that now in this Learned and Inquisitive Age they have at last found out the true and solid Philosophy They do now perceive the intimate essence of all things and have discovered Nature in all her works and can tell you the true cause of every effect from the sole principles of matter and motion If you will believe them they can inform you exactly how God made the World for they do now comprehend the greatest mysteries in nature and understand and Oeconomy of living Bodies Nay they understand also very exactly the Theory of the Soul how it thinks and by what methods it operates on the Body and the Body on it These indeed are great discoveries and might well demand our esteem and admiration if they were real But that we may see how well they deserve such a Character I will here set down some of their sentiments both as to the Intellectual and Natural System Spinosa pretends to demonstrate that there is but one individual Substance in the Universe and that all particular beings are different modifications of the same substance Another Philosopher viz. Dr. More will have Souls besides the three dimensions which belong to Bodies to have a fourth which he calls the Souls essential spissitude by which it can contract or dilate it self when it pleases Mr. Hobbs thinks Incorporeal Substances a flat contradiction and that therefore it is altogether impossible there should be any such But a new Philosopher has much out-done any I have yet mentioned in a Book lately Printed concerning Reason there he assures us that there is but one universal Soul in the World which is omnipresent and acts upon all particular organized Bodies and makes them produce actions more or less perfect in proportion to the good disposition of their Organs so that in Beasts that Soul is the principle of the sensitive and vital functions in Men it does not only perform these but also all other rational actions just as if you would suppose a hand of a vast extension and a prodigious number of fingers playing upon all the Organ pipes in the world and making every one sound a particular note according to the disposition and frame of the pipe so this Universal Soul acting upon all Bodies makes every one produce various actions according to the different disposition and frame of their Organs This opinion he as confidently asserts to be true as other men believe that it is false tho it is impossible he should any other way be sure of it but by Revelation and I believe he will find but few that will take it upon his word Mons. Malbranch the famous inquirer after Truth having made a long and deep search how the Soul comes to have its Ideas has found out at last that we perceive not the things themselves but only their Ideas which the Soul sees in God For says he the Soul is united to God in a much stricter and more essential manner than she is united to the Body and this union is by his presence so that it may be said that God is the place of Spirits as space is the place of Bodies He tells us also that since God has the Ideas of all beings in himself the Soul must needs see what there is in God which represents created beings for Bodies are not visible of themselves they not being able to act upon our mind nor represent themselves to it therefore they being unintelligible in their own Natures there is no possibility of seeing them except in that being which contains them after an intelligible manner Bodies therefore and their properties are seen in God so that a man who reads this Book does not really see the Book it self but only the Idea of it which is in God Is not a man now much the wiser for this unintelligible jargon I would fain know what the Author meant by his seeing every thing in God by its Idea for I must confess that the oftner I read his long Illustration on this point I understand it the less and I know as little how I have my Ideas as I did before If he had told me that the Soul saw its Ideas under the Concave of the Moons Orb where they say Plato placed them I could have had some sort of confused notion of that manner of seeing but this manner of seeing Ideas is far beyond my imagination I am sure that I can neither see the Idea of it in God or any where else The truth is I have not so couragiously resisted my senses as that Philosopher advises as to be able to penetrate such a solid piece of nonsense The same Philosopher affirmes that Bodies of their own nature are neither heard seen smelt nor tasted and when for example we tast any thing the Body tasted cannot produce any savour in us but God Almighty takes that occasion to stir up that sensation in us to which the body does not really concur Nay according to him it is impossible for any man to move his own Arm but when he is willing to move it God takes it and moves it up and down as the man whose Arm it is wills If a Rebellious Son or Subject murther his Father or his Prince by stabbing him the Man himself does not thrust the Poiniard into his Fathers or Princes Breast but God Almighty does it without any other concurrence of the Man but his will These indeed are strange and unaccountable fancies But he proceeds still further and affirmes that no second causes act so that no Body tho moved with never so great a velocity against another can be able to drive that other before it or move it in the least but God takes that occasion to put it in motion At this rate one need not fear his headpiece tho a Bomb were falling upon it with all the force that Powder can give it for it could not so much as break his Skull or singe his hair if God did not take that occasion to do it The most natural agents with him are