WEIGHTS AND MEASURES. = Troy Weight is used by jewellers and at the Mint. Its denominations are the pound, lb., - 12 ounces = 5,760 grains; ounce, oz., 480 grains; and per ny weight, dwt., : = 24 grains. = Apothecaries' Weight is used in prescribing and dispensing medicines, and in chemical and pharmaceutical operations generally. It is the offici nal standard of the U. S. Pharmacopoeia. The British Pharmacopoeia uses the avoirdupois pound and ounce; hence the two agree only in the grain measure. The denominations of apothecaries' weight are the pound, tb, 12 ounces = 5,760 grains; the ounce, 3j, 8 drachms: = 480 grains; the drachm, 3j, = 3 scruples 60 grains; the scruple, j, 20 grains; and the grain, gr. Avoirdupois Weight is the commercial weight, and is generally employed in the receipts in this volume. Its pound, lb., 16 ounces, oz., grains. The ounce contains 437 5 grains. The apothecaries' or troy ounce contains 42 grains more than the avoirdupois ounce, and the apothecaries or troy pound contains 1.240 grains less than the commercial or avoirdupois pound. The troy pound contains 12 oz., the avoirdupois 16 oz. 7,000 76,800 Imperial. 1 fluidounce 1 fluidrachm 1 minim 437.5" f3j=f3viii= Congj= Öviii = 70.000 66 Imperial (Br.) into Wine (U. S. P.) = Measure. 0 66 1 20 66 2.5" 1.04" THE DECIMAL SYSTEM, Adopted in France and on the Continent, is used in this country in scientific research. The standard of length is the metre (70.000.000 of a quadrant of the earth's meridian), which is equal (as corrected by Prof. Bache) to 39-36850535 inches, or, roughly, about 3 feet. This, as well as the measures of capacity and weight, is increased or divided decimally. The prefixes are deca (10 times), hecto (100 times), kilo (1000 times), and myria (10,000 times); deci (,'%), centi (185), mille (1) The kilometre is equal to about two-thirds of a mile. The cubic decimetre is the unit of capacity, and is called a litre, and is equal to 1.765 imperial pints, or 2-1135 wine pints (the latter are used in the United States). The weight of 1 litre of water, at 39-10°, is called a kilogramme, and that of a millilitre of water a gramme 15:434 grains. The kilogramme is rather less than 2 lbs. avoirdupois. The metrical pound of France is half a kilogramme. One fluid ounce equals in capacity 29-53 cubic centimetres. Comparative Table of Decimal with Avoirdupois and Apothecaries' (U. S.) Weights. inches deep, A box 20 inches square, and 16 will contain 1 barrel (3 bushels). A box 15 inches square, and 144 inches deep, will contain half a barrel. A box 17 inches by 14 inches, and 9 inches deep, will contain 1 bushel. A box 10 inches by 12 inches, and 9 inches deep, will contain half a bushel. A box 8 inches square, and 83 inches deep, will contain 1 peck. A box 8 inches square, and 4 inches deep, will contain 1 gallon (dry) bushel 2684 cubic inches. = SURFACE MEASUREMENT. - Product of two Linear Dimensions (proportioned to the squares of similar sides). 144 square inches 1 square foot. 9 66 feet 66 =1 yard. 43,560 square feet 4480 yards = (660 X 66 feet). Acre Square mile 640 acres. = or 1. Parallelogram (square, rectangular side X by perpendicular height. rhomboidal) the product of the length of one = the perpendicular height. the half sum of the three sides subtract each side 4. Trapezoid the sum of the two parallel sides X by half the perpendicular height. 5. Circle the square of the diameter X 7854, or square of the circumference X 07958. 6. Sector of a Circle = radius of the circle X by A box 4 inches square, and 4331⁄2 inches deep, will one-half the arc of the sector. contain 1 quart. LINEAR MEASUREMENT. 7. Segment of a Circle.-Find the area of a seotor of a circle having the same arc, and deduct the triangle formed between the two radii and the chord of the arc. Superficial Area of Solids. 8. Cube. 10. Prism. 66 12 66 = 1.00000 Inches expressed in Decimals of a Foot. 0.08333 foot. 7 inches 0.16666 66 8 0.25000 66 2 inches 3 4 66 }-{ Sum of area of sides and bases. 11. Cylinder circumference of base X height + area of bases. 11 = 0.2500 = 5 =0·3125=0·0260415 0-8125 13 16 = 0-0624996 Cubic foot 66 Barrel yard =27 = 1,728 cubic ins. cubic ft. 46,656 66 Gallon (wine): 0.37500-0312498 7=0·4375=0·036458115 0.5000 = 16 = 0.0833328 = Ton 2240 lbs. avoirdupois. 1 gallon of water weighs 58,328-8 grains troy➡ 10-126 lbs. troy. Cylindrical inches X 66 feet Cubic 0004546 X .02909 inches X 00058 cubic feet. yards. the cir feet X 7.48 U. States gallon. 66 inches X 004329 = Cylindrical feet = 4. Given a chord and versed sine-to find the diameter of the circle. Divide the square of half the chord by the versed sine, and add the versed sine to the product the diameter. X 5.874 inches X 0034 Contents of Casks.