive Principle, becaufe it cannot create its Objeds, but receive thofe prefented to it : That it is infinite, is plain, becaufe its adequate Objea is infinite, and the fupeme \ fufreme Infinite : It being beftowM on ■ in^ telligent Beings, in order to communicate with the abfolute Infinite. The Neceffity of this third Part of the Compofition of the mentioned Rank of intelligent Beings fliail be aftei-wards demonftrated ; I proceed to confider in a few Words the Nature of fome others of thefe Faculties, belonging to the fufreme S fir it. Trofofition XV. The "Defire is infinite in its Capacity j, the moft cardinal^ mofl: quick^ ZDdifenfible^ and mofl: aSiive Faculty of the Mind or fpiritual Part of compounded intelligent Beings, and the IVill^ and the AffeHions are but Modijications of it. "Demonfirat. To be convinced of the Truth of this Trofofitionj we need only refleO: on the Source of all the Happinefs or Mifery of intelligent Beings, and we fhall find it arifes from the Enjoyment or Difappoint- ment of their T)efires. There is in all in- telligent Beings a refitlefs Affetite or TOefir^ of Happinefs: From the Moment of their Being, through all the Ages of Eternity, all their Labour ^ and Travel is for this Pur-^ pofe: Nor are they devoid of it, either im- mediately^ in the End^ or mediately in the Meansy for one Infi:ant of lime, in all their F 2 end- \ f I J \ 68 |0Dttofo{Ancai )^;Hintiples; endlefs "Duration. Now this is the necefla- ry EfFea of the Faculty of "Dejire^ no Ob- jeft lefs than Infinite can fatisfy it. For let it be fuppofed to have come to the Pofleflion of any ObjeQ: lels than Infinite^ its plain, it can dejire yet a greater, and a greater, with- out Bounds or Limits ; that is, it can de- fire an infinitely ^reat Object ^ that is, the ^efireit (elf is inhnite in its Capacity ; its ABs are inftantaneous^ and its Enjoyments or Difappointments for a Time fwallow up the ji£ts of all the other Faculties : And therefore it is the moft quick and fenfible : It fets all the Powers of the whole Compo- fition on Aftion, to obtain its Ends^ and therefore it is the moft aBive : And upon all thefe Accounts, the moft cardinal Facul- ty of the Mind : Choofing or refufing, that is willing^ is but the Defire apply'd to a particular Objed ; the AffeStims are but the Complexions of the©f/7r^, as apply'd to this particular Objcft : And therefore are both but Modifications of the Defires^ wherefore, Mc. q. e. d. in Scholium. To apprehend how infinitely capacious, aftive, and fenfible the Defire is, we need only imagine our felves, fcparated from the Obje£ls of Senfe, and the prefent Amufement of of Beligion^ 69 of Life^ with all the Faculties of the Soul awake : And we fhall then be able to con- jefture how ftrong^ aBive^ reft lefs ^ and «»- fatiable our Defires wou'd be. So as to fwal- low up and extinguifh all the other A6ls of the Faculties of the whole Compound. Tliofe only can moft fenfibly feel the Force of this Reafoning,whohave in fome Meafure, and for fome Time been in this State. Corollary I. Since the Defire is infinite in jits Capaci- ty, and may be dilated beyond any finite GbjeQ:, how great foever, 'it is evident it cannot be over-fiUM, or fuper-abundantly ^fo to fpeak) fatisfied with any Objefl: lefs than infinite : Since alfo, the greateft rela- tive Infinite, cannot be aflignable by Corol- lary I. Vrojf. I. Therefore the 2)^r^ can- not be adequally and over-filPd with any lefs Objefl: than the abfolute Infinite ; it be- ing capable of being enlarged beyond the Dimenfions oizny relative ovcrcaturely Infir nite afllgnable : And fince by Corollary 6. Trop. 1 2 . no Creature can be abfolute ly In- finite^ therefore the Defire can be perfeftly and adequately fill'd and fuper-abundantly {a- tisfied, by nothing lefs tlian xh^fupreme and increoited Infinite^ F 3 Corol- \ '■\ t/ t) lii 70 #j)ttofopWcm ^&?tnciples Corollary II. Since the 'Defire is infinite, when fiU'd andfetisfied with its ^proper smd adequate 06- Jeffsy it muft be infinitely happy ; for fince Nothing, by the freceeding Corollary, but the abfolute and increated Infinite, can ade- quatelv fill, and fuper-abundantly fatisfy it. The abfolute and increated Infinite ,muft be its proper Objeft, and the 'T>efire infinite in it felt; fiU'd and perfeftly fatisfy'd with its proper ObjcQ:, thefupreme and increated In- finite, mult of Neceflity be infinitely happy. Happinefs arifing from the Congruity of the Objed with the Faculty, and this fuf rente and increated Infinite being the proper, and indeed the onlj^ proper Objea, (fmce the fupreme Infinite is one) it muft alone be the congruous Objea, and fo the Faculty be- ing tnfintte, the Objed infinite^ and they mtinitely congruous to one another. The Tiefire, in the PolTeffion or Enjoyment of this Objea, muft of Neceffity be infinitely happy. . . Tropfition XVI. In regard of intelligent Beings, every Thing that is in the Vniverfitas rerum, may be fully comprehended under thefe three ge- neral 4r ii i i ii ii of ^KeUgton. 71 ncral Heads, to wit, the Faculty or 'T>efire, the ObjeB of this Faculty or "Dejire^ and the Senfation arifing from the Congruity or Incongruity between thefe two. "Demonftrat. All the diftind Subfiftences that aftually exifl, are comprehended under thefe two general Heads, t\\Q fupreme and abfolute Infinite^ and the Creature^ and thefe can be only Objefts of the Faculty or "De- fire. The Faculty or "Defire being infinite, by the freceeding TropfitioUj may contain or receive both thefe, and the Senfation ari- fing from their Congruity or Incongruity to the Faculty, muft together with thefe two general Heads mentioned, comprehend every Thing in the Vniverfitas rerum in regard to any particular intelligent Being. For nothing can be imagined in the whole Extent of Be- ing, real or intelleBual^ that may not be re- duced to F^r///()/, ObjeB:, or Senfation ari- fing from thefe. Therefore, ^c. q. e. d. Tro^ofition XVII. An intelligent Beings compounded of a Body, Soul, and Spirit^ with proper Rela- tions, and in Subordination to each other, is a real Efttomej Image j or Refrefentation of the ^niverfitas rerum omnium. "Demonjlrat. This is fo evident from the Analogy oi T\\in^^ \ that there can be no F 4 Diffi- i I 1 I 7^ )^I)tiofopI)ical l^^inctple^i alt EeUstott. I t Difficulty in it, to thofe who will confider, that tht fufreme Infinite cou'd have nothing more perfeQ: than himfelf and his other Works, and his own perfea Adminiftration and Government of thefe ; to form this com- pounded Being upon. He muft be confillent lyith h|mfelf, and his compounded Works^ in their component Parts, muft refemble in the kffer Compofitions, the fim'thr Parts of the Greater. This intelligent compounded Be- ingj being to have a material VdiXt^ what can it have more worthy of the Work of infinite Perfedion, than his greater Syftem of material Beings to refemble ? His Soul or rational Part can refemble nothing mor^ worthy of Him^ than the other higher Or- ders of created Spirits : And his fufrem$ Sprit or Mind^ will bear its beft Refem- blance, when it reprefents tht/iipreme Infi- nite. His Adminiltration and Government of the whole Sjftem of created Beings, can be reprefented by nothing fo aptly, as the Relations and Subordination of thefe to each other, and to the reft of intelligent Beings, which thefe cou'd only be formed upon. In a Word^ it is impoffible that any Idea of a compounded intelligent Beings made up of feveral Parts^ each fimilar to fome greater Part of the Vniverfitas rerum^ already ex- l^cnty cou'd enter to the divine Mind wliich couM be more perfeft and more wof- tliy \ 7? thy of Him^ than this, that each interior Part fhou'd be an Epitome and Refemblance of his Works already made, and the higheft Part of Himfelf^ and that their Relations and Subordination fliou'd refemble his Ad- miniftration of the whole. I fay it is im- poflible it fhou'd be otherwife, to preferve his Confiftency with himfelf, and to carry on this Analogy^ through every individual Part of his Works^ through tlie whole Scale of Beings, as it moft certainly is car- ried. ^ And this is not a meer metaphori^ cal Pifture, and Refemblance^ but the real and phyfical Nature of compounded intelli- gent Beings. Wherefore^ Q:c. q. e. d. Corollary I. From this Foundation, by a proper Ana- logy^ with the due Limitations ; all the Re^ lations2inA moralT>uties^ oi intelligent com^ pounded Beings^ to th^fupr erne Infinite^ to fimilar intelligent Beings^ and to t hem/elves^ may be eafily deduced ; for Inftance, do we refenible thtfupreme Infinite /m om fupreme Spirit : Then as he is the tirft in Order of Beings^ fo is this E^rt of our Compofition, the firft and moft principal, in our Order of Parts. All the reft muft be fubfervient and fubordinate in us, to this, as the reft of the fever^i Ranks of Beings ar(? to him : This (I 1 r we '-W =^ i ■• i •I 7 4 |&Dilofbpi)«^^/and material Pzvts of com* pounded intelligent Beings and of thcVnion between thefe, as far as they may be known by mere human Reafon, is to be deduced. Compounded intelligent Bcm^^s ^reEptomes or Images of the Vniverjitas rerum. In their 1 of aaeligion* 75 their Bodies they refemble the material Sy^ flem of Things, in their fpiritual Tarts they refemble the fpiritual World, the Uni* on of thefe two is a Refemblance of ( or is maintained and preferv'd after) the Manner^ the fufreme Being governs the material Syfiem of Things : Who being intimately prefent with every individual Atom of Mat- ter, yet more eminently afts from his fupe* rior Throne of Glory ^ having the whole Sy^ Jiem of Creatures in one View prefented to him, in th^ univerfal Sface^ his ipecial Jefire, now this being fuppofed^ to belong to a fufremely infinite intelligent Being, muft be an infinitely aHivCj ardent^ ftrongj and powerful Thought. And that^ not as crea- ted^ or relative Infinitude exprefles it, but as the abfolute and fufreme Infinitude ele- vates this Defire. Now then this fupreme* ly infinite 1>efire^ this adlive and ardent thirft after Happinefs^ or after a fulb pie* nary, and compleat, beautifying Objeft^ we Ihall of Eeiigiam 81 fliall fuppofe to reprefent the FATHER, thd original and firft Trincijple in the divine Nature : Seeing then, there is no Confidera- tion here of any Thing but of God himfelf, nor is it poflTible for any other Objeft, but God himfe If to fatisfy, and adequately to fill this fupremely infinite Ardor, Thirft^ and ^efire of Hapfinefs. Therefore He him^ felf, reflefted in upon Himfelf, viewing and contemplating his own infinite Perfections : The infinite ardent Defire, fiU'd and fatis- fy'd with his own eflential Happinefs : The Brightnefs of his Glory ^ and the exprefs /- inagCj (the eflential Idea) of his Subfiance, reflefted in upon himfe If : (jr God himfelf redupUcatively contemplating himfelf ( he having nothing elfe poflible, to be the Ob- jefl of his Love, delight, or T^efire') reprc- fents to us the begotten T^eity^ the SON, the fecond divine Trinciple in the Order of the Godhead, Upon this RefleBion^ Contem- plation, and Polfeflion of God himfelf in himfelf; there muft of Neceflity arile a Joy, Happinefs, Acquiefcencej and Satisfaction of God himfelf vj'ithin himfelf fo much the movQ perfect^ fullj, extreme^ and infinite, as his T>efire, Thirft, and Ardor after Happi- nefs was ^(?/w and 7?r^«'j^. And this may fhadow out to us the third and laft in Order of thefe eflential Trinctples in this myfteri- ens Ternary, to wit, the HOLY GHOST. Part H- G And f r r Heads or Principles. TheS^r^^the Objelty and the Senfation arifing from the Congruity or Incongruity between the Faculty and the Object. Since laftly^ this Analogy is pre- fer vM full and clear J through the ffiritual 9Lnd material VfoiidSy and each particular Body, that is^ through the whole Syjlem of Creatures : It is highly probable, fo con* ftant and univerfel an Analogy can arife from nothing^ but from its Tatern and Archityfe in the divine Nature : And without all per- adventure^ cou'd we fiiUy and clearly carry it up to its Source ; we fhouM there find the Origin and Source of this HOLY TER- NARY ; or of thefe three effential Relati- ons, of the whole^ to the whole in the com- pletion of the GODHEAD. Let us there- fore try^ in fome poor low Manner, to car- ry up this Analogy^ as high as poflible we can. The tirft Thing then that we are to confider in the divine Nature is, the Dejire^ now this being fuppofed^ to belong to a fufremely infinite intelligent Beings muft be an infinitely aStivCj ardent^ firongj and powerful Thought. And that^ not as crea- ted^ or relative Infinitude exprefles it, but as the abfolute and fufreme Infinitude ele- vates this Defire. Now then this fupreme* ly infinite T>efire^ this a£live and ardent Thirft after Happinefs^ or after a fulL pie* nary, and compleat, beautifying Objeft^ we • ftiall df E^ligifim 8i fliall fuppofe to reprefent the FATHER, the original and firft Principle in the divine Nature : Seeing then, there is no Confidera- tion here of any Thing but of God himfelf^ nor is it poffible for any other Obje£t, but God himfe If to fatisfy, and adequately to fill this fupremely infinite Ardor ^ Thirft^ and ^efire of Ha^ptnefs. Therefore He him- filfy reflefted in upon Himfelf^ viewing and contemplating his own infinite Perfedlions : The infinite ardent T>efire^ fiU'd and fatis- fyM with his own