not so much as instruments but only occasions of what is produced by them so that a man might freely pass thorow the fire or jump down a precipice without any harm if God Almighty did not take that occasion to burn him or dash out his brains To prove that our moderns are as wild extravagant and presumptuous as any of the Ancients either Poets or Philosophers I may instance in Dr Conner whose imagination has taken a flight beyond the spheres of sense and reason Other Philosophers were only ambitious to explicate nature and the common effects of it but no less a subject can satisfy him than the Omnipotent Author of nature and his extraordinary and miraculous acts which he pretends to explain for he thinks he understands them as well as he does the common Phaenomena of Nature This I believe will be granted him without much difficulty for there is very good reason to believe that the works of Nature
and consequently the one will descend when the other cannot As for example suppose a sphere of an inch diameter was put into an oily fluid whose resistance was just equal to the force of gravity in the descending body there being an aequilibrium the former would swim in the latter Now if another sphere of two inches diameter and of the same intensive gravity were put in the same fluid in gravity or force by which it would separate the particles of the fluid would be eight times greater than the descending force of the former sphere and if in resistance were also eight times greater it is plain that it also could not descend but the resistance being always as I noted before as the surface of the descending body is only in the present case four times greater which will not equal the force of its gravity and therefore the sphere must descend So in our present case tho' some small grains of dust or earth may swim upon the surface of Oil yet these when increas'd by the addition of a great many others which fall upon them augment their weight the same resistance continuing and must fall to the bottom Besides this the earthy particles falling from a great height some of them descending from places as high as the Moon as the Theorist will have them must needs in their descent â—â—â—â—ire a very considerable degree of velocity with which falling upon the surface of the oily Orb they will not only by that force descend themselves but also carry down with them and condense whatsoever bodies they met in their way or found swimming upon the surface of the oil Now that the force of a descending body is so great as to perform this effect I think is clear to any who considers that a heavy body runs down fifteen foot in a second and that the spaces thro' which it does move are always in duplicate proportion to its times as is demonstrated by Galileo and confirmed by the experiments of Riscioli from whence by calculation it will follow that a body would run down four thousand miles in the space of twenty three seconds abstracting from the resistance of the air But if we will suppose but the hundredth part of this space run thro' in that time allowing all the rest for the resistance of the Medium yet even in that case the velocity would far exceed that of the swiftest bullet that can be shot out of a Cannon Thus I think I have made it evident that the particles of earth after falling thro' the air could not rest upon the surface of the oily Orb to form there an hardened habitable 〈◊〉 not only upon the account of their greater gravity which the Theorist acknowledges and is also plain by experience common earth being near twice as heavy as water but also upon the account of the great force by which they must of necessity fall upon the liquid Orb which will carry them down towards the Center I hope now it will appear to any thinking man plainly impossible that either oil or water should sustain such an immense heavy Orb in which was not only the soft earth which in few places in ten foot deep but also a prodigious quantity of stones and minerals much heavier than water for it is certain that these great heavy bodies must have sunk to the bottom if they were left to themselves and yet these bodies make up the greatest part of our outward earth I know the Theorist does boldly affirm that there was neither Metals nor Minerals in the primitive earth but this is both contrary to reason and Scripture for the Holy Scriptures tell us that Tuhal Cain before the floud was an instructer of every Artificer in Brass and Iron and I would fain know how there could be such Artificers before the flood when according to him there was no such thing to be seen as Metals Besides 't is hardly possible to build an Ark that should contain all the terrestrial and aerial animals without Iron The Americans without any Iron made themselves small Cannoes of one solid piece of Timber which they hollowed by burning but it would be a strange Tree that was of the dimensions of the Ark and could contain so many animals as it did These things do in my judgement plainly show that the Theorists opinion in this point is utterly false From what I have already said I think it may be clearly demonstrated that the Fabrick of the 〈◊〉 can never be deduced from a Chaos by the sole help of Mechanical principles and Natural causes For it is evident to any one who has eyes tho there have been some wise Philosophers of another opinion that the Land is higher than the Water and it is also plainly experienced that common arable earth or clay is much heavier than water and if we descend into the Mines or Pits we shall find the matter there to be three or four times heavier than the earth above Now it is plain from