part15-第6节

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of　measures；　weights　and　coins；　and　you　ask　my　ideas　on　it；　insulated

as　my　situation　is；　I　am　sure　I　can　offer　nothing　but　what　will　occur

to　the　committee　engaged　on　it；　with　the　advantage　on　their　part　of

correction　by　an　interchange　of　sentiments　and　observations　among

themselves。　　I　will；　however；　hazard　some　general　ideas　because　you

desire　it；　and　if　a　single　one　be　useful；　the　labor　will　not　be　lost。




　　　　　　　　The　subject　to　be　referred　to　as　a　standard；　whether　it　be

matter　or　motion；　should　be　fixed　by　nature；　invariable　and

accessible　to　all　nations；　independently　of　others；　and　with　a

convenience　not　disproportioned　to　its　utility。　　What　subject　in

nature　fulfils　best　these　conditions？　　What　system　shall　we　propose

on　this；　embracing　measures；　weights　and　coins？　and　in　what　form

shall　we　present　it　to　the　world？　　These　are　the　questions　before　the

committee。




　　　　　　　　Some　other　subjects　have；　at　different　times；　been　proposed　as

standards；　but　two　only　have　divided　the　opinions　of　men：　first；　a

direct　admeasurement　of　a　line　on　the　earth's　surface；　or　second；　a

measure　derived　from　its　motion　on　its　axis。　　To　measure　directly

such　a　portion　of　the　earth　as　would　furnish　an　element　of　measure；

which　might　be　found　again　with　certainty　in　all　future　times；　would

be　too　far　beyond　the　competence　of　our　means　to　be　taken　into

consideration。　　I　am　free；　at　the　same　time；　to　say　that　if　these

were　within　our　power　in　the　most　ample　degree；　this　element　would

not　meet　my　preference。　　The　admeasurement　would　of　course　be　of　a

portion　of　some　great　circle　of　the　earth。　　If　of　the　equator；　the

countries　over　which　that　passes；　their　character　and　remoteness；

render　the　undertaking　arduous；　and　we　may　say　impracticable　for　most

nations。　　If　of　some　meridian；　the　varying　measures　of　its　degrees

from　the　equator　to　the　pole；　require　a　mean　to　be　sought；　of　which

some　aliquot　part　may　furnish　what　is　desired。　　For　this　purpose　the

45th　degree　has　been　recurred　to；　and　such　a　length　of　line　on　both

sides　of　it　terminating　at　each　end　in　the　ocean；　as　may　furnish　a

satisfactory　law　for　a　deduction　of　the　unmeasured　part　of　the

quadrant。　　The　portion　resorted　to　by　the　French　philosophers；　（and

there　is　no　other　on　the　globe　under　circumstances　equally

satisfactory；）　is　the　meridian　passing　through　their　country　and　a

portion　of　Spain；　from　Dunkirk　to　Barcelona。　　The　objections　to　such

an　admeasurement　as　an　element　of　measure；　are　the　labor；　the　time；

the　number　of　highly…qualified　agents；　and　the　great　expense

required。　　All　this；　too；　is　to　be　repeated　whenever　any　accident

shall　have　destroyed　the　standard　derived　from　it；　or　impaired　its

dimensions。　　This　portion　of　that　particular　meridian　is　accessible

of　right　to　no　one　nation　on　earth。　　France；　indeed；　availing　herself

of　a　moment　of　peculiar　relation　between　Spain　and　herself；　has

executed　such　an　admeasurement。　　But　how　would　it　be　at　this　moment；

as　to　either　France　or　Spain？　and　how　is　it　at　all　times　as　to　other

nations；　in　point　either　of　right　or　of　practice？　　Must　these　go

through　the　same　operation；　or　take　their　measures　from　the　standard

prepared　by　France？　　Neither　case　bears　that　character　of

independence　which　the　problem　requires；　and　which　neither　the

equality　nor　convenience　of　nations　can　dispense　with。　　How　would　it

now　be；　were　England　the　deposit　of　a　standard　for　the　world？　　At　war

with　all　the　world；　the　standard　would　be　inaccessible　to　all　other

nations。　　Against　this；　too；　are　the　inaccuracies　of　admeasurements

over　hills　and　valleys；　mountains　and　waters；　inaccuracies　often

unobserved　by　the　agent　himself；　and　always　unknown　to　the　world。

The　various　results　of　the　different　measures　heretofore　attempted；

sufficiently　prove　the　inadequacy　of　human　means　to　make　such　an

admeasurement　with　the　exactness　requisite。




　　　　　　　　Let　us　now　see　under　what　circumstances　the　pendulum　offers

itself　as　an　element　of　measure。　　The　motion　of　the　earth　on　its　axis

from　noon　to　noon　of　a　mean　solar　day；　has　been　divided　from　time

immemorial；　and　by　very　general　consent；　into　86；400　portions　of　time

called　seconds。　　The　length　of　a　pendulum　vibrating　in　one　of　these

portions；　is　determined　by　the　laws　of　nature；　is　invariable　under

the　same　parallel；　and　accessible　independently　to　all　men。　　Like　a

degree　of　the　meridian；　indeed；　it　varies　in　its　length　from　the

