UNIFICATION OF WEIGHTS AND MEASURES.
THE
ITS CLAIMS
AS AN
INTERNATIONAL  STANDARD  OF METROLOGY.
BY
JAMES  B. THOMSON, LL.D.,
CHAIRMAN OF THE COMMITTEE ON WEIGHTS AND MEASURES OF THE NATIONAL EDUCATIONAL
ASSOCIATION.
NEW  YORK:
CLARK & MAYNARD, PUBLISHERS,
No. 5 BARCLAY STREET.
I874.




PUBLISHERS' NOTICE.
THE publishers beg leave to refer those, who wish to become
acquainted with the
METRIC WEIGHTS AND MEASURES,
to the lucid explanation of the principles and applications of the
System contained in
Thomson's New  Practical Arithmetic.
I-Ion. JOHN A. KASSON, Chairman of the Congressional Committee
on Weights and Measures, says, respecting it:
"I have observed with care your section devoted to the Metric
System of Weights and Measures, now in legal use in the United
States.  No Arithmetic can now be complete, or claim public approval,
without giving instruction to the student upon this system.  It seems
to me you have admirably combined its elements in a few pages."
President F. A. P. BARNARD, LL.D., Columbia College, after paying
a flattering compliment to the author's New Arithmetic, adds:
"But the feature of your book which it pleases me most to see, is
the presentation of the Metric System of Weights and Measures."
Professor H. A. NEWTON, LL.D., Yale College, remarks:
"I like the presentation of the Metric System, and I am glad to see
such progress in rejecting the obsolete and obsolescent in other parts
of Weights and Measures."
Entered according to Act of Congress, in the year 1874, by
JAMES B. THOMSON,
In the Office of the Librarian of Congress, at Washington.
Electrotyped by SMITH & McDoUGAL, 82 Beekman St., N. Y.




P RE F A CE.
AT the annual meeting of the National Educational Association,
held at Trenton, N. J., August, I869, a committee of three
was appointed to report on "The practicability of introducing the
Metric System of Weights and Measures into the United States,
and the best means to accomplish that object." The committee consisted of Professor James B. Thomson, LL.D., City of New York,
Chairman; Professor Charles Davies, LL.D., Fishkill-on-the-Hudson,
and Professor Edward Brooks, A.M., Millersville, Pa.
At the meeting of the University Convocation of the State of
New York, the same year, a committee of three was also appointed,
charged with the duty of reporting "What further steps, if any, may
be necessary in respect to the introduction of the Metric System of
Weights and Measures." This committee consisted of Professor
Charles Davies, LL.D., Chairman; Hon. Robert Hale, LL.D., and
Professor James B. Thomson, LL.D.
At the meeting of the National Association, held in Cleveland,
Ohio, Aug., I870, the Chairman presented the substance of the following report. The Association accepted the report and passed the
series of resolutions appended to it, setting forth,
"The Importance of the Unification of Weights and Measures to
the progress of science, to civilization and commerce throughout
the world."
"That in the judgment of the Association, the Metric System is
nearer perfect than any other reached," and therefore has the
"strongest claims to universal adoption."
"That its early introduction into our schools and seminaries of
learning be recommended as the best means to popularize the system,
and secure its general use among the people."




iv                       PREFA CE.
A copy of the report was requested for publication, but for want
of means to verify some statistical matters, it was deemed inexpedient
to allow it to be published at that time.
At the meeting of the University Convocation at Albany, the
same year, Professor Davies made his first written report against the
Metric System. In a prefatory note to that report, he says, "Prof.
Thomson has not acted with the committee, and is, of course, not
responsible for its doings."
Lest his non-action should be ascribed to indifference to the subject, justice requires him to say that he had no knowledge that his
associates intended to make a report, or desired his co-operation,
until after their report was submitted to the Convocation. The
reason he did not enter his protest against the views expressed in the
report at the time of its presentation, was because personal illness
prevented his attendance upon the meeting.
The University Convocation in I871 was favored by Rev. F. A.
P. Barnard, S.T.D., LL.D., President of Columbia College, with an
erudite and exhaustive address upon the " Origin and Nature of the
Metric System of Weights and Measures."
The same committee being continued, the Chairman in 1872
made his second report against the system. At that meeting the substance of the following paper was submitted as a counter-report,
urging the necessity of metrological reform, and advocating the
claims of the Metric System to universal adoption.
With this brief explanation, it is now, at the solicitation of
numerous friends of progress, offered to the public. With the exception of a few slight emendations of the text, and the addition of a
few explanatory items, it will be recognized as the paper presented
on the occasions referred to.
If it shall deepen the interest already felt in metrological reform,
and contribute in any degree to the realization of a common international system of Weights and Measures throughout the world, its
aim will be accomplished.
NEW YORK, Feb. 23d, I874.




THE METRIC SYSTEM.
Mr. Chairman,; Ladies and Gentlemen of the Association.
The committee appointed at your last annual meeting to
report upon "The Practicability of introducing the Metric System
of Weights and Measures into the United States, and the best means
to accomplish that object," respectfully submit the following:
In common with other important enterprises for the advancement of civilization, the Metric System has received in different
lands its full share of opposition.  Among the most remarkable
attacks it has encountered in this country are the strictures recently
presented by gentlemen distinguished for mathematical and legal
learning, to the University Convocation of the State of New York.
These strictures are the more extraordinary as one of the gentlemen, from whom they emanated, had previously declared his conviction, over his own signature,* "that the Metric System is nearer
perfect than any which can be reached, and that its adoption would
greatly simplify and abridge all the applications of numbers to the
various operations of commerce and business."  The explanation
of these conflicting views, this radical change of opinion, is chiefly
found, we apprehend, in a misconception of the aims of the friends
of metrological reform, and of the practical working of the Metric
System, if introduced into our country.
Our opponents assume that the friends of metrological reform
demand the adoption of the Metric System and the exclusion of our
present system, simultaneously. They assert that the question is,
"Shall the Metric System of Weights and Measures be adopted by
* The Metric System explained, etc., by Charles Davies, LL.D.




6                  THE MEtTRIC SYSTEMS.
compulsory legislation, and the use of every other system forbidden?"
They accuse "the friends of the Metric System of attempting to
give such direction to public sentiment as shall lead to that result.
Again, they declare that "wherever the Metric System has been
introduced, the exclusion of every other system, by penal enactments,
has been found necessary." Allusion is also made to "dragooning
the people into its use;" "fierce conflicts" are predicted in this
country, where " the people are free and less habituated to blind obedience to imperial edicts."  We have heard, Mr. Chairman, of the
"Poetry of Mathematics." Here we have a specimen of what may
be called Sensational Mathematics.  These mathematico-sensational
flourishes, if they have any meaning, assume that the friends of the
Metric System have some sinister design concealed under the garb
of metrological reform; that their aim is to take the people by surprise; to cheat them out of the old system and force them into the
immediate use of the new.
We beg leave to assure the Association and the public that the
advocates of metrological reform in this country, repudiate all such
designs. They neither ask nor desire such legislation. Their object
is alike pacftc and beneficent, and while they pursue it with untiring
zeal, they intend to employ no other than peaceful measures.
Object of Metrological Reform,
The object of the advocates of metrological reform is this:
First. To establish a uniform, international system of weights and
measures, of such a character that its base and derivative units shall
be commensurable quantities.
Second. That its derivative units shall increase and decrease by
the decimal, or a unzform scale.
Third. That its different denominations shall be designated by a
convenient, common nomenclature. The manner by which they hope
to secure this reform will be explained hereafter.
The origin of the present system of weights and measures is
veiled in obscurity. We received it from the father land; England




OBJECT OF METROLOGICAL REFORM.                   7
borrowed it from Rome, Rome from the Greeks, the Greeks from
their ancestors, and so on to a remote age. Whoever may have
suggested its original units, the grain, the barley-corn, the hand, the
foot, etc., and whatever may be said of thefitness of these standards
of comparison, certain it is, the details of the system were not the offspring of philosophical research, but of ignorance or chance. Yet
amid the rise and fall of States and Empires, and all the political
revolutions that have swept the earth during the past 2000 years;
amid the gigantic conquests in science, in agriculture, and in commerce: amid the vast improvements in simplifying and abbreviating
mathematical computations, which followed the introduction of the
decimal notation into Europe, strange as it may seem, the essential
features of this anomalous system of weights and measures, which
sprung up in the world's gray dawn, held undisputed sway over all
enlightened lands down to the commencement of the nineteenth
century, and are still in vogue among all the English-speaking peoples of the present day. True, our Anglo-Saxon fathers expanded
it into different kinds of weights and different kinds of measures, and
substituted the foot and arm of some modern hero or potentate for
those of an ancient or fabulous predecessor; but its leading features
are still essentially the same, with its absurdities not only unmitizated,
but increased. However well the system may have answered the few
and simple wants of remote periods of antiquity, we need not say
that it is totally inadequate to the demands of the present enlightened
age; an age in which space is annihilated by the applications of
science, and knowledge is communicated from land to land by lightning lines stretching around the globe.
Objections to the Present System.
Among the numerous objections to the present system are:
First. The standards by which its base units are determined, are
arbitrary and perishabae.  These characteristics destroy all confidence in the experiments and researches of other ages and countries,
encourage fraud, defeat the ends of commercial justice, and thus
weaken the bonds that hold society together.




8                    THE METRIC S YSTEM.
Second. Several of its base-units are incommensurable with each
other.  Thus, the linear rod (i6 — feet) is incommensurable with the
hand, the foot and the yard; the square rod (272'- sq. ft.), with the
square foot and the square yard; and the cubic foot, the bushel and
the gallon, with each other.
T/ird. Its base-units are also incommensurable with the baseunits of all other systems of metrology. Weights and measures
are the necessary instruments of commerce. Hence, incommensurability of the base-units of weights and measures in different countries, is a serious obstacle to diplomatic and commercial intercourse.
Fourth. The scale of increase and decrease is irregular and variable. It ranges all the way from 2 to I728; and, as if to complete
the inconvenience and absurdity of the system, ten of these ratios
are mixed numbers. iTaking the hand and foot as base-units, the
application of the decimal scale to the various denominations arising
from  them, is impracticable; for, io hands are more than a foot, Io
feet more than a yard and less than a rod, etc.
Fzfth. Most of the terms by which its 70 different denominations
are designated, are primitive words, which are neither suggestive of
the thing signified, nor analogous to each other; and therefore afford
no aid to the learner in remembering them.
Sixth. Its nomenclature is a monument of confusion and absurdities. It employs three nominally different pounds besides the money
pound, three kinds of length measure, and four kinds of capacity
measure. In the subdivisions, it employs 9 terms in two different
senses, 4 in three different senses, and 5 in four different senses;
while the term ton, is used to signify a long ton, a short ton, a cubic
ton, a shipping ton, a register ton, and a liquid tun.  These double,
triple and quadruple significations of the same word, make uncertainty more uncertain, and, taken together, form a medley calculated
to bewilder the brain of the child, and blast all the redeeming qualities of the system.
Seventh. Owing to these great irregularities and apparent contradictions, the system necessarily consumes a vast amount of time and
labor in learning it, and, when learned, is difficult to retain.