what I have already proved that in a Chaos the true change that would follow from Mechanical principles and Natural causes is that if all were fluid the heaviest solidest Bodies would subside and fall to the Center every one taking place according to the specifick gravity so that the lighter Bodies would always be forced uppermost the earth therefore being heavier than the water must of necessary place it self nigher the Center and leave the water to cover the face of the whole Orb. Thus the surface of the World could never be inhabited by any other Animal than Fishes But in how much wiser order than this has the great Creator of the World plac'd all the Bodies of the earth so that notwithstanding the greater gravity of the Land it is raised higher than the Sea and thereby made fit and habitable both for man and beasts without the help of Natural and Mechanical causes which would have produc'd the contrary effect Several other arguments might be brought to demonstrate that the fâ—â—me of this World was the result of wisdom and counsel and not of the necessary and essential Laws of motion and gravitation which could never have either made or supported the World I always wonder'd at the wild and extravagant fancy of the Philosophers who thought that brute and stupid matter would by it self without some supreme and intelligent director fall into a regular and beautiful structure whose parts should be so extreamly well adapted to various uses as if they had been the result of wisdom and contrivance I will conclude this Chapter with a discourse of the Theorist in his 10 th Chap. lib. 2. In the construction of the Body of an Animal says he there is more of thought and contrivance more of exquisite invention and fit dispositions of parts than is in all the Temples Palaces Ships Theaters or any other pieces of Architecture the World ever yet saw and not Architecture only but all other Mechanism whatsoever Engines
still there remains the final cause to be inquired into which will do as well for our purpose For if I prove them to be as useful to the inhabitants of the primitive earth as they are now to us and that in our present state they are absolutely necessary not only for our well being but also for our bare subsistance I think from thence it will demonstratively follow that they were in the primitive earth as well as in ours And therefore the groundless assertion of the Theorist that the face of the Antediluvian earth was smooth regular and uniform is as false as 't is bold and daring I know there is a sort of men in this age who have excluded all final causes from the consideration of a Philosopher as being unworthy of his enquiry supposing his business is only to find out the true formal and efficient causes of all things and not to concern himself with the design of nature or the great end for which the God of Nature made any thing But indeed these men have been so unhappy in their searches that I dare boldly say they have not so much as discovered the true real and efficient cause of any one of the Phaenomena which was not known and better explain'd before tho' they have pretended to lay open the essences and formal causes of all things and to shew the manner how the Universe was formed from the principles of Matter and Motion But whatever they pretend certain it is that final causes are worthy of the consideration of all men and much more of a Philosopher By them we are led into the admiration of the wisdom of God and discover his care and providence over the world By them we demonstrate that the World could never be made by chance but it must be a being of Infinite wisdom that form'd it for such various uses as are to be seen in it And therefore by all wise and considering men they are much more to be valued than efficient causes if they could be discovered which only tell us how the thing was perform'd and not the use for which it was design'd 'T is true indeed it is not easy to discover the use of every thing in the Universe but from the admirable contrivance of those things the uses of which we do know and from the infinite wisdome of God it may be easily concluded that every thing in nature has its use and is in some manner serviceable to the good of the whole They who desire to see more concerning the usefulness of final causes may consult Mr. Boyle of final causes Mr. Ray's wisdome of God in the works of the Creation and some late ingenious essays upon the nature and evidence of faith by Dr. Cockburn I must confess I cannot but think it a strange and presuming boldness in the Theorist to assert that Mountains are plac'd in no order one with another that can either respect use or beauty and that if they are singly consider'd they do not consist of any proportion of parts that is referable to any design or hath the least footsteps of art or counsel Notwithstanding this strange assertion I am sure if we were without these shapeless and ill figur'd old Rocks and Mountains as he calls them we should soon find the want of them It being impossible to subsist or live without them For setting aside the use they may have in the production of various Plants and Metals which are usefull to mankind and make a part of the compleat whole and the Food which they yield to several Animals which are design'd by Nature to live upon them The high Hills being a refuge for the wild Goats and the Rocks for the Conies and not to mention the end they serve for in directing the Inland winds and altering the weather in fencing and bounding Empires and Countries in all which without doubt they do us very considerable service there is moreover one great