A R C A R C 381 sists of two books, and may be called the foundation of theoretical mechanics, for the previous contributions of Aristotle were comparatively vague and unscientific. In the first book there are fifteen propositions, with eight postulates; and demonstrations are given, much the same as those still employed, of the centres of gravity (1) of any two weights, (2) of any parallelogram, (3) of any triangle, (4) of any trapezoid. The second book is devoted to the finding the centres of gravity of parabolic segments. (G.) The Quadrature of the Parabola, (Terpaycovicr/Aos >:rar>a./3orj<>) is a book in twenty-four propositions, demon strating that the area of a parabola is f of the triangle having its double ordinate for base and abscissa for height. His method of arriving at this result is most interesting, as being a sort of rude approximation to the modern process of area summation by integration. The expedients to which he resorted to avoid the idea of infinity are no less curious than they are admirable. (7.) On Bodies floating in Liquids (Tltpl TOJV rSart (<j)io-Tap.ei>(av), is a treatise in two books, on the principles of floating, and the positions of equilibrium of floating parabolic conoids. (8.) The Psammites (6 i^a/^urn??, Lat. Arcnarius, or sand counter), a small treatise, dedicated to Gelo, the eldest son of Hiero, on arithmetical numeration, applied to reckoning grains of sand, is curious as containing the germ of the modern system of logarithms. (9.) A collection of Lemmas, consisting of fifteen pro positions in plane geometry. This has come down to us through a Latin version of an Arabic manuscript, and its authenticity has been questioned. In the edition of Archimedes, published by Revault at Paris in 1G15, the following works are said to be lost : On the Crown of Hiero ; on the Cochleon, or Water-Screw ; on the Helicon, or Endless Screiv ; on the Trispaston, or Com bination of Wheels and Axles ; on the Machines employed at the Siege of Syracuse ; on the Burning Mirror; on the .Machines moved by Air and Water ; and on the Material Sphere. We do not know, however, that he ever committed nccounts of his mechanical inventions to writing. The Edito princcps of the works of Archimedes, with the commen tary of Eutocius, is that printed at Basil, in 1544, in Greek and Latin, by Hervagius. A Latin translation of them was published by Isaac Barrow in 1675 (London, 4to). Nicholas Tartalea (a celebrated algebraist), published in Greek and Latin the treatises on the Centre of Gravity, on the Quadrature of tJic Parabola, and on Floating Bodies (Venice, 1 543). Frederic Commandine edited the beautiful Aldine edition of 1558, 4to, which contains Circuli JJimcnsio, Do Lincis S^nralibus, Quadraliira Farabolcs, <t-c., Conoidibus ct Splicroidibus, and DC wimcro Arcncc ; and in 15G5 the same mathematician published the two books De Us qitce r- kuntur in Aqud. The most complete and magnificent edition of the works is that edited by Torelli, and published with the com mentaries of Eutocius at Oxford, in 1792, folio. The most valuable edition of the Arenarius, which is also the first modern translation of any part of Archimedes, is that published in English by Anderson (London, 1784), with useful notes and illustrations. The first modern translation of the works is the French edition published by F. Peyrard (Paris, 1808, 2 vols. Svo). A German translation, by Nizze, was published at Stralsund in 1S24, and another by Gutenacker, at "Wurzburg, 1S28, Svo. See Quart. Ecv., vol. iii. p. 89; PlvAaieh sLifeofJIfareelha; PopeBlount s Ccnsura Cclcbrium Authorum (London, 1690) ; the Arennrius of Archimedes, Oxford, IS" 7; Ed. Ret:, vol. xi. p. 185; Powell s History of Natural Philo sophy (Lardner s Cycl.), p. 40. ARCHIMEDES, SCREW OF, a machine for raising water, said to have been invented by Archimedes, for the purpose of removing water from the hold of a large ship that had been built by King Hiero. It consists of a water tight cylinder, enclosing a chamber walled off by spiral divisions running from end to end, inclined to the horizon, with its lower open end placed in the water to be jaised. A section of it is shown in the accompanying woodcut. The water, hile occupying the lowest portion in each suc cessive division of the spiral chamber, is lifted mechanically by the turning of the machine. Another form of tha Screw of Archimedes. screw has the spiral revolving free in a fixed cylinder, but neither of the machines is now much used. ARCHIPELAGO, a name -which, though it is now applied to any island-studded sea, was formerly the distinctive designation of what, though still known aa the Archipelago, is often distinguished as the Grecian Archipelago, namely, that part of the Mediterranean whick lies between Greece and Thessaly on the W. and Asia Minor on the E. the ^Egean Sea ( Aiycuov IleAayos) of the ancients. Several etymologies of the name have been proposed, as (1), It is a corruption of the ancient name; (2), it is from the modern Greek, Ayio LTcAayo, the Holy Sea; (3), it arose at the time of the Latin empire, and means the Sea of the Kingdom (Arche}; (4), it is a trans lation of the Turkish name, Ak Deguiz, Argon Pdagos, the White Sea ; (5), it is simply Archipelagus, the Chief Sea. The Grecian Archipelago abounds in islands, of which the following are the chief : Thaso, near the Rumelian (Thradan) coast, opposite the mouth of the Karasu (Westus) ; Samothraki, fronting the Gulf of Saros ; Imbro and Lemnos, in prolongation of the peninsula of Gallipoli (Chersonesus Thradca) ; Skiathos, Skopelo, Celadroni, Peristeria, &c., running out from the southern extremity of the Thessalian coast ; Negropont (IJubcea), the largest of all, along the east coast of Greece; Skyros, with its satellites, east of Negropont ; Mitylene (Lesbos) and Chios, off Asia Minor ; Samo and Nikari (Icaria), in prolonga tion from Cape St Maria (Mycale Pr.) ; Stancho (Cos, la-- rav-Kw), in the Gulf of Cos, with Kalymno to the north ; and finally, the great group of the Cyclades, of wlu ch the- most important are Andros, Tenos, Myconos, and Delos, in prolongation of Eubcea, Zea (Ceos), and Cythnos, running out from the south of Attica, and Melos, Kimolos, Siphnos, Antiparos, Paros, Naxos, Amorgos, Astynactea, forming a curve, from west to east, with its convexity to the north,, while to the south are a number of smaller islands. This profusion gives beauty and picturesqueness to the sea, but renders its navigation difficult and dangerous, notwith standing the large number of safe and commodious gulfs and bays. Many of the islands are of volcanic formation ; while others, as Paros, are mainly composed of pure white marble. The larger islands have some very fertile and well- watered valleys and plains. The chief productions are wheat, wine, oil, mastic, figs, raisins, honey, wax, cotton, and silk. The people are employed in fishing for coral and sponges, as well as for bream, mullet, and other fish. The men are hardy, well built, and handsome ; and the women are noted for their beauty, the ancient Greek type being well preserved. The Cyclades belong to Greece ; most of the other islands to Turkey. The other Archipelagoes, portions of ocean with numerous islands in close contiguity, as the Indian, Caribbean,
Patagonian, <i-c., will be described in their respective places.