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-a division which we may almost say is never required to be made. If a purchaser does not require the whole of a yard of cloth, it is almost always half a yard, or a quarter of a yard, or a third of a yard, that he asks for; not once in a hundred times is it anything else. He can have either of these without a fraction in the use of the English shilling; but in the use of the American quarter he can have only one-fifth of a yard, a portion which be never wants. In other words, the English coin gives him all the convenience that he requires, while the American, so far as the quarter of a dollar is concerned, gives him absolutely none.

As, however, innumerable instances occur in the ordinary transactions of business where commodities and prices must be halved and quartered, we are compelled to halve and quarter our denominations of coin, and the result is an endless confusion of fractions. Purchases come to six-and-a-quarter cents, and twelve-and-a-half

, and eighteen-and-three-quarters cents, where in England it is simply three-pence, six-pence, and nine-pence. The amount of it is, that the shopkeepers and their customers, in all the stores in Broadway and the Bowery, are kept in constant confusion with fractional amounts, in order that the clerks in the banks in Wall-street may have an easy time in adding up their columns.

The same difference exists between the two systems in respect to integration of numbers as in the subdivision of them. If a single article in Eng. land is, in price, two-pence, two will be four-pence-a third of the shilling; three will be six-pence--half the shilling; four will be eight-pence_twothirds of the shilling; five will be ten-pence, and six will be a shilling. Again; if the price of a single article be three-pence, it is a third of the shilling, and then two articles will be six-pence-half the shilling again; three will be nine-pence-three-quarters of the shilling; and four will be twelve-pence-the whole shilling. And if the single price be four-pence, a double price is eight-pence--two-thirds of the shilling; and a treble price twelve-pence—the whole shilling. Thus, everything goes smoothly, and

On the other hand, where the decimal ratio governs, all works wrong in such cases.

If the postage of a single letter is two cents, a double rate is four cents, a treble rate is six cents, and a quadruple rate is eight cents, neither of which numbers is an aliquot part of a dime. The half-dime will not pay exactly for any one of the letters. In same manner, if the single rate is three cents, å double rate is six, still avoiding the half-dime; the treble is nine, and the quadruple is twelve. Not one in either series can be paid for with any one coin of the Federal currency, whereas, in the English system, every one of both series can be paid for with a single coin as soon as the amount becomes large enough to reach the lower limit of the silver coinage.

There is another view of the subject which will put the difference between the two systems in a clear light, and that is a comparison of the proportional value of the coins in relation to each other. In the English system erery small coin will be found to be some simple aliquot part of the larger ones; thusProportional value.

Proportional value Sovereign is..... Pound. Sixpence...

Shilling Half sovereign.

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Pound. Fourpence

} Shilling. Pound. Penny

1-12 Shilling, Pound. Halfpenny.

Penny. Shilling.. 1-20 Pound. Farthing

Pendy.

comes out even,

English coins.

English coins.

Orown
Half crown.....

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?? not the elements of 2 and 5, those of the American system. The numbers

2 and 3, with their composites, 4, 6, 12, 16, occur continually in these tapp bles, being far more common than any others. Thus, 12 and 16 ounces 1. make a pound, not 10 and 15; 4 quarts, not 5, make a gallon ; 3 feet make

a yard ; 12 inches a foot; 12 hours (or 24, which consists of the same elements) a day; 12 months a year, and

many
other cases.

Whether these tables were original, planned by ingenious men, who took into account, in constructing them, the necessity of having the several denominations easily divisible by 2, 4, and 3, or whether the tables formed themselves, as it were, the several divisions growing naturally, in process of time, out of the actual transactions of trade, is now unknown. In either case the fact is, that the elements 2, 3, and 4, and not 2 and 5, prevail everywhere, and the result is a far more convenient system than if the decimal ratio had prevailed. In fact, difficult as it proves to be to introduce the decimal system in actual practice for money, it would have been absolutely impossible to introduce it ia weights and measures.

Another striking illustration of the importance of the elements 2, 3, and 4, in the composition of a number that is to be frequently employed, is the great use that is made among all nations of the number twelve, which is the smallest number in which all these three elements are contained. The number 12 has a distinct name in all languages--a dozen--and it is the first number above 2, which we call a couple, that has such a distinct name. Almost all articles that are sold in small quantities by count, are sold by the dozen. This is because that number can be halved and quartered, and also, if necessary, divided by three, a property which neither the number ten nor any other number, in fact, except twelve, possesses. The numbers 24, 36, &c., possess it, it is true, but 24 is nothing more nor less than two twelves, and 36 three twelves, and so on. The number 12, therefore, and its multiples, are the only possible numbers of which you can take evenly one-half, onethird, or one-quarter, as you may desire.

The substance of what has been advanced in the preceding paragraphs may be briefly expressed thus :

1. The American currency is a system constructed from the elements 2 and 5, and the several denominations are divisible only by these numbers and their composites.

