BOARD MEASURE. In measuring sawed timber, all estimates are made in board feet. A Board Foot is 1 foot long, 1 foot wide, and 1 inch thick. Round timber is generally estimated in cubic feet. Hewn timber may be estimated either by cubic or by board measure. Board feet are changed to cubic feet by dividing by 12, and cubic feet to board feet by multiplying by 12. Mechanics make use of duodecimals in the measurement of lumber. Duodecimals are compound quantities, whose denominations vary in such a manner that 12 units of any lower denomination make 1 of the next higher. The denominations are feet, inches or primes, seconds, thirds, etc. TABLE. - 1 second = (1"). 12 seconds make 1 inch or prime= (1') 12 inches or primes make 1 foot = (1 ft.) Note.—The product of any two duodecimal quantities, takes a sign equal to the sum of the signs of both factors. Thus, 1"X1"=1", or (1.)? x ()=(11_)*; as in decimals .12X.12=.14 or .0001. To find the contents of sawed or of hewn timber. in the multiplicand by the 9 of the multiplier; 6' X 9=54"=4' and 6''. 15 sq. ft. 4' 6" Writing the 6" as a part of the product, we reserve the 4' to add to the next product, 20 ft. X 9 = 180'; and 180% +4=184' =15 sq. ft. and 4’, which we write as the remainder of the product; 15 sq. ft. 4' 6"=15 sq. ft. 54 sq. in. RULE. Write the multiplier under the multiplicand so that units of the same order shall stand in the same column. Multiply as in compound numbers, carrying a unit for every twelve from each lower to the next higher denomination. 2. How many cubic feet in a stick of timber whose length is 30 ft. 6 in., width 13 in., and thickness 14 in.? ANALYSIS.—We proceed as directed in 30 ft. 6 the rule, and multiply by the 13',obtain13' ing 33 sq. ft. 0' 6'' as the board measure 33 sq. ft. O'6" of one surface of the stick. Multiplying this surface by 14' we obtain 38 cu. ft. 14' 6' 7" as the cubical contents. 38 cu. ft. 38 cu. ft. 6' 7" 6'7"=38 cu. ft. 948 cu. in. The same result can be obtained by the ordinary rules of mensuration. Thus, 30 1 x 11 x 1}= 61 x 1 x = 5544=38144 cu. ft. =38 cu. ft. 948 cu. in. 3. How many board feet in the piece of timber described in the last example? 38 cu. ft. 6' 7" x 12 = 462 sq. ft. 7' or 462 sq. ft. 84 sq. in., board measure. ANALYSIS.-As boards are estimated at 1 inch in thickness, the 38-79, cu. ft. in the piece of timber will furnish 12 times that number of board feet =462 sq. ft., or 462 sq. ft. 84 sq. in. 4. How many board feet in a piece of hewn timber which measures 35 ft. 5 in. in length, 1 ft. 6 in. in width, and 1 ft. 8 in. in thickness? How many cubic feet? 5. Paid $28 a thousand feet, board measure, for 25 pieces of hewn timber, each 24 ft. long, 9 in. wide, and 4 in. thick; what was the entire cost? 6. How many board feet in 260 joists, each 30 ft. long, 13 in. wide, and 5 in. thick? To find the contents of round timber. RULE. To four times the area of a middle section add the areas of the ends, and multiply by one-sixth the length. Fourfifths of the contents will be the equivalent value of hewn timber. Note. To find the middle dimension, take half the sum of the dimensions at the ends. 1. How many cubic feet of timber in a log, which measures 3 ft. in circumference at one end, 5 ft. at the other, and 4 ft. in the middle, the length being 40 ft.? ANALYSIS.—(42 x 4 +52 + 32) x .07958 x 40 =51.99 cu. ft., contents. 51.99 cu. ft. X =41.59 cu. ft. of hewn timber. 2. How many cubic feet of hewn timber can be obtained from a log 50 ft. long, 4 ft. in diameter at one end, 7 ft. at the other, and 5 ft. 6 in, in the middle? 3. What is the exact volume of a log 96 ft. in length, and 15 ft. in circumference in the middle, the ends measuring 12 ft. and 18 ft. in circumference, respectively? 