effential Happinefs : The Brightnefs of his Glory ^ and the exprefs /- inagCj (the effential Idea) of his Sub fiance^ refleded in upon himfblf : (jr God himfe If reduplicatively contemplating himfe If ( he having nothing elfe poflible, to be the Ob- jeft of his Love^ Delight^ or T>efire) repre- fents to us the begotten T)eity^ the SON, the fecond divine Trinciple in the Order of the Godhead. Upon this Reflect ion^ Contem^ plation^ and Poffeffion of God himfelf in himfclf; there mufl: of Neceffity arife a Joy^ Happinefs^ Acqutefcence„ and Satisfailion of God himfelf v^'itXun himfelf fo much the movQ perfect ^ full^ extreme^ and infinite^ as his T^efire^ Thirft^ and Ardor after Happi- nefs was aiiive and ftrong. And this may fhadow out to us the third and laft in Order of thefe effential Principles in this my fieri- ons Ternary, to wit, the HOLY GHOST. Part 1L G And 8i 0Dflo(fl#- premely infinite Wifdom of the ALL-PER- FECT. Wherefore, ^c. q. e. d. Corollary I. . Hence we may difcover the Source of natural Confcience^ and of all thofe Motions and Convulfions, that are raifed in the Breafts of compounded intelligent Beings, upon the Commiffion and Omijfion of certain Aftions: Of that Comfort^ Joy^ and Support in fome ; and of that 'Dejeltion^ Dready and Terror on the Minds of others ; where no natural Caules can be afllgn'd. Hence thtmbledinAfublime 'Dtfioveries of the«»r*- ent Heathen Tbilofophers, in the Principles of moral Virtues, without the Affiftance of Revelation. Hence it is, that Scelerats can by no Arts, nor any Amufements how vio- lent foever, ftifle the Cries of a wounded Confcience ; and hence alfo, it is, that honeft and upright Minds are fometimes fwallow'd up by a Tranquility and Peace that furpalTes natural Underftanding. That this Trinci- pie of Reunion is detaced, buried, and in lomeMeafure as it were obliterated by con- trary Attr anions y by Senjitality^^^ad the vio- lent Amufements of Licentiouliiefs in com, pounded 89 pounded mtelligent Beings, is no more an Argument againft its ejfent tally belonging to intelligent Beings, than the Ideotifm of fome is an Argument againft the Principle of Rea- fon in human Nature. But, Corollary II, From this Trincipleh being fo radically implanted in all the Individuals of intelli- gent Beings, and fi-om the fo very few In- ftances and Remains of it, confpicuous in the human Race ; we may gather the infi- nite and univerfal Degeneracy and Corrup- tion of this Set of intelligent Beings, from their primitive and original Inftitution. This Principle was moft certainly implanted in their Creation, in the very Fund and Subftance of their Natures, and yet there remains but it^ Footfteps, and Inllances of Its Being or E fells. There are indeed (as in the greater World) fome legible Charac- ters, Jtrong Out. lines , ^nA prominent Line- amentsorm original Beauty, fome magni- JicentRumSy which fhew what it had been enough to demonttrate the original ImpreC. >». Beauty, and real Being, of fuch a Frmctple, m all the Individuals of this Race, as is evident from theTangs and Tor- tures oi natural Confcience, when it is coun- ter-aaed. But the little EfFea it lias, from what 90 |^l)itofopl)tcai |3?mctptcs what it was defignM to have, is an evident Demonftration of the deep and univer&l Corruption ot this Set of intelligent Beings, Corollary IIL Hence we may farther difcover the Force^ Truth, and Univerfality of this wonderful Analogy of Things ; whatever we difcover of the Works of Nature, is from this Source, and whenever we get the ieaft glymffe into the Manner of the divine Operating, we difcover frefh Inftances of this Analogy, This Principle of Reunion in inteUigent Beings, wonderfully analogifes with that of AttraEtion in the material World : As to the fupreme Infinite ^ it may be very properly called his AttraBion of them, and as to them, their central Tenden- cy or Gravitation (fo to fpeak) toward him ; and this Principle of Reunion^ if attended to, duly cultivated, and expanded, wouM as certainly bring about the temporal and eternal Happinefs of all intelligent Beings in the Jpiritual World; as that oi AttraBi- on brings about the comely and harmonious Motions of the great Bodies of the materi- al World. This Trinciple of Reunion is the efire\ in re- gard to its firft Caufe and original Imprefli- on by thtjiipreme Infinite. This Trinci- pie of Reunion^ as it is confidered, as an in- finitely aBive^ quick J and fenfible Faculty, in the fpiritual Part of compounded intelli- gent Beings, is the "Defire of Happinefs ; as it is confidered as a theological Virtue, it is Charity > and as it is confidered as a Rule of Aftion, it is natural Confidence. But the Principle of Reunion^ in its whole Ex- tent, as it was originally imprefs'd upon, and quite interwoven with the intimate Fund and Subftance of the fpiritual Part of compounded intelligent Beings, is the Source yOrigin^ and Root of all thefe. Corollary IV. Hencb, the true and genuine Nature of moral Good and Evtl^ and of all the moral Virtues, and fiocial Duties of Life, as from their genuine Fountain and Source, is to be derived. Whatever retards, or oppofes this Reunion in intelligent Beings, is to them moral Evil^ whatever pf omotes or advances this Reunion^ is to them moral Good. Be- fides, this 'Principle ofi Reunion duly culti- vated, regularly unfolded, and carefully at- tended to, muit neceffarily produce and per- ted 9i i0l)«tofop!)fcai i&nnttpies of JHeMgtmt* 95 I fed in the Soul univerfal Charity ; that is, the Love of the fupreme Being, and of all his Images in a due Subordination ; and thereby inftrufl:, and beget in the Soul, all the moral Nivtn^s znA facial Duties of Life. All thefe being virtually and necelTarily included in Charity. But to explain this Matter (which is of the utmoft Confe- quence towards a right Apprehenfion of fo- lid Religion) a little farther, I fay Tropojition XIX. Charity^ or the Love ot the fufreme Be- ings and of all his Images in a proper Sub- ordination, according to their Rank in the Scale of Subhftences, is the necelfary Effeft of this Trincifle of Reunion^ w hen fully expanded and let at freedom. Tiemonftrat. By Corollary ji^. Trop. 17. nothing but the fupreme and abfolute Inji^ nite can adequately fill and fuperabundant- \j fatisfy the infinite T>efires of intelligent Beings ; the TJefire in intelligent Being is their Love^, for no intelligent Being can jde* lire anyThing in Order to make it happy, but what it loves > or can love any Thing, but what it defires to enjoy, {In differ encey^t-- ing the m' .die State, and Averfionx\\Q e- qual Oppofite, both to Love and Defre.) So that an infinite T)efre of the fupreme and and abfolute Infinite j is an ardent Love of that Being. But the Principle of ReunioHj expanded, fet at freedom^ and arrived at its ultimate End and Center^ is intirely the fame with the infinite "Defire in intelli- gent Creatures, poflefs'd of its fole and pro- per Objeft, the fupreme and abfolute Infi- nite. Confequently the Principle of Re- union^ expanded, and fet at freedom, in order to arrive at this ultimate End and Center y muft neceffarily beget in the Spirits of intelligent Creatures, this infinite ^efire of the fole and proper Objeft ; that is, an infinite Love of the fupreme Being : And by neceflary Confequence, a Love of all his Images in Proportion to their Refemblance of him ; that is, the Principle of Reunion when expanded, and fet at freedom, muft neceffarily beget in the Spirits of intelli- gent Beings, a Love of the fupreme Beings and of all his Images in a proper Subor- dination, according to their Rank in the Scale of Subfirtcnccs, that is Charity. q. e. d. Corollary I. Hence, Charity., or the Loije of they?/- preme Beings, and of all his Images in a proper Subordination, in its true and ge- nuine Nature, is not founded on Interefi^ or I the I ' 94 #Dtlofopl)ical |g>?innplfs; of jaeligion^ 9^ III the Views oi Rewards and Tuntjhments^ but altogether on the abftra£Jed Terfe£fions of its Objeft, the fufreme Infinite. Chari^ iy in its Origin, and as it ought to be, ac- cording to the true Analogy of Things, is a ^hyflcal and necelfary Confequence of the Principle of Reunion: It flows naturally from an implanted Faculty, and has for its Object i\\^ fupreme Infinite y in his own in- dependent and effential Nature, as he is ab^ Jblutely good and perfeO:, without any coL lateral Views or Regards. Charity is in a higher Degree, and in a more noble Crea- ture (one^ to wit, endowed with freedom and liberty of afting) what Motion^ proce- ding from the Principle of Gravitation^ is in Brute-matter^ or what the Tendency of the Tlanets is towards the Sun^ viz. a na- tural Confeguence of an implanted Princi- ple. This is fo clear and fo certain in true Tbilofothy^ that it is Matter of Aftonifh- ment to me^ how it came once to be doubt- ed, much lefs difputed. Henry Moor\ Argument on this Head is as cogejit and juft^ as any Demonftration in Euclid or . Apollonius. " As the ObjeB of the Intel- '" /^^ (fays he) is that which is fimply " true^ and is ajfented to as fuch^ and not ** as true to this particular Intellect which *' contemplates itj fo there is an ObjeB that *' isfim^ly Good and Lovely j and to be lov- I '' ed " ed as fiichj without regard to the "Party " that thus loves it. And in another Place^ he ufes the familiar lUuftration of Ginger- ^ Bread and Mathematicks^ wherein he grants the former may be a Spur to the latter> 'till Age and good Senfe, with the Know- ledge of the intrinfic Beauty and Worth of the latter, makes the Student in love with the Study it felf, without any Confideration of the childijh Bait. As in natural Love, Perfons become often enamoured of out- ward Beauty J without any particular Knowledge of its Poireffor, or its attaina- blenefs by them ; fo without all peradven- ture, infinite Terfe^fion^ for its own intrin- lic Tulchritude^ muft be the proper ObjeQ: of divine Charity^ without any particular regard to the Party loving it. Not that Interefi^ or a View to Rewards and Pu- niJhmentSj is not often the only Motive of divine Love : And always is a very proper ^nd laudable one, when infinite Terfe£iion is the OhjeO:. And in reality, it is as high as moll of the lap fed Race of Adam^ in their degenerate State, can rife to. But as Things are in their original Natures ^ were in their Integral J and mull be in their reintegrated State. Infinite Beauty^ or Perfctlicn, with- out any regard to Selflntereft^ or any View to Rewards or Tunifr?ments^ is, was, and mult I I 96 mmioj^imi l^^tnnpieg muft be, the proper and fole Objeft of pure and perfed divitte Love or Charity. Corollary II. HENCEthe Service^ Worjhif^ and Homage^ we owe to the fufreme Beings is founded intiiely upon his own original Excellencies^ and Perfeftions, and not on his Rewards 2ivA 'Puntjhments ; there neither ever was, nor ever cou'd be any room for Contrads^ or TaBions, between the fu^retne Beings and his intelligent Creatures, in the original Conftitution of Things. He made all Things by the Word of his Tower, and for bts Tleafure they are and were created. In- finite TerfeElion is to be lov'd, admir'd. flor'd, znAferv'd, for being infinitely per- fect, antecedent ly^&ndi without any regard to Creatures : And when Creatures are brougiit JntoExiftence,this/r/V»^^)' Reafon oiLove and Adoration fubfifts, and in order of Na- ture and Dignity is prior and preferable to all other Reafons. Creation adds nothing eflential to infiniteTerfetrton, but n^Circum- ftance only, which too intirely vaniflies when brought into Comparifon with the original Beauty of the abfolute Infinite. All his Creatures, that aft naturally, correfpond, and are faithful, to the greatert Exaftnefs, to his ortgmal Imfrejfmis, and his appoin- ted of i^eligion. 97 ted and defign'd Ends on them. The Ce- kftialOrbs^ the Stin^ TlanetSj Comets^ and fix^d Stars^ thole huge unweildy MalTes of Matter, revolve in regular Periods and conftant Order, by their imprefs'd Power of Gravitation and primitive Frame. The vegetable Tribes are faithful to his appoin- ted Seafons. The Brute Animals j, facredly obey their inbred Infiin6ts, Only his com- pounded intelligent Creatures, if they at all obey, do it for their own, not his fake, that is, they themfelves are their own ul- timate End^ contrary to what was "Demon- ftrated^ Corollary 4^- Vrop. 17. It is true in the Nature of Things, it's abfolutely im- poflible, to feparate the Duty and Felicity of intelligent Creatures, thtir Hafpnefs con- filling in their being in the Order of their Nature, that is, of GOD it^s Author j, and their only Duty being faithfully to obey this Order. Yet thefe two may be confi- dered apart, and mentally abftrafted the one from the other : And the laft mull: be An- terior to, and in the Order of Things, muft precede the former : So that when w^e in- vert this Order ^ and bring in our Haj^fi- nefs^ as the fole Motive^ or the preferable Motive to our "Duty^ w^e become guilty of the moft grofs and blackeft Idolatry : For he who loves and worihips the fnpretne Beings only becaufe his one Happi-^fi i^ thereby Part IL H brought jt4 98 |^])ao(opl)icai ^mipies of WitiiQim. 