UNITED STATES RULE ILLUSTRATED. By applying the United States Rule, it will be noticed that the payment of $50 does not appear on the diagram until 6 months after it was paid, and then only to cancel a debt of interest that would not draw interest if left unpaid. Practically it reduces the $60 interest due at the time of the payment to $10, making the interest due at the time of the next payment $40 instead of $90. The same may be seen in the payment of $20. MERCANTILE RULE ILLUSTRATED. In the Mercantile Rule, there is evidently a compounding of interest at the end of the first year, as the principal then becomes larger than at first. There is nevertheless a compounding of interest at the end of the 2d and 3d years, though by reason of the payments being larger, the principal is less. It is visible to the eye at the end of the 3d year. It will be observed that interest is compounded three times also in the use of the United States Rule, and would have been five times if the payments of $50 and $20 had equalled the interest then due. In fact, the loss of interest on these amounts till the next payment is a fair equivalent Principal $1000. to compounding so much of the interest then due. Had the payments been more frequent, the amount due at maturity, by the United States Rule, would have been larger, as compared with the other rules, than in the present instance. It is recommended to the pupil to study these diagrams till he becomes perfectly familiar with the reason why different rules give different results, and also to work other examples, drafting diagrams to correspond. With the use of proper mathematical instruments, tolerably accurate results may be obtained by drafting alone. Especially should the pupil notice that rate per cent. is the ratio between the principal and interest, and is represented in the diagram by the degree of divergence of the interest line from the horizontal base line. In the same diagram the less the principal, the less the divergence. CURRENCY AND MONEY. METALLIC CURRENCY. ART. 111. BARTER is simply exchanging one or more commodities for others, as giving one bushel of wheat for two bushels of corn. MONEY is an instrument to facilitate exchanges, and, strictly speaking, should possess an intrinsic value equivalent to that for which it is exchanged. Various articles have at different times and by different nations been used for this purpose, as shells, leather, corn, cattle, etc., but the precious metals, gold and silver, have been found to be most serviceable for the following reasons: 1st. They possess great value in small bulk. 2d. Their value remains quite uniform, changing only by slow degrees. 3d. They can be used or hoarded without much wear or decay. 4th. The pieces can be united or subdivided without loss of value. 5th. They are homogeneous in their structure, and easily identified, Gold and silver, by being used as money, become the standard of reference for expressing the value of other commodities. The price of a commodity is usually its value expressed in the denominations of money. When prices or obligations in debit and credit and barter are thus expressed, and business transacted without the intervention of money, we have what is called the "money of account." The denominations in the "money of account" may be even different from the denominations of the money in circulation, and if the denominations of both be the same, the values represented by them may be different. Still further, there may be a "money of account" where there is no money in actual use, in which case (as to a certain extent in all cases) prices are only expressions showing the relative value of commodities, and, like the terms used in the measure of arcs and angles, are indefinite until referred to other commodities, or to the same commodity of different amount. Gold and silver have an intrinsic value, depending upon their cost of production and uses. They derive a value from their capacity to facilitate exchanges, just as horses, mules, and railroads derive their value from facilitating transportation. Government can no more create a value to gold and silver than to sugar. It does, however, increase their value by coining them into pieces convenient for use, and declaring them legal tender in payment of debt. Coinage being only a certificate of value already existing in the metal, it is not necessarily the work of government, neither is legal tender a necessary element of even a metallic currency, as is seen in the coinage of copper and nickle. Coining gold and silver enhances their value in the same way that manufacturing steel enhances the value of the iron used, or as the brand of an official inspector renders certain articles of merchandise more salable. Making gold and silver coins legal tender increases their value because it increases their demand. For when other articles of value can not be used in liquidating indebtedness, these will always answer the purpose. Money, by being legal tender, becomes naturally a standard of value for other property. But money itself is not an invariable measure of value, for the reason that its value, like that of other kinds of property, is affected by cost of production, supply, demand, etc. The debasement of coins by government is not here taken into the account. If gold alone were used as money and legal tender, its gradual change of value would be perceptible only as it caused an increase or decrease of prices. A diminution in value of gold would raise prices, and vice versa. But frequently gold and silver both are legal tender, as it was in the United States until A.D. 1853. In making both legal tender, it is necessary for government to establish their relative value. If the legal relative value be the actual commercial relative value, then both will circulate equally well, except so far as convenience may dictate. But as both are constantly changing in their commercial value, while the legal relative value remains the same, the metal that has the greatest commercial value will be used to make foreign purchases, while the cheaper metal will remain at home. It is a general principle in currency, that if several different articles be allowed to circulate as money, the cheaper will displace the dearer. If a thousand silver dollars will pay a larger debt in a foreign country than a hundred gold eagles, then silver will be shipped in payment. By making silver legal tender for small sums only, its legal relative value, or mint valuation, may be considerably higher than its commercial or marketable value, and still the currency will not be burdened by its abundance, and gold will be retained for the reason that it will be demanded for the payment of those debts that are above the silver limit. Whenever both are legal tender for any amount, there must be frequent necessity for government to change the legal or nominal value. In A.D. 1853, silver coins in the United States were made "legal tender for all sums not exceeding five dollars,” and its nominal |