OB7ECTIONS TO THE PRESENT SYSTEM.                  9
No one who has ever mastered these tables of weights and
measures, and their applications, can forget the time and toil the victory cost him; and some, no doubt, can call to mind the tinzging
sensations which sometimes accompanied these efforts. And yet
there are few, it is believed, who appreciate the amount of time and
labor thus expended. Lord Brougham, after extensive consultation
with teachers, came to the conclusion that "one-third of the time
spent in mastering arithmetic would be saved by the adoption of a
decimal system of weights and measures."  Prof. Barret, a distinguished instructor for the artillery service, thinks " tzewo years might
be saved;" and Prof. de Morgan asserts that " the time devoted to
arithmetic might be reduced by one-haof, if not more, by the introduction of a decimal system." The opinions of practical teachers
in our own country, who have been consulted as to the time consumed on this part of arithmetic, range from one and a half to two
and a half years.
Assuming the arithmetical mean of these opinions as the standard, it takes pupils two years to acquire a tolerable knowledge of the
system. The population of these United States, in round numbers,
is 40 millions, and the average age of man 33-I years. In 33~ years,
then, a whole generation of forty millions of children is to be educated. If one pupil wastes two years in mastering the present system, forty millions of pupils must waste eighty millions of 5'ears in
a single generation. And if we multiply these eighty millions of
wasted years by the countless generations in our own and other
English-speaking lands, whose intellects have been and still are
trammeled by these shackles, the product swells beyond comprehension.
Moreover, after all this toil and expense in storing away these
incongruities, how often the memory fails to reproduce them when
wanted. How few people, how few men, even of liberal culture, can
change Troy to avoirdupois weight, or liquid to dry measure, and
vice versa, without the help of a book! How few can even read the
cabalistic characters which represent the denominations of apothecaries' weight, and which so effectually conceal from the people not




Io                 THtE ME TRIC SYSTEM.
only the art of healing, but also the ignorance and blunders by which
druggists and druggists' clerks every month, send so many to untimely graves.
Eighth. But the waste of time and toil caused by the system are
not confined to childhood.  It follows our young men from the
schools to the counting-room and custom-house, and subjects them
to immense inconvenience and labor, in regulating their accounts and
adjusting the duties required by law. It presents its formidable front
to the countless multitudes who throng the busy marts of trade, and
imposes upon them also an intolerable burden in computing the
quantities of the manifold exchangeable commodities, embracing the
products of the earth and of human industry, as coal, minerals, lumber, fruits, cereals, etc., and manufactures, from the coarsest to the
finest fabrics. We hazard nothing in saying that the time and labor
of the thousands of business men who are daily engaged in computing the values of these exchangeable commodities through the
instrumentality of our present weights and measures, would be
diminished a hundred per cent. by the substitution of a uniform
international system of metrology founded upon the decimal scale.
The last objection to which we would advert, is the great hindrance
which the system presents to the progress of science. We have seen
that the base-units of the system are not only incommensurable with
each other, but also with the base-units of all other systems of
metrology in Christian lands. To appreciate the obstructions which
the system interposes to the progress of science, let us briefly refer to
the abnormal and inconvenient relations between the different denominations of the linear unit to those of capacity and weight by
which they are determined. The books say that a cubic foot of
water is equal to iooo ounces avoirdupois. But this is merely its
approximate weight, and in exact calculations must be taken with
many grains of allowance.
According to the experiments of Mr. Hassler, a cubic foot of
distilled water, at its maximum density, weighs only 998.o607 ounces,
the bushel is equal to I.24444 cubic feet, or 77.6274 pounds, and the
gallon to o. 13368 cubic feet, or 8.38888 pounds of distilled water at its




CHARACTERISTICS OF A  UNIVERSAL SYSTEM.    II
maximum density. Now, suppose the chemist or scientist wishes to
deduce, by exact calculation, the weight of a body from its capacity,
or its capacity from its weight, an operation of daily occurrence, who
can estimate the expenditure of time and labor of a single operation?
And when to these unnatural relations between its own different
denominations, we add the fact that its base-units are incommensurable with those of all other systems which, until recently, have prevailed in civilized lands, who can fail to see that the vast amount of
time and labor required to change the results of experiments from
the denominations of one system into those of another, has been and
still is a most serious hindranzce to the progress of science? With
this incubus hanging over the world, the knowledge of one nation,
in the language of Professor Hoffman, " is practically a sealed book
to the students of others."
In view of these objections, we are brought to the inevitable
conclusion that there is an urgent necessity for metrological reform;
that the interests of commerce, of science, and of civilization, imperiously demand a unzform, international system of weights and
measures. The great problem is, to find a system in which the
entire family of civilized nations will unite.
Characteristics of a Universal System.
All agree that the base-unit of a universal system should be a
common measure of all its derivative units; that its derivative units
should increase and decrease by the decimal, or some unzform scale;
that its denominations should be expressed by convenient terms; and
that its standard unit should be such as will remain unchanged from
age to age; will be secure against accident and fraud and the ravages of time; one that may be verified when desirable, and restored
if lost.  In a word, that it shall be invariable, indestructible and
reproducible.  Fortunately for man, nature presents two such objects,
each of which combines the three qualities of invariability, indestructibility and reproducibility, viz.: the linear dimensions of the




I2                 THE ME TRIC SYSTEM.
earth and the linear measure of its attractive force embodied in the
pendulum vibrating seconds.
Huygens, a distinguished Dutch astronomer, suggested a meridian as a standard as early as I685, and the commission adopted it
as the base of the Metric System in I79I. Cassini of Paris, suggested the pendulum as a base about the commencement of the last
century. England adopted this standard in I824, and declared the
length of a standard yard to be 36 inches, such that 39.I3929 of them
are equal to the length of a pendulum vibrating seconds in vacuo, at
the level of the sea, in the latitude of London.* As the English
and the Metric Systems are the only systems whose standards are
based upon the laws of nature, and are already in extensive use,
it is the opinion of distinguished scholars that the choice of a universal system must lie between them. Let us briefly compare their
claims.
While the advocates of the English system insist on retaining the
" short, sharp terms," now employed in its nomenclature, they generally admit that its derivative units must be brought into commensurability with its base-units, and the increase and decrease of its
denominations into harmony with the decimal or a uniform scale, in
order to answer the conditions of a universal system.
Felton's Proposed Method.
Among the various plans embodying these changes, the most
popular that has come under our notice is the one developed by Mr.
J. H. Felton, of England, and recently indorsed by the joint committee of the Chamber of Commerce and the Geographical Society
of the City of New York. Its outlines are as follows:
The unit of linear measure is the present legal foot. This is subdivided into inches and seconds, and has only one multiple, which is
called a rod. These denominations increase by the scale of ten; Io
seconds making I inch, io inches I foot, To feet i rod. In square
or surface measure, the link, the chain and the acre are the same as
* Note I.




FEL TON'S PROPOSED ME THOD.                    I3
ours. Its denominations are links, staffs, reeds, plats, chains and
acres, which increase by the scale of Io. The present legal pound
is the unit of weight, the subdivisions of which are called grains,
scruples, drams and ounces, and its multiples are stones, hundreds
and tons.  The unit of dry and liquid measure is the gallon,
which contains io pounds avoirdupois of distilled water. Its divisions are called grains, scruples, drams, gills and pints, and its multiples ankers and tuns.
The chief arguments in favor of this system are: Fierst. That its
nomenclature consists of short, English words which are familiar to
the ear. Second. Its principal units correspond in name with those
already in use. These are plausible considerations. If we can pass
from the present heterogeneous patchwork system to one that is
acceptable to the brotherhood of nations, so easily as here set forth,
the change is an object devoutly to be wished. But let us analyze
the plan here proposed.
It is first assumed that children have a clear and definite idea of
the meaning of the terms of the present system, because they are
familiar to the ear.  But however- familiar to adults (everybody
knows), they are new and strange to children. Again, of the twentysix terms or denominations which it employs in the four measures of
distance, surface, capacity, and weight, only five of them are taken
in their present signification, twenty-one have new definitions, and
three are used both in measures of weight and capacity, and therefore have a double meaning. The gallon or unit of capacity, differs
from the present dry or liquid gallon, and therefore has no claim
arising from present use.  The foot, the chain and the pound are the
only three of its units now established by law. Aside then from the
antipathy to new words which led our ancestors to misrepresent the
exactness of numbers, by calling I6 a dozen, II2 pounds a hundred
weight, etc., an antipathy largely inherited by their descendants, the
reasons in favor of this system are reduced to two-Fi'st. Three of
its units are established by law. Second. Five of its terms are taken
in their present signification.




14                 THE METRIC SYSTEM.
Defects of the Plan for Decimalizing the Present System,
The plan proposed to decimalize the present system of weights
and measures, has numerous and grave defects. Some of the more
prominent are the following:
Ist. Several of its units are incommensurable with each other.
Thus, the gallon (io pounds avoirdupois of distilled water) equals
22I.8I92 cubic inches. Again, the linear unit is the natural connection between linear and surface measure. But the linear link
(7.92 inches), the square of which is a unit of land measure, is
neither a decimal, nor yet an aliquot part of a linear foot or yard;
consequently the square foot is incommensurable with the surveyor's
unit of length and unit of surface.
2d. Some of its terms are employed in a double sense, and these
meanings being different from those in which they are now used, are
calculated to produce confusion in their application.
3d. Twenty-one of its boasted familiar terms have new significations. These familiar terms are wrested from that particular
meaning which long established usage has assigned them, and are
invested with a new and unfamiliar one.
The question here arises, how are we to know whether these
twenty-one terms express the new or the old signification? And how
is the pupil to decide which is the true meaning of these ambiguous
terms? It may well be doubted whether these old names with new
significations and double meanings, names which have no analogy to
the thing signified, are not more objectionable and produce more
perplexity than new names which are suggestive of the new ideas
designed to be expressed.
In like manner it may be shown, that all attempts to engraft
upon our English nomenclature, commensurability of base and derivative units with the decimal notation, are attended with inherent,
insurmountable difficulties, and are calculated to perpetuate the evils
they profess to remedy.