99 brought about, makes himfelf and his own Happinefs his ultimate End^ and fo places himtelf in the Rank and Order that belongs to GOD only, and himfelf becomes his own IdoL He only can be faid truly to Love GOD, with a Love undivided, and worthy of him, who having Uwed him, as far as Rewards and Tumjhments will carry him, goes on ftill further to love him^ lofes all views of thefe mercenary Motives^ and feeks for no Fuel to feed the celeftial Flame, but the unexhauftible Tulcbritude^ and Perfedi- ons of the beloved ObjeB. Tropofition XX. Charity^ or the pure and difinterefted Love of GOD, and of all his Images in a proper Subordination, is the end of the Law ; the Accom^lijhment of all the Graces^ and the confummate Ferieftion of Chrijlianity. Dew^onftrat. On thefe Two, to wit, the Love (?/GOD and our Neighbour^ hang both the Law and the Trofhets, fays the ADO- RABLE AUTHOR OF CHRISTIANITY, and the Afofle fays, the end of the Law is Charity, if the fupreme Being is the ulti- mate Objed of the Felicity of all intelli- gent Creatures, and Charity the mean to attain this end, as is evident from the fre- ceding Tropofition : then is Charity the con- fummate Terfeeiiofi of Chripanity. The whole whole of Chrijiianity is nothing but Rules for attaining this Love^ or Meafures where- by to remove the Impediments that hin- der this ^Principle of Reunion (the fource of C/;^ri^y) from operating, or Means todeftroy the contrary Attractions which difturb the natural Operation of this Trinciple of Re^ union ; which wou'd of it felf^ if not llifled, oppofed, and counterafted, necelfarily beget this "Divine Charity^ whereby the Soul wou'd inftantly be united with it's Center^ and ultimate End^ th^fiipreme and abfo lutein^ finite, q. e. d. Scholium, To this Doftrine of pure Love^ there are made but two Objetbions which have any Weight or Force in them. The Firft is, that the Motives for Love and Obedi- ence, urged by Mofes and the Trophets^ CHPvIST and his Apoftles, are founded on Rewards and Tunijhments^ and that there- fore without Blafphemy, we are not to of- fer at, or pretend to, more liigh and fublime Motives or Principles, than the Friend of GOD, and the SON OF GOU, (the Stan- dard in their feveral Difpenfations, of Pu- rity and Pertedioii) thought lit to prefs or propofe. The plain and genuine Aiiiwer to this Objeaion is, that the Author of our Jibing J who loves all his Creatures better H 2 tbd:i ".", 100 ia|n!ofop))tcai Wni\^\t& of 3aeiisiott» lOI than they can love themfelves^ ufes all Mo- tives that are honeft, laudable, and>«/?^ to gam them ; he knows perfeftly the Frame and originalComflexion of all his Creatures, and that in their lapfed State they muft afcend to Perfeaion by Steps and Degrees : and confequently that fome are to be wrought upon by one Motive^ others by another, and that generally the firft Steps are mounted by the Force of the Terrors of the Lord, ^fore the Love of GOD is Jhed in their Hearts. There are Babes in CHRIST as \vei\zs grown andferfea Men, and their Food (or Motives to Cliarity) muft be as their I ears and Strength are: But our SAVIOUR tells us, we muft love the LORD our GOD with all our Heart , with all our Soul, with allour Strength, andwithallour Mind, and Hlo, welhall have very little Zow left behind for our felves. And his beloved 'Difciple tells us, that f erf e6t Love cajieth out Fear ^dconlequently Hofe, that is, Rewards and Fumjhments, which are true, good, and y2r///j^ry Motives, tho' not the belt. The fe- cond Obiettion is h-om the impofllbility of Ijyvmg or begetting Love without a Re- gard to Rewards or Tnntjhments. But this Objeftion arifes fiom Ignorance of the true Nature of this Afedion of the Soul. Love >s the Complexion of the Will or "DeCires aswaslhown Trop. 15. it belongs to the itnm* minlightefCd Faculty oix\\t Mind, the /F/7/, and not to the enlighten'd Faculty, as the 'U;^^ derfianding is, and fo naturally^ and of it felf has no real Refped to Rewards or Tuntjh^ mentSj which are Motives ofFer'd by the Uiiderllanding : We love^ becaufe we will love without Rea/oning^ or becaufe the Ob- jeft of our Love is amiable, and not becaufe it will hurt or heal us. Loveis blind, and be. longs intirely to t\\^JVill^ and not to the In- ielle£l. But pafling this, as perhaps too me-- taphyjical^ lanfwer, 2^/y,as we may for one fingle Infiant, and for onq fmgle A£l, ab- ftra£t from a Reward, forget it, or counter- aft it, (which no Body who knows the prefcindent Faculties of the Soul, and that Love and Rewards are effentally united in their own Natures can deny) fo we may thus abjira£t again, and again^ and fo in Infinitum^ and thus beget a Habit for what may once be done, may for any impoflibi- lity m the Nature of the thing be done for ever: This is "Demonjiration, But I pro- ceed. Tropjltion XXL In all intelligent Beings, there muft be Faculties fitted tor all the feveral Ranks of Objefts, in the Vniver^tas reritm ; that is fiace there are evidently three Ranks of H 3 Objeas, of ^aeltston* 103 Qhjefts, in the Vniverfitas rerum ; to wit, the material Syftem of Things, the Jpiritml World of created Spirits, and the fufreme mdahfolute Infinite. Intelligent Beings muft neceflarily be fitted with Faculties fuited to thefe three generical Ranks of Objefts. Demonftrat. This is evident from the fe- veral different Mediums^ which all infer the fame Conclufion. i- Intelligent Beings are Images of the /iipreme Infinite j who alone perfectly comprehends and knows himfelf and all his Creatures, that is, all thefe three generical ObjeBs^ in the Vniverfitas rerum. He has different Senlations and Perceptions (as far as "Diverfity can be confiftent with his infinite Simplicity) arifing in himfelf from all thefe three different Objefts, and confequently Faculties fitted for them : Therefore intelligent Creatures, his Images^ the Refrefentations of all his communica- ble Perfeftions, mufl: of neceffity have ana-^ kgous Faculties, fitted for all thefe three different Objeas. 2. There are Relations^ incumbent upon all intelligent Beings to- wards each other, and towards t\\tfufreme Infinite^ ; fuch as Love^ and Benevolence. Therefore intelligentBeings mufl: be endow'd with Faculties fitted for receiving the Im» preiFions, and to perceive the Effefts of thefe Relations^ elfe they wou'd be in vain : And tlitk are two of the diSerent Ranks of Objefts •, and no Body^ queftions intelligent Beings, being fitted with Faculties for the third ; to wit, thi^material Syftem of Things. 3. As to the fpritual World^ including the fupreme and abfolute Infinite as its Head. The Trincifle of Reunion^ whofe neceffity in intelligent Beings, I have now demon- flrated, makes it abfolutely necelTary, they fhou'd be provided v^ithFaculties fit for Com- munication and Union with x\\e fupreme In- finite ; elfe, they were not fufceptible of that Happinefs which was the file End of their Being. 4. That which is the apodeiEiick "Demonftration of the Truth of this Trofo- fitionj and at the fame Time proves the Diverfity of thefe feveral Faculties, to be as real as that of the Objeds is, is the manner after which compounded intelligent Beings are provided with Faculties for the ma- terial Syftem of Things. Material Things are prefented to them only through their Senfes; they have a real and material in- flux on thefe, elfe they are not really per- ceived ; and all real Knowledge of material Things is conveyM into the Underftanding, through thefe Senfes : Wherefore it is evi- dent, compounded intelligent Beings are endowed with a Faculty of perceiving or receiving material Things, thro' their Senfes, which is called Perception. Next they have a Faculty of painting thefe Perceptions or H 4 their 104 0i)iMopI)tcal Wntipxm their Images when the Objefts are abfent and this is called Imagination, and lafily a Faculty of combimng and comparing the real Perceptions of tliefe material Things or their Images^ and this Faculty is called Reafan. And all thefe three dillinft Ope- rations belong to the rational Sotil^ ix)^ order to fit it for Communication with the material World. Now by the Analogy of Things, fuch like and fimilar Faculties muft of neceflity belong to the ffiritual part of compounded intelligent Beings, to fit them for a Communication with the two remaining Ranks of Objeds ; to wit, a fpiritual Perception ^ndJpiritualSenfes^lma- gination and VnderJiaJiding^ for thtjpiritual World of intelligent Beings, and divine Sen- fesj Tercej?tion_, Imagination and Vnder- Jlanding^ tor communicating with the fu- freme Infinite, For this Analogy will perpe- tually hold good and true, from the Simfli^ city and Vnity of the divine Nature ; to wit fuch as the Faculties are by which we corn- municate with the material World fuch analogically^ and with proper Limitations, are thole hj which v/q commnnicafe with the World of Spirits, and thc/ti/remelnfinite. And as we fee compounded mtellisent Be- ings have bodily Sen/es, which lolely be- lorg to the material World, lb in the Ana^ /i^ of Tilings^ they muft have Faculties different of Eeligiom 105 different and diftinO: in themfelves pecu- liarly fitted appropriated to the other Ob- jefts in the Vniverfitas rerum. Wherefore ^c. q. e. d. Corollary. I. Hence we may conceive the Reafonwhy in holy Writ^ the whole Man is diftin- guifhed into Z?^^, Soul znd Sprit -^ whence comes the Diftinttion of the natural and Jpiritual^ or inward Man^ between the Law of the Members^ and the Law of the Mind. Thefe Diftinftions and Divifions, I fay, are eafily conceivM from the foregoing 2^r(?^^- fition. For the Body and rational Soul belong to this material Syftem of Thin^^s and are fitted with Faculties for communi- cating with it, and is called the outward Man ; and the following it's praflical Dictates in Rtbeilion again ft^ and in Oppoficion to the Didates ohht Spirit^ the inward Man: TheelTential Principle of Reunion^ the Law of the Mindj which is fitted only for com^ municating with the fupreme Infinite ; I iay, the following the pra6ti:al Di£tates of the firft, in Oppolition to the "Dilates of the latter, is called in the Language of the Sfi- rit^ the following the Law of the Members. Corol^ io6 #l)flofop!i(cal iB^unciples Corollary II. A s there are three different Principles, Orders, or Predicaments of Being ; to wit, GOD the Creator of all Things,, created Sprits J and material Bodies : So there are analogicallyj in compounded intelligent Be- ings,' three different and diftinO: Principles, adapted and appropriated, for communicating with, and enjoying thefe refpeaive Objefts: Whereof every one is endowed with proper Senfes^ Ta^xTrs and Faculties^ different and diftinftfrom each other; that is, as the mate- rial S)J}em of Things, is the proper Objefl of the Senfes, and rational Soul ; and as this Principle is fitted with outward Senfes^ 'Per- ception^ Imagination^ Vnderftanding^ and Will^ So the Principle, whereby they are fit- ted to communicate with thecreatedfpiritual World, is endowed with inward Senfes j, Ima- gination j ^nderftandingj and//^^/7/y and tlie fupreme Spirit y or third Principle, whereby they are fitted to communicate with the fiipreme uncreated Infinite, is endowed with inmoft (fo to fpeak) Senfes j Imagination^ Vnderftanding and JVill; and all thefe in t\mv primitive and original Conffitution, in Subordination, Harmony ^ and^ Agreement, without Contrariety or Coiifufion one with another. of 5Religion^ 107 another. This Corollary is as certain as the Analogy of Things is. Corollary III. Hence we may deduce the true and ge- nuine Nature, and Extent, of the "Degene^ racy^ Corruption and Fall of the hurnan Race of intelligent Creatures, which confifts in the Confuflon^ T>ifcordj Rebellion, and Contrariety of thefe different and diftin£t Principles one with, and againft another ; in throwing off* that due Subordination j Subje- Bion, and proper Rank and Order, that was originally eftablifhed among thefe Fa- culties ; according to the Dignity of thefe different Objefts ; the Order of Nature, and the Analogy of Things, and following the practical DiEiates, and Conclufions deduced from thefe rebellious Faculties. That is, when in this anarchical and rebellious State of human Nature, the Faculties belong- ing to the material World prefume to judge 0^ and determine the Nature of the Sub- jefts belonging to the fupreme Spirit ; take the Government and Adminiftration of the whole Man, which properly belongs; in the Order of Nature^ to this third Prin- ciple; lead the other Principles as Slaves and Captives, and force them to comply withthepraa:ical©i^^^^J- they prefcribe, and 1 08 iai)tfof optical l^^mdpif g ot iacitgton^ 109 and deduce in their ufurp'd Superiority; and under this compliance, begetting and produ- cing phyfical and durable EflFefts, the whole Order of Nature, and the material Syjletn of Things, fofar as thefe/Z^TKr^^/and durable Efteds reach, becomes diltorted, inverted, and corrupted. Tropfition XXIL The rational Soul is not that Faculty in compounded intelligent Beings, which in the Order of Nature, and the Analogy of Things, is appropriated for the fpiritual World (including the funreme Infinite as it's Head.) T^emonfirat. Tho' this be a necelHuy c/- rollary from the preceding Tropfition^ yet fince it is of great Confequence to true di- vine Knowledge, to have it'^s Truth efta- bhfhed beyond all polFibility of Gafi;//; I fliall here luggeft Ibme other MedmmSj or fet thofe already fuggefted in another Li- mit, from whence the fame Conclujion may be deduced. And i . This is evident from the Nature of this Faculty^ and tlie man- ner of its operating. Reafoning is the com- paring, or the conlidering the congrtiity^ or incongruity of the Perceptions, fuggefted by the Senfes, or of the ideas lodg'd in the Memory, or painted on the Imagination to one another; and Reafon is the Faculty whereby whereby this is performed. Now the Senfes fend in only the Influxes of material Things, and the Imagination and Memory prefenc only their Pidures or Images^ when tlic^ Objefts themfeves are abfent ; and here is all the rational Soul can do. But nothing of thefe belong to ths fupreme and increated Infinite^ nor the fpiritual World. 