C
T
HE
O PY R I G H T , 1
H A R T F OR D
AN D
S
BY
TE
AM
I N S UR AN CE
PR E S S O F T H E C A S E
,
898,
BO I LE R
C
I N S PE CT I ON
O M PA N Y
L O C K \V O O D
BR
.
AI N A R D
CO
.
PR E FA C E
.
etri c ystem of Wei hts and M eas
ures is used universally in foreign
and periodicals th at much time is con
sumed and little annoyance incurred by
the Ameri can reader in translating these
units into their nglish and American
equivalents by the aid of any of th e
tion tables that h ave yet been published
t th erefore occurred to th e undersigned
that a handy pocket volume for
ing comparisons of th is kind might be
acceptable to engineers and scientific
workers generally This is the
of the present little book Th e work of cal
the tables and reading the proof
has been done by M r A D
A sso
ciate ditor of
L C M T I VE whose
experience in the computing division of
th e nited tates C oast and eodeti c
vey should be a su cient guarantee of the
care and ac curacy with which his task has
been done M r
h as also pre
pared brief account of the inception
and adoption of the M etric ystem in
F rance whic h adds materially to the
T
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FACE
.
interest and value of the volume The
M etric ystem is now in commo n use in
F rance ermany A ustria H ungary taly
pain P ortugal weden N orway B el
gium T he N etherlands oumania ervia
gypt M exico C osta ica uatemala
N icaragua alvador B ra il C olombia
B olivia C hile Th e A rgentine
epublic
H aiti and anto D omingo
t has also
been adopted o cially by ene uela ru
guay T urkey and B ritish ndia although
in these four countries it can hardly yet
be said to be in common use Japan too
has announced her intention of adopting a
modified form of it and even China has a
system of weights and measures
although it is not the French M etric
tem ngland ussia and the nited
tates are the only great nations that still
refuse to adopt the M etric ystem ts
advantages are many and the only really
serious objection appears to be that the
change from our present units to th e new
ones would be more or less confusing and
annoying for the first wyears M uch
this annoyance and confusion could be pre
vented by providing sch ool children with
cheap sets of metric measures and weigh ts
and requiring each child to measure and
weigh a certain number of objects every
week n this w the units and their
.
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PR E
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5
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names woul d be c ome tolerably familiar to
th e next generation and the transition
w ould be far ea ier Th e form i dable deci
mals that th e metri c system suggests to
the average citi en ( and which are h ere
v ery much in evidence ) constitute no part
of the system itself and they coul d be
gratefully dismissed the moment the met
ric system came into use T hey owe th eir
e istence to the fact that the foot pound
and quart are not commensurable wi th th e
meter gramme and liter and when we
cease to use our present units we sh ould
also cease to use the long numbers that
e press th eir val ues in metric units
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artford C onn M ay
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L L E N Pr es i den t
2, 1
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898
.
.
W
E IG HTS
T H E I I E T R I C S Y S T E M OF
‘
A N D M E A S UR E S
.
V SI Y SY
F rom t h e earliest days of civili ation
men have measured and weigh ed things
and hence th ey have had to ha e at least
the rudiments of a system of weigh ts and
measures A t first however there was
no attempt at precision in the standards
used A foot meant something of sub
the same length as the king s
oot and an in ch was sometimes con
to be the twelfth part a foot
and at other times it was defined as the
space covered by three good plump ker
nels of barley plac ed end to end ach
community had its own units whi ch in
most cases bore no relati on whatever to
the units employed in oth er c ommunities
A s wealth increased an d commerce gre w
it became necessary to pro vi de for a
greater degree of pre cision in standards
and for a c ompariso n of those used in dif
localities ndoubtedly the innate
dish onesty
also had something to
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do with th e establishment of more definite
standards because in the absence of these
there was nothin to prevent a person who
was so inclined from buying by a long
measure and selling by a short one At
all events at the present time the units
used in weighing and measuring have
been defined by law in all civili ed coun
tries T his has secured for each country
a certain degree uniformity throughout
its own ter tory but among the stand
ards of
countries there is a diver
almost as great as ever
ven in the nited tates there are an
enormous number of units in vogue
example for measuring l engths we have
the inch ell nail link foot yard athom
rod chain furlong mile knot and doubt
l ess many others and the units in use for
area capacity and weight are even more
numerous M any of th ese units have dif
val es too according to the nature
of the substance to be measured or weighed
T hus we have several kinds of ounces and
p unds and at least two kinds of quarts
T here is no regularity W
hatever in th e
number of units of one kind that make one
unit of the next higher kind and some of
the tables that the schoolboy has to learn
are extremely distressing We well
member wh at stickler it was in our day
8
MET I C
T HE
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th at it sh ul d take
OF
HI
METER
T HE
9
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square yards to
make one square rod f we had a simpler
meth od of mensuration the children in
our schools could be spared a great part of
this trou l esome lumber and the time
sav ed in thi s W could be devoted to
some far more profitable subje ct T aking
e erything into consideration it is cer
h umiliating to re ect upon the heter
system of weights and meas
ures in use at th e present day in a country
as proud as civili ed and as advan c ed (in
other respe cts) as our own nited tates
A merica We are not unique in this
respect it is true for many other nations
have systems of measurement th at are
fully as confusing as our own but this is
migh ty c ol d comfort
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H ST
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OR Y
OF T H E M E TE R
o F rance belongs the honor of m aking
the first systematic attempt to break
through the customs of antiqui ty and to