OB7ECTIONS TO  THE METRZC SYSTEM.                    I5
The Metric System,
The other plan proposed to secure international uniformity of
weights and measures, is the adoption of the Metric System.* The
Metric System receives its name from the Miter, its principal standard unit of length. The meter is a ten-millionth part of the distance
from the equator to the pole, and is equal to 39.37 inches nearly.
From the meter, or unit of length, are derived the unit of surface,
called the dre, the unit of capacity called the Alter and the unit of
weight called the grdm.*
The several ascending and descending denominations are decimal
multiples and submultiples of these units, and therefore, increase and
decrease regularly by the scale of Io.
The names of the higher denominations are formed by prefixing
to the several units, the Greek numerals dek'a, kec'to, kil'o and myr'ia,
which respectively denote Io, Ioo, Iooo, and Ioooo; as, dekameter,
hectometer, kilometer, myriameter. Those of the lower denominations are formed by prefixing to the same units, the Latin numerals
de'ci, cen'ti, and mil'li, which denote I,    ta-bo; as decimeter,
centimeter, millimetert
Objections to the Metric System.
We are first met by the objection of Sir John Herschell, that the
quadrant of a meridian is not the best possible standard, that the
earth's equatorial diameter, or polar axis, or "the length of a pendulum vibrating seconds under certain definite and normal circumstances," would be preferable. It is also added that "all meridians
are not of the same length; and that the meter is not exactly the
ten-millionth part of the distance from the equator to the pole," etc.
Without stopping to inquire whether the objection of the learned
astronomer may not justly be regarded as hypercritical; waiving also
* For the details and application of the Metric System, the reader is referred to Thomson's New Practical Arithmetic.                  t Note 2.




6                 THE METRIC SY'STEMEI.
the assertion that all meridians are not of the same length, and that
the meter was inaccurately determined, points which, according to
eminent authority,* have not yet been proved, it is sufficient for our
present purpose to say, that if all that-is claimed on these points be
true, this would not detract essentially from the value of the Metric
System.  For, it should be observed, the meter is no longer an
abstract idea, or a mathematical conception. It is a definite lengththe length of a material object. It consists of a bar of platinum
deposited in the archives of France, and is therefore a concrete unit.
In this respect it is on equal footing with the present standard yard
of the English system.t It is exactly copied in nieasures within the
reach of every branch of industry, and from its wide diffusion among
the nations, may readily become a universal standard.
Again, it is objected that the introduction of the Metric System
would cause certain manufacturing establishments great incqnvenience and expense in changing their patterns and machinery.
In support of this objection, quotations have been freely made
from a late speech of the Hon. Mr. Stephenson before the British
Parliament. That his audience and the public may duly appreciate
the weight of his testimony in favor of the present system, the Hon.
member informs us that he is a Manufacturing Chemist; that the
units, pound and cubic foot are constantly used, and are thebases of
all his plans and arrangements.  In making Sulphuric Acid, he
says, he constructs his cisterns so that every inch, or one-tenth of an
inch in depth, corresponds to i or io cubic feet, etc. Here you will
observe the importance of the decimal scale, spontaneously cropping
out. While arguing against the adoption of a system based upon it,
the Hon. M. P. inadvertently acknowledges the importance of the
principle, by employing it in graduating his cisterns. He also admits
that a French Chemist can turn kilograms into htns more easily than
he can pounds.  And why?  Because, he adds, "the Frenchman
divides by Iooo, and he has to divide by 2240." These, Mr. Chairman, are important admissions, coming as they do from the foremost
antagonist of the Metric System  in the British Parliament.  They
* Barnard on the Metric System.              t Note I.




OBYECTIONS TO THE METRIC SYSTEMA1.                I7
clearly show the importance of a Decimal System  of Weights and
Measures, and the great inconvenience of the ever varying scales of
our own system, to those who are called upon to make calculations
by thenm. But what is the motive power that prompts this earnest
opposition to the Metric System? Its introduction would oblige
him to re-gauge his cisterns, make a new set of capacity measures, new
scales, etc., and thus put him to' an expense of some thousands of
pounds sterling.  Mr. Chairman, we submit whether a man who has
a large pecuniary interest at stake, is a competent witness upon this
subject? How is the testimony of self-interested witnesses regarded
in our civil and criminal courts?
But the Hon. gentleman enumerates other parties among the
various departments of industry who would suffer from the introduction of the Metric System; as coopers, sawyers, manufacturers of
hinges, bolts, screws, etc. " If the pound is abolished," he asks, " how
can the candle-maker know how to make his 4's, 6's, and 8's to a
pound; and how will the housewife know whether her 6 candles
weigh a pound?" To cap the climax, the honorable member indulges his grief over the anticipated abolishment of the milestones
on the higlhways. " Are these to be shifted," he asks, " and are
parliamentary trains, at a penny a mile, no longer to be heard of?"
This was too touching! Parliament straightway voted down the obnoxious reform! The disinterestedness of such objections reminds
us of a whaling merchant who opposed free schools on the ground
that, "if boys are educated, they will no longer go before the mast;
and who," he asks, "will then man our whale ships? The introduction of free schools," exclaimed the deluded man, "will destroy the
whale fishery and beggar our families 1"
With regard to the manufacturers of hinges, butts, etc., to whom
reference has been made, whether in Manchester, Eng., or Waterbury,
Conn., we can only say that inprovement is the order of the day;
these varying patterns are footprints in its march; and if the present owners of these establishments adhere to the styles now in vogue
for ten years, the tyrant fashion, will rule both them  and their
goods out of market. But suppose the introduction of the Metric




I 8                 THEE  I METRIC SY'STEL.
System should cause manufacturers a temporary inconvenience and
expense, shall the temporary interest of the few, with their annual
dividends of twenty or thirty per cent., be allowed to override the
welfare of the many, for all time?
It is also objected that the Metric System is inconvenient because it requires so many words or denominations to express ordinary
quantities. In the next breath we are told that numbers, as a general rule, are read in the lowest unit, which makes the number too
large for convenience. These objections contradict each other, and
therefore both cannot be tenable.  Moreover, it requires but a slight
glance at the system to see that neither is valid. What would be
thought of the knowledge of an American who should read 78 dollars
62 I cents, as "7 eagles, 8 dollars, 6 dimes, 2 cents and 5 mills," or as
78,625 mills?   Equally unnatural is it to read 78.625 meters, as
"7 dekameters, 8 meters, 6 decimeters, 2 centimeters and 5 millimeters," or as "78,625 millimeters."  Again, that troublesome " lot
of ground of 25 feet front by Ioo deep," which it is said must be
described, as " 7 meters, 6 decimeters and 2 centimeters front by 30
meters, 4 decimeters and 8 centimeters deep," is properly described
as 7.62 meters front by 30.48 meters deep. And instead of expressing 150 miles, the reputed distance from  New York to Albany, by
229,680 meters, it is naturally expressed in round numbers, by(.
kilometers, the ordinary unit for long distances.  It is unnecessary
to say that a quantity expressed by the Metric System, may be read
in any single denomination which shall be chosen as the unit, the
lower denominations always being decimals of the unit which is
selected.
It is further asserted that the introduction of the Metric System
"would change the records of our entire landed property."  Does
the objector mean by this that all our farmers would be obliged to
have their deeds recorded again, in order to preserve a legal title to
their property?  Every school-boy knows that ex post facto laws are
unconstitutional. What effect the use of the Metric System can have
upon the past records of our landed property, we confess our inability
to see.  Every transfer of real estate requires a new record, but this




OB  CTIO NS TO THE METRIC SYSTEM.                 19
record does not disturb the former. The validity of titles, the great
landmarks, the boundary lines, etc., of estates, are no more affected
by translating the dimensions from  the given number of rods, feet
and inches, "more or less," as formerly described, into meters and
decimals of a meter, than if expressed in chains and decimals of a
chain, according to present usage.*
It is also urged that the introduction of the Metric System would
obliterate, to a certain extent, all present knowledge; that as great
confusion would follow as " if we were forbidden to speak any language but the French."  The obliteration of all or any considerable
portion of the present knowledge the world possesses, would indeed
be a great calamity; and the.attempt of uninstructed Americans to
speak French would present a ludicrous jargon. But we confess we
do not see how this obliteration of knowledge is to be brought about,
by the introduction of the Metric Language. Suppose the people
were to learn the Metric System before they abandon the present
system, would they have any reason to apprehend these deplorable
consequences? Such forebodings then are purely imaginary-they
arise fromn the preposterous supposition that the people are to be
required to use certain instruments of calculation of which they are
totally ignorant. The objection assumes that the human intellect is
so constituted that learning a new science necessarily crowds out an
old one, and consigns it to oblivion. It implies that new ideas are
necessarily hostile to old ones, and by reason of their "incompatibility," they cannot dwell together harmoniously.
Finally, it is insinuated that "the system comes from  a foreign
land," and "is the offspring of infidelity."  Such insinuations do
great injustice to the intelligence and candor of Americans. Why
should a system of metrology, derived from these sources, be any
more obnoxious to the American mind than a system of Algebra,
Geometry, the Mecanique Celeste, etc., borrowed from the same
source; or, than the Arabic Notation, which came from a foreign
pagan land, a land long known as the bitterest foe to Christianity.
Such objections are too frivolous to require refutation.
* Note 3.




20                  THE iMETRIC SYSTEM.
Claims of the Metric System,
Let us now turn our attention to some of the more prominent
claims of the Metric System.
First. Its base unit is a common measure or multiple of all its
derivative units. This, we have seen, is an indispensable characteristic of a system designed for universal adoption.
Second. It is constructed upon the principles of the decimal notation; its denominations, like those of our National currency, and the
orders of simple numbers, increase and decrease regularly by the
scale of ten.
But it is said that, however convenient the decimal scale may be
for scientific calculations, for some practical purposes it is not so well
adapted as the binary, quaternary, etc., and the adoption of the half
meter, the quarter meter, etc., would be an abandonment of the
system. This assertion adroitly assumes that if we adopt a system,
we are necessarily tied down to all its details, and if we vary them,
if we add to or subtract from them, we discard the system.
Let us examine this hypothesis.  In our monetary system we
employ the half dollar, the quarter dollar, etc., as subsidiary coins; and
yet who will presume to say that we have abandoned the Decimal
Currency of our fathers?  The whole civilized world uses the half,
the third, the fourth of a unit, yet who ever dreamed that the great
principles of the Arabic notation are abandoned by so doing?  Why
then should the use of the half-meter, quarter-mneter, etc., as subsidiary
measures, in business matters, be proscribed as an abandonment of
the Metric System.
Tihird. The Metler is a convenient, medium standard of measurement.  It is worthy of remark, that the length of the meter is
practically identical with the arithmetical mean of the English and
American standard yard, the archine of Russia, the old French
ell, and the pendulum  which vibrates seconds; the difference
being less than o-7U0 of an inch.  Whatever may be the opinion of
our opponents, taking the practical judgment of these enlightened




