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. d. E. 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 .228 4.4444 21 shillings 1 guinea 4.6724 12 pence FRENCH MONEY. 100 centimes make 1 franc, value $.1875. TROY WEIGHT. OZ. 24 grains (gr.) make 1 penny-weight dwt. 1 ounce Ib. By this weight are weighed jewels, gold, silver, corn, bread, and liquors. 12 oz. APOTHECARIES WEIGHT. 3 sc. 20 grains (gr.) make 1 scruple SC. 1 dram dr. or 3 8 dr. 1 ounce oz. or 3 12 oz. 1 lb. * The above are the coins which were at first contemplated, but the double-dime has never been coined. Twenty-five-cent piecco and wall-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. AVOIRDUPOIS WEIGHT. 16 oz. 4 qrs. 10 drams (dr.) make 1 ounce OZ. Ib. qr. hundred-weight cwt. T. 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. DRY MEASURE. 8 qts. 2 pints (pt.) make 1 quart qt. I peck pk. 4 pks. 1 bushel bu. 8 bu. 1 quarter fr. The diameter of a Winchester bushel is 184 inches, and its depth 8 inches.—And one gallon by dry measure contains 2682 cubic inches. By this measure salt, lead ore, oysters, corn, and other dry goods are measured. ALE OR BEER MEASURE. 4 qts. 9 gals. 2 pints (pt.) make 1 quart qt. 1 gallon gal. 3 gals. 1 firkin of ale fir. I firkin of beer fir. 2 fir. 1 kilderkin kil. 2 kil. 1 barrel bar. 3 kil. 1 hogshead hhd. 3 bar. 1 butt butt. The ale gallon contains 282 cubic inches. In Londou the ale firkin contains 8 gallons, and the beer firkin 9 ; other measures being in the same proportion WINE MEASURE. 4 qts qt. gal. 63 gals. 2 pints (pt.) make 1 quart 1 gallon 42 gals. I tierce tier. 1 hogshead hhd. 84 gals. 1 puncheon pun. 2 hhds. 1 pipe or butt 2 pipes 1 tun T. 18 gals. I runlet 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. p. or b. run. CLOTH MEASURE. 21 inches make 1 nail 1 quarter I ell English 1 aune or ell French. The French aune is 42 inches. nl. 4 qrs. 3 qrs. 5 qrs. Ell Eng. LONG MEASURE. ft. 1 yard 3 barley corns make 1 inch in. 12 in. 1 foot 3 ft. yd. 5) yds. I pole or rod pole 40 poles I furlong fur. 8 fur. I mile ml. 3 mls. 1 league I. Also, 4 inches make 1 hand 1 geometrical pace 1 fathom 6 points 1 line 12 lines 1 inch SQUARE MEASURE. ft. yd. 144 inches make 1 foot 1 yard 1 pole, rod, or perch. 1 acre. } The true length of the solar year is 265 days, 5 hours, 48 min. 57 seconds Reflections on Mathematical Reasoning. If 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 are 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 gll parts are properly units of a lower order. As we say sin |