substitute a new metrology for the old
ntil the latter part of the eighteenth cen
tury there was th e same condition of
a fairs in that country th at prevails to day
in the nited tates and in M chain and
D e l ambre s
we read of syst me
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incoh rent de nos mesures
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THE MET I C SYSTEM
scandaleuse diversit de nos mesures
etc e v eral ine ectual attempts to
form the F rench system of weights and
measures had been made previous to
but it is from that year that the present
metric system dates n M ay M
de T alleyrand proposed to th e N ational
A ssembly of F rance that a new system of
measures should be devised on strictly
scientific principles and that the units of
length and weight in this system should
be based on some natural and invariable
standard the M ay the A ssembly
passed a resolution requesting th e king
L ouis
to open a correspondence on the
lus d une f is
pre sent é des pr ets d e
r fer e g uverne en qui les
f ait e a iner
ais algr é les rapp rt les plus f av rables algre
la b nne v l nt é des inistres
centntrt uleururs des nan c es rren cubles ipr E ets
av i
n
v eu d une esure uni f r e f ut nsign é dans les
c a h iers de quelques
quelques
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enten d re leur v i L es esprits é t i t al rs d i p e
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ent usias m e t utes les r efer m es
utiles L e s ystem e i h e t de
m esures
utre
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ater l b l i t i
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H I ST O Y THE METER
II
subject with th e king of ngland desiring
him to invite the British P arliamen to
operate with the N ational A ssembly of
F ran c e in fixing the natural unit w h ich
was to serve as the basis of the proposed
system of weights and measures T he
work was to be put in the hands of a joint
commission of scientific men half of whom
were to be appointed by the F rench A cad
emy of ciences and the other half by the
oyal ociety of L ondon n conformity
with the resolution L ouis laid the matter
before the nglish king but owing to the
temper and the public troubles of th e
times h is overture met with no response
imilar applications to other nations were
more successful and in subsequent pro
pain taly the N etherlands
wit erland D enmark and weden par
by sending delegates to an inter
national commission The system itsel
was however atured by the labors a
committee of the A cademy of ciences
embracing B orda L agrange L aplace
M ong and C ondorcet five of the ablest
mathematicians of
L avoisier
though not a member of this committee
contributed largely to its proceedings and
the standards that were afterwards pre
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.
THE METR I C SYSTEM
pared were made under his supervision
L avoisier for some reason has not received
the recognition that is due him in this
matter his work being usually credited to
B orda
T here were two reasons advanced
basing the new unit of length upon some
absolute and invariable quantity in nature
t was said that the selection of an arbi
unit would violate the most funda
mental principle the proposed reform
th e one distinctive feature of the new
system was to be the exclusion of the last
vestige of arbitrariness T his argument
seems to us to be hardly wor h serious
consideration for however satisfactory the
unit finally chosen might be the
of th at unit would necessarily be arbitrary
and hence the unit itself would be so in
ome sense T he other reason advanced
for the selection of a natural unit was
much more logical t was urged that a
system of weigh ts and measures based on
some permanent and invariable natural
quantity could be entirely reconstructed
with any desired degree of precision even
th ough every standard in existence were
utterly destroyed
M de T alleyrand proposed to adopt as
the fundamental unit of length the length
of a pendulum vibrating seconds in lati
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H I ST O RY THE METER
tude ou toute autre latitude qui pour
roit tre pr f r e (or such other latitude
as might be preferred T he committee of
th e A cademy of ciences considered the
adv sability of adopting the seconds pen
dulum as th e unit of length but finally
reje cted it principally because it involved
the conception of
t seemed to them
preferable to base the proposed unit on
j
f
and after much deliberation it
was decided to adopt some one of the di
of the earth itself the di fer
ent dimensions proposed the two that met
with the most fav or were the equatorial
circumference and the meridian quadrant
and of th ese two th e meri dian quadrant
was finally selected because it could be
measured with greater accuracy (T he
measurement of a
involves
of
while the measurement
of the
inv olves bservations of
and before the invention of th e
ele c ric telegraph longi tude measures
were subje ct to large errors ) n order to
guard against possible di erences in th e
lengths of the various meridian quadrants
it was decided to re commend that the new
system of measures be based on the par
meridian th at passes through P aris
h is le n gt h about
miles) woul d be
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THE METR I C SYSTEM
entirely out of the questi on as a practical
unit for business purposes H owever a
rough calculation showed that a standard
having a l ength equal to one ten millionth
part of this quadrant would be convenient
and th e ET E R (as the wunit was na ed)
1
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OF T H E
was therefore defined to be
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di s ta n ce
fr o m
M
ETE R
.
t/z e ten -m i ll i onth
t/i e
equ a to r
t o t/ze
ig
illustrates this definition of th e meter very
graphically
n o r t/
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ol e ,
m ea s u r ed
m er idi a n
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p
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a s s i ng
a l o ng
t/ze
t/z r oug /z
sea - l ez l el ,
Pa r i s
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I
H IS
O Y
T R
OF
T HE
METER
1
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5
he report of th e committee embodying
th e points explained above and d ted
M arch
was approved ythe N a
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1
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79 1 ,
N
FIG
.
SHO
2.
W
ING T HE
IN E
T H AT
W
AS
M
E ASUR E D
.
and the work
in g th e meridian passing through P aris was
begun This operation involved immense
t i o n al
A ssembly
L
.