CLAIMS OF THE  IMETRIC SYSTEM.                 2 I
nations in connection with one of the elements of nature as our
guide, we are warranted in saying, that the meter is a convenient
medium standard of measurement.
Fourth. It commends itself by the brevity and signficance of its
nomenclature. And yet some complain "that the terms are new
and hard. That each word consists of two parts, a base and a prefix," etc. Let us analyze this objection. Is a science to be discarded because its technical terms are new and hard?  If so, what
will become of modern chemistry, mineralogy, botany, and the whole
catalogue of natural sciences?  With what consistency can the
advocates of a system embracing such terms as " avoirdupois weight,
apothecaries' weight, hundred-weight, penny-weight, hogsheads, scruples," etc., complain of the "'long-worded language" of the Metric
System?
It is -agreed by all parties that the technical terms of every
science should be simple, exact, comprehensive, and few as possible.
Let us apply this test to the metric nomenclature. To designate
the different denominations of distance, surface, capacity, and weight,
the Metric System employs twenty-eight terms only. Of these terms,
seventeen, like eagles and dimes in our decimal currency, are not
used in business calculations. Eleven zeords, then, practically constitute its whole vocabulary. Of these eleven terms, the four baseunits, the meter, dre, li'ter and gram, are primitive words. The
remaining seven are formed by prefixing to the base, certain numeral
adjectives, four of which are Greek and three Latin
We ask, then, can another nomenclature be found; nay, is it
possible to conceive of another, by which the weight and measurement of all objects, from the minutest animalcule that floats in air,
to the mightiest globe that revolves through space, can be expressed
by fewer, more simple, exact, and comprehensive terms?  Each
denomination has a distinct name, and each name a definite meaning,' "no two words express the same thing, and no two things
are signified by the same word."  With respect, then, to simplicity,
exactness, comprehensiveness, and fewness of terms, the metric
nomenclature, we venture to affirm, stands unrivaled.




22                 THE METRIC SYSTEM.
FJift. The metric nomenclature has the further recommendation
of being emphatically cosmopoalitan. A terminology borrowed from
a living language, can hardly fail to excite the prejudice of inferior
nationalities, much more that of rivals and superiors.  But the
Metric denominations being derived from the classic languages of
Greece and Rome, which have had an important instrumentality in
molding all modern tongues, and have so greatly enriched the
science and literature of all modern nations, is beyond the reach of
jealousy and criticism, and must readily secure universal favor.
Sixth. Another advantage of the Metric System is, that it is
easily learned, easily retained, and easily practiced.  Instead of
requiring months and years to become familiar with a long catalogue
of varying scales, and the practical applications of terms of double
and triple meaning, which are often forgotten in less time than is
spent in memorizing them, the pupil has to learn only I I words, 7 of
which are suggestive of their exact signification, and the system is
effectually and permanently mastered. Nay, more; as soon as the
value of the " four base-units " are fixed in the mind, the values of all
the derivative units, being formed by multiplying or dividing the base
by io, are at once apprehended.  Its denominations are reduced
from  higher to lower, and from lower to higher terms, by simply
removing the decimal point to the right or left, as in reducing our
national currency to higher or lower denominations; and all its
operations, in adding, subtracting, etc., are identical with those in
simple numbers and decimals.
Seven/t/. The system has the cordial support of the great commercial, scientific, and educational interests of the age.
The International Statistical Congress, an institution inaugurated
within the last twenty years for the purpose of collecting the facts
pertaining to the different exchangeable quantities of commerce,
both natural and industrial, at once felt the necessity of having a
common standard of comparison and common terms of weights and
measures in which to express the results of their inquiries in order
to make them  available.  This learned body of political economists and statesmen adopted the Metric System  as the standard of




CLAIMS OF THE METRIC SYSTEM.                    23
comparison, and employ its terms in recording all statistical information respecting the objects of their researches.*
The system was unanimously indorsed by the International Conference on Weights, Measures and Money, held at Paris in I867.
At this conference twenty-two different nations were represented,
among which were Great Britain, Russia, and the United States, and
among its accredited delegates were Professors Leone Levi of London, De Jacobi of St. Petersburg, F. A. P. Barnard of New York,
and many of the most eminent mathematicians and scientists of
the age.
Again, the British Association for the Advancement of Science,
and the Imperial Academy of Sciences of St. Petersburg have
repeatedly memorialized their respective governments in favor of its
adoption.
In England its adoption has been asked by more than forty chambers of commerce and boards of trade, farmers' clubs and workingmen's associations, and been advocated by such eminently scientific
and practical men as Sir Wm. Armstrong, Sir Joseph Whitworth, and
Sir Wmin. Fairbairn.
In our own country its adoption has also been recommended by
the National Academy of the United States, by the American Association for the advancement of Science, by the National Educational Association, the American Institute of Instruction, the New
York State Teachers' Association, etc., etc.  On the other hand,
it is believed that within the last twenty years not a single scientific
association in this or foreign lands, of respectable standing, has
voted against its adoption.  Is then the University Convocation,
the highest educational representative body in the Empire State,
prepared to be the first to put itself upon record in opposition to
the system?
Finally. The Metric is the most available system  of weights and
measures that has any claim to universal adoption. The commercial
and scientific movements of the nations that have recently been
* Report of Hior. Samuel B. Ruggles, Commissioner of the United States to the International Statistical Congress.




24                 THE ME TRzIC S YSTEM.
brought into juxtaposition by the electric wires, clearly indicate the
certainty that a universal, international system of metrology must and
will prevail.  Its final triumph is a mere question of time. But we
have already seen that the choice lies between the Metric and the
English systems. Which of these systems then presents the most
favorable prospects of success? Mr. Adams in his elaborate Report
on Weights and Measures, truly remarks, "If universal uniformity,
so desirable to human contemplation, be an obtainable perfection, it
is now attainable only by the adoption of the new French System of
Metrology, in all its important parts."
Scarcely seventy-five years have elapsed since the former was
inaugurated. Its early history was surrounded by many of the most
unpropitious circumstances.  For years it was opposed by the combined influence of long established habits of ignorance, bigotry, political jealousy and hate; yet its simplicity and exactness have conquered the deep rooted prejudices of one people after another, till
to-day it numbers among its followers twenty-one different countries,
and is the only legal system of more than two-thirds of all civilized
lands. Can any sane man therefore expect that all these peoples
will be ready to abandon a system so highly satisfactory to themselves, and adopt our English system, with which they are but slightly
acquainted, and whose irregularities they instinctively dread?  The
action of the British Parliament and of our own Congress seem
to have anticipated the answer. The former, in I864, and the latter,
in a866, passed laws permitting the employment of the Metric
System throughout their dominions, with the evident expectation of
its ultimate use. Indeed, it has already become the principal method
used by the British and American analytic chemists and physicists
in recording the results of their labors.
In view of these movements, every nation imbued with a spirit
of liberality and a just regard for the good of the race, must pause
before it opposes, on the narrow grounds of a personal preference
for a vernacular nomenclature, a system which, confessedly, has all
the fundamental elements of usefulness, and has already advanced
so far in its career to universal adoption.*
t Ncte 4.




SCIENTIFIC REFORMS OF THE PAST.                    25
But here we are asked   " Is the introduction of. the Metric
System into our country a possibility?"  "Can full-grown Americans
be persuaded to lay aside their old tables and learn new ones?"
"Will the minor tradesmen be induced to sell their wares by mleteers,
liters and grams?"  These questions neither surprise nor alarm  us.
They are evidently the suggestions of self-interest, or of the love of
ease which too often springs up in the minds of men on the shady
side of fifty.
Scientific Reforms of the Past,
Among human achievements during the past thousand years are
three memorable reforms, which were as radical and difficult as the
one now proposed. We allude to the Introduction of the Arabic
Notation, the Reformation of the Calendar, and the Substitution in
our own country of the Decimal for English Currency.
When the Arabic Notation was first brought to the doors of
Europe, and asked for admission, the veteran conservatives and petty
tradesmen of that age asked the same questions and interposed the
same objections.*  Nevertheless, the simplicity and comprehensiveness of the system, without prestige, or royal patronage, or compulsory legislation, swept the cumbersome modes of calculation of
previous ages into oblivion, and at length secured universal use.
So thought and talked the nations of Christendoln when the
Reformation of the Julian Calendar was first suggested, and finally
inaugurated* by Gregory XIII, in I582.t  This reform  set forward
the Vernal Equinox from the IIth to the 21st of March, and thereby
changed all the social, ecclesiastical, political, and scientific dates of
more than twelve hundred years. When the New Calendar was
adopted by the English Parliament, in 1752, the excitement was so
intense, it is said the people ran after the carriages of the ministry
shouting, "Give us back our i i clays." Nevertheless, so great was
the importance to science, to social and religious institutions, of
having civil dates coincide from  age to age with the return of the
* Note 5.                                1 Note 6.




26                 THE ME TRIC SYSTEM.
several seasons of the year, that at length it won a favorable hearing
for the new calendar.  Individual and national prejudice being
overcome, one country after another wheeled into the ranks of its
supporters, until every Christian land save Russia, long since adopted
it to the exclusion of the Julian method.
So, likewise, felt many of our revolutionary fathers, when, in I786,
the Congress of the United States adopted the Decimal System of
Currency. Nevertheless, after a sharp and protracted conflict, the
old sixpences and shillings and pistareens, worn smooth by the pinchings of avarice, have been swept into the crucible and transformed
into Decimal Currency. The superiority of the Decimal over the
old State currencies, at length conquered ancestral prejudice, and
trod under-foot the selfishness of petty shopkeepers and moneychangers.  The logic of these events is without a flaw. They clearly
show the power of man to reform usages which have been intrenched
behind the strongholds of prejudice for ages.  The last of these
reforms was achieved on American soil, and affords living proof that
free-born Americans will be ready to lay aside a cumbersome, obnoxious system of metrology for a new and better one, as soon as
they see that interest and convenience require the change.
How this Change is to be Effected.
The change from our own to the Metric System is doubtless to
be accomplished, if accomplished at all, by the irresistible force of
public opinion. But how is public opinion to be enlightened and
concentrated upon this point?  We answer, by giving to the Metric
System the same facilities for being understood and practiced that
are accorded to our own. But our opponents say that "legislation
has placed the Metric System, in all respects, on the same footing
with our own," and admonish us that "this is all which its friends
have a right to ask."  It is true, Congress, in i866, passed a law
permitting the Metric System to be used throughout the United
States, but provided no means for disseminating a knowledge of it
among the people.




