Charles Davies.

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.XV







*







-





m V






\




THE



METEIC SYSTEM,



CONSIDERED WITH REFERENCE TO ITS INTRODUCTION INTO
THE UNITED STATES;



EMBRACING



THE REPORTS OF THE HON. JOHN QUINCY

ADAMS, AND THE LECTURE OF

SIR JOHN HERSCHEL.



Br CHARLES DAYIES, LL. D.,

Chairman of the Committee on Coins, Weights and Measures of the
University Convocation of the State of New York.







A. S. BARNES AND COMPANY,

NEW YORK AND CHICAGO.

1871.



DAY IE S'

COURSE OF MATHEMATICS,



Davies' Primary Arithmetic and Table-BookDesigned for Beginners;

containing the elementary tables of Addition, Subtraction, Multiplication,
Division, and Denominate Numbers ; with a large number of easy and prac-
tical questions, both mental and written.

Davies' First Lessons in Arithmetic Combining the Oral Method with the
Method of Teaching the Combinations of Figures by Sight.

Davies' Intellectual Arithmetic An Analysis of the Science of Numbers,
with especial reference to Mental Training and Development.

Davies' New School Arithmetic Analytical and Practical.

Key to Davies' New School Arithmetic.

Davies' Grammar of Arithmetic An Analysis of the Language of Numbers

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Davies' University Arithmetic Embracing the Science of Numbers, and their

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Key to Davies' University Arithmetic.

Davies' Elementary Algebra Embracing the First Principles of the Science.
Key to Davies' Elementary Algebra.
Davies' Elementary Geometry and Trigonometry With Applications in

Mensuration.
Davies' Practical Mathematics With Drawing and Mensuration applied to

the Mechanic Arts.
Davies' University Algebra Embracing a Logical Development of the

Science, wi^h graded examples.
Davies' Bourdon's Algebra Including Sturm's and Horner's Theorems, and

practical examples.

Davies' Legendre's Geometry and TrigonometryRevised and adapted
to the course of Mathematical Instruction in the United States.

Davies' Elements of Surveying and Levelling Containing descriptions of
the Instruments and necessary Tables.

Davies' Analytical Geometry Embracing the Equations of the Point, the
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Davies' Differential and Integral Calculus.

Davies' Descriptive Geometry With its application to Spherical Trigonom-
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Davies' Shades, Shadows, and Perspective.

Davies' Logic and Utility of Mathematics With the best Methods of In-
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Davies' and Peck's .Mathematical Dictionary and Cyclopedia of
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Entered according to Act of Congress, in the year 1870, '

BY A. S. BARNES & COMPANY
In the Office of the Librarian of Congress, at Washington.



r



V




PREFACE.



IT is, perhaps, not generally known that the Metric
System of Weights and Measures has been adopted, per-
missively, by the Congress of the United States, and that
any Merchant, Mechanic, or Tradesman may, if he pleases,
in strict conformity to law, render all his bills and keep
his accounts according to that system.

The mind of the civilized world, brought into sympathy
and close connection by the Wires of the Telegraph, is
now earnestly directed to the question of uniformity in the
language of business relations ; and the Metric System of
France is presented as a means of effecting such uni-
formity.

In May, 1866, the following bill was passed by the Con-
gress of the United States :

A BILL TO AUTHORIZE THE USE OF THE METKIC
SYSTEM OF WEIGHTS AND MEASURES.

Be it enacted by the Senate and House of Representa-
tives of the United States of America in Congress assem-
bled, That from and after the passage of this act, it shall
ue lawful throughout the United States of America to



4 PREFACE.

employ the weights and measures of the Metric System ;
and no contract, or dealing, or pleading in any court,
shall be deemed invalid or liable to objection, because the
weights or measures expressed or referred to therein are
weights or measures of the Metric System.

SEC. 2. And be it further enacted, That the tables in
the schedule hereto annexed shall be recognized in the
construction of contracts, and in all legal proceedings, as
establishing, in terms of the weights and measures now in
use in the United States, the equivalents of the weights
and measures expressed therein in terms of the Metric
System; and said tables may be lawfully used for com-
puting, determining, and expressing in customary weights
and measures the weights and measures of the Metric
Svstem.