and Universal use which makes them absolutely necessary for the subsistance of Mankind For without them it is certain we should have no Rivers nor fresh currents of waters and consequently we should want one of the greatest supports of Life This the Learned and Ingenious Mathematician and Philosopher Mr. Edmund Halley has effectually proved in the Philosophical Transactions where he gives us an account of the rise of Springs and Rivers from Vapours That are raised copiously in the Sea and by the winds are carried over the low Land to the high ridges of Mountains where they are compelled by the stream of the air to mount up with it to the tops of the Mountains where they presently precipitate gleeting down by the cranies of the stones and part of the Vapour entring into the Caverns of those Hills the waters thereof gather as in an Alembick into the basons of stone it finds which being once filled all the overplus of water that comes thither runs over by the lowest place and breaking out by the sides of the Hills forms single Springs many of these running down by the valleys or gutts between the ridges of the hills and coming to unite form little rivulets or brooks many of these again meeting in one common valley and gaining the plain ground being grown less rapid become a River and many of these being united in one common channel make such streames as the Rhine the Rhone and the Danube which last one would hardly think the collection of waters condensed out of vapours unless we consider how vast a tract of ground that River drains and that it is the summ of all those springs which break out upon the South side of the Carpathian Mountains on the North side of the immense ridge of the Alpes which is one continued chain of Mountains from Switzerland to the black Sea so that it may almost pass for a rule that the magnitude of a River or the quantity of water which it evacuates is proportional to the length and height of the ridges from whence its fountain arises All this I take to be undeniably evident For that vapours are raised by the heat of the Sun from the Sea in such vast quantities as will be sufficient to serve all the Rivers the same ingenious Mr. Halley has demonstrated by Calculations But it is also demonstrable that these vapours being of the same specifick gravity with the air in which they swim must follow its motion that is they must be carried by the winds over land untill they meet with such an obstacle as a hill in their way which resists their motion where they must precipitate and gleet down by its side and so form Rivers and Springs All this is not only clear from reason but is also confirmed by the experience of the same Mr. Halley while he was at St. Helena as he tells you in the Philosophical Transactions And now methinks 't is plain that hills are so very far from being placed in the earth without any art or
writers of Hydrostaticks that a sphere whose centre of Gravity is the same with its centre of Magnitude if put in a fluid of the same specifick gravity with it self will retain any given position and therefore there can be no reason drawn from the earths gravity or equilibration why the position of its axis should be perpendicular to the plane of the Ecliptick rather than any other of its diameters CHAP. V. Of Rivers THE Theorist having represented to us the first Earth as a smooth regular and uniform body without Mountains and without a Sea In the 5th Chap. of his second book he starts a great difficulty how it was watered from what causes and in what manner how could Fountains rise or Rivers flow in an Earth of that form and nature he has shut up the Sea with thick walls on every side and taken away all communication that could be 'twixt it and the external earth he has removed all the Hills and Mountains where the Springs use to rise and whence the Rivers descend to water the face of the ground and lastly he has left no issue for these Rivers no Ocean to receive them or any place to disburthen themselves into So that his new found World is like to be a dry and barren wilderness and so far from being Paradisaical that it would scarce be Habitable These indeed are great difficulties and the Theorist has acknowledged them to be such for he sayes there was nothing in his whole Theory that gave so rude a stop to his thoughts as that part of it concerning the Rivers of the first Earth But as the difficulties are great and as one would think insuperable so no doubt the glory that redounds to the Theorist must be nothing less if they be clearly taken away To understand therefore what the state of the primitive Rivers and waters would be he finds it necessary to consider and examine how the rains fell in the first Earth and he tells us that the order of nature in the Regions of the an would be very different from what it is now there could be no violent motions there nor any thing that proceeded from extremity of cold as Ice Snow or Hail and as for Winds they could neither be impetuous nor irregular in that Earth of his seeing there were no Mountains nor any other inequalities to obstruct the course of the vapours nor any unequal seasons nor unequal actions of the Sun but as for waters meteors dews and rains there could not but be plenty of these in some part or other of that Earth for the action of the Sun in raising vapours was very strong and very constant and the Earth was at first moist and soft and according as it grew more dry the rayes of the Sun would pierce more deep into it and reach at length the great abyss which lay underneath and was an unexhausted storehouse of new vapours Now the same heat which