Tables of Coin, Weights, and Measures. Denominations of Federal money as determined by an Act of Congress, Aug. 8, 1786. 10 mills make 1 cent marked c. 10 cents 10 dimes 10 dollars The coins of Federal money are two of gold, four of silver, and two of copper. The gold coins are an eagle and half-eagle; the silver, a dollar, half-dollar, double-dime, and "dime; the copper, a cent and half-cent. The standard gold and silver is eleven parts fine, and one part alloy. The weight of fine gold in the eagle is 246.268 grains; of fine silver in the dollar, 375.64 grains; of copper in 100 cents 21 lbs. avoirdupois.* ENGLISH MONEY. 4 farthings make 1 penny d. value in U. S. $0.019 100 centimes make 1 franc, value $.1875. TROY WEIGHT. 24 grains (gr.) make 1 penny-weight dwt. By this weight are weighed jewels, gold, silver, corn, bread, and liquors. *The above are the coins which were at first contemplated, but the double-dime has never been coined. Twenty-five-cent pieces and half-dimes nave been coined. Apothecaries use this weight in compounding their medicines; but they buy and sell their drugs by Avoirdupois weight. Apothecaries' is the same as Troy, having only some different divisions. By this weight are weighed all things of a coarse and drossy nature; such as butter, cheese, flesh, grocery wares, and all metals except gold and silver. 1 quarter Jr. The diameter of a Winchester bushel is 18 inches, and its depth 8 inches.-And one gallon by dry measure contains 2684 cubic inches. By this measure salt, lead ore, oysters, corn, and other dry goods are measured. The ale gallon contains 282 cubic inches. In London the ale firkin contains 8 gallons, and the beer firkin 9; other measures being in the same proportion 31 gallons 1 barrel bar. The wine gallon contains 231 cubic inches. By this measure brandy, spirits, perry, cider, mead, vine gar, and oil are measured. 5 qrs. 1 ell English 5 qrs. 1 aune or ell French. The French aune is 42 inches. yd. 1 league 60 geographical miles, or 69 statute miles 1 degree nearly, deg. or 360 degrees the circumference of the earth. Reflections on Mathematical Reasoning. Ir the learner has studied he preceding pages attentively, he has had some practice in mathematical reasoning. It may now be pleasant, as well as useful, to give some attention to the principles of it. By attending to the objects around us, we observe two properties by which they are capable of being increased or diminished, viz. in number and extent. Whatever is susceptible of increase and diminution is the object of mathematics. Arithmetic is the science of numbers. All individual or single things arc naturally subjects of number. Extent of all kinds is also made a subject of number, though at first view it would seem to have no connexion with it. But to apply number to extent, it is necessary to have recourse to artificial units. If we wish to compare two distances, we cannot form any correct idea of their relative extent, until we fix upon some length with which we are familiar as a measure. This measure we call one or a unit. We then compare the lengths, by finding how many times this measure is contained in them. By this means length becomes an object of number. We use different units for different purposes. For some we use the inch, for others the foot, the yard, the rod, the mile, &c. In the same manner we have artificial units for surfaces, for solids, for liquids, for weights, for time, &c. And in all there are different units for different purposes. When a measure is assumed as a unit, all smaller measures are fractions of it. If the foot is taken for the unit, inches are fractions. If the rod is the unit, yards, feet, and inches are fractions, and the smaller, being fractions of the larger, are fractions of fractions. It may be remarked, that all parts are properly units of a lower order. As we say sin |