file :i* includes ! orig9al illu/rations4 ,see #cejbd-;h4htm or #cejbd-;h4zip3 7https3_/_/www4gut5b]g4org_/ca*e_/epub_/ #cejbd_/pg#cejbd-;images4html7 or 7https3_/_/www4gut5b]g4org_/files_/#cejb d_/cejbd-;h4zip7 ,transcrib]'s note3 ,?is is ,pap] #dd f ! ,smi?sonian ,in/itution ,unit$ ,/ates ,national ,museum ,bullet9 #bdj1 compris+ ,pap]s #cd-dd1 :i* w also be available z a complete e-book4 ,! front mat]ial1 introduction & relevant index entries f ! ,bullet9 are includ$ 9 ea* s+le-pap] e-book4 ,ma!matical notation us$ 9 ?is e-text3 #a4 ,greek lett]s are repres5t$ by ! "n ( ! lett] 9 squ>e brackets2 e4g41 pi4 #b4 ,subscripts are d5ot$ by und]score foll[$ by ! subscript 9 curly braces2 e4g41 ,tn4 ,sup]scripts are d5ot$ by a c>et foll[$ by ! sup]script 9 curly braces2 e4g41 ,tn4 ,to avoid possible confusion1 subscript$ v>iables :i* are rais$ to a p[] are enclos$ 9 brackets1 ?us 7,t#a7b repres5ts ',t "o squ>$'4 #c4 ,squ>e root is d5ot$ by sqrt4 #d4 ,to improve readability1 italic m>kup 7und]scores enclos+ text7 has be5 omitt$ f lett]s us$ 9 ma!matical =mulae1 & "s equations h be5 set 'out ( l9e'4 ,please see ! end ( ! book = a li/ ( corrections4 ,smi?sonian ,in/itution ,unit$ ,/ates ,national ,museum ,bullet9 #bdj ,illu/ration ,smi?sonian ,press ,museum ( ,hi/ory & ,te*nology ,contributions f ! ,museum ( ,hi/ory & ,te*nology ,pap]s #cd-dd ,on ,sci5ce & ,te*nology ,smi?sonian ,in/itution 4 ,wa%+ton1 ,d4,c4 #aiff 99 99 99 99 99 ,publications ( ! ,unit$ ,/ates ,national ,museum ,! s*ol>ly & sci5tific publications ( ! ,unit$ ,/ates ,national ,museum include two s]ies1 ,proce$+s ( ! ,unit$ ,/ates ,national ,museum & ,unit$ ,/ates ,national ,museum ,bullet94 ,9 ^! s]ies1 ! ,museum publi%es orig9al articles & monographs deal+ ) ! collections & "w ( its con/itu5t museums--,! ,museum ( ,natural ,hi/ory & ! ,museum ( ,hi/ory & ,te*nology--sett+ =? newly acquir$ facts 9 ! fields ( an?ropology1 biology1 hi/ory1 geology1 & te*nology4 ,copies ( ea* publication are di/ribut$ to libr>ies1 to cultural & sci5tific organizations1 & to speciali/s & o!rs int]e/$ 9 ! diff]5t subjects4 ,! ,proce$+s1 begun 9 #ahgh1 are int5d$ = ! publication1 9 sep>ate =m1 ( %ort] pap]s f ! ,museum ( ,natural ,hi/ory4 ,^! are ga!r$ 9 volumes1 octavo 9 size1 ) ! publication date ( ea* pap] record$ 9 ! table ( cont5ts ( ! volume4 ,9 ! ,bullet9 s]ies1 ! fir/ ( :i* 0 issu$ 9 #ahge1 appe> long]1 sep>ate publications consi/+ ( monographs 7occasionally 9 sev]al p>ts7 & volumes 9 :i* are collect$ works on relat$ subjects4 ,bullet9s are ei!r octavo or qu>to 9 size1 dep5d+ on ! ne$s ( ! pres5tation4 ,s9ce #aijb pap]s relat+ to ! botanical collections ( ! ,museum ( ,natural ,hi/ory h be5 publi%$ 9 ! ,bullet9 s]ies "u ! head+ ,contributions f ! ,unit$ ,/ates ,national ,h]b>ium1 & s9ce #aiei1 9 ,bullet9s titl$ ,contributions f ! ,museum ( ,hi/ory & ,te*nology1 h be5 ga!r$ %ort] pap]s relat+ to ! collections & rese>* ( t ,museum4 ,! pres5t collection ( ,contributions1 ,pap]s #cd-dd1 comprises ,bullet9 #bdj4 ,ea* ( ^! pap]s has be5 previ\sly publi%$ 9 sep>ate =m4 ,! ye> ( publication is %[n on ! la/ page ( ea* pap]4 ,,frank ,a4 ,,taylor ,director1 ,unit$ ,/ates ,national ,museum 99 99 99 99 99 ,contributions f ! ,museum ( ,hi/ory & ,te*nology3 ,pap] #dd ,,developm5t ,,( ,,gravity ,,p5dulums ,,9 ,,! #ai,,? ,,c5tury by ,victor ,f4 ,l5z5 & ,rob]t ,p4 ,mul?auf ,,galileo1 ,,huyg5s1 ,,& ,,newton #cjd ,,figure ,,( ,,! ,,e>? #cjf ,,e>ly ,,types ,,( ,,p5dulums #cji ,,kat]',s ,,conv]tible ,,& ,,inv>iable ,,p5dulums #cad ,,repsold-,,bessel ,,rev]sible ,,p5dulum #cbj ,,peirce ,,& ,,def=ges ,,inv>iable1 ,,rev]sible ,,p5dulums #cbg ,,von ,,/]neck ,,& ,,m5d5hall ,,p5dulums #cca ,,absolute ,,value ,,( ,,gravity ,,at ,,potsdam #cch ,,application ,,( ,,gravity ,,surveys #cdb ,,summ>y #cdf ,,victor ,f4 ,,l5z5 ,,& ,,rob]t ,p4 ,,mul?auf ,,developm5t ,,( ,,gravity ,,p5dulums ,,9 ,,! #ai? ,,c5tury ,illu/ration3 ,figure #a4--;,a ,,/udy ,,( ,,! ,,figure ,,( ,,! ,,e>? ,,0 "o ( ! e>lie/ projects ( ! ,fr5* ,academy ( ,sci5ces4 ,9 ord] to te/ ! effect ( ! e>?'s rotation on its gravitational =ce1 ! ,academy 9 #afgb s5t ,jean ,ri*] to ! equatorial isl& ( ,cay5ne to comp>e ! rate ( a clock :i* 0 kn[n to h kept accurate "t 9 ,p>is4 ,ri*] f\nd t ! clock lo/ #b m9utes & #bh seconds at ,cay5ne1 indicat+ a sub/antial decrease 9 ! =ce ( gravity on ! p5dulum4 ,subsequ5t p5dulum exp]im5ts reveal$ t ! p]iod ( a p5dulum v>i$ n only ) ! latitude b also regionally1 "u ! influ5ce ( topographical features su* z m\nta9s4 ,x became cle> t ! measurem5t ( gravity %\ld be made a "p ( ! "w ( ! geodetic surveyor4 ,! hi/ory ( gravity p5dulums dates back to ! "t ( ,galileo4 ,aft] ! discov]y ( ! v>iation ( ! =ce ( gravity ov] ! surface ( ! e>?1 gravity measurem5t became a major conc]n ( physics & geodesy4 ,?is article traces ! hi/ory ( ! developm5t ( in/rum5ts = ?is purpose4 ,,! ,,au?ors3 ,victor ,f4 ,l5z5 is ,pr(essor ( ,physics1 ,em]itus1 at ! ,univ]sity ( ,cali=nia at ,b]keley & ,rob]t ,p4 ,mul?auf is ,*airman ( ! ,dep>tm5t ( ,sci5ce & ,te*nology 9 ! ,smi?sonian ,in/itution's ,museum ( ,hi/ory & ,te*nology4 ,! int5sity ( gravity1 or ! accel]ation ( a freely fall+ body1 is an important physical quantity = ! sev]al physical sci5ces4 ,! int5sity ( gravity det]m9es ! weight ( a /&>d p\nd or kilogram z a /&>d or unit ( =ce4 ,9 physical exp]im5ts1 ! =ce on a body may be measur$ by det]m9+ ! weight ( a kn[n mass :i* s]ves to e/abli% equilibrium aga9/ x4 ,?us1 9 ! absolute det]m9ation ( ! amp]e ) a curr5t balance1 ! =ce betwe5 two coils c>ry+ curr5t is balanc$ by ! e>?'s gravitational =ce ^u a body ( det]m9able mass4 ,! int5sity ( gravity ent]s into det]m9ations ( ! size ( ! e>? f ! angul> velocity ( ! moon1 its di/ance f ! e>?1 & ,newton's inv]se squ>e law ( gravitation & ! laws ( motion4 ,pr$iction ( ! motion ( an artificial satellite requires an accurate k ( gravity = ?is a/ronomical problem4 ,! gravity field ( ! e>? also provides data = a det]m9ation ( ! figure ( ! e>?1 or geoid1 b = ?is problem ( geodesy relative values ( gravity are suffici5t4 ,if g is ! int5sity ( gravity at "s ref]5ce /ation1 & ,deltag is ! diff]5ce betwe5 int5sities at two /ations1 ! values ( gravity 9 geodetic calculations ent] z ratios 7,deltag7_/g ov] ! surface ( ! e>?4 ,gravimetric inve/igations 9 conjunction ) o!r =ms ( geophysical inve/igation1 su* z seismology1 furni% data to te/ hypo!ses conc]n+ ! int]nal /ructure ( ! e>?4 ,:e!r ! int5sity ( gravity is s\ght 9 absolute or relative measure1 ! mo/ widely us$ in/rum5t = its det]m9ation s9ce ! creation ( classical me*anics has be5 ! p5dulum4 ,9 rec5t decades1 !re h be5 inv5t$ gravity met]s bas$ ^u ! pr9ciple ( ! spr+1 & ^! in/rum5ts h made possible ! rapid det]m9ation ( relative values ( gravity to a high degree ( accuracy4 ,! gravity met]1 h[ev]1 mu/ be calibrat$ at /ations :]e ! absolute value ( gravity has be5 det]m9$ by o!r means if absolute values are s\ght4 ,= absolute det]m9ations ( gravity1 ! p5dulum hi/orically has be5 ! pr9cipal in/rum5t employ$4 ,al?\gh alt]native me?ods ( det]m9+ absolute values ( gravity are n[ 9 use1 ! p5dulum reta9s its value = absolute det]m9ations1 & ev5 reta9s x = relative det]m9ations1 z is exemplifi$ by ! ,cambridge ,p5dulum ,app>atus & t ( ! ,dom9ion ,obs]vatory at ,ottawa1 ,ont>io4 ,! p5dulums employ$ = absolute or relative det]m9ations ( gravity h be5 ( two basic types4 ,! fir/ =m ( p5dulum us$ z a physical in/rum5t consi/$ ( a weight susp5d$ by a fib]1 cord1 or f9e wire1 ! upp] end ( :i* 0 atta*$ to a fix$ support4 ,su* a p5dulum may be call$ a simple p5dulum2 ! enclosure ( ! ^w simple by quotation m>ks is to indicate t su* a p5dulum is an approximation to a simple1 or ma!matical p5dulum1 a conceptual object :i* consi/s ( a mass-po9t susp5d$ by a weightless inext5sible cord4 ,if l is ! l5g? ( ! simple p5dulum1 ! "t ( sw+ 7half-p]iod 9 ! s5se ( physics7 = vibrations ( inf9itely small amplitude1 z d]iv$ f ,newton's laws ( motion & ! hypo!sis t weight is proportional to mass1 is ,t pisqrt7l_/g74 ,! second =m ( p5dulum is ! comp\nd1 or physical1 p5dulum4 ,x consi/s ( an ext5d$ solid body :i* vibrates ab\t a fix$ axis "u ! action ( ! weight ( ! body4 ,a comp\nd p5dulum may be con/itut$ to oscillate ab\t "o axis only1 9 :i* case x is nonrev]sible & applicable only = relative measurem5ts4 ,or a comp\nd p5dulum may be con/itut$ to oscillate ab\t two axes1 9 :i* case x is rev]sible 7or conv]tible7 & may be us$ to det]m9e absolute values ( gravity4 ,capt4 ,h5ry ,kat]1 ,f4,r4,s41 dur+ ! ye>s #ahag-ahah 0 ! fir/ to design1 con/ruct1 & use a comp\nd p5dulum = ! absolute det]m9ation ( gravity4 ,he con/ruct$ a conv]tible p5dulum ) two knife edges & ) x det]m9$ ! absolute value ( gravity at ! h\se ( ,h5ry ,br[ne1 ,f4,r4,s41 9 ,portl& ,place1 ,london4 ,he !n con/ruct$ a simil> comp\nd p5dulum ) only "o knife edge1 & swung x to det]m9e relative values ( gravity at a numb] ( /ations 9 ! ,briti% ,isles4 ,! #ai? c5tury witness$ ! developm5t ( ! !ory & practice ( obs]vations ) p5dulums = ! det]m9ation ( absolute & relative values ( gravity4 ,galileo1 ,huyg5s1 & ,newton ,! p5dulum has be5 bo? an objective & an in/rum5t ( physical inve/igation s9ce ! f\ndations ( classical me*anics 7 fa%ion$ 9 ! #ag? c5tury4#a ,x is tradition t ! y\?ful ,galileo discov]$ t ! p]iod ( oscillation ( a p5dulum is con/ant by obs]vations ( ! sw+s ( ! great lamp susp5d$ f ! ceil+ 9 ! ca!dral ( ,pisa4#b ,! lamp 0 only a r\gh approximation to a simple p5dulum1 b ,galileo lat] p]=m$ m accurate exp]im5ts ) a simple p5dulum :i* consi/$ ( a heavy ball susp5d$ by a cord4 ,9 an exp]im5t design$ to confirm 8 laws ( fall+ bodies1 ,galileo lift$ ! ball to ! level ( a giv5 altitude & releas$ x4 ,! ball asc5d$ to ! same level on ! o!r side ( ! v]tical equilibrium position & !reby confirm$ a pr$iction f ! laws4 ,galileo also discov]$ t ! p]iod ( vibration ( a simple p5dulum v>ies z ! squ>e root ( its l5g?1 a result :i* is express$ by ! =mula = ! "t ( sw+ ( ! ideal simple p5dulum4 ,he also us$ a p5dulum to measure lapse ( "t1 & he design$ a p5dulum clock4 ,galileo's exp]im5tal results are important hi/orically1 b h requir$ correction 9 ! light ( subsequ5t measurem5ts ( great] precision4 ,m]s5ne 9 #afdd made ! fir/ det]m9ation ( ! l5g? ( ! seconds p5dulum1#c t is1 ! l5g? ( a simple p5dulum t beats seconds 7half-p]iod 9 ! s5se ( physics74 ,subsequ5tly1 he propos$ ! problem to det]m9e ! l5g? ( ! simple p5dulum equival5t 9 p]iod to a giv5 comp\nd p5dulum4 ,?is problem 0 solv$ by ,huyg5s1 :o 9 8 fam\s "w ,horologium oscillatorium 444 7#afgc7 set =? ! !ory ( ! comp\nd p5dulum4#d ,huyg5s d]iv$ a !orem :i* has provid$ ! basis = ! employm5t ( ! rev]sible comp\nd p5dulum = ! absolute det]m9ation ( ! int5sity ( gravity4 ,! !orem is t a giv5 comp\nd p5dulum possesses conjugate po9ts on opposite sides ( ! c5t] ( gravity2 ab\t ^! po9ts1 ! p]iods ( oscillation are ! same4 ,= ea* ( ^! po9ts z c5t] ( susp5sion ! o!r po9t is ! c5t] ( oscillation1 & ! di/ance betwe5 !m is ! l5g? ( ! equival5t simple p5dulum4 ,e>li]1 9 #afeg1 ,huyg5s indep5d5tly _h inv5t$ & pat5t$ ! p5dulum clock1 :i* rapidly came into use = ! measurem5t ( "t4 ,huyg5s also creat$ ! !ory ( c5tripetal =ce :i* made x possible to calculate ! effect ( ! rotation ( ! e>? ^u ! obs]v$ value ( gravity4 ,! !ory ( ! gravity field ( ! e>? 0 f\nd$ ^u ! laws ( motion & ! law ( gravitation by ,isaac ,newton 9 8 fam\s ,pr9cipia 7#afhg74 ,x foll[s f ! ,newtonian !ory ( gravitation t ! accel]ation ( gravity z det]m9$ on ! surface ( ! e>? is ! resultant ( two factors3 ! pr9cipal factor is ! gravitational attraction ( ! e>? ^u bodies1 & ! subsidi>y factor is ! effect ( ! rotation ( ! e>?4 ,a body at re/ on ! surface ( ! e>? requires "s ( ! gravitational attraction = ! c5tripetal accel]ation ( ! body z x is c>ri$ 9 a circle ) con/ant spe$ by ! rotation ( ! e>? ab\t its axis4 ,if ! rotat+ e>? is us$ z a frame ( ref]5ce1 ! effect ( ! rotation is express$ z a c5trifugal =ce :i* acts to dim9i% ! obs]v$ int5sity ( gravity4 99 99 99 99 99 ,,gloss>y ,,( ,,gravity ,,t]m9ology ,,absolute ,,gravity3 ! value ( ! accel]ation ( gravity1 also express$ by ! l5g? ( ! seconds p5dulum4 ,,relative ,,gravity3 ! value ( ! accel]ation ( gravity relative to ! value at "s /&>d po9t4 ,,simple ,,p5dulum3 see !oretical p5dulum4 ,,!oretical ,,p5dulum3 a heavy bob 7po9t-mass7 at ! end ( a weightless rod4 ,,seconds ,,p5dulum3 a !oretical or simple p5dulum ( su* l5g? t its "t ( sw+ 7half-p]iod7 is "o second4 7,?is l5g? is ab\t "o met]47 ,,gravity ,,p5dulum3 a precisely made p5dulum us$ = ! measurem5t ( gravity4 ,,comp\nd ,,p5dulum3 a p5dulum 9 :i* ! support+ rod is n weightless2 9 o!r words1 any actual p5dulum4 ,,conv]tible ,,p5dulum3 a comp\nd p5dulum hav+ knife edges at diff]5t di/ances f ! c5t] ( gravity4 ,huyg5s demon/rat$ 7#afgc7 t if su* a p5dulum 7 to sw+ ) equal p]iods f ei!r knife edge1 ! di/ance betwe5 ^? knife edges w\ld be equal to ! l5g? ( a !oretical or simple p5dulum ( ! same p]iod4 ,,rev]sible ,,p5dulum3 a conv]tible p5dulum :i* is also symmetrical 9 =m4 ,,inv>iable ,,p5dulum3 a comp\nd p5dulum ) only "o knife edge1 us$ = relative measurem5t ( gravity4 99 99 99 99 99 ,f ,newton's laws ( motion & ! hypo!sis t weight is proportional to mass1 ! =mula = ! half-p]iod ( a simple p5dulum is giv5 by ,t pisqrt7l_/g74 ,if a simple p5dulum beats seconds1 #a pisqrt7lambda_/g71 :]e lambda is ! l5g? ( ! seconds p5dulum4 ,f ,t pisqrt7l_/g7 & #a pisqrt7lambda_/g71 x foll[s t lambda l_/,t#b4 ,!n g pi#blambda4 ,?us1 ! int5sity ( gravity c be express$ 9 t]ms ( ! l5g? ( ! seconds p5dulum1 z well z by ! accel]ation ( a freely fall+ body4 ,dur+ ! #ai? c5tury1 gravity usually 0 express$ 9 t]ms ( ! l5g? ( ! seconds p5dulum1 b pres5t practice is to express gravity 9 t]ms ( g1 = :i* ! unit is ! gal1 or "o c5timet] p] second p] second4 ,illu/ration3 ,figure #b4--,,?is ,,draw+1 ,,f ,,ri*]',s ,obs]vations a/ronomiques et physiques faites en l'isle de ,cai5ne 7,p>is1 #afgi71 %[s mo/ ( ! a/ronomical in/rum5ts us$ by ,ri*]1 namely1 "o ( ! two p5dulum clocks made by ,?uret1 ! #bj-;foot & ! #e-;foot telescopes & ! l>ge quadrant4 ,! figure may be int5d$ z a portrait ( ,ri*]4 ,?is draw+ 0 done by ,seba/ian ,le ,cl]c1 a "y illu/rator :o made _m illu/rations ( ! e>ly "w ( ! ,p>is ,academy4 ,figure ( ! ,e>? ,a pr9cipal contribution ( ! p5dulum z a physical in/rum5t has be5 ! det]m9ation ( ! figure ( ! e>?4#e ,t ! e>? is sph]ical 9 =m 0 accept$ doctr9e among ! anci5t ,greeks4 ,py?agoras is said to h be5 ! fir/ to describe ! e>? z a sph]e1 & ?is view 0 adopt$ by ,eudoxus & ,ari/otle4 ,! ,alex&rian sci5ti/ ,erato/h5es made ! fir/ e/imate ( ! diamet] & circumf]5ce ( a suppos$ly sph]ical e>? by an a/ronomical-geodetic me?od4 ,he measur$ ! angle betwe5 ! directions ( ! rays ( ! sun at ,alex&ria & ,sy5e 7,aswan71 ,egypt1 & e/imat$ ! di/ance betwe5 ^! places f ! l5g? ( "t requir$ by a c>avan ( camels to travel betwe5 !m4 ,f ! c5tral angle correspond+ to ! arc on ! surface1 he calculat$ ! radius & h5ce ! circumf]5ce ( ! e>?4 ,a second measurem5t 0 und]tak5 by ,posidonius1 :o measur$ ! altitudes ( />s at ,alex&ria & ,rhodes & e/imat$ ! di/ance betwe5 !m f ! "t requir$ to sail f "o place to ! o!r4 ,) ! decl9e ( classical antiquity1 ! doctr9e ( ! sph]ical %ape ( ! e>? 