special system of weights. A troy pound (of what value is unknown) is first mentioned in Britain in 1414, long before which period the standard pound of twelve ounces, as well as another pound of twelve ounces (the Tower pound), was in use. The term "troy" was first applied to the standard pound in 1495, but at the same time no change seems to have been made in its value, and it continued, as before, to be exclusively employed by the dealers in the precious metals, gems and drugs. The troy pound contains twelve ounces, each ounce twenty pennyweights, and each pennyweight twenty-four grains; thus the pound contains 5,760 grains, and is to the avoirdupois pound as 144 to 175, while the troy ounce is to the avoirdupois ounce as 192 to 175. (The apothecaries' ounce and pound are now practically obsolete; drugs are bought and sold by avoirdupois, though compounded by apothecaries' weight.) The old English pound, to which the term troy was afterwards applied, was doubtless the pound of silver; and the Tower pound of twelve ounces differed from it only by three-fourths of an ounce.

THE AREA OF A CIRCLE.

Of all plane figures the circle is the most capacious, or has the greatest area within the same limits. It is geometrically demonstrable that it has the same area as a right-angled triangle with a base equal to its circumference, and a perpendicular equal to its radius, that is, half the product of the radius and circumference. It is obviously larger than any figure, of however many sides, inscribed within its perimeter, and smaller than any circumscribed polygon. As a result of laborious calculations on this basis (pushed in one instance to 600 places of decimals without reaching the end), it has been ascertained that the ratio of the diameter to the circumference of any circle (sufficiently exact for all practical purposes), is as 1: 3.1416 (3.141592653+) or in whole numbers, approximately, as 7: 22, or more nearly as 113: 355. Hence, to find the circumference or diameter, the other quantity being known, multiply or divide by 3.1416; and to find the area, multiply half the diameter by half the circumference, or the square of the diameter by .7854 (3.1416÷4).

TO FIND THE SURFACE OF A GLOBE, multiply the square of the diameter by 3.1416.

TO FIND THE SOLIDITY OF A GLOBE, multiply the cube of the diameter by .5236.

COAL WEIGHED BY MEASURE.

There is a difference between a ton of hard coal and one of soft coal. For that matter, coal from different mines whether hard or soft, differs in weight, and consequently in cubic measure, according to quality. Then there is a difference according to size. To illustrate: careful measurements have been made of Wilkesbarre anthracite, a fine quality of hard coal, with the following results:

For soft coal the following measures may be taken as nearly correct; it is simply impossible to determine any exact rule, even for bituminous

coal of the same district: Briar Hill coal, 44.8 cubic feet per ton of 2,240 pounds; Pittsburgh, 47.8; Wilmington, Ill., 47; Indiana block coal, 42 to 43 cubic feet.

MEASURE OF EARTH, ETC.

One ton of soil = 18 feet cube.

45 cubic feet of soil = 21⁄2 tons.

A cubic foot contains 6 gallons and 1 quart of water, weighing 621⁄2 lbs.

15

cubic feet of chalk weighs....

clay
earth
gravel
sand

44

1 ton.

1

1

1

TRADE SIZES OF BOOKS.

The name indicates the number of pages in the sheet, thus: in folio book, 4 pages or 2 leaves 1 sheet; a quarto. or 4to., has 8 pages or 4 leaves to a sheet; an octavo, or 8vo., 16 pages or 8 leaves to a sheet. In a 12mo., 24 pages or 12 leaves 1 sheet, and the 18mo., 36 pages, or 18 leaves 1 sheet, and so on. The following are the approximate sizes of books:

=

VALUE OF DIAMONDS,

Diamonds averaging one-half carat each, 860 per carat.

Diamonds averaging three-quarters carat each, 880 per carat.

Diamonds averaging one carat each, $100 per carat.

Diamonds averaging one and one-quarter carats each, $110 per carat.

Diamonds averaging one and one-half carats each, 8120 per carat.

Diamonds averaging one and three-quarters carats each, $145 per carat.

Diamonds averaging two carats each, $175 per carat.

In other words, the value of the gem increases in the geometrical ratio of its weight. Four diamonds weighing together two carats are worth $120; but one diamond weighing just as much is worth $350. Stones weighing over two carats are about the same price per carat as two-carat stones; they should be dearer, but they are not, simply because the demand for them is limited. If the demand for diamonds were as imperative as the demand for flour or beef, the geometrical ratio would again come into play, and fivecarat stones would be valued in the thousands.

VALUABLE CALCULATIONS.

