I will not entertain this Auditory with an account of the Demonftration; but referring the Curious to the Book it felf for full fatisfaction, I shall now proceed and build upon it as a Truth folidly established, That all Bodies weigh according to their Matter; provided only that the compared Bodies be at equal distances from the Center toward which they weigh. Because the further they are removed from the Center, the lighter they are: decreafing gradually and uniformly in weight, in a duplicate proportion to the Increase of the Distance.

(3.) Now fince Gravity is found proportional to the Quantity of Matter, there is a manifeft Neceffity of admitting a Vacuum, another principal Doctrine of the Atomical Philofophy. Because if there were every where an abfolute plenitude and density without any empty pores and interftices between the Particles of Bodies, then all Bodies of equal dimenfions would contain an equal Quantity of Matter; and confequently, as we have fhewed before, would be equally ponderous: so that Gold, Copper, Stone, Wood, r. would have all the fame fpecifick weight; which Experience affures us they have not: neither would any of them defcend in the Air, as we all fee they do; because, if all Space was Full, even the Air would be as dense and specifically as

B

heavy

heavy as they. If it be faid, that, though the difference of fpecifick Gravity may proceed from variety of Texture, the lighter Bodies being of a more loose and porous compofition, and the heavier more denfe and compact; yet an ethereal fubtile Matter, which is in a perpetual motion, may penetrate and pervade the minuteft and inmoft Cavities of the clofeft Bodies, and adapting it felf to the figure of every Pore, may adequately fill them; and fo prevent all Vacuity, without increafing the weight: To this we anfwer; That that fubtile Matter it felf must be of the fame Substance and Nature with all other Matter, and therefore It alfo must weigh proportionally to its Bulk; and as much of it as at any time is comprehended within the Pores of a particular Body muft gravitate jointly with that Body: fo that if the Prefence of this æthereal Matter made an abfolute Fullness, all Bodies of equal dimensions would be equally heavy which being refuted by experience, it necessarily follows, that there is a Vacuity; and that (notwithstanding fome little objections full of cavil and sophistry) mere and simple Extenfion or Space hath a quite different nature and notion from real Body and impenetrable Subftance..

(4.) This

of Air and

(4) This therefore being established; in the next place it's of great confequence to our prefent enquiry, if we can make a computation, How great is the whole Summ of the Void fpaces in our fyftem, and what proportion it bears to the corporeal fubftance. By many and ac- Mr. Boyle curate Trials it manifeftly appears, that Refined Poroty Gold, the most ponderous of known Bodies, of Bodies. (though even that must be allowed to be po rous too, being diffoluble in Mercury and Aqua Regis and other Chymical Liquors; and being naturally a thing impoffible, that the Figures and Sizes of its conflituent Particles fhould be fo juftly adapted, as to touch one another in every Point,) I fay, Gold is in fpecifick weight to common Water as 19 to 1; and Water to common Air as 850 to 1: fo that Gold is to Air as 16150 to 1.Whence it clearly appears, feeing Matter and Gravity are always commenfurate, that (though we should allow the texture of Gold to be intirely clofe without any vacuity) the ordinary Air in which we live and refpire is of fo thin a composition, that 16149 parts of its dimenfions are mere emptiness and Nothing; and the remaining One only material and real fubftance. But if Gold it felf be admitted, as it must be, for a porous Concrete, the proportion of Void to Body in the texture of common Air will be fo much the greater.

В 2

And

ibid.

And thus it is in the lowest and densest region of the Air near the furface of the Earth, where the whole Mafs of Air is in a state of violent compreffion, the inferior being prefs'd and conftipated by the weight of all the incumbent. But, fince the Air is now certainly known Mr. Boyle to confift of elastick or springy Particles, that have a continual tendency and endeavour to expand and difplay themfelves; and the dimenfions, to which they expand themselves, to be reciprocally as the Compreffion; it follows, that the higher you afcend in it, where it is lefs and lefs comprefs'd by the fuperior Air, the more and more it is rarefied. So that at the hight of a few miles from the furface of the Earth, it is computed to have fome million parts of empty space in its texture for one of folid Matter. And at the hight of one TerreNewton ftrial Semid. (not above 4000 miles) the Æther Philof. is of that wonderfull tenuity, that by an exact calculation, if a small Sphere of common Air of one Inch Diameter (already 16149 parts Nothing) fhould be further expanded to the thinnefs of that Ether, it would more than take up the Vaft Orb of Saturn, which is many million million times bigger than the whole Globe of the Earth. And yet the higher you afcend above that region, the Rarefaction still gradually increafes without ftop or limit: fo

Nat.Prin

cipia. Math. P. 503.

that,

*

that, in a word, the whole Concave of the Firmament, except the Sun and Planets and their Atmospheres, may be confider'd as a mere Void. Let us allow then, that all the Matter of the Syftem of our Sun may be 50000 times as much as the whole Mafs of the Earth; and we appeal to Aftronomy, if we are not liberal enough and even prodigal in this conceffion. And let us fuppofe further, that the whole Globe of the Earth is intirely folid and compact without any void interftices; notwithstanding what hath been fhewed before, as to the texture of Gold it felf. Now though we have made fuch ample allowances; we shall find, notwithstanding, that the void Space of our Syftem is immenfly bigger than all its corporeal Mafs. For, to proceed upon our fuppofition, that all the Matter within the Firmament is 50000 times bigger than the folid Globe of the Earth; if we affume the Diameter of the Orbis Magnus (wherein the Earth moves about the Sun) to be only 7000 times as big as the Diameter of the Earth (though the latest and most accurate Obfervations make it thrice 7000) and the Diameter of the Firmament to be only 100000 times as long as the Diameter of the Orbis Magnus (though it cannot poffibly be less than that, but may be vaftly and unfpeakably bigger) we muft pronounce, after fuch large conceffions

on