0 lo/1 & only "o inve/igation1 t by ! ,arabs "u ,calif ,al-,mamun 9 ,a4,d4 #hbg1 is record$ until ! #af? c5tury4 ,9 #aebe1 ! ,fr5* ma!matician ,f]nel measur$ ! l5g? ( a degree ( latitude betwe5 ,p>is & ,ami5s by ! revolutions ( ! :eels ( 8 c>riage1 ! circumf]5ce ( :i* he _h det]m9$4 ,9 ,engl&1 ,norwood 9 #afce measur$ ! l5g? ( an arc betwe5 ,london & ,york ) a *a94 ,an important =w>d /ep 9 geodesy 0 ! measurem5t ( di/ance by triangulation1 fir/ by ,ty*o ,brahe1 9 ,d5m>k1 & lat]1 9 #afae1 by ,willebrord ,snell1 9 ,holl&4 ,( hi/oric importance1 0 ! use ( telescopes 9 ! triangulation = ! measurem5t ( a degree ( arc by ! ,abbe ,jean ,pic>d 9 #affi4f ,he _h be5 commission$ by ! newly e/abli%$ ,academy ( ,sci5ces to measure an arc correspond+ to an angle ( #a deg41 #bb'1 #ee ( ! m]idian betwe5 ,ami5s & ,malvois9e1 ne> ,p>is4 ,pic>d propos$ to ! ,academy ! measurem5t ( ! m]idian ( ,p>is ?r\gh all ( ,france1 & ?is project 0 support$ by ,colb]t1 :o obta9$ ! approval ( ! ,k+4 ,9 #afhd1 ,giovanni-,dom5ico ,cass9i & ,de la ,hire comm5c$ a trigonometrical measure ( an arc s\? ( ,p>is2 subsequ5tly1 ,jacques ,cass9i1 ! son ( ,giovanni-,dom5ico1 add$ ! arc to ! nor? ( ,p>is4 ,! project 0 complet$ 9 #agah4 ,! l5g? ( a degree ( arc s\? ( ,p>is 0 f\nd to be great] ?an ! l5g? nor? ( ,p>is4 ,f ! diff]5ce1 #eg1jig toises#g m9us #ef1ifj toises1 x 0 conclud$ t ! pol> diamet] ( ! e>? is l>g] ?an ! equatorial diamet]1 i4e41 t ! e>? is a prolate sph]oid 7fig4 #c74 ,illu/ration3 ,figure #c4--,,measurem5ts ,,( ,,! ,,l5g? ( a degree ( latitude :i* 7 complet$ 9 diff]5t p>ts ( ,france 9 #affi & #agah gave diff]+ results :i* sugge/$ t ! %ape ( ! e>? is n a sph]e b a prolate sph]oid 7#a74 ,b ,ri*]'s p5dulum obs]vation ( #afgb1 z expla9$ by ,huyg5s & ,newton1 indicat$ t its %ape is t ( an oblate sph]oid 7#b74 ,! disagreem5t is reflect$ 9 ?is draw+4 ,9 ! #agcj's x 0 resolv$ 9 favor ( ! latt] view by two ,fr5* geodetic exp$itions = ! measurem5t ( degrees ( latitude 9 ! equatorial & pol> regions 7,ecuador--!n "p ( ,p]u--& ,lapl&74 ,mean:ile1 ,ri*] 9 #afgb _h be5 s5t to ,cay5ne1 ,fr5* ,guiana1 to make a/ronomical obs]vations & to measure ! l5g? ( ! seconds p5dulum4#h ,he took ) him a p5dulum clock :i* _h be5 adju/$ to keep accurate "t 9 ,p>is4 ,at ,cay5ne1 h[ev]1 ,ri*] f\nd t ! clock 0 ret>d$ by #b m9utes & #bh seconds p] day 7fig4 #a74 ,he also fitt$ up a simple p5dulum to vibrate 9 seconds & measur$ ! l5g? ( ?is seconds p5dulum sev]al times e week = #aj mon?s4 ,^u 8 return to ,p>is1 he f\nd t ! l5g? ( ! simple p5dulum :i* beat seconds at ,cay5ne 0 #a-a_/d ,p>is l9es#i %ort] ?an ! l5g? ( ! seconds p5dulum at ,p>is4 ,huyg5s expla9$ ! r$uction 9 ! l5g? ( ! seconds p5dulum--&1 !re=e1 ! less] int5sity ( gravity at ! equator ) respect to ! value at ,p>is--9 t]ms ( 8 !ory ( c5tripetal =ce z appli$ to ! rotation ( ! e>? & p5dulum4#aj ,a m complete !ory 0 giv5 by ,newton 9 ! ,pr9cipia4#aa ,newton %[$ t if ! e>? is assum$ to be a homog5e\s1 mutually gravitat+ fluid globe1 its rotation w result 9 a bulg+ at ! equator4 ,! e>? w !n h ! =m ( an oblate sph]oid1 & ! int5sity ( gravity z a =m ( univ]sal gravitation w v>y ) position on ! surface ( ! e>?4 ,newton took into acc\nt gravitational attraction & c5trifugal action1 & he calculat$ ! ratio ( ! axes ( ! sph]oid to be #bcj3bbi4 ,he calculat$ & prep>$ a table ( ! l5g?s ( a degree ( latitude & ( ! seconds p5dulum = e #e deg4 ( latitude f ! equator to ! pole4 ,a discrepancy betwe5 8 pr$ict$ l5g? ( ! seconds p5dulum at ! equator & ,ri*]'s measur$ l5g? 0 expla9$ by ,newton 9 t]ms ( ! expansion ( ! scale ) high] temp]atures ne> ! equator4 ,newton's !ory t ! e>? is an oblate sph]oid 0 confirm$ by ! measurem5ts ( ,ri*]1 b 0 reject$ by ! ,p>is ,academy ( ,sci5ces1 = x contradict$ ! results ( ! ,cass9is1 fa!r & son1 ^: measurem5ts ( arcs to ! s\? & nor? ( ,p>is _h l$ to ! conclusion t ! e>? is a prolate sph]oid4 ,?us1 a controv]sy arose betwe5 ! ,engli% sci5ti/s & ! ,p>is ,academy4 ,! conflict 0 f9ally resolv$ by ! results ( exp$itions s5t by ! ,academy to ,p]u & ,sw$54 ,! fir/ exp$ition1 "u ,b\gu]1 ,la ,condam9e1 & ,god9 9 #agce1 w5t to a region 9 ,p]u1 &1 ) ! help ( ! ,spani>d ,ullo1 measur$ a m]idian arc ( ab\t #c deg4 #g' ne> ,quito1 n[ 9 ,ecuador4#ab ,! second exp$ition1 ) ,maup]tuis & ,clairaut 9 #agcf1 w5t to ,lapl& )9 ! ,arctic ,circle & measur$ an arc ( ab\t #a deg4 9 l5g?4#ac ,! nor!rn arc ( #a deg4 0 f\nd to be long] ?an ! ,p]uvian arc ( #a deg41 & ?us x 0 confirm$ t ! e>? is an oblate sph]oid1 t is1 flatt5$ at ! poles1 z pr$ict$ by ! !ory ( ,newton4 ,illu/ration3 ,figure #d4--,,! ,,direct ,,use ,,( ,a ,,clock to measure ! =ce ( gravity 0 f\nd to be limit$ 9 accuracy by ! necess>y me*anical connection ( ! p5dulum to ! clock1 & by ! unavoidable diff]5ce betwe5 ! *>act]i/ics ( a clock p5dulum & ^? ( a !oretical 7usually call$ simple7 p5dulum1 9 :i* ! mass is conc5trat$ 9 ! bob1 & ! support+ rod is weightless4 ,aft] #agce1 ! clock 0 us$ only to "t ! sw+ ( a deta*$ p5dulum1 by ! me?od ( co9cid5ces4 ,9 ?is me?od1 inv5t$ by ,j4 ,j4 ,mairan1 ! l5g? ( ! deta*$ p5dulum is fir/ accurately measur$1 & ! clock is correct$ by a/ronomical obs]vation4 ,! deta*$ p5dulum is !n swung be=e ! clock p5dulum z %[n "h4 ,! two p5dulums sw+ m or less out ( phase1 com+ into co9cid5ce ea* "t "o has ga9$ a vibration4 ,by c\nt+ ! numb] ( co9cid5ces ov] sev]al h\rs1 ! p]iod ( ! deta*$ p5dulum c be v accurately det]m9$4 ,! l5g? & p]iod ( ! deta*$ p5dulum are ! data requir$ = ! calculation ( ! =ce ( gravity4 ,! p]iod f ,erato/h5es to ,pic>d has be5 call$ ! sph]ical era ( geodesy2 ! p]iod f ,pic>d to ! end ( ! #ai? c5tury has be5 call$ ! ellipsoidal p]iod4 ,dur+ ! latt] p]iod ! e>? 0 conceiv$ to be an ellipsoid1 & ! det]m9ation ( its ellipticity1 t is1 ! diff]5ce ( equatorial radius & pol> radius divid$ by ! equatorial radius1 became an important geodetic problem4 ,a significant contribution to ! solution ( ?is problem 0 made by det]m9ations ( gravity by ! p5dulum4 ,an epo*-mak+ "w dur+ ! ellipsoidal era ( geodesy 0 ,clairaut's treatise1 ,!orie de la figure de la t]re4#ad ,on ! hypo!sis t ! e>? is a sph]oid ( equilibrium1 t is1 su* t a lay] ( wat] w\ld spread all ov] x1 & t ! int]nal d5sity v>ies s t lay]s ( equal d5sity are coaxial sph]oids1 ,clairaut d]iv$ a hi/oric !orem3 ,if gamma,e1 gamma,p are ! values ( gravity at ! equator & pole1 respectively1 & c ! c5trifugal =ce at ! equator divid$ by gamma,e1 !n ! ellipticity alpha 7#e_/b7;c - 7gamma,p - gamma,e7_/gamma,e4 ,laplace %[$ t ! surfaces ( equal d5sity might h any ne>ly sph]ical =m1 & ,/okes %[$ t x is unnecess>y to assume any law ( d5sity z long z ! ext]nal surface is a sph]oid ( equilibrium4#ae ,x foll[s f ,clairaut's !orem t if ! e>? is an oblate sph]oid1 its ellipticity c be det]m9$ f relative values ( gravity & ! absolute value at ! equator involv$ 9 c4 ,obs]vations ) nonrev]sible1 inv>iable comp\nd p5dulums h contribut$ to ! application ( ,clairaut's !orem 9 its orig9al & contempor>y ext5d$ =m = ! det]m9ation ( ! figure & gravity field ( ! e>?4 ,e>ly ,types ( ,p5dulums ,! p5dulum employ$ 9 obs]vations ( gravity prior to ! #ai? c5tury usually consi/$ ( a small weight susp5d$ by a filam5t 7figs4 #d-f74 ,! pione] exp]im5t]s ) simple p5dulums *ang$ ! l5g? ( ! susp5sion until ! p5dulum beat seconds4 ,pic>d 9 #affi det]m9$ ! l5g? ( ! seconds p5dulum at ,p>is ) a simple p5dulum :i* consi/$ ( a copp] ball an in* 9 diamet] susp5d$ by a fib] ( pite f jaws 7pite 0 a prep>ation ( ! leaf ( a species ( aloe & 0 n affect$ appreciably by moi/ure74 ,a celebrat$ set ( exp]im5ts ) a simple p5dulum 0 conduct$ by ,b\gu]#af 9 #agcg 9 ! ,&es1 z "p ( ! exp$ition to measure ! ,p]uvian arc4 ,! bob ( ! p5dulum 0 a d\ble truncat$ cone1 & ! l5g? 0 measur$ f ! jaw susp5sion to ! c5t] ( oscillation ( ! ?read & bob4 ,b\gu] all[$ = *ange ( l5g? ( 8 measur+ rod ) temp]ature & also = ! buoyancy ( ! air4 ,he det]m9$ ! "t ( sw+ by an elem5t>y =m ( ! me?od ( co9cid5ces4 ,! ?read ( ! p5dulum 0 swung 9 front ( a scale & ,b\gu] obs]v$ h[ long x took ! p5dulum to lose a numb] ( vibrations on ! seconds clock4 ,= ?is purpose1 he not$ ! "t :5 ! beat ( ! clock 0 he>d &1 simultane\sly1 ! ?read mov$ pa/ ! c5t] ( ! scale4 ,a hi/oric aspect ( ,b\gu]'s me?od 0 t he employ$ an inv>iable p5dulum1 t is1 ! l5g? 0 ma9ta9$ ! same at ! v>i\s /ations ( obs]vation1 a proc$ure t has be5 describ$ z hav+ be5 inv5t$ by ,b\gu]4 ,s9ce ,t pisqrt7l_/g71 x foll[s t 7,t#a7b_/7,t#b7b g#b_/;g#a4 ,?us1 if ! absolute value ( gravity is kn[n at "o /ation1 ! value at any o!r /ation c be det]m9$ f ! ratio ( ! squ>es ( times ( sw+ ( an inv>iable p5dulum at ! two /ations4 ,f ! above equation1 if ,t#a is ! "t ( sw+ at a /ation :]e ! int5sity ( gravity is g1 & ,t#b is ! "t at a /ation :]e ! int5sity is g ,deltag1 !n ,deltag_/g 7,t#a7b_/7,t#b7b - #a4 ,b\gu]'s inve/igations ) 8 inv>iable p5dulum yield$ me?ods = ! det]m9ation ( ! int]nal /ructure ( ! e>?4 ,on ! ,p]uvian exp$ition1 he det]m9$ ! l5g? ( ! seconds p5dulum at ?ree /ations1 includ+ "o at ,quito1 at v>y+ di/ances above sea level4 ,if values ( gravity at /ations ( diff]5t elevation are to be comp>$1 !y mu/ be r$uc$ to ! same level1 usually to sea level4 ,s9ce gravity decreases ) height above sea level 9 accordance ) ! law ( gravitation1 a free-air r$uction mu/ be appli$ to values ( gravity det]m9$ above ! level ( ! sea4 ,b\gu] orig9at$ ! additional r$uction = ! increase 9 gravity on a m\nta9 or plateau caus$ by ! attraction ( ! matt] 9 a plate4 ,f ! relative values ( gravity at elevat$ /ations 9 ,p]u & at sea level1 ,b\gu] calculat$ t ! mean d5sity ( ! e>? 0 #d4g times great] ?an t ( ! cordill]as4#ag ,= great] accuracy 9 ! /udy ( ! int]nal /ructure ( ! e>?1 9 ! #ai? c5tury ! ,b\gu] plate r$uction came to be supplem5t$ by corrections = irregul>ities ( t]ra9 & by diff]5t types ( iso/atic r$uction4 ,la ,condam9e1 :o l ,b\gu] 0 a memb] ( ! ,p]uvian exp$ition1 conduct$ 8 own p5dulum exp]im5ts 7fig4 #d74 ,he exp]im5t$ 9 #agce at ,santo ,dom+o en r\te to ,s\? ,am]ica1#ah !n at v>i\s /ations 9 ,s\? ,am]ica1 & aga9 at ,p>is ^u 8 return to ,france4 ,8 p5dulum consi/$ ( a copp] ball susp5d$ by a ?read ( pite4 ,= exp]im5tation ! l5g? initially 0 ab\t #ab feet1 & ! "t ( sw+ #b seconds1 b !n ! l5g? 0 r$uc$ to ab\t #c feet ) "t ( sw+ #a second4 ,e>li]1 :5 x 0 believ$ t gravity 0 con/ant ov] ! e>?1 ,pic>d & o!rs _h propos$ t ! l5g? ( ! seconds p5dulum be *os5 z ! /&>d4 ,la ,condam9e 9 #agdg reviv$ ! proposal 9 ! =m t ! l5g? ( ! seconds p5dulum at ! equator be adopt$ z ! /&>d ( l5g?4 ,subsequ5tly1 he inve/igat$ ! expansion ( a toise ( iron f ! v>iation 9 ! p]iod ( 8 p5dulum4 ,9 #agee1 he obs]v$ ! p5dulum at ,rome ) ,boscovi*4 ,la ,condam9e's p5dulum 0 us$ by o!r obs]v]s & f9ally 0 lo/ at sea on an exp$ition ar\nd ! _w4 ,! k ( ! p5dulum acquir$ by ! end ( ! #ah? c5tury 0 summ>iz$ 9 #aghe 9 a memoir by ,boscovi*4#ai ,illu/ration3 ,figure #e4--;,,an ,,app>atus ,,= ,,! ,,practice ,,measurem5t ( ! l5g? ( ! p5dulum devis$ on ! basis ( a s]ies ( prelim9>y exp]im5ts by ,c4 ,m4 de la ,condam9e :o1 9 ! c\rse ( ! ,fr5* geodetic exp$ition to ,p]u 9 #agce1 devot$ a #c-mon? soj\rn on ! isl& ( ,santo ,dom+o to p5dulum obs]vations by ,mairan's ,me?od4 ,9 ?is arrangem5t1 %[n "h1 a v]tical rod ( ironwood is us$ bo? z ! scale & z ! support = ! app>atus1 hav+ at its top ! brass p5dulum support 7,a7 &1 bel[1 a horizontal mirror 7,o7 :i* s]ves to align ! app>atus v]tically ?r\gh visual obs]vation ( ! reflection ( ! po9t] project+ f ,a4 ,! p5dulum1 ab\t #cg in*es long1 consi/s ( a ?read ( pite 7a humidity-resi/ant1 natural fib]7 & a copp] ball ( ab\t #f ounces4 ,its exact l5g? is det]m9$ by adju/+ ! micromet] 7,s7 s t ! ball ne>ly t\*es ! mirror4 ,x w be not$ t ! clock p5dulum w\ld be obscur$ by ! scale4 ,la ,condam9e seems to h det]m9$ ! times ( co9cid5ce by visual obs]vation ( ! occasions on :i* ! p5dulums sw+ p>allel4 7,portion ( plate #a1 ,memoires publies p> la ,societe francaise de ,physique1 vol4 #d47 ,illu/ration3 ,figure #f4--,,! ,,result ( e>ly p5dulum exp]im5ts 0 (t5 express$ 9 t]ms ( ! l5g? ( a p5dulum :i* w\ld h a p]iod ( "o second & 0 call$ ! seconds p5dulum4 ,9 #agib1 ,j4 ,c4 ,borda & ,j4 ,d4 ,cass9i det]m9$ ! l5g? ( ! seconds p5dulum at ,p>is ) ?is app>atus4 ,! p5dulum consi/s ( a plat9um ball ab\t #a-a_/b in*es 9 diamet]1 susp5d$ by a f9e iron wire4 ,! l5g?1 ab\t #ab feet1 0 su* t its p]iod w\ld be ne>ly twice z long z t ( ! p5dulum ( ! clock 7,a74 ,! int]val betwe5 co9cid5ces 0 det]m9$ by obs]v+1 ?r\gh ! telescope at ! left1 ! times :5 ! two p5dulums em]ge toge!r f beh9d ! scre5 7,m74 ,! exact l5g? ( ! p5dulum 0 measur$ by a plat9um scale 7n %[n7 equipp$ ) a v]ni] & an auxili>y copp] scale = temp]ature correction4 ,:51 at ! end ( ! #ah? c5tury1 ! ,fr5* revolution>y gov]nm5t e/abli%$ ! metric sy/em ( weights & measures1 ! l5g? ( ! seconds p5dulum at ,p>is 0 consid]$1 b n adopt$1 z ! unit ( l5g?4 7,plate #b1 ,memoires publies p> la ,societe francaise de ,physique1 vol4 #d47 ,! practice ) ! simple p5dulum on ! "p ( ,pic>d1 ,b\gu]1 ,la ,condam9e & o!rs 9 ,france culm9at$ 9 ! "w ( ,borda & ,cass9i 9 #agib at ! obs]vatory 9 ,p>is#bj 7fig4 #f74 ,! exp]im5ts 7 und]tak5 to det]m9e :e!r or n ! l5g? ( ! seconds p5dulum %\ld be adopt$ z ! /&>d ( l5g? by ! new gov]nm5t ( ,france4 ,! bob consi/$ ( a plat9um ball #af-a_/f ,p>is l9es 9 diamet]1 & #i1iaa gra9s 7slightly m ?an #ag ounces7 9 weight4 ,! bob 0 held to a brass cup cov]+ ab\t "o-fif? ( its surface by ! int]position ( a small quantity ( grease4 ,! cup ) ball 0 hung by a f9e iron wire ab\t #ab ,p>is feet long4 ,! upp] end ( ! wire 0 atta*$ to a cyl9d] :i* 0 "p ( a w$ge-%ap$ knife edge1 on ! upp] surface ( :i* 0 a /em on :i* a small adju/able weight 0 held by a screw ?read4 ,! knife edge re/$ on a /eel plate4 ,! weight on ! knife-edge app>atus 0 adju/$ s t ! app>atus w\ld vibrate ) ! same p]iod z ! p5dulum4 ,?us1 ! mass ( ! susp5d+ app>atus c\ld be neglect$ 9 ! !ory ( motion ( ! p5dulum ab\t ! knife edge4 ,illu/ration3 ,figure #g4--,,results ,,( ,,exp]im5ts 9 ! det]m9ation ( ! l5g? ( ! seconds p5dulum at ,ko5igsb]g by a new me?od 7 report$ by ,f4 ,w4 ,bessel 9 #ahbf & publi%$ 9 #ahbh4 ,) ?is app>atus1 he obta9$ two sets ( data f ! same p5dulum1 by us+ two diff]5t po9ts ( susp5sion4 ,! p5dulum 0 ab\t #aj feet long4 ,! di/ance betwe5 ! two po9ts ( susp5sion 7a & b7 0 #a toise 7ab\t six feet74 ,a micrometric balance 7c7 bel[ ! bob 0 us$ to det]m9e ! increase 9 l5g? due to ! weight ( ! bob4 ,he project$ ! image ( ! clock p5dulum 7n %[n7 onto ! gravity p5dulum by means ( a l5s1 ?us plac+ ! clock "s di/ance away & elim9at+ ! di/urb+ effect ( its motion4 7,portion ( plate #f1 ,memoires publies p> la ,societe francaise de ,physique1 vol4 #d47 ,9 ! e>li] susp5sion f jaws !re 0 unc]ta9ty z to ! po9t ab\t :i* ! p5dulum oscillat$4 ,borda & ,cass9i hung _! p5dulum 9 front ( a seconds clock & det]m9$ ! "t ( sw+ by ! me?od ( co9cid5ces4 ,! times on ! clock 7 obs]v$ :5 ! clock ga9$ or lo/ "o complete vibration 7two sw+s7 on ! p5dulum4 ,suppose t ! wire p5dulum makes n sw+s :ile ! clock makes #bn #b4 ,if ! clock beats seconds exactly1 ! "t ( "o complete vibration is #b seconds1 & ! "t ( sw+ ( ! wire p5dulum is ,t 7#bn #b7_/n #b7a #a_/n74 ,an error 9 ! "t caus$ by unc]ta9ty 9 det]m9+ ! co9cid5ce ( clock & wire p5dulum is r$uc$ by employ+ a long int]val ( obs]vation #bn4 ,! :ole app>atus 0 enclos$ 9 a box1 9 ord] to exclude di/urbances f curr5ts ( air4 ,corrections 7 made = buoyancy1 = amplitude ( sw+ & = v>iations 9 l5g? ( ! wire ) temp]ature4 ,! f9al result 0 t ! l5g? ( ! seconds p5dulum at ! obs]vatory 9 ,p>is 0 det]m9$ to be #ddj4eeic ,p>is l9es1 or #iic4ec mm41 r$uc$ to sea level #iic4he mm4 ,"s ye>s lat] ! me?ods ( ,borda 7 us$ by o!r ,fr5* inve/igators1 among :om 0 ,biot :o us$ ! plat9um ball ( ,borda susp5d$ by a copp] wire #fj cm4 long4 ,ano!r hi/oric simple p5dulum 0 ! "o swung by ,bessel 7fig4 #g7 = ! det]m9ation ( gravity at ,ko5igsb]g #ahbe-ahbg4ba ,! p5dulum consi/$ ( a ball ( brass1 copp]1 or ivory t 0 susp5d$ by a f9e wire1 ! upp] end ( :i* 0 wrapp$ & unwrapp$ on a horizontal cyl9d] z support4 ,! p5dulum 0 swung fir/ f "o po9t & !n f ano!r1 exactly a toise de ,p]u#bb high] up1 ! bob be+ at ! same level 9 ea* case 7fig4 #g74 ,bessel f\nd ! p]iod ( vibration ( ! p5dulum by ! me?od ( co9cid5ces2 & 9 ord] to avoid di/urbances f ! comp>ison clock1 x 0 plac$ at "s di/ance f ! p5dulum "u obs]vation4 ,bessel's exp]im5ts 7 significant 9 view ( ! c>e ) :i* he det]m9$ ! corrections4 ,he correct$ = ! /iffness ( ! wire & = ! lack ( rigidity ( connection betwe5 ! bob & wire4 ,! necessity = ! latt] correction _h be5 po9t$ out by ,laplace1 :o %[$ t ?r\gh ! circum/ance t ! pull ( ! wire is n[ on "o side & n[ on ! o!r side ( ! c5t] ( gravity1 ! bob acquires angul> mom5tum ab\t its c5t] ( gravity1 :i* _c be acc\nt$ = if ! l9e ( ! wire1 & !re=e ! =ce t x ex]ts1 always pass$ ?r\gh ! c5t]4 ,9 addition to a correction = buoyancy ( ! air consid]$ by 8 pr$ecessors1 ,bessel also took acc\nt ( ! in]tia ( ! air set 9 motion by ! p5dulum4 ,illu/ration3 ,figure #h4--,,mode ,,( ,,susp5sion ( ,bessel's p5dulum is %[n "h4 ,! iron wire is support$ by ! ?umbscrew & clamp at ! left1 b passes ov] a p9 at ! c5t]1 :i* is actually ! upp] t]m9al ( ! p5dulum4 ,bessel f\nd ?is cyl9d] ( unroll+ sup]ior to ! clamps & knife edges ( e>li] p5dulums4 ,! c\nt]weight at ! "r is "p ( a sy/em = support+ ! scale 9 su* a way t x is n elongat$ by its own weight4 ,) ?is app>atus1 ,bessel det]m9$ ! ratio ( ! l5g?s ( ! two p5dulums & _! times ( vibration4 ,f ?is ! l5g? ( ! seconds p5dulum 0 calculat$4 ,8 me?od elim9at$ ! ne$ to take into acc\nt su* s\rces ( inaccuracy z flexure ( ! p5dulum wire & imp]fections 9 ! %ape ( ! bob4 7,portion ( plate #g1 ,memoires publies p> la ,societe francaise de ,physique1 vol4 #d47 ,illu/ration3 ,figure #i4--;,,fri$ri* ,,wilhelm ,,bessel 7#aghd-ahdf71 ,g]man ma!matician & a/ronom]4 ,he became ! fir/ sup]9t5d5t ( ! ,prussian obs]vatory e/abli%$ at ,ko5igsb]g 9 #ahaj1 & rema9$ !re dur+ ! rema9d] ( 8 life4 ,s important 7 8 _m contributions to precise measurem5t & calculation 9 a/ronomy t he is (t5 consid]$ ! f\nd] ( ! mod]n age 9 t sci5ce4 ,?is *>act]i/ic also %[s 9 8 v5ture into geodesy1 #ahbf-ahcj1 "o product ( :i* 0 ! p5dulum exp]im5t report$ 9 ?is article4 ,! latt] effect _h be5 discov]$ by ,du ,buat 9 #aghf1bc b 8 "w 0 unkn[n to ,bessel4 ,! l5g? ( ! seconds p5dulum at ,ko5igsb]g1 r$uc$ to sea level1 0 f\nd by ,bessel to be #ddj4hagi l9es4 ,9 #ahce1 ,bessel det]m9$ ! int5sity ( gravity at a site 9 ,b]l9 :]e obs]vations lat] 7 conduct$ 9 ! ,imp]ial ,(fice ( ,weights & ,measures by ,*>les ,s4 ,peirce ( ! ,u4,s4 ,coa/ ,survey4 ,kat]'s ,conv]tible & ,inv>iable ,p5dulums ,! sy/ematic survey ( ! gravity field ( ! e>? 