extracted these vapours so copiously would also hinder them from condensing into rain in the warmer parts of the Earth and there being no mountains or contrary winds or any such causes to stop or compress them they would take their course where they were least resisted which is towards the Poles and the colder regions of the Earth for East and West they would meet with as warm an air and vapours as much agitated as themselves which therefore will not yield to their progress that way but North and South they will find a more easy passage so that the concourse of vapours which were raised chiefty about the Equinoctial and middle parts of it would be towards the extreme parts or the Poles When these vapours thus driven by the heat of the Sun were arrived in the cooler Regions near the Poles they would be condensed into rain for wanting there the cause of their agitation namely the heat of the Sun their motion would soon begin to languish and they would fall close to one another in the form of water Thus he thinks he has found a sufficient source for waters in the first earth which would never fail neither diminish nor overflow But tho' he esteems this an inexhaustible store-house and an easy way to furnish Waters yet if it be narrowly examined he will find it not in the least sufficient for such an effect For first according to his own hypothesis there could be no Rivers for a long time after the formation of the Earth till the Sun had crackt the outward crust thereof and its heat had reacht the great abyss which the Theorist must needs own will require a very considerable space of time one would think it would be several hundreds of years before the Suns heat could perform such an effect during all which time the inhabitants of the Earth must be without waters and rivers and lead very sad and uncomfortable lives Is this the fruit of the Golden Age or is this consistent with the happiness of the antediluvian Fathers in my opinion it is directly contrary to the Scriptures for they give us an account of rivers immediately after the formation of the Earth But 2 dly I will hereafter prove that the Suns Beams did never yet reach so deep in the Earth as the thickness of the first crustation must have been and consequently there never could arise any vapours from the abyss to furnish the rivers 3 dly Supposing the heat of the Sun to have crackt the crust and to have raised vapours from the abyss yet it is certain it could not do it in such a quantity as would be sufficient to furnish the Earth with waters And now the Theorist will tell us what can be more sufficient than the whole orb of water sure this would do or else nothing could this he will say is an inexhaustible treasure that the rivers could never drain and therefore there was no fear of want of waters from thence Yes there was reason to fear it very much for supposing that there was enough in the abyss yet perhaps the action of the Sun would not raise so much as would be sufficient to water the Earth so there may be enough of Gold in the bowels of the earth but if we cannot come at it we shall never be the richer for it That I may examine this I will suppose that the mouths of these cracks which the Sun is said to have made by its heat to be a 1 10000 part of the surface of the earth this will exceed 2600 square miles which I think is as much as the Theorist can reasonably allow them for if it were but one continued crack round the equator of a miles breadth it would not exceed 25000. miles 2 dly I will suppose with the Theorist that one half of the surface of the present earth is Land and the other is Sea and by consequence the mouths of those pits or cracks must be one five thousandth part of the whole of the now Ocean Now it is evident
as happened from pure Mechanical principles and causes and the true reason why there remain no records or traditions of facts done in the time beyond four or five thousand years is because there has happened a Deluge the memory of which is still preserved and this Deluge being the necessary consequence of natural causes did sweep away all mankind and with them the memorials of all former ages only a couple of ignorant country people some way or other saved themselves from the universal Catastrophe and from their ofspring the earth was again replenished and arts and sciences invented which our forefathers before that deluge understood more perfectly than we do now This they will tell you is their hypothesis and they will not be beaten easily from it since it may be defended as well as any other Philosophical Theory which pretends to give an account of the origination of the World and is as precarious as their own system of principles which they pretend is very possible since several Philosophers have shew'd various ways how there might have happened so universal a deluge from Mechanical principles and the necessary laws of motion Thus we see how these flood-makers have given the Atheists an argument to uphold their cause which I think can only be truely answer'd by proving an universal Deluge from Mechanical causes altogether impossible And therefore I design to shew that the most ingenious Theories fram'd upon that account come far short of the design of the Framers and that the great and wonderful effects which they indeavour to explain could never have risen from the causes they assign This I intend to do by shewing that their Theories are neither consonant to the established laws of motion nor to the acknowledged principles of natural Philosophy of that Philosophy I mean which is founded upon observations and calculations both which are undoubtedly