At the meeting of the University Convocation of the
State of New York, at Albany, in the summer of 1866,.
the Hon. John A. Kasson, Member of Congress and
Chairman of the Committee of the House of Representa-
tives, on a "Uniform System of Coinage, Weights, and
Measures," called the attention of the members to the
action of Congress, and earnestly asked such attention to
the subject as in their judgment might seem wise and
proper.

A Committee, consisting of the Chancellor, J. V. L.
Pruyn, Professor Charles Davies, and Regent Robert S.



PREFACE. 5

Hale, was appointed, and instructed to report "What
measures, if any, the Convocation should adopt in regard
to a Uniform System of Weights and Measures."

The duty of collecting the materials for the report of
the Committee was assigned, by the Chairman, to the
second member named, and it seemed to be the unani-
mous opinion of the Committee that a report would be
made, favorable to the introduction of the system into
general use. On examination, however, it did not appear
to the Committee, and especially to the one who had been
charged with making the examinations, that the Convoca-
tion should commit itself, hastily, to the great and radical
changes which the introduction of the Metric System
would occasion. At 'the meeting of the Convocation in
1869, the Committee made a partial report, and explained,
very fully, the changes which an examination of the sub-
ject had produced on the minds of some of its members,
whereupon the Committee was discharged and a new Com-
mittee appointed, composed of Professor Charles Davies,
Robert S. Hale, and Professor James B. Thompson. Pro-
fessor Thompson has not acted with the Committee, and
is, of course, not responsible for its doings.

The Committee have given the subject a very full and
careful examination. They have shared the enthusiasm
which the hope of a common Currency, a common unit of
Weight, and a common unit of Measure, for all nations,
has awakened throughout the world. They honor the
French nation for having taken the first step in so great



6 PREFACE.

an undertaking. But in their judgment, the adoption of
the Metric System, without modifications, and the entire
obliteration of every unit of weight and measure which
now form the warp of our language and the base of our
traffic and commerce, while it is yet uncertain how far it
may be adopted by other nations, would be most unwise.

We must not forget that the introduction of the Metric
System carries with it the necessity of abandoning our
own Saxon, and introducing a language entirely foreign,
and which the masses will be obliged to use.

The report of the International Committee of the Paris
Universal Exposition, states : "It will be observed that the
French orthography is retained throughout. This is done
for uniformity, and to avoid the word gram. * * * * The
orthography should be retained for the sake of uniformity
also. The Metric System is destined to be generally inter-
national. The names and orthography of all its divisions
should be equally so. For this reason, alone, we should
refrain from Anglicizing the French names."

The Committee have been most anxious to state all the
facts of the case, in their regular order; and hence, they
have given in Part I. the Metric System itself, with its
weights and measures, which are its proper supplements.

In Part II. they have sought to give a fair and just
analysis of the Metric System, considered specially with
reference to its connection with our systems of public
instruction.

Part III. is the able and extraordinary report of Mr.



PREFACE. 7

John Quincy Adams. He examined the whole subject
with the minuteness and accuracy of mathematical science
with the keen sagacity of statesmanship, and the pro-
found wisdom of philosophy. To that report nothing can
be added, and from it nothing should be taken away.
Hence, the Committee have published it in full, that the
public, and especially the teachers of the country, may
understand the entire subject, in all its phases and in all
its relations.

Part IV.. is the lecture of Sir John Herschel, on the
Pendulum, the Yard, and the Metre, regarded as a stand-
ard. In this lecture the subject is examined from the
standpoint of exact science, and in this regard it is well
worthy of attention.

The Committee, in compliance with a vote of the Con-
vocation, submit to the public not only the results of their
own labors, but also the more important essays forming
Parts III. and IV., in the hope that all may contribute to
the advancement of science, the diffusion of knowledge,
and to the final adoption, by all nations, of a common
system of Weights and Measures



CONTENTS.



PART I.



METRIC SYSTEM



PART II.
REPORT OF THE COMMITTEE 19

PART m.
REPORT OF THE Ho^. JOHN^ QUI^CY ADAMS 55

PART IV.
LECTURE OF SIR JOH^ HERSCHEL.. . 297



PAET I.



METEIC SYSTEM.