,
of
m e as u r
1
6
T HE
SYS T E M
ME TRI C
.
labor and seven years were required to
complete it T he meridian through P aris
is shown by the heavy vertical line in Fig
t strikes the N orth at D unkirk
near the trait of D over in latitude
and the M editerranean at
a
small
place
in
the
suburbs
(
j
B arcelona pain in latitude
T he northern half of this arc was measured
under the direction of D elambre and the
southern half under M chain A b ie
account of the method of measurement
employed and of the subsequent computa
tions will be ound in first chapter of
C larke s
and the operations and
calculations are described in full in M chain
and D elambre s
to which we have already refer
red Th e unit of length used in measuring
the meridian was the and th e fina
result of the seven years work was that
the distance from the B arcelona end of the
line to the D unkirk end was
toises t will be found from the data
given above that the di erence in latitud
between the two ends was
N ow the latitude of the equator is o
the latitude of the pole is and there
fore the earth were a true sphere the
distance from the equator to the pole woul
be given by the simple proportion
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SYS T E M
ME T RI C
T HE
.
platinum which was to be ever afterward
the standard meter o f the world
.
E
M EA U RE
U N I T S DE R I V E D F R OM T H
L
O
S
M ET E R
.
e meter is th eoretically equal to the
ten millionth part of the meridian quadrant
that passes through P aris but as all
man measurements are liable to error we
cannot suppose that M chain and D elam
bre s determination o f this length is
exact and therefore practical
purposes the meter is defined to be
N G
.
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l eng t/z
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t/z e
os i ted
comparison of this
bar with the units in use in this country
shows that th e meter is about inches
longer than a yard stick A more exact
comparison made by Professor ogers
indicates that the pre cise length of the
standard meter is
inches and
similar determination by eneral C omstock
gave
inches T he average these
two determinations is
inch es which
is the value adopted in this essay as the
true length of the meter
T o make the new system available for
general purposes it was decided to divide
the meter into ten equal parts which were
called meters ach o f these parts
i n tne
ti ona l
t/z e A
Co m m i ss i on
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3 9 3 7 00 6
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TS D R I VE D F O M THE METE
was further subdivided into te n parts
called meters and each centimeter
was also divi ded into ten parts called
meters (The italicised prefixes stand
for tenth hundredth and thou
sandth respectively just as the words
dime cent and mill stand for th e
tenth h undredth and thousandth part of
a dollar We h ave a decimal system of
coinage and we reali e its simplicity and
general utility Why not apply the same
idea to our weights and mea ures ) F ig
is a E C M ET E R T he decimeter is shown
subdivided into ten C E T M ET E R S and each
centimeter is further subdivided into ten
M I I METERS T en of these de cimeters
placed end to end woul d make
and
of them if laid end t o end
along the curved surfac e of the earth
would just reach from th e equator to the
north pole
F or measuring b i g distances it was
proposed to establish a special uni t equal
to
meters T o this unit th e name
I METER was gi ven ( kilo being de
rived from a reek word meaning a
T he meter being equal to
inches it follo ws that th e I
M E T E R is equal to
inches that is
to
feet or
of a mile
UNI
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1
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THE METR I C S Y STEM
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g
TS D E I VE D F M METER
T he table for long measure in the M etri c
ystem is v ery simple t is as ollow
millimeters
centimeter
centimeters (cm ) decimeter
decimeters ( ) meter
meters ( ) kilometer
S R E ME S U RE
Th e tables for square measure and c ubi c
measure easily derived from this table
for long measure T he area of a rectangle
square for example is equal t o the
product o f length and breadth A
square decimeter (or centimeters) each
way will therefore h ave an area of
square centimeters hence square deci
meter square centimeters Th e rest
of the table for square measure is con
structed in th e same way and h ence we
h ave the following table
square millimeters (sq mm )
square centime er
square centimeters (sq c m )
souare decimeter
square decimeters (sq )
square meter
square meters (sq m )
square kil ometer (sq
T
h
e etters i n parent h eses i nd i c te t h e c ust ar
abbrev i at i n t h e un i ts pp site h i ch t h e an
UN
I
R
RO
T HE
2 1
.
,
S
,
I
.
10
f
s
1
10
2
.
dm
10
m
.
1
'
.
1
.
:
.
1
.
QU A
A
.
are
.
or
,
,
t he
.
10
1
1 00
1
:
1 00
.
,
1 00
t
1
.
.
.
1 00
.
.
1
.
1
.
1 00
dm
.
.
.
1
.
.
l
a
o
fo r
o
o
w
om
y st
y
d
.
THE METR I C SYS E
C U B I C ME A S U RE
Th e table for cubic measure is con
structed in the same way by rememberi ng
that the volume of a cube is equal to the
product the length breadth n height
T hus a c ubic meter being
decimeters
each way will have the same volume as
cubic decimeters H ence we have
the following table
cubic millimeters ( mm ) cubic
centimeter
cubic centimeters (c c ) I cubic
decimeter
cubic decimeters ( c ) cubic
meter
cubic meters ( m ) cubic
kilometer (c
Th e cubic meter was former l y called a
and the units derived from it were
called
etc T hese
names are now practically out o f use those
given the foregoing table being gener
ally preferred
MEA SU RES M ASS
T he unit of
in the metric system is
th e RA MME A gramme is the quantity of
matter in a cubic centimeter of pure water
at th e temperature of its maximum density
about
t might seem more nat
ural t o take as th e unit of mass th e quan
T
22
M
.
.
,
Of
,
a
,
d
.
10
,
,
.
,
0
1
.
.
.
.
.
.
.
dm
1
.
.
0
1
.
.
.
s ter e,
deci s ter es
,
cen ti s ter es ,
.
,
in
.
OF
m a ss
G
.
,
,
.