equator　to　the　pole；　and　like　it；　too；　requires　to　be　reduced　to　a

mean。　　In　seeking　a　mean　in　the　first　case；　the　45th　degree　occurs

with　unrivalled　preferences。　　It　is　the　mid…way　of　the　celestial　ark

from　the　equator　to　the　pole。　　It　is　a　mean　between　the　two　extreme

degrees　of　the　terrestrial　ark；　or　between　any　two　equi…distant　from

it；　and　it　is　also　a　mean　value　of　all　its　degrees。　　In　like　manner；

when　seeking　a　mean　for　the　pendulum；　the　same　45th　degree　offers

itself　on　the　same　grounds；　its　increments　being　governed　by　the　same

laws　which　determine　those　of　the　different　degrees　of　the　meridian。




　　　　　　　　In　a　pendulum　loaded　with　a　Bob；　some　difficulty　occurs　in

finding　the　centre　of　oscillation；　and　consequently　the　distance

between　that　and　the　point　of　suspension。　　To　lessen　this；　it　has

been　proposed　to　substitute　for　the　pendulum；　a　cylindrical　rod　of

small　diameter；　in　which　the　displacement　of　the　centre　of

oscillation　would　be　lessened。　　It　has　also　been　proposed　to　prolong

the　suspending　wire　of　the　pendulum　below　the　Bob；　until　their

centres　of　oscillation　shall　coincide。　　But　these　propositions　not

appearing　to　have　received　general　approbation；　we　recur　to　the

pendulum；　suspended　and　charged　as　has　been　usual。　　And　the　rather　as

the　the　laws　which　determine　the　centre　of　oscillation　leave　no　room

for　error　in　finding　it；　other　than　that　minimum　in　practice　to　which

all　operations　are　subject　in　their　execution。　　The　other　sources　of

inaccuracy　in　the　length　of　the　pendulum　need　not　be　mentioned；

because　easily　guarded　against。　　But　the　great　and　decisive

superiority　of　the　pendulum；　as　a　standard　of　measure；　is　in　its

accessibility　to　all　men；　at　all　times　and　in　all　places。　　To　obtain

the　second　pendulum　for　45　degrees　it　is　not　necessary　to　go　actually

to　that　latitude。　　Having　ascertained　its　length　in　our　own　parallel；

both　theory　and　observation　give　us　a　law　for　ascertaining　the

difference　between　that　and　the　pendulum　of　any　other。　　To　make　a　new

measure　therefore；　or　verify　an　old　one；　nothing　is　necessary　in　any

place　but　a　well…regulated　time…piece；　or　a　good　meridian；　and　such　a

knowledge　of　the　subject　as　is　common　in　all　civilized　nations。




　

　　　　　　　　Those　indeed　who　have　preferred　the　other　element；　do　justice

to　the　certainty；　as　well　as　superior　facilities　of　the　pendulum；　by

proposing　to　recur　to　one　of　the　length　of　their　standard；　and　to

ascertain　its　number　of　vibrations　in　a　day。　　These　being　once　known；

if　any　accident　impair　their　standard　it　is　to　be　recoved　by　means　of

a　pendulum　which　shall　make　the　requisite　number　of　vibrations　in　a

day。　　And　among　the　several　commissions　established　by　the　Academy　of

Sciences　for　the　execution　of　the　several　branches　of　their　work　on

measures　and　weights；　that　respecting　the　pendulum　was　assigned　to

Messrs。　Borda；　Coulomb　&　Cassini；　the　result　of　whose　labors；

however；　I　have　not　learned。




　　　　　　　　Let　our　unit　of　measures　then　be　a　pendulum　of　such　length　as

in　the　latitude　of　45　degrees；　in　the　level　of　the　ocean；　and　in　a

given　temperature；　shall　perform　its　vibrations；　in　small　and　equal

arcs；　in　one　second　of　mean　time。




　　　　　　　　What　ratio　shall　we　adopt　for　the　parts　and　multiples　of　this

unit？　　The　decimal　without　a　doubt。　　Our　arithmatic　being　founded　in

a　decimal　numeration；　the　same　numeration　in　a　system　of　measures；

weights　and　coins；　tallies　at　once　with　that。　　On　this　question；　I

believe；　there　has　been　no　difference　of　opinion。




　　　　　　　　In　measures　of　length；　then；　the　pendulum　is　our　unit。　　It　is　a

little　more　than　our　yard　and　less　than　the　ell。　　Its　tenth　or　dime；

will　not　be　quite　。4　inches。　　Its　hundredth；　or　cent；　not　quite　。4　of

an　inch；　its　thousandth；　or　mill；　not　quite　。04　of　an　inch；　and　so

on。　　The　traveller　will　count　his　road　by　a　longer　measure。　　1；000

units；　or　a　kiliad；　will　not　be　quite　two…thirds　of　our　present　mile；

and　more　nearly　a　thousand　paces　than　that。




　　　　　　　　For　measures　of　surface；　the　square　unit；　equal　to　about　ten

square　feet；　or　one…ninth　more　than　a　square　yard；　will　be　generally

convenient。　　But　for　those　of　lands　a　larger　measure　will　be　wanted。

A　kiliad　would　be　not　quite　a　rood；　or　quarter　of　an　acre；　a　myriad

not　quite　2　1/2　acres。




　　　　　　　　For　measures　of　capacity；　wet　and　dry；




　　　　　　　　The　cubic　Unit　=　。1　would　be　about　。35　cubic　feet；　。28　bushels

dry；　or　7/8　of　a　ton　liquid。

　　　　　　　　Dime　=　。1　would　be　about　3。5　cubic　feet