1000000030

n .

" in:I,., ;,

DOll x.7 851 ;

\Vhieh di\i,kJ by Zj l (,he "roofúrm lO Ihe En",hll'¡:"

,otl.II

':~

lhe rOOlCII: "f

.. ollmh., 01 eub,",1 lOches in a \Vioe'Galloo ) g,res

I)L)H .,

eylioth,e vc¡re! io fud, f"llIlS tS lound uy muhiplyinr.

.. X 0014.

lhe eooleOI in \Vine·gallolls. !SlIl lhough " lhe (eluare "f lhe ellillneler by lhe he'gl",

«.d

lh,s

" ,he eh.lIges io Ihe exeife are maJe (by

natul~)

e'o lhe "proOttcq hy

.000.24\ .

.. (ul'pulilloo lhat lhe \V,oe' g,lIoo eum.i ns

23 1

cubical

" Wheo lhe lell,oo ,,( lhe vdrd is 001 a ci,c!c,

~1I1

.. ioches ; yel il is (aid, lhal

111

1;'le.

224

ellb,e,tI inehes, "ao cJl'pfis, lhe proJuél 01' lhe greald l diame'er by

,he

.. lhe eomeol o( lhe (hoJard IIlc,lulCcI al GlI,ldhall (., " Iealt, is

be fll blltlUlU¡ iD,hu,e rults fu r lhe ('luare o(

.. IV'S

meolJolled auove) are all"wed

Ue a wioe'g,llon. .. ,he di,meler.

•. 11.

S"ppofiog lhe Eogltih ale galloo lO eun'a,o

282

VII. To eompule Ihe eOOleol of a nrrcl 'hal

"la Y

.. ruui,al ioches, ,he conleOI o( a eyhod ric I'crrd is como .. be eooGde«d as a

/ ruj/uIIJ

uf acolle io aoy 01' lhule

.. pUleJ in fu eh gallons. uy IlIl1lti l'lyiog Ihe (quare of lhe .. meafures .

.. di,mele< of a .dl;'1by i" heighl as lorme,ly, aoJ Ihei r

.. Lel A reprefeol Ihe oumber of ioclle' in Ihe eliame.

" produél

bl'

Ihe decimal (raélioll

.0.027.85 1 :

Ihal is, .. ler

Ihe greatcr b.,fc,

lhe ouotbtr of ,oches io lhe

" Ihe

("l,d

COOlenl in alc.g.'¡loos is

ODHX .o,027,851. ..

diJOICler 01' Ihe ldl'er bafe. C""'pllle Ihe f1 uare of

" 111.

Suppofiog

Ih~

Seols piOI

eool?io abOUI ..

Ihe produa .of A mU/ liplied uy

, 0J lhe (quare

.. 103 .4

cu~ical

ioches. (which is lhe meafure gireo uy .. of !l, and collea Ihe(e iOlO a (11m . T hco filld lhe

.. lhe ¡¡aodmls al Edinburgh. aeeordiog 10 experimeols " Ihird pm of Ihis (u

111 ,

aod (uh/lilule il in Ihe

prece4in~

" ottolJlloed above), Ihe COoleOI of a eylinelrie vcrre! is .. rules io Ihe place of lhe (qo"e of ¡he cli, m"er ; norl

.. compuleJ in SCOIS piOlS , hy mol,iplyiog lhe (qoare of .. proceed io all olher refpléls

uefore. Thus,

f",

"x.

.. ¡he d,ameler of Ihe verrd by

il!

heighl, and Ihe pro· .. ample, Ihe cooleOI io wioe galiuns is

Mi<

-,Ul

x'liTI

.. dua of Ih& by the decimal f,.llion

0076.

Or Ihe .. X

.00]4 .

.. conleOl offueh a veOel io SCOlS piOlS is

DDHx .0076.

Or, lO lhc fq u,re of h,lf Ihe fumof Ihe diamerars

" Suppofing Ihe W,oeheller uufhel lO eoolai o

2187 ..

,nd

add ooe Ihird pan of Ihe fquare01 half Iheir

" cubical inchcs, lhe COntel" of a cylindrie reOel is eom· .. dilfaeoce, ?od f"bllilule lhis fum io Ihc

prec~ding

rules

.. pUled io lho(e buO,els

mul,iplyiog Ihe (quarc of Ihe .. for lhe (quare of the diameler of lhe , ,,Oel ; lor lhe

" diamm r of ,he \'errd by lhe hcighl, aod ¡he proJua .. (quare of

added lO

of Ihe fquare oC :

.. by lhe decimal 'raéhoo

.0,003,606.

Bnt

Ihe flao· ..

/I-t

gives : AA

/l H

llB.

.. dard bufh el haring been mea/ured by Mr Everard aoJ

VIII.

Whcn a

veO'",

is a

frujlUI/l

of , parabolic

.. olhers io

1696,

it was fouod lOcoolai o ooly

2145 6 ..

coooid, mea(ure Ihe di,mmr of lhe frlliooal Ihe mid.

" (olid ioehes: and Ihereforc il was enaaed io Ihe aa ..

dle.of

Ihe heighl of

lhe¡rrif/um :

and lhe cootcOl will Ue

.. (01' laying a dUly upoo mal!,

nal tuer} round DUjhtf,

precifely Ihe I, me as of a cylioder of Ihis diameter, of

wilh. ploi/l . /ld ,u,n b,Oom, bdng

tSt

incha dio·

Ihe fame heighl wilh Ihe \'erTe!.