,
(
39
I
°
,
,
TS D ER I V D F O M THE METE
tity of matter in a cubic centimeter of water
at th e f
p
T here were two rea
sons why this was not done n the first
place it is di cult in experimenting with
water at the exact free ing point to make
sure that the water does not contain minute
needles of ice certainly will contain
them if any part of the water under exam
is exposed even momentarily t o a
temperature that is the least raction of a
degree w the free ing point and the
presence of such particles of i ce would
modi y the density of the water to such an
extent that it would be impossible to deter
mine the value the gramme with the
requisite degree of precision T he second
reason for preferring the temperature of
maximum density in defining the gramme
is that at this point the coe ficient of
sion of water is ero th at a small ch ange
in temperature produc es no sensibl e varia
tion the density of th e water
ther units of mass were derived from
the gramme in precisely the same way
that other units o f lengt h were derived
from the meter T hus the tenth part of
a gramme was called a gram the hun
part of a gramme was called a
gram the thousandth part of a gramme
was called a gram and a weight equal
t o a thousand grammes was called a
UN I
E
r eez
R
oi n t
i ng
R
.
23
.
I
.
‘
ffi
,
,
z
,
it
—
i n at i o n
,
,
f
oel o
z
—
f
of
.
f
,
z
,
e x pan
so
in
.
O
,
.
,
deci
,
d re d t h
cen ti
,
mil l i
,
tai l o
THE METR I C S Y STEM
gram T he kilogram is therefore
cally equal to th e
f
w
p
f p
f
T he weight of this
quantity of water was determined
mentally by the C ommission that prepared
the standard platinum meter and a stand
ard mass of platinum having this same
weight as nearly as the unavoidable errors
of experiment would llow w deposited
in the Archives of F rance by the C om is
sion on June
F or practical and
legal purposes therefore
w
g
fi
f
M iller s com
f p
parison of this weight with the equivalents
used in our own country indicates that the
I
R A M is equal to
IS O
S T he avoirdupois pound
ing equal to
troy grains it follows
that the RA MME is equal to
TR OY R S T he table for weights in
the M etri c ystem is as follows
milligrams (mgm ) centigram
centigrams cgm ) decigram
deci grams ( )
gramme
grammes ( ) kilogram
kilograms ( ) millier
t will be noticed that we h ave preserved
th e F rench spelli g in the case of th e
24
.
t h e o re t i
.
m a ss
m et er
a ter ,
ur e
o
m ax i m u m
a
o
i ts tem
at
cu bi c
deci
er a tu re
o
dens i ty
.
e x p e ri
,
,
a
as
,
m
,
22,
,
1
799
.
,
de
n ed
s ta n da r d
K
t/z e
as
m a ss
/z t
ez
in
,
l a ti nu m
o
LOG
PO
t/z e ki l og
,
va cu o
,
ram
t/z i s
o
’
.
2 20 46 2 1 2 5 A V 0 1 R D U
.
P UN D
be
.
,
G
G
AIN
.
S
:
10
1
.
10
(
10
dg m
.
1
.
.
1
.
gm
kg m
.
1
.
.
.
9"
1
I
n
A s c alle d
“ l
o
is
“
t nne
o
"
,
or
“
t n n eau
o
”
.
SYS T E M
the table for l ong measure i s derived from
26
T HE
ME T RI C
.
th e meter Thus we have
milliliters (ml ) centiliter
centiliters (cl ) decil ter
deciliters (dl ) liter
liters
kiloliter (
T here is
istinction in the M etri c
ystem between wet an d dry meas
ure
A D MEA S U RE
convenience in measuring the
unit called the A RE w proposed T he
A RE is equal t o the area of a square wh ose
edges are each meters long and h ence
it is equivalent to
of an acre T he
table for land measure is as follows
milliares (ma ) centare
centares ( ) I deciare
deciares (da
are
ares
decare
decares (dc )
hectare ( )
T he E C T E equal to
acres is
th e unit common y empl oyed in measuring
tracts of l and of any c on si derable si e
M I S C ELLA N E U S U I TS
n addition to the units of measurement
that h av e already been mentio ed certain
compound units hav e been tabulated in the
.
10
.
10
.
10
1
i
1
1
.
kl )
1
d
no
,
“
S
.
“
”
”
,
.
L
N
.
l and
For
,
as
.
10
;
.
:
10
.
0a
10
10
.
.
)
(a )
10
AR
hc
1
.
H
1
1
.
10
1
,
.
,
.
l
z
O
N
.
I
n
,
.
TS D ER I VE D F O M THE METE
pages that follow is belie v ed that these
will be
e planatory T he ng
lish and American unit for the measure
ment of WO R is th e FOO T UN D which is
the work that must be done t o raise a
pound through a heigh t of one foot T he
corresponding metric unit is the I LO RA M
M E T E R w h ich i s the work t h at must be
done in order to raise a weigh t of one
kilogram th rough a heigh t of one meter
ince a kilogram i s equal to
pounds
and a meter is equal to
feet it fol
lows that one I RA M METER is equal
to
F OT OU D S
T he other compound units are derived in
the same simple way Th e only units
that still call for special mention appear to
be those used for the measurement of
and p w T he nglish unit of heat is the
quantity of heat required to raise the tem
of one pound of water one degree
on the F ahrenheit scale The correspond
ing metric unit i s the C O R E whi ch is th e
h eat required to raise the temperature of a
kilogram water one degree on the C en
scale A kilogram being equal
to
pounds and a C entigrade
degree being equal to F ahrenh ei
degrees it follows that the C A R I E is
equal to
nglish
heat units T he metric unit for meas
UNI
R
R
2
.
7
It
:
‘
al m o s t s e l f-
x
E
.
K
-
PO
,
.
G
K
,
.