TO MEASURE BULK WOOD.-To measure a pile of wood, multiply the length by the width, and that product by the height, which will give the number of cubic feet. Divide that product by 128, and the quotient will be the number of cords. A standard cord of wood, it must be re

membered, is four feet thick; that is, the wood must be four feet long. Farmers usually go by surface measure, calling a pile of stove wood eight feet long and four feet high a cord. Under such circumstances thirty-two feet would be the divisor.

GRAIN MEASURE-To find the capacity of a bin or wagon-bed, multiply the cubic feet by .8 (tenths). For great accuracy add one-third of a bushel for every 100 cubic feet. To find the cubic feet, multiply the length, width and depth together.

LAND MEASURE-To find the number of acres in a body of land, multiply the length by the width (in rods), and divide the product by 160. When the opposite sides are unequal, add them, and take half the sum for the mean length or width.

CISTERN MEASURE-To find the capacity of a round cistern or tank, multiply the square of the average diameter by the depth, and take three-sixteenths of the product. For great accuracy, multiply by .1865. For square cisterns or tanks, multiply the cubic feet by .23%. The result is the contents in barrels.

TO MEASURE CASKS OR BARRELS-Find mean diameter by adding to head diameter two-thirds (if staves are but slightly curved, threefifths) of difference between head and bung diameters, and dividing by two. Multiply square of mean diameter in inches by .7854, and the product by the height of the cask in inches. The result will be the number of cubic inches. Divide by 231 for standard or wine gallons and by 282 for beer gallons.

TO ASCERTAIN the Weight oF CATTLE-Measure the girt close behind the shoulder, and the length from the forepart of the shoulderblade along the back to the bone at the tail, which is in a vertical line with the buttock, both in feet. Multiply the square of the girt, expressed in feet by ten times the length, and divide the product by three; the quotient is the weight, nearly, of the fore quarters, in pounds avoirdupois. It is to be observed, however, that in very fat cattle, the fore quarters will be about one-twentieth more, while in those in a very lean state they will be one-twentieth less than the weight obtained by the

rule.

MEASURES OF CAPACITY-The following table, showing contents of boxes, will often be found convenient, taking inside dimensions: 24 in. x 24 in. x 14.7 will contain a barrel of 31% gallons.

15 in. x 14 in. x 11 in. will contain 10 gallons.

84 in x 7 in. x 4 in. will contain a gallon.

4 in. x 4 in x 3.6 in. will contain a quart.

24 in. x 28 in. x 16 in. will contain 5 bushels.

16 in. x 12 in. x 11.2 in. will contain a bushel.

12 in. x 11.2 in. x 8 in. will contain a half bushel.

7 in. x 6.4 in. x 12 in. will contain a peck.

8.4 in. x 8 in. x 4 in. will contain a half peck, or 4 dry quarts!

6 in. x 5 in., and 4 in. deep, will contain a half gallon.

4 in. x 4 in., and 2 in. deep, will contain a pint.

HOW TO MEASURE A TREE.-Very many persons, when looking for a stick of timber, are at a loss to estimate either the height of the tree or the length of timber it will cut. The following rule will enable any one to approximate nearly to the length from the ground to any position desired on the tree: Take a stake, say six feet in length, and place it against the tree you wish to measure. Then step back some rods, twenty or more if you can, from which to do the measuring. At this point a light pole and a measuring rule are required. The pole is raised between the eyes and the tree, and the rule is brought into position against the

pole. Then by sighting and observing what length of the rule is required to cover the stake of the tree, and what the entire tree, dividing the latter length by the former and multiplying by the number of feet the stake is long, you reach the approximate height of the tree. For example, if the stake at the tree be six feet above ground and one inch on your rule corresponds exactly with this, and if then the entire height of the tree corresponds exactly with say nine inches on the rule, this would show the tree to possess a full height of fifty-four feet. In practice it will thus be found an easy matter to learn the approximate height of any tree, building, or other such object.

RULES FOR MEASURING CORN IN CRIB, Vegetables, etC., AND HAY IN MOW-This rule will apply to a crib of any size or kind. Two cubic feet of good, sound, dry corn in the ear will make a bushel of shelled corn; to get, then, the quantity of shelled corn in a crib of corn in the ear, measure the length, breadth and height of the crib, inside the rail; multiply the length by the breadth and the product by the height, then divide the product by two, and you have the number of bushels of shelled corn in the crib.