-Add into one sum 39 times the square of the bung diameter, 25 times the square of the head diameter, and 26 times the product of the two diameters; then multiply the = foot in diameter and 10 feet high, would contain 10 cubic feet, 10 X 1000 X 7.207 72.070 oz.4500 lbs. Specific Gravity of Solids. vessel, brim full, put in the body, it will displace 1. By the Pitcher.- a pitcher, or similar its own bulk of water; catch this water as it overflows and weigh it. Divide the weight of the body by that of the water displaced, the quotient will be its specific gravity. A very neat instrument for performing this process accurately has been con 1. Cube: side X side X side, or area of base trived by Messrs. Eckfeldt and Dubois, of the X perpendicular height. 2. Parallelopipidon Prism Cylinder 3. Cone Pyramid} { }-{ Area of base by perpendicular height. Area of bases by the perpendicular height. 4. Frustrum of Cone or Pyramid = sum of the areas of the two ends + the square root of their product X by of the perpendicular height. 5. Sphere cube of the diameter X 0.5236. 6. Spherical Segment 3 times the square of the radius of its base + the square of its height X the height X 0-5836. = = MEASUREMENT OF STONE-WORK. 1 Perch, Masons' or Quarrymen's Measure. 164 feet long, 22 cubic feet. To be measured in wall. 16 inches wide, 12 high, 16 feet long, 18 inches wide, 12 66 high, = { = { 24.75 cubic feet. To be mea- 1 cubic yard 3 feet X 3 feet X 3 feet = feet. = 2 cubic weight of the heavy body in water being known the weight of the light body in air, will give the specific gravity. Thus, a bit of wood weighed in air 200 grains, attached to a piece of copper the two weighed in air 2247 grains, and in water 1620 grains, suffering a loss of 627 grains, the copper alone loses in water 230 grains, 627-230=397, the loss of the wood; 200+ 397.504, s. g. of the wood. the difference between these losses divided into When the Solid is Soluble in Water. Take its s. g. in regard to some liquid which does not dissolve it, multiply this by the s. g. of the liquid. The cubic yard has become the standard for all it lost in oil of turpentine 217.5. 400 contract work of late years. Stone walls less than 16 inches thick count as if 16 inches thick to mason;.over 16 inches thick, each inch additional is measured. Bricks required for Walls of various Thickness. – When the Body is in Powder. Introduce it into a counterpoise bottle, of which the capacity is known. Fill the bottle with pure water at 60°. It will hold as much less as is equal to the bulk of the powder, and the weight of the powder in air divided by this difference will give the s. g. Thus, the bottle holds 1000 grs. of water; 100 grs. of emery are introduced, and the bottle filled up with water. If no water were displaced the two should weigh 1100 grs., they really weigh 1070; the difference, 30 grs. = the weight of water displaced; 100 ÷ 30 3.333, s. g of the emery. When the Solid is Compound, As a nugget of gold and quartz. Take the s. g. of the nugget, that of gold and quartz being known, then apply the following formulæ : In ordinary language the terms density and specific gravity (s. g.) are used to represent the relative weights of equal bulks or volumes of different substances. In order to compare these conveniently, pure water at 60° is taken as the standard. A cubic foot of water weighs 1000 oz., hence to determine the weight of a given bulk of any body the specific gravity of which is known, mul- Take a bit of glass rod, note its loss when tiply the cubic content in feet by 1000, and this by weighed in water and in the liquid under trial. Dithe s. g., and the product will be the weight in vide the latter by the former, the quotient will be ounces avoirdupois. Thus, the s. g. of cast-iron the s. g. of the liquid. Thus a glass rod loses in is 7.207, that is, it is 7.207 times heavier than an water 171 grs., in alcohol, 143 grs. 143÷171equal bulk of water. A cylinder of cast-iron 1.836. s. g. of the alcohol. By the Balance. Specific Gravity bottles. The specific gravity in table also represents the number of ounces in each substance in 1 cubio 1 cubic foot of Cast Iron........... 1 66 = White Pine......... Water.......................... 1 22 46 These are made to hold 100 or 1000 grs. of pure water at 60°, and are accompanied by a counter-foot+16== lbs. poise. It is only necessary to fill the bottle with the liquid to be tested. Counterpoise and weigh; the weight in grains will be the s. g. Oily and viscous matter should never be introduced into the s. g. bottle. In case the s. g. bottle is not at hand any light flask will do. Make a file mark on the neck, counterpoise it, fill to the mark with pure water at 60°, note the weight of the water. Empty, dry thoroughly and fill with the liquid to be tested; the weight of this divided by that of the waters. g. Hydrometers Coal Gas GAS. To Read the Gas Meter. 