0 giv5 a great impetus by ! contributions ( ,capt4 ,h5ry ,kat]1 ,f4,r4,s4 ,9 #ahag1 he design$1 con/ruct$1 & appli$ a conv]tible comp\nd p5dulum = ! absolute det]m9ation ( gravity at ! h\se ( ,h5ry ,br[ne1 ,f4,r4,s41 9 ,portl& ,place1 ,london4#bd ,kat]'s conv]tible p5dulum 7fig4 #aa7 consi/$ ( a brass rod to :i* 7 atta*$ a flat circul> bob ( brass & two adju/able weights1 ! small] ( :i* 0 adju/$ by a screw4 ,! conv]tibility ( ! p5dulum 0 con/itut$ by ! provision ( two knife edges turn$ inw>ds on opposite sides ( ! c5t] ( gravity4 ,! p5dulum 0 swung on ea* knife edge1 & ! adju/able weights 7 mov$ until ! times ( sw+ 7 ! same ab\t ea* knife edge4 ,:5 ! times 7 judg$ to be ! same1 ! di/ance betwe5 ! knife edges 0 inf]r$ to be ! l5g? ( ! equival5t simple p5dulum1 9 accordance ) ,huyg5s' !orem on conjugate po9ts ( a comp\nd p5dulum4 ,kat] det]m9$ ! "t ( sw+ by ! me?od ( co9cid5ces 7fig4 #ab74 ,he correct$ = ! buoyancy ( ! air4 ,! f9al value ( ! l5g? ( ! seconds p5dulum at ,br[ne's h\se 9 ,london1 r$uc$ to sea level1 0 det]m9$ to be #ci4acibi in*es4 ,! conv]tible comp\nd p5dulum _h be5 conceiv$ prior to its realization by ,kat]4 ,9 #agib1 on ! occasion ( ! proposal 9 ,p>is to e/abli% ! /&>d ( l5g? z ! l5g? ( ! seconds p5dulum1 ,b>on de ,prony _h propos$ ! employm5t ( a comp\nd p5dulum ) ?ree axes ( oscillation4#be ,9 #ahjj1 he propos$ ! conv]tible comp\nd p5dulum ) knife edges ab\t :i* ! p5dulum c\ld complete sw+s 9 equal times4 ,de ,prony's proposals 7 n accept$ & 8 pap]s rema9$ unpubli%$ until #ahhi1 at :i* "t !y 7 discov]$ by ,def=ges4 ,! ,fr5* decision 0 to exp]im5t ) ! ball p5dulum1 & ! det]m9ation ( ! l5g? ( ! seconds p5dulum 0 c>ri$ out by ,borda & ,cass9i by me?ods previ\sly describ$4 ,bohn5b]g] 9 8 ,a/ronomie 7#ahaa71bf made ! proposal to employ a conv]tible p5dulum = ! absolute det]m9ation ( gravity2 ?us1 he has receiv$ cr$it = priority 9 publication4 ,capt4 ,kat] indep5d5tly conceiv$ ( ! conv]tible p5dulum & 0 ! fir/ to design1 con/ruct1 & sw+ "o4 ,illu/ration3 ,figure #aj4--;,,h5ry ,,kat] 7#aggg-ahce71 ,engli% army (fic] & physici/4 ,8 sci5tific c>e] began dur+ 8 milit>y s]vice 9 ,india1 :]e he assi/$ 9 ! great trigonometrical survey4 ,return$ to ,engl& because ( bad heal?1 & retir$ 9 #ahad1 he pione]$ 7#ahah7 9 ! developm5t ( ! conv]tible p5dulum z an alt]native to ! approximation ( ! simple p5dulum = ! measurem5t ( ! seconds p5dulum4 ,kat]'s conv]tible p5dulum & ! inv>iable p5dulum introduc$ by him 9 #ahai 7 ! basis ( ,engli% p5dulum "w4 7,photo c\rtesy ,national ,portrait ,gall]y1 ,london47 ,aft] 8 obs]vations ) ! conv]tible p5dulum1 ,capt4 ,kat] design$ an inv>iable comp\nd p5dulum ) a s+le knife edge b o!rwise simil> 9 ext]nal =m to ! conv]tible p5dulum#bg 7fig4 #ac74 ,?irte5 ( ^! ,kat] inv>iable p5dulums h be5 report$ z con/ruct$ & swung at /ations ?r\gh\t ! _w4#bh ,kat] himself swung an inv>iable p5dulum at a /ation 9 ,london & at v>i\s o!r /ations 9 ! ,briti% ,isles4 ,capt4 ,edw>d ,sab9e1 betwe5 #ahbj & #ahbe1 made voyages & swung ,kat] inv>iable p5dulums at /ations f ! ,we/ ,indies to ,gre5l& & ,spitzb]g54#bi ,9 #ahbj1 ,kat] swung a ,kat] inv>iable p5dulum at ,london & !n s5t x to ,gold+ham1 :o swung x 9 #ahba at ,madras1 ,india4#cj ,also 9 #ahbj1 ,kat] suppli$ an inv>iable p5dulum to ,hall1 :o swung x at ,london & !n made obs]vations ne> ! equator & 9 ! ,s\!rn ,hemisph]e1 & at ,london aga9 9 #ahbc4ca ,! same p5dulum1 aft] its knives 7 regr\nd1 0 deliv]$ to ,adm4 ,luetke ( ,russia1 :o obs]v$ gravity ) x on a trip ar\nd ! _w betwe5 #ahbf & #ahbi4cb ,illu/ration3 ,figure #aa4--,,! ,,attempt ,,to ,,approximate ! simple 7!oretical7 p5dulum 9 gravity exp]im5ts end$ 9 #ahag-ah :5 ,h5ry ,kat] inv5t$ ! comp\nd conv]tible p5dulum1 f :i* ! equival5t simple p5dulum c\ld be obta9$ accord+ to ! me?od ( ,huyg5s 7see text1 p4 #cad74 ,develop$ 9 connection ) a project to fix ! /&>d ( ,engli% measure1 ,kat]'s p5dulum 0 call$ comp\nd because x 0 a solid b> r ?an ! f9e wire or /r+ ) :i* e>li] exp]im5t]s _h tri$ to approximate a weightless rod4 ,x 0 call$ conv]tible because x is alt]nately swung f ! two knife edges 7a & b7 at opposite ends4 ,! weights 7f & g7 are adju/$ s t ! p]iod ( ! p5dulum is ! same f ei!r knife edge4 ,! di/ance betwe5 ! two knife edges is !n equal to ! l5g? ( ! equival5t simple p5dulum4 ,illu/ration3 ,figure #ab4--,,! ,,kat] ,,conv]tible ,,p5dulum 9 use is plac$ be=e a clock1 ^: p5dulum bob is directly beh9d ! ext5d$ tail ( ! ,kat] p5dulum4 ,a :ite spot is pa9t$ on ! c5t] ( ! bob ( ! clock p5dulum4 ,! obs]v+ telescope1 left1 has a diaphragm ) a v]tical slit ( su* wid? t its view is j fill$ by ! tail ( ! ,kat] p5dulum :5 x is at re/4 ,:5 ! two p5dulums are sw++1 ! :ite spot on ! clock p5dulum c be se5 on ea* sw+ except t 9 :i* ! two p5dulums are 9 co9cid5ce2 ?us1 ! co9cid5ces are det]m9$4 7,portion ( plate #e1 ,memoires publies p> la ,societe francaise de ,physique1 vol4 #d47 ,illu/ration3 ,figure #ac4--,,?is ,,draw+ ,,accompani$ ,john ,gold+ham's report on ! "w done 9 ,india ) ,kat]'s inv>iable p5dulum4 ,! value ( gravity obta9$1 directly or indirectly1 9 t]ms ( ! simple p5dulum1 is call$ absolute4 ,once absolute values ( gravity 7 e/abli%$ at a numb] ( /ations1 x became possible to use ! mu* simpl] relative me?od = ! measurem5t ( gravity at new /ations4 ,because x has only "o knife edge1 & does n involve ! adju/m5ts ( ! conv]tible p5dulum1 ?is "o is call$ inv>iable4 ,9 use1 x is fir/ swung at a /ation :]e ! absolute value ( gravity has be5 e/abli%$1 & ?is p]iod is !n comp>$ ) its p]iod at "o or m new /ations4 ,kat] develop$ an inv>iable p5dulum 9 #ahai1 :i* 0 us$ 9 ,engl& & 9 ,madras1 ,india1 9 #ahba4 ,:ile ! ,briti% 7 engag$ 9 sw++ ! ,kat] inv>iable p5dulums to det]m9e relative values ( ! l5g? ( ! seconds p5dulum1 or ( gravity1 ! ,fr5* also s5t out exp$itions4 ,capt4 de ,freyc9et made initial obs]vations at ,p>is ) ?ree inv>iable brass p5dulums & "o wood5 "o1 & !n c>ri$ out obs]vations at ,rio de ,janeiro1 ,cape ( ,good ,hope1 ,ile de ,france1 ,rawak 7ne> ,new ,gu9ea71 ,guam1 ,maui1 & v>i\s o!r places4#cc ,a simil> exp$ition 0 conduct$ 9 #ahbb-ahbe by ,capta9 ,dup]ry4#cd ,dur+ ! ye>s f #ahbg to #ahdj1 v>i\s types ( p5dulum 7 con/ruct$ & swung by ,francis ,baily1 a memb] ( ! ,royal ,a/ronomical ,society1 :o report$ 9 #ahcb on exp]im5ts 9 :i* no less ?an #da diff]5t p5dulums 7 swung 9 vacuo1 & _! *>act]i/ics det]m9$4#ce ,9 #ahcf1 ,baily und]took to advise ! ,am]ican ,lt4 ,*>les ,wilkes1 :o 0 to head ! ,unit$ ,/ates ,explor+ ,exp$ition ( #ahch-ahdb1 on ! procurem5t ( p5dulums = ?is voyage4 ,wilkes ord]$ f ! ,london in/rum5t mak]1 ,?omas ,jones1 two unusual p5dulums1 :i* ,wilkes describ$ z ^? consid]$ ! be/ =m by ,mr4 ,baily = travel+ p5dulums1 & :i* ,baily1 himself1 describ$ z precisely ! same z ! two inv>iable p5dulums belong+ to ?is ,royal ,a/ronomical ,society1 except = ! location ( ! knife edges4 ,illu/ration3 ,figure #ad4--,,vacuum ,,*amb] ,,= ,,use ) ! ,kat] p5dulum4 ,( a numb] ( extrane\s effects :i* t5d to di/urb ! accuracy ( p5dulum obs]vations ! mo/ important is air resi/ance4 ,exp]im5ts report$ by ! ,gre5wi* 7,engl&7 obs]vatory 9 #ahbi l$ to ! developm5t ( a vacuum *amb] )9 :i* ! p5dulum 0 swung4 ,! unusual feature ( ^! p5dulums 0 9 _! symmetry ( mass z well z ( =m4 ,!y 7 made ( b>s1 ( iron 9 "o case1 & ( brass 9 ! o!r1 & ea* _h two knife edges at opposite ends equidi/ant f ! c5t]4 ,?us1 al?\gh !y resembl$ rev]sible p5dulums1 _! symmetry ( mass prev5t$ _! use z su*1 & !y 7 r equival5t to f\r sep>ate inv>iable p5dulums4#cf ,wilkes 0 taught ! use ( ! p5dulum by ,baily1 & conduct$ exp]im5ts at ,baily's h\se1 :]e ! latt] _h c>ri$ out ! "w report$ on 9 #ahcb4 ,! subsequ5t exp]im5ts made on ! ,u4,s4 ,explor+ ,exp$ition 7 "u ! *>ge ( ,wilkes1 himself1 :o made obs]vations on #aa sep>ate occasions1 beg9n+ ) t 9 ,london 7#ahcf7 & foll[$ by o!rs 9 ,new ,york1 ,wa%+ton1 ,d4,c41 ,rio de ,janeiro1 ,sydney1 ,honolulu1 ,p5dulum ,peak 7,mauna ,loa71 ,m\nt ,kanoha1 ,nesqually 7,oregon ,t]ritory71 &1 f9ally1 two m times 9 ,wa%+ton1 ,d4,c4 7#ahda & #ahde74 ,wilkes' results 7 communicat$ to ,baily1 :o appe>s to h f\nd ! "w defective because ( insuffici5t att5tion to ! ma9t5ance ( temp]ature con/ancy & to c]ta9 alt]ations made to ! p5dulums4#cg ,! results 7 also to h be5 includ$ 9 ! publications ( ! ,exp$ition1 b 7 "p ( ! unpubli%$ #bd? volume4 ,=tunately !y /ill exi/1 9 :at appe>s to be a pr9t]'s pro(4#ch ,! ,kat] inv>iable p5dulums 7 us$ to inve/igate ! int]nal con/itution ( ! e>?4 ,airy s\ght to det]m9e ! d5sity ( ! e>? by obs]v+ ! times ( sw+ ( p5dulums at ! top & bottom ( a m9e4 ,! fir/ exp]im5ts 7 made 9 #ahbf at ! ,dolcoa? copp] m9e 9 ,cornwall1 & fail$ :5 ! p5dulum fell to ! bottom4 ,9 #ahed1 ! exp]im5ts 7 aga9 und]tak5 9 ! ,h>ton coalpit1 ne> ,sund]l&4#ci ,gravity at ! surface 0 great] ?an bel[1 because ( ! attraction ( a %ell equal to ! dep? ( ! pit4 ,f ! d5sity ( ! %ell z det]m9$ f specim5s ( rock1 ,airy f\nd ! d5sity ( ! e>? to be #f-a_/b times great] ?an t ( wat]4 ,t4 ,c4 ,m5d5hall1 9 #ahhj1 us$ a ,kat] conv]tible p5dulum 9 an inv>iable mann] to comp>e values ( gravity on ,fujiyama & at ,tokyo1 ,japan4#dj ,he us$ a simple p5dulum ( ! ,borda type to det]m9e ! absolute value ( gravity at ,tokyo4 ,f ! values ( gravity on ! m\nta9 & at ,tokyo1 & an e/imate ( ! volume ( ! m\nta91 he e/imat$ ! mean d5sity ( ! e>? z #e4gg times great] ?an t ( wat]4 ,9 #ahgi1 ,maj4 ,j4 ,h]s*el1 ,r4,e41 /at$3 ,! ye>s f #ahdj to #ahfe are a complete blank1 if we except ,airy's relative d5sity exp]im5ts 9 #ahed4 ,?is pause 0 brok5 simultane\sly 9 ?ree diff]5t ways4 ,two p5dulums ( ! ,kat] patt]n 7 s5t to ,india2 two aft] ,bessel's design 7 set to "w 9 ,russia2 & at ,g5eva1 ,plantam\r's zeal\s exp]im5ts ) a p5dulum ( ! same k9d m>k ! comm5cem5t ( an era ( r5ew$ activity on ! ,european cont95t4#da ,) ! /atem5t t ,kat] inv>iable p5dulums nos4 #d & #f 7#ahba7 7 us$ 9 ,india betwe5 #ahfe & #ahgc1 we n[ consid] ! o!r ev5ts m5tion$ by ,h]s*el4 ,illu/ration3 ,figure #ae4--,,"o ,,( ,,francis ,,baily',s ,,p5dulums 7#fb-a_/b in*es long71 %[n on ! left1 is n[ 9 ! possession ( ! ,sci5ce ,museum1 ,london1 &1 "r1 two views ( a simil> p5dulum 7#cg-e_/h in*es long7 made 9 ! late #ai? c5tury by ,edw>d ,kuebel1 ,wa%+ton1 ,d4,c41 :i* is no4 #caf1hgf 9 ! collection ( ! ,u4,s4 ,national ,museum4 ,among a l>ge numb] ( p5dulums tri$ by ,baily 9 ,london 7#ahbg-ahdj71 0 "o :i* resembles ! rev]sible p5dulum sup]ficially1 b :i* is actually an inv>iable p5dulum hav+ knife edges at bo? ends4 ,! purpose 0 app>5tly economy1 s9ce x is equival5t to two sep>ate inv>iable p5dulums4 ,?is is ! type ( p5dulum us$ on ! ,u4,s4 ,explor+ ,exp$ition ( #ahch-ahdb4 ,x is n kn[n :at use 0 made ( ! ,kuebel p5dulum4 ,repsold-,bessel ,rev]sible ,p5dulum ,z we h not$1 ,bessel made det]m9ations ( gravity ) a ball 7simple7 p5dulum 9 ! p]iod #ahbe-ahbg & 9 #ahce at ,ko5igsb]g & ,b]l91 respectively4 ,9 ! memoir on 8 obs]vations at ,ko5igsb]g1 he set =? ! !ory ( ! symmetrical comp\nd p5dulum ) int]*angeable knife edges4#db ,bessel demon/rat$ !oretically t if ! p5dulum 7 symmetrical ) respect to its geometrical c5t]1 if ! times ( sw+ ab\t ea* axis 7 ! same1 ! effects ( buoyancy & ( air set 9 motion w\ld be elim9at$4 ,laplace _h already %[n t ! knife edge mu/ be reg>d$ z a cyl9d] & n z a m]e l9e ( support4 ,bessel !n %[$ t if ! knife edges 7 equal cyl9d]s1 _! effects 7 elim9at$ by inv]t+ ! p5dulum2 & if ! knife edges 7 n equal cyl9d]s1 ! diff]5ce 9 _! effects 0 cancel$ by int]*ang+ ! knives & aga9 det]m9+ ! times ( sw+ 9 ! s-call$ erect & inv]t$ positions4 ,bessel fur!r %[$ t x is unnecess>y to make ! times ( sw+ exactly equal = ! two knife edges4 ,! simplifi$ discussion = inf9itely small oscillations 9 a vacuum is z foll[s3 ,if ,t#a & ,t#b are ! times ( sw+ ab\t ! knife edges1 & if h#a & h#b are di/ances ( ! knife edges f ! c5t] ( gravity1 & if k is ! radius ( gyration ab\t an axis ?r\gh ! c5t] ( gravity1 !n f ! equation ( motion ( a rigid body oscillat+ ab\t a fix$ axis "u gravity 7,t#a7b pi#b7k#b 7h#a7b7_/;gh#a1 7,t#b7b pi#b7k#b 7h#b7b7_/;gh#b4 ,!n 7h#a7,t#a7b - h#b7,t#b7b7_/7;h#a - h#b7 7pi#b_/;g77h#a h#b7 tau#b4 tau is !n ! "t ( sw+ ( a simple p5dulum ( l5g? h#a h#b4 ,if ! diff]5ce ,t#a - ,t#b is suffici5tly small1 tau 7h#a,t#a - h#b,t#b7_/7;h#a - h#b74 ,prior to its publication by ,bessel 9 #ahbh1 ! =mula = ! "t ( sw+ ( a simple p5dulum ( l5g? h#a h#b 9 t]ms ( ,t#a1 ,t#b _h be5 giv5 by ,c4 ,f4 ,gauss 9 a lett] to ,h4 ,c4 ,s*uma*] dat$ ,novemb] #bh1 #ahbd4dc ,! symmetrical comp\nd p5dulum ) int]*angeable knives1 = :i* ,bessel gave a po/hum\sly publi%$ design & specifications1#dd has be5 call$ a rev]sible p5dulum2 x may !reby be di/+ui%$ f ,kat]'s unsymmetrical conv]tible p5dulum4 ,9 #ahfa1 ! ,swiss ,geodetic ,commission 0 =m$1 & 9 "o ( its fir/ sessions 9 #ahfb x 0 decid$ to add det]m9ations ( gravity to ! op]ations connect$ ) ! measurem5t--at diff]5t po9ts 9 ,switz]l&--( ! arc ( ! m]idian trav]s+ c5tral ,europe4#de ,x 0 decid$ fur!r to employ a rev]sible p5dulum ( ,bessel's design & to h x con/ruct$ by ! firm ( ,a4 ,repsold & ,sons1 ,hamburg4 ,x 0 also decid$ to make ! fir/ obs]vations ) ! p5dulum 9 ,g5eva2 accord+ly1 ! ,repsold-,bessel p5dulum 7fig4 #af7 0 s5t to ,pr(4 ,e4 ,plantam\r1 director ( ! obs]vatory at ,g5eva1 9 ! autumn ( #ahfd4df ,! ,swiss rev]sible p5dulum 0 ab\t #efj mm4 9 l5g? 7di/ance betwe5 ! knife edges7 & ! "t ( sw+ 0 approximately #c_/d second4 ,at ! extremities ( ! /em ( ! p5dulum 7 movable cyl9drical disks1 "o ( :i* 0 solid & heavy1 ! o!r holl[ & light4 ,x 0 int5d$ by ! me*anicians t equality ( times ( oscillation ab\t ! knife edges w\ld be a*iev$ by adju/+ ! position ( a movable disk4 ,! p5dulum 0 hung by a knife edge on a plate support$ by a tripod & hav+ an atta*m5t f :i* a measur+ rod c\ld be susp5d$ s t ! di/ance betwe5 ! knife edges c\ld be measur$ by a comp>ator4 ,plantam\r f\nd x impracticable to adju/ a disk until ! times ( sw+ ab\t ea* knife edge 7 equal4 ,8 colleague1 ,*>les ,cell]i]1#dg !n %[$ t if 7,t#a - ,t#b7_/,t#a is suffici5tly small s t "o c neglect its squ>e1 "o c det]m9e ! l5g? ( ! seconds p5dulum f ! times ( sw+ ab\t ! knife edges by a !ory :i* uses ! di/ances ( ! c5t] ( gravity f ! respective knife edges4 ,?us1 a role = ! position ( ! c5t] ( gravity 9 ! !ory ( ! rev]sible p5dulum1 :i* _h be5 set =? e>li] by ,bessel1 0 discov]$ indep5d5tly by ,cell]i] = ! ,swiss obs]v]s ( p5dulums4 ,9 #ahff1 ,plantam\r publi%$ an ext5sive memoir ,exp]i5ces faites a ,g5eve avec le p5dule a rev]sion4 ,ano!r memoir1 publi%$ 9 #ahgb1 pres5t$ fur!r results ( det]m9ations ( gravity 9 ,switz]l&4 ,plantam\r 0 ! fir/ sci5ti/ 9 we/]n ,europe to use a ,repsold-,bessel rev]sible p5dulum & to "w out me?ods = its employm5t4 ,! ,russian ,imp]ial ,academy ( ,sci5ces acquir$ two ,repsold-,bessel p5dulums1 & obs]vations ) !m 7 begun 9 #ahfd by ,pr(4 ,sawits*1 ,univ]sity ( ,/4 ,pet]sburg1 & o!rs4#dh ,9 #ahfi1 ! ,russian p5dulums 7 loan$ to ! ,india ,survey 9 ord] to enable memb]s ( ! ,survey to supplem5t obs]vations ) ! ,kat] inv>iable p5dulums nos4 #d & #f 7#ahba74 ,dur+ ! transport ( ! ,russian app>atus to ,india1 ! knives became ru/$ & ! app>atus _h to be recondition$4 ,capt4 ,heaviside ( ! ,india ,survey obs]v$ ) bo? p5dulums at ,kew ,obs]vatory1 ne> ,london1 9 ! spr+ ( #ahgd1 aft] :i* ! ,russian p5dulums 7 s5t to ,pulk[a 7,russia7 & 7 us$ = obs]vations !re & 9 ! ,caucasus4 ,! introduction ( ! ,repsold-,bessel rev]sible p5dulum = ! det]m9ation ( gravity 0 accompani$ by ! creation ( ! fir/ int]national sci5tific association1 "o = geodesy4 ,9 #ahfa1 ,lt4 ,g54 ,j4 ,j4 ,baey]1 director ( ! ,prussian ,geodetic ,survey1 s5t a memor&um to ! ,prussian m9i/] ( w> 9 :i* he propos$ t ! indep5d5t geodetic surveys ( ! /ates ( c5tral ,europe be coord9at$ by ! creation ( an int]national organization4#di ,9 #ahfb1 invitations 7 s5t to ! v>i\s ,g]man /ates & to o!r /ates ( c5tral ,europe4 ,! fir/ ,g5]al ,conf]5ce ( ! association1 initially call$ ,die ,mittel-,europaeis*e ,gradmessung1 also ,l',association ,geodesique ,int]nationale1 0 held f ! #ae? to ! #bb;d ( ,octob] #ahfd 9 ,b]l94#ej ,! ,conf]5ce decid$ ^u que/ions ( organization3 a g5]al conf]5ce 0 to be held ord9>ily e ?ree ye>s2 a p]man5t commission initially consi/+ ( sev5 memb]s 0 to be ! sci5tific organ ( ! association & to meet annually2 a c5tral bureau 0 to be e/abli%$ = ! reception1 publication1 & di/ribution ( reports f ! memb] /ates4 ,illu/ration3 ,figure #af4--;,,f ,a ,,design ,,left ,,by ,,bessel1 ?is portable app>atus 0 develop$ 9 #ahfb by ! firm ( ,repsold 9 ,hamburg1 ^: f\nd] _h assi/$ ,bessel 9 ! con/ruction ( 8 p5dulum app>atus ( #ahbf4 ,! p5dulum is conv]tible1 b diff]s f ,kat]'s 9 be+ geometrically symmetrical &1 = ?is reason1 ,repsold's is usually call$ rev]sible4 ,j to ! "r ( ! p5dulum is a /&>d scale4 ,to ! left is a v]tical comp>ator design$ by ,repsold to measure ! di/ance betwe5 ! knife edges ( ! p5dulum4 ,to make ?is measurem5t1 two micromet] microscopes :i* project horizontally ?r\gh ! comp>ator are alt]nately focus$ on ! knife edges & on ! /&>d scale4 ,"u ! topic ,a/ronomical ,que/ions1 ! ,g5]al ,conf]5ce ( #ahfd resolv$ t !re %\ld be det]m9ations ( ! int5sity ( gravity at ! greate/ possible numb] ( po9ts ( ! geodetic network1 & recomm5d$ ! rev]sible p5dulum z ! in/rum5t ( obs]vation4#ea ,at ! second ,g5]al ,conf]5ce1 9 ,b]l9 9 #ahfg1 on ! basis ( favorable reports by ,dr4 ,hirs*1 director ( ! obs]vatory at ,neu*atel1 ( ,swiss practice ) ! ,repsold-,bessel rev]sible p5dulum1 ?is in/rum5t 0 specifically recomm5d$ = det]m9ations ( gravity4#eb ,! title ( ! association 0 *ang$ to ,die ,europaeis*e ,gradmessung2 9 #ahhf1 x became ,die ,int]nationale ,erdmessung1 "u :i* title x cont9u$ until ,_w ,w> ,i4 ,on ,april #a1 #ahff1 ! ,c5tral ,bureau ( ,die ,europaeis*e ,gradmessung 0 op5$ 9 ,b]l9 "u ! presid5cy ( ,baey]1 & 9 #ahfh !re 0 f\nd$ at ,b]l91 also "u 8 presid5cy1 ! ,royal ,prussian ,geodetic ,in/itute1 :i* obta9$ regul> budget>y /atus on ,janu>y #a1 #ahgj4 ,a rev]sible p5dulum = ! ,in/itute 0 ord]$ f ,a4 ,repsold & ,sons1 & x 0 deliv]$ 9 ! spr+ ( #ahfi4 ,! ,prussian in/rum5t 0 symmetrical geometrically1 z specifi$ by ,bessel1 b diff]5t 9 =m f ! ,swiss & ,russian p5dulums4 ,! di/ance betwe5 ! knife edges 0 #a met]1 & ! "t ( sw+ approximately #a second4 ,! ,prussian ,repsold-,bessel p5dulum 0 swung at ,leipzig & o!r /ations 9 c5tral ,europe dur+ ! ye>s #ahfi-ahgj by ,dr4 ,albre*t "u ! direction ( ,dr4 ,bruhns1 director ( ! obs]vatory at ,leipzig & *ief ( ! a/ronomical section ( ! ,geodetic ,in/itute4 ,! results ( ^! fir/ obs]vations appe>$ 9 a publication ( ! ,royal ,prussian ,geodetic ,in/itute 9 #ahga4ec ,results ( obs]vations ) ! ,russian ,repsold-,bessel p5dulums 7 publi%$ by ! ,imp]ial ,academy ( ,sci5ces4 ,9 #ahgb1 ,pr(4 ,sawits* report$ ! "w = we/]n ,europeans 9 ,les v>iations de la pesanteur dans les prov9ces occid5tales de l',empire russe4#dh ,9 ,novemb] #ahgc1 ! ,au/rian ,geodetic ,commission receiv$ a ,repsold-,bessel rev]sible p5dulum & on ,septemb] #bd1 #ahgd1 ,pr(4 ,!odor von ,oppolz] report$ on obs]vations at ,vi5na & o!r /ations to ! ,f\r? ,g5]al ,conf]5ce ( ,die ,europaeis*e ,gradmessung 9 ,dresd54#ed ,at ! f\r? session ( ! ,conf]5ce1 on ,septemb] #bh1 #ahgd1 a ,special ,commission1 consi/+ ( ,baey]1 z *airman1 & ,bruhns1 ,hirs*1 von ,oppolz]1 ,pet]s1 & ,albre*t1 0 appo9t$ to consid] 7"u ,topic #c ( ! program73 ,obs]vations = ! det]m9ation ( ! int5sity ( gravity1 ! "q1 ,:i* ,p5dulum-app>atuses are pref]able = ! det]m9ation ( _m po9ts8 ,aft] ! adoption ( ! ,repsold-,bessel rev]sible p5dulum = gravity det]m9ations 9 ,europe1 "w 9 ! field 0 begun by ! ,u4,s4 ,coa/ ,survey "u ! sup]9t5d5cy ( ,pr(4 ,b5jam9 ,peirce4 ,!re is m5tion 9 reports ( obs]vations ) p5dulums prior to ,peirce's direction to 8 son ,*>les on ,novemb] #cj1 #ahgb1 to take *>ge ( ! ,p5dulum ,exp]im5ts ( ! ,coa/ ,survey & to direct & inspect all p>ties engag$ 9 su* exp]im5ts & z (t5 z circum/ances w p]mit1 to take ! field ) a p>ty4444#ee ,sy/ematic & important gravity "w by ! ,survey 0 begun by ,*>les ,s&]s ,peirce4 ,^u receiv+ notice ( 8 appo9tm5t1 ! latt] promptly ord]$ f ! ,repsolds a p5dulum simil> to ! ,prussian in/rum5t4 ,s9ce ! firm ( me*anicians 0 engag$ 9 mak+ in/rum5ts = obs]vations ( ! transit ( ,v5us 9 #ahgd1 ! p5dulum = ! ,coa/ ,survey c\ld n be con/ruct$ imm$iately4 ,mean:ile1 dur+ ! ye>s #ahgc-ahgd1 ,*>les ,peirce conduct$ a p>ty :i* made obs]vations ( gravity 9 ! ,hoosac ,tunnel ne> ,nor? ,adams1 & at ,nor?ampton & ,cambridge1 ,massa*usetts4 ,! p5dulums us$ 7 nonrev]sible1 inv>iable p5dulums ) conical bobs4 ,among !m 0 a silv] p5dulum1 b simil> p5dulums ( brass 7 us$ also4#ef ,illu/ration3 ,figure #ag4--,,repsold-,,bessel ,,rev]sible ,,p5dulum app>atus z made 9 #ahge1 & us$ 9 ! gravity "w ( ! ,u4,s4 ,coa/ & ,geodetic ,survey4 ,cont95tal geodesi/s cont9u$ to favor ! g5]al use ( conv]tible p5dulums & absolute det]m9ations ( gravity1 :ile _! ,engli% colleagues _h turn$ to inv>iable p5dulums & relative det]m9ations1 except = base /ations4 ,p]haps ! fir/ important ,am]ican contribution to gravity "w 0 ,c4 ,s4 ,peirce's demon/ration ( ! error inh]5t 9 ! ,repsold app>atus ?r\gh flexure ( ! /&4 ,illu/ration3 ,figure #ah4--;,,*>les ,,s&]s ,,peirce 7#ahci-aiad71 son ( ,b5jam9 ,peirce1 ,p]k9s ,pr(essor ( ,a/ronomy & ,ma!matics at ,h>v>d ,college4 ,c4 ,s4 ,peirce graduat$ f ,h>v>d 9 #ahei4 ,f #ahgc to #ahia1 z an assi/ant at ! ,u4,s4 ,coa/ & ,geodetic ,survey1 he accompli%$ ! important gravimetric "w describ$ 9 ?is article4 ,peirce 0 also int]e/$ 9 _m o!r fields1 b above all 9 ! logic1 philosophy1 & hi/ory ( sci5ce1 9 :i* he wrote ext5sively4 ,8 greate/ fame is 9 philosophy1 :]e he is reg>d$ z ! f\nd] ( pragmatism4 ,9 #ahgd1 ,*>les ,peirce express$ ! desire to be s5t to ,europe = at lea/ a ye>1 beg9n+ ab\t ,m>* #a1 #ahge1 to le>n ! use ( ! new conv]tible p5dulum & to comp>e x ) ^? ( ! ,european measure ( a ,degree & ! ,swiss & to comp>e 8 inv>iable p5dulums 9 ! mann] :i* has be5 us$ by sw++ !m 9 ,london & ,p>is4#eg ,*>les ,s4 ,peirce1 assi/ant1 ,u4,s4 ,coa/ ,survey1 sail$ = ,europe on ,april #c1 #ahge1 on 8 mission to obta9 ! ,repsold-,bessel rev]sible p5dulum ord]$ = ! ,survey & to le>n ! me?ods ( us+ x = ! det]m9ation ( gravity4 ,9 ,engl&1 he conf]r$ ) ,maxwell1 ,/okes1 & ,airy conc]n+ ! !ory & practice ( rese>* ) p5dulums4 ,9 ,may1 he cont9u$ on to ,hamburg & obta9$ deliv]y f ! ,repsolds ( ! p5dulum = ! ,coa/ ,survey 7fig4 #ag74 ,peirce !n w5t to ,b]l9 & conf]r$ ) ,g54 ,baey]1 :o express$ d\bts ( ! /ability ( ! ,repsold /& = ! p5dulum4 ,peirce next w5t to ,g5eva1 :]e1 "u arrangem5ts ) ,pr(4 ,plantam\r1 he swung ! newly acquir$ p5dulum at ! obs]vatory4#eh ,9 view ( ,baey]'s express$ d\bts ( ! rigidity ( ! ,repsold /&1 ,peirce p]=m$ exp]im5ts to measure ! flexure ( ! /& caus$ by ! oscillations ( ! p5dulum4 ,8 me?od 0 to set up a micromet] 9 front ( ! p5dulum /& &1 ) a microscope1 to measure ! displacem5t caus$ by a weight pass+ ov] a pulley1 ! friction ( :i* _h be5 det]m9$4 ,peirce calculat$ ! correction to be appli$ to ! l5g? ( ! seconds p5dulum--on acc\nt ( ! sway+ ( ! /& dur+ ! sw+s ( ! p5dulum--to am\nt to ov] #j4b mm4 ,al?\gh ,peirce's measurem5ts ( flexure 9 ,g5eva 7 n z precise z 8 lat] measurem5ts1 he believ$ t failure to correct = flexure ( ! /& 9 det]m9ations previ\sly made ) ,repsold p5dulums 0 responsible = appreciable errors 9 report$ values ( ! l5g? ( ! seconds p5dulum4 ,! ,p]man5t ,commission ( ,die ,europaeis*e ,gradmessung met 9 ,p>is1 ,septemb] #bj-bi1 #ahge4 ,9 conjunction ) ?is meet+1 !re 0 held on ,septemb] #ba a meet+ ( ! ,special ,commission on ! ,p5dulum4 ,! basis ( ! discussion by ! ,special ,commission 0 provid$ by reports :i* _h be5 submitt$ 9 response to a circul> s5t out by ! ,c5tral ,bureau to ! memb]s on ,febru>y #bf1 #ahgd4ei ,g54 ,baey] /at$ t ! di/ance ( #a met] betwe5 ! knife edges ( ! ,prussian ,repsold-,bessel p5dulum made x unwieldy & unsuit$ = transport4 ,he decl>$ t ! in/ability ( ! /& also 0 a s\rce ( error4 ,accord+ly1 ,g54 ,baey] express$ ! op9ion t absolute det]m9ations ( gravity %\ld be made at a control /ation by a rev]sible p5dulum hung on a p]man5t1 & !re=e /able /&1 & he said t relative values ( gravity ) respect to ! control /ation %\ld be obta9$ 9 ! field by means ( a ,b\gu] inv>iable p5dulum4 ,dr4 ,bruhns & ,dr4 ,pet]s agre$ ) ,g54 ,baey]2 h[ev]1 ! ,swiss inve/igators1 ,pr(4 ,plantam\r & ,dr4 ,hirs* report$ 9 def5se ( ! rev]sible p5dulum z a field in/rum5t1 z did ,pr(4 von ,oppolz] ( ,vi5na4 ,! circum/ance t an inv>iable p5dulum is subject to *anges 9 l5g? 0 (f]$ z an argum5t 9 favor ( ! rev]sible p5dulum z a field in/rum5t4 ,peirce 0 pres5t dur+ ^! discussions by ! memb]s ( ! ,special ,commission1 & he report$ t 8 exp]im5ts at ,g5eva demon/rat$ t ! oscillations ( ! p5dulum call$ =? a flexure ( ! support :i* hi!rto _h be5 neglect$4 ,! obs]v]s :o us$ ! ,swiss & ,au/rian ,repsold p5dulums cont5d$1 9 opposition to ,peirce1 t ! ,repsold /& 0 /able4 ,! outcome ( ^! discussions 0 t ! ,special ,commission report$ to ! ,p]man5t ,commission t ! ,repsold-,bessel rev]sible p5dulum1 except = "s small *anges1 satisfi$ all requirem5ts = ! det]m9ation ( gravity4 ,! ,special ,commission propos$ t ! ,repsold p5dulums ( ! sev]al /ates be swung at ! ,prussian ,ei*ungsamt 9 ,b]l9 :]e1 z ,peirce po9t$ out1 ,bessel _h made 8 det]m9ation ( ! int5sity ( gravity ) a ball p5dulum 9 #ahce4 ,peirce 0 enc\rag$ to sw+ ! ,coa/ ,survey rev]sible p5dulum at ! /ations 9 ,france1 ,engl&1 & ,g]many :]e ,borda & ,cass9i1 ,kat]1 & ,bessel1 respectively1 _h made hi/oric det]m9ations4 ,! ,p]man5t ,commission1 9 ^: sessions ,peirce also p>ticipat$1 by resolutions adopt$ ! report ( ! ,special ,commission on ! ,p5dulum4#fj ,dur+ ! mon?s ( ,janu>y & ,febru>y #ahgf1 ,peirce conduct$ obs]vations 9 ! ,gr&e ,salle du ,m]idi5 at ! obs]vatory 9 ,p>is :]e ,borda1 ,biot1 & ,capt4 ,edw>d ,sab9e _h swung p5dulums e>ly 9 ! #ai? c5tury4 ,he conduct$ obs]vations 9 ,b]l9 f ,april to ,june #ahgf &1 by exp]im5t1 det]m9$ ! correction = flexure to be appli$ to ! value ( gravity previ\sly obta9$ ) ! ,prussian in/rum5t4 ,subsequ5t obs]vations 7 made at ,kew4 ,aft] 8 return to ! ,unit$ ,/ates on ,augu/ #bf1 #ahgf1 ,peirce conduct$ exp]im5ts at ! ,/ev5s ,in/itute 9 ,hobok51 ,new ,j]sey1 :]e he made c>eful measurem5ts ( ! flexure ( ! /& by /atical & dynamical me?ods4 ,9 ,g5eva1 he _h secur$ ! con/ruction ( a vacuum *amb] 9 :i* ! p5dulum c\ld be swung on a support :i* he call$ ! ,g5eva support4 ,at ! ,/ev5s ,in/itute1 ,peirce swung ! ,repsold-,bessel p5dulum on ! ,g5eva support & det]m9$ ! effect ( diff]5t pressures & temp]atures on ! p]iod ( oscillation ( ! p5dulum4 ,^! exp]im5ts cont9u$ into #ahgh4fa ,mean:ile1 ! ,p]man5t ,commission met ,octob] #e-aj1 #ahgf1 9 ,brussels & cont9u$ ! discussion ( ! p5dulum4#fb ,g54 ,baey] report$ on ,peirce's exp]im5ts 9 ,b]l9 to det]m9e ! flexure ( ! /&4 ,! diff]5ce ( #j4ah mm4 9 ! l5g?s ( ! seconds p5dulum z det]m9$ by ,bessel & z det]m9$ by ! ,repsold in/rum5t agre$ ) ,peirce's e/imate ( error caus$ by neglect ( flexure ( ! ,repsold /&4 ,dr4 ,hirs*1 speak+ = ! ,swiss survey1 & ,pr(4 von ,oppolz]1 speak+ = ! ,au/rian survey1 cont5d$1 h[ev]1 t _! /&s possess$ suffici5t /ability & t ! results f\nd by ,peirce appli$ only to ! /&s & bases inve/igat$ by him4 ,! ,p]man5t ,commission propos$ fur!r /udy ( ! p5dulum4 ,! ,fif? ,g5]al ,conf]5ce ( ,die ,europaeis*e ,gradmessung 0 held f ,septemb] #bg to ,octob] #b1 #ahgg1 9 ,/uttg>t4#fc ,peirce _h in/ructions f ,supt4 ,patt]son ( ! ,u4,s4 ,coa/ ,survey to att5d ?is conf]5ce1 & on arrival pres5t$ a lett] ( introduction f ,patt]son reque/+ t he1 ,peirce1 be p]mitt$ to p>ticipate 9 ! sessions4 ,^u invitation f ,pr(4 ,plantam\r1 z approv$ by ,g54 ,ibanez1 presid5t ( ! ,p]man5t ,commission1 ,peirce _h s5t on ,july #ac1 #ahgg1 f ,new ,york1 ! manuscript ( a memoir titl$ ,de l',influ5ce de la flexibilite du trepi$ sur l'oscillation du p5dule a rev]sion4 ,?is memoir & o!rs by ,cell]i] & ,plantam\r confirm+ ,peirce's "w 7 publi%$ z app5dices to ! proce$+s ( ! conf]5ce4 ,z app5dices to ,peirce's contribution 7 publi%$ also two notes by ,pr(4 von ,oppolz]4 ,at ! second session on ,septemb] #bi1 #ahgg1 :5 ,plantam\r report$ t ! "w ( ,hirs* & himself _h confirm$ exp]im5tally ! indep5d5t !oretical "w ( ,cell]i] & ! !oretical & exp]im5tal "w ( ,peirce on flexure1 ,peirce describ$ 8 ,hobok5 exp]im5ts4 ,dur+ ! discussions at ,/uttg>t on ! flexure ( ! ,repsold /&1 ,h]ve ,faye1 presid5t ( ! ,bureau ( ,longitudes1 ,p>is1 sugge/$ t ! sway+ ( ! /& dur+ oscillations ( ! p5dulum c\ld be ov]come by ! susp5sion f "o support ( two simil> p5dulums :i* oscillat$ ) equal amplitudes & 9 opposite phases4 ,?is proposal 0 criticiz$ by ,dr4 ,hirs*1 :o decl>$ t exact obs]vation ( passages ( a d\ble p5dulum w\ld be difficult & t two p5dulums sw++ s close toge!r w\ld int]f]e ) ea* o!r4 ,! proposal ( ! d\ble p5dulum came up aga9 at ! meet+ ( ! ,p]man5t ,commission at ,g5eva 9 #ahgi4fd ,on ,febru>y #ag1 #ahgi1 ,peirce _h complet$ a pap] ,on a ,me?od ( ,sw++ ,p5dulums = ! ,det]m9ation ( ,gravity1 ,propos$ by ,m4 ,faye4 ,9 ?is pap]1 ,peirce pres5t$ ! results ( an analytical me*anical inve/igation ( ,faye's proposal4 ,peirce set up ! diff]5tial equations1 f\nd ! solutions1 int]pret$ !m physically1 & arriv$ at ! conclusion t ! sugge/ion ( ,m4 ,faye 444 is z s\nd z x is brilliant & (f]s "s peculi> advantages ov] ! exi/+ me?od ( sw++ p5dulums4 ,9 a report to ,supt4 ,patt]son1 dat$ ,july #ahgi1 ,peirce /at$3 ,i ?9k x is important be=e mak+ a new p5dulum app>atus to exp]im5t ) ,faye's propos$ me?od4#fe ,he wrote fur!r3 ,! me?od proves to be p]fectly s\nd 9 !ory1 & z x w\ld greatly facilitate ! "w x is probably de/9$ ev5tually to prevail4 ,we mu/ un=tunately leave to o!r surveys ! m]it ( practically te/+ & introduc+ ! new me?od1 z our appropriations are insuffici5t = u to ma9ta9 ! lead+ position 9 ?is matt]1 :i* we o!rwise might take4 ,copies ( ! publi%$ v]sion ( ,peirce's rem>ks 7 s5t to ,europe4 ,at a meet+ ( ! ,academy ( ,sci5ces 9 ,p>is on ,septemb] #a1 #ahgi1 ,faye pres5t$ a report on ,peirce's f9d+s4#ff ,! ,p]man5t ,commission met ,septemb] #af-bj1 #ahgi1 9 ,g5eva4 ,at ! ?ird session on ,septemb] #ai1 by action ( ,g54 ,baey]1 copies ( ,peirce's pap] on ,faye's propos$ me?od ( sw++ p5dulums 7 di/ribut$4 ,dr4 ,hirs* aga9 comm5t$ adv]sely on ! proposal1 b mov$ t ! "q be inve/igat$ & report$ on at ! com+ ,g5]al ,conf]5ce4 ,! ,p]man5t ,commission accept$ ! proposal ( ,dr4 ,hirs*1 & ,pr(4 ,plantam\r 0 nam$ to report on ! matt] at ! ,g5]al ,conf]5ce4 ,at ,plantam\r's reque/1 ,*>les ,cell]i] 0 appo9t$ to jo9 him1 s9ce ! problem ess5tially 0 a !oretical "o4 ,! ,six? ,g5]al ,conf]5ce ( ,die ,europaeis*e ,gradmessung met ,septemb] #ac-af1 #ahhj1 9 ,muni*4#fg ,topic ,,iii1 "p #g ( ! program 0 entitl$ ,on ,det]m9ations ( ,gravity ?r\gh p5dulum obs]vations4 ,:i* con/ruction ( a p5dulum app>atus corresponds completely to all requirem5ts ( sci5ce8 ,special report on ! p5dulum4 ,! conf]5ce receiv$ a memoir by ,cell]i]#fh on ! !ory ( ! d\ble p5dulum & a report by ,plantam\r & ,cell]i]4#fi ,cell]i]'s ma!matical analysis began ) ! equations ( ,peirce & us$ ! latt]'s notation z f> z possible4 ,8 g5]al discussion includ$ ! results ( ,peirce1 b he /at$ t ! difficulties to be ov]come did n ju/ify ! employm5t ( ! d\ble p5dulum4 ,he pres5t$ an alt]native me?od ( correct+ = flexure bas$ ^u a !ory by :i* ! flexure caus$ by ! oscillation ( a giv5 rev]sible p5dulum c\ld be det]m9$ f ! behavior ( an auxili>y p5dulum ( ! same l5g? b ( diff]5t weight4 ,?is me?od ( correct+ = flexure 0 recomm5d$ to ! ,g5]al ,conf]5ce by ,plantam\r & ,cell]i] 9 _! jo9t report4 ,at ! f\r? session ( ! conf]5ce on ,septemb] #af1 #ahhj1 ! problem ( ! p5dulum 0 discuss$ &1 9 consequ5ce1 a commission consi/+ ( ,faye1 ,helmholtz1 ,plantam\r 7replac$ 