To find the number of bushels of apples, potatoes, etc., in a bin, multiply the length, breadth and thickness together, and this product by eight, and point off one figure in the product for decimals.

To find the amount of hay in a mow, allow 512 cubic feet for a ton, and it will come out very generally correct.

THE STORY OF OUR COINAGE.

Among the North American Indians strings of beads made from shells were used as currency. They were called wampum. In Colonial times the general court of Massachusetts soon recognized this money and fixed an arbitrary rate of exchange. Six white beads made from the sea-conch, or three purple beads made from the muscle-shell, were taken as equivalent to an English penny. Later four white and two purple ones were declared to have the same value. Musket balls were made legal tender for small amounts and furs and peltry for large sums. coins brought from England and Holland tended to flow back to Europe, and the remaining ones were insufficient for the needs of the colonists.

tree.

The

In 1652, therefore, the general court of Massachusetts established a mint in Boston, and John Hull, mint-master, struck silver shillings, sixpences and threepences. All of these coins bore the device of the pineThey were of the same fineness as the English coins of like denomination, but of less weight. This mint continued in operation for thirty-six years. After a while the "royal oak" was substituted for the pine-tree in order to conciliate King Charles II., who disliked this minting by a colony. All the above named coins bore the date of 1652; but two-penny pieces were added with the date of 1662. No other colony had a mint until 1659, when Lord Baltimore caused shillings, sixpences and groats to be coined for use in Maryland. James II. issued ten coins for circulation in America, though few of these have found their way hither. In 1722, 1723 and 1733 copper coins were minted in England with the legend "Rosa Americana." There were also copper half-pence issued in 1773 for circulation in Virginia, and in 1774 silver shillings were added. Florida and Louisiana had colonial coins of their own before they became parts of the United States.

After the Revolutionary war the Continental Congress passed an act in 1786 which established a mint and regulated the value and alloy of the national coin. The government prescribed the device for copper coin the next year. Under this authority the so-called "Franklin Penny," with the legend "Mind Your Business," was made by contract. By the Federal Constitution, ratified in 1789, the right of coining money was transferred from the States to the United States. Under this constitution the United States mint was established at Philadelphia in 1792, and the regular coinage began in the following year. Four have since been added: New Orleans (1835), San Francisco (1854), Carson City and Denver- all under the charge of the Bureau of the Mint of the United States Treasury Department.

By the act of Congress establishing the United States Mint the following coins were authorized, Gold, eagle, half-eagle, quarter-eagle; silver, dollar, half-dollar, quarter-dollar, dime, half-dime; copper, cent, half-cent. Changes have been made at various times, not only in weight and fineness, but also in the metals used for the minor coins. At present the following coins are struck: Gold, double-eagle, eagle, half-eagle, three-dollar, quarter-eagle, dollar; silver, dollar, half-dollar, quarter-dollar, dime; minor coins, of nickel and bronze, five-cent, three-cent and cent.

By the act of February 12, 1873, the metric system was to a certain extent used in determining the weight of the silver coins. Thus, the half-dollar was to weigh 121⁄2 grams, the quarter-dollar 61⁄2 grams, the dime 21⁄2 grams.

Till 1837 the obverse of our coins had generally a female head, either with a liberty cap, or with a fillet bearing the word "Liberty.' Afterwards it was replaced by a full-length seated figure with a liberty-cap on a pole, and a shield with a band inscribed "Liberty." The reverse of the principal coins has the eagle, often with a shield, arrows and olive branch. But in the minor coins the denomination of the piece is encircled by a wreath.

Up to 1849 eagles or ten-dollar gold pieces were the highest denomination authorized. But the discovery of gold in large quantity in California caused the demand for a larger coin, and the double-eagle was authorized by act of March 3, 1849, and issued in 1850. By the same act gold dollars were also authorized. Beside the govermental issues there were octagonal and ring dollars and even gold half-dollars and quarters issued in California. The Mormans in Utah also had gold coins of their These had peculiar devices, and their favorite inscription, "Holiness to the Lord."

own.

NUMISMATICS AS A STUDY.

Besides its bearing upon the history, the religion, the manners, and the arts of the nations which have used money, the science of numismatics has a special modern use in relation to art. Displaying the various styles of art prevalent in different ages, coins supply us with abundant means for promoting the advancement of art among ourselves. If the study of many schools be at all times of advantage, it is especially so when there is little originality in the world. Its least value is to point out the want of artistic merit and historical commemoration in modern coins, and to suggest that modern types should be executed after some study of the rules which controlled the great works of former times.