100. THOUSAND 8 9 450 lbs. 34.6" 62-5 " 1- " 1- « Are instruments for determining the specific gravity of liquids by noting the depth to which a stem sinks. They consist of a cylinder with a weight beneath it to make it float upright, and a graduated stem. When intended for liquids lighter than water, the 0 or point at which they float in pure water at 60° is at the lower point of the stem, and as the liquid is lighter they sink more deeply; for liquids heavier than water the 0 is at the top of the scale. Many are graduated according to their the entire circle it denotes ten hundred, and is reproposed use, as alcoholometers, lactometers, sac-gistered by the hand in the centre circle, pointing charometers. (See DISTILLATION). The graduation to one-each figure in the centre circle being a most empoyed is that of Beaumé. Excellent hy-thousand-this entire circle being ten thousand, drometers with the degrees and the true s. g. on and is registered on the index of the left hand the same stem are made by Dr. W. H. Pile of Phil- circle by the hand, there denoting by each figure, adelphia. To Convert Degrees Beaumé into Specific Gravity. 1. For liquids heavier than water-Subtract the degree B. from 145, and divide into 145, the quotient is the s. g. 2. For liquids lighter than water-Add the degree B. to 130, and divide it into 140. The quotient is the s. g. To Convert Specific Gravity into Degrees Beaumé. 1. For liquids heavier than water.-Divide the B. g. into 145, and subtract from 145. The remainder is the degree B. 2 For liquids lighter than water.-Divide the 8. g. into 140 and subtract 130 from the quotient. The remainder will be the degree B. The following are those in common use: Batswing. This has a single slit at the top of the burner. It is very steady; does not change its form under any pressure. It is, therefore, used in street lamps. It is not, however, economical. Fish-tail. This form is generally used in houses; it has two openings in the top, from which the jets of gas issue and form a flat flame, the plane of which is at right angles to that of the openings. When the pressure is too great the flame elongates and sings, thus calling attention to the waste. It is an economical burner, but flickers. This unsteadiness is trying to the eyes, and the fish-tail should never be used to read or write by. Argand. These are the steadiest and most economical burners, but require a chimney. The gas is allowed to escape by a ring of holes, and the air is admitted both inside and outside of this ring. In the patent Argand the outer ring of air passes through a series of small openings, and the 0-0848 inner ring is deflected into the flame by a button; 1.25 SILVER COINS, FROM THE ANNUAL RE- Explanatory Remarks. The first column embraces the names of the It requires a swelled chimney. By cutting off the | A STATEMENT OF FOREIGN GOLD AND button a steadier light is obtained, and the economy is nearly the same; straight chimneys are more easily obtained than the others. The best flint-glass chimneys are in the end the cheapest; great loss of light ensues if they are not kept clean. But putting a chimney into hydrant-water, and gradually heating it, it may be cleaned safely; paper gives the best finish. The larger the burner the greater the relative economy. Relative Light for Unit of Gas. countries where the coins are issued; the second contains the names of the coin, only the principal proportional; and when this is not the case, the denominations being given. The other sizes are deviation is stated. The third column expresses the weight of a single piece in fractions of the Troy ounce, carried to the thousandth, and in a few cases to the ten thousandth, of an ounce. The method is preferable to expressing the weight in grains for commercial purposes, and corresponds better with the terms of the Mint. It may be readily transferred to weight in grains by the following rule: Remove the decimal point; from one-half deduct four per cent. of that half, and the remainder will be grains. The fourth column expresses the fineness in thousands, i. e., the number of parts of pure gold or silver in 1000 parts of the coin. The fifth column expresses the valuation of coin The value of silver fluctuates. 66 66 66 8 "40 m. Gold Coins. Denominations. 0.281 Thous. $ 5.32.37 Souverain 0.363 New Union Crown (assumed) 0.357 0.254 0.867 Twenty Milreis 0.575 Old Doubloon |