HOW  THE CHANGE IS TO BE EFFECTED.                 27
The Sultan of Turkey recently issued an edict permitting his
subjects to embrace and practice the Christian religion throughout
his dominions.  By parity of reasoning, then, Christianity, " in all
respects, is placed on the same footing with" Mohammedism
throughout the Ottoman Empire.
Let us see how the case stands.  From time immemorial, the
Moslem has been taught to love and obey the Koran; he inhaled its
spirit upon his mother breast; his veneration for its principles has
grown with his growth and strengthened with his strength.  Around
it cluster the influence of prestige, the traditions of many a hardfought battle in its defense, and the sacred memories of a long line
of ancestors, who sacrificed their lives in the propagation of its
dogmas. At length the devotees of Mohammed are informed that
the Bible presents a more excellent religion than the Koran, and the
Sublime Porte grants them permission to adopt it. But as yet the
masses know nothing of this new religion, except that it is a rival
code of morals, which imposes upon them new doctrines and duties,
the nature and extent of which they do not understand.
This is precisely the condition in which the Metric System is now
placed in the United States. We ask, then, does the legal permission
to use a system of metrology, of whose principles and application the
people are ignorant, place that system in all respects on the same
footing with one which for centuries has held a prominent place in
every curriculum  of study, and which every man, woman and child
in the land, from the chief magistrate down to the humblest citizen,
is compelled to use in procuring the daily necessaries of life? Is it
unreasonable, then, for the friends of metrological reform to ask that
the disadvantages, not to say disabilities, under which the Metric
System is now placed in this country, may be removed, and that all
classes of the community may become sufficiently acquainted with
the system to pronounce an intelligent judgment upon its merits.
But how are the people to be made acquainted with its principles
and applications? We answer, not by simple legislation; not by
the strong arm  of power, "vi et armis;" nor yet by mere resolutions of distinguished scholars and learned societies.  No human




28                 THE METRIC SYSTEM.
legislation nor arbitrary power can transform  ignorance into knowledge; neither can individual or associated resolutions enlighten the
public mind; consequently, however important all these instrumentalities may be in directing attention to the subject, they cannot
remove the difficulties by which it is surrounded.
The first and most important instrumentality in removing these
obstacles is the Schoo/-room. Let the system be introduced and carefully taught side by side with our own in all places of learning, from
the primary school to the university, and the most formidable of the
obstructions will at once be removed. We, therefore, most earnestly
commend this step to School Committees, to Boards of Education,
to Superintendents of Public Instruction, and to all Corporate
Bodies whose province it is to direct the studies of children and
youth.
Another important method of disseminating a knowledge of the
system is, to discuss its claims in Lyceums, Atheneums, and other
associations for mutual improvement.
In the next place, let all quantities of domestic and foreign goods
upon which excise or import duties are levied, and all the legal
weights of matter allowed to be transmitted through the Post-office
Department, with all medical prescriptions and recipes of druggists,
be expressed, both in the denominations of our own and the Metric
System. Again, let all documents issued by the Bureau of Statistics, and the different State Departments which refer to exchangeable
quantities, be expressed both in Metric and English denominations.
Last, but not least, let the co-operation of the press be invoked
by the friends of reform. In the dissemination of knowledge, and
the formation of public opinion, the power of the press is proverbial;
I had almost said omnipotent. This stupendous power, we need not
say, is ever ready to lend its services to the advancement of knowledge and the cause of humanity.
Let all these moral forces be secured, and the difficulties which
now surround the system will disappear, and the people be prepared
to appreciate its merits.  The favorable tide of public opinion,
formed at the well-springs of education, will soon roll through the




HOIW  THE CHIANGE IS TO BE EFFECTED.               29
land with irresistible force. Seeing its great simplicity, its comprehensiveness, and its superiority over the present cumbersome system,
all classes of the business community will readily adopt it, and the
change be peaceably consummated.
We have now glanced at the leading features of the two rival
systems of weights and measures, and the means by which we expect
to see the final triumph of the Metric over our own. Viewed fromn this
stand-point, it is not too much to say, that the system we advocate
possesses the essential elements of simplicity, comprehensiveness,
and universality; that its general adoption would cause civilization
and commerce, by a single leap, to spring forward half a cenlury.
If these views are correct, it follows that of all the great problems
which now engross the attention of the world, few are more important and far-reaching than the unification of weights and measures.
It is a problem, to the solution of which, every nation on the globe
is bound to contribute according to its ability, and in which all classes
of society, from the rudest to the most refined, have a common
interest.
Our country was the first to inaugurate a system of decimal currency, which won general admiration. Though we cannot be first in
extending this principle to weights and measures, Heaven forbid that
we should oppose its application to them.  Such a course would
argue demoralization of intellect, and bring lasting reproach upon
our national character.
But we leave the subject with the guardians of science and those
who minister at the altars of education, with the fullest confidence
that its intrinsic merits are destined to win for it universal favor.
In the prophetic words of the venerated John Quincy Adams, "If
man upon earth be an improvable being, if that universal peace
which was the object of a Savior's mission, and which is the desire
of the philosopher, the longing of the philanthropist, and the trembling hope of the Christian, is a blessing to which the futurity of
mortal man has a claim  of more than mortal promise, then this
system of common instruments to accomplish all the changes of
social and friendly commerce will furnish the links of sympathy




30                  THE ME TRIC S1YSTEM.
between the inhabitants of the most distant regions; the Meter will
surround the globe in USE as well as in multiplied extension, and one
language of weights and measures will be spoken from the equator
to the poles."
In this cursory view of the subject, we have endeavored to show
the importance of metrological reform, the defects of our own system,
the advantages of the metric, and the means by which a universal
system may be secured. The conclusions we have reached may be
summed up in the following resolutions:
Whereas, The commercial, diplomatic, and scientific intercourse
between different nations is widely extended and rapidly increasing;
and whereas, international intercourse, heretofore seriously impeded
by the irregularities and imperfections of our own and other systems
of weights and measures, would be greatly facilitated by a common
system, in which all quantities of exchangeable commodities, scientific experiments and statistical information might be expressed;
therefore,
Resolved, That in the judgment of this convention, effectual
measures should at once be taken by Governments, by the friends
of commerce and of science, to establish a uniform system of metrology for the use of the civilized world.
Resolved, That in order to be acceptable to the great family of
nations and fulfill the great objects of its mission, said system should
be founded upon an invariable standard and the decimal notation,
that its base-units and derivative-units should be commensurable
with each other, and be expressed in simple, concise terms.
And whereas, The Metric System, by common admission, "combines these elements in a higher degree than any other system
reached;" and whereas, this system has already been adopted by so
many enlightened nations; therefore,
Resolved, That we earnestly recommend its substitution for our
own system, as soon as the people can be prepared for the change.
Resolved, That the quickest and best way to familiarize the people with its principles and applications, is to teach them in all our
public and private schools, and, in connection with the present
system, to begin to practice them in ordinary traffic, in competitive
examinations for the civil service, in the requirements for entering
college, scientific schools, the naval and military academies, etc.




NOTES.
NOTE I.-THE  PENDULUM  (p. I2).
Science is indebted to Galileo for the discovery of the great law of the
pendulum, viz: the isoclronism of its vibrations. His attention was attracted
to the subject by the swinging of a lamp suspended from the ceiling of
a church, and he applied the principle to the measurement of short intervals
of time, in astronomical observations, by counting the vibrations. Huygens
first demonstrated the relation between the length of the pendulum and the
time of its vibrations, and connected it with clock-work. But in order to
become available in measuring time, determining the figure of the earth, the
force of gravity, or as a standard measure, its length, that is, the distance between the point of suspension and the center of oscillation, must be ascertained with exact precision. This problem involved many practical difficulties. The method in general was to suspend an experimental pendulum from
a delicate point, and placing it before a good clock vibrating seconds of mean
time, count the vibrations by the method of coincidences: that is, by starting
both in the same direction, and observing the lapse of time before one of
them gains or loses exactly two vibrations. The time of vibration being thus
determined, the distance from the point of suspension was measured by a
scale, and the proper corrections for the position of the center of oscillation
were applied.
Borda, near the close of the last century, undertook a series of experiments
with a view of making the pendulum the basis of a system of metrology,
but this was afterwards abandoned, and an arc of a meridian adopted. Ilis
pendulum consisted of a slender iron wire about I3 feet long, terminated by
a ball of platinum about Il. inch in diameter, the other end being attached to
a point on a knife-edge suspension.  The vibrations were performed in 2
seconds, and continued for I2 hours, the number being reckoned from the
coincidences with the pendulum of an astronomical clock.
Among English scholars who have made the study of the pendulum a
specialty, are Capt. Henry Kater and Francis Bailey. The convertible pendulum constructed by Capt. Kater on the principle first demonstrated by
Huygens, viz.: that the point of suspension and the center of oscillation are
interchangeable, seemed to promise entire accuracy, and was urged by the
inventor as a standard of linear measure. The Astronomer Royal, in I8i6,
was directed to take suitable measures for ascertaining the length of the
pendulum vibrating seconds, and for comparing the French and English
standards with each other. At his request, a committee of nine were appointed to co-operate with him.  Before any legislation took place with
reference to the results of their experiments, the subject, in I818, was
submitted to a new commission consisting of Sir Joseph Banks, Sir George




32                           NVO TES.
Clark, Mr. Davies Gilbert, Dr. WV. Hyde WVollaston, Dr. Thomas Young, and
Capt. Henry Kater.
This commission, in their final report, recommended the adoption of the
parliamentary yard made by Bird in I760, as the standard, which, according
to their last correction, bears the proportion of 36 to 39.1393 inches to a
pendulum vibrating seconds under the conditions therein stated, the experiments beingmade at the temperature of 62~ Fahrenheit.
Parliament, in 1824, passed a bill declaring the yard of I76o, by Bird, to
be the Unit of Length, and called it the "Imperial Standard Yard," which,
compared with a pendulum vibrating seconds of meantime in a vacuum, in
the latitude of London, at the level of the sea, is in proportion of 36 to 39.1393
inches. It was also enacted, "That, if at any time hereafter, the said Imperial
standard yard shall be lost, or destroyed, defaced or otherwise injured, it shall
be restored by making a new standard yard, bearing the same proportion to
such pendulum aforesaid, as the said Imperial standard yard bears to such
pendulum." The new Imperial Measures went into use Jan. I, 1826; and
were made compulsory from Jan. I, I836.
It is worthy of notice, that since the standard yard was destroyed by the
burning of the Houses of Parliament in 1834, a new standard yard, the one
now in use, has been formed, not by resorting to the pendulum as a standard,
but by a comparison of all the most reliable scales which could be collected.
The commission consisting of Airy, Bailey, Herschel, Lubbock, and Sheepshanks, appointed in 1838, to restore the lost standards, reported in I84I,
that since the act of I824, several elements of reduction of the pendulum
experiments had been found to be doubtful or erroneous, etc.; that with the
aid of the Astronomical Society scale, and a few other highly accurate copies,
the standard could be restored without sensible error. The new standards
were legalized in July, I855.
NOTE II.-ORIGIN  OF THE METRIC  SYSTEM  (p. I5).
The origin of the Metric System is due to France. In I79o, Talleyrand
circulated among the members of the Constituent Assembly a proposition to
reform the heterogeneous system of weights and measures then in vogue, or
rather to form a new one, founded upon a universal standard. This proposition was adopted by the Assembly, and on the 22d of August, I790, sanctioned
by Louis XVI. At the request of the Assembly, the King wrote to the King
of Great Britain, inviting the formation of a joint commission of members
of the "Royal Society" and the "Academy of Sciences," to determine the
standard, the object being to secure the co-operation of England and of other
leading nations of Europe.
The political difficulties which soon sprang up between these two nations
prevented the acceptance of this beneficent proposition. Spain, Italy, the
Netherlands, Denmark, and Switzerland were represented in the Academy of
Sciences, and took part in the proceedings. By a decree of the Assembly, a
committee of five, Borda, Lagrange, Laplace, Monge, and Condorcet, were
appointed to report to that body a standard, with the principles appropriate to
the accomplishment of the object.
Three objects were suggested as suitable natural standards of length, viz.:




