a history of science-1-第36节

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s　taken；　busily　seeking　out　by　himself　the　demonstration　of　some　geometrical　proposition　which　he　had　drawn　in　figure；　and　so　earnestly　occupied　therein；　as　he　neither　saw　nor　heard　any　noise　of　enemies　that　ran　up　and　down　the　city；　and　much　less　knew　it　was　taken：　he　wondered　when　he　saw　a　soldier　by　him；　that　bade　him　go　with　him　to　Marcellus。　Notwithstanding；　he　spake　to　the　soldier；　and　bade　him　tarry　until　he　had　done　his　conclusion；　and　brought　it　to　demonstration：　but　the　soldier　being　angry　with　his　answer；　drew　out　his　sword　and　killed　him。　Others　say；　that　the　Roman　soldier　when　he　came；　offered　the　sword's　point　to　him；　to　kill　him：　and　that　Archimedes　when　he　saw　him；　prayed　him　to　hold　his　hand　a　little；　that　he　might　not　leave　the　matter　he　looked　for　imperfect；　without　demonstration。　But　the　soldier　making　no　reckoning　of　his　speculation；　killed　him　presently。　It　is　reported　a　third　way　also；　saying　that　certain　soldiers　met　him　in　the　streets　going　to　Marcellus；　carrying　certain　mathematical　instruments　in　a　little　pretty　coffer；　as　dials　for　the　sun；　spheres；　and　angles；　wherewith　they　measure　the　greatness　of　the　body　of　the　sun　by　view：　and　they　supposing　he　had　carried　some　gold　or　silver；　or　other　precious　jewels　in　that　little　coffer；　slew　him　for　it。　But　it　is　most　certain　that　Marcellus　was　marvellously　sorry　for　his　death；　and　ever　after　hated　the　villain　that　slew　him；　as　a　cursed　and　execrable　person：　and　how　he　had　made　also　marvellous　much　afterwards　of　Archimedes'　kinsmen　for　his　sake。〃　We　are　further　indebted　to　Plutarch　for　a　summary　of　the　character　and　influence　of　Archimedes；　and　for　an　interesting　suggestion　as　to　the　estimate　which　the　great　philosopher　put　upon　the　relative　importance　of　his　own　discoveries。　〃Notwithstanding　Archimedes　had　such　a　great　mind；　and　was　so　profoundly　learned；　having　hidden　in　him　the　only　treasure　and　secrets　of　geometrical　inventions：　as　be　would　never　set　forth　any　book　how　to　make　all　these　warlike　engines；　which　won　him　at　that　time　the　fame　and　glory；　not　of　man's　knowledge；　but　rather　of　divine　wisdom。　But　he　esteeming　all　kind　of　handicraft　and　invention　to　make　engines；　and　generally　all　manner　of　sciences　bringing　common　commodity　by　the　use　of　them；　to　be　but　vile；　beggarly；　and　mercenary　dross：　employed　his　wit　and　study　only　to　write　things；　the　beauty　and　subtlety　whereof　were　not　mingled　anything　at　all　with　necessity。　For　all　that　he　hath　written；　are　geometrical　propositions；　which　are　without　comparison　of　any　other　writings　whatsoever：　because　the　subject　where　of　they　treat；　doth　appear　by　demonstration；　the　maker　gives　them　the　grace　and　the　greatness；　and　the　demonstration　proving　it　so　exquisitely；　with　wonderful　reason　and　facility；　as　it　is　not　repugnable。　For　in　all　geometry　are　not　to　be　found　more　profound　and　difficult　matters　written；　in　more　plain　and　simple　terms；　and　by　more　easy　principles；　than　those　which　he　hath　invented。　Now　some　do　impute　this；　to　the　sharpness　of　his　wit　and　understanding；　which　was　a　natural　gift　in　him：　others　do　refer　it　to　the　extreme　pains　he　took；　which　made　these　things　come　so　easily　from　him；　that　they　seemed　as　if　they　had　been　no　trouble　to　him　at　all。　For　no　man　living　of　himself　can　devise　the　demonstration　of　his　propositions；　what　pains　soever　he　take　to　seek　it：　and　yet　straight　so　soon　as　he　cometh　to　declare　and　open　it；　every　man　then　imagineth　with　himself　he　could　have　found　it　out　well　enough；　he　can　then　so　plainly　make　demonstration　of　the　thing　he　meaneth　to　show。　And　therefore　that　methinks　is　likely　to　be　true；　which　they　write　of　him：　that　he　was　so　ravished　and　drunk　with　the　sweet　enticements　of　this　siren；　which　as　it　were　lay　continually　with　him；　as　he　forgot　his　meat　and　drink；　and　was　careless　otherwise　of　himself；　that　oftentimes　his　servants　got　him　against　his　will　to　the　baths　to　wash　and　anoint　him：　and　yet　being　there；　he　would　ever　be　drawing　out　of　the　geometrical　figures；　even　in　the　very　imbers　of　the　chimney。　And　while　they　were　anointing　of　him　with　oils　and　sweet　savours；　with　his　finger　he　did　draw　lines　upon　his　naked　body：　so　far　was　he　taken　from　himself；　and　brought　into　an　ecstasy　or　trance；　with　the　delight　he　had　in　the　study　of　geometry；　and　truly　ravished　with　the　love　of　the　Muses。　But　amongst　many　notable　things　he　devised；　it　appeareth；　that　he　most　esteemed　the　demonstration　of　the　proportion　between　the　cylinder　（to　wit；　the　round　column）　and　the　sphere　or　globe　contained　in　the　same：　for　he　prayed　his　kinsmen　and　friends；　that　after　his　death　they　would　put　a　cylinder　upon　his　tomb；　containing　a　massy　sphere；　with　an　inscription　of　the　proportion；　whereof　the　continent　exceedeth　the　thing　contained。