" mrla Ihroughoul, o/ld

incha dup, j/lould b. ej/UIII'

IX.

Wheo a.errelisa

¡rujlum

of afphere. ifyou mea•

rd o I'gol

Winehener

bu/he/.

Aecordiog lO Ihis atl "fure Ihe diaol<!ler of lhe fdlion " Ihe middle

of.

lhe

.. (ralified in the Grn year of

~een

Anoe) Ihe legal .. h<ight of lhe

/rtif/urn,

Ihen compole Ihe eootenl·of a

.. Wioehener bUlhel conlaios only

2 150'4 2

folid ioéhes. .. eylmder of ¡his diameter o( lhe lame heighl \\'ilh lite

" Aod Ihe COOleOl of a ey liod rie verrel is cempured io .. velfel, and from lhis (ubtrafl

of lhe eOoleol of a

.. fuch bufhels, by multiplyiog lhe fq\we of Ihe di ame· .. eylioder of Ihe fame heighl, 00 a ba(e \Vhofe diameler

" ler by Ihe

hei~hl ,

aod lheir produa by ¡he decimal .. is <qual ¡OilS heighl ; Ihe remaind., will gi"e lhe con.

.. fralllon

.0,0°3,625 ,

Or Ihe,COOlent of Ihe "efiel io .. teOl of Ihe vcrr. f. That is, if

rcprcftol Ihe diame .

.. lhofe bufhe!s is

DL)H X .0,003 ,625,

ler of Ihe OIiddle (célioo. aod

I-J

lhe h ighl of

Ih~

.. V.

Suppofiog Ihe SCOlS wheal fi rlot lOcoota io

21:'

" ¡rujlUIR,

y,'u are

(ubnilUlC

OD-t

for Ihe

.. Seols plOIS, (as is appoio.ecl bYlhe nalule

1618),

aocl .. fqua re of lhe diamcter of lhe eylind ric I't'lftl io lhe

.. lhe p,nl lO be coofo,m 10 Ihe Edioburgh tl, odards " firfl fix rules.

.. above mentioned, lhe COOleol of a eylioJeie verre! in

"X.

Wlten lhe \'Crrd isa

¡rllj/ulII

of a fpheroid. if Ihe

.. fueh firlols is cOOlpuled by muhiplyiog lhe fq'Jare of .. bafes are egual, Ihe eooreol is reodi ly louod by Ih

.. Ihe diameler by lhe heigh l, aod their produ,q by Ihe "rule. o p

70S.

lo olner cafls, let lhe axi, of lhe f"lid

" deci;n.1 (rallioo

.00,318.

T his firl ol, io

1426,

is .. be to thc conjugatc

te>

1 ;

Irl

be lhe di:t·

" appoio'ed lOcootaill

piots;io tH7,ilwasappoiol' " meter of Ihe mieldle felqioo of Ih:

¡ ,,¡fI:IIH,

11;:

" td lO COOIdIO

piols; i,)

'587,

'5 1

pims ; in .. heighl ur leol'.lh of lhe

/ruj/um;

aod fublli""e io Ihe

1618.

piols: aod lhough lhis I:dl IIdl ule al"

.. firlllix rub

D--~

for lhe fqu,trc of Ih e fou.1I e

" pedrs

'r¡

It"le Leeo f"uoded 00 wroog compulalioos in .. of lhe diameler of lht:::rrd.

" Itver,I"(peds; yel lhis p'" of lhe

a!l lh~r

rel.,les

Xl..

Wheo ,he.

nlr"

is ao hype,h"l'e con,);,I, 1"1

" 10

Ihe ounther "f P'OIS in lhc firl ul (c<ms

be Ihc

lhe

ó1"¡

o( lite fu!tJ be lO,he

t'"oJu~.lIe

a ·;s as

.. Ic-n

excepliun.~I,;;

¡orllh«cfure we fuppofe lhe fir· "

lhe d'.I(".lr, 01' Ihe f'lqi l," .11 lhe l1I:uJle of

" IUllO

c~o,.in

2':

"iOlS

lhe Eeliubu'gh IIdo(/."J, or

"fruj/UIII,

,he la i&11I

I,og h: (ulltrUlt

X...!...

.. atuul

" ',7

"u,e:d ioches;

hieh a li,,1e excec.!s lhe

' ,

" \1'

I fl

O I

l·

l ' h'

b' "

X Illí. •

0,.1fuhllilule litis

IUl11

lor lite fn""c

,,1'

lhe

'oc ,e ll ' u

H'.

!UII'

\\')JI'

IlI'Y

lave ceo Ort

·,

. II

" di,oll'ler ul l;,e n l:n.! ,ie vdlcl ,o ,he lirJl li,

Il,b.

g,oa

n'pi':d

" VI

, Ih

'1 I e ol,,'n "Sel(

" XIl, lo gro" ,",

is ulu;,1

u",afure any rOlll'rl

,'''/,;'''''"~

e )r,,·u,

,It

o o

( ,

" p:nr& ,

( . I;VJ(lIH)~

lO 1111; :t.ltUU.:

16 ¡e),

and

I:l~

pint

CI \'(:[ ..

JI.lld~I1;r.lill)'

il iUlo

L.\ ~r.tlli l·P"YII.

:ml!

\ .

l' ,.

l,.h;:

OL.

" L.

I(J.