two ends together, and take half of this sum for the mean breadth, which sum multiplied by that breadth will give the number of square feet. Example 2.-How many square feet are there in a Board 18 feet long, 13 inches wide at one end and 17 inches at the other?-(Average breadth 15 inches.) 18 feet X 15 inches 27012224 feet area. In measuring timber or plank which runs tapering, both in width, and thickness, the common rule is, to add together the area of the two ends and one half of the sum multiplied by the length and divided by 144, will give the solid contents. Example 1.-Required the solidity of a tapering square stick of timber, the largest end being 14 inches square, the lesser end 10 inches, and the length 40 feet. Answer,-Contents by the common rule, 41.11 cubic feet. 14 X 14 196+100÷2X4014441-11 cubic feet. FRUSTRUM, CONE, TIMBER, &c. The correct rule for finding the solidity of any frustrum is to multiply the areas of the two ends together, and to the square root of the product add the two areas; this sum multiplied by one third of the length, will give the solidity of the frustrum. A different result from the above, is here shown by this Example. 140 square root of product of areas. 14x14196 area of largest end 10×10 = 100 66 196 lesser 66 100 CUBIC, OR SOLID MEASUre. To find the Cubical Content in a Stick of Timber, Block of Stone, Box, Bin, &c. If all the Dimensions are in Feet, multiply the Length by the Breadth, and this product by the Depth to obtain the number of Cubic Feet. If the Length is in Feet and the width and depth in Inches, multiply the length by the width and this Product by the depth in inches,-then divide the last Product by 144 for the Cubic Feet. If all the Dimensions are in Feet and Inches reduce the whole to Inches, then multiply the Length, Brealth and Depth together, and divide the Product by 1728 to obtain the Cubic Feet. CIRCLES. To find the area of a Circle multiply the square of the Diameter by the Decimal 7854, and the Product will be the area [The square of any number is that number multiplied by itself. Thus: 2 x 2 = 4, the square of 2. Example. Required the area of a Circle whose diameter is 6 inches? 6 X 6 36 X 7854 = 28-24 Square Inches. The area of the internal diameter of a Cylinder, multiplied by its depth, equals its cubical capacity. The area of a Cylinder, multiplied by its Length, equals its solid contents. Example. Required the Solid Content of an Iron Roller, 2 feet 6 inches in diameter, and 12 feet in length? 58.905 Cubic Feet. 2 ft. 6 in. 30 in. X 30 X 7854 X 12 - 144 Rule 9th.-To find the capacity of a can, cistern, reservoir, bin, crib, &c., &c., find its cubic (or solid) contents in inches, by the preceding rules, then if the capacity be required in gallons, divide by 231, U. S. standard; if in bushels, by 2150-42, or if heaped bushe's, by 2747-70; and if in pounds of water, multiply the number of gallons by 8.3389, or divide the cubic inches by 27-7015; the quotient is the capacity. MEASURE OF SOLIDITY, SURFACE, WEIGHT & LENGTH. 77 Example 1.-How many wine gallons are there in a cistern whose diameter is 30 inches, and whose depth is 50 inches? Answer,-153 gallons. 30X30X7854 X 50-231-153 gallons. 30 crib. 30785450÷2150·42 = 16·4 bushels of meal, grain, &c., in a bin or NOTE. By the foregoing rules the exact capacity of any measure may be determined. First, by reducing the capacity of the measure, whether dry or liquid, to cubic inches, and then by dividing the number of cubic inches contained in such measure by the divisors. Example 2.-How many gallons will a can of oil contain, whose diameter is 2 feet 6 inches, and its depth 4 feet 2 inches. Find the area of the base in inches, as by Example 1;-or by the Area of Circles, (see Table,) = 706.8600 which X 50 the depth in inches, 35343 ÷ 231 153 gallons. MEASURES. MEASURE OF SOLIDITY, OR CUBIC MEASURE.