〃＇2＇　It　should　be　observed　that　neither　Polybius　nor　Plutarch　mentions　the　use　of　burning…glasses　in　connection　with　the　siege　of　Syracuse；　nor　indeed　are　these　referred　to　by　any　other　ancient　writer　of　authority。　Nevertheless；　a　story　gained　credence　down　to　a　late　day　to　the　effect　that　Archimedes　had　set　fire　to　the　fleet　of　the　enemy　with　the　aid　of　concave　mirrors。　An　experiment　was　made　by　Sir　Isaac　Newton　to　show　the　possibility　of　a　phenomenon　so　well　in　accord　with　the　genius　of　Archimedes；　but　the　silence　of　all　the　early　authorities　makes　it　more　than　doubtful　whether　any　such　expedient　was　really　adopted。　It　will　be　observed　that　the　chief　principle　involved　in　all　these　mechanisms　was　a　capacity　to　transmit　great　power　through　levers　and　pulleys；　and　this　brings　us　to　the　most　important　field　of　the　Syracusan　philosopher's　activity。　It　was　as　a　student　of　the　lever　and　the　pulley　that　Archimedes　was　led　to　some　of　his　greatest　mechanical　discoveries。　He　is　even　credited　with　being　the　discoverer　of　the　compound　pulley。　More　likely　he　was　its　developer　only；　since　the　principle　of　the　pulley　was　known　to　the　old　Babylonians；　as　their　sculptures　testify。　But　there　is　no　reason　to　doubt　the　general　outlines　of　the　story　that　Archimedes　astounded　King　Hiero　by　proving　that；　with　the　aid　of　multiple　pulleys；　the　strength　of　one　man　could　suffice　to　drag　the　largest　ship　from　its　moorings。　The　property　of　the　lever；　from　its　fundamental　principle；　was　studied　by　him；　beginning　with　the　self…　evident　fact　that　〃equal　bodies　at　the　ends　of　the　equal　arms　of　a　rod；　supported　on　its　middle　point；　will　balance　each　other〃；　or；　what　amounts　to　the　same　thing　stated　in　another　way；　a　regular　cylinder　of　uniform　matter　will　balance　at　its　middle　point。　From　this　starting…point　he　elaborated　the　subject　on　such　clear　and　satisfactory　principles　that　they　stand　to…day　practically　unchanged　and　with　few　additions。　From　all　his　studies　and　experiments　he　finally　formulated　the　principle　that　〃bodies　will　be　in　equilibrio　when　their　distance　from　the　fulcrum　or　point　of　support　is　inversely　as　their　weight。〃　He　is　credited　with　having　summed　up　his　estimate　of　the　capabilities　of　the　lever　with　the　well…known　expression；　〃Give　me　a　fulcrum　on　which　to　rest　or　a　place　on　which　to　stand；　and　I　will　move　the　earth。〃　But　perhaps　the　feat　of　all　others　that　most　appealed　to　the　imagination　of　his　contemporaries；　and　possibly　also　the　one　that　had　the　greatest　bearing　upon　the　position　of　Archimedes　as　a　scientific　discoverer；　was　the　one　made　familiar　through　the　tale　of　the　crown　of　Hiero。　This　crown；　so　the　story　goes；　was　supposed　to　be　made　of　solid　gold；　but　King　Hiero　for　some　reason　suspected　the　honesty　of　the　jeweller；　and　desired　to　know　if　Archimedes　could　devise　a　way　of　testing　the　question　without　injuring　the　crown。　Greek　imagination　seldom　spoiled　a　story　in　the　telling；　and　in　this　case　the　tale　was　allowed　to　take　on　the　most　picturesque　of　phases。　The　philosopher；　we　are　assured；　pondered　the　problem　for　a　long　time　without　succeeding；　but　one　day　as　he　stepped　into　a　bath；　his　attention　was　attracted　by　the　overflow　of　water。　A　new　train　of　ideas　was　started　in　his　ever…receptive　brain。　Wild　with　enthusiasm　he　sprang　from　the　bath；　and；　forgetting　his　robe；　dashed　along　the　streets　of　Syracuse；　shouting：　〃Eureka！　Eureka！〃　（I　have　found　it！）　The　thought　that　had　come　into　his　mind　was　this：　That　any　heavy　substance　must　have　a　bulk　proportionate　to　its　weight；　that　gold　and　silver　differ　in　weight；　bulk　for　bulk；　and　that　the　way　to　test　the　bulk　of　such　an　irregular　object　as　a　crown　was　to　immerse　it　in　water。　The　experiment　was　made。　A　lump　of　pure　gold　of　the　weight　of　the　crown　was　immersed　in　a　certain　receptacle　filled　with　water；　and　the　overflow　noted。　Then　a　lump　of　pure　silver　of　the　same　weight　was　similarly　immersed；　lastly　the　crown　itself　was　immersed；　and　of　coursefor　the　story　must　not　lack　its　dramatic　sequelwas　found　bulkier　than　its　weight　of　pure　gold。　Thus　the　genius　that　could　balk　warriors　and　armies　could　also　foil　the　wiles　of　the　silversmith。　Whatever　the　truth　of　this　picturesque　narrative；　the　fact　remains　that　some；　such　experiments　as　these　must　have　paved　the　way　for　perhaps　the　greatest　of　all　the　studies　of　Archimedesthose　that　relate　to　the　buoyancy　of　water。　Leaving　the　field　of　fable；　we　must　now　examine　these　with　some　precision。　Fortunately；　the　writings　of　Archimedes　himself　are　still　extant；　in　which　the　resul