S
,
,
K
LOG
-
x
O
-
P
N
.
nea t
o
er
E
.
,
ra
t
e
u re
p
.
AL
I
,
of
t i g ra d e
.
,
t
LO
,
x
.
E
28
T HE
MET IC
R
SYS T E M
.
uring th e power of a team e ngine or
other prime moveris the FO RC E C HEV A
which is defined as equal to th e performing
of kilogram meters per minute A
kilogram meter being
foot
pounds it follows that the FO RC E C E
is equal to
foot pounds
per minute T he O R S E O WE R being
qual to th e performance of
foot
pounds of work per minute it ollows that
th e FO R C E C HEV A L is equal to
of a O R S E OWE R
THE M O METER SC A L ES
T he C entigrade thermometer scal e
though not properly a part of the M etric
ystem may be mentioned in this place
th e F ahrenheit scale the free ing point
of water i s defined as and the Si e
the degrees is fixed by defining the di er
ence in temperature between th e free ing
and boiling points to be
T his is a
clumsy sort of scale and little can be said
in favor of it except that it is in use in
ngland and the nited tates T he
C entigrade scal e was determined by
ing the free ing point of water to be
and th e boiling point to be
T he fol
lowing rules result from these definitions
T o convert a gi ven reading on the F ahre n
heit scale to its equival ent on the C e nti
’
s
L
DE
,
-
.
e q u al
-
.
to
DE
,
4
’
,
500 x
V
H
AL
-
P
H
.
-
e
f
,
DE
H
-
P
.
R
.
,
S
,
.
On
z
of
z
ff
z
1 80
°
,
U
E
S
.
d e fin
z
1 00
°
:
U SE
T A BLE S
THE
OF
2
.
9
ade scale subtract and divide the re
by T o convert a given read
on the C entigrade scale to its
lent the F ah renheit scale multiply it
by and to the product add
r
g
32
,
°
m ai n d e r
e q u i va
i ng
on
,
US E
'
O F T H E T A BLE
S
he tables appended h ereto are intended
to facilitate the comparison of the metric
system with the weights and measures
used in this country T hey are arranged
in order beginning with simple measures
of distance under which head centimeters
are compared with inches meters with feet
and kilometers with miles The next set
of tables refers to measures of
and
square inches square feet square ards
square miles and acres are compared with
the correspon ng metric measures
measure is next considered and cubic
inches cubic feet cubic yards uid
ounces dry quarts liquid quarts gallons
etc are tabulated M easures of w g
come next and i this set tables we
find grains ounces pounds tons c
T he last set of tables contains miscellane
ous complex units such as foot pounds
pounds per square inch etc which are
compared with the corresponding metric
units
t is belie ved that th ese tables require
.
T
.
,
,
,
,
.
a r ea ,
,
y
,
,
,
,
di
Cu bi c
.
,
fl
’
,
,
,
.
,
,
,
,
ez
.
,
n
,
,
f
o
,
,
/z t
,
et
.
-
,
-
-
,
-
,
.
I
.
,
MET IC
T HE
0
3
S
R
YS T E M
.
but littl e furth er explanation f we open
at any part we find a table for
ing a gi ven number of units in th e met
system to th e corresponding units em
ployed in this country and
ately following we find a similar table
for performing the converse operati on
namely for reducing a given number of
nited tates units to the corresponding
metric equivalent F or example if we
wish to know w many square inches
there are in square centimeters we
turn to page where we see at once
th at square centimeters are equivalent
to
square inches f we wish to
know how many square centimeters there
are in square inch s we look in the
immediatel y following table and there
we find that square inch es are
lent to
square centimeters t will
be noticed that the tables run only to
units of any give n kind f we wish to
know the value of a larger number of
units than t is we may proceed as fol
lows f the proposed number is com
posed entirely of ciphers exc ept for the
first or two figures we can deduce
the desired equivalent directly from the
tables by merely shifting the decimal
point one place to the r ght for every
cipher that follows the significant figures
I
.
re du c
,
ri c
i m m e di
;
,
U
S
,
.
ho
38
60
,
,
38
I
.
26
e
,
,
e q u i va
26
.
I
1 00
I
.
h
,
I
:
,
one
,
,
i
U SE
OF
T HE
T A BL E S
3
.
1
wi th which the proposed number begin s
T hus suppose we wished to reduce
c ubic meters to its equi valent in cubic
yards Th e table that we hav e to use
is gi ven on pages and We find
here that cubic t
cubic
yards and hen c e cubic meters
cubi c yards f we were required to
reduce cubic meters to cubic yards
we should find th at cubic
c ub i c yards and hence
cubi c
meters
cubic yards imilarly
c ubic meters
cubic ya ds
and
cubic
cubic
yards f th e proposed number conta n s
th an two significant figures we may
split it up into two or more other numbers
each of which consists of not more than
two such figures and then we can deduc e
th e values of each of these partial numbers
and by adding the equivalent numbers so
found we can deduce the equi valent of the
n umber o gi nally proposed Th us sup
pose we wished to know how many inches
there are in centimeters T he table
that we ave to use is given on pages
and
We see that
H ence the operation is as f l lows
in
cm
in
cm
.
9 80
,
.
88
me
98
,
89
,
.
ers = 1 2 8 1
7 90
.
= 1 28 1
9 80
;
7 90
.
I
.
4600
,
m e t e r s = 6o
46
1 6 57
4600
,
=6
,
016
.
57
S
.
= 70, 6 2
.
.
9
.
,
r
2
I
,
i
mo r e
,
,
,
,
,
ri
.
,
.
(
h
44
o
4 1 00 c m
89
41
89
.