2. The English currency is a system constructed chiefly from the elements 2, 3, and 4, and the several denominations are divisible by each of these numbers and their composites.

3. The American system, resulting, as it does, in a decimal ratio between the denominations, is inuch the most convenient for all written arithmetical operations.

4. The English system, being subject to the divisions which are most commonly required in practice, is much the most convenient for actual use in all business transactions,

5. The difficulty which has been and still is experienced in introducing the pure American system into common use is owing not to the difficulty of changing old habits, but to the intrinsic inconvenience of the system itself.

Whether there are any conceivable remedies for the evils of our present system, and if so, whether such conceivable remedies are at all practicable, are questions which may, perhaps, be considered in a future article.

culty of changing them. There is a substantial inconvenience that is inherent in the very constitution of the currency itself. That this is the true explanation, is evident from the fact that the Federal currency was at once and universally introduced throughout the country in keeping accounts ; for that is a function which its nature admirably adapts it to fulfill. In the day-books and ledgers of merchants, brokers, banks, and treasuries throughout every State in the Union, the Federal system reigns supreme. In re gard to this field no difficulty was experienced in the universal introduction of the system, for here was a purpose that it was fitted for. On the otiler hand, all efforts to introduce it as a circulating currency in the ordinary transactions of life have everywhere failed, and must continue to fail as long as tenths and fifths are less convenient fractions than halves, quarters, and thirds.

In fact, the government itself seems at length to begin to yield to the icexorable necessity which demands other multiples and divisors than five and ten, in a currency for popular use. We have now a three-cent coin, the is suing of which is a flagrant departure from the decimal system, or rather the introduction of a wholly new element into it; namely, the prime 3. The number three is a very important element of the English system, as se have seen ; and the introduction of this new coin is, therefore, an attempt to incorporate a feature of the English system upon ours. It is extremely doubtful, nevertheless, how far this limited and partial atternpt at a remedy will succeed. It is yet too early to see the practical result of the experiment, but all the theoretical considerations which bear upon the subject indicate that it will fail-making the coinage more confused and complicated, without gaining the advantage

intended. That is to say, the two systems, nansly, the one in which 2 and 5 are the elements, and the other in which the elements are 2, 3, and 4, are so entirely different, that part of the one cannot be grafted upon and made to harmonize with the other. The three cent coin, for example, is incommensurable with every silver coin in the whole Federal currency; that is, no number of these coins will make either a half-dime, a dime, a quarter of a dollar, a half dollar, a dollar, a quartereagle, a half-eagle, or an eagle. Observe, now, the striking contrast when we turn to the corresponding piece in the English system, the three-penny piece 2 of them make the sixpenny piece. 4 of them make the shilling.

40 of them make the half sovereign

80 of them make the sovereign. Whereas, with the American three-cent piece-11 of thein make the half dime.

164 of them make the half dollar. 3of them make the dime.

33% of them make the dollar. 8] of them make the quarter dollar.

Thus, in the one case, everything is commensurable and simple. In the other, the results are all perplexing and unmanageable fractions, showing w that the whole system must be constructed with the element three as an essential constituent of it throughout, and all attempts to introduce it incidentally into a system formed from the elements 2 and 5, will lead to endles intricacy and confusion.

It is curious to observe how the elements 2, 3, and 4, which are the ele. ments of the English system, reign everywhere in the construction of almost all the tables of weights and measures in use among civilized nations, and

20 of them make the crown.

10 of them make the half crown.

cases.

not the elements of 2 and 5, those of the American system. The numbers 2 and 3, with their composites, 4, 6, 12, 16, occur continually in these tables, being far more common than any others. Thus, 12 and 16 ounces make a pound, not 10 and 15; 4 quarts, not ő, make a gallon : 3 feet make a yard; 12 inches a foot; 12 hours (or 24, which consists of the same elements) a day; 12 months a year, and so in many

other

Whether these tables were original, planned by ingenious men, who took into account, in constructing them, the necessity of having the sereral denominations easily divisible by 2, 4, and 3, or whether the tables formed themselves, as it were, the several divisions growing naturally, in process of time, out of the actual transactions of trade, is now unknown. In either case the fact is, that the elements 2, 3, and 4, and not 2 and 5, prevail everywhere, and the result is a far more convenient system than if the decimal ratio had prevailed. In fact, difficult as it proves to be to introduce the decimal system in actual practice for money, it would have been absolutely impossible to introduce it in weights and measures.

Another striking illustration of the importance of the elements 2, 3, and 4, in the composition of a number that is to be frequently employed, is the great use that is made among all nations of the number twelve, which is the smallest number in which all these three elements are contained. The number 12 has a distinct name in all languages--a dozen-and it is the first number above 2, which we call a couple, that has such a distinct name. Almost all articles that are sold in small quantities by count, are sold by the dozen. This is because that number can be halved and quartered, and also, if necessary, divided by three, a property which neither the number ten nor any other number, in fact, except twelve, possesses. The numbers 24, 36, &c., possess it, it is true, but 24 is nothing more nor less than two twelves, and 36 three twelves, and so on. The number 12, therefore, and its multiples, are the only possible numbers of which you can take evenly one-half, onethird, or one quarter, as you may

desire. The substance of what has been advanced in the preceding paragraphs may be briefly expressed thus :

1. The American currency is a system constructed from the elements 2 and 5, and the several denominations are divisible only by these numbers and their composites.

