ARCHIMEDES, transliitod from the Dutch in Gilbert's " Aiinnlcn <]er I'hysik," vol. liii. p. •24"2. The most pro- });ible conclusion seems to be, that Archimedes had oil some occasion set fire to a ship or ships by means of a burning mirror, and that later writers I'alscly connected the circumstance with the sioge of Syracuse. (See Ersch and Gruber's Cyclop, art. ArcJiim. note, and Gibbon, chap. 40.) The following additional instances of Archi- mi-des' skill in the application of science have been collected from various authors by Rivaltus (who edited his works in lb' 1 5) and others. He detected the mixture of silver in a crown which Hiero had ordered to be made of gold, and detennined the proportions of the two metids, by a method suggested to him by the overflowing of the water hen he stepped into a bath. When the thought struck him he is said to have been so much pleased that, forgetting to put on his clothes, he ran home shouting cupTj/ca, euprj/ca. The par- ticulars of the calculation are not preserved, but it probably depended upon a direct comparison of the weights of certain volumes of silver and gold with the weight and volume of the crown ; the volumes being measured, at least ii. the case of the crown, by the quantity of water displaced when the masfe v.'as immersed. It is not likely that Archimedes was at this time acquainted with the theorems demonstrated in his hydrostatical treatise con- cerning the loss of xfcight of bodies immersed in water, since he would hardly have evinced such lively gratification at the obvious discovery that they might be applied to the problem of the crown; liis delight must rather have arisen from his now first catching sight of a line of investigation which led immediately to the solution of the problem in question, and ultimately to the important theorems referred to. (Vitruv. ix. 3. ; Proclus. Comm. in lib. i. Eucl. ii. 3.) He superintended the building of a ship of ex- traorflinary size for Hiero, of which a description is given in Athenaeus (v. p. 206, u), where he is also said to have moved it to the sea by the help of a screw. According to Proclus, this ship was intended by Hiero as a present to Ptolemy ; it may possibly have been the occasion of Archimedes' visit to Eg}-pt. He invented a machine called, from its form. Cochlea, and now known as the water-screw of Archimedes, for pumping the water out of the hold of this vessel ; it is said to have been also used in Eg}-pt by the inhabitants of the Delta in irrigating their lands. (Died. i. 34; Vitruv. x. 11.) An investigation of the mathematical theory of the water screw is given in Ersch and Gruber. The Arabian historian Abulpharagius attributes to Archimedes the raising of the dykes and bridges used as defences against the overflowing of the Nile. (Pope-Blount, Censura, p. 32.) Tzetzes and Oribasius {de Much, xxvi.) speak of his Tria- p(isl, a machine for moving large weights; probably a combination of pulleys, or wheels and axles. A In/dratdic organ (a musical instrument) is mention- ed by Tertullian (c/e Anima, cap. 14), but Pliny (vii. 37) attributes it to Ctesibius. (See also Pap- pus, Math. Coll. lib. 8, introd.) An apparatus called loculus. apparently somev/hat resembling the Chinese puzzle,, is also attributed to Archimedes. ( Fortunatianus, do Arte Metrica,, p. 2G84.) His most celebrated performance was the construction of a spluire ; a kind of orrery, representing the ARCHIMEDES. 271 movements of the heavenh' bodies, of which we have no particular description. (Claudian, Kpigr. xxi. in Sphueram Archimcdis; Cic.A'it<^ Dcor.'n. 35, Tiisc. Di^p. i. 2.5 ; Sext. Empir. adv. Math. ix. 115; Lactant. Dii'. Inst. ii. 5 ; Ov. Fust. vi. 277.) When Syracuse was taken, Archimedes was killed by the Roman soldiers, ignorant or careless who he might be. The accounts of his death vary in some particulars, but mostly agree in describing him as intent upon a mathematical problem at the time, lie was deeply regretted by Marcellus, who directed his burial, and befriended his surviving relations. (Liv. xxv. 31; Vaier. Max. viii, 7. § 7; Plut. ^[arcetl. 19 ; Cic. de fin. v. 19.) Upon his tomb was placed the figure of a sphere inscribed in a cylinder, in accordance with his known wisli, and in commemoration of the discovery which he most valued. When Cicero was quaestor in Sicily (n. c. 75) he found this tomb near one of the gates of the city, almost hid amongst briars, and forgotten by the Syracusans. {Tnsc. Disp. v. 23.) Of the general character of Archimedes we have no direct account. But his apparently disinterest- ed devotion to his friend and admirer Hiero, in whose service he was ever ready to exercise his ingenuity upon objects which his own taste would not have led him to choose (for there is doubtless some truth in what Plutarch says on this point) ; the afl'ectionate regret which he expn^sses for his deceased master Conon, in writing to his surviving friend Dositheus (to whom most of his works are addressed) ; and the luiaffected simplicity with which he announces his own discoveries, seem to afford probable grounds for a favourable estimate of it. That his intellect was of the very highest order is unquestionable. He possessed, in a degree never exceeded unless by Newton, the inventive genius which discovers new provinces of inquiry, and finds new points of view for old and familiar objects; the clearness of conception which is essential to the resolution of complex phaenomena into their constituent elements ; and the power and habit of intense and persevering thought, with- out which other intellectual gifts fire comparatively fruitless. (See the introd. to the treatise " De Con. et Sphaer.") It may be noticed that he resembled other great thinkers, in his habit (^-pomplete ab- straction from outward things, when inflecting on subjects which made considerable demands on his ment{il powers. At such times he would forget to eat his meals, and require compulsion to take him to the bath. (Plut. /. c.) Compare the stories of Newton sitting great part of the day half dressed on his bed, while composing the Principia ; and of Socrates standing a whole day and night, thinking, on the same spot. (Plat. Symp. p. 220, c. d.) The success of Archimedes in conquering difficulties seems to have made the expression irpSSKyj/xa 'Ap- X'/U-^Sciot' proverbial. (See Cic. ad Ait. xiii. 28, pro Cluent. 32.) The following works of Archimedes have come down to us : A treatise on Equiponderants and Centi-es of Grainty, in Avhich the theory of the equilibrium of the straight lever is demonstrated, both for commensurable and incommensurable weights ; and various properties of the centres of gravity of plane surfaces bounded by three or four straight lines, or by A straight line and a parabola, are established. Tlic Quadrature of the Parabola^ in which it is proved, that the area cut off from a parabola by