4. How many cubic feet of hewn timber will the log last mentioned yield, and how many board feet? 5. A log in the form of a cylinder is sawed into boards one inch in thickness; how many feet of boards will there be, allowing 20% for waste, the log measuring 60 ft. in length and 5 ft. in diameter? 6. A tapering mast measures 9 feet in circumference at the base, and 2 feet in circumference at the top; how many board feet does it contain if the length is 30 feet? 79. How many cubic feet of hewn timber in a section of a tree which measures 30 feet in diameter at one end, and 8 feet in diameter at the other, the length being 90 feet? BRICK WORK. RULE. To each of the dimensions of a brick add the thickness of the mortar in which it is laid, and find the contents in cubic inches. Divide the contents of the wall in cubic inches by the contents thus found, and the quotient will be the number of bricks required. 1. The thickness of a wall is 8 inches; the bricks measure 81 x 45 x 23 in., and the courses of mortar are 1 of an inch in thickness; how many bricks are in the wall, if the height is 28 ft. and the length 30 ft.? 30 x 28 x 8 x 1728 8.7 X 4 x 25 x 12 = 10842 bricks Note.- When a wall is said to be a certain number of bricks in thickness, to obtain the thickness, we add to the width of a brick the thickness of the mortar, and multiply by the number denoting the thickness. 2. How many bricks 81 x 41 x 23 in. will be required to build a wall 60 ft. long, 35 ft. high, and 174 in. thick, the mortar being of an inch in thickness? 3. How many bricks 81 x 41 x 23 in. will be required to build a wall 40 ft. long, 6 ft. high, and 131 in. thick, the courses of mortar being of an inch in thickness ? 4. How many bricks 81 x 41 x 23 in. were used in laying a pavement 300 ft. long, and 8 ft. wide? 5. The thickness of a wall is 174 inches; the bricks measure 84 x 41 x 23 in.; how many bricks in a section of the wall 1 ft. square and 174 in. thick? 6. How many cubic feet in a wall which contains 15000 bricks, the size of a brick being 81 x 41 x 23 in., and the thickness of the mortar in., if the wall is 8} in. thick? HAY. Hay varies so much in weight, according to the manner in which it is packed, and the quality of the grass, that no rule will give exact results. Baled hay varies from 10 lb. to 25 lb. to the cubic foot. Hay in the mow, if well settled, will weigh from 4 lb. to 5 lb. to the cubic foot. In an old and well-settled stack, it will weigh from to 9 1b. to the cold and well-serisha from 4 16.boc foot. Hay To estimate the weight of hay in a mow or stack. RULE. For hay in the mow, multiply the contents in cubic feet by 4 for clover, or by 5 for timothy. In a well-settled stack, multiply the contents by ry for clover, or by 9 for timothy hay, and the product will be the weight in pounds. 1. How many pounds of clover in a mow 25 x 20 x 8 ft.? 25 X 20 X 8*4=16000 pounds. 2. How many pounds of timothy hay in a well-settled conical stack, 8 ft. in diameter and 6 ft. in height? 3. How many pounds of clover hay in a stack which is equal in volume to a cube 12 feet on a side? 4. If a bale of hay measures 8 x 6 x 4 ft., what is its weight in pounds, if a cubic foot weighs 19 lb. ? 5. How many pounds of hay in a bale which measures 31 x 21 x 11 ft., if a cubic foot weighs 17 lb.? 6. The dimensions of a hay-mow are 30 feet in length, 15 feet in width, and 12 feet in height; how many tons of clover hay will it contain? 7. How many tons of timothy hay in a conical stack, if the diameter at the base is 12 ft., the diameter at the top 2 ft., and the height 12 ft. ? |