.NO TES.                               33
a quarter of the terrestrial meridian, a quarter of the earth's equator, and the
pendulum vibrating seconds.
After careful deliberation the committee selected a quarter of the meridian
as the standard of length, and proposed that its ten-millionth part should be
taken as the unit of linear measure; that as a second standard of comparison
with it, the pendzlnzm vibrating seconds at the 45th degree of latitude, should
be assumed; and that the weight of distilled water at the point of freezing
measured by a cubical vessel in decimal proportion to the linear standard
should determine the standard of weights, and vessels of capacity. This
report was adopted by the Assembly. The most difficult part of the great
problem was to determine by trigonometrical measurement, the length of the
meridian extending from Dunkirk to Barcelona, a distance of about Io
degrees, or nearly 700 miles. This work was committed to Mlechain and
Delambre. Subsequently the prolongation of this meridian was measured by
Biot and Arago as far as the Island of Formentara. From these measurements, in connection with the former measurement of the arc of a meridian
in Peru, the length of the quadrant of a meridian was deduced. Dividing
this distance by Io,ooo,ooo, one of the equal parts was called a Meter and
adopted as the Unit of length.
The other great point to be determined was the  znit of weight, which
should bear a known relation to the unit of length, already adopted. The
determination of this unit was assigned to Lefevre Gineau and Fabbroni.
They selected a standard made of platinum, called a kilogram, which should
represent the weight of a cubic decimeter of distilled water in a vacuum, at
its maximum density. The thousandth part of this platinum standard was
called a Graim, and adopted as the unit of weight. Now, as there are Iooo
cubic centimeters in a cubic decimeter, it follows that the gram is the weight
of a cubic centimeter of distilled water in a vacuum, at its maximum density.
But the Assembly did not wait for the completion of this measurement before
it gave the system a legal existence, deducing the meter from the length of a
degree of latitude as formerly determined. The system, therefore, was provisionally established, Aug. Ist, I793; and the nomenclature by which its various
denominations are now distinguished, was adopted April 7th, I795.
The commissions charged with these important operations, commenced
their labors, under the auspices of the government, March 3Ist, I791, but,
owing to the causes mentioned, it was not until the 22d of June, I799, that the
meter and kilogram were finally determined as units of length and weight.
On that occasion Laplace, the President of the National Institute, presented
the results of their labors to the two branches of the National Assembly,
with a standard meter of platinum made by Lanoir, and a kilogram of the
same metal made by Fortin. The new system was approved by the government, and ordered to be used as the legal standards after Nov. 2d, I8oI.
NOTE III.-DIVISIONS OF THE CIRCLE (p. i9).
It is often asked, why is not the Metric system applied to circular measure?
We answer: First. Because the circle is independent of all exchangeable
quantities; therefore it presents no obstacles to commercial intercourse
between different nations. Second. The divisions of the circle are now the




34                          NOTES.
same in all civilized lands; and as uniformity is the chief object of metrological
reform, it is deemed inexpedient to change them.
NOTE IV.-PROGRESS OF THE METRIC  SYSTEM  (p. 24).
The following countries have adopted the Metric System unconditionally:
France, the French colonies, Holland, the Dutch colonies, Belgium, Spain,
the Spanish colonies, Portugal, Italy, Germany, Greece, Roumania, British
India, Mexico, New Grenada, Ecuador, Peru, Brazil, Uruguay, Argentine
Confederation, and Chili, the total population of which is 336,4I9,598.
Wurtemburg, Bavaria, Baden, Hesse, Switzerland, Denmark, Austria and
Turkey, whose population is 84,039,209, have adopted metric values, and may
be regarded as committed to its future use. Add to these Great Britain and
the United States, with a population of over 70,000,000, whose laws permit
its use, and we have a grand total of more than 490,000,000.
NOTE V.-ORIGIN  OF THE ARABIC NOTATION (p. 25).
We have no positive knowledge to whom the invention of the Arabic
Notation is due. Not even the date nor the place of its origin, is known.
The Arabians evidently became acquainted with it in the East, with which
they had extended intercourse from the 9th to the I2th century. They called
it Zindasi, which is an indication that they obtained it in India. Whether it
was invented by the Hindoo philosophers, or borrowed from their neighbors,
are unsettled theories. The prevailing opinion favors the former. But, however this may be, it is agreed that the Arabians communicated the new system to their flourishing Institutions of learning in Spain, and are justly entitled
to the honor of introducing it into Europe.
This is commonly supposed to have taken place about the commencement
of the Ioth century. Some, however, place it as late as the middle of the I3th
century. Assuming the latter as the correct date, more than three hundred
years elapsed before it was generally used in business calculations among the
nations of Europe. It had to contend not only with ignorance and selfinterest, with the stolid inertia of so-called conservatism, and the strong
attachment to the Roman System, which had long been in common use, but
also with the deep-rooted prejudices of Christian nations, who at first
regarded the decimal notation as one of the diabolical artifices, which the
Mohammedans had obtained from the Powers of Darkness.
So strong was this prejudice against everything connected with the
"Prophet," that the famous Roger Bacon, who visited the Saracen Institutions
of Spain to perfect himself in Mathematics and Philosophy, was sharply persecuted by his countrymen for his rashness, and thrown into prison, on the
charge of " practicing the arts of magic."
The Astronomers were the first to appreciate its importance, and according to Voscius, began to use it about the year I250. The great question was,
how to disseminate it among the people in Christian lands. This was at
length accomplished, not by compulsory legislation, nor by force of arms, but
by philosophical strategy. The Astronomers of France or Germany composed Almanacs, using the decimal notation, and incorporated in them a brief
explanation of the system. These almanacs were sent to the various monas



NO TES.                               35
teries and religious houses in Europe, and were purchased with great
avidity. In order to consult them respecting the festivals, seed-time and
harvest, the weather, etc., the people were obliged to learn the Arabic characters, and the mode of calculating by them. The plan was triumphant. The
great simplicity of the new system won the admiration of all, and began to
supplant the old method. It is worthy of remark that then, as now, there
were those of liberal culture, whose conservatism led them to stand aloof
from innovations. Even some of the English Universities, from which better
things might have been hoped, adhered to the Roman numerals in keeping
their college accounts, till the I6th century; and in the parish registers of the
South, the Arabic characters were not adopted before the year I6oo.
NOTE VI.-THE  GREGORIAN  CALENDAR  (p. 25).
The civil calendar of the United States and of modern Europe, was borrowed from the Romans. Previous to the time of Julius Coesar, the Roman
calendar had been subject to great confusion. So imperfectly had it been
regulated through the ignorance or vice of the Pontiffs, to whose charge it
was committed, that the Spring months were carried back into Winter, the
Summer into Spring, etc., the discrepancy between the calendar and the
seasons amounting to three months. To put an end to this confusion between
civil dates and the return of the seasons, Julius Cocsar abolished the former
calendar, and established a new one known as the Julian Calendar. He
fixed the length of the year at 3651 days, and through the advice of Sosigenes,
an eminent Astronomer, restored the vernal equinox to the 25th of March,
the place it occupied at the time of Numa, the second King of Rome. He
also transferred the commencement of the year which originally began with
March, as indicated by September, October, etc., to the Ist day of January,
in the year 46 B.c. To provide for the fractional part of a day, he ordered an
additional day to be given to February by reckoning the sixth of the calends
of March or the 24th day of February twice, naming it bissextus, the second
sixth. Hence, the years in which this extra day was intercallated, were
called Bissextile, and correspond to our Leap Year.
In distributing the days among the several months, he assigned 3I days
to the odd months, the first, third, fifth, etc., and 30 days to each of the even
months excepting February, which in common years had only 29 days. This
arrangement was alike sensible and convenient to be remembered. But it
was soon disturbed by Augustus, whose vanity led him to entail his name
upon the calendar by calling the sixth month August. And in order to make
this month equal to July, which was named after his predecessor, a day was
taken from February and added to it. This brought three months, July,
August and September together, each of which had 3I days. To avoid this
coincidence, September and November were each reduced to 30 days; October and December were increased to 3I days. The error of the Julian Calender consisted in making the civil year 365- days, which exceeded a mean
solar year II minutes Io.3 seconds. By this error, the Vernal Equinox, which
from the reign of Numa had been the great landmark for regulating civil
time, gradually receded towards the beginning of the year, until in 325, when
the council of Nice was held, it corresponded with the 2Ist of March.