THE primary base, in this system, for all denominations
of weights and measures, is the one-ten-millionth part of
the distance from the equator to the pole, measured on the
earth's surface. It is called a METRE, and is equal to 39.37
inches, very nearly. ,

The change from the base, in all the denominations, is
according to the decimal scale of tens : that is, the units
increase ten times, at each step, in the ascending scale, and
decrease ten times, at each step, in the descending scale.



MEASURES OF LENGTH.
Base, 1 metre =39.37 inches, nearly.

Tafcle.

Ascending Scale. Descending Scale.











g


1

o>





1


I





f


0>

\

^0


i

3
8


ecame


w

PH
g


s


M


W


P


3


1


1


1


1


i










1*



.1 a



-



Q



10



METRIC SYSTEM.



The names, in the ascending scale, are formed by prefix-
ing to the base, Metre, the words, Deca (ten), Hecto (one
hundred), Kilo (one thousand), Myria (ten thousand), from
the Greek numerals ; and in the descending scale, by pre-
fixing Deci (tenth), Centi (hundredth), Milli (thousandth),
from the Latin numerals. Hence, the name of a unit
indicates whether it is greater or less than the standard ;
and, also, how many times. The table is thus read :



10 millimetres
10 centimetres
10 decimetres

10 METKES

10 decametres
10 hectometres
10 kilometres


make
make
make
make
make
make
make


1 centimetre.
1 decimetre.

1 METRE.

1 decametre.
1 hectometre.
1 kilometre.
1 myriametre.



Table of Equivalents.



1


1


6

o>


1


1

1


I


I


?


L


10


.


. =


1


10 =


100


.


1 =


10 =


100 =


1,000


1 =


10 =


100 =


1,000 =r.


10,000


10 =


100 =


1,000 =


10,000 =


100,000


100 =


1,000 =


10,000 =


100,000 =


1,000,000



1 = 10 = 100 = 1,000 = 10,000 = 100,000 = 1,000,000 = 10,000,000

Table of Equivalents in English Measure.
1 Millimetre 0.0394 inches, nearly.
1 Centimetre = 0.3937 " .
1 Decimetre = 3.9370 "



MEASURES OF LENGTH. 11

1 METRE = 39.37 in. = 3.280833 ft.

1 Decametre = 32 ft. 9.7 in.

1 Hectometre = 19 rd. 14 ft. 7 in.

1 Kilometre 4 fur. 38 rd. 13 ft. 3 in.

1 Myriametre = 6 mi. 1 fur. 28 rd. 6 ft. 4 in.

Besides a clear apprehension of the length of the base,
1 metre, it is well to consider the length of the largest unit,
the myriametre, equal to nearly 6 and one-fourth miles;
and also the length of the smallest unit, the millimetre,
about four-hundredths of an inch. Compare also, each of
the smaller measures, the decimetre and centimetre, with
the inch.

When, in the metric system, the value of any single unit
is fixed in the mind, the values of all the others may be
readily apprehended, since they always arise from multiply-
ing or dividing by 10.

NOTE. In all the tables, the UNIT is in small capitals, and should
be constantly referred to.

Methods of Reading.

The number 25365.897 metres, is read, in English,

Twenty-five thousand three hundred and sixty-five
metres, and 897 thousandths of a metre. But in the
language of the metric system, it may be read,

Two myriametres, 5 kilometres, 3 hectometres, 6 deca-
metres, 5 metres, 8 decimetres, 9 centimetres, and 7 milli-
metres. It may also be read, beginning with the lowest
denomination, 7 millimetres, 9 centimetres, etc., etc.

In reading, remember that the unit of any place is one-
tenth of the unit in the place next at the left, and ten



12



METRIC SYSTEM.



times as great as the unit of the place next at the right.
Hence, the change from one unit to another, and the
methods of reduction and reading, are 1 identical with those
in the system of decimal currency.

1. Write, numerate, and read, five hundred and ninety-
six hectometres.

2. Write, numerate, and read, eighty-nine thousand and
forty-one centimetres.

MEASURES OF SURFACES, OR SQUARE MEASURE.

Base, 1 Are = the square whose side is 10 metres.
= 119.6 square yards, nearly.
= 4 perches or square rods, nearly.

The unit of surface is a square whose side is 10 metres.
It is called an ARE, and is equal to 100 square metres.