2. It is acknowledged by all, and every one's Experience demonilrates it to him^ that the rational Soul is fitted for communis eating with the material fVorld, Now fince Body and Spirit are precile and proper Op- pofites, it wouM be as dijfonant and incon- gruous in the Analogy of Things, that the fame Faculty ihouM be the Principle of Communication with thefe two Objeflis fo widely diftant, as that the Eye iliouM both hear and fee. It is true, it may be faid, that the rational Soul might have been ori-= ginally endowed with fuch Energy and Ca- pacity, as to be fitted for communicating \v\x\\both Worlds ; but this is mt^x\^ gratis T^icium^ and per feftly contrary to the Ana- logy of Things; it being impomble to bring an Inftance of Nature, where Things fo widely diftant, and precifely oppofite, are received by one and the fame Facuky. We fee in the Body^ or lowjft part of the hu- man CompofuioQ that it is inftrufted with Organs fitted for all the poiTible Ways, ma- I tCilc.l n w ,■ t^i gt l\ iio i^l^f lorop|)ical id^inciples terial Things can aft upon iL And they are not near fo widely diftant and different in the manner of operating, as Bodies and Spirits in their Natures are. 5. There is a Two-fold Knowledge of material Things, one Realj, when the Thing it felf, and the real Action and Impreffion thereof on our Senfes is perceiv'd : The other iJea/^ when the Image or I^ea of a thing ablent in it Mi] is reprefented to, and confidered on the Imagination :For Inftance, the Heat^ Lights and chearful Influences of the Stm fhining on us, are widely different from -the view and Confideration of its Image^ or Idea on our Fancy. In the Analogy of Things, and according to the conftant Order of Nature^ fuch muft our Knowledge of/piritual Oh]td:s be ; to wit, the one realj when the Objefts make a real Impreflion upon the apfrofriated Faculty ; the other Ideal^ when we frame a Notion ot its abfent Subftance and Qua- lities. Now it is very plain, the rational Soul is not fitted for this firft kind of Knowledge or Perception diffiritual Ob- jefts, fince a great many fhilofofhical and learned yitUy who have exercifed this Fa- culty in its greateft Strength and Vigor^ have deny'd the Exiftence of fuch Objects. 4. Laftly, That moft certain and felf evi- den metafhyfical Axiom ; to wit, that no- thing can be in the Vnderftandingj that was of aHeligiott* III was not firfl in the Senfes^ is a certain Demonflration^ that the rational Soul is not the Faculty in intelligent Beings, appro^ friated to thi^ Jpiritual World ; for every Body allows, that ffiritual Beings, as fuch ^ can never be convey'd, through the bodily Senfes, to the Underftanding. And therefore we muft either be intirely deprived of Fa-* culties, for communicating with ffiritual Beings (that is, we muft be deprived of the only means oi owx fiif rente Felicity^ and for attaining the End, for which alone we were created ; to wit, communicating with the fufreme and abfoltite infinite Sprit.) Orelfe^ we muft be endowM with Faculties diftin^t from the rational Soul for that purpole: Upon all which Accounts it is evident be-» yond the moft remote poflibility of doubt, that the rational Soul is not that Faculty ia compounded intelligenf Beirigs, which in the Order of Nature, and the Analogy of Things^ is apfropiated ibr the fpiritual World: But that they are endowM with 2ira- tionalSoul^ and bodily Senfc, to communicate with the material World, and with a Spirit and divine Senjes'^ to communicate with the fupreme Infinite. So that the mentioned me- taphyfical Axiom continues juft and true, as it fhouM accorciiug to the Analogy of Things: That as material mmgs are conveyed to the rational Soul ^ chioughthe bodily Senfes ^{0 I ffiritual Ill IdftiJofopl^icalt^^tnciples of ^tligim. *ij Jpirituanhings (thofe that relate to /id- freme Infinite) are convey'd through the divine Senfes^ to the Sprit, q. e. d. Corollary I. Hence, in the Analog of Things^ as the Light of the Sun (that noble and' glorious ^ Reprefentationj Image ^ and Vicegerent of thtfufreme Infinite^ in the material World) is the Medium^ through which material Things are feen and perceivM in our Syftem^ fo the ejfential Light of thtjufreme Infinite himfelfj is the fole Medium^ by and through which, his Nature and infinite Perfeftions are to be underftood, and comprehended : And therefore, as certainly as the Sun fends forth his Light on the whole material World without Bounds or Limits, on the Jufty and on the ^njuft ; fo certainly, the Sun of Ri^hteoujhefsj the Tat tern and Ar- chityfe ot our material Sun^, fends forth his enlightening and enlivening Beams on all the Syfiem ot created intelligent Beings ; and is, that Light which enlightens every Man that cometh into the fVorldi Corollary II. Hence it is evident, that he who wou'd / judge, determine^ and purfue the praftical Con- Goncliifions of thefe Determinations, about the Nature and Properties oifpritual and itvine Things J by his Reafon^, wou'd aft as incongruoufly, and contrary to the Ana^ kgy of Nature^ as he who wouM tafte Colours (as fuch) and look into Sounds. The higheft that this Faculty can juftly and congruoufly pretend to in thefe Matters, is from the known, certain, and experienced Nature, and Properties o{ material Things, (to which the rational Faculty is in fome meafure adequate) by a proper Analogy : And from the V'tfible\ being low Images of the invifible^ and Jpiritual ; to frame fimilar^ but iMv^^^ltdiLikenejfeSy and Reprefentations of thefe fuperior Objefts, their Natures and Properties, as we have endeavoured to do in the preceeding Trofofitions y and this really, and in feft, is all that Reafon can do in thefe fublime Matters. Corollary III. IIence, we may difcover the Errors and Impieties of Sfmofa and Hobbes ; and the Millakes of a later Thilofopher^ I mean (the other wife ingenious) Mr. Lock, l^h^firfi of thefe confidered this univerfal Syftem of Things^ as a kind o( 3, Huge-brute-animal^ aftuated by a fatal, neceHary, unintelligent,, undefigning Principle ; without either Wif- Part II. I don* ! b\ f\ III idDil0fopl)ical|d|luciples of laeUgion. iij /piritual Things (thofe that relate to y?/- freme Infinite) are convey'd through the ^iw»^ Senfes^ to the iS]piri^. q. e. d. Corollary I. Hence, in the Analogy of Things^ as the Z/g;^/ of the Sun (that noble and glorious ^ ReprefentatioHj, Image ^ and Vicegerent of t\it Jupreme Infinite^ in the material World) is the Medium^ through which material Things are feen and perceivM in our Syftem^ fo the ejfential Light of xXx'^fufreme Infinite himfelfj is the fole Medium^ by and through which, his Nature and infinite Perfeftions are to be underftood, and comprehended : And therefore, as certainly as the Sun fends forth his Light on the whole material World without Bounds or Limits, on the Juft^ and on the ^njuft ; fo certainly, the Sun of Right eon file fs^ the Tat tern and Ar- chitype oiowv material Sun J fends forth his enlightening and enlivening Beams on all the Syjiem ot created intelligent Beings ; and is, that Light which enlightens every Man that comet h into the World. Corollary IL Hence it is evident, that he who wou'd ^ judge, determine^ and purfue the praftical Con- Gonclufions of thefe Determinations, about the Nature and Properties oijpiritual and divine Things j, by his Reafon^, wou'd aft as incongruoufly, and contrary to the Ana- logy of Nature^ as he who wou'd tafte Colours (as fuch) and look into Sounds. The higheft that this Faculty can juftly and congruoufly pretend to in thefe Matters, is from the known, certain, and experienced Nature, and Properties oi material Things, (to which the rational Faculty is in fome meafure adequate) by a proper Analogy : And from the Vtfihle\ being low Images of the invifible^ and ffiritual ; to frame fimilar^ but imperfeftZ/i^^/^^jT^J*, and Reprefentations of thefe fuperior Objefts, their Natures and Properties, as we have endeavoured to do in the preceeding Vrofofitions y and this really, and in feft, is all that Reafon can da in thele fublime Matters. Corollary IIL IIence, we may difcover the Errors and Impieties of Sfinofa and Hobbes ; and the Millakes of a later Thilofbpher„ I mean (the other wife ingenious) Mr. Lock. Thofirji of thefe confidered this univerfal Syfiem of Things^ as a kind of a Huge-brute-animal^ aftuated by a fatal, neceffary, unintelligent, undefigning Principle ; without either Wif- Part II. I don> ■*# 1 14 |e|)tloCopt)tcai t^imtpies dom or Choice. The fecond confidered human Nature (not as it really is, in its prefent State of Trobation and Turtfication. a Mixture of moral and natural Good and Evil, but) in its diabolical and reprobated Eftate : Not as groaning under its prefent State of Corruption, and waiting and pant- ing /(?r the glorious Liberty of the Sons and Children of God ; but as it will be in an habitual confirm'd Eftate of the Anarchy and Rebellion of its Faculties one againlt another. In a Word, he confidered human Nature only, as it is in the worft of Men ; or as It is fuppofed to be at laftin a State of fnal Impenitence^ and hardenM Impiety; and this he took as his Original to copy after, and his Model^ whereupon he was to frame his human Creature : And it muft be al- lowed he has wrouglit it up to the Life. The third confiderM Man and his Facul- ties ; not indeed in their already reprobated and hellifl) Efiate ; but as he really now is, intheWorId,aComporitionofmoral and na- tural Good and Evil : And this State he has very fairly and juftly reprefented fo far as it goes. But then, either having no Notion, or at leaft no Regard to his loigher Faculties (which in natural and lapfed Man lye buried under the Rubbilh of his prefent Corruptions and Senfuality; ) nor to his regenerated^ red- integratedmd refablijhcd Eftate^ (to which he of Eeligiott. 115 he muft be reftored, before he can reach the Endoi\\\% Being^ No, not fo much as to confider Man as he really is, a faWn^ depraved^ vitiated Crt^tinXj (in which State his lower ^ his rational Faculties are impair- ed ; his higher Faculties in fome meafure obliteratea^ at leaft buried and opprefTed by the Load of prefent Corruption and Senfuality : And all of them in 2l State of Anarchy J, Rebellion, and contrariety one to another.) I fay, from having no Regard to thofe other different real Eftates of human Nature^ his Accounts of its Faculties are lame and imperfect. His Trinciples when apply'd (by himfelf or his Difciples) toSub- jefts (to which Faculties are appropriated, higher than thofe he elicits out of the meer lapfed State of human Nature) of a more elevated Order (fuch as Chriftianity and its holy Myjleries^ Faith j Grace ^ divine Reve- lation and Inspiration^ and the Means of Man's Recovery) debafe thefe into meer heathenijh Morals^ or htman Thilofophy^ and fink the Oeconomy of the whole Wifdom of the GQdhead^ even below the poor Contri- vances and barren Speculations of many of t\\t gentile Sophijis. But thofe who fully underftand the Trinciples j and are convin- ced of the Truth of the Tropofitionsj I have laid down, will eafily perceive the ground of the Errors and Miftakes of thefe three I 2 Setts i ii ii6 i^ pof opt)tcai i^nucipies Setts of Thihfofhers^ and be able to an- fwer their Arguments without my being obliged to detail them. Tropjition XXIIL In the Analogy of Things^ and order of Nature, as the material World is to unlver- fal Sf ace, Its higheft Limit and Boundary, fo is xh^Jpiritual World to tht^fufreme and abfolute Infinite^ the higheft Limit and Boundary of all Things.^ "Demonjirat. This is evident from Lemma I. with Trop. 9. and 17. There is a beau- tiful Analogy and Uniformity running thro' the whole Syftem of Creatures. The V'tjible and the Created are Images of the Invifh ble and of the Increated. The Syftem of intelligent Beings are more exalted, more no- ble, and more immediate Images of the fu- freme Infinite. The Analogy of Things runs quite through the whole Syftem of Crea- tures, up to their original Pattern and Ar- chitype in the divine Nature, in a continu- ed Subordination and Scale^ according to their refpeftive Natures. The material World is an Image of the fpiritual World, as the fftritual World is of the Jufreme Infinite. As infinite Space is the Locus and Boundary of the material World, fo is the fupreme Infinite^ the analogical Locus (in whom of )aeltgton« "7 whom they all live^ move^ and have their Being) and the Omega of all Things, Jpi^ ritual and material. And as Space isfimilar to a fpiritual Subftance, fo is that to the divine Subftance^ therefore, &c. q. e. d. Corollary I. Hence mater iaUnd /piritual Subftances are both of them extended ; for fince the matnial World is to univerfal Space ^ as iht fpiritual World is to the fupreme In- finite ; and fince both Matter and Space are extended, fo alfo muft fpiritual Subftances be : And the divine Vbiquity^ and Omni- frefencCy not virtually only, but fubftan- tially and ejfentially^ makes it not unlikely that there may be, in the divine Subftance^ a Refemblance of Extenfion (fo far asa Refem- blance and Similitude of Subftances can reach, between a relative Infinite^ fuch as univerfal Space \% 2SiAt\\Q fupreme Infinite') but infinitely more pure and perfeft, than that of created Space is, or can be. Corollary IL Yb.