9 #ahhb by ,hirs*71 & von ,oppolz] 0 appo9t$ to /udy app>atus suitable = relative det]m9ations ( gravity4 ,! ,p]man5t ,commission met ,septemb] #aa-ae1 #ahhb1 at ,! ,hague1#gj & at its la/ session appo9t$ ,pr(4 von ,oppolz] to report to ! ,sev5? ,g5]al ,conf]5ce on diff]5t =ms ( app>atus = ! det]m9ation ( gravity4 ,! ,sev5? ,conf]5ce met ,octob] #ae-bd1 #ahhc1 9 ,rome1#ga &1 at its eigh? session1 on ,octob] #bb1 receiv$ a compreh5sive1 critical review f ,pr(4 von ,oppolz] entitl$ ,ueb] die ,be/immung d] ,s*w]e mit ,hilfe v]s*i$5] ,app>ate4#gb ,von ,oppolz] especially exp\nd$ ! advantages ( ! ,bessel rev]sible p5dulum1 :i* comp5sat$ = air effects by symmetry ( =m if ! times ( sw+ = bo? positions 7 ma9ta9$ betwe5 ! same amplitudes1 & comp5sat$ = irregul> knife edges by mak+ !m int]*angeable4 ,pr(4 von ,oppolz] review$ ! problem ( flexure ( ! ,repsold /& & /at$ t a solution 9 ! "r direction 0 ! proposal--made by ,faye & !oretically pursu$ by ,peirce--to sw+ two p5dulums f ! same /& ) equal amplitudes & 9 opposite phases1 b t ! proposal 0 n practicable4 ,he conclud$ t = absolute det]m9ations ( gravity1 ! ,bessel rev]sible p5dulum 0 highly appropriate if "o swung two exempl>s ( diff]5t weight f ! same /& = ! elim9ation ( flexure4 ,pr(4 von ,oppolz]'s important report recogniz$ t absolute det]m9ations 7 less accurate ?an relative ones1 & %\ld be conduct$ only at special places4 ,! discussions initiat$ by ,peirce's demon/ration ( ! flexure ( ! ,repsold /& result$1 f9ally1 9 ! ab&onm5t ( ! plan to make absolute det]m9ations ( gravity at all /ations ) ! rev]sible p5dulum4 ,illu/ration3 ,figure #ai4--,,?ree ,,p5dulums ,,us$ ,,9 ,,e>ly ,,"w at ! ,u4,s4 ,coa/ & ,geodetic ,survey4 ,%[n on ! left is ! ,peirce inv>iable2 c5t]1 ! ,peirce rev]sible2 &1 "r1 ! ,repsold rev]sible4 ,peirce design$ ! cyl9drical p5dulum 9 #ahha-ahhb to /udy ! effect ( air resi/ance accord+ to ! !ory ( ,g4 ,g4 ,/okes on ! motion ( a p5dulum 9 a visc\s field4 ,?ree examples ( ! ,peirce p5dulums are 9 ! ,u4,s4 ,national ,museum4 ,peirce & ,def=ges ,inv>iable1 ,rev]sible ,p5dulums ,! ,repsold-,bessel rev]sible p5dulum 0 design$ & initially us$ to make absolute det]m9ations ( gravity n only at initial /ations su* z ,kew1 ! obs]vatory 9 ,p>is1 & ! ,smi?sonian ,in/itution 9 ,wa%+ton1 ,d4,c41 b also at /ations 9 ! field4 ,an inv>iable p5dulum ) a s+le knife edge1 h[ev]1 is adequate = relative det]m9ations4 ,z we h se51 su* inv>iable p5dulums _h be5 us$ by ,b\gu] & ,kat]1 & aft] ! exp]i5ces ) ! ,repsold app>atus _h be5 recomm5d$ aga9 by ,baey] = relative det]m9ations4 ,b an inv>iable p5dulum is subject to uncontrollable *anges ( l5g?4 ,peirce propos$ to detect su* *anges 9 an inv>iable p5dulum 9 ! field by comb9+ ! inv>iable & rev]sible pr9ciples4 ,he expla9$ 8 proposal to ,faye 9 a lett] dat$ ,july #bc1 #ahhj1 & he pres5t$ x on ,septemb] #af1 #ahhj1 at ! f\r? session ( ! six? ,g5]al ,conf]5ce ( ,die ,europaeis*e ,gradmessung1 9 ,muni*4#gc ,z record$ 9 ! ,proce$+s ( ! ,conf]5ce1 ,peirce wrote3 ,b ,i obviate x 9 mak+ my p5dulum bo? inv>iable & rev]sible4 ,e alt]ation ( ! p5dulum w be reveal$ imm$iately by ! *ange 9 ! diff]5ce ( ! two p]iods ( oscillation 9 ! two positions4 ,once discov]$1 x w be tak5 acc\nt ( by means ( new measures ( ! di/ance betwe5 ! two supports4 ,peirce add$ t x seem$ to him t if ! rev]sible p5dulum p]haps is n ! be/ in/rum5t to det]m9e absolute gravity1 x is1 on condition t x be truly inv>iable1 ! be/ to det]m9e relative gravity4 ,peirce fur!r /at$ t he w\ld wi% t ! p5dulum be =m$ ( a tube ( drawn brass ) heavy plugs ( brass equally drawn4 ,! cyl9d] w\ld be t]m9at$ by two hemisph]es2 ! knives w\ld be atta*$ to tongues fix$ ne> ! ends ( ! cyl9d]4 ,dur+ ! ye>s #ahha & #ahhb1 f\r inv>iable1 rev]sible p5dulums 7 made aft] ! design ( ,peirce at ! (fice ( ! ,u4,s4 ,coa/ & ,geodetic ,survey 9 ,wa%+ton1 ,d4,c4 ,! report ( ! sup]9t5d5t = ! ye> #ahhj-ahha /ates3 ,a new patt]n ( ! rev]sible p5dulum has be5 inv5t$1 hav+ its surface z ne>ly z conv5i5t 9 ! =m ( an elongat$ ellipsoid4 ,?ree ( ^! in/rum5ts h be5 con/ruct$1 two hav+ a di/ance ( "o met] betwe5 ! knife edges & ! ?ird a di/ance ( "o y>d4 ,x is propos$ to sw+ "o ( ! met] p5dulums at a temp]ature ne> #cb deg4 ,f4 at ! same "t t ! y>d is swung at #fj deg4 ,f41 9 ord] to det]m9e anew ! relation betwe5 ! y>d & ! met]4#gd ,! report = #ahha-ahhb m5tions f\r ( ^! ,peirce p5dulums4 ,a description ( ! ,peirce inv>iable1 rev]sible p5dulums 0 giv5 by ,assi/ant ,e4 ,d4 ,pre/on 9 ,det]m9ations ( ,gravity & ! ,magnetic ,elem5ts 9 ,connection ) ! ,unit$ ,/ates ,sci5tific ,exp$ition to ! ,we/ ,coa/ ( ,africa1 #ahhi-ij4ge ,! inv>iable1 rev]sible p5dulum1 ,peirce no4 #d1 n[ pres]v$ 9 ! ,smi?sonian ,in/itution's ,museum ( ,hi/ory & ,te*nology 7fig4 #cd71 may be tak5 z typical ( ! met] p5dulums3 ,9 ! same memoir1 ,pre/on gives ! diamet] ( ! tube z #fc4g mm41 ?ickness ( tube #a4e mm41 weight #aj4fhj kilograms1 & di/ance betwe5 ! knives #a4jjj met]4 ,! comb9ation ( inv>iability & rev]sibility 9 ! ,peirce p5dulums 0 an innovation = relative det]m9ations4 ,inde$1 ! comb9ation 0 criticiz$ by ,maj4 ,j4 ,h]s*el1 ,r4,e41 ( ! ,indian ,survey1 at a conf]5ce on gravity held 9 ,wa%+ton 9 ,may #ahhb on ! occasion ( 8 visit to ! ,unit$ ,/ates = ! purpose ( connect+ ,engli% & ,am]ican /ations by relative det]m9ations ) ?ree ,kat] inv>iable p5dulums4 ,^! ?ree p5dulums h be5 designat$ z nos4 #d1 #f 7#ahba71 & #aa4gf ,illu/ration3 ,figure #bj4--,,support ,,= ,,! ,,peirce ,,p5dulum1 #ahhi4 ,mu* ( ! "w ( ,c4 ,s4 ,peirce 0 conc]n$ ) ! det]m9ation ( ! error introduc$ into obs]vations made ) ! portable app>atus by ! vibration ( ! /& ) ! p5dulum4 ,he %[$ t ! popul> ,bessel-,repsold app>atus 0 subject to su* an error4 ,8 own p5dulums 7 swung f a simple b rugg$ wood5 frame to :i* a h>d5$ /eel be>+ 0 fix$4 ,ano!r novel *>act]i/ic ( ! ,peirce p5dulums 0 ! ma9ly cyl9drical =m4 ,pr(4 ,george ,gabriel ,/okes1 9 a pap] ,on ! ,effect ( ! ,int]nal ,friction ( ,fluids on ! ,motion ( ,p5dulums#gg t 0 read to ! ,cambridge ,philosophical ,society on ,decemb] #i1 #ahej1 _h solv$ ! hydrodynamical equations to obta9 ! resi/ance to ! motions ( a sph]e & a cyl9d] 9 a visc\s fluid4 ,peirce _h /udi$ ! effect ( visc\s resi/ance on ! motion ( 8 ,repsold-,bessel p5dulum1 :i* 0 symmetrical 9 =m b n cyl9drical4 ,! ma9ly cyl9drical =m ( 8 p5dulums 7fig4 #ai7 p]mitt$ ,peirce to pr$ict f ,/okes' !ory ! effect ( viscosity & to comp>e ! results ) exp]im5t4 ,8 report ( ,novemb] #bj1 #ahhi1 9 :i* he pres5t$ ! comp>ison ( exp]im5tal results ) ! !ory ( ,/okes1 0 n publi%$4#gh ,peirce us$ 8 p5dulums 9 #ahhc to e/abli% a /ation at ! ,smi?sonian ,in/itution t 0 to s]ve z ! base /ation = ! ,coa/ & ,geodetic ,survey = "s ye>s4 ,p5dulum ,peirce no4 #a 0 swung at ,wa%+ton 9 #ahha & 0 !n tak5 by ! p>ty ( ,lieut5ant ,greely1 ,u4,s4,a41 on an exp$ition to ,lady ,frankl9 ,bay :]e x 0 swung 9 #ahhb at ,=t ,cong]1 ,gr9nell ,l&1 ,canada4 ,peirce nos4 #b & #c 7 swung by ,peirce 9 #ahhb at ,wa%+ton1 ,d4,c42 ,hobok51 ,new ,j]sey2 ,montreal1 ,canada2 & ,albany1 ,new ,york4 ,assi/ant ,pre/on took ,peirce no4 #c on a ,u4,s4 eclipse exp$ition to ! ,c>ol9e ,isl&s 9 #ahhc4 ,peirce 9 #ahhe swung p5dulums nos4 #b & #c at ,ann ,arbor1 ,mi*igan2 ,madison1 ,wiscons92 & ,i?aca1 ,new ,york4 ,assi/ant ,pre/on 9 #ahhg swung ,peirce nos4 #c & #d at /ations 9 ! ,hawaiian ,isl&s1 & 9 #ahij he swung ,peirce nos4 #c & #d at /ations on ! we/ coa/ ( ,africa4#gi ,! new patt]n ( p5dulum design$ by ,peirce 0 also adopt$ 9 ,france1 aft] "s ye>s ( exp]i5ce ) a ,repsold-,bessel p5dulum4 ,peirce 9 #ahge _h swung 8 ,repsold-,bessel p5dulum at ! obs]vatory 9 ,p>is1 :]e ,borda & ,cass9i1 & ,biot1 _h made hi/oric obs]vations & :]e ,sab9e also _h det]m9$ gravity by comp>ison ) ,kat]'s value at ,london4 ,dur+ ! spr+ ( #ahhj1 ,peirce made /udies ( ! supports = ! p5dulums ( ^! e>li] det]m9ations & calculat$ corrections to ^? results = hydrodynamic effects1 viscosity1 & flexure4 ,on ,june #ad1 #ahhj1 ,peirce address$ ! ,academy ( ,sci5ces1 ,p>is1 on ! value ( gravity at ,p>is1 & comp>$ 8 results ) ! correct$ results ( ,borda & ,biot & ) ! transf]r$ value ( ,kat]4#hj ,9 ! same ye> ! ,fr5* ,geographic ,s]vice ( ! ,army acquir$ a ,repsold-,bessel rev]sible p5dulum ( ! small] type1 & ,def=ges conduct$ exp]im5ts ) x4#ha ,he introduc$ ! me?od ( measur+ flexure f ! movem5t ( int]f]5ce fr+es dur+ motion ( ! p5dulum4 ,he f\nd an appreciable diff]5ce betwe5 dynamical & /atical coeffici5ts ( flexure & conclud$ t ! correction =mula ( ,peirce & ,cell]i] is suit$ p]fectly to practice & repres5ts exactly ! v>iation ( p]iod caus$ by sway+ ( ! support1 on ! condition t "o uses ! /atical coeffici5t4 ,def=ges develop$ a !ory = ! employm5t ( two simil> p5dulums ( ! same weight1 b ( diff]5t l5g?1 & hung by ! same knives4 ,?is !ory elim9at$ ! flexure ( ! support & ! curvature ( ! knives f ! r$uction ( obs]vations4 ,p5dulums ( #a-met] & ( #a_/b-met] di/ance betwe5 ! knife edges 7 con/ruct$ f ,def=ges' design by ,brunn] ,bro!rs 9 ,p>is 7fig4 #ba74 ,^! ,def=ges p5dulums 7 cyl9drical 9 =m ) hemisph]ical ends l ! ,peirce p5dulums1 & 7 hung on knives t project$ f ! sides ( ! p5dulum1 z 9 "s unf9i%$ ,gauti] p5dulums design$ by ,peirce 9 #ahhc 9 ,p>is4 ,illu/ration3 ,figure #ba4--,,rev]sible ,,p5dulum ,,app>atus ( ,def=ges1 z con/ruct$ by ,brunn]1 ,p>is1 ab\t #ahhg4 ,! clock & telescope us$ to obs]ve co9cid5ces are n %[n4 ,! telescope %[n is "p ( an int]f]omet] us$ to measure flexure ( ! support4 ,"o mirror ( ! int]f]omet] is atta*$ to ! p5dulum support2 ! o!r to ! sep>ate masonry pill> at ! left4 ,illu/ration3 ,figure #bb4--;,,because ,,( ,,! ,,great] ,,simplicity ( its use1 ! inv>iable p5dulum sup]s$$ ! conv]tible p5dulum t[>ds ! end ( ! #ai? c5tury1 except at v>i\s national base /ations 7,kew1 ,p>is1 ,potsdam1 ,wa%+ton1 ,d4,c41 etc474 ,%[n "h are1 "r to left1 a p5dulum ( ! type us$ by ,peirce at ! ,hoosac ,tunnel 9 #ahgc-gd1 ! ,m5d5hall #a_/b-second p5dulum ( #ahij1 & ! p5dulum design$ by ,peirce 9 #ahha-ahhb4 ,illu/ration3 ,figure #bc4--,,! ,,ov]all ,,size ( portable p5dulum app>atus 0 greatly r$uc$ ) ! introduction ( ?is #a_/b-second app>atus 9 #ahhg1 by ! ,au/rian milit>y (fic]1 ,rob]t von ,/]neck4 ,us$ ) a vacuum *amb] n %[n "h1 ! app>atus is only ab\t #b feet high4 ,co9cid5ces are obs]v$ by ! reflection ( a p]iodic electric sp>k 9 two mirrors1 "o on ! support & ! o!r on ! p5dulum itself4 ,illu/ration3 ,figure #bd4--,,?omas ,c4 ,,m5d5hall 7#ahda-aibd74 ,al?\gh l>gely self-educat$1 he became ! fir/ pr(essor ( physics & me*anics at ! ,ohio ,agricultural & ,me*anical ,college 7lat] ,ohio ,/ate ,univ]sity71 & 0 subsequ5tly connect$ ) sev]al o!r univ]sities4 ,9 #ahgh1 :ile tea*+ at ! ,tokyo ,imp]ial ,univ]sity 9 ,japan1 he made gravity measurem5ts betwe5 ,tokyo & ,fujiyama f :i* he calculat$ ! mean d5sity ( ! e>?4 ,:ile sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey1 #ahhi-id1 he develop$ ! p5dulum app>atus :i* be>s 8 "n4 ,von ,/]neck & ,m5d5hall ,p5dulums ,:ile sci5ti/s :o _h us$ ! ,repsold-,bessel p5dulum app>atus discuss$ its defects & limitations = gravity surveys1 ,maj4 ,rob]t von ,/]neck ( ,au/ria-,hung>y began to develop an excell5t app>atus = ! rapid det]m9ation ( relative values ( gravity4#hb ,maj4 von ,/]neck's app>atus conta9$ a nonrev]sible p5dulum #a_/d-met] 9 l5g?1 & #a_/b-second "t ( sw+4 ,! p5dulum 0 hung by a s+le knife edge1 :i* re/$ on a plate t 0 support$ by a tripod4 ,! p5dulum 0 swung 9 a *amb] f :i* air 0 exhau/$ & :i* c\ld be ma9ta9$ at any desir$ temp]ature4 ,times ( sw+ 7 det]m9$ by ! obs]vation ( co9cid5ces ( ! p5dulum ) *ronomet] signals4 ,9 ! f9al =m a small mirror 0 atta*$ to ! knife edge p]p5dicul> to ! plane ( vibration ( ! p5dulum & a second fix$ mirror 0 plac$ close to x s t ! two mirrors 7 p>allel :5 ! p5dulum 0 at re/4 ,! *ronomet] signals work$ a relay t gave a horizontal sp>k :i* 0 reflect$ into ! telescope f ! mirrors4 ,:5 ! p5dulum 0 at re/1 ! image ( ! sp>k 9 bo? mirrors appe>$ on ! horizontal cross wire 9 ! telescope1 & dur+ oscillation ( ! p5dulum ! two images appe>$ 9 t position ^u co9cid5ce4 ,9 view ( ! r$uc$ size ( ! p5dulum1 ! *amb] 9 :i* x 0 swung 0 readily portable1 & ) an improv$ me?od ( obs]v+ co9cid5ces1 relative det]m9ations ( gravity c\ld be made ) rapidity & accuracy4 ,by #ahhg ,maj4 von ,/]neck _h p]fect$ 8 app>atus1 & x 0 widely adopt$ 9 ,europe = relative det]m9ations ( gravity4 ,he us$ 8 app>atus 9 ext5sive gravity surveys & also appli$ x 9 ! silv] m9es 9 ,saxony & ,bohemia1 by ! previ\sly describ$ me?ods ( ,airy1 = inve/igations into ! int]nal con/itution ( ! e>?4 ,on ,july #a1 #ahhi1 ,?omas ,corw9 ,m5d5hall became sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey4 ,e>li]1 he _h be5 pr(essor ( physics at ! ,univ]sity ( ,tokyo & _h direct$ obs]vations ( p5dulums = ! det]m9ation ( gravity on ,fujiyama & at ,tokyo4 ,supt4 ,m5d5hall1 ) ! coop]ation ( memb]s ( 8 /aff 9 ,wa%+ton1 design$ a new p5dulum app>atus ( ! ,von ,/]neck type1 & 9 ,octob] #ahij he ord]$ con/ruction ( ! fir/ model4#hc ,l ! ,von ,/]neck app>atus1 ! ,m5d5hall p5dulum app>atus employ$ a nonrev]sible1 inv>iable p5dulum #a_/d-met] 9 l5g? & ( slightly m ?an #a_/b-second 9 "t ( sw+4 ,initially1 ! knife edge 0 plac$ 9 ! head ( ! p5dulum & hung on a fix$ plane support1 b aft] "s exp]im5tation ,m5d5hall atta*$ ! plane surface to ! p5dulum & hung x on a fix$ knife edge4 ,an app>atus 0 provid$ ) a set ( ?ree p5dulums1 s t if discrepancies appe>$ 9 ! results1 ! p5dulum at fault c\ld be detect$4 ,!re 0 also a dummy p5dulum :i* c>ri$ a !rmomet]4 ,a p5dulum 0 swung 9 a receiv] 9 :i* ! pressure & temp]ature ( ! air 7 controll$4 ,! "t ( sw+ 0 measur$ by co9cid5ces ) ! beat ( a *ronomet]4 ,! co9cid5ces 7 det]m9$ by an optical me?od ) ! aid ( a fla% app>atus4 ,illu/ration3 ,figure #be4--,,m5d5hall',s #a_/d-,,met] 7#a_/b-,,second7 ,,app>atus4 ,%[n on ! left is ! fla% app>atus &1 on ! "r1 ! vacuum *amb] )9 :i* ! p5dulum is swung4 ,! fla% app>atus consi/s ( a k]os5e lant]n & a telescope1 m\nt$ on a box conta9+ an electromagnetically op]at$ %utt]4 ,! op]ation ( ! %utt] is controll$ by a *ronograph 7n %[n71 s t x emits a slit ( light at regul> int]vals4 ,! telescope is focus$ on two mirrors )9 ! app>atus1 "o fix$1 ! o!r atta*$ to ! top ( ! p5dulum4 ,x is us$ to obs]ve ! reflection ( ! fla%es f ^! mirrors4 ,:5 ! two reflections are align$1 a co9cid5ce is m>k$ on ! *ronograph tape4 ,! second telescope atta*$ to ! bottom ( ! vacuum *amb] is = obs]v+ ! amplitude ( ! p5dulum sw+4 ,! fla% app>atus 0 conta9$ 9 a light metal box :i* support$ an obs]v+ telescope & :i* 0 m\nt$ on a /&4 ,)9 ! box 0 an electromagnet ^: coils 7 connect$ ) a *ronomet] circuit & ^: armature c>ri$ a long arm t mov$ two %utt]s1 9 bo? ( :i* 7 horizontal slits ( ! same size4 ,! %utt]s 7 beh9d ! front face ( ! box1 :i* also _h a horizontal slit4 ,a fla% ( light f an oil lamp or an electric sp>k 0 emitt$ f ! box :5 ! circuit 0 brok51 b n :5 x 0 clos$4 ,:5 ! circuit 0 brok5 a spr+ caus$ ! arm to rise1 & ! %utt]s 7 actuat$ s t ! ?ree slits came into l9e & a fla% ( light 0 emitt$4 ,a small circul> mirror 0 set 9 ea* side ( ! p5dulum head1 s t f ei!r face ( ! p5dulum ! image ( ! illum9at$ slit c\ld be reflect$ into ! field ( ! obs]v+ telescope4 ,a simil> mirror 0 plac$ p>allel to ^! two mirrors & rigidly atta*$ to ! support4 ,! *ronomet] signals broke ! circuit1 caus+ ! ?ree slits mom5t>ily to be 9 l9e1 & :5 ! images ( ! slit 9 ! two mirrors co9cid$1 a co9cid5ce 0 obs]v$4 ,a co9cid5ce occurr$ :5ev] ! p5dulum ga9$ or lo/ "o oscillation on ! beat ( ! *ronomet]4 ,! relative int5sity ( gravity 0 det]m9$ by obs]vations ) ! fir/ ,m5d5hall app>atus at ,wa%+ton1 ,d4,c41 at /ations on ! ,pacific ,coa/ & 9 ,alaska1 & at ! ,/ev5s ,in/itute1 ,hobok51 ,new ,j]sey1 betwe5 ,m>* & ,octob] #ahia4 ,illu/ration3 ,figure #bf4--,,vacuum ,,receiv] )9 :i* ! ,m5d5hall p5dulum is swung4 ,! pressure is r$uc$ to ab\t #ej mm4 to r$uce ! di/urb+ effect ( air resi/ance4 ,:5 ! app>atus is seal$1 ! p5dulum is lift$ on ! knife edge by ! lev] q & is />t$ to sw+ by ! lev] r4 ,! arc ( sw+ is only ab\t #a deg4 ,! /ation>y mirror is %[n at g4 ,! p5dulum %[n 9 outl9e 9 ! c5t]1 is only ab\t #i4g in*es long4 ,"u ,supt4 ,m5d5hall's direction a small]1 #a_/d-second1 p5dulum app>atus 0 also con/ruct$ & te/$1 b did n (f] advantages ov] ! #a_/b-second app>atus1 :i* !re=e cont9u$ 9 use4 ,9 accordance ) ,peirce's !ory ( ! flexure ( ! /& "u oscillations ( ! p5dulum1 det]m9ations ( ! displacem5t ( ! receiv] ( ! ,m5d5hall app>atus 7 "p ( a relative det]m9ation ( gravity by memb]s ( ! ,coa/ & ,geodetic ,survey4 ,initially1 a /atical me?od 0 us$1 b dur+ #aijh-aiji memb]s ( ! ,survey adapt$ ! ,mi*elson int]f]omet] = ! det]m9ations ( flexure dur+ oscillations f ! %ift ( fr+es4#hd ,! fir/ ,m5d5hall p5dulums 7 made ( bronze1 b ab\t #aibj inv> 0 *os5 because ( its small coeffici5t ( expansion4 ,ab\t #aicj1 ,lt4 ,e4 ,j4 ,br[n ( ! ,coa/ & ,geodetic ,survey made significant improvem5ts 9 ! ,m5d5hall app>atus1 & ! new =m came to be kn[n z ! ,br[n ,p5dulum ,app>atus4#he ,illu/ration3 ,figure #bg4--,,! ,,mi*elson ,,int]f]omet]4 ,! horizontal compon5t ( ! =ce act+ on ! knife edge ?r\gh ! sw++ p5dulum causes ! support to move 9 unison ) ! p5dulum1 & !reby affects ! p]iod ( ! oscillation4 ,?is movem5t is ! s-call$ flexure ( ! p5dulum support1 & mu/ be tak5 into acc\nt 9 ! mo/ accurate obs]vations4 ,9 #aijg1 ! ,mi*elson int]f]omet] 0 adapt$ to ?is purpose by ! ,u4,s4 ,coa/ & ,geodetic ,survey4 ,z %[n "h1 ! int]f]omet]1 re/+ on a wood5 beam1 is introduc$ into ! pa? ( a light beam reflect$ f a mirror on ! vacuum *amb]4 ,movem5t ( t mirror causes a correspond+ movem5t 9 ! int]f]5ce fr+es 9 ! int]f]omet]1 :i* c be measur$4 ,! orig9al ,von ,/]neck app>atus & t ( ,m5d5hall provid$ = ! oscillation ( "o p5dulum at a "t4 ,aft] ! adoption ( ! ,von ,/]neck p5dulum 9 ,europe1 !re 7 develop$ /&s on :i* two or f\r p5dulums hung at ! same "t4 ,?is proc$ure provid$ a conv5i5t way to obs]ve m ?an "o inv>iable p5dulum at a /ation = ! purpose ( detect+ *anges 9 l5g?4 ,pr(4 ,m4 ,haid ( ,k>lsruhe 9 #ahif describ$ a f\r-p5dulum app>atus1#hf & ,dr4 ,s*umann ( ,potsdam subsequ5tly describ$ a two-p5dulum app>atus4#hg ,illu/ration3 ,figure #bh4--;,,app>atus ,,:i* ,,0 ,,develop$ ,,9 #aibi by ! ,gulf ,rese>* & ,developm5t ,company1 ,h>m>ville1 ,p5nsylvania4 ,x 0 design$ to a*ieve an accuracy )9 "o t5-million? ( ! true value ( gravity1 & repres5ts ! extreme developm5t ( p5dulum app>atus = relative gravity measurem5t4 ,! p5dulum 0 design$ s t ! p]iod w\ld be a m9imum4 ,! case 7! top is miss+ 9 ?is photograph7 is dehumidifi$ & its temp]ature & electro/atic condition are controll$4 ,specially design$ p5dulum-lift+ & -/>t+ me*anisms are us$4 ,! problem ( flexure ( ! case is ov]come by ! ,faye-,peirce me?od 7see text7 9 :i* two dynamically mat*$ p5dulums are swung simultane\sly1 #ahj deg4 ap>t 9 phase4 ,! multiple-p5dulum app>atus !n provid$ a me?od ( det]m9+ ! flexure ( ! /& f ! action ( "o p5dulum ^u a second p5dulum hung on ! same /&4 ,?is me?od ( det]m9+ ! correction = flexure 0 a developm5t f a ,wippv]fahr5 inv5t$ at ! ,geodetic ,in/itute 9 ,potsdam4 ,a dynamomet] 0 us$ to imp>t p]iodic impulses to ! /&1 & ! effect 0 obs]v$ ^u a p5dulum initially at re/4 ,ref9em5ts ( ?is me?od l$ to ! developm5t ( a me?od us$ by ,lor5zoni 9 #ahhe-ahhf to det]m9e ! flexure ( ! /& by action ( an auxili>y p5dulum ^u ! pr9cipal p5dulum4 ,dr4 ,s*umann1 9 #ahii1 gave a ma!matical !ory ( su* det]m9ations1#hh & 9 8 pap] cit$ ! ma!matical me?ods ( ,peirce & ,cell]i] = ! !ory ( ,faye's proposal at ,/uttg>t 9 #ahgg to sw+ two simil> p5dulums on ! same support ) equal amplitudes & 9 opposite phases4 ,illu/ration3 ,figure #bi4--,,! ,,gulf ,,p5dulum is ab\t #aj4g in*es long1 & has a p]iod ( 4#hi second4 ,x is made ( fus$ qu>tz :i* is resi/ant to ! influ5ce ( temp]ature *ange & to ! e>?'s magnetism4 ,qu>tz p5dulums are subject to ! influ5ce ( electro/atic *>ge1 & provision is made to c\nt]act ?is ?r\gh ! pres5ce ( a radium salt 9 ! case4 ,! be>+s are made ( ,pyrex glass4 ,9 #aijb1 ,dr4 ,p4 ,furtwa5gl]#hi pres5t$ ! ma!matical !ory ( c\pl$ p5dulums 9 a pap] 9 :i* he ref]r$ to ,faye's proposal ( #ahgg & report$ t ! difficulties pr$ict$ ^u its application _h be5 f\nd n to occur4 ,f9ally1 dur+ ! gravity survey ( ,holl& 9 ! ye>s #aiac-aiba1 9 view ( in/ability ( supports caus$ by ! mobility ( ! soil1 ,f4 ,a4 ,v5+ ,me9esz adopt$ ,faye's propos$ me?od ( sw++ two p5dulums on ! same support4#ij ,! obs]vations 7 made ) ! ord9>y ,/ueckra? app>atus1 9 :i* f\r ,von ,/]neck p5dulums swung two by two 9 planes p]p5dicul> to ea* o!r4 ,?is successful application ( ! me?od--:i* _h be5 propos$ by ,faye & _h be5 demon/rat$ !oretically to be s\nd by ,peirce1 :o also publi%$ a design = its application--0 rapidly foll[$ = p5dulum app>atus = relative det]m9ations by ,potsdam1#ia ,cambridge 7,engl&71#ib ,gulf ,oil & ,developm5t ,company1#ic & ! ,dom9ion ,obs]vatory at ,ottawa4#id ,heiskan5 & ,v5+ ,me9esz /ate3 ,! be/ way to elim9ate ! effect ( flexure is to use two syn*roniz$ p5dulums ( ! same l5g? sw++ on ! same app>atus 9 ! same plane & ) ! same amplitudes b 9 opposite phases2 x is cle> !n ! flexure is z]o4#ie ,9 view ( ! fact t ! symmetrical rev]sible p5dulum is nam$ = ,bessel1 :o creat$ ! !ory & a design = its application by ,repsold1 x appe>s appropriate to call ! me?od ( elim9at+ flexure by sw++ two p5dulums on ! same support ! ,faye-,peirce me?od4 ,its successful application 0 made possible by ,maj4 von ,/]neck's inv5tion ( ! %ort1 #a_/d-met] p5dulum4 ,illu/ration3 ,figure #cj4--,,! ,,accumulat$ ,,data ,,( ,,gravity obs]vations ov] ! e>?'s surface h indicat$ t irregul>ities su* z m\nta9s d n h ! effect :i* w\ld be expect$ 9 modify+ gravity1 b are someh[ comp5sat$ =4 ,! mo/ satisfactory solution to ?is /ill unansw]$ "q has be5 ! !ory ( iso/asy1 accord+ to :i* v>iations 9 ! d5sity ( ! mat]ial 9 ! e>?'s cru/ produce a k9d ( hydro/atic equilibrium betwe5 its high] & l[] p>ts1 z !y float on ! e>?'s fluid core4 ,! metals ( diff]5t d5sity float+ 9 m]cury 9 ?is diagram illu/rate iso/asy accord+ to ! !ory ( ,pratt & ,hay=d4 ,absolute ,value ( ,gravity at ,potsdam ,! developm5t ( ! rev]sible p5dulum 9 ! #ai? c5tury culm9at$ 9 ! absolute det]m9ation ( ! int5sity ( gravity at ,potsdam by ,kuehn5 & ,furtwa5gl] ( ! ,royal ,prussian ,geodetic ,in/itute1 :i* !n became ! _w base = gravity surveys4#if ,we h previ\sly se5 t 9 #ahfi ! ,geodetic ,in/itute--f\nd$ by ,lt4 ,g54 ,baey]--_h acquir$ a ,repsold-,bessel rev]sible p5dulum :i* 0 swung by ,dr4 ,albre*t "u ! direction ( ,dr4 ,bruhns4 ,dissatisfaction ) ?is in/rum5t 0 express$ by ,baey] 9 #ahge to ,*>les ,s4 ,peirce1 :o !n1 by exp]im5t & ma!matical analysis ( ! flexure ( ! /& "u oscillations ( ! p5dulum1 det]m9$ t previ\sly report$ results ) ! ,repsold app>atus requir$ correction4 ,dr4 ,f4 ,r4 ,helm]t1 :o 9 #ahhg succe$$ ,baey] z director ( ! ,in/itute1 secur$ con/ruction ( a build+ = ! ,in/itute 9 ,potsdam1 & "u 8 direction ! sci5tific /udy ( ! int5sity ( gravity 0 pursu$ ) vigor4 ,9 #ahid1 x 0 discov]$ 9 ,potsdam t a p5dulum con/ruct$ ( v flexible mat]ial yield$ results :i* diff]$ m>k$ly f ^? obta9$ ) p5dulums ( great] /iffness4 ,dr4 ,kuehn5 ( ! ,in/itute discov]$ t ! dep>ture f expectations 0 ! result ( ! flexure ( ! p5dulum /aff itself dur+ oscillations4#ig ,peirce1 9 #ahhc1 _h discov]$ t ! recesses cut 9 8 p5dulums = ! ins]tion ( tongues t c>ri$ ! knives _h result$ 9 ! flexure ( ! p5dulum /aff4#ih ,by exp]im5t1 he also f\nd an ev5 great] flexure = ! ,repsold p5dulum4 ,9 ord] to elim9ate ?is s\rce ( error1 ,peirce design$ a p5dulum ) knives t ext5d$ f ea* side ( ! cyl9drical /aff1 & he receiv$ au?orization f ! sup]9t5d5t ( ! ,coa/ & ,geodetic ,survey to arrange = ! con/ruction ( su* p5dulums by ,gauti] 9 ,p>is4 ,peirce1 :o _h made 8 plans 9 consultation ) ,gauti]1 0 call$ home be=e ! p5dulums 7 complet$1 & ^! new in/rum5ts rema9$ undeliv]$4 ,9 a memoir titl$ ,effect ( ! flexure ( a p5dulum ^u its p]iod ( oscillation1#ii ,peirce det]m9$ analytically ! effect on ! p]iod ( a p5dulum ) a s+le ela/ic connection betwe5 two rigid p>ts ( ! /aff4 ,?us1 ,peirce discov]$ exp]im5tally ! flexure ( ! /aff & d]iv$ = a simplifi$ case ! effect on ! p]iod4 ,x is n kn[n if he ev] f\nd ! integrat$ effect ( ! cont9uum ( ela/ic connections 9 ! p5dulum4 ,lor5zoni1 9 #ahif1 (f]$ a solution to ! problem1 & ,almansi1 9 #ahii1 gave an ext5d$ analysis4 ,aft] ! indep5d5t discov]y ( ! problem at ! ,geodetic ,in/itute1 ,dr4 ,helm]t took up ! problem & criticiz$ ! !ories ( ,peirce & ,lor5zoni4 ,he !n pres5t$ 8 own !ory ( flexure 9 a compreh5sive memoir4#ajj ,9 view ( ! previ\s neglect ( ! flexure ( ! p5dulum /aff 9 ! r$uction ( obs]vations1 ,helm]t direct$ t ! ,geodetic ,in/itute make a new absolute det]m9ation ( ! int5sity ( gravity at ,potsdam4 ,= ?is purpose1 ,kuehn5 & ,furtwa5gl] us$ ! foll[+ rev]sible p5dulums :i* _h be5 con/ruct$ by ! firm ( ,a4 ,repsold & ,sons 9 ,hamburg3 #a4 ,! seconds p5dulum ( ! ,geodetic ,in/itute procur$ 9 #ahfi4 #b4 ,a seconds p5dulum f ! ,a/ronomical ,obs]vatory1 ,padua4 #c4 ,a heavy1 seconds p5dulum f ! ,imp]ial & ,royal ,milit>y-,geographical ,in/itute1 ,vi5na4 #d4 ,a light1 seconds p5dulum f ! ,imp]ial & ,royal ,milit>y-,geographical ,in/itute4 #e4 ,a #a_/b-second1 rev]sible p5dulum ( ! ,geodetic ,in/itute procur$ 9 #ahib4 ,"w 0 begun 9 #ahih1 & 9 #aijf ,kuehn5 & ,furtwa5gl] publi%$ _! monum5tal memoir1 ,be/immung d] ,absolut5 ,groesze d] ,s*w]kraft zu ,potsdam mit ,rev]sionsp5deln4 ,! accel]ation ( gravity 9 ! p5dulum room ( ! ,geodetic ,in/itute 0 det]m9$ to be #iha4bgd - #j4jjc cm_/sec#b4 ,9 view ( ! exceptionally c>eful & ?or\gh det]m9ation at ! ,in/itute1 ,potsdam 0 accept$ z ! _w base = ! absolute value ( ! int5sity ( gravity4 ,! absolute value ( gravity at "s o!r /ation on ! ,potsdam sy/em 0 det]m9$ f ! times ( sw+ ( an inv>iable p5dulum at ! /ation & at ,potsdam by ! relation 7,t#a7b_/7,t#b7b g#b_/;g#a4 ,?us1 9 #aijj1 ,assi/ant ,g4 ,r4 ,putnam ( ! ,coa/ & ,geodetic ,survey swung ,m5d5hall p5dulums at ! ,wa%+ton base & at ,potsdam1 & by transf] f ,potsdam det]m9$ ! int5sity ( gravity at ! ,wa%+ton base to be #ihj4aab cm_/sec#b4aja ,9 #aicc1 ,lt4 ,e4 ,j4 ,br[n made comp>ative measurem5ts ) improv$ app>atus & rais$ ! value at ! ,wa%+ton base to #ihj4aah cm_/sec#b4ajb ,9 view ( discrepancies betwe5 ! results ( v>i\s relative det]m9ations1 ! ,coa/ & ,geodetic ,survey 9 #aibh reque/$ ! ,national ,bureau ( ,/&>ds to make an absolute det]m9ation = ,wa%+ton4 ,heyl & ,cook us$ rev]sible p5dulums made ( fus$ silica hav+ a p]iod ( approximately #a second4 ,_! result1 publi%$ 9 #aicf1 0 int]pret$ to indicate t ! value at ,potsdam 0 too high by #bj p>ts 9 #a million4#ajc ,?is e/imate 0 l[]$ slightly by ,sir ,h>old ,jeffreys ( ,cambridge1 ,engl&1 :o recomput$ ! results ( ,heyl & ,cook by diff]5t me?ods4#ajd ,illu/ration3 ,figure #ca4--,,map ,,%[+ ,,! ,,di/ribution ( gravity /ations ?r\gh\t ! ,unit$ ,/ates z ( ,decemb] #aijh4 ,illu/ration3 ,figure #cb4--,,map ,,%[+ ,,! ,,di/ribution ( gravity /ations ?r\gh\t ! ,unit$ ,/ates 9 #aibc4 ,9 #aici1 ,j4 ,s4 ,cl>k publi%$ ! results ( a det]m9ation ( gravity ) p5dulums ( a non-f]r\s ,y-alloy#aje at ! ,national ,physical ,laboratory at ,t$d+ton1 ,engl&1 &1 aft] recomputation ( results by ,jeffreys1 ! value 0 f\nd to be #ab4h p>ts 9 #a million less ?an ! value obta9$ by transf] f ,potsdam4 ,dr4 ,hugh ,l4 ,dryd5 ( ! ,national ,bureau ( ,/&>ds1 & ,dr4 ,a4 ,b]ro? ( ! ,geodetic ,in/itute at ,potsdam1 h recomput$ ! ,potsdam data by diff]5t me?ods ( adju/m5t & conclud$ t ! ,potsdam value 0 too high by ab\t #ab p>ts 9 a million4#ajf ,det]m9ation ( gravity at ,l5+rad by ,russian sci5ti/s likewise has indicat$ t ! #aijf ,potsdam value is too high4 ,9 ! light ( pres5t in=mation1 x appe>s ju/ifiable to r$uce ! ,potsdam value ( #iha4bgd by 4#jac cm_/sec#b = purposes ( comp>ison4 ,if ! ,br[n transf] f ,potsdam 9 #aicc 0 tak5 z accurate1 ! value = ! ,wa%+ton base w\ld be #ihj4aje cm_/sec#b4 ,9 ?is connection1 x is ( int]e/ to note t ! value giv5 by ,*>les ,s4 ,peirce = ! comp>able ,smi?sonian base 9 ,wa%+ton1 z det]m9$ by him f comp>ative me?ods 9 ! #ahhj's & report$ 9 ! ,annual ,report ( ! ,sup]9t5d5t ( ! ,coa/ & ,geodetic ,survey = ! ye> #ahij-ahia1 0 #ihj4ajag cm_/sec#b4ajg ,?is value w\ld appe> to indicate t ,peirce's p5dulums1 obs]vations1 & me?ods ( r$uction ( data 7 n inf]ior to ^? ( ! sci5ti/s ( ! ,royal ,prussian ,geodetic ,in/itute at ,potsdam4 ,d\bts conc]n+ ! accuracy ( ! ,potsdam value ( gravity h /imulat$ _m new det]m9ations ( ! int5sity ( gravity s9ce ! end ( ,_w ,w> ,,ii4 ,9 a pap] publi%$ 9 ,june #aieg1 ,a4 ,h4 ,cook1 ,metrology ,division1 ,national ,physical ,laboratory1 ,t$d+ton1 ,engl&1 /at$3 ,at pres5t ab\t a doz5 new absolute det]m9ations are 9 progress or are be+ plann$4 ,heyl & ,cook's rev]sible p5dulum app>atus is 9 use 9 ,bu5os ,aires & fur!r rev]sible p5dulum exp]im5ts h be5 made 9 ! ,all ,union ,sci5tific ,rese>* ,in/itute ( ,metrology1 ,l5+rad 7,v ,n ,i ,i ,m7 & are plann$ at ,potsdam4 ,a me?od us+ a v long p5dulum 0 tri$ out 9 ,russia ab\t #aiaj & aga9 m rec5tly & !re are plans = simil> "w 9 ,f9l&4 ,! fir/ exp]im5t ) a freely fall+ body 0 t c>ri$ out by ,volet :o photograph$ a graduat$ scale fall+ 9 an enclosure at l[ air pressure4 ,simil> exp]im5ts h be5 complet$ 9 ,l5+rad & are 9 progress at ! ,physikalis*-,te*nis*e ,bundesan/alt 7,brunswick7 & at ! ,national ,rese>* ,c\ncil 7,ottawa71 & analog\s exp]im5ts are be+ prep>$ at ! ,national ,physical ,laboratory & at ! ,national ,bureau ( ,/&>ds4 ,f9ally1 ,pr(essor ,m$i1 ,director ( ! ,i/ituto ,nazionale di ,ge(isica 7,rome71 is attempt+ to measure ! focal l5g? ( ! p>aboloidal surface ( a liquid 9 a rotat+ di%4#ajh ,application ( ,gravity ,surveys ,we h not$ previ\sly t 9 ! anci5t & e>ly mod]n p]iods1 ! e>? 0 presuppos$ to be sph]ical 9 =m4 ,det]m9ation ( ! figure ( ! e>? consi/$ 9 ! measurem5t ( ! radius by ! a/ronomical-geodetic me?od inv5t$ by ,erato/h5es4 ,s9ce ! e>? 0 assum$ to be sph]ical1 gravity 0 inf]r$ to be con/ant ov] ! surface ( ! e>?4 ,?is conclusion appe>$ to be confirm$ by ! det]m9ation ( ! l5g? ( ! seconds p5dulum at v>i\s /ations 9 ,europe by ,pic>d & o!rs4 ,! obs]vations ( ,ri*] 9 ,s\? ,am]ica1 ! !oretical discussions ( ,newton & ,huyg5s1 & ! measurem5ts ( degrees ( latitude 9 ,p]u & ,sw$5 demon/rat$ t ! e>? is an oblate sph]oid4 ,illu/ration3 ,figure #cc4--;,,gravity ,,*>act]i/ics ,,( ,,! ,,globe4 ,d$uctions z to ! di/ribution ( matt] 9 ! e>? c be made f gravity measurem5ts4 ,?is globe %[s worldwide v>iations 9 gravity z !y n[ appe> f obs]vations at sea 79 subm>9es7 z well z on l&4 ,x is bas$ on data f ! ,in/itute ( ,geodesy at ,ohio ,/ate ,univ]sity4 ,! !ory ( gravitation & ! !ory ( c5tral =ces l$ to ! result t ! int5sity ( gravity is v>iable ov] ! surface ( ! e>?4 ,accord+ly1 det]m9ations ( ! int5sity ( gravity became ( value to ! geodesi/ z a means ( det]m9+ ! figure ( ! e>?4 ,newton1 on ! basis ( ! meag] data available to him1 calculat$ ! ellipticity ( ! e>? to be #a_/bcj 7! ellipticity is def9$ by 7a-b7_/a1 :]e a is ! equatorial radius & b ! pol> radius74 ,obs]vations ( ! int5sity ( gravity 7 made on ! hi/oric missions to ,p]u & ,sw$54 ,b\gu] & ,la ,condam9e f\nd t at ! equator at sea level ! seconds p5dulum 0 #a4bf ,p>is-l9es %ort] ?an at ,p>is4 ,maup]tuis f\nd t 9 nor!rn ,sw$5 a c]ta9 p5dulum clock ga9$ #ei4a seconds p] day on its rate 9 ,p>is4 ,!n ,clairaut1 f ! assumption t ! e>? is a sph]oid ( equilibrium1 d]iv$ a !orem f :i* ! ellipticity ( ! e>? c be d]iv$ f values ( ! int5sity ( gravity4 ,illu/ration3 ,figure #cd4--;,,an ,,exhibit ,,( ,,gravity ,,app>atus at ! ,smi?sonian ,in/itution4 ,susp5d$ on ! wall1 f left to "r1 are ! inv>iable p5dulums ( ,m5d5hall 7#a_/b-second71 ,peirce 7#ahgc-ahgd71 & ,peirce 7#ahha-ahhb72 ! d\ble p5dulum ( ,edw>d ,kuebel 7see fig4 #ae1 p4 #cai71 & ! rev]sible p5dulum ( ,peirce4 ,on ! display c\nt]1 f left to "r1 are ! vacuum *amb]1 telescope & fla% app>atus = ! ,m5d5hall #a_/d-second app>atus4 ,%[n bel[ ^! are ! f\r p5dulums us$ ) ! ,m5d5hall app>atus1 ! "o on ! "r hav+ a !rmomet] atta*$4 ,at bottom1 "r1 is ! ,gulf app>atus 7cov] remov$7 m5tion$ 9 ! text1 %[n ) "o qu>tz p5dulum4 ,e>ly 9 ! #ai? c5tury a sy/ematic s]ies ( obs]vations began to be conduct$ 9 ord] to det]m9e ! int5sity ( gravity at /ations all ov] ! _w4 ,kat] inv>iable p5dulums1 ( :i* #ac examples h be5 m5tion$ 9 ! lit]ature1 7 us$ 9 surveys ( gravity by ,kat]1 ,sab9e1 ,gold+ham1 & o!r ,briti% p5dulum sw+]s4 ,z has be5 not$ previ\sly1 a ,kat] inv>iable p5dulum 0 us$ by ,adm4 ,luetke ( ,russia on a trip ar\nd ! _w4 ,! ,fr5* also s5t out exp$itions to det]m9e values ( gravity4 ,aft] sev]al decades ( relative inactivity1 ,capts4 ,basevi & ,heaviside ( ! ,indian ,survey c>ri$ out an important s]ies ( obs]vations f #ahfe to #ahgc ) ,kat] inv>iable p5dulums & ! ,russian ,repsold-,bessel p5dulums4 ,9 #ahha-ahhb ,maj4 ,j4 ,h]s*el swung ,kat] inv>iable p5dulums nos4 #d1 #f 7#ahba71 & #aa at /ations 9 ,engl& & !n br\ght !m to ! ,unit$ ,/ates 9 ord] to make obs]vations :i* w\ld connect ,am]ican & ,engli% base /ations4#aji ,! ext5sive sets ( obs]vations ( gravity provid$ ! basis ( calculations ( ! ellipticity ( ! e>?4 ,col4 ,a4 ,r4 ,cl>ke 9 8 ,geodesy 7,london1 #ahhj7 calculat$ ! ellipticity f ! results ( gravity surveys to be #a_/7bib4b - #a4e74 ,( int]e/ is ! calculation by ,*>les ,s4 ,peirce1 :o us$ only det]m9ations made ) ,kat] inv>iable p5dulums & correct$ = elevation1 atmosph]ic effect1 & expansion ( ! p5dulum ?r\gh temp]ature4#aaj ,he calculat$ ! ellipticity ( ! e>? to be #a_/7bia4e - #j4i74 ,! #ai? c5tury witness$ ! culm9ation ( ! ellipsoidal era ( geodesy1 b ! rapid accumulation ( data made possible a bett] approximation to ! figure ( ! e>? by ! geoid4 ,! geoid is def9$ z ! av]age level ( ! sea1 :i* is ?