.
cm
.
= 161
4 1 72
=
.
.
.
= 16
49 2 1 1 3 5
.
.
THE
2
3
SYS T E M
METRIC
As
.
th e table does not give us the equiv
of
centimeters to more than
three decima places the value of
centimeters as obtained above cannot be
regarded as correct to more than three
places of decimals H ence we reject the
last two decim ls in the result already
found and we have
centimeters
inches
course we may divi de up th e proposed
number in any way we please for the pur
pose resolving it into other numbers of
w S gnificant figures each We wrote
merely because that is the
easiest decomposition of this sort that can
be found B ut we might h ave decomposed
it in any other manner F or example we
migh t split it up this way
Th en t h e work would be
in
cm
cm
in
cm
in
cm
in
cm
in
H ere as before we must regard th e last
two figures as inaccurate because the
tabl e does not give us the value of
al e n t
4 1 00
l
4 1 89
,
,
,
-
.
a
,
41
89
:
1 649 2 1 1
.
.
Of
,
of
t
o
i
.
.
,
.
:
3 8 00
.
2 90
43
6
5
1 49 6 0 6 2
.
.
:
.
.
=
.
.
.
.
,
2
1
56
.
,
,
3 8 00
34
THE
M E TR I C
S
1 92
g
YS T E M
.
on pages to will ive at a glance a
good idea of how these two scale c ompare
at di ferent points and the tables enable
us to calculate to the nearest hundredth
of a degree the reading either one of
these scales which corresponds to a given
reading on the other one T he rule for per
forming this calculation
the tables
has been given already on page t
only remains to show how the calculation
is acilitated by the use of the tables T he
table on page gives a direct comparison
for every five degrees on the C entigrade
scale up to and then for every ten
degrees up to
uppose that a F ah
thermometer and a C entigrade
thermometer are exposed side by side to
a given temperature f the C entigrade
i nstrument reads
we see from the
table that th e F ahrenheit instrument will
read if the C entigrade thermometer
reads the F ahrenheit one will read
if the F ahrenheit one reads the C enti
grade one will read and if the F ah
one reads the C entigrade one
will read
A given temperature on
either scale may thus be translated directly
into its equivalent on the other one pro
the given temperature can be found
in the table on page
f it cannot be
found there we have to make use of the
1
90
,
,
s
f
;
,
on
,
,
.
m i t/coa t
,
28
,
f
I
.
.
1
88
S
re n h ei t
,
,
I
.
r e n h ei t
,
vi d e d
1
,
88
.
I
OF T H E
USE
S
5
as il lustrated in
T A BL E
3
.
au iliary table on page
the examples which follow uppose th e
C entigrade instrument reads
and we
wish to know the corresponding reading
on the F ahrenheit one We do find
in the C enti rade column but we
find and its equivalent in the F ahren
heit system is
T u ning now to t h e
auxiliary table on th e next page we see
that a interval on a C entig ade th er
is equivalent to an interval of
on a F ahrenh eit instrument H ence
we obtain the equivalent of
as
follows
F ahr ( p
p(
C orrect i on for
F ahr
H ence
We migh t have based our calcul ation on
any other reading in the main table which
is within of the ven temperature of
the
being
the
greatest
interval
(
tabulated on page
T hus we could
base it upon the reading in the first
column We note that
and
the calculation is as follows
C orrection for
H e ce
C
F ahr
which i s the same result as we obtained
before B y way of completing the
x
1
89
,
S
.
not
.
42
°
g
do
,
r
,
2
°
r
m o m e te r
36
°
.
42
C
°
.
,
:
C =
°
0
4
l o4
.
C
2°
o
.
.
.
.
°
2
4
,
.
.
,
20
42
°
20
gi
°
°
,
55
42
.
°
°
55
°
:
n
.
,
55
°
1
°
3
42
C
C
.
.
°
.
:
23
1 07
.
.
4
o
6
o
.
e x pl a
36
ME T RIC
T HE
S
Y
S
TEM
.
nation of these tables let us suppose that
it is desired to reduce F ahrenheit tem
to its equivalent on the
C entigrade scale T he work is as follows
T hen
C
C orrection for
C (p
,
t he
pe rat u re
:
.
698
698
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5
0
.
8
0
.
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.
u
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u
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0
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H
0
.
0
u
H
ence
B ut Since the correction for
F ahr is only
given to two places of decimals the
decimal in th e result cannot h ave any pre
tension to accuracy so that preserving the
nearest unit in the
decimal place
our conclusion is that when a F ahrenheit
thermometer reads
a C entigrade
thermometer exposed to the same condi
tions will read
.
H
09
.
7 0 3 8 9 F a hr
°
,
.
.
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;
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.
G rammes
1
2
3
4
5
2 400 8 8
6
7
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9
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1 1
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0
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I
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1
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5
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6
1
7
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8
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9
20
21
22
23
24
25
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.
R
M E A SU E S
OF
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G RA IN S TO G R AMM E S
G ra i ns
.
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es
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.
.
G rammes
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5
52
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.
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4
.
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.
T H E ME T RI
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C SYS T E M
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n
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R
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1
.
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O
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1
.
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55
56
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.
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69
70
71
2
7
73
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1
1
THE M
2
3
E
I
T R I C SY S T E M
K L OGRA M S TO AVO
K
i l ogram s
.
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o
.
.
I RD U POI S PO UN DS
K il ograms P
.
ou
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.
.
I
59 625
2
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2
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2
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6
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20
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22
23
24
25
46 -2 9 7
1
34
T HE
MET
I U I
RI C
SYS T E M
U
.