2. The English currency is a system constructed chiefly from the elements 2, 3, and 4, and the several denominations are divisible by each of these numbers and their composites.

3. The American system, resulting, as it does, in a decimal ratio between the denominations, is inuch the most convenient for all written arithmetical operations.

4. The English system, being subject to the divisions which are most commonly required in practice, is much the most convenient for actual use in all business transactions.

5. The difficulty which has been and still is experienced in introducing the pure American system into common use is owing not to the difficulty of changing old habits, but to the intrinsic inconvenience of the system itself.

Whether there are any conceivable remedies for the evils of our present system, and if so, whether such conceivable remedies are at all practicable, are questions which may, perhaps, be considered in a future article.

Art. III.--THE FINANCES AND TRADE OF THE UNITED KINGDOM.

INTRODUCTORY REMARKS—REVENUE AND EXPENDITURES IN YEAR ENDING JANUARY, 1872-13 CIAL CONDITION OF UNITED KINGDOM-SLAVE COMPENSATION LOAN–IRISH DISTRESS LOAN CIVIL

CIVIL, NAVAL, AND JUDICIAL SERVICES-SALARIES AND ALLOWANCE

LIST-PENSIONS FOR

COURTS OF JUSTICE--MISCELLANEOUS CHARGES-CONSOLIDATED FUND-RECEIPTS UNDER SETELA

HEADS OF TAXATION AND INCOME FROM 1846 to 1851-TAXES REPEALED OR REDCCED

AND PROPERTY TAX-REVENUE OF STAMPS-LETTERS DELIVERED IN UNITED KINGDOM ron 1840 to 1851---POST-OFFICE REVENUE-SUGAR AND LUMBER TRADE-IMPORTS AND Coxsu TOY OF VARIOUS ARTICLES-VALUE OF BRITISH MANUFACTURES-CORN, GRAIN, AND MEAL, IMPORTO IN EACH YEAR FROM 1845 to 1851-BRITISH NAVIGATION LAWS-TONNAGE OF BRITISE SEIN

ENTERED AND CLEARED-FLUCTUATIONS IN TRADE-EFFECTS OF THE NAVIGATION LAW or les

THE “ facts and figures" collected in the following pages, from parliamen. tary and other authentic documents, and published in pamphlet form in London in January of the present year, present a very complete outline of the present state of the finances and trade of the United Kingdom, as colapared with their state at a recent period. The English people are not accustomed to rush headlong into political changes—they examine, discuss, and reflect; there are debates in Parliament; public meetings are held; articles are written in newspapers and reviews; pamphlets and books are published; before a measure is sanctioned by an enlightened public opinion, and passed by the British Legislature. But in proportion as the English people are slow in adopting political changes, they are tenacious of real benefits which they have obtained. They watch the consequences of new laws, and, when they see that a measure has been followed by beneficial results, they recognize the connection of cause and effect, and they are not easily cajoled, or cheated, or terrified out of the valuable acquisition. When, therefore, they consider such facts as these set forth in the statements" of the intelligent author of the following pages, they will infallibly continue not less reluctant than they have hitherto been, to part with a fiscal policy of which these are the legitimate fruits. Hence the effects of the new Derby administration to legislate back to the corn laws will assuredly fail.

“ There are some men,” says Dr. Johnson, in his Life of Drake, "of narrow views and groveling conceptions, who, without the instigation of personal malice, treat every new attempt as wild and chimerical, and look upon every ezdeavor to depart from the beaten track as the rash effort of a warm imagination, or the glittering speculation of an exalted mind, that may please and dazzle for a time, but can produce no real or lasting advantage. These men value thenselves upon a perpetual scepticism, upon believing nothing but their own senses, upon calling for demonstration when it cannot possibly be obtained, and, sometimes upon holding out against it when it is laid before them ; upon inventing arguments against the success of any new undertaking, and, where arguments cannot be found, upon treating it with contempt and ridicule. Such have been the most formidable enemies of the great benefactors to mankind."

The class of persons so accurately described by Johnson in this passage, have given every opposition in their power to the various improvements in the fiscal and commercial legislation of the United States of America as weli as the United Kingdom of Great Britain, Ireland, and Scotland.

We are indebted for an early copy of this pamphlet to Messrs. DELF and TRUBNER, importers in London of American books; and as it contains so much interesting information relating to the fiscal and commercial affairs of a nation with which we hold such important commercial and monetary relations, we presume that its republication in this place will be regarded as

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