>^c^ Matter zvidi Spirit are Oppofites in every other Quality, except in that of Exten- fion ; for fince by Converfion of Ratio' Sy the material"^ ov\d is to tht/pir it ual'^ovld, I 3 ^^ 1 1 8 |i^litlo(opl}tcal i&^mctples; as infinite Space is to the fufreme Infinite ; and fince thefe two laft, to wit, univerfal Space^ and the fufreme Infinite^ are op- pofites in every other Quality, but in a Refemblance of Subftances, and that too, at an abfolutely infinite Diftance, as is evident at firll View ; therefore the other fwo muft be oppofite in every other Quality but Ex- tenfion. For tho' extended Matter be divi- fible by being extended; yet Space is not aftually to be divided, or one part of it feparated from another. Since it is the uni- verfal Locus of, and penetrates all Bodies : And it is in this Senfe, that the Oppofition of thefe two Qualities in Body and Spirit is meant here. Tropofition XXIV. By the Analogy of Things^ and according to the order of Nature, a Spirit is an ex- tended^ penetrable^ alfive^ indivifible^ intel- ligent Subftance. tended, impenetrable fpaffive^ unintelligent j divifible Subftance: And fince by t\\t pre- ceding Corollary^ Matter and Spirit are in every other Quality oppofite, except in that of Extenfion \ therefore in Place of all the Qualities in the "Definition of Matter^ put- t^g their Oppofites, excepting m that of extended of JReligton* 119 extended Subftance, (for Extenfion muft im- ply a Subject) and then a • Spirit will be- come according to the Tropofition, an ex- tended^ penetrable J active] indivifible^ intel- //^^«^ Subftance. I have chofen the Word Intelligent in this, and its oppofite Vnin- telligent in the other Defijiition. To wit, in that of Body^ rather than that of Think- ings becaufe Intelligence is the Source and Principle of Thinkings and exprefTes the whole of all the Faculties oUfpiritual Sub- ftances. Corollary I. Hence, in Refpeftto their Subftances on- ly, a material Subftance is an infinitely condenfed or incraffated fpiritual Subftance: And on the other Hand, 2. Jpiritual ^v\h- ftance is an infinitely rarifyM or refin'd materiafSubftance. As we have it in Ho- ly Writ, there is a natural (or material) Body^ and there is a fpiritual and a glori- fied Body. For fince Matter and Spirit have the Foundation of their Qualities com- mon to both, to wit, an extended Subftance: Since all their other Qualities are > the one, refpedively the Oppofite or Negative of the other. Since rarifying any Qiiality in Bo- dy 2.xm\ Spirit^ is fubtrafting from its In- tenfion and Energy : and theretore an infi- I 4 nite y ^ ,1 I lo iai)t!of opl)!cal l^^moples nite Rarefaftion of a Quality is fubtrafting it intirely ; and there being no mean be- tween Penetrability and Impenetrability^ between Tajfivity and ABivity^ TUvifibility and Indivifibility^ Intelligence znAVnintelli- gencejthty being contrary and oppofite^ there- fore the infinite Rarefeaion of the one Qua- lity is the Pofition of its contrary ; for tho' the finite Subtraction of a negative Qua- lity (admitting no mean) puts nothing, yet the infiniteiy^^/r^^iw of fuch a negative Qua- lity puts the affirmative (thus — 02 x — - = -f o. but — 00 o H 0=4^0) there- fore in Matter J fubtraBing infinitely^ all its pfitive Qualities, or which is the fame, Q^ythQprecedingCorollary') in Matter ^fub^ traping infinitely the negative Qualities of Sprite and then a material Subftance will become 2i/piritual Subftance ; but fince an infinite Rarefaftion of a contrary Quality is the fame with an infinite SubtraBion of that contrary Qiaality, and fince the fame manner of Reafoning holds good in an in- finite Condenfation ofthe Qualities in Spirit : Therefore in Refped of their Subftances only a iWi^/fm/ Subftance, S?r. q,e.d. The Cafe in ftiort, as I conceive it, is thus : A Jpiritual Subftance, when infinitely conden- kd and incrafated, lofes its Qualities of Tenetrabihty, ABivity^ Indtvifibility^ and Intelligence. Thefe being locked up, and as • It of laeltcpion. m it 'WtTtcramftj in this Condenfation of their Subjiratum (or the Subftance in which they effentially inherM,) thus infinitely comfrefs'd. The ABuality (as thtMetafhyficians fpeak) odhok/piritual Qiialities being thus fhut up and imprifon'd, tho' tbm' "Potentiality be aot quite deftroy'd, and thus a cra/s, ex- tended^ impenetrable^ faffive^ divifible^, unin- telligent Subftance is generated, which we call Matter ; but when this Matter thus form 'd of a j^/V/^^eity of this inferior World. Is there not a plain and obvious Image of the EVER-BLESSED-TRINITY IN UNITY, in every Order of Creatures ? In the three Dimenfions of Bodies? In Nature^s never rifmg above the third Dimenfion in her regular Operations, as was fliown in Scho- lium Trop. 1 2 ? In the three infinite Pow- ers of univerfal Sface ? In the three gene- rical Divifions of Objeds ? Matter^ created Sprity Of IReligioti^ ii9 spirit ^ and the Jupreme Infinite in the three Diftinftions and univerfal Trincifles that comprehend the whole of material intelligent Beings? The Faculty^ ObjeEi^ and the Qon^u-* ity or Incongruity between thefe ? The Tro- fane and Ignorant may make a jeft of this ternary Chain, and afcribe it to Chance or Fortune. But the Analogy of things _, and the regular Uniformity in Nature, make it e- vident to a T>emonftration^ that it mufl: have had its Rife in its originalTattern and Archi- type^ the divine Nature. Even the eternal Generation of the fecond Principle in the Godhead^ of ih^firji^ and the eternal Tro- cejflon of the ^A/r/ Principle from t\\tfirji and fecond J comes evidently out of this an-^ dlogical Ternary^ when elevated to its Ori- gin in the divine Nature ; as w^as fhewn in Scholium 2. Trop, ij. And the Impoflibihty of increafing or multiplying the divine and fupreme LifinitudCy even by it felf, fo far as that it is uncapable of Increafe, or Diminu- tion ; as was fhewn in Corollary 7. Trop. 12* piftures forth the ^nity of the divine Na- ture, in thefe three Relations of the whole to the whole. How noble a Reprefentation in created Things, is the univerfal Space of the divine Ubiquity j Infinitude^ and fpiri- tnalNaturel How lively a Pifturein the in- telle£iual Species of things, of Creation^ or of Gods producing the things that be, out of Part IL K the <3 I* 30 iat)Mopt)icai f^zmtiples the things that were not, is that Tropfition demonftrated Corol i 2. Trof. 2 . i+ i+i+ i-hi+ i€gf> xo=ooxo-rzx. or©4-©+©+©+© ^c. X ^=:CD®x^z=r©? The Produc- tion of a Tlant from its Miniature in the Seed ; and of an Animal from an Animalcule^ is an aftonifhing Reprefentation of the Re- furreftion of the Body. Thefe and many fuch Refemblanccs, and Images in Nature, in the fenjible and vijible things, and in the intelleBual Sfectes of things , derived through the Senfcs ; miglit be brought to illii- ftrate and confirm the greatelt Difficulties and moft abftrufe Myfteries of Religion^ and its Thilafipl:fy. So certain and univerfai is the beautiful Analogy of Things^ and fo careful has the kind and boumiful Author of our Beings been, to fupply us with Evidences in our lower Faculties^ and laffed Eftate, of thofe Truths he requires us to believe and receive. Thtfull and commie at Conception and Knowledge of which belong not but to omfuferior Faculties, and to our rejiored and re-eftablijhed Ellate. May we then life the Affiftanccs^ Reafon^ and the di- vine Bounty^ has afforded us, (I may al- mofl: fay, even beyond and out of their na- tural^ Order) for increafing our Faithj cul- tivating and expanding our Juferior FacuU ties^ relcuing us out ot our i>egeneracy and Corrup- of Eelicjion. 13^ i: Corruption^ into the glorious Liberty of the Sons and Children ofGod^ and then, iu his Light we Jhall fee Light ^ Amen. c HAP. III. Of tk VSE of the oy^rithmetkk for Jnfnites. § I.T N arithmetical Progreflion ; in which JL let a denote the firft, v the laft term, X. the Difference, t the Number of Terms, and z the Sum of all the Terms, which in an afcending Progreflion zxe a,a-\-x,a-\-2 x,a-\-^x^ &c. but in a defcending Progref- fion aja — x.a—2 x, a —3 a-, ^c. Having any three of thefe five a, v, x, t. z, you may find the other two by help of thefe two Lemma's. i Lem. I.? v=:a-\-t x—x^hut v=:a—tx+x. Lem. 2.S2^=^X«4->v^when it defcends. I Ihall here only treat of afcending Pro- greflions, judging thofe that defcend as not* properly belonging to the Arithmetick ot Infinites. Now in afcending Progreflions both t and V are infinite. v ^ r r Therefore Corol. iXv^t xlm the Cafe ot .^225:= ^x'S Infinites. And Coroi. 2 K 2 Becaufe 1 31 #Dtt6fopDfcat |&?mctpUg Becaufe Infinites are not all equal, but vary in their Ratio's to one anotlier, as much as fi- nite Quantities do ; therefore to avoid Con- fufion, I fijppofex^^=ooX I=I^-I-^l-t-I+ I + 1 &c. ^ II So fi-om Carol, i. ^ = ^=«» X — = — • X X X -e?r. X X ic 00 yr^ +5?^r. -=iz>z=i , that is, the Sum of all 2 the natural Numbers continued in infinitum is equal to half the Square of Infinite: And here it is to be noted, that in this Cafe only ^--^_-QQXI=ri + I+I + l"i-"I ®^- Examf. 7. Let at^I, then i +1 | +2+ 2 1 +5 +5 1 ^c. — z^ i=r 00 * = to the Square of Infinite. And thus may you find the Ratio between the Sum of any afcending arithmetical Pro- greflion, and the Square ot Infinite ; and note tliat by infinite, is always underlbod Infinite in of Beligtom 3 J in General, or Infinite of the fimpleft Nature and lowefl: Degree, i+i+i+i, €^r. unlefs it be other wife exprefly declared. I Corol. 00 H is the Root of a Square, • ^/ 2X which Square is equal to the Sum of any a- rithmetical Progreffi on afcending 'witnfinitum. Examf. Let =a; 2, thenoo x \ (or an infinite number of I) is the Root of a Square equal to the Sum of t hat Pr o greffion , viz. 1 +3+5 +7 ggf. - I + i + 1 + i SJr. I % VoroL 2. Let a^=: cxd n^v^=^co m. t:= 00 /. Thefe values of a^ v^ t^ being fubfl:itu ted in Lem. 2. will give you 2 ^ — 00 / %con'\-co m ' 00 '- x/ «^+/ ;/ r=oo * X fn-^-fniy or z zzz , and the common Difference x. m 2 n ,as you may /> eafily find^rom Lem. i . Youi|pByexprefsthe Sum-s otherwife, for *u — a V — ^ t:=z' by Lem. i. Therefore X X X v'" — a^ v-f-amizhY Lemma 2d that is ^=: 2 oc 00 ^m^ — 00 V/;/ 00^ xmm nu 2X 2X K 3 Corol. 1 34 i^DflofopDical ia?wciples CoroL ^. From Vrof. i. and Corol. 2. it is evident that in two arithmetical Progreflions having the fame common Difference Xj the Sum of that vi^hofe Terms are infinite, is to the Sum of that, whofe Terms are finite, as nP' — »no r. For the Sum of the tirft, by CoroL 2. is 00 ^ X m^ — «* 5 X the Sum of the other, by Tro^, i. 2 X is 00 ^ X I X. CoroL 4. From hence may be folved this Problem. Any arithmetical ProgreflSon being given as a, a-^x, a-\-7x^ a-h^x^ &c. whofe terms are finite; to find another confifting of infinite Terms, that fliall have the fame Dif- ference Xj and whofe Sum fhall be equal to the Sum of the given Progreffion. Solution, m — «* = I from CoroL 3. ^ ex hypotheji. Therefore ;»* = 1+;^' ; fo to find m and », is an indetermin'd Problem, whofe Solution by the known Methods m = will give mo^ . 2e e — 1' where e is any Number (Ai) taken at Pleafure-^ So then thefe Values of m and n beinp fubflrituted in the Values of ^and t/, of Corol. 2. will give you the firll Term a = ooX -ji — - andthelaft'^;=cox~-- ^ — I' e^ — I and calling the common Difference x^ you will Of Beiiston^ i?5 willhaveaProgreffion, each of whofe Terms is infinite, and whofe Sum fhall be equal to the Sum of any other arithmetical Progreflion, whofe tirft Term is finite^ and the conimon Difference x ; and becaufe e is an arbitrary Number, therefore you have as many of fuch Progreflions as you pleafe^ to anfwer the Troblem. _ ^ Ex amp. Let the given Progrefli on be 1 H- 2 4-04.4+5 ggf. where ;v — 1, fo the Sum thereofis^oo ' x \i:^smEx.i.Trof.i)novi 2 e taking e:=^ij you will liave n^- z=z^ ^c mz=z ^ ^ ja^* i ^ W IT "■"I"'*' 1 .— |j which from the fecond Expreflion oi Corol. 2. will give the Sum of the Series (00 X -t, I +00 4, 2 + cx) I, 3 +~ T, SJO oo^X =,00* X — = 00= Xi, which IS *1 X 2 *V the fame with that of the given Progremon confifting of finite Terms. Schol. The Problem may be made more ge- neral, and the Solution as eafy,.it it were re- quired, that the Sum ot the Series, confiftmg of infinite Terms, fhould be to that ot the o- ther confifting ot finite Terms in any given Ratio of rHo J% for then it muft be to find ♦ X w and «, fuch that «?^-»' K 4 xV.r^-.s^. 'Pro^.. 1^6 iai)i!ofopi)ical la^inaples; of laeltston* 157 Trof. 2. Let all Things be as in Trop. i. except the laft Term, which here we fhall futw pofe v=. 