I
AVO R D PO S PO N DS T O K L O GRA M S
Po u nd s
.
K ilogra
m
s
.
Po unds
.
K ilograms
1
2
3
4
5
6
7
8
9
10
II
49 8 9 5
12
3
14
1
1
5
1
6
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7
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8
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9
20
21
22
23
24
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.
I
8 5 9 73
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9 5 04 5
.
1
.
.
M E A U RE
S
S
OF
MA
SS
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1
T HE METR I C SYSTEM
8
3
U
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s
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h
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.
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I
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r
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.
m
s
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T H E METR I C S Y STEM
44
O S O T TONS
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.
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n
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T HE METR I C S Y STEM
46
O
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.
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.
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ME
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1
METR I C Y T E M
K L O G A M P SQ U A E M ET E R
T
P R QU A R
K
il o gra s P o nd s p e r
K il ogra s Pquare
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u
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ra s
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MI E LL A E T A B L E
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P
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Ppero undquasre Kpeilrograquarse pePro undq uars e pKerilograms
quar e
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5
1
MET I C SYSTEM
KI L O G R AM S P R SQ U A R E E T I M E T E
POU N S P
SQ UA R E NC
Kperilograquarse SPquare
K
il
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s
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91
.
M I C SY ST M
D P R SQ UA E TO KILOG AMS
P
P R SQ U A RE C E NT I M E T E R
Ppe ro uqun dasre Keilrograquares pePr o undsuare Kpeilrogquar
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54
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M I S C E LL A N O U T AB L ES
KI L OG RA M S
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P SQ U A R E C E N T M ET E
P
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p er q uar e
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Inc h C e nt i e te r I n ch C en ti et er
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I N CH TO
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ER
SI
1
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6 6089
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.
1
6
5
T HE
METR I C SYSTEM
KI LOOR AM =M ETER S
3233
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14
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1}
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7
.
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O
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23
24
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3 3 9 -9 S I
.
1
T H E ME C S Y STEM
TRI
8
5
D
L O G R A M M ET E R S
KMil oegram
F
oo t
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ilogram
t ers
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n
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1
60
METR I C SYSTEM
T HE
CA
LO RI E S TO
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'
BR ITI S H HE A T
B ritis h
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1
.
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.
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21
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23
24
95
24
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94 45
.
1
62
MET I C S Y STEM
T HE
R
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H
B ritis h
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o
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N
w
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.
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B ritis h
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52
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UN T S T O CA LO I E S
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64
ME
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T
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METR I C S Y STEM
THE
70
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CU B IC C E NT I METE R
OU N C ES IN
CU B IC I N CI I
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ram
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THE T
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ra
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OU N C S
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rammes
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r
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T
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P O U N DS I N
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METR I C S Y S EM
T
.
A CUB IC FOO O ILO GRA S
I N A CU B IC
Ki nilaograC ubics i nPao undC ubics Ki niloga Crubic
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.
M I S C E L A N E O U S T AB ES
P O U N DS I N A CU B IC FOO T O I L OG R
I N A CU B IC
Pi n ao uCnubic
ds
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ubic
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m
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1
.
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52
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METR I C SYSTEM
T HE
M I LL I E R S
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er s
in
M
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.
.
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C
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1
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36
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21
22
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3
24
25
40 -4 5 3
METR I C SYSTEM
O
O N S I A CU B IC
D TO
I LLI R N A CU B IC
h ort T on s
M
ill i e rs
ho r t T o n s
M
ill i e rs
in a
i n a C ubic
in a
i n a C ubic
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1
82
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SH R T
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M I S C E L A E U S T AB L ES
S O
ON
N A CU B IC
D TO
I LL I R N A CU B IC
R
ho rt T on s M ill i e s i n a
ho rt T ons M illi e rs in a
i n a C ubic C ubic M ete r
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1
HE
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T
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M
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MS IN
Minilligrams
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.
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SY
ST E M
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TE
R
.
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METR I C SYSTEM
A U
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0
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A
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ams
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1
2
3
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5
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1
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3 59 4
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23
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24
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R
.
I
MS
.
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G rai n s i n a
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.
Mi nillig
rams
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M I SC E LL N E O U S T AB ES
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L
A
G RAI
N
.
IN
Gra in s i n a
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.
.
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.
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.
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AMS
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L iter U Gallon in Lit e r
m
.
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T HE
CO M P
ARI ON
S
METR I C SYSTEM
.
OF TH E R M O METE R S C A L ES
.
.
e
e
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1
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5
1
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9
METR I C SYSTEM
T HE
C
Fahr
.
10
°
50
40
30
20
—
10
°
C
.
Fahn
.
60
°
1
40
°
1
°
50
30
°
°
0
1 20
°
1 10
°
°
°
10
0
°
1 00
0
°
0
0
9
30
°
80
°
°
73
20
C o m pari s o n
60
of
°
T H E R M OM E T E R
S C A LE S
.
10
°
°
50
C MP A R I
O
OF
S ON
TH E
R M OM E
TE S
R
.
1
1
9
Fahr
.
1 10
°
1
°
2 20
1 00
60
°
3 20
310
°
3 00
°
2 00
2 90
280
1
80
o
2 70
1
30
1
°
°
1 20
1
°
1
60
1
50
40
o
°
°
°
°
°
°
2 50
2 40
1 10
°
°
2 60
6
°
°
210
70
°
°
°
°
°
2 30
1
9
THE
2
ME
T
RIC
SY S T E M
.
C
.