the most certain principles that a Philosopher can build upon It is in vain to think that a system of Natural Philosophy can be framed without the assistance of both for without observations we can never know the appearances and force of nature and without Geometry Arithmetick we can never discover whether the causes we assign are proportional to the effects we pretend to explain This the various systems of the Philosophers do evidently shew which are by far more distant from the truth than they are from one another And I hope it will appear yet plainer by the following examination of Dr. Burnet's Theory of the Earth Which tho it has been published many years and has been animadverted upon by several yet it has not been so fully refuted as it might have been nor has any one shew'd the greatest mistakes in it Nay Mr. Erasmus Warren who has wrote the greatest Volum against it in my opinion has spoken the least sense about it He begins his discourse with a saying of an old Heathen that Philosophy is the greatest gift that ever God bestowed on man Which I will not deny since he has been at so much pains to make a Panegyrick on the usefulness of it But it is plain to any who will be at the pains to read his Book that God has thought fit to bestow but very little of that great gift upon him And that the world may not think that this is said out of ill nature and without grounds I will give them a tast of his Philosophy Geometry or Geography call it which you please He designs to calculate how much colder the Poles would be if the earth were of an Oval figure than if it were perfectly Spherical To do which he supposes that a Circle formed into a moderate Oval will have its Poles at least a fortieth part farther distant from the aequator than if it were perfecty spherical Now according to this proportion allowing the earth to be 7000. miles in Diameter and adding a fourth part to render it Oval viz. 1750 miles thickness the earth at each Pole must bear above fourteen degrees latitude more than if it had been round So that the hypothesis which removes its Poles so much farther from the Sun must also allow the cold thereabouts to be proportionably augmented And though in the hundred and fourth degree of latitude as we must call it on each side of the aequator that is at the very Poles there might have been a perpetual day c. This is the first time I ever heard that there could be more than ninety degrees between the pole and the aequator but he thinks he has fairly made it out that there can be a huâ—dred and four degrees between them therefore there must be four hundred sixteen degrees in the whole circumference and then every right angle being only proportioonal to ninety degrees there must be more than four right angles about one point and therefore the Corollary of the 13 th of the first of Euclid must be false Thus has that subtle Philosopher not only subverted Dr. Burnet's Theory but also Euclid's demonstrations and that by an argument which the dull Mathematicians could never discover But I will leave Euclid to his mercy and answer that part of his argument that concerns the Theory which is easily done if he will consider that the difference between the poles of the earths distance from the Sun and the aequator of the earths distance from the Sun even tho the earth were ten times more Oval than he would have it is so very inconsiderable that it does almost bear the same proportion to the whole that a point does to a line for the Mathematicians know that the diameter of the earth is but a point in respect of its distance from the Sun and therefore two lines drawn from the Suns centre to any two points of it are very near in a proportion of equality so that upon the account of a greater or lesser distance of the parts of the earth from the Sun there can be no sensible alteration of heat or cold But I am afraid this is a little too far beyond Mr. Warren's capacity however to surprize him a little more I will tell him he is so far out in his account of the cold at the poles that tho the North pole be much colder in the Winter than it is in the Summer yet is it some hundred thousands of miles nearer to the Sun in Winter than in Summer If he pleases to consult the Astronomers they can demonstrate the truth of this to him I beg Mr. Warren's pardon for bringing him into this place I ought to have been favourable to him he being one of my Associates against Dr. Burnet But I was willing to produce him as an instance to shew how unfit a man who understands no Geometry is to write a book of Natural Philosophy But to return to the Theory I cannot but acknowledge that there was never any book of Philosophy written with a more lofty and plausible stile than it is the noble and
at rest or which is the same thing a heavy body placed at either of the Poles where there is no diurnal rotation and consequently no centrifugal force which weighs 289 pounds if it were brought to the aequator will weigh only 288 pounds Having thus determined the proportion of the centrifugal force at the aequator to the force of gravity it will be easy from thence to shew their proportions in any parallel for it is compounded of the proportion of 1 to 289 and of the co-sine of the Latitude to the Radius for if two bodies describe different peripheries in the same time their centrifugal forces are proportional to their peripheries or to the semi-diameters of these Peripheries as is determined by Mons. Hugens in his Theoremata de vi centrifuga motu circulari but the Periphery which a body in the aequator describes has its semi diameter equal to the radius or semi diameter