00 », in which Cafe I iay<5;=oo * x Rxamf. I . Let »=2 ,*•— i ; « =1 , fo the Pro- greffion will be i, 2, 3, 4, 5, ^c. till the laft Term be 00 2,1 lay the Sum 1-1-2+34-4+5, tSc. —z—co ' X 2= double the Square of In- finite. §. II. In geometrical Progreflion^ let a de- note the firft, and x; the laft Term, the Ratio of the Terms, that of r to j, / the Number, and z. the Sum of all the Terms of any geo* metrical Progreflion, which will be a. s a s^ a s^ a s* a ' > i » * r r* r' r* Of thefe five Things, 'y/.s. the firft Term«, T the laft Term v, the Ratio of the Terms — , the number ?,and the Sum of the Terms ;s, hav- ing any three, you may find the other two by thefe t\yo Lemma's. ' Lem. 1. 1;— — . r Lem.i ^z-^r^z , ^^ From i ra — sv From Lemma 2d. it follows that Zz=z r — s when the Progreflion afcends, that is^w hen r/^ s. But when the Progreflion defcends, that is, when r>j-, then rrom Lemma II. it will s^ — ra htZ:=i J" — r Cafe 1 '. In defcending Progreflions where the Number of Terms are infinite, the laft Term v will be = o. Trojf. I. In all defcending Progreflion^, whofe Number of Terms are infinite, and firft Term finite, the Sum of the Progreflion is ^ r a\ finite quantity, viz. Zz=z r — J* mnl Corol. I . Let ^ = r, then z = Examf. Let r=iyS=ly then i+l+Hr, 16 r — s Trob. Having the firft Term a^ and the r Ratio of the TermsTofany geometrical Pro- greflion defcending in infimtum^ till v^ -. o to find another Progreflion defcending in i7ij\ni- ^m^whok firft Term fhall be any given num- ber ^ V ^iS^^'. ' I t' 138 ^ftttoCopftical !&?inctpies ber b, and its Sum equal to the Sum of the CTJven Progreflion. ^ r ^ rr* Co/ Let w to « be the Ratio of the Terms r a of the Progrefllon fought ; now is tlie Sum of the given Progreflion, by Trof. i . and m b for the fame reafon — muft be the Sum of the m — « promeflion fought, therefore from the Condi- tion of the Problem fought m — » » r — J (m%ra— rb-^sb whichgives«=; . ^^'l^^f^'^' ^' •''^ are given, and m may be taken at Pleafure ; and fo you have « from this Equation ; and con|- quently the Progrefllon fought is found, loi fpSeflion is fSund, when you have the firft Tei-m ^, and the Ratio of the Temis m to .. Example. Let r— i^s-=^,a^i, t> ---■,, I affume^-l C-^) ^ the Eq^tion^wdl give »— i, therefore i+i+4-rT «''^- —r-r-^ t '' And here it is to be noted that fince m is taken at Pleafure, the Problem is indetermi- ned and fo you may find as many Progrelli- ons'as you pleafe, 4ofe Sum M be equal to the Sum of any given Progreffion. ^^^^^^ of iEleUgtotu ^39 Schol, The Problem will be more general if it be required that the Sum of the given Pro- r a grefTion be to the Sum of the Progrefli- r — J" m b on fought in any given Ratio h to kvtz^ ra m — n mb : : h\k^ which gives ^ = r— J" m — ;/ m%(i rk-^b hs '—b h r where m is at Plea- fure. a k r Cafe 11. In afcending Progrellions, whole number of Terms are infinite, the laft Term V will be nr 00 X e* ; but firft I lliall confider thefe Progreflions in which ^ = i, that is, where the laft Term is an infinite Number of Units. s sv ( =z: ) for r a yrdl!j< '/' 140 01)itofopt)ti;al ^mtiplts s This being premifed, it is ey ident that — is s — r the infinitely fmall and equal part, of which an infinite Number gives the Sum of any geo- metrical Progreflion afcending in infinitum, Examf. I. Let r=ziy j = 3, then =r J. — r l^ which (hews z~ 00 x i, that is i +3 + 9+ 27 + 81 ?^r. —z^i^L+^^c. s Examp. 2. Let rzri, j = i, fo - — = 3^ J" — r Ergo iS cr 00 X 3, that is, i+^-H^-ris !S^r. = 34-3 +-3 -H3 ®^. "Problem. TofindaProgrefTion^which fhall have any given Number {a) for the equal Part of which its Sum confifts. Solution. Letr be the firft^ and s the fecond Term of the Pro- s greflion fought, then (becaufe is the e- qua! Part for ev^ry Progreflion) = a which gives /:=; s — r r a — — , fo taking the firft Term r at Pleafure, a — I the fecond fliall be r a of Religion. 141 a Examf Examf. To find a Progreflion whofe Sum ftiall be = cxj X 2. In this Cafe a zn 2, fo'ta- ra king ^rzi, it win give = 2 whichftiews a — I that the Sum of a Progreflion,whofe firftTerm is I, and fecond Term is 2 = 00 2, or i+2-|- 4+9 S^f. =2+2+2-1-2 &C. Scholium. Becaufe r is taken at Pleafure, therefore you may find as many Progreflions as you pleafe, whofe Sums fhall be all equal, becaufe each of them is =r 00 X a. Trob, 2. Having any Progreflion afcend^ ing, to find another whofe Sum fhall be equal to the Sum of the given one. Let r be the firfl, s the fecond Term of the given Progref- fion ; and m the firfl:^ n the fecond Term of s the Progreffion fought, then 00 X — — is the s — r m Sum of the given one, and 00 X is the m — n Sum of the Progreffion fought, Ergo 00 X s m = oqX J s — r m — n s m T m or ' =r ^ which gives »=■ ^m may s — r m — n s be taken at Pleafure, and foyou have n. H 1 41 fai)tlof0pt)tcai Wndplm SchoL So may you find a Progreflion, whofe Sum ftiall be to the Sum of the given one, in m- s any given Ratio h to kj for then — 1 m — n S'—r h\k\ {o that n =: m%s hy^rk — sk s h §. III. Before I proceed to other Progreffions it will be neceffary to fubjoin fome Things, which were omitted in§ I. concerning arith- metical Progreflion, and which fliould have immediately preceeded § 2 . I Lemma, z =00 ^ X — ,wIient;zz:oo x i . by 2 X Trop. I. of § I. Trob. Having the common Difference at, and the laft Term t/nr 00 x i of any arithmetical Progreflion afcending in infinitum ; to finda- nother arithmetical Progreflion, whofe Sum fhallbe equal to the Sum of the given one. Let e be the common Difference, 00 X » the laft, and J the Sum of all the Terms of the nn Progreflion fought; then j = 00^. x — : by 2e I jPr^/. 2. of § I .Now htQ2iMkz:=zoo * X — is the 2X Sum of the given Progreflion, therefore from 2 tl>e of aaeiigtdn^ M-5 the Condition of the Problem nn -, fo e 'X 2X 2e n n ; you may take n at Pleafure, and fo you have e and confequentlytheProgreflionfought. ExafHp. 1. Let the given Progreflion be i, 2, 3, 4, 5,®f.to 00 +1, where x:=.i^ fo e^n n\ calling » =2, you have ^=4 for the com- mon Difference of the Progreflion Ibught, viz^ I, 5, 9, 15, ^f to 00 X 2. I fay then that the Sums of thefe t wo Progreflions are equaL Corol. n =' — fo taking e at pleafure you ^/ X have », as in the former Example^if you call Bj 2, then //=r>v/2, fo the Progreflion foi^ht is, I) 3> % l-i ®^- to 00 X V 2, whofe Sum (hall be equal to i+2+3+$+6 ^c. to 00 X i. So that in folving this Problem, you may ei- ther make the common Difference, or the infi- nitely fmall Part (//) of the laft Term, what you pleafe ; and becaule one of the two may be taken at Pleafure, therefore the Problem is indetermined, and confequently you may find as many Progreffions as you pleafe, whofe Sums ftiall each of them be equal to the Sum of the given Progreffion. Scholium, in the lame Manner you may find as many Progreffions as you pleafe, the Sum of each of which ftiall be to the Sum of the gi- ven one in any given Ratio of i& to h ; for then ;/ // .Ju- ♦ H ■ 144 |^Daofop{)tcal ^inttpks 2 e t a X lik\h^ which gives kez=ihx H^ '^{o that of thefe two ( e^fi) taking one at Pleafurcj you have the other from this Equation. Problem. 2. Having the Surn oo^xq of any Progreflion, to find another that fhall have a given common Difference e^ and whofe Sum Jliall be equal to the given Sum* Let c3o X ». be the laft Term of the Progreffion fought, then its Sum wll be=oo * X — ; therefore by the 2 6 Condition of the Problem — =q, fo that n — 2 e sj leq : but, Sff. Ihould be equal to -^^ or half the Square of Infinite, as it appears by Ex. I . of Trop. I . of § I . And yet the lame Sum is — 00' or the whole Square of Infinite, as appears by Art. id. of Cafe i. of the hA Lemma. Thisfeeming Contradiftion may be reconciled, if we fuppofe 00 x i to be the laft Term in the Progreflion of Ex. I. Trof. I. § I. which will make the Sum ~ ; and 00 X v'a to be the laft Term in the Progreffion of Art. id. of Cafe i. of the laft Lemma ; for that will make the Sum of the PTo^relfion = oo% as appears by Ex. i. of Trob. 2. § 5. So that tho' it be the fame Progreflion going on in infinitum^ yet the one goes on to a greater Infinite, viz. 00 x ^/■2 than the other which ends at 00 X i. Bu T the plain way of reconciling the Matter depends on the common Rules of Multiplica- tion. i+2-j-3-j-4-f 5 ^^- == =2 = •I I I — I but —-=1 + I -f I 4- 1 ®r. and there fore i - f 2 -fg-f 4+$ ^c . — i -j- i -f i Let us now make an adual Multiplicati- on of fix Terms only, thus 1+ of ^antsottt* mmm i+i+i+i+i-f-i From the Procefs It is evident, that add- ing the feveral Columns, their Sums make I, 2^ 9, 4, 5, 6. which is the greateft, viz. B C (trom which they defcend in the fame Or- der to 2)) tnd this BC is always the Number of Units in each Faftor ; fo that if the Number of Units, multiplied into it felf, had been tqop^ then B C the laft Term of the Progreffion af- cending from -^^ would have been 1000 ; and confequently if the Number of Units, multi- plied into it felf,^ had beenco X ij then BC the laft Term of the Progreffion would have been 00 X i. Now the Progreffion defcends from BC to 2) in the fame Order as it afcends from Ato B C y but JIB C is the Sum of the Progreffion i, 2, 5, 4, 5, 6, ^c. ending at 5 C = 00 X i ; and this Sum AB C is but half the Produd (of which BCT> is the other) that is to fay, half the Square of Infinite : Thus you fee that the Procefs . L 4 of 1 51 |^!niofopt)tt:al i^iindples oiArt.'i. of Cafe I. agrees exaftly with that of Trof. i. of ^ i. 'only that oi Art. 2. Cafe I. gives you the ProgrefTion twice over, and fo makes it double of what it is in Ex. i . 'Pfop. I. § I. Schol. Fiom this Solution it appears that the Suna of the Progreflion vaArt. 3. Cafe r. viz. i-f 2+3+6-j-io-f 2i,C?r. is notpre- cifely 00? or the Cube of Infinite for -^— X I — I I — 1 ' + '+' + 1 ^C' X I-i-I+ ^\t^c. X I + 1 + 1 -f- 1 e?f. contains that Progreflion oftner than once ; and the feme Js to be confidered in all the Pitgteflions, except when e=i. § VI. Tlie Arithmetick^of Infinites appli- ed to Quadratures of curvilinear Spaces. Let 2)Z./'be a- c i»« ny of the Hjmer- bola's,whofe Alym- ptots are AC^AH^ let AK=x,KL—yj ^ and the Equation comprehending all the Hyperbola's j *"= 1. By of Ecugton* 153 By the commonr^ .j^,_. i ^ • Methods, Y ^ '^I'Z:^ ^^'~' And alfo HAGLF= ft n — I Xa;'-»' Carol. I. Let A- = I J then CAKUD= and HAG L F I— », Cafe I. Let. » — !, fo the Equation willbe^A? = I for the common Hyperbola^ in which CAKLT>. i=r =1 + 1 + 1, 5^C. =r I — I 00 X I. = 1 + And like wife HAGLF = ~ I +1 +1^ ^c. = 00 X I. From whence it appears, that the Area of the Apollonian Hyperbola is infinite both ways. Cafe. 2 . Let n—7 ; fojy a;^ =i defines the next Hyperbola in which CAKUD—-^—\^ 2+ 4 + 8 + 16, C^f.= C30 X 2. Cafe general. If you refolve into aSeries, I — n you wiirhave CAKUD= = i-\-ny.n^ i—n -H^3+»4+»T^ ^c. and becaufe the Terms of this Series are in a geometrical ProgreflTion af- cending (fuppofing « < i ( in the Ratio of i to », there- "mm i IdlKlof 0{^tcal !^;nt{tdplr$ ot iaeitgtoiu ii therefore by Trojf.i. §. 2. the Sum thereof muft be I +» -t- »*+»' + «* + «S ®^' Now becaufe«<;i, therefore— ^ is < i ; therefore in aU thefe Hyperbola's (in which n ftood the meaning of the Geometers, who call thefe Spaces greater thian infinite, that is,; greater than oo X i or infinite in general. CoroL 3. In all the Hyperbola's (except the ApUoniati) the infinite Area CAKUD (adja- cent to the Afymptote AC^ is equal to an infi- nite Number of the finiteArea/Z^GLF) adja- cent to the Afymptote AH) in the fame Hy- perbola. n ^DemonftratitmCAKUD^oo x^— ''ythe n general Cafe, but HAGLF—-^\>^ Corol. I. § 6. Therefore ^CAKUD- 00 X HAGlA ^ E. T>. Troblem. Let 00 X ^ be the infinite Area CAKUD of any given Hyperbola, it is requi- red to find another Hyperbola, whofe infinite I Space ^5$ Space fhall be to the Space (00 x e) of the siven Hyperbola in any given Ratio, as of /> to i Sol Let y a;"^. , be the Equation of the Hyper-' bola fought,then by the generalCafe foregoing its Area is= «> X ~ ; therefore by the Con- dition of the Problem, ^. .; ;^. , . ^y,,, will give »—-^-£j;fothatj^7rr7 _. ^ is theEquation-to-theHyperbolafought; but / and ^ are given Numbers, and therefore this IS a known Equation, and confequently the Hyoerbola defined by it is alfo known Examj>. To find an Hyperbola whofe Area Ihall be to that of the Apollonian, as 2 to i NowtheApollonianis = a> xi.fo^li,and T=^yErgotht Equation isyxi.=j^ whofe Area by the general Cafe foregoing is=.oo x 3, which is triple of the Apollonian. Trob 2 To find an Hyperbola, whofe inter- minated Space HKLF {hall be equal to any givenNumber(«)letjVA;»=idefinethe Hyper, bola fought, where « < i, then HAGLF — n -_j puttingjy = I {=GL-GA. ) by Corol. ''^•ttl*^"ife"i^ ^GZ-iT^i, therefore it will be HAGLF— 4GLK(^^HKLE)~ irj — I • Therefore by the Condition of the Problem n 1 56 01)tlofopf)tt:al ^nmiplts Ji fe /)• 4tf Problem ; —1=^. which gives n a fo the Equation to the Hyperbola fought is • XI Let (as before) AC,C ^//betheAfymptotes of any Hyperbola©!, ^defined by this Equa- tion J' x-= I, in wluchC the Abfciffa^^^**, and Ordinate KL = ^, ^ and « is fuppos'd either equal to, or greater than Unity, i ' It appears that in all Hyperbola's the interminate Space CAKUD is infinite, and the interminate Space HAGLF (except in the Afollonian where » = 1) is finite. 