experiment experiment 18th century experiment determine mean density earth funded grant conducted summer scottish mountain experiment involved measuring tiny attraction nearby mountain considered ideal location search candidate mountains thanks isolation symmetrical shape experiment noted survey mason line experiment previously considered rejected practical demonstration theory team scientists notably royal convinced effect undertook conduct experiment angle depended relative volumes earth mountain density volume density earth known turn yield approximate values planets sun previously known terms relative additional benefit concept lines devised process surveying mountain later standard technique background hangs straight downwards symmetrical field sufficiently large mass mountain nearby attraction pull bob slightly true change line angle known object star carefully measured opposite sides mountain mass mountain independently established determination volume estimate mean density rocks values provide mean density earth extension mass considered effect thought real mountain produce small measure effects wrote scale newton calculations suggested minutes arc mile high mountain angle slight theoretical capability instruments day experiment test newton idea provide supporting evidence law universal estimates mass density earth masses astronomical objects known terms relative mass earth provide reasonable values planets sun data capable determining value newton constant goal references value appear scientific literature years later finding mountain pair french named attempt experiment conducting measurements metre volcano ecuador expedition left france south_america try measure arc length degree latitude near equator took advantage opportunity attempt experiment december difficult conditions terrain climate conducted pair measurements altitudes wrote paper able detect seconds arc significance results suggesting experiment better carried easier conditions france england added experiment proved earth hollow shell day including suggested attempt experiment proposed suggested experiment honour nation proposed yorkshire cumberland suitable targets formed consider matter appointing members committee surveyor find suitable mountain lengthy search summer mason reported best candidate spelled metre peak lying central scottish highlands mountain stood isolation nearby hills reduce influence symmetrical east west ridge calculations steep northern southern slopes allow experiment sited close centre mass effect mason declined conduct work offered commission guinea day task fell granted temporary leave duties aided task mathematician surveyor mathematician workforce labourers engaged construct assist surveying science team particularly equipped astronomical instruments included inch brass quadrant cook transit venus expedition foot sector precision clock timing astronomical observations acquired chain surveying mountain pair measuring altitude generous funding experiment available transit venus expedition turned society king measurements astronomical constructed north south mountain plus accommodate equipment scientists workforce housed rough canvas tents astronomical measurements conducted necessary determine distances respect line set stars precise time passed south weather conditions frequently unfavourable mist rain south observatory able measurements stars direction observations stars north conducted set observations stars set stars conducting sets measurements plane sector facing east west successfully avoided systematic errors arising sector determine mountain necessary account earth observer moving north south local shift angle change latitude accounting effects light showed difference locally determined observers north south arc seconds surveying team provided difference latitude stations able rounding accuracy observations announce sum north south published initial results preliminary data mountain shape position center gravity led expect mean earth equal half able preliminary announcement mean density earth approximately double accurate value await completion surveying process took opportunity note exhibited attraction mountains newton square law confirmed presented medal biographer later noting doubts remained respect truth system totally removed surveying work surveying team greatly hampered weather took complete task find volume mountain necessary divide set vertical volume task falling considerable obtained thousands thousand points mountain coincide surveyed heights sense data hit idea series lines set intervals measure values marking points equal height easily determine heights lines instant impression form terrain invented lines common use depicting relief individual attractions formed grid process survey task occupied time years present results page paper found attraction bob earth times sum attractions mountain north south stations density earth actual implied ratio accounting effect latitude gravity able state earth mean density formula formula mountain lengthy process surveying mountain greatly affected outcome calculations took density announced density earth formula comparison modern accepted figure density earth error mean density earth greatly exceed surface rocks naturally meant dense material lying deeper correctly core material likely metallic density estimated metallic portion occupy diameter earth value mean density earth able set values tables previously able express major solar system objects relative terms repeat experiments accurate measurement mean density earth years sensitive balance measure attraction large masses lead figure currently accepted value result significantly improved care conducted experiment accuracy result led associated carried second survey basis rock strata suggested density elderly vigorously defended original value paper society calculations raised density closer modern value low significantly poorer years earlier experiment repeated director general ordnance survey instead hill arthur seat central edinburgh resources ordnance survey disposal james extended survey kilometre radius taking far borders obtained density experiment undertook variation work instead computing local differences experiment accurate comparison period period function local acceleration expected run slowly altitude mass mountain act reduce difference experiment advantage considerably easier conduct achieve desired accuracy necessary measure period million experiment yielded value mass earth corresponding mean density modern examination data able account factors team benefit radius digital elevation model greatly improved knowledge geology particular computer report produced mean earth density compared modern figure stood testament accuracy astronomical observations mathematical procedure consider force right greatly exaggerated analysis simplified considering attraction mountain bob mass situated distance centre mass mountain mass density small angle attraction weight directed earth sum results tension string earth mass radius density forces bob given newton law formula newton constant eliminated taking ratio formula volumes mountain earth static horizontal vertical components string tension related forces angle formula formula known measured value ratio obtained formula
Schiehallion experiment