-1729 inches = 1 cubic foot; 27 cubic feet = 1 cubic yard; 40 cubic feet of round timber=1 ton; 50 cubic feet of hewn timber=1 ton; 16 cubic feet of wood 1 foot of wood, 8 feet of wood (or 128 cubic feet,) = 1 cord. MEASURE OF SURFACE, OR SQUARE MEASURE.-144 square inches=1 square foot; 9 feet 1 square yard; 30 yards = 1 square rod, or pole; 40 square rods= 1 square rood; 4 square roods=1 square acre, (or 43,560 feet;) 640 square acres 1 square mile. MEASURE OF WEIGHT.- Avoirdupois: 16 drams equal 1 ounce ;-16 ounces 1 pound; 112 pounds one hundred weight; 20 hundred weight 1 ton.- Troy : -4 grains equal carat; 24 grains 1 pennyweight; 20 pennyweights 1 ounce; 12 ounces 1 pound.- Apothecaries:- 20 grains equal 1 scruple (3); 3 scruples 1 dram (3); 8 drams 1 ounce (3); 12 oz. 1 (b) lb; IMPERIAL (BRITISH) MEASURE.-1 quarter of wheat 8 bushels; 231 cubic inches1 Winchester, or U. S. gallon; 282 cubic in. = 1 do. ale gall.; 2150.42 cubic in. 1 U. S. bushel; 277.274 cubic in. 1 Imperial gallon for dry, beer, and wine. MEASURE OF LENGTH: 16 feet equal 1 rod or pole; 40 rods, 1 furlong; 8 furlongs, (or 5280 feet,) 1 mile; 60 geo. miles 1 degree. ROPES AND CABLES-6 feet are equal to 1 fathom; 120 fathoms, to 1 cable's length. METALS IN THEIR ORDER OF DUCTILITY.-Wire Drawing Ductility:-Gold, Silver, Platinum, Wrought Iron, Copper, Zine, Tin, Lead-Laminable Ductility:-Gold, Silver, Copper, Tin, Platinum, Lead, Zinc, Wrought Iron WEIGHT OF VARIOUS SUBSTANCES:-lbs. Avoirdupois.-1 cubic foot of bricks weighs 124 pounds; 1 do. of clay, 130; 1 do. of sand, or loose earth, 95; 1 do. of common soil, 124; 1 do. of cork, 15; 1 do, of clay and stones, 160; 1 do. of Marble, 166; 1 do. of Granite, 169; 1 do. of Cast Iron, 450-55; 1 do. of Wrought Iron, 486-65; 1 do. of Steel, 489-8; 1 do. Copper, 555; 1 do. Lead, 708-75 1 do. Brass, 537-75; 1 do. Tin, 456; 1 do. White Pine, 29-56; 1 do. Sea Water, 64-3; 1 do. Fresh. 625.; 1 do. Air, 07529; 1 do. Steam, '03689. Weight of a Cubic Inch of Lead 4103 lb.; Sheet Copper 3225; Sheet Brass 3037; Sheet Iron 279; Cast Iron 263; Cast Tin 2636; Cast Zinc 26. Weight of 1 Bushel of wheat, 60 lbs. ; 1 of Beans, or Peas, 63; 1 do. Corn, or Rye, 56; 1 do Barley, 52; 1 do. Potatoes, or clover seed, 60; 1 do. salt, 65; 1 do. hemp. 44; 1 do. castor oil beans, or timothy seed, 56; 1 do. apples, (dried) 22; 1 do. Peaches, (dried,) 23. Gallons: 1 gallon of oil weighs 7.45 pounds; 1 do. water, 8.00; 1 do. proof spirits, 7.40; 1 do vinegar, 8.64. NUMBER OF CUBIC FEET IN A TON (2240 lbs.) OF VARIOUS BODIES:-Marble, 13.07; Granite, 13-5; Common Stone, 14-22; Paving Stone, 14-83; Sand, 235; Tallow, 38; English Oak, 37; American Oak, 41; Ash, 47; Elm, 64.5; Beech, 505; Teak, 48; Spanish Mahogany, 45: Honduras Do 55; Maple, and Riga Fir, 47-8; Larch. 658; Pich Pine, 53-6; Oil, 39; Proof Spirits, 386; Distilled Water, 35-6; Sea Water, 34-7; Grindstones, 17; Brick 17. Average weight of men 150 lbs. each. 5 men can stand in a space of 1 square yard. The strength of a horse is equivalent to that of five men. .... TABLE FOR MEASURING BRICKWORK. BRICKLAYERS' WORK-Brickwork is estimated at the rate of a number of bricks in thickness, estimating a brick at 4 inches thick. The dimensions of a building are usually taken by measuring half round on the outside, and half round on the inside; the sum of these two gives the compass of the wall,-to be multiplied by the height, for the content of the materials. Chimneys are by some measured as if they were solid, deducting only the vacuity from the hearth to the mantel, on account of the trouble of them. EXAMPLE. The end wall of a house is 28 feet long, and 37 feet high to the eaves: 15 feet high is four bricks or 16 inches thick, other 12 feet is three bricks or 12 inches thick, and the remaining 10 feet is two bricks or 8 inches thick; above which is a triangular gable 12 feet high and one brick or 4 inches in thickness. What number of bricks are there in the said wall? A Table by which to ascertain the Number of Bricks necessary to construct any Piece of Building, from a four-inch Wall to twenty-four inches in Thickness. 