\ght ( z ext5d$ ?r\gh ! cont95ts4 ,! basis ( geodetic calculations1 h[ev]1 is an ellipsoid ( ref]5ce = :i* a gravity =mula expresses ! value ( normal gravity at a po9t on ! ellipsoid z a function ( gravity at sea level at ! equator1 & ( latitude4 ,! g5]al assembly ( ! ,int]national ,union ( ,geodesy & ,geophysics1 :i* 0 f\nd$ aft] ,_w ,w> ,i to cont9ue ! "w ( ,die ,int]nationale ,erdmessung1 adopt$ 9 #aibd an int]national ref]5ce ellipsoid1#aaa ( :i* ! ellipticity1 or flatt5+1 is ,hay=d's value #a_/big4 ,9 #aicj1 ! g5]al assembly adopt$ a correlat$ ,int]national ,gravity ,=mula ( ! =m gamma gamma,e7#a betas9#b phi epsilons9#b #bphi7 :]e gamma is normal gravity at latitude phi1 gamma,e is ! value ( gravity at sea level at ! equator1 beta is a p>amet] :i* is comput$ on ! basis ( ,clairaut's !orem f ! flatt5+ value ( ! m]idian1 & epsilon is a con/ant :i* is d]iv$ !oretically4 ,! plumb l9e is p]p5dicul> to ! geoid1 & ! compon5ts ( angle betwe5 ! p]p5dicul>s to geoid & ref]5ce ellipsoid are deflections ( ! v]tical4 ,! geoid is above ! ellipsoid ( ref]5ce "u m\nta9s & x is bel[ ! ellipsoid on ! oceans1 :]e ! geoid co9cides ) mean sea level4 ,9 physical geodesy1 gravimetric data are us$ = ! det]m9ation ( ! geoid & compon5ts ( deflections ( ! v]tical4 ,= ?is purpose1 "o mu/ r$uce obs]v$ values ( gravity to sea level by v>i\s r$uctions1 su* z free-air1 ,b\gu]1 iso/atic r$uctions4 ,if g#j is obs]v$ gravity r$uc$ to sea level & gamma is normal gravity obta9$ f ! ,int]national ,gravity ,=mula1 !n ,deltag g#j - gamma is ! gravity anomaly4#aab ,9 #ahdi1 ,/okes d]iv$ a !orem :]eby ! di/ance ,n ( ! geoid f ! ellipsoid ( ref]5ce c be obta9$ f an integration ( gravity anomalies ov] ! surface ( ! e>?4 ,v5+ ,me9esz fur!r d]iv$ =mulae = ! calculation ( compon5ts ( ! deflection ( ! v]tical4 ,geometrical geodesy1 :i* 0 bas$ on a/ronomical-geodetic me?ods1 c\ld give in=mation only conc]n+ ! ext]nal =m ( ! figure ( ! e>?4 ,! gravimetric me?ods ( physical geodesy1 9 conjunction ) me?ods su* z ^? ( seismology1 enable sci5ti/s to te/ hypo!ses conc]n+ ! int]nal /ructure ( ! e>?4 ,heiskan5 & ,v5+ ,me9esz summ>ize ! pres5t-day a*ievem5ts ( ! gravimetric me?od ( physical geodesy by /at+#aac t x alone c give3 #a4 ,! flatt5+ ( ! ref]5ce ellipsoid4 #b4 ,! undulations ,n ( ! geoid4 #c4 ,! compon5ts ( ! deflection ( ! v]tical xi & eta at any po9t1 oceans & isl&s includ$4 #d4 ,! conv]sion ( exi/+ geodetic sy/ems to ! same _w geodetic sy/em4 #e4 ,! r$uction ( triangulation base l9es f ! geoid to ! ref]5ce ellipsoid4 #f4 ,! correction ( errors 9 triangulation 9 m\nta9\s regions due to ! effect ( ! deflections ( ! v]tical4 #g4 ,geophysical applications ( gravity measurem5ts1 e4g41 ! iso/atic /udy ( ! e>?'s int]ior & ! exploration ( oil fields & ore deposits4 ,) a/ronomical obs]vations or ) exi/+ triangulations1 ! gravimetric me?od c accompli% fur!r results4 ,heiskan5 & ,v5+ ,me9esz /ate3 ,x is ! firm conviction ( ! au?ors t ! gravimetric me?od is by f> ! be/ ( ! exi/+ me?ods = solv+ ! ma9 problems ( geodesy1 i4e41 to det]m9e ! %ape ( ! geoid on ! cont95ts z well z at sea & to conv]t ! exi/+ geodetic sy/ems to ! _w geodetic sy/em4 ,x c also give invaluable help 9 ! computation ( ! ref]5ce ellipsoid4#aad ,summ>y ,s9ce ! creation ( classical me*anics 9 ! #ag? c5tury1 ! p5dulum has be5 a basic in/rum5t = ! det]m9ation ( ! int5sity ( gravity1 :i* is express$ z ! accel]ation ( a freely fall+ body4 ,basis ( !ory is ! simple p5dulum1 ^: "t ( sw+ "u gravity is proportional to ! squ>e root ( ! l5g? divid$ by ! accel]ation due to gravity4 ,s9ce ! l5g? ( a simple p5dulum divid$ by ! squ>e ( its "t ( sw+ is equal to ! l5g? ( a p5dulum t beats seconds1 ! int5sity ( gravity also has be5 express$ 9 t]ms ( ! l5g? ( ! seconds p5dulum4 ,! rev]sible comp\nd p5dulum has s]v$ = ! absolute det]m9ation ( gravity by means ( a !ory develop$ by ,huyg5s4 ,inv>iable comp\nd p5dulums ) s+le axes also h be5 us$ to det]m9e relative values ( gravity by comp>ative times ( sw+4 ,! hi/ory ( gravity p5dulums beg9s ) ! ball or simple p5dulum ( ,galileo z an approximation to ! ideal simple p5dulum4 ,det]m9ations ( ! l5g? ( ! seconds p5dulum by ,fr5* sci5ti/s culm9at$ 9 a hi/oric det]m9ation at ,p>is by ,borda & ,cass9i1 f ! correct$ obs]vations ) a long ball p5dulum4 ,9 ! #ai? c5tury1 ,bessel f\nd ! l5g? ( ! seconds p5dulum at ,ko5igsb]g & ,b]l9 by obs]vations ) a ball p5dulum & by orig9al !oretical consid]ations4 ,dur+ ! c5tury1 h[ev]1 ! comp\nd p5dulum came to be pref]r$ = absolute & relative det]m9ations4 ,capt4 ,h5ry ,kat]1 at ,london1 con/ruct$ ! fir/ conv]tible comp\nd = an absolute det]m9ation ( gravity1 & !n he design$ an inv>iable comp\nd p5dulum1 examples ( :i* 7 us$ = relative det]m9ations at v>i\s /ations 9 ,europe & else:]e4 ,bessel demon/rat$ !oretically ! advantages ( a rev]sible comp\nd p5dulum :i* is symmetrical 9 =m & is hung by int]*angeable knives4 ,! firm ( ,a4 ,repsold & ,sons 9 ,hamburg con/ruct$ p5dulums f ! specifications ( ,bessel = ,european gravity surveys4 ,*>les ,s4 ,peirce 9 #ahge receiv$ deliv]y 9 ,hamburg ( a ,repsold-,bessel p5dulum = ! ,u4,s4 ,coa/ ,survey & obs]v$ ) x 9 ,g5eva1 ,p>is1 ,b]l91 & ,london4 ,^u an initial /imulation f ,baey]1 f\nd] ( ,die ,europaeis*e ,gradmessung1 ,peirce demon/rat$ by exp]im5t & !ory t results previ\sly obta9$ ) ! ,repsold app>atus requir$ correction1 because ( ! flexure ( ! /& "u oscillations ( ! p5dulum4 ,at ! ,/uttg>t conf]5ce ( ! geodetic association 9 #ahgg1 ,h]ve ,faye propos$ to solve ! problem ( flexure by sw++ two simil> p5dulums f ! same support ) equal amplitudes & 9 opposite phases4 ,peirce1 9 #ahgi1 demon/rat$ !oretically ! s\ndness ( ! me?od & pres5t$ a design = its application1 b ! d\ble p5dulum 0 reject$ at t "t4 ,peirce also design$ & _h con/ruct$ f\r examples ( a new type ( inv>iable1 rev]sible p5dulum ( cyl9drical =m :i* made possible ! exp]im5tal /udy ( ,/okes' !ory ( ! resi/ance to motion ( a p5dulum 9 a visc\s fluid4 ,comm&ant ,def=ges1 ( ,france1 also design$ & us$ cyl9drical rev]sible p5dulums1 b ( diff]5t l5g? s t ! effect ( flexure 0 elim9at$ 9 ! r$uction ( obs]vations4 ,maj4 ,rob]t von ,/]neck1 ( ,au/ria-,hung>y1 initiat$ a new era 9 gravity rese>* by ! inv5tion ( an app>atus ) a %ort p5dulum = relative det]m9ations ( gravity4 ,/&s 7 !n con/ruct$ 9 ,europe on :i* two or f\r p5dulums 7 hung at ! same "t4 ,f9ally1 e>ly 9 ! pres5t c5tury1 ,v5+ ,me9esz f\nd t ! ,faye-,peirce me?od ( sw++ p5dulums hung on a ,/ueckra? f\r-p5dulum /& solv$ ! problem ( in/ability due to ! mobility ( ! soil 9 ,holl&4 ,! #bj? c5tury has witness$ increas+ activity 9 ! det]m9ation ( absolute & relative values ( gravity4 ,gravimet]s h be5 p]fect$ & h be5 widely us$ = rapid relative det]m9ations1 b ! comp\nd p5dulums rema9 z indisp5sable in/rum5ts4 ,m5d5hall's replacem5t ( knives by planes atta*$ to nonrev]sible p5dulums has be5 us$ also = rev]sible ones4 ,! ,geodetic ,in/itute at ,potsdam is pres5tly apply+ ! ,faye-,peirce me?od to ! rev]sible p5dulum4#aae ,p5dulums h be5 con/ruct$ ( new mat]ials1 su* z inv>1 fus$ silica1 & fus$ qu>tz4 ,m9imum p5dulums = precise relative det]m9ations h be5 con/ruct$ & us$4 ,rev]sible p5dulums h be5 made ) ,i cross sections = bett] /iffness4 ,) all ^! modifications1 h[ev]1 ! f\ndations ( ! pres5t designs ( comp\nd p5dulum app>atus 7 creat$ 9 ! #ai? c5tury4 ,,footnotes3 #a ,! basic hi/orical docum5ts h be5 collect$1 ) a bibliography ( works & memoirs publi%$ f #afbi to ! end ( #ahhe1 9 ,collection de memoires relatifs a la physique1 publies p> la ,societe francaise de ,physique h]e9aft] ref]r$ to z ,collection de memoires3 vol4 #d1 ,memoires sur le p5dule1 prec$es d'une bibliographie 7,p>is3 ,gau?i]-,vill>s1 #ahhi72 & vol4 #e1 ,memoires sur le p5dule1 "p #b 7,p>is3 ,gau?i]-,vill>s1 #ahia74 ,important second>y s\rces are3 ,c4 ,,wolf1 ,introduction hi/orique1 pp4 #a-db 9 vol4 #d1 above2 & ,,george ,,biddell ,,airy1 ,figure ( ! ,e>?1 pp4 #afe-bdj 9 vol4 #e ( ,encyclopa$ia metropolitana 7,london1 #ahde74 #b ,galileo ,galilei's pr9cipal /atem5ts conc]n+ ! p5dulum occur 9 8 ,disc\rses ,conc]n+ ,two ,new ,sci5ces1 transl4 f ,italian & ,lat9 into ,engli% by ,h5ry ,crew & ,alfonso de ,salvio 7,evan/on3 ,nor?we/]n ,univ]sity ,press1 #aici71 pp4 #ie-ig1 #agj-agb4 #c ,p4 ,,m>9 ,,m]s5ne1 ,cogitata physico-ma!matica 7,p>is1 #afdd71 p4 #dd4 #d ,,*ri/iaan ,,huyg5s1 ,horologium oscillatorium1 sive de motu p5dulorum ad horologia adaptato demon/rationes geometricae 7,p>is1 #afgc71 proposition #bj4 #e ,! hi/orical ev5ts report$ 9 ! pres5t section are f ,,airy1 ,figure ( ! ,e>?4 #f ,,abbe ,,jean ,,pic>d1 ,la ,mesure de la t]re 7,p>is1 #afga74 ,,john ,w4 ,,olm/$1 ,! ',application' ( ,telescopes to ,a/ronomical ,in/rum5ts1 #affg-affi1 ,isis 7#aidi71 vol4 #dj1 p4 #bac4 #g ,! toise z a unit ( l5g? 0 #f ,p>is feet or ab\t #a1idi millimet]s4 #h ,,jean ,,ri*]1 ,obs]vations a/ronomiques et physiques faites en l'isle de ,cai5ne 7,p>is1 #afgi74 ,,john ,w4 ,,olm/$1 ,! ,exp$ition ( ,jean ,ri*] to ,cay5ne #afgb-afgc1 ,isis 7#aidb71 vol4 #cd1 pp4 #aag-abh4 #i ,! ,p>is foot 0 #a4jff ,engli% feet1 & !re 7 #ab l9es to ! in*4 #aj ,,*ri/iaan ,,huyg5s1 ,de la cause de la pesanteur1 ,div]s ouvrages de ma!matiquesma!matiques et de physique p> ,,mm4 de l',academie ,royale,royal des ,sci5ces 7,p>is1 #afic71 p4 #cje4 #aa ,,isaac ,,newton1 ,philosophiae naturalis pr9cipia ma!matica 7,london1 #afhg71 vol4 #c1 propositions #ah-bj4 #ab ,,pi]re ,,b\gu]1 ,la figure de la t]re1 det]m9ee p> les obs]vations de ,messieurs ,b\gu] et de ,la ,condam9e1 envoyes p> ordre du ,roy au ,p]\1 p\r obs]v] aux environs de l'equateur 7,p>is1 #agdi74 #ac ,p4 ,l4 ,,moreau ,,de ,,maup]tuis1 ,la figure de la t]re det]m9ee p> les obs]vations de ,messieurs de ,maup]tuis1 ,clairaut1 ,camus1 ,le ,monni]1 l',abbe ,ou?i] et ,celsius1 faites p> ordre du ,roy au c]cle polaire 7,p>is1 #agch74 #ad ,p>is1 #agdc4 #ae ,,george ,,gabriel ,,/okes1 ,on ,attraction & on ,clairaut's ,!orem1 ,cambridge & ,dubl9 ,ma!matical ,j\rnal 7#ahdi71 vol4 #d1 p4 #aid4 #af ,see ,collection de memoires1 vol4 #d1 p4 ,b-#cd1 & ,j4 ,h4 ,,poynt+ & ,,sir ,j4 ,j4 ,,?omson1 ,prop]ties ( ,matt] 7,london1 #aibg71 p4 #bd4 #ag ,,poynt+ & ,,?omson1 ibid41 p4 #bb4 #ah ,,*>les ,m4 ,,de ,,la ,,condam9e1 ,de la mesure du p5dule a ,sa9t ,dom+ue1 ,collection de memoires1 vol4 #d1 pp4 #c-af4 #ai ,,p]e ,r4 ,j4 ,,boscovi*1 ,op]a p]t95tia ad ,opticam et ,a/ronomiam 7,bassani1 #aghe71 vol4 #e1 no4 #c4 #bj ,j4 ,c4 ,,borda & ,j4 ,d4 ,,cass9i ,,de ,,?ury1 ,exp]i5ces p\r connaitre la longueur du p5dule qui bat les secondes a ,p>is1 ,collection de memoires1 vol4 #d1 pp4 #ag-fd4 #ba ,f4 ,w4 ,,bessel1 ,unt]su*ung5 ueb] die ,la5ge des e9fa*5 ,secund5p5dels1 ,abh&lung5 d] ,ko5igli*5 ,akademie d] ,wiss5s*aft5 zu ,b]l91 #ahbf 7,b]l91 #ahbh74 #bb ,bessel us$ z a /&>d ( l5g? a toise :i* _h be5 made by ,=t9 9 ,p>is & _h be5 comp>$ ) ! orig9al ( ! toise de ,p]u by ,arago4 #bc ,l4 ,g4 ,,du ,,buat1 ,pr9cipes d'hydraulique 7,p>is1 #aghf74 ,see exc]pts 9 ,collection de memoires1 pp4 ,b-#fd to ,b-#fg4 #bd ,,capt4 ,,h5ry ,,kat]1 ,an ,acc\nt ( ,exp]im5ts = ,det]m9+ ! ,l5g? ( ! ,p5dulum ,vibrat+ ,seconds 9 ! ,latitude ( ,london1 ,philosophical ,transactions ( ! ,royal ,society ( ,london 7#ahah71 vol4 #ajh1 p4 #cc4 ,h]e9aft] abbreviat$ ,phil4 ,trans4 #be ,m4 ,g4 ,,de ,,prony1 ,me?ode p\r det]m9] la longueur du p5dule simple qui bat les secondes1 ,collection de memoires1 vol4 #d1 pp4 #fe-gf4 #bf ,collection de memoires1 vol4 #d1 p4 ,b-#gd4 #bg ,phil4 ,trans4 7#ahai71 vol4 #aji1 p4 #ccg4 #bh ,,john ,,h]s*el1 ,notes = a ,hi/ory ( ! ,use ( ,inv>iable ,p5dulums1 ,! ,great ,trigonometrical ,survey ( ,india 7,calcutta1 #ahgi71 vol4 #e4 #bi ,,capt4 ,,edw>d ,,sab9e1 ,an ,acc\nt ( ,exp]im5ts to ,det]m9e ! ,figure ( ! ,e>?1 ,phil4 ,trans4 7#ahbh71 vol4 #aah1 p4 #gf4 #cj ,,john ,,gold+ham1 ,obs]vations = ,asc]ta9+ ! ,l5g? ( ! ,p5dulum at ,madras 9 ! ,ea/ ,indies1 ,phil4 ,trans4 7#ahbb71 vol4 #aab1 p4 #abg4 #ca ,,basil ,,hall1 ,lett] to ,capta9 ,kat] ,communicat+ ! ,details ( ,exp]im5ts made by him & ,mr4 ,h5ry ,fo/] ) an ,inv>iable ,p5dulum1 ,phil4 ,trans4 7#ahbc71 vol4 #aac1 p4 #baa4 #cb ,see ,collection de memoires1 vol4 #d1 p4 ,b-#ajc4 #cc ,ibid41 p4 ,b-#hh4 #cd ,ibid41 p4 ,b-#id4 #ce ,,francis ,,baily1 ,on ! ,correction ( a ,p5dulum = ! ,r$uction to a ,vacuum1 ,toge!r ) ,rem>ks on ,"s ,anomalies ,obs]v$ 9 ,p5dulum ,exp]im5ts1 ,phil4 ,trans4 7#ahcb71 vol4 #abb1 pp4 #cii-dib4 ,see also ,collection de memoires1 vol4 #d1 pp4 ,b-#aje1 ,b-#aab1 ,b-#aae1 ,b-#aaf1 & ,b-#aag4 #cf ,"o 0 ( case brass & ! o!r ( roll$ iron1 #fh 94 long1 #b 94 wide1 & #a_/b 94 ?ick4 ,triangul> knife edges #b 94 long 7 ins]t$ ?r\gh triangul> ap]tures #ai4g 94 f ! c5t] t[>ds ea* end4 ,^! p5dulums seem n to h surviv$4 ,!re is1 h[ev]1 9 ! collection ( ! ,u4,s4 ,national ,museum1 a simil> brass p5dulum1 #cg-e_/h 94 long 7fig4 #ae7 /amp$ ) ! "n ( ,edw>d ,kuebel 7#ahbj-if71 :o ma9ta9$ an in/rum5t bus9ess 9 ,wa%+ton1 ,d4,c41 f ab\t #ahdi4 ,! hi/ory ( ?is in/rum5t is unkn[n4 #cg ,see ,baily's rem>ks 9 ! ,mon?ly ,notices ( ! ,royal ,a/ronomical ,society 7#ahci71 vol4 #d1 pp4 #ada-adc4 ,see also lett]s m5tion$ 9 footnote #ch4 #ch ,?is docum5t1 toge!r ) c]ta9 manuscript notes on ! p5dulum exp]im5ts & six lett]s betwe5 ,wilkes & ,baily1 is 9 ! ,u4,s4 ,national ,ar*ives1 ,navy ,records ,gp4 #cg4 ,^! 7 ! s\rce mat]ials = ! in=mation pres5t$ "h on ! ,exp$ition4 ,we are indebt$ to ,miss ,doris ,ann ,es* & ,mr4 ,joseph ,rudmann ( ! /aff ( ! ,u4,s4 ,national ,museum = call+ our att5tion to ?is e>ly ,am]ican p5dulum "w4 #ci ,g4 ,b4 ,,airy1 ,acc\nt ( ,exp]im5ts ,und]tak5 9 ! ,h>ton ,colli]y1 = ! ,purpose ( ,det]m9+ ! ,mean ,d5sity ( ! ,e>?1 ,phil4 ,trans4 7#ahef71 vol4 #adf1 p4 #big4 #dj ,t4 ,c4 ,,m5d5hall1 ,measurem5ts ( ! ,=ce ( ,gravity at ,tokyo1 & on ! ,summit ( ,fujiyama1 ,memoirs ( ! ,sci5ce ,dep>tm5t1 ,univ]sity ( ,tokyo 7#ahha71 no4 #e4 #da ,j4 ,t4 ,,walk]1 ,acc\nt ( ,op]ations ( ,! ,great ,trigonometrical ,survey ( ,india 7,calcutta1 #ahgi71 vol4 #e1 app4 no4 #b4 #db ,,bessel1 op4 cit4 7footnote #ba71 article #ca4 #dc ,c4 ,a4 ,f4 ,,pet]s1 ,briefwe*sel zwis*5 ,c4 ,f4 ,gauss und ,h4 ,c4 ,s*uma*] 7,altona1 ,g]many1 #ahfj71 ,b& #b1 p4 #c4 ,! correction requir$ if ! times ( sw+ are n exactly ! same is said to h be5 giv5 also by ,bohn5b]g]4 #dd ,f4 ,w4 ,,bessel1 ,con/ruction e9es symmetris* ge=mt5 ,p5dels mit reciprok5 ,ax51 von ,bessel1 ,a/ronomis*e ,na*ri*t5 7#ahdi71 vol4 #cj1 p4 #a4 #de ,e4 ,,plantam\r1 ,exp]i5ces faites a ,g5eve avec le p5dule a rev]sion1 ,memoires de la ,societe de ,physique et d'hi/oire naturelle de ,g5eve1 #ahfe 7,g5eva1 #ahff71 vol4 #ah1 p4 #cji4 #df ,ibid41 pp4 #cji-daf4 #dg ,c4 ,,cell]i]1 ,note sur la ,mesure de la ,pesanteur p> le ,p5dule1 ,memoires de la ,societe de ,physique et d'hi/oire naturelle de ,g5eve1 #ahfe 7,g5eva1 #ahff71 vol4 #ah1 pp4 #aig-bah4 #dh ,a4 ,,sawits*1 ,les v>iations de la pesanteur dans les prov9ces occid5tales de l',empire russe1 ,memoirs ( ! ,royal ,a/ronomical ,society 7#ahgb71 vol4 #ci1 p4 #ai4 #di ,j4 ,j4 ,,baey]1 ,ueb] die ,groesse und ,figur d] ,erde 7,b]l91 #ahfa74 #ej ,comptes-r5dus de la ,conf]5ce ,geodesique ,int]nationale reunie a ,b]l9 du #ae-bb ,octobre #ahfd 7,neu*atel1 #ahfe74 #ea ,ibid41 "p ,,iii1 subp>t ,e4 #eb ,b]i*t ueb] die ,v]h&lung5 d] vom #cj ,septemb] bis #g ,octob] #ahfg zu ,b]l9 abgehalt55 allgeme95 ,conf]5z d] ,europaeis*5 ,gradmessung 7,b]l91 #ahfh74 ,see report ( f\r? session1 ,octob] #c1 #ahfg4 #ec ,c4 ,,bruhns & ,,albre*t1 ,be/immung d] ,la5ge des ,secund5p5dels 9 ,bonn1 ,leid5 und ,mannheim1 ,a/ronomis*-,geodaetis*e ,arbeit5 im ,jahre #ahgj 7,leipzig3 ,v]oeff5tli*ung5 des ,ko5igli*5 ,preussis*5 ,geodaetis*5 ,in/ituts1 #ahga74 #ed ,b]i*t ueb] die ,v]h&lung5 d] vom #bc bis #bh ,septemb] #ahgd 9 ,dresd5 abgehalt55 vi]t5 allgeme95 ,conf]5z d] ,europaeis*5 ,gradmessung 7,b]l91 #ahge74 ,see report ( second session1 ,septemb] #bd1 #ahgd4 #ee ,,c>olyn ,,eisele1 ,*>les ,s4 ,peirce--,n9ete5?