3 a s
? 1 ?

The table is thus read :

100 centiares make 1 ARE.
100 ares make 1 hectare

Table of Equivalents.

Hectare. ABE. Centiare

1 = 100
1 = 100 = 10,000



MEASURES OF VOLUMES.

Equivalents in acres, roods, and perches.

1 Centiare '= 1.195985 sq. yards, nearly.
1 ARE = 3.95367 perches.
1 Hectare = 2A. IR. 35.367P.



MEASURES OF VOLUMES.

Base, 1 Litre = the cube on the decimetre.
= 61.023378 cubic inches.
= a little more than a wine quart.

The unit for the measure of volume is the cube whose
edge is one-tenth of the metre that is, a cube whose edge
is 3.937 inches. This cube is called a LITRE, and is one-
thousandth part of the cube constructed on the metre, as
an edge.

Ascending Scale. Descending Scale.



(8

QQ H

H ^

55

I J p

1118

W W Q i "i
1 1 11

The table is thus read :

10 millilitres make

10 centilitres make

10 decilitres make

10 litres make

10 decalitres make

10 hectolitres make



I I I

=3 i



1 centilitre.

1 decilitre.

1 litre.

1 decalitre.

1 hectolitre.

1 kilolitre, or stere.



METRIC SYSTEM.



Table of Equivalents.



Ill i I 4



ft


9


fi


5


10


.


.


1 =


10 =


100


.


1 =


10 =


100 =


1,000


1 =


10 =


100 =


1,000 =


10,000


10 =


100 =


1,000 =


10,000 =


100,000



1 =

1 = 10 = 100 = 1,000 = 10,000 = 100,000 = 1,000,000

NOTE. The kilolitre, or stcre, is the cube constructed on the metre,
as an edge. Hence, the litre is one-thousandth part of the kilolitre.

Equivalents in Cubic Measure.

1 millilitre = .061023 cubic inches.

1 centilitre = .610234 cubic inches.

1 decilitre = 6.102338 cubic inches.

1 LITHE = 61,023378 cubic inches.

1 decalitre = 610.233779 cubic inches.

1 hectolitre = 6102.337795 cu. in. = 3.53 14454 cu. ft.

1 kilolitre, or stere= 61023.377953 cu. in. = 35.314454 cu.ft.

NOTE. Law of change in the units, and methods of reading, are
the same as in Linear Measure.

DRY MEASURE.
EQUIVALENTS I3ST THE WINCHESTER BUSHEL.

Since 1 bushel = 2150.4 cu. in. ; 1 pk. = 537.6 cu. in.;
1 qt. = 67.2 cu. in. 1 pt. = 33.6 cu. in. ; therefore,



LIQUID MEASURES. WEIGHTS. 15

1 millilitre = .001816 pints.

1 centilitre = .018160 pints.

1 decilitre = .181606 pints.

1 LITRE = 1.816060 pints.

1 decalitre = 1 pk. 1.8083000 qt.

1 hectolitre = 2 bu. 3 pk. 2 qt. 1.6 pt.

1 kilolitre, or stere = 28 bu. 1 pk. 4 qt.

NOTE. The litre, or standard, is a little less than 1 quart, and the
stere, nearly 30 "Winchester bushels.

LIQUID MEASURE.
EQUIVALENTS IN THE WINE GALLON.

Since 1 wine gallon contains 231 cubic inches, 1 quart
will contain 37.75 cubic inches; 1 pint, 28.874 cubic
inches; and 1 gill, 7.21875 cubic inches; we have,

1 millilitre t = 0.008453 gils.

1 centilitre = 8.084534 gils.

1 decilitre = 0.845320 gils.

1 LITHE = 1 qt. 1.1335 pt.

1 decalitre = 2 gal. 2 qt. 1.1335 pt.

1 hectolitre = 26 gal. 1 qt. 1 pt. 1.34 gils.

1 kilolitre, or stere = 1 tun, 12 gal. 1 pt. 1.44 gils.

WEIGHTS.