2". In every Hyperbola, one part of it continually approaches nearer and nearer to the Afymptote A C, and the other part continually nearer to the other Afymp- tote A H; that is, L © meets with yK. at a Point infinitely diftant from/4 , and LF meets with AH At a. Point infinitely diftant from A. 3 ". In two different «-' \d. Hyperbola's 'DZ-F,*// /jifwefuppofeatobe greater in the Equati- on of dlfthsn it is in ^ the Equation of 2)Z/i% ^ then L T) fhall meet q^ fooner witli A C than • •iiiiintK.i*; ll. u of aacligton* IV Id with a c, but Z/lhall be longer in meet- ing with A H than //with a h. Therefore fince thefe Meetings are at infinite Diftance trom -^and «, it follows neceffarily that thefe infinite Diftances muft be one greater than another, viz. ac AH- and m the fame Hyperbola AC <: A Hand. »c meets with the Afymptote ^C,and the Point -« where L i^ meets with the Afymptote A H, for any Hyperbola T>LF, whofe Equa- tion y xn — lis given. ^ Solution. It is evident that the Ordinates L K ^~y =^) increafeas the AbfciiTa's ^Ar(= X) decreale, fo the laft Ordinate muft co-incide with tlie Afymptote AC, in which Cafe the Abicifla Jf =r o =ri _ I. Therefore A C— • I — l|« x' ^ Exam^. I . To find AC in the common Hy- J>erbola 4 h ■ ■• 15& jaMlofoplXcai^jmrtpies I ferhUy = — .Becaufe in this »=i, therefore ^C =-^ = (by ^rf.i.of§ 5)1+1+1+1* I — I ^C. =00 X !• Examf. 2. To find A C in the Hyperbola whofeEquationis^=— . Becaufe in this n X z=z 2, therefore from the general Solution A C I -^=j 2 = I+2+3+4+5+6j ®r. r:=: I a ; That is, ^ C is an infinite Number of equal Parts, each of which is 00 | : So that A Cin this is an infinite Number of equal Parts, each of which is \ AC in the common Hy- perbola. Schol. If we could give the precife Sum of the Series in Art. 5, 4^ ®r. oiCafe i.of § 5, we fhould then have AC for all the other Hyperbola's; but thatisnoteafily to bedone^ as is declared in the Scholium at the End of § 5. Only this much we fee (by Caje 4. of § 5.) That A C increafes as the Powers of 00 whofe Exponents are n. So in the Hyperbola jr = — , ^ C is as 00 ; in the Hyperbola^ = _ , AC is as 00 * in the Hyperbola jv =— , A JX ** C is 00 ' ; and fo onr Tart^ t/t 3ReHgton. M> ^arf. U To find ^/^when L F meets with Its Afymptote ^H. Here wPmnAl fiderGZ il.U theOrdina;," d 1:7- ^as the AbfcilTa Now when GZ b1co4« ^//,thenjy=o. But univerfally GL{~x) ~ "^ therefore A H ~=-zz ^~2l^.^ put T » — e^ and then by Lent, of § 5. ^^_ 2x3 Ij+li = g Xf+i Xg-f-2Xg-f-3> ®r 2x3x4 Butfince we cannot afligntheSum ofthele ProgrefTions, therefore this Series is of no Ufe in the Solution of the Problem. We ftiall there- fore confider the Problem (as to the finding AH) under two Cafes, firft Vhen n is an In° teger, and fecondly when it is a Fraftion. Cafe I. When »is an Integer. Soif»— 1 (as in the common Hyperbola) then AH(^ =-i_ ~ I-{-l-hI, C^f . = CO X l=^C If»— 2 then AH(^=^ = 1^ v.i. =-/ ^TTT) is a mean proportional between i and infinite. If » =r 3,then AH(,- =^ i. .- ]J~~ i-ij 1-1 I ^V' oar *mt *i U 'i '' if! 1 60 i^iiilofotAXtal {^nplrs Ji V C30 X I is the firft of two mean Proportionals between i and Infinite. And univerfally if be- tween I and Infinite there be fuppofed as many mean Proportionals as there are Units in»-i. n c then A Hi- ==^= -^7~ = /oo X O fliall be the firft of thefe Means. Cafe 2d. When «isa Fradion, fuppofe»=: J- ' but/<; 3^, becaufe we always fuppofe n^/f=Vcx) Xi| Or^/. From both thefe Cafes it is evident, that the greater Number we fuppofe n to be,fo much the fooner will LF meet with AH\ for the greater we fuppofe n to be, fo much the lefs will -or(Mbe;but ~(or ^) is the Expo- nent or (or 00 ) which gives the Value \ — I of AH. Ergo the greater that n is, the fhorter will AH\>q. ^ E. U. 1 SchoU of Beltgton. Idl Schol. Since in all Hyperbola's AH— -I 1 I — I » ~ i^Ti I ~ ^i — I h = Vcjo X I 1^ is ibme mean Proportional between i and oo x i,itis worth the while to confider what fort ofiSFum- bers thefe means are, w-s. whether they be fi- nite, infinite, or neither. It is certain they cannot be finite, for then it would follow that theSquare of a finiteNumber fhould be infinite which is abfurd. Nor can they be properly efteemed infinite, for the equal part of fuch an Infinite muft be i divided by fuch a mean. "Demon. Ltt a denote that equal part, then CO X^=:V""ool , which give a^zj—fz^ ^ V I ^EfDSJEx.gra^^/ cx) x lora mean between I I and infinite muft be oo x — or an infinite Vcx) Number of equal Parts, each of which is or I divided by the mean between i and oo X i So that this equal part is neither finite nor infinitely fmall, nor infinitely great, and confequentlythemeanVoo x^i is not proper- ly an infinite Number.^Andhecce we fee that Part IL M there Voo I 1 6z |gpolopl)tcai ^2tttttples there areProgreflions of Numbers whofe Sums are neither finite nor infinite,but betweenboth. Ex.gra.^oo X I where/ =2, j^r^i ,fo Voo x i =1-14-1+5+^; 4-xTt Sfr.isaNum- I — 1| bcr neither finite nor infinite : And fo all the means between i and Infinite, are neither fi- nite nor infinite. I have hitherto confiderM only thefe Cafes in which «— or<: i ; let us now fee what would be the Refult if we fuppofe ;/ :::i ^ . It is evident then that the general Equmon^viz. ypc^=: i to ail Hyperbola's would in this Cafe bejy = i , fo tliat the Hyperbola's will in this Cafe degene- rate into a fl:rait Line ©L /% parallel to AH.Bnt confider- ing it as the fimpleft Hyper- bola, let us confider at what diihnce it will meet with its ^ Afymptotes. Now univerfally-^C^r K I H X n by the *y^/ of part. i.okTrob.'^.^ when x -c, but Hziio by Suppofition : iBr^(7, be a: what it will, Xo::^iyErgo^ AC—i^ 2°. From the Solution of part 2. of Trob. 3. we have found that =1-1 which in this Cafe will give AH= 1 — 1|» I — IIZT or the infinite Power of infinite. Co- of Beiijpon. Corol. i.Confidering a fl:rait Line as an Hy- perbola, it can have but one Afymptote, viz. AH^ whofe Concurfe with AH\^2X greater Diftance from A than any other Hyperbola whatfoever. Corol. 2. All the Hyperbola'sjv at-— r whol^ Afymptotes are AC, AH mufl: interfeft 2) F^ and the greater » is, fo much the more they bend towards ^dTi/and recede from ©F; and as they all interfefl: 2)i% fo they all interfe£t one another in one Point only ; and afiier the Interfeftion, that, in which n is greateft, ftill falls loweft or approaches neareft to AH. Schol. If you fuppofe n infinitely great, w^. »= ~Zr'^ ^^^^ ^^ Hyperbola will be a ftrait Line parallel to the Afymptote AC SeB. 7. We have now finiihed this Bufmels oftheHyperbola's which has afforded us a new Speculation of Numbers, viz. of fuch as are neither finite nor infinite, \\ hich defer ves to be confiderM better than either my Time or my Capacity will permit. However^ I Ihali here fet down a few thoughts about them, till I have more leifure to profecute them. Firji then, todifl:inguifli them from finite and infinite^ I fliall call them indefinite Num- bers, and denote them by this Sign a* 1^. Indefinite Numbers 1 fuppofe to be inter- mediate Numbers lying between fii ite and in- finite : For as we do not defcend. from 1 to o M 2 at 1 ht 1 64 laiHlof opl)tcal |&?tnoptes at one Step, but muft pais through an infinite Series of Fradtions, |, j, ^, ; , &c. So it is impoflible that in afcending from i to 00 ,we Ihould pafs immediately from finite to infinite ; therefore theSteps between thefe two are inde- finite Numbers ; thus before we arrive from i to 00 1, we muft come at Voo i^ and before we comeat^^co X i wemuftfirft come at Voo X i and fo on. 5°. The Rules for the Arithmetick of Inde- finites may be made afi:er the fame manner as is done for that of infinites by D. Chyne. To which I fliall add, that an Indefinite as 00^ or VoD I multiplied by another Indefinite as od I— makes theProduft"SlX-f--l thisProduQ: be- comes infinite when it happens that <7 J + /r ps. And if an inde- finite as oo| J. be divided by another inde- finite as 00 [_i- , the Quotient °o^J- is infinite when qs — fr is <: or z=ps ; but it is finite when ^j — ^/r = Oj and indefi- nite when qs — fv^^fs. Note^ That in exprefling an indefinite Number by<»|JL, I always fuppofe the Nume- of dKeMgion^ 16 s Numerator q lefs than the Denominator/ • for if q be either <: or =/, then 65" ji_, is an Infinite. That thefe Numbers ar J not inhnite, may be thus demonftrated. If Ux. gr^ Voo X I were infinite, then oo X - ^ - V 00 i—y/oo X i) mufl: be infinite, and alfo= V CO muft be = o; Ergo oo X o zz: oo x -— — . Voo V= V oo) = infinite, but oo X o = i : Er- go I = infinite, which is abfurd. SeB. 8, Containing fome mifcellaneous 1 hmgs relatmg to infinites. Lem.'L^tFBT>de be a Logarithmick Curve whole firft Or- dinate AB — i^ Ah'f d: ^ fciifa AC — X, Ordi^ J=f nate C 2) -jy^ and A- fymptote E e : Now from the known Pro- perty of this Curve, it follows, 1°. That ^C are the Logarithms of C2? /. e. If you make the Ordinate y — CT> re- prefent a Number, then its Abfciffa x (=^C) Ihall be the Logarithm thereof. 2^ That the Logarithm of i is nothing ; for Ma ^ the ai i • 166 0DilofopDtcai l&nnciplts of ^Religion. 167 the firft Ordinate ABz=zi^ but its Abfcillais =0, therefore (by 1°) theLog.of i=:o. ?*'. That the Ordinatesr^/ (to the left of jiB) denoting FraQ:ions, their refpeftive Ab- fciffa's A c are the Logarithms of thefe Fra£ti- ons : So that as x is the Log.of any Integer, C© in the like manner — x denotffs the Log. of any Fraftion (c d). 4^. That the Log. of any Fraftion-?- is e- qual to— Log. of n. So that the Log. of any Fraftion (whole Numerator is 1) is equal in Magnitude to the Log.of that wholeNumber, which is the Denominator ; there being no Difference between theLog.of that Fraftion 11 and the Log. of this Integer », but that this is ■4-^(becaule it lies to the right from^towards E) and the other — x becaufe it lies to the left from A towards e. I "Demonjlration. — fignifiesi divided by », therefore by the Rules of Divifion /; i — /; «z=Log, of the Quotient, viz. I: — . But /.• 1=0 (by 2°) Ergo— I: n=: I: -i. ^£. 2). 5*"- If this Curve be continued {utrinque) from B minfinitumy then f will me^t with the Alymptoteat an infinite Difta nee Ae: But it will will diverge from the Afymptote on the other fide,fo that at an infinite Di(tance-^^£' the laft Ordinate E F will be infinite. And fince the ^aft Ordinate ^/is=o,whofe Abfcilfa Ae= oo. It is evident that the Log.of ois= oo or rather rr: — 00 : It is evident likewife the laft Ordinate EF is = 00, whofe AbfcifTa AE is alfozir oo. So that the Log. of o and the Log. of cc are equal, only the one is+- oo and the other — oo . I Trof. I. — = 00 = I -f- 1 +i-f-i+f ^ ^c. This may feem abfurd, but theDemonftration is evident from the (orcmmgLemma.For — - = — . Let then =y.That is i— il — -^* o I — I Thisred ucMto a logarithmicalEquation gives — I x/: i — i = /:j;thatis — i x/:o =l:jy. But /: o = — 00 (by Arf. 5. of the Lem.) Ergo — I X — CO l:y^ that is-f-oo— l:y. There- fore jy is infinite {/c\y ^ 00) for noNumber has an affirmative and infinite Logarithm, except an infinite Number. Since then^= 00, then 1 — I o ^^ iyjW. But by o cannot be underftood abfb- lute nothing, for an infinite Number of abfo- lute Nothings cannot make i ; but bye is un- derftood an infinitely fmall part, as in tht calc. U 4 dif. i. If 1(58 0poropt)tcai ^?mt\pug Hiff. ^ AT is an infinitely fmall part of ;v, fo that d A* is as c to x:Not that dx is abfolutely nothings for it is divifible into an infinite Number of Parts, each of which is ddx. And therefore the Demonftration jwhich fuppofing/and e meet- ing at an infinite Difl:ance Ae^ makes the lafl: Ordinate f/=o,implies no more but tliat ^/= dxMvLt then it maybe inquirM what is theQuo- dent that a riles from theDivifionof i byabfo- lute Nothing J fay there is noQuotient becaufe there is no Divifion : Therefore it is aMifiake to fay.the Quotient is i or Unity undivided, which is demonftrably falfe,neither is theQiio- tient = o. For properly fpeaking therc is no Quotient, and therefore it is an Error to aflign any. In like manner, it is an Error to fajr, that o%a makes the Produft o ; for properly fpeak- ing there is no Produd. It is true, this of Multiplication has no influence upon Pra- £tice, but that of Divifion has. From hence it appears, tliat a Curve is fkid to meet with its Afymptote, when the Ordinate is infinitely little. of JEleUgton* 169 This This feme Notion does explain how it comes to pafs that i divided by a negative IN umber gives a Quotient greater than infi- mte. For if (when you call L M-x, KL=y ) fe~dx tiien becaufe the Points /and e are mhni tely near,we may conceive the Logarith- mick Curve continued as interfefting AHin the Point e ; fo that FBf^f^ £2 F2 G makes but one continued Curve, whereof the Part above reprefents the affirmative Numbers by its Ordinates, and the neeative xNumbers ar^ i^eprefented by the Ordinates of the Part below; but ^is the Beginning i^ i^'pj^' the Logarithms of both, vil ^^2 ^//,(5f. are the Logarithms ofthe affir- mativelntegers/^, Gff, ^c.Ac the Loga- rithm of any affirmative Fraftion, Ae the Logarithm of an infinitely little Fradion fe ^ dx. A 2 AA2 E, &c. Vhe Logarithms of the negative Numbers, 2A2B^2E2F &c Now let n be any Number greater thanUni- ty,tlien i~n will be a negative Number let US I 0DiMop})tcai i^nndplrs; ot Beitsion. us now fee what the Quotient of— -will be, I — n let it be^jfo-^-J,'-^- ,-M-=7,this reducMtoa logarithmic Equation^ Equation ^^^ut"!— « is a negative Number, fuppofe (ex ir^ of 2 ^ 2^, then AzA is = ^: »-»» ^.and^e^-oojtherefore^a^*^--*^. Let then A^A=- co % a (where «<: i) then — I X - 00 /» = /: J*, that is oo X « =/• j., but CO X.