of the Earth and in any other place the parallels in which Bodies move have the co-sines of their Latitude for their semidiameters and therefore it will follow that the force of gravity is to the centrifugal force in a proportion compounded of the radius to the co-sine of the Latitude and of 289 to 1. and therefore at the Latitude of 51 degrees 46. minutes for example it will be as 466 to 1. By this also it will appear that the direction of heavy Bodies is not to the Centre of the Earth as has been alwayes supposed For if we take a heavy Body and hang it by a thread the thread produced will not pass through the Centre any where but at the Poles and the AEquator for in the Figure the thread is carryed by the centrifugal force of the Body B from the position AC into the position AB where it will rest From hence also it will appear that it is not the line AC which being produced passes through the Centre but the line AB that is perpendicular to the curve PQ for all the particles of the fluid will settle themselves in such a position that their lines of direction downwards must be perpendicular to the surface of the Body which they compose for otherwise the parts of the fluid would not be in an AEquilibrium one with another and therefore altho the lines of direction of heavy Bodies do not pass through the Centre of the Earth yet are they still perpendicular to their Horizons and upon this account there could arise no error in levelling of lines and in finding the risings and fallings of the ground It is upon the account of this diminution of gravity according as we approach the Equator that pendulums of the same length in different Latitudes take different times to perform their vibrations for because the accelerating force of gravity is less at the Equator than under any parallel and under any parallel it is still less than under another which is nearer the Poles it do's plainly from thence follow that a body plac'd in the Equator or in any parallel will take a longer time to descend through an arch of a given circle than it would do at the Poles and the farther a body is removed from the Poles the longer time it will take to descend through any given space From hence it follows that the length of pendulums which perform their vibrations in equal times in different Latitudes are directly as the accelerating forces of their gravities For the time a Body takes to descend through an Arch of a Cycloid is to the time it will take to fall through the Axis of the Cycloid always in a given proportion viz. as the Semiperiphery of a circle is to its Diameter by the 25 th Prop. of Hugens Horologium Oscillatorium and therefore when the times in which a body descends through the Axes of two different Cycloids are equal the times of the descent through the Cycloids will be also equal but when the times of the descent through the Axes are equal these Axes and consequently the lengths of the pendulum which vibrates in these Cycloids are proportional to the accelerating forces of their gravities By this if we know the length of a pendulum which performs its vibrations in a given time in any one part of the Earth it is easy to determine the length of a pendulum which performs its vibrations in the same time in any other part of the Earth as for example the length of a pendulum which vibrates seconds at Paris is three foot eight lines and a half let it be required to find the length of a pendulum which vibrates seconds at the Equator Because the gravity at the Pole is to the gravity at the Equator as 692 is to 689 therefore the decrease of gravity at the Equator is 3 692 parts of the whole gravity but as I have before demonstrated the decrease of gravity at the Equator is to its increase in any other Latitude as the square of the radius is to the square of the sine of the Latitude now the Latitude of Paris being 48â—â— 45 its sine is 75. 183 and therefore the square of the Radius is to the square of the sine of the Latitude as 1000000 to 565248 but as 1000000 is to 565248 so is 3.000 the number which represents the decrease of gravity at the Equator to 1. 695 the number which represents its increase at Paris which added to 689 the gravity at the Equator makes 690.695 the number which will represent the gravity at Paris But I have already shewed that as the gravity at Paris is to the gravity at the Equator so is the length of a pendulum which vibrates seconds at Paris to the length of a pendulum which vibrates seconds at the Equator that is as 690,695 to 689 so is 36,708 the length of a pendulum at Paris which performs its vibration in a second to 36,616 which therefore is the length of a pendulum which performs its vibrations in a second at the Equator so that the difference btween these two pendulums is 92 1000 parts of an inch which comes pretty near the observations of Mons. Richer who at the island of Cayen whose Latitude is 5 degrees found that a pendulum which vibrates seconds there was a tenth part of an inch shorter than a pendulum which vibrates seconds at Paris Thus we see that the principles and hypothesis and withal their consequences upon which the broad Spheroidical Figure of the Earth is founded do exactly agree with observations and therefore there is no doubt to be made but that the Earth is really of such a Figure and that the hypothesis upon which this Figure is grounded viz. the diurnal rotation of the Earth and by consequence the centrifugal force of all Bodies upon it must be admitted for a true one since the different vibrations of Pendulums of the same length in different Latitudes can depend upon no other cause for the change of