Base, 1 Gramme = weight of a cubic centimetre of rain-water.
= 15.432 grains, Troy, nearly.
= .0352746 ounces, Avoirdupois, nearly.
The unit of weight is also equal to the one-millionth
part of the weight of a cubic metre of pure rain-water,
weighed in vacuum. It is called a GRAMME, and is equal
to 15.432 grains, Troy, which is equal to .0352746 ounces,
Avoirdupois, very nearly.



16



METRIC SYSTEM.



Ascending Scale.



Descending Scale.





g o5 o5

i 1111

-M o3 p c8 P


H ^K
fc o3

f 3 1 1 1






rf ^ & a & g


^ s Si ^






<r> -M c8 gn o bo

a 1 & a i !

3 a? a M W P


3 f 1 I

o p o 3


1


The table is thus read :




10 milligrammes make


1 centigramme.






10 centigrammes make


1 decigramme.






10 decigrammes make


1 GRAMME.






10 GRAMMES make


1 decagramme.






10 decagrammes make


1 hectogramme.






10 hectogrammes make


1 kilogramme.






10 kilogrammes make


1 myriagramme.






10 myriagrammes make


1 quintal.






10 quintals make


1 millier, or tonneau.


Table of Equivalents.


1

Q


a>






B




s |


i




3 & f o 5 1)




6


a


^ *C o o S


'3 "


i


1


C? j? M W P 8


S 1






.


1=


10




.


1= 10=


100




1=


10= 100=


1,000




1= 10=


100= 1,000=


10,000




1= 10= 100=


1,000= 10,000=


100,000




. . 1= 10= 100= 1,000=


10,000= 100,000=


1,000,000




1= 10= 100= 1,000= 10,000=


100,009= 1,000,000=


10,000,000




1= 10= 100= 1,000= 10,000= 100,000=


1,000,000= 10,000,000=


100,000,000



1=10=100=1,(X)0=10 1 000=1()0,(XX)=1,0()0,(X)0=10,0()0,()()0=1()0,()()0,()()0=1,0^^



GENERAL PRINCIPLES. 17

Equivalents in Avoirdupois and Troy Weights.

1 milligramme = 0.0154 grains, Troy.

1 centigramme = 0.1543 grains, "

1 decagramme = 1.5432 grains, "

1 GRAMME = 15.4327 grains, ft

1 decagramme 0.3527 ounce^, Avoirdupois.

1 hectogramme = 3.5274 ounces, "

1 kilogramme 2.2046 pounds, "

1 myriagramme 22.046 pounds, w

1 quintal = 220.46 pounds, ft

1 millier, or tonneau = 2204.6 pounds, "

NOTE. Law of change in the units, and methods of reading, the
same as in Linear Measure.

NATURE OF THE METRIC SYSTEM.

The Metric system is based on the METRE. From the
metre, three other units are derived ; and the four consti-
tute the primary units of the system. They are :

METRE = 39.37 inches, nearly : unit of length.
ARE = a square on 10 metres : unit of surface.
LITRE = a cube whose edge is a decimetre: unit of

volume.
GRAMME = the weight of a cube of rain-water, each edge

of which is a centimetre: unit of weight.

From these four units all others are derived, according
to the decimal scale.

Every system of weights and measures must have an
invariable unit for its base; and every other unit of the
entire system should be derived from it, according to a
fixed law.



18



METKIC SYSTEM.



The French Government, in order to obtain an invaria-
ble unit, measured a degree of the arc of a meridian on the
earth's surface ; and from this computed the length of the
meridional arc from the equator to the pole. This length
they divided into ten million equal parts, and then took
one of these parts for the unit of length, and called it a
METRE. The length of this metre is equal to 1 yard, 3
inches, and 37 hundredths of an inch, very nearly. Thus
they obtained the length of the unit which is the base of
the Metric System of Weights and Measures.

The next step was to fix the law by which the other
units should be obtained from the base. The scale of tens
was adopted.



PRONUNCIATION.



ME'TRE. ARE.

Mil'li-me-tre.

Oen'ti-me-tre. Cen'tiare.

Dec'i-me-tre.

Dec'a-me-tre.

Hec'to-me-tre. Hec'tare.

Kil'o-me-tre.

Myr'i-a-me-tre.



LI'TRE.


GRAMME.


Mil'li-li-tre.


Mil'li-gramme.


Cen'ti-li-tre.


Oen'ti-gramme.


