§ These feven are broad and and want Streights, 11. The Gulph of Mexico, between North and South America. . | 2. The Gulph.of Bengal, between Indoftan and Malacca. 1 3. The Bay [ of Siam] between Malacca and Cambodia. 4. The White Sea, between Lapland and Muscovy. | 5. The Lantchidol Sea, between New-Hol land and New-Guinea. 6. The Gulph between Nuyt's Land, and Van Diemen's Land. | 7. Hudson's Bay; between New-France and New-Denmark. 3. Streights. 1. THE Streights of Magellan, which join the Atlantic to the Pacific Ocean. These are longer than any of the rest. 2, THE Streights of La Maire near those of Magellan, and of the same use. 3. THE supposed Streights of Anian, which join the Pacific to the Tartarian Ocean. . 4. DAVIS's Streights which join [Baffin's Bay] to the Atlantic, near which are Forbishers's Streights. 5. THE Streights of Waygats, which join the Icy Sea, perhaps, to the Tartarian Ocean, if the Ice do not interpose. 6. THE Streights of Gibralter, which join the Allanlic to the Mediterranean Sea. 7. THE Streights of Denmark, or the Sound, join the Atlantic to the Baltic. 8. THE Streights of Babelmandel, at the mouth of the Arabian Gulph. 9. THE Streights of Ormus, at the mouth of thé Persian Gulph. . - 10. THE 10. THE Hellefpont and Bosphorus, which join the Archipelago to the Euxine or Black Sea... WHETHER the Caspain Sea be a Lake or a broad Bay, which is joined to the main Ocean by some fubterraneous Streights, is not settled among Geographers, : :***!CH A P. XIII. Of the Ocean, and certain Properties of it's Parts. :: PROPOSITION I. The Surface of the Ocean, and of all other Liquids, is round and spherical: Or the Surface of the watery Part joined to the Surface of the dry Part, do both together make up the Superficies of the terraqueous Globe. T HE Truth of this Theorem is proved from 1 the Arguments used in Chapter iii. to prove the spherical Figure of the Earth, for they hold as well here as there ; but because those Proofs are chiefly built upon the Phänomena that are reasonably supposed to proceed from such a Figure, that is, rather from the Effects than the Cause ; we shall propose, in this place, a Demonstration which is wholly founded upon natural Causes, and by which Archimedes proved the Superficies of all liquid Bodies to be spherical : in order to which he a ondo...N3 i n took towałefceiding; oftulatan is not to herefore he ficies be took for granted the thrée following Postulata : 1, That the Earth hath a Center, and is therefore fpherical. 2. That it is the Nature of all Liquids, whose Parts are continued and lie at equal Distances from the Center, that the Parts lefs prefsed are expelled from their Places by those that are more pressed, as is manifest from Experience, 3. That every part of the Liquid is pressed by that Part which is above it, perpendicularly, towards the Center of the Earth, if the whole be descending, or is preffed by any other Body. Besides these Poftulata, Archimedes uses a Geome, trical Proposition which is not found demonstrated any where in the Elements; and therefore he demonstrates it himself, which is this: If a Superficies be cut by several Planes, all passing thro' one Point, and each Section be the Periphery of a Circle, whose Center is that one point, then will the Superficies be spherical, and that Point the Center of the Sphere ; as is easily demonstrated, · LET the Superficies of any Body be cut by the Plane I FKEP (Fig. 16.) thro! D, and let the Perimeter of the Section IFKEP be circular, haying D for it's Center ; also let every other Section, made thro' D, have circular Perimeters, and D for their Center. It is to be shewn, that the Superficies of this Body is spherical, and that D is its Center ; i. e. that all the Points in the Superficies are equidistant from D. For we may imagine several right Lines to be drawn from D to other Points of the Superficies, and we must prove them to be all equal. We may suppose a Plane to pass thro' any of them drawn from D to the Superficies, and also thro' DF (for two right Lines cutting one another, or meeting, are in the same Plane by Euclid Lib. ii. Prop. 2.) and the Periphery of the Section will be circular by the Hypothesis ; therefore, the supposed Line drawn will be equal to DF, and so will all other Lines drawn from D to the Superficies be in like manner equal to DF (a). Hence we prove the Superficies to be spherical, having D for it's Center (b): This being premised, the Superficies of all Liquids are thus demonstrated to be spherical. Let us suppose a Liquid at Rest, in the form of EFGH, (Fig. 17.) and let the Earth's Center be D, and imagine this Liquid to be cut by a Plane passing thro' D, so as the Section may be represented in the Superficies by EFGH. We are first to prove that this Line EFGH is circular, or an Arch of the Periphery of a Circle, whose Center is D. If it were poffible not to be circular, then would two Lines, drawn from D to it, be unequal. Let the unequal Lines D E, D G be drawn, viz. let D G be greater than DE, also let the one be the least, and the other the greatest that can be drawn from D. Then draw another right Line DF to EFGH, bisecting the Angle GDE, so as to be longer than DE, but shorter than D G. With this D F as a Radius upon the Center D, describe in the same Plane the Arch IFKH, which will cut the Line D E produced in the Point I, and the Line D G on this Side G, in the Point K, . drawn LIKEWISE with the Radius DL, fomething less than DE, upon the Center D, describe the Arch LMN within the Liquid in the same Plane IFKH. Then are the Parts of the Liquid within the Arch LMN continued, and at equal distances from the Center D: but the Parts between MN are more pressed than those between LM, having above them a greater Quantity, and therefore a greater Weight of Water.. (a) By the Definition of a I (6) By the Definition of a Circle Chap. ii. Article 3. | Globe Cháp. ti. Article 1 2. N 4 . AND AND the Parts of the Liquid within LM, being less pressed, are driven out of their Places by those within M N which take them up, and put the Liquid in Motion. But it was before supposed to lie in this Form at Rest, and still: So that the Liquid, by this, will be both at Rest and in Motion, which is inconsistent. Wherefore the right Lines, drawn from D to EFGH, are not unequal, but equal; and so the Line EFGH is an Arch of a Circle, whose Center is D. The saime may be demonstrated in all Planes cutting the Superficies of the Liquid, and passing thro' D, viz, that the Section is an Arch of a Circle whose Center is D. Therefore since, in the Sur perficies of Liquids, all Planes passing any how thro’ D, are found to produce circular Sections, it will follow, from the foregoing Proposition, that the Superficies of all Liquids is fpherical ; having the Point D, that is, the Center of the Earth, for their Center; as will more manifestly appear from the Proof of the following Proposition. PROPOSITION II. The Sea is not higher than the Land, and therefore the Earth and Water are almost every where of ibe Same Altitude, high Mountains excepted. "THE Truth of this is demonstrated by the preceeding Proposition. For if the Superficies of the Ocean be spherical, and have the same Center with the Superficies of the Earth, and also if the Sca, near the Shore, be no higher than the Land, neither will the middle of the Ocean be elevated above the Earth, because both their Surfaces make up the Superficies of one and the fame Sphere, But some perhaps will not believe the former Proposition, by Reason of the assumed Hypothesis ; . therefore 2 |