* <», £'X^J'« a Number creater than infinite. ^ And here it is obfervable, that there are affirmative Numbers lefs than nothmg, de- noted by the ft veral Powers of ^ IhTik. ixK fSc. or by the fecond, third, ®f. Ditte- rences, and theft Numbers may be aptly re- prefented by the Ordinates of the bgarith- mick Curve, c°""""5d f-'^?' ■>" ^^^''t ids when d:f is affirmative, or from 2 /towards i^when ^ AT* is negative. ■ Another way oi explaining what is meant by — = 00- o Let/4//"produ- \ ced indefinitely be }~^ S1X'°^?, C2), -DE, ®.. fo that a Pa. of this Llae tall denote any Number, fuppj^ X 171 fing ^5=1, let then x denote any Number, (ex.gr.) Letx=AB. 2sAy—Ab. fo — L_— y—x I X _ X-^ Ar3 A"f c^ Now fuppofe b ixifiaitely near to B^ thenj-Ar — Bb — dx^{o that -i_ _ J_. But at — J' — X ax dx-{-dx-\-dx, &c. That is i x x=:dx x l+i +1-H1, e^f. And therefore-i-_-l. . J_ . dx x~^x~^ ^H-— ®^- But by Suppofition x~4B =1. Ergo^ ^i+j+i+i, e^f. = CO X r. But -I-=i-t-i-f-i4-i^g?f.£y^<,^__ I ^^ o o ^^ <^ Jc= o, but dxxs not abfolute nothing, and therefore when we fay -L=:i4-i-f-i_^ ^c. o does not denote abfolute nothing, but onlv dx or an infinitely fmall part of a-. And there- fore when (in the Qiiotient -i— ) we fay let y — X y—x^ the meaning is not that jy is abfolutely '^rirf~^'^^ I ^^ual to X, (for then there would be no Divi- fion,andconfequently no Quotient) but only that jy exceeds x by an infinitely fmallQuantity dx, which is fufficient to make them equal. I have 1 71 ^i)tlof opDttai Wntiplts I have hitherto confidered no Progreflions of Numbers except tliefe that are in arithme- tical and geometrical Progreflions, and thefe I thatarife from ==| e as in § 5. I fliall now I— 1| proceed to treat of other ProgrefTions, and thefe, which offer themfelves firft,are the fe- deral Powers of Numbers in an arithmetical jProgreflion. Let then z> denote the Sum of any arithmetical Progreflion a^a-^-x, tf-f-2^, a-^^Xj a-i^/^Xj ^c. A the Sum of their Squares, B the Sum of their Cubes, C the Sum of their Biquadrates, (^c. that is, let -f- (^4-4 at) Sg)^^ 4^X\- &C. ^ 3 And fo on to higher Powers. Now in or- der to find the Sum of any of thefe Progrelfi- ons afcending till the laft Term is— 00 X i, I Ihall premife thefe following Z.r;»;^?^'s, by the Help whereof you may find ^, A^ B^ C, ^c. for any Number of Terms. Calling therefore t the Number of Terms in each Series, and 'v the laft Term of the firft whofe Sum is z. I fay xi^ X XV "{^ ax — a2 Lem. I. ;s z= Y ^^ 2 X Lem, of ^aeltgimi* 175 3« Lem. 3. B: 4 w IPX? A — 10 x^ B In each ot'which fx—v+x-'aQyv Lem. j f I.) and it is eafy to continue thefe Zmza^'c lor higher Powers. Before we apply thefe Lemma's to the finding the Sum of any Progreflion whofe laft Term IS infinite, it will be necelfary to fubftitute the Values of ^ ^, A, B, C, &c. When you have made this Subftitution, you muft rejed out of the Lemma's every Term in which v does not occur ; tor the laft Term being infinite will make -z/ an indefinite Number, and fmce all the other Terms (in which v is not) are finite therefore they are as not' ing in Refpeft of V, and confequently to be rejefted. So, for Progreflions whofe laft Term is = ex. , the Lemmas will be. V'' j-xv Lem. I. z=: • Lem. 7. A=z- 2 a; Z/J — AT* V V' X V 3 X Lsw, rl 1 '1 i 174 Wlofopl)icai!&?tnrtples Lem. 3. -B = 4 X V^ 1 5 X;4 ^ 1 ox V^ — 59 AT^ V Lem. 4. C= — ^ $x 90 Let us now confider what the Value of 1; is, in each of the Lemmd*s Aj Bj C, S?( . An Example or two will make the Thing plain. Ex. 1. Let Cr, 2, 3, 4, 5, ®r. to v^ ^whofe Sum is z. Then for L^w.s.S 1,4, 9, 16,25, ©r.to^s ^whofe Sum is ji. But t;*=cx)(by&//.) Therefore ^=rV 00 ="ob!l fo that c3o| is the Value oft; in Lem. 2d. In like manner Voo or 00^ is the Value of V in Z/^w. 3. And univerfally if ^ denote the Exponent of the Power to which each of the Terms of any arithmetical Progrefll- 2 I on is raifed, then v=^oo — ^'^. in the Lemma that gives the Sum of thefe Terms (whole laft is 00 ) vaifed to this Power. Trof. I . To find the Sum of a Series of Numbers (continued till the laft Term is 00) whofe Terms are the Squares of any arith- metical JProgreflion. . ^3 — x^ V By Lem. 2. the Sum fought is Az=z — 3X t;* of meitgiom 175 V^ — XV J but in this Cafe v ~ y'oo or 00 1» therefore all theTerms except the higheft muft evanilli, and confequently the Sum of the t;l CX)||3 00 1 oof ^x Squares ^=r z=z' =: — ^i=r ooX ^x 3Ar ^x Examp. Let a; be = i^ fo i, 2, 3, 4^&c. to Voo is the arithmetical Progreffion, the Sum (^) of whofe Squares is fought ; I fey i-f4f9-f-i6 S?r. 00 xjVo^, that is, the Sum of the Progreffion is an infinite Num- ber of equal Parts, each of which is fVo^. "Prop. 2. To find the Sum of the Cubes of any arithmetical Progreffion. 3 In this Cafe -i/^a/co or 00 f . Therefore ia Lem.^. all the Terms except the higheft muft evanifh, fothat^— zz: cojj^rr 4^ 4^ 4X zn 00 X '■'. ^x . f^-Let^-i, ibr,2, ^,4,5,Srr.toV^ IS the arirhmetical Progreffion, the Sum (B) of whofe Cubes is ioughc^ I fayi ^8j-27'\-6i + 125 Wc. — coX ^- 00 J^ jProp. I I -' 1 76 i^Dilof opt)tcal |^;ruu;iple5 Trap. 3. To find the Sum of the Biqua- drates of any arithmetical Progreflion. lHdma6.='vooor=oJ.Thereforeby Lemma ^d. C=:-7^=— 00^ f — 00- $ X 5 $^ = c]oX oox 5x £«:. Let :5e=i, fo i, 2, 3, 4, C^r. to v cx> is the arithmetical Progreflion; I fay then that oo|- fl-f I^+82-f 256 ^C. =ooX— • Trof.A^. Vniverfal. Let e denote the Ex- ponent of any Power, to which the Terms of any arithmetical Progreflion aai-^x.a-^-^x. a-{'3X^ ^c. are raifed, and it is required to find the Sum of the T er ms fo ra ife d, I fa y 1 oo^i e?r.=ooX^^^- Scholium. From hence may be eafiiy de- duced the Quadratures of all the Parabola's ;k— jy* (where ^ is the Ordinate,)/ the Abfcif- fa^ and e an affirmative Number) which is one remarkable Ufe of this Arithmetick of Infi- 177 of HeUfjjon. Infinites. For if in thilpi^ 'x gure^^^jv, BC^2, and * ■z -jy', it is plain that if you puitjy=:i,2,;,4, 5,^^.^0-3? celUvely, then will a — i ', 2', ^% 4% &c. fucceflively i which fhews that the Ordi- 'V nates are the Terms of an arithmetical Pro- greflion rais'd to a Power, whofe Exponent IS e, and that («) the common Difference is I : But if the firft Abfcilfajy^r be infinitely (or indefinitely fmall) then tlie Ordinates will be infinitely near to one another, and the laft Ordinate B C will be an oo Number ot thefe Ones. Therefore fince to find tl e Area /IBC, is, in efFcft, to find the Sum of the Ordinates, and^ fince the Ordinates are r, 2% ^', 4", 5', ^c, till you come to the lalt, whi-h is BC= 00, Therefore by Prop.' 00 4. ABC= CO % 5f,,that is ABCz=BCk BZj f._j. , » tl^e fame which is found by the or- dinary Methods of Quadratures. And note that the whole Abfciflk AB denotes the N umiber ot the Terms. N. B. TAe ^adrature of all Sorts of Lurves exfrefs'd by one Term thus afTmi'd tt ts eafy by the Method of Ajfumptions of denes' s to extend this Method to all Sorts oj ^adratures hitherto difcovired^ Part II. >i ^q_. t :/« lyS ?0l)ilof(!|^ical l&jiinciples Additions. I have fhewn in /. i6o. ^c. that mean Proportionals between i and oo are neither finite nor infinite. For a farther Illuftration of what I have faid upon this Head, let us confider what thefe Progreflions are, whofe Sum is more than finite and lefs than infinite. Trop. I. V 00 is a Mean between i andin- I finite J but oo = j j, therefore V oo = ^ I — — 1| T^TITJ = ^ "^ ^ » wliich by Sir I/aac Newton's Theorem gives V«> = i_, '=x + H 1x3,1x5x5 I X3X5X7 i "■•» ' 2x4 ' 2X4x6'^ 2x4x6x8' ^c. that is ' ' ' ' 2x4^^2x4x6 I I-X-^ X % X 7, •^2x4x6x8 • And fo (by fquaring each Side of this E- quation) you will find it in FaQ: to be i -f i -}-i, C^f. =:i4-i4-i, ^c. From hence it appears that the Progreffion, whofe Sum (being neither finite nor infinite) is V^ confilts of Fraftions, whofe Numerators arc the Produfts of the continual Multiplication of Of ^tli^tu ^79 of the arithmetical Progreffion r, r, 3, y, 7, dj ^c. and the Denominators a/e tl^ Pro puas of the Multiplications of tTeT^m^'of this arithmetical Progreffion 2, 4,6, 8, lo S?°. Ortf/. In like manner you may find ,/ 00 ■^-* - I V 00 C^f . by refolving = I i } ^<: iV^w?<7»'s Theorems. So ^c. into a Series by Sir Vi — I 4.1X4x7-, 3x6x9 where the Numerators and Denominators are in arithmetical Progreffi- ons, whofe common Difference is 2; I x6 V 00 = -=rl— II Vl— I I 1X6 XII .. ' T— ■ —cgf. Voo=r 5x10x15 -/ I — I e%ie^ie^ Aff "*" ^ ^ , . . 0<2£X3^X4^ ^+•1 X3f x/ZS vj H yj z::z I —X But — —. r= I -f- J -{-. J* -4- j5 -|- j4 ^f . I X But calling i; the laft Term of this afcend- ing geometrical Progreflion i + -^ + J"" + J*3 -f @^. we fliall (as is fhewn in Page i ^6. of this Chapter) have i -f •^ + *^^ + -^^ + sv x4 4- t§c. = , therefore "DEGBji = X — I sv . So that we have three different Expref- X— I fions of the Area T>EGBJ^ viz. I — X X V of JReUgton^ i^i X V 'j and the Series i •\' s '\- s^ -{ s^ -{- s'^^c. X — I But what this Number v is (which denotes the laft Term of the Progreflion i -f- x -j- x' -j- x3 SJf .) is not fo eafy to determine ; certainly it cannot be v=oo X i or i -f i -j- 1 ^c. For then X ^EGBA^n 00 X ' ; therefore if in one X— I Hyperbola we put x=2, ffciLy x'^zzii) we haiVtDEGBAzrz oo x 2 ; and putting in ano- ther 1=3 Cfcil.y Ar5iiri) we have "DGEBA =r 00 X ^ ; now this would make the Area of the Hyperbola jv a:^ = i fcil. 00 x 2 greater than the Area of the Hyperbola j x^zuxfclh 00 X I ; (becaufe 2 <:::: 4- ) but it is eafy to de- monftrate, that in the Hyperbola"'sjy:x:^= i. the greater we fuppofe the Exponent x, fo fhall the Area T^EGBA (adjacent to B G) be the greater, and confequently the laft Term v of the Series i -fj" f J"-[--f^ ^c. cannot be co or i-f-i-j-l-l-i-fi ^^- for upon that Value of X V Vj the Expreflion-^;^ would make the A- rea ^EGBA to decreafe as x did increafe. To difcover the Value of v^ we have "DGEBA— — T-z ■; which gives v X — I X — I : 2= X X— X X I — X I I — N 4 Hav- ' ■^ I S^ 0hi!ofopDtcal TO'xipUs — 3 edupon:^for Having found -z/zz: — , we fee that in — jf two different Hyperbola's {Ex.gr.yx^'z:^ i, aAcJ jy^^=i,) V cannot have the fame Value; fcri„ the former v=-!,wl,ich is lefs then. I = — ', in the other. —3 Secondly. From the Value of i;™ X — - s i-j- we lee that the laft Term v is equal to the Sum of the Series {viz. i -f J + J^ -f -^^ ^^0 niultipli- — — is m-f-j^j^-f j-j tSc. Or^/. I fay the laft Term v cannot be oo X », take what Number you will for n (ex- cept in the Cafe of the common Hyperbola, where s=:i.) For if it were poffible, let v s — I =r op X » ; then muft - — ^ = oo X ;/, there- fore,_.= cox,.-»;rwhiohgive:. = » ns—ns'' I _ns — ns^ X - — - , and confequentiv — ~ — <» — I * "' oc s — I but— =0, therefore —~^ — o which giveJnrr. ^E.7). Corol. 2. It is evident that x; is fome Pow- er oi J, let the Exponent of that Power be n^fcil. •z/=:j»,but — r=-^ , therefore JXJ^ s *»»•♦- 1 " ~^ I ~ ' ^THJf which reduced to a Jogai-ithmick Equation gives ^i x/; a:=/.- •■i~},which gives »-^i£ili^i7^. ^n A N s w E R /o ^r. VarignonV Reflexions upon Sf ace: greater than infinite. L^'^,^^,.'^^.'"^^'^"S ^ "g'^t Angle K I nr^^^ , Afymptotes of any Hyper- bola ^G^; the Abfcilfe CZ=rc, and Ordi- "n^fr .-^ ', ^"^ ^'^^ g^n^ral Equation to all Hyperbola's J jc= i . Then becaufejy — J^-xr% wehavejy^ix-x-'dx, therefore f-ydx — f: x-'dx; but by the Calculus " 9 , therefore f : y I— e i-e Int^gralisf: x-' dx -. find ACMGJ=z f^M'Zlbut e — I ^ 3^ ^ i-e . therefore ACMG A^'l^^ from which if you fubftrad CMGL —y x ^ir ;3C '■"* the Remainder will be (as Mr. va- rigmn fays) JGLA-—, which is in- deed the Negative of ~ ,1— e 1—e But hisConclufion is falfe and groundlefs, t;/'5 That '^' is not the Expreflion of the i~e Space Of 3Reitgimi. 187 Space BGLCB but only (whcn^<: i) tlie negative ExpreOion ofits Complement ^G LA, For (according to the Principles of the Cakulus Integralis) — is as certainly the Expreflion of the Space BGLCB, as itsNe- gative — is the Expreffion ofits Comple- ment AG LA. And this is fuitable to Na- ture's Proceedings, vit. to do things in the wnplefl: and molt general Method, and con- lequently to give one Expreflion of the Area Ota Figure and ofits Complement, when it can be done. And may it not (with as good Reafon) be feid that j—^ is not the Expref- fion of the Space AG LA, but of its Comple- ment -ff G Z, C ^ ; and not only it mav be faid but Mr. Varignon muft fay fo in all the in- numerable Cales where e:> 1 • and to lay it is not when ^ < i, and it is when ^ > i y what is this but to fay backward and for- ward, according as it will anfwer his Con- ceit of denying that there are Spaces greater than Infinite ? But to put this Controverfy beyond all Difpute, let us refolve thefe two finite Bxpreflions of the Spaces BGLCB and AG L A into infinite Series's. ' ^" i-^=''^'~'x ^ + ^+^'+f'+c. when you \\\ '\ \ •' I 1 88 flKlof oplitcm l&^inaplrs you begin the Divifion with i, as here it jiaturaiiy fliould x'"* t I I I o When you begin the Divifion with — e. v'— * fill e-i e €"• e3 e^ When you begin the Divifion with 189 •f 8fC. e-i Thefe are plain and obvious Conclufions deduced from the known and common Oce- rations of Arithmetick, and utterly over- throw all that Mr. Varignon alled^ts aeainft Spaces greater than Infinite. " For without any Limitation (except ^