-,c5tury ,man ( ,sci5ce1 ,scripta ,ma!matica 7#aiei71 vol #bd1 p4 #cje4 ,= ! acc\nt ( ! "w ( ,peirce1 ! au?ors are greatly indebt$ to ?is pione] pap] on ,peirce's "w on gravity4 ,x is wor? not+ t ! hi/ory ( p5dulum "w 9 ,nor? ,am]ica goes back to ! celebrat$ ,mason & ,dixon1 :o made obs]vations ( ! go+ rate ( a clock at ! =ks ( ! riv] ,br&iw9e 9 ,p5nsylvania1 9 #agff-fg4 ,^! obs]vations 7 publi%$ 9 ,phil4 ,trans4 7#agfh71 vol4 #eh1 pp4 #cbi-cce4 #ef ,! p5dulums ) conical bobs are describ$ & illu/rat$ 9 ,e4 ,d4 ,,pre/on1 ,det]m9ations ( ,gravity & ! ,magnetic ,elem5ts 9 ,connection ) ! ,unit$ ,/ates ,sci5tific ,exp$ition to ! ,we/ ,coa/ ( ,africa1 #ahhi-ij1 ,report ( ! ,sup]9t5d5t ( ! ,coa/ & ,geodetic ,survey = #ahhi-ij 7,wa%+ton1 #ahia71 app4 no4 #ab4 #eg ,,eisele1 op4 cit4 7footnote #ee71 p4 #caa4 #eh ,! record ( ,peirce's obs]vations 9 ,europe dur+ #ahge-gf is giv5 9 ,c4 ,s4 ,,peirce1 ,measurem5ts ( ,gravity at ,initial ,/ations 9 ,am]ica & ,europe1 ,report ( ! ,sup]9t5d5t ( ! ,coa/ ,survey = #ahge-gf 7,wa%+ton1 #ahgi71 pp4 #bjb-ccg & #daj-daf4 ,peirce's report is dat$ ,decemb] #ac1 #ahgh1 by :i* "t ! "n ( ! ,survey _h be5 *ang$ to ,u4,s4 ,coa/ & ,geodetic ,survey4 #ei ,v]h&lung5 d] vom #bj bis #bi ,septemb] #ahge 9 ,p>is ,v]e9igt5 ,p]man5t5 ,commission d] ,europaeis*5 ,gradmessung 7,b]l91 #ahgf74 #fj ,ibid4 ,see report = fif? session1 ,septemb] #be1 #ahge4 #fa ,! exp]im5ts at ! ,/ev5s ,in/itute1 ,hobok51 7 report$ by ,peirce to ! ,p]man5t ,commission :i* met 9 ,hamburg1 ,septemb] #d-h1 #ahgh1 & 8 report 0 publi%$ 9 ! g5]al ,b]i*t = #ahgh 9 ! ,v]h&lung5 d] vom #d bis #h ,septemb] #ahgh 9 ,hamburg ,v]e9igt5 ,p]man5t5 ,commission d] ,europaeis*5 ,gradmessung 7,b]l91 #ahgi71 pp4 #aaf-abj4 ,assi/ant ,j4 ,e4 ,hilg>d att5d$ = ! ,u4,s4 ,coa/ & ,geodetic ,survey4 ,! exp]im5ts are describ$ 9 detail 9 ,c4 ,s4 ,,peirce1 ,on ! ,flexure ( ,p5dulum ,supports1 ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhj-ha 7,wa%+ton1 #ahhc71 app4 no4 #ad1 pp4 #cei-dda4 #fb ,v]h&lung5 d] vom #e bis #aj ,oktob] #ahgf 9 ,brussels ,v]e9igt5 ,p]man5t5 ,commission d] ,europaeis*5 ,gradmessung 7,b]l91 #ahgg74 ,see report ( ?ird session1 ,octob] #g1 #ahgf4 #fc ,v]h&lung5 d] vom #bg ,septemb] bis #b ,oktob] #ahgg zu ,/uttg>t abgehalt55 fu5ft5 allgeme95 ,conf]5z d] ,europaeis*5 ,gradmessung 7,b]l91 #ahgh74 #fd ,v]h&lung d] vom #af bis #bj ,septemb] #ahgi 9 ,g5f ,v]e9igt5 ,p]man5t5 ,commission d] ,europaeis*5 ,gradmessung 7,b]l91 #ahhj74 #fe ,assi/ants' ,reports1 ,u4,s4 ,coa/ & ,geodetic ,survey1 #ahgi-hj4 ,peirce's pap] 0 publi%$ 9 ! ,am]ican ,j\rnal ( ,sci5ce 7#ahgi71 vol4 #ah1 p4 #aab4 #ff ,comptes-r5dus de l',academie des ,sci5ces 7,p>is1 #ahgi71 vol4 #hi1 p4 #dfb4 #fg ,v]h&lung5 d] vom #ac bis #af ,septemb] #ahhj zu ,mu5*5 abgehalt55 se*/5 allgeme95 ,conf]5z d] ,europaeis*5 ,gradmessung 7,b]l91 #ahha74 #fh ,ibid41 app4 #b4 #fi ,ibid41 app4 #b;a4 #gj ,v]h&lung5 d] vom #aa bis zum #ae ,septemb] #ahhb im ,haag ,v]e9igt5 ,p]man5t5 ,commission d] ,europaeis*5 ,gradmessung 7,b]l91 #ahhc74 #ga ,v]h&lung5 d] vom #ae bis #bd ,oktob] #ahhc zu ,rom abgehalt55 sieb5t5 allgeme95 ,conf]5z d] ,europaeis*5 ,gradmessung 7,b]l91 #ahhd74 ,g54 ,cutts att5d$ = ! ,u4,s4 ,coa/ & ,geodetic ,survey4 #gb ,ibid41 app4 #f4 ,see also1 ,zeits*rift fu] ,in/rum5t5kunde 7#ahhd71 vol4 #d1 pp4 #cjc & #cgi4 #gc ,op4 cit4 7footnote #fg74 #gd ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhj-ha 7,wa%+ton1 #ahhc71 p4 #bf4 #ge ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhi-ij 7,wa%+ton1 #ahia71 app4 no4 #ab4 #gf ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahha-hb 7,wa%+ton1 #ahhc74 #gg ,transactions ( ! ,cambridge ,philosophical ,society 7#ahef71 vol4 #i1 "p #b1 p4 #h4 ,also publi%$ 9 ,ma!matical & ,physical ,pap]s 7,cambridge1 #aija71 vol4 #c1 p4 #a4 #gh ,peirce's comp>ison ( !ory & exp]im5t is discuss$ 9 a report on ! ,peirce memoir by ,,william ,,f]rel1 dat$ ,octob] #ai1 #ahij1 ,m>t9sburg1 ,we/ ,virg9ia4 ,u4,s4 ,coa/ & ,geodetic ,survey1 ,special ,reports1 #ahhg-ahia 7,,ms1 ,national ,ar*ives1 ,wa%+ton74 #gi ,! /ations at :i* obs]vations 7 conduct$ ) ! ,peirce p5dulums are record$ 9 ! reports ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey f #ahha to #ahij4 #hj ,comptes-r5dus de l',academie des ,sci5ces 7,p>is1 #ahhj71 vol4 #ij1 p4 #adja4 ,,h]ve ,,faye's report1 dat$ ,june #ba1 #ahhj1 is 9 ! same ,comptes-r5dus1 p4 #adfc4 #ha ,,comm&ant ,c4 ,,def=ges1 ,sur l',int5site absolue de la pesanteur1 ,j\rnal de ,physique 7#ahhh71 vol4 #ag1 pp4 #bci1 #cdg1 #dee4 ,see also1 ,,def=ges1 ,obs]vations du p5dule1 ,memorial du ,depot g5]al de la ,gu]re 7,p>is1 #ahid71 vol4 #ae4 ,9 ! latt] "w1 ,def=ges describ$ a p5dulum rev]sible inv]sable1 :i* he decl>$ to be truly inv>iable & !re=e appropriate = relative det]m9ations4 ,! knives rema9$ fix$ to ! p5dulums1 & ! effect ( int]*ang+ knives 0 obta9$ by int]*ang+ weights )9 ! p5dulum tube4 #hb ,pap]s by ,,maj4 ,,von ,,/]neck 9 ,mitteilung5 des ,k4 u4 ,k4 ,milita]-geographis*5 ,in/ituts1 ,wi51 #ahhb-hg2 see1 9 p>ticul>1 vol4 #g 7#ahhg74 #hc ,t4 ,c4 ,,m5d5hall1 ,det]m9ations ( ,gravity ) ! ,new ,half-,second ,p5dulum4441 ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahij-ia 7,wa%+ton1 #ahib71 "p #b1 pp4 #ejc-efd4 #hd ,w4 ,h4 ,,burg]1 ,! ,measurem5t ( ! ,flexure ( ,p5dulum ,supports ) ! ,int]f]omet]1 ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #aiji-aj 7,wa%+ton1 #aiaa71 app4 no4 #f4 #he ,e4 ,j4 ,,br[n1 ,a ,det]m9ation ( ! ,relative ,values ( ,gravity at ,potsdam & ,wa%+ton 7,special ,publication ,no4 #bjd1 ,u4,s4 ,coa/ & ,geodetic ,survey2 ,wa%+ton1 #aicf74 #hf ,m4 ,,haid1 ,neues ,p5del/ativ1 ,zeits*rift fu] ,in/rum5t5kunde 7,july #ahif71 vol4 #af1 p4 #aic4 #hg ,,dr4 ,r4 ,,s*umann1 ,ueb] e9e ,me?ode1 das ,mits*w+5 bei relativ5 ,s*w]emessung5 zu be/imm51 ,zeits*rift fu] ,in/rum5t5kunde 7,janu>y #ahig71 vol4 #ag1 p4 #g4 ,! design = ! /& is simil> to t ( ,peirce's ( #ahgi4 #hh ,,dr4 ,r4 ,,s*umann1 ,ueb] die ,v]w5dung zwei] ,p5del auf geme9sam] ,unt]lage zur ,be/immung d] ,mits*w+ung1 ,zeits*rift fu] ,ma!matik und ,physik 7#ahii71 vol4 #dd1 p4 #dd4 #hi ,p4 ,,furtwa5gl]1 ,ueb] die ,s*w+ung5 zwei] ,p5del mit annaeh]nd glei*] ,s*w+ungsdau] auf geme9sam] ,unt]lage1 ,sitzungsb]i*te d] ,ko5igli*] ,preussis*5 ,akademie d] ,wiss5s*aft5 zu ,b]l9 7,b]l91 #aijb7 pp4 #bde-bec4 ,peirce inve/igat$ ! plan ( sw++ two p5dulums on ! same /& 7,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhj-ha1 ,wa%+ton1 #ahhc1 p4 #bf2 also 9 ,,*>les ,,s&]s ,,peirce1 ,collect$ ,pap]s1 #f4bgc74 ,at a conf]5ce on gravity held 9 ,wa%+ton dur+ ,may #ahhb1 ,peirce aga9 advanc$ ! me?od ( elim9at+ flexure by hang+ two p5dulums on "o support & oscillat+ !m 9 antiphase 7,report ( a conf]5ce on gravity det]m9ations held 9 ,wa%+ton1 ,d4,c41 9 ,may1 #ahhb1 ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahha-hb1 ,wa%+ton1 #ahhc1 app4 no4 #bb1 pp4 #ejc-eaf74 #ij ,f4 ,a4 ,,v5+ ,,me9esz1 ,obs]vations de p5dule dans les ,pays-,bas 7,delft1 #aibc74 #ia ,a4 ,,b]ro?1 ,s*w]emessung5 mit zwei und vi] glei*zeitig auf demselb5 ,/ativ s*w+5d5 ,p5deln1 ,zeits*rift fu] ,geophysik1 vol4 #a 7#aibd-be71 no4 #c1 p4 #ic4 #ib ,p5dulum ,app>atus = ,gravity ,det]m9ations1 ,eng9e]+ 7#aibf71 vol4 #abb1 pp4 #bga-bgb4 #ic ,,malcolm ,w4 ,,gay1 ,relative ,gravity ,measurem5ts ,us+ ,precision ,p5dulum ,equipm5t1 ,geophysics 7#aidj71 vol4 #e1 pp4 #agf-aia4 #id ,l4 ,g4 ,d4 ,,?ompson1 ,an ,improv$ ,bronze ,p5dulum ,app>atus = ,relative ,gravity ,det]m9ations1 publi%$ by ,dom9ion ,obs]vatory 7,ottawa1 #aiei71 vol4 #ba1 no4 #c1 pp4 #ade-agf4 #ie ,w4 ,a4 ,,heiskan5 & ,f4 ,a4 ,,v5+ ,,me9esz1 ,! ,e>? & its ,gravity ,field 7,mc,graw3 ,new ,york1 #aieh74 #if ,f4 ,,kuehn5 & ,p4 ,,furtwa5gl]1 ,be/immung d] ,absolut5 ,groesze d] ,s*w]kraft zu ,potsdam mit ,rev]sionsp5deln 7,b]l93 ,v]oeff5tli*ung5 des ,ko5igli*5 ,preussis*5 ,geodaetis*5 ,in/ituts1 #aijf71 new s]41 no4 #bg4 #ig ,report$ by ,dr4 ,f4 ,kuehn5 to ! fif? session1 ,octob] #i1 #ahie1 ( ! ,elev5? ,g5]al ,conf]5ce1 ,die ,int]nationale ,erdmessung1 held 9 ,b]l9 f ,septemb] #be to ,octob] #ab1 #ahie4 ,a footnote /ates t ,assi/ant ,o4 ,h4 ,tittmann1 :o repres5t$ ! ,unit$ ,/ates1 subsequ5tly report$ ,peirce's prior discov]y ( ! influ5ce ( ! flexure ( ! p5dulum itself ^u ! p]iod 7,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhc-hd1 ,wa%+ton1 #ahhe1 app4 #af1 pp4 #dhc-dhe74 #ih ,assi/ants' ,reports1 ,u4,s4 ,coa/ & ,geodetic ,survey1 #ahhc-hd 7,,ms1 ,national ,ar*ives1 ,wa%+ton74 #ii ,c4 ,s4 ,,peirce1 ,effect ( ! ,flexure ( a ,p5dulum ,^u its ,p]iod ( ,oscillation1 ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhc-hd 7,wa%+ton1 #ahhe71 app4 no4 #af4 #ajj ,f4 ,r4 ,,helm]t1 ,beitraege zur ,!orie des ,rev]sionsp5dels 7,potsdam3 ,v]oeff5tli*ung5 des ,ko5igli*5 ,preussis*5 ,geodaetis*5 ,in/ituts1 #ahih74 #aja ,j4 ,a4 ,,du]ks51 ,p5dulum ,gravity ,data 9 ! ,unit$ ,/ates 7,special ,publication ,no4 #bdd1 ,u4,s4 ,coa/ & ,geodetic ,survey2 ,wa%+ton1 #aidi74 #ajb ,ibid41 p4 #b4 ,see also1 ,e4 ,j4 ,,br[n1 loc4 cit4 7footnote #he74 #ajc ,,paul ,r4 ,,heyl & ,,guy ,s4 ,,cook1 ,! ,value ( ,gravity at ,wa%+ton1 ,j\rnal ( ,rese>*1 ,national ,bureau ( ,/&>ds 7#aicf71 vol4 #ag1 p4 #hje4 #ajd ,,sir ,,h>old ,,jeffreys1 ,! ,absolute ,value ( ,gravity1 ,mon?ly ,notices ( ! ,royal ,a/ronomical ,society1 ,geophysical ,supplem5t 7,london1 #aidi71 vol4 #e1 p4 #cih4 #aje ,j4 ,s4 ,,cl>k1 ,! ,accel]ation ,due to ,gravity1 ,phil4 ,trans4 7#aici71 vol4 #bch1 p4 #fe4 #ajf ,,hugh ,l4 ,,dryd51 ,a ,reexam9ation ( ! ,potsdam ,absolute ,det]m9ation ( ,gravity1 ,j\rnal ( ,rese>*1 ,national ,bureau ( ,/&>ds 7#aidb71 vol4 #bi1 p4 #cjc2 & ,a4 ,,b]ro?1 ,das ,fundam5talsy/em d] ,s*w]e im ,li*te neu] ,rev]sionsp5delmessung51 ,bullet9 ,geodesique 7#aidi71 no4 #ab1 pp4 #ahc-bjd4 #ajg ,t4 ,c4 ,,m5d5hall1 op4 cit4 7footnote #hc71 p4 #ebb4 #ajh ,a4 ,h4 ,,cook1 ,rec5t ,developm5ts 9 ! ,absolute ,measurem5t ( ,gravity1 ,bullet9 ,geodesique 7,june #a1 #aieg71 no4 #dd1 pp4 #cd-ei4 #aji ,see footnote #hi4 #aaj ,c4 ,s4 ,,peirce1 ,on ! ,d$uction ( ! ,ellipticity ( ! ,e>?1 f ,p5dulum ,exp]im5ts1 ,report ( ! ,sup]9t5d5t ( ! ,u4,s4 ,coa/ & ,geodetic ,survey = #ahhj-ha 7,wa%+ton1 #ahhc71 app4 no4 #ae1 pp4 #ddb-def4 #aaa ,,heiskan5 & ,,v5+ ,,me9esz1 op4 cit4 7footnote #ie71 p4 #gd4 #aab ,ibid41 p4 #gf4 #aac ,ibid41 p4 #cji4 #aad ,ibid41 p4 #caj4 #aae ,k4 ,,rei*5$]1 ,me?od ( ! ,new ,measurem5ts at ,potsdam by ,means ( ! ,rev]sible ,p5dulum1 ,bullet9 ,geodesique 7,m>* #a1 #aiei71 no4 #ea1 p4#gb4 ,u4,s4 ,,gov]nm5t ,,pr9t+ ,,(fice3 #aife ,= sale by ! ,sup]9t5d5t ( ,docum5ts1 ,u4,s4 ,gov]nm5t ,pr9t+ ,(fice ,wa%+ton1 ,d4,c41 #bjdjb--,price #gj c5ts4 ,,index ,airy1 ,g4 ,b41 #cai1 #cbd1 #ccb ,albre*t1 ,k>l ,!odore1 #cbb1 #cch ,al-,mamun1 sev5? calif ( ,bagdad1 #cjf ,almansi1 ,emilio1 #cci ,ari/otle1 #cjf ,baey]1 ,j4 ,j41 #cba1 #cbb1 #cbd1 #cch1 #cdf ,baily1 ,francis1 #cag ,basevi1 ,james ,palladio1 #cde ,b]ro?1 ,a41 #cdb ,bessel1 ,fri$ri* ,wilhelm1 #cac1 #cad1 #cai1 #cbj1 #cbd1 #cbe1 #cch1 #cdf ,biot1 ,jean ,bapti/e1 #cbe1 #cbi ,bohn5b]g]1 ,johann ,gottlieb ,fri$ri*1 #cae ,borda1 ,j4 ,c41 #caa1 #cab1 #cae1 #cbe1 #cbi1 #cdf ,boscovit*1 ,p]e ,r4 ,j41 #caj1 #caa ,b\gu]1 ,pi]re1 #cjg1 #cji1 #cbg1 #cdc1 #cde ,brahe1 ,ty*o1 #cjf ,br[n1 ,e4 ,j41 #ccd1 #cci ,br[ne1 ,h5ry1 #cjd1 #cad ,bruhns1 ,c41 #cbb1 #cbd1 #cch ,brunn] ,bro!rs 7,p>is71 #cbi ,cass9i1 ,giovanni-,dom5ico1 #cjf1 #cjg ,cass9i1 ,jacques1 #cjf ,cass9i de ,?ury1 ,j4 ,d41 #caa1 #cab1 #cae1 #cbe1 #cbi1 #cdf ,cell]i]1 ,*>les1 #cbj1 #cba1 #cbe1 #cbf1 #cbi1 #ccf ,clairaut1 ,alexis ,claude1 #cjh1 #cji1 #cdc1 #cde ,cl>k1 ,j4 ,s41 #cdb ,cl>ke1 ,a4 ,r41 #cde ,colb]t1 ,jean ,bapti/e1 #cjf ,cook1 ,a4 ,h41 #cdb ,cook1 ,guy ,s41 #cci1 #cdb ,def=ges1 ,c41 #cad1 #cbi1 #cdf ,de ,freyc9et1 ,l\is ,claude de ,saulses1 #cag ,de la ,hire1 ,gabriel ,philippe1 #cjf ,de ,prony1 ,m4 ,g41 #cad ,dryd51 ,hugh ,l41 #cdb ,du ,buat1 ,l4 ,g41 #cad ,dup]ry1 ,capt4 ,l\is ,isidore1 #cag ,erato/h5es1 #cjf1 #cjh1 #cdb ,eudoxus ( ,cnidus1 #cjf ,faye1 ,h]ve1 #cbe1 #ccf1 #cdf1 #cdg ,f]nel1 ,jean1 #cjf ,furtwa5gl]1 ,p41 #ccg ,galilei1 ,galileo1 #cjd1 #cje1 #cdf ,gauss1 ,c4 ,f41 #cbj ,gauti]1 ,p41 #cci ,god91 ,l\is1 #cjg ,gold+ham1 ,john1 #caf1 #cde ,greely1 ,a4 ,w41 #cbi ,gulf ,oil & ,developm5t ,company1 #cch ,haid1 ,m41 #cce ,hall1 ,basil1 #caf ,heaviside1 ,w4 ,j41 #cba1 #cde ,heiskan51 ,w4 ,a41 #cch1 #cde1 #cdf ,helm]t1 ,f4 ,r41 #cch1 #cci ,helmholtz1 ,h]mann von1 #cbf ,h]s*el1 ,john1 #cai1 #cbh1 #cde ,heyl1 ,paul ,r41 #cci1 #cdb ,hirs*1 ,adolph1 #cbb1 #cbd ,huyg5s1 ,*ri/iaan1 #cjd1 #cje1 #cjg1 #cad1 #cdb1 #cdf ,ibanez1 ,c>los1 #cbe ,jeffreys1 ,sir ,h>old1 #cdb ,jones1 ,?omas1 #cah ,kat]1 ,h5ry1 #cjd1 #cad1 #cbe1 #cbg1 #cbi1 #cde1 #cdf ,kuehn51 ,f41 #cch1 #cci ,la ,condam9e1 ,*>les ,m>ie de1 #cjg1 #caj1 #caa1 #cdc ,laplace1 ,m>quis ,pi]re ,simon de1 #cji1 #cac1 #cbj ,lor5zoni1 ,giuseppe1 #ccf1 #cci ,luetke1 ,c\nt ,feodor ,petrovi*1 #caf1 #cde ,maup]tius1 ,p4 ,l4 ,moreau de1 #cjh1 #cdc ,maxwell1 ,james ,cl]k1 #cbd ,m$i1 ,enrico1 #cdb ,m5d5hall1 ,?omas ,corw91 #cai1 #cca1 #ccb1 #ccd1 #cdg ,m]s5ne1 ,p4 ,m>91 #cje ,newton1 ,sir ,isaac1 #cjc1 #cjg1 #cjh1 #cdb1 #cdc ,norwood1 ,ri*>d1 #cjf ,oppolz]1 ,!odor von1 #cbb1 #cbd ,patt]son1 ,c>lile ,pollock1 #cbe1 #cbf ,peirce1 ,*>les ,s&]s1 #cad1 #cbb1 #ccb1 #ccf1 #cdb1 #cde ,pet]s1 ,c4 ,a4 ,f41 #cbb1 #cbd ,pic>d1 ,abbe ,jean1 #cjf1 #cjh1 #cdb ,plantam\r1 ,e41 #cai1 #cbd ,posidonius1 #cjf ,pre/on1 ,e4 ,d41 #cbh1 #cbi ,putnam1 ,g4 ,r41 #cci ,py?agoras1 #cjf ,repsold1 ,a41 & ,sons 7,hamburg71 #cbj1 #cbb1 #cch1 #cci1 #cdf ,ri*]1 ,jean1 #cjg1 #cdb ,sab9e1 ,capt4 ,edw>d1 #cae1 #cbe1 #cbi1 #cde ,sawits*1 ,a41 #cba1 #cbb ,s*uma*]1 ,h4 ,c41 #cbj ,s*umann1 ,r41 #cce1 #ccf ,snell1 ,willebrord1 #cjf ,/]neck1 ,rob]t von1 #cca1 #ccb1 #cce1 #cch1 #cdf ,/okes1 ,george ,gabriel1 #cbd1 #cbh1 #cbi1 #cde1 #cdf ,ulloa1 ,antonio de1 #cjh ,v5+ ,me9esz1 ,f4 ,a41 #ccg1 #cch1 #cde ,volet1 ,*>les1 #cdb ,wilkes1 ,*>les1 #cag1 #cah 99 99 99 99 99 ,transcrib]'s note3 ,footnotes h be5 mov$ to ! end ( ! pap]4 ,illu/rations & ! ,,gloss>y ,,( ,,gravity ,,t]m9ology section h be5 mov$ to avoid breaks 9 p>agraphs4 ,m9or punctuation errors h be5 correct$ )\t note4 ,typographical errors & inconsi/5cies h be5 correct$ z foll[s3 ,p4 #cbj 'diff]5ce ,t#a - ,t#b is suffici5tly'--_h 'sufficl5tly4' ,p4 #cba 'faites a ,g5eve avec le p5dule a rev]sion'--_h 'rev]sion4' ,p4 #cbf ',s*w]e mit ,hilfe v]s*i$5] ,app>ate'--_h 'v]s*i$5e4' ,p4 #cbh 'betwe5 ! y>d & ! met]4'--clos+ quote m>k delet$4 ,p4 #ccd ',m5d5hall app>atus 7 "p ('--'0' *ang$ to '74' ,p4 #cdb '( ! ,geodetic ,in/itute at ,potsdam'--_h ',po/dam4' ,p4 #cde ',! gravimetric me?ods ( physical'--_h 'mtehods4' ,footnote #a ',societe francaise de ,physique'--_h ',francaise4' ,footnote #c ',cogitata physico-ma!matica'--_h 'physica4' ,footnote #aj 'ma!matiques et de physique p> ,,mm4 de l',academie ,royale'--_h 'ma!matiques1' ',royal4' ,footnote #ab 'p> ordre du ,roy au ,p]\1 p\r obs]v]'--_h ',p]\1 p\r obs]vir4' ,footnote #ai ',opticam et ,a/ronomiam'--_h ',a/ronomian4' ,footnote #bj 'connaitre la longueur du p5dule qui'--_h 'connaitre la longu]4' ,footnote #ba ',abh&lung5 d] ,ko5igli*5 ,akademie'--_h ',ko5igli*e4' ,footnote #be 'p\r det]m9] la longueur du p5dule'--_h 'longeur4' ,footnote #da ',survey ( ,india 7,calcutta1 #ahgi7'-- _h ',surey4' ,footnotes #de & #dg ',societe de ,physique et d'hi/oire'--_h 'd'hi/orire4' ,footnote #di ',ueb] die ,groesse und ,figur d] ,erde'--_h ',grosse4' ,footnote #ec ',be/immung d] ,la5ge'--_h ',lange'2 ',a/ronomis*-,geodaetis*e ,arbeit5'--_h ',a/ronomis*e'2 ',v]oeff5tli*ung5 des ,ko5igli*5'--_h ',ko5igli*e4' ,footnote #ee '7#agfh71 vol4 #eh1 pp4 #cbi-cce4'--;_h '#cbi-bce4' ,footnote #ff ',comptes-r5dus de l',academie'--_h ',l',academie4' ,footnote #ha ',sur l',int5site absolue'--_h 'l',int5site4' ,footnote #hi ',sitzungsb]i*te d] ,ko5igli*]'--_h ',ko5igli*e4' ,footnote #ajj ',v]oeff5tli*ung5 des ,ko5igli*5' _h ',v]oeff5tli*ung5 ,ko5igli*e4' ,capitalisation ( ',von'_/'von' has be5 regulaiz$ to 'von' = all p]sonal names1 except at ! beg9n+ ( a s5t5ce1 & :5 ref]r+ to ! ,von ,/]neck p5dulum4