Dec'i-li-tre.


Dec'i-gramme.


Dec'a-li-tre.


Dec'a-gramme.


Hec'to-li-tre.


Hec'to-gramme.


Kil'o-ll-tre.


Kil'0-gramme.


Myr'i-a-ll-tre.


Myr'i-a-gramme.



The following are the Weights and Measures established
by law in France, and now in general use :



MEASURES AND WEIGHTS IN ACTUAL USB.

Measures of Length.

Double decametre.

Decametre.

Demi-decametre.

Double metre.

Metre.

Demi-metre.

Double decimetre.
Decimetre.

Measures of Volume, for Grain.

Hectolitre.
Demi-hectolitre.

Double decalitre.

Decalitre.

Demi-decalitre.

Double litre.

Litre.

Demi-litre.

Double demi-litre.

Decilitre.

Demi-decilitre.

Measures of Volume, for Liquids.

Double litre.
Litre.



20 METRIC SYSTEM.

Demi-litre.
Double decilitre.
Decilitre.
Demi-decilitre.
Double centilitre.
Centilitre.

Weights in Iron.

Fifty kilogrammes.
Twenty kilogrammes.
Ten kilogrammes.
Five kilogrammes.
Double kilogramme.
Kilogramme.
Demi-kilogramme.
Double hectogramme.
Hectogramme.
Demi-hectogramme.

Weights in Copper.

Twenty kilogrammes.
Ten kilogrammes.
Five kilogrammes.
Double kilogramme.
Kilogramme.
Demi-kilogramme.

Double hectogramme.

Hectogramme.

Demi-hectogramme.

Double decagramme.



MEASURES AND WEIGHTS. *\

Decagramme.
Demi-decagramme.

Double gramme.

Gramme.

Demi-gramme.

Double decigramme.

Decigramme.

Demi-decigramme

Double centigramme.
Centigramme.
Demi- centigramme.

Double miligramme.
Miligramme.

It will be seen from the above tables, that the weights
and measures in general use do not at all follow the
decimal scale; for, in all Weights, and in all Measures
of Volume, each decimal measure has its double and its
half, while the tables are constructed entirely on the
decimal scale. This discrepancy between the tables and
the numbers in use must give rise to much confusion,
and is a striking departure from the decimal system.

The entire Metric System, as now used, is given, that
the reader may not be at the trouble of searching else-
where for references in reading the report of the Com-
mittee, and the other more elaborate and more important
documents which follow.




PAET II.



BEPORT OF THE COMMITTEE,



THE metric system of France had its origin in the stormy
hours of the French revolution. In the year 1790, Prince
de Talleyrand, then Bishop of Autun, introduced into the
constituent assembly of France the proposition to estab-
lish a new system of weights and measures on the basis of
a single and universal standard.

Two standards were considered :

1. The length of a pendulum which should vibrate sec-
onds at a given point on the surface of the earth ; and,

2. A given portion of the arc of a meridian.

It was finally agreed to adopt the one-ten-millionth part
of the quadrant of the meridian passing through Barce-
lona and Dunkirk, as the universal standard.

This distance is called a metre. It is equal to 39.37
inches in length, and is the base of the metric, or French
system. From this primitive base, or standard, every
weight and measure is derived by the application of the
decimal scale of tens.

The larger, or multiple units of the base, are designated
by prefixing to the base the Greek numerals; and the



REPORT OF COMMITTEE. 23

smaller units, or sub-multiples, by prefixing to the base the
Latin numerals.

In space, there are four kinds of quantity to be meas-
ured, viz., 1st, Distances; 2d, Surfaces; 3d, Volumes;
and, 4th, Angles; hence, there must be four units of
measure.

I. DISTANCE. For this the unit is the metre, which is
increased and diminished according to the scale of tens.

II. SURFACES. For small surfaces, the square metre,
and the squares constructed on its decimal divisions, are
used. For the area of land, the base-unit is the square
constructed on the deca-metre, called an Are; hence, an are
contains 100 square metres, each of which is called a centi-



Online LibraryCharles DaviesThe metric system, considered with reference to its introduction into the United States [electronic resource] embracing the reports of the Hon. John Quincy Adams, and the lecture of Sir John Herschel → online text (page 1 of 28)