2 10
°
260
°
490
2 00
°
2 50
°
°
480
4 70
240
°
°
°
46 0
3 60
1
80
°
°
2 30
3 50
3 40
1
70
1
0
60
43 0
2 20
3 30
3 20
°
°
°
°
°
°
°
°
°
°
420
21 0
°
°
41 0
1
F oo t
METR I C SYSTEM
T HE
94
.
p o u n d s t o cal o ri es 1 66
t o k il o g ra m m ete rs 1 5 8
F o rce s d e c h e vau x t o h o rs e p o wer 1 6 8
G al l on s Britis h t o l i te rs 1 1 4
U S t o l i te rs 1 06
G rai n s t o gra m m es 1 2 6
i n a U S gal l o n t o m il ligra m s I n a l it e r
G ra m m e s to grai n s 1 2 4
t o av o i rd up o i s o u n ce s 1 2 8
t o T r oy o u n ces 1 3 6
i n a c ub i c ce n t i m et e r t o o u n ces i n a cubic
i n ch 1 72
H eat u n its Briti s h t o cal o ri es 1 6 2
H ectare s t o acre s 7 6
H o rs e p o we r t o fo rce s d e C h evau x 1 7 o
n c h es t o ce n ti m et ers 46
K il o gra m m et e rs t o foot p o u n ds 1 5 6
K il o gra m s t o av o i rd up o is p o u n d s 1 3 2
t o T r oy p o u n d s 1 40
i n a cubi c m et e r t o p o u n ds i n a cubic
foo t 1 7 6
p e r squ are c e n ti m ete r t o p o u n ds pe r
squ are i n c h 1 5 2
pe r squ are m ete r t o p o u n d s p e r s qu are
foo t 1 48
K il o m ete rs t o m i le s 5 6
L i qu i d S e e Qu a r ts G a l l o n s a n d L z l e r s
L ite rs t o Briti s h gal l on s 1 1 2
t o Briti s h li qu i d qu arts 1 08
t o U S l i qu i d quar t s 1 00
t o U S gal l o n s 1 04
t o U S d ry qu arts 1 1 6
M eters t o fe et 48
t o y ard s 5 2
M i l e s t o k il om eters 5 8
-
.
,
-
,
.
,
,
,
.
.
,
,
.
,
,
.
.
.
.
.
,
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.
,
.
,
.
,
,
,
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.
,
I
.
.
,
.
,
-
-
,
.
.
,
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,
.
,
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,
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,
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—
,
.
,
,
.
.
,
.
.
.
.
.
.
.
,
.
,
,
,
.
,
.
,
.
.
IN
DE
T AB ES
L
T O
X
1
.
i ll i e rs t o s h o rt t o n s 1 44
i n a cubi c m et er t o t on s i n a cubic y ard
M i ll igra m s i n a l ite r t o grai n s i n a U S gal l o n
O u n ces av o ird up o i s t o gra m m es 1 3 0
U S fl u id t o cubi c c e n t i m eters 9 8
T r oy t o gra m m es 1 3 8
i n a cubic i n c h t o gra m m e s i n a c ubi c
M
.
,
.
.
.
.
,
,
,
,
t i m e t e r, 1 74
,
1 80
.
1 84
.
.
.
,
,
,
.
,
Po u n ds ,
95
ce n
.
av o ird up o is t o k i l o gra m s 1 3 4
T r oy t o k i l o gra m s 1 42
p e r s qu are i n c h t o k il o gra m s p e r square
c e n t i m e te r 1 5 4
p e r s qu are foo t t o k i l o gra m s pe r s quare
m et e r 1 5 0
i n a cubic foo t t o k i l o gra m s i n a cubic
m e te r 1 7 8
Qu arts Brit is h l i qu i d t o lite rs 1 1 0
U S l iqu id t o l ite rs 1 02
U S d r y t o l ite rs 1 1 8
S cale s t h e r mom ete r c o m paris on of 1 8 8 1 8 9 1 9 0
S h o rt t on s t o m i l l i e rs 1 46
i n a c ubic y ard t o m i l l ie rs i n a cubic
m et e r 1 8 2
S qu are ce n t i m et e rs t o squ are i n c h e s 6 0
fe e t t o squ are m et ers 66
i n c h es t o s qu are c e n ti m et e rs 6 2
k i l o m et e rs t o square m i l e s 7 2
m ete rs t o squ are fe et 64
t o s qu are y ard s 68
m il e s t o squ are k i l o m et e rs 7 4
y ards t o s qu are m et e rs 7 0
S te re s t o U S bu s h els I 20
T e m pe ratu r e
S e e T he r m o m e te r
T h e r m om e te r scal es c om paris on of I 8 8 1 8 9 1 90
T on n e s a n d T on n e au x
S ee M i ll i ers
,
.
,
,
,
,
.
,
.
.
,
,
.
.
.
.
.
,
,
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.
,
,
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,
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.
,
.
.
.
,
.
,
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.
.
—
.
,
,
,
—
.
.
,
.
METR I C S Y STEM
1
6
9
I
on s s h o rt t o m il l i ers I 46
on s i n a cubic y ard t o m i ll i e rs
T
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T HE
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1
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in
a c ubic m ete r
,
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r oy o u n ce s t o gra m m es 1 3 8
p o u n ds t o k i l o gra m s 1 42
U n it e d S tat e s bu s h e ls t o st e re s I 2 2
d r y qu art s t o l ite rs 1 1 8
fl u id o u n ce s t o cubic c e n ti m et e rs
gal l o n s t o l ite rs 1 06
l i qu i d qu arts t o l ite rs 1 02
Y ards t o m et e rs 5 4
T
.
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.
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,
98
.

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