36                            NOTES.
As the means of Astronomical Calculations improved, this error became
better established. In 730 the celebrated Bede discovered that the precession
of the Equinoxes since the meeting of the council of Nice, amounted to
about three days; and Roger Bacon, who died in 1292, in his "Treatise De
Reformatione Calendarii," showed that the error amounted to seven or eight
days. This discrepancy continued to increase till, in 1582, Gregory XIII
established the new Calendar known as the " Gregorian Calendar," or " New
Style." The error then amounted to Io days, and the Vernal Equinox corresponded with the IIth of March.
In order to restore the commencement of the year to the same place in
the seasons which it occupied at the time of the council of Nice, he ordered
the 5th day of October to be reckoned the I5th of that month. This change
restored the Vernal Equinox to the 2Ist of March, and the movable feasts of
the church to the times fixed by the council of Nice, the two prominent objective points in the reformation of the Calendar. But it had been discovered
that the error of the Julian Calendar was only three days in four hundred
years, and consequently there should be only ninety-seven leap years in four
centuries. To remedy this error, only one centennial year in every four was
regarded as a leap year. Hence, the Gregorian rule for intercallation is this:
Every year the number of which is divisible by 4 without a remainder, is
a leap year, except the centennial years, which are leap years only when
divisible by 400 without a remainder. According to this rule the discrepancy
between the Julian Calendar and solar time, which in 1582 was Io days,
continued the same till 1700; but 1700 being a leap year in the former, and a
common year in the latter, the error during the I8th century was 11 days.
Again, I8oo being a common year, during the present century it is 12 days;
and from 1900 to 2I00 it will be 13 days.
But by more refined instruments of observation and elaborate calculations, eminent modern Astronomers have shown that the civil year with the
corrections of the Gregorian rule, exceeds the true solar year by 22.38
seconds, which amount to one day in 3866 years, or in round numbers one
day in 4000 years. To correct this error, it has been proposed to make the
year 4000 and all its multiples, 8000, 1200, etc., common years. With this
last correction, the Vernal Equinox or commencement of the year, would not
vary more than one day in Ioo,ooo years.
The Gregorian Calendar was generally adopted by the Catholic countries
of Europe soon after its promulgation; but Denmark and most of the Protestant states of Germany opposed its introduction with great pertinacity till
I700, and in some instances till nearly i8oo. England resisted its introduction till I752, a period of nearly 200 years. Amidst great popular excitement,
the old Calendar was then abolished by Act of Parliament, and the new one
adopted by dropping II days, and calling the 3d of September the I4th.
Russia still adheres to the Julian Calendar.  Dates reckoned by the
Julian Calendar are called Old Style; those reckoned by the Gregorian, New
Style. To change a date from 0. S. to N. S. at the present time, 12 days must
be added to the former. Thus, Jan. Ist, I874, 0. S., is Jan. I3th, N. S.




NEW GRADED S E RIES
OF
ARITHMETIC S.
By JAMES B. THOMSON, LL.D.
COMPLETE IN THREE BOOKS,
I.-NXew  liienttal Arithnmetic, I44 pp., i6mo.. Price $o.35
II.-New Rudiments of Airithmetic, 224 pp., I6mo..5~
III.-New Practical Arithmetic, 384 pp., I2mo......oo
Since the issue of the author's former Series of Arithmetics, of
which MILLIONS HAVE BEEN SOLD, great changes have taken place
in the commercial world.   These changes necessarily demand
changes in Text-books.  To meet this demand  "T ie Netw
Graded  Series"  was undertaken, at the earnest request of
many practical Educators.
The Publishers respectfully invite the attention of Teachers and
School Officers to the plan and characteristics of the New Series.
I. GENERAL PLAN.
I. The Series consists of three Books-the cbject being
CONVENIENCE and ECONOMY.
2. Each Book  is complete in itself; hence, each can be used
independently, or in connection with any series.
3. The Definitions and Rules COMMON to the three books,
are expressed in the same lanzguage.
4. The respective Books abound in Examzples for Practice;
but no two examples in the different books are alike.
5. The Obsolete and Obsolescent in the Tables of Weights
and Measures, the old State Currencies, &c., are eliminated.




2
6. Sinmplicity, Brevity, and Comprehensiveness in
the Definitions and Rules, have been carefully studied.
7. The Series is designed to unite thorough discipline with
a practical business education, the raxcimuin of attainments
with the  tinimumtniu     of time and expense.
8. Finally, the Great Objective Point has been to embody
the best of the improved methods of treating each topic embraced
in the series.
II. DISTINCTIVE FEATURES.
I. In the Newz   Miental, the elementary ideas of liinmbers are
developed by the aid of counters, or sensible objects, which the pupil
can both see and handle.
2. The Steps from counting to the simple combinations of numbers in solving concrete examples, are carefully graded.
3. The Pupil is treated, not as a passive  Recipient, but as
an active Agent, capable of thinking and doing.
4. His In~ventiveness is called into frequent exercise, by the
use of counters, the slate, etc., in illustrating for himself, the principles involved.
5. The Method of Self-help  is extensively employed to
cultivate an interest in the study.  Children delight in having
something to do.
6. Int connections with the Mental Exercises, he is taught to
express numbers by figures, and perform  the more simple Slate
exercises in adding, subtracting, etc.
I. The NTew Rudiments or Second Book, combines Mental
with WFritten Arithmetic, in alternate exercises.
2. The Eltementary Prin7ciples of the science are developed by Oral Examples.
3. The pupil is taught to apply  these principles to the
solution of problems requiring the use of the slate.




3
4. He is then led  to generalize them to put the steps of
the solution into a concise Rule.
5. Acccuracy and Rapidity in the combination of numbers
are secured by appropriate practice.
6. "A thoroughl  mastery  of this little book will prepare
the learner for most of the problems arising in common life."(ILL. SCHOOLMASTER.)
I. The New  Practical or Third and last Book, is literally
what its title indicates -A PracticalzArithmetic.
2. The Prtinciples of  the Science  are presented in a
Series of distinct and consecutive Projositions.
3. Analysis-the "Grand Common-Sense Rule," with its
various applications, is a prominent feature throughout the book.
4. No principte is used in the explanation of another, until
it has itself been explained or demonstrated.
5. The Rules are deduced from the analysis of examples, and
are so constructed as to suggest the principles upon which they are
based.
6. The Whys and Wherefores are distinctly given and illustrated.
7. The Arrangement of Subjects is in accordance with
the natural order of the science. Hence,
8. The Commto~n Applications of Surface and Solid
Mllieasure to the farm, the garden, artificer's work, etc., are placed
immediately after Reduction.
9. Percentage anad its Application, to  Commission,
Profit and Loss, Interest, Banking, Stock Investments, U. S. Bonds,
Exchange, etc., have received particular attention.
io. The Worlk contains much valuable information relative
to business forms, and matters of science, not found in other books
of the kind.
II. It is a Coim^plete Arithmnetic- sufficiently thorough
and extensive- for Grammar Schools, High Schools, and Academies.




RECOMM.ENDATIONS.
From F. A. P. BAERINARD, LL.D,, Presidelnt of Columbice College, Ni. Y.
You have shown the relations of numbers to many matters of commonlife interest not usually noticed in elementary treatises on Arithmetic; and
have done this in such a manner as fully to justify the title you have given to
your work, of " Practical." The instructions in regard to the estimation of
rates per cent, and to find the quantities corresponding to a given rate
when the base is given, are clear, and in manner of presentation quite original. In the treatment of involution and evolution, you happily convey the
geometrical notions corresponding to the arithmetical operations.   * X'
From Professor J. IT. TVl_ Ai~ 12~ [2 GE, A,.13-., Columnbia College, 2New Yo]ork.
I am much pleased with your " New Practical Arithmetic." The subject
is developed consecutively and logically. The analysis of examples and the
generalization of the results in the deduction of rules, is calculated to fix the
attention of a learner, and to form a habit of correct reasoning.  * 
You have given much information pertaining to business forms and matters of science, and have thus adapted your work to the wants of every-day
life among all classes of persons.
From  FI IFOWARD  CIOSBY, D. D., Chancellor of the N. Y. U. Iiversity.
I have examined Dr. Thomson's " New Practical Arithmetic" with enjoyment of its lucid method and attractive style.
Dr. Thomson's name is sufficient guarantee that the work is well done,
the public having known him many years as a thorough, painstakis-taking, and
sound scholar. The puzzling subjects of the " greatest common divisor"
and the " least common multiple," " involution" and " evolution" are made
clear and attractive. I know of no other Arithmetic which I prefer.
The Fraznklin figures are used in the work, and add much to its beauty.
Firom l Rev. TH01fMAS W. HUJiEiS, D. D., Chancello'r of East Tent,. Uhnirversity, Kn~oxville.
The Series is evidently the work of a mind discriminating and thoroughly
informed upon the subject; and besides its general excellence, it has meritorious features which specially adapt it to use in our schools.
From Prof. E. W. EVANSA  Corlnell University, Ithaca, NX. y.
I am favorably impressed with it (The Practical); indeed, I should expect
to be with any book of yours.
Fromn G(EO. TV. CLAHiE, Ph.D., President Ml]lounit Washingtot n Collegiate
Institutte, New Yo7rk City.
Having used for a year Thomson's " New Graded Arithmetics," it gives
me pleasure to say that they have been a source of unusual profit to my
pupils, and of great " aid and comfort" to my teachers.
From Prof. L. Jr. JOBHlNSON, A.M., Prin. State Normal School, N.,J.
Upon careful examination of Thomson's " New Arithmetics," we decided
to use them in our Normal and Model Schools, as the best suited to our
wants. They have given great satisfaction to all parties.




RE COMiiE NDA TIONS..From G. W. SAM1SON  D.D., President Rutger's Feimale College, Fifth
A4venue, New York City.
The Arithmetics of Dr. Thomson were selected for use in this College
last Autumn, because they were regarded as superior to any before used.
They have given entire satisfaction to both teachers and patrons.
From PREINCIPALS of:Male Grammar Schools, New York City.
The undersigned have examined Thomson's "New Arithmetics," and
take pleasure in saying that we consider them a decided improvement on
his former series, and admirably adapted to the wants of our pupils. *  * *
(Signed by forty-five Principals.)
From PRINCIPALS of eiemale Grammar Schools, New York City.
The undersigned have examined Prof. Thomson's " New Arithmetics,"
and take much pleasure in saying that we regard them as works of great
merit, and admirably adapted to the wants of our schools.   *'   *
They are, withal, eminently practical. The amount of information pertaining to business matters found in them is an important consideration in the
education of girls as well as boys, and cannot fail to commend them to the
attention of all practical educators. (Signed by forty-three Principals.)
lFrom Prof. IL IL. 2M1.ARTIN, A.M., Supt. State Mlodel School, N. J.
Thomson's " New Graded Arithmetics" are now used in the New Jersey
State Model School.
In clearness and brevity of rules, accuracy of definition, simple and practical analysis, rejection of obsolete matter, close adaptation to actual business
usages, we consider them decidedly superior.
Fromn Prof. JOB~N  BROCKLESBY, Trinity College, YHartford, Conn.
"The Practical" covers all the ground required, and within a reasonable
number of pages. I think it well adapted for the purpose intended.
Fi'om C. C. STIMfE TS, A.M., Prof. 117th. State Normal School, N. dr.
Thomson's " New Graded Series of Arithmetics," especially the "Practical," I take pleasure in heartily commending.
I am much pleased by the conciseness to which he has arrived in working out the completeness of the subject. Also, by the practical applications and
the introduction of various new topics, bringing the work rep to the times.
-From  Prof. HT. B. SPRAGUE, Prim. of Adelphi Academny, Brooklyn.
I am greatly pleased with the " New Practical." It is difficult to see how
it could be much improved.
From cJ. F. STREET, A.1M., Prin. Farnumn? Preparatory State Normal Sch.,
Beverly, N. J.
We have adopted "Thomson's New Arithmetics" because we like them
better than any others.
lFrom Hon. J. B. BJAMliES, Supt. of Public Instructiont, Newark, Ohio.
I have examined Thomson's work on Arithmetic (" New Practical "), and
have no hesitancy in pronouncing it good.