6 66 45 66 3416 For ascertaining (in an expeditious manner) the Number of SQUARE Feet in BOARDS. PLANKS, PAVEMENTS, PLASTERING, FLOORING, &c.-and the CUBICAL FEET, or SOLID Content, in TIMBER, TREES, HEWN TIMBER, STONE, BOXES, and PACKAGES of all kinds. RULE. In multiplying Decimals, point off as many right hand figures in the product as th re are decimal figures in the multiplicand; the figures on the left hand give the number of feet, those on the right the decimal parts of a foot.-(See Examples) Decimals signify tenths: thus, the decimal of a foot is the tenth part of a foot, the decimal of that tenth is the hundredth of a foot, and the decimal of that hundredth the thousandth.-To reduce the decimal of a foot to inches, multiply the decimal by 12. An Answer can be more quickly obtained from these Decimal Tables, than by referring to the pages of a Ready Reckoner. The last two figures of the Decimals, (when the length of the article consists of but a few feet) may be dropped, and the remaining figures only multiplied. TABLE OF SUPERFICIAL, OR, FLAT MEASURE, By which the Content in SUPERFICIAL FEET, of Boards, Plank, Paving, &c., of any LENGTH and BREADTH can be obtained, by multiplying the decimal expressed in the table by the length of the board, &c. Area of a Breadth Area of a Breadth Area of a Breadth Area of a Breadth in inches lineal foot. in inches. lineal foot. in inches. lineal foot. in inches. lineal foot. Example 1. Required the number of square feet in a strip of board 10 feet long by 2 inches wide? Opposite 2 is 1667 which multiplied by (X) 10 equals (=) 1 foot 8 inches. Example 2. Required the number of square feet in a board or plank. 41 feet long by 242 inches wide? Opposite 3 is 0625, to which add 2 to the left of the decimal for feet (when the width of the board exceeds 113 inches, add 1 to the left of the decimal for each foot); then 2.0625 X 41 feet 84 feet 7 inches. Example 3. The pavement of a side-walk is 40 feet long by 6 feet 6 inches wide; required the number of square feet. Opposite 6 is 5116, to which add 6 for feet: then, 6.5416 X 40261 feet 8 inches. Example 4. A room measures 16 feet by 15 feet 3 inches, how many square feet of flooring does it contain. Opposite 3 is 2916, to which add 15 for feet; then, 15.2916 × 16 == 244 feet 8 inches. If yards are required divide the Product by 3. Example 5. Required the number of square feet in a board 14 feet long 15 inches wide at one end and 9 at the other? (add together the width of the two ends and divide by 212 inches, mean width.) Opposite 12 is 1. X 14 = 14 feet. 6.5416 40 261-6640 Ans. 262 feet. 15.2916 917496 244-6656 Ans. 245 feet 1. 14 14 Ans. 14 feet. It is customary, in measuring boards, &c., to count as nothing all fractions under 6 inches, and to count as one foot 6 inches and all fractions over. ROUND AND EQUAL-SIDED TIMBER MEASURE. Table for ascertaining the number of Cubical Feet, or Solid Contents, in a Stick of Round or Equal-sided Timber, Tree, &c. RULE. Multiply the area in Feet, corresponding to the 4th Girt, by the length of the stick of Timber, and the product is the solidity in feet and decimal parts of a foot. Example 1. A stick of Timber is 18 feet long and 14 inches girt, how many cubic feet does it contain? Opposite 14 is 1.361 which X 1824 feet 6 inches. 1.361 18 10888 1361 24-498 Ans. 25 feet. RULE. If a tree, or timber, is tapering, girt it about one-third of the way from the butt to the top-or add together the area at the two ends, and divide the sum by 2, to obtain the mean girth; or take the girth of the tree at equal distances from each other, add all the girths together, and divide the sum by this number, for the mean girth. It is usual to allow, on account of the bark, in oak 1-10th or 1-12th part of the circumference, beech, ash, &c., should be less. |