RE COMlMEN XDA TIONS.
From Hon. IEYNEJY KLIDDLE, AM.1, A.. Sperinztendent of Public Instructio0n, City of' New  ork.
I have examined the new Series of Arithmetics by James B. Thomson,
LL.D., and am much pleased with the improvements introduced therein.
These books have been adopted by the Board of Public Instruction of the
City of New York, and I have no doubt they will prove a valuable addition
to the text-book list.
The above expresses very fully and clearly my own views of the practical
value of Prof. Thomson's New Series of Arithmetics.
T. P. F. HAlRRISO, A.3l~., Asst. Supt. and( Prof. of M1Iethods of Teachiny.
From J. IK. PAPYNE, A.M., Prof. Math. -E. Tenn. Uniiversity, Knoxville.
I find so many admirable points, that I will not attempt to enumerate. I
consider them superior to any of their competitors. They will win on their
merits. I shall recommend their adoption in our city schools. Your books
will do much to facilitate the progress of pupils everywhere-especially in
the common schools, where the teachers can afford but little help to the
learner beyond that contained in the text.   *   *   *
-From the PIRINVCIPALS of Grammar Schools, City of Brooklyn.
The undersigned have examined Thomson's "New Graded Series," and
are free to say that they are much pleased with the plan and its execution.
The author has evidently " struck the /Key-note," combining the principles
of numbers with their practical application to business.
The definitions and rules are clear and concise, the examples fresh and
abundant, the " whys and wherefores " clearly stated, the works embody the
very best of the improved methods of treating the subjects, and are fully up
to the times. (Signed by thirty-two Principals.)
-From Prof. TV. B. D.  IGHT, A.M., State 1Normal School, Conn.
We regard this as one of the most valuable and faultless of the recent
contributions to arithmetical school literature.  X *  *  In all departments
of the study, constant reference is made to the actual processes employed in
business transactions; and many important topics not usually found in arithmetics, are introduced..From J. H]. FAN1NING, A.l-r., Asst. Supt., City of New York.
Prof. Thomson's " New Series of Arithmetics" contain many improvements over other works of the kind, which, in my judgment, add greatly to
their value as text-books.
[rom W. HASBROUTCK, A,.1r., Ph. D., Prin. Hasbrouck Ilzstitute,
Jersey City, N. J.
I have used for more than a year Thomson's " New Practical Arithmetic"
in all the departments of my school, having upwards of one hundred and
fifty pupils in Arithmetic. All of my teachers are much pleased with the
work. We like its arrangement of subjects, the conciseness and clearness
of its rules, its variety of examples, and their practical and commercial character. The Analysis of Examples is most excellent, and I can most unreservedly recommend the book to all teachers and officers of schools.




RECOMIMENDA TIONS.
Fj'ron IRA MAZYHEW, A.iM., President of ilayhew's Business College,
Detroit, llich.
Thomson's Arithmetics, as formerly published, were excellent. I consider his "New Graded Series" an improvement on the old. The " New
Practical" will hereafter be used as the text-book in this department of the
Mayhew Business College.
Prom J. E. SEAMAtN, A.M1., Prof. Mlathematics, Central high School,
New Orleans.
The simplicity and clearness with which the principles of the Science are
presented in "The New Practical," the progressive character of the work,
and the great variety and adaptability of the examples to business calculations, commend it as a model book for Grammar Schools.
From IWil. W. PAYNYE A.lMl., Professor of M~ath., Carlton College, iffinr.
It (The New Practical) contains just enough matter in extent and
variety, is sharp, clear, and terse in principle and illustration, and carries on
the face of its pages marks of practical business life which pupils cannot
imbibe too early.
From  Prof. Mi[. L. BRO WN, A.M11., Prin. Young Ladies Institute,
tAuburn, N. Y.
I desire to express my unqualified approval of it, "The New Practical,"
and my desire that it shall be introduced into the schools of this vicinity.
From T. C. i3MENDERITALL, A.M., Professolr of Physics and Mfechanics,
Ohio'Agr4icultural antl Mlechanical College.
I have examined with great pleasure " Thomson's New Graded Series."
The primary book contains many useful and ingenious suggestions to the
teacher, in regard to the gradual development of the idea of number, while
the " Practical" is comprehensive and complete.
From TWMi. F. PITELgPS, A.M., Prin. State lormal School, Mlinn.
I have looked over your books with care, and am pleased to note that
you have kept pace with the march of improvement in methods of instruction,
and have adapted your books to the most advanced requirements of modern
teaching. * * *  You have the whole matter in a nut-shell.
From orl.    E. fYER, A.1ML., Prlin. Auburn, HTigh School, N. Y.
I am especially pleased with the practical points of Thomson's " New
Practical Arithmetic."    *  
Fromt, Prof. WAISHtINGTON CIHOATE, Adelphi Alcademyl, Brooklyn.
For the omission of much that is unimportant, and the introduction of
new rules, and improved methods of instruction; for a complete analysis of
the various operations, and a logical arrangement of topics, I commend
Thomson's works as superior to all others now in use.:     *
I most heartily concur with Prof. Choate in regard to Dr. Thomson's
Arithmetics.          (Signed)       J. W. CHANDLER, list. in A4ith.




RE COMfENXDA TIONS.
From J. ESTERIBROOKI A. Tr., Prin. Mlich. State Normal School.
I have just given Thomson's New Series of Arithmetics a somewhat
careful examination. I used his Old Series many years with great satisfaction; and I am delighted with the new.  They are not excelled by any I
have examined, in the following important subjects:
i. In conciseness and comprehensiveness of definitions. 2. In the order
and arrangement of topics. 3. In clear and logical analysis of examples.
4. In the copiousness, variety, and practical nature of the examples. I
heartily commend these books to the consideration of friends of education.
P'Frowm T V.. L. DICKINSON, Esq., City Supt. of Schools, TJe.sey City and
Hudson CoutLty, A. J.
In fullness and accuracy of definitions, in lucidness of explanation and
conciseness of expression, the "New Practical Arithmetic" exceeds all
Arithmetics I have yet seen. The New Mental and Rudiments are fit precursors of the " New Practical."
From Rev. J. A. lPEWIlING, Prin. Columbia Classical Institute, Penn.
Thomson's " New Series of Arithmetics" has been used in my school
during the past year with entire satisfaction.
From T. If. FWRZIGHT, A.-~., Prin. IMIunroe Col. Institute, NV Y.
I have carefully examined Thomson's "New Arithmetics," and think
they stand among the first in use.
-From the PRINCIPALS of the Grammar Schools, Auburn, N. Y.
We have used Prof. Thomson's " New Practical Arithmetic" the past year
with much satisfaction. It is at once clear and complete.
From the S-UPERINTIENDENT and P3RINCIPALS of the Grammar
Schools, P'aterson, iN. J.
The undersigned have examined Prof. Thomson's " New Arithmetics,"
and take pleasure in saying that they consider them works of unusual merit.
From A. laIOlRSE, A.lM., Prin. N. School, Hartford, Couttn.
It affords me pleasure to say, that in my judgment, Thomson's "New
Series of Arithmetics" in all the particulars that constitute superior textbooks, is " equalled by few, and excelled by none."
Frorm B. G. AM7,ES, Esq., Supt. of Schools, Cumnberland Co., N. rJ.
Thomson's " New Arithmetics " I like very much. I most heartily endorse them, and shall be glad to see them introduced into the schools of
our county.
Frnom the S UPERINTENDENlT and PRINCIPALS of the Grammar Schools,
Hoboken, N. J.
The undersigned have carefully examined Thomson's "New Graded
Series of Arithmetics." We think it better adapted to the wants of our
schools than any other series with which we are acquainted.
Fromr Rev. J.'I. HtEALY, D.D., Chancellor of Strailghat Univ., New Orleans.
I have carefully examined "Thomson's New Graded Series of Arithmetics," and regard them the best of the kind now before the public. * * *




RECOL.ZMEzVDA TIONVS.
From Prof.. i. 1. SEYiMOIJ,' A.-l., Supt. of Schools, Blue Island, Ill.
The omissions of useless items in the Tables of Compound Numbers
should commend the book (the " New Practical ") to all Practical Teachers.
* * *  Percentage and its applications merit the approval of critics.
In conclusion, the book is philosophical in its arrangement, clear in its
definitions, truthful in its treatment of doubtful or disputed points, and very
practical in the character of its problems.
Front IRev. A. FLACK, Ph.D., Pres. of Claverack College, N. Y.
We have used with much satisfaction for the past year Thomson's " New
Rudiments of Arithmetic.":From Prof. G.. I GAGE, A.M1-., Supt. of Schools, St. Paul, iinnz.
It gives me pleasure to say that Thomson's " New Arithmetics," by their
directness, conciseness, and completeness, are worthy the careful examination of School Boards intending to make a change.
From 1L. G. i31ARSIHAI5L, A.iM1., Print. Gradeld City School, Cynthiana, Ky.
I have looked pretty thoroughly over Thomson's "New Arithmetics,"
and that too with great interest and pleasure. I am delighted with the " New
Practical" especially.
Fromn lE. IF. SNEIDMER, lEsq., Sch. Coinem. Washifngton Co.
I have carefully examined Thomson's Arithmetics, and believe them to
be superior to any others which have come under my observation.
Fronmz R. IV. GlREEVE  E.sq., Sch. Con?mm., ivifngston C0., N. Y.
The arrangement of matter, the conciseness and clearness of definitions,
and, above all, the distinctness with which the " whys and wherefores " are
set forth, makes it the most valuable text-book on the subject with which I
am acquainted.
Ftrom E. P. JACKSONY, A.Mi., Pres. Ottawa College, Canada.
Thomson's " New Practical Arithmetic" is evidently the result of long,
vigorous, and original thought. The rules and explanations are clear, sharp,
and sensible, and follow in logical order.
Front F. S. CAPE~Y, Prof. of Math., Normal Schlool, Cortland, N. Y.
I have examined and am highly pleased with Dr. Thomson's " New Series
of Arithmetics."  I have placed the "Practical" in my recitation-room as a
reference-book for students.
_Fro?'JOIHNl R. CARNEiL L, Esq., Prin. Troy Business College.
I have examined with special care the methods contained in Thomson's
"New Practical Arithmetic " for teaching the subjects of Percentage, Interest, and Equation of Payments. I believe they are more easily taught, and
may be more easily comprehended by rhe student than those contained in
any other Arithmetic with which I am acquainted.
From C. IT. RICHARIDS, A.lhr., Prin. High School, Ossgefo, Nr. Y.
I have examined Thomson's " Practical Arithmetic," and am well pleased
with it.




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Thomson's Day's Algebra.
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