1.5625 the square of one end. Common multiplier of a circle, .7854 62500 78125 125000 109375 1.22718750 content of base. Solid feet, 49.08750000 LESSON 1. In a bin of wheat 6 feet long, 4 feet wide, and 3 feet deep, how many bushels? 4.5 feet wide. 6 feet long. 27.0 superficial feet. 3 feet deep. 81 solid feet. 1728 solid inches in a foot. 81 feet. 1728 13824 Inch. in a bu. 2150.4)139968.0000(65.089 bushels. Thus 3.136 fourths of gills. we have for an Answer, 65 bush. 2 qts. 6 gills, 3 quarters of a gill, [or more naturally, jill.] DUODECIMALS. That is, decimals of 10 and 2; or of 12. This Rule is very convenient for workmen and artificers in casting up the contents of their work: we shall operate with it in the same manner as with Compound Multiplication, without reducing the several denominations into one number, and shall invariably carry at every twelve till coming to feet. The denominations are as follow. 12 fourths," make Inches are called primes; but the plainer our expressions, the better: call them inches. When multiplying by Duodecimals, it is customary to begin with the highest number at the left hand, and produce one product with feet; setting inches under inches, and feet under feet. Then begin with inches and set the first figure in the product one place further towards the right, under seconds, &c. NOTE.-Inches multiplied by feet, produce inches and feet. Inches mul tiplied by inches, produce seconds and inches. Inches multiplied by seconds, produce thirds and seconds, &c. Therefore we must be cautious and mentally divide every product by twelve, and set the remainder one place further towards the right. EXAMPLES. LESSON 1. A joiner has a piece of board 8 feet, 6 inches long, and 1 foot 6 inches wide; how many superficial square feet? Answer, 12 ft. 9 in. that is, 12 square feet and 2 of another foot. 7 3 11 24 10 11 Ans. Begin with the 1 foot on the left and say, one time 7 inches is 7; set 7 in the inches; one time 17 is 17; set 17 in the feet: then begin with the inches and say, 5 times 7 are 35; not 35 inches, but 35 seconds: 12 in 35? twice and 11 over; set 11 in the seconds and carry 2 to the inches; then say, 5 times 17 are 85, and 2 I carried are 87: 12 in 87? 7 times and 3 over; set 3 in the inches and 7 in the feet. Add the two products and the work is done. LESSON 3. "How many solid feet in a stick of timber 12 feet 10 inches long, 1 foot 7 inches wide, and 1 foot 9 inches thick ?" Ans. 35 ft. 6 in. 8" 6" In multiplying the feet, the whole amount of the product must be ascertained, and whatever number of inches are carried, must be added; then divide by 12, set the remainder in the place of inches, and carry the quotient to the feet. Example: in the last line of multiplication we say, 9 times 20 make 180, and 2 to carry make 182. 12 in 182 15 times and 2 over; set 2 for inches and carry 15 to the feet. LESSON 4. "How many solid or cubic feet of wood in a load 6 feet 7 inches long, 3 feet 5 inches high, and 3 feet 8 inches wide?" Ans. 82 ft. 5 in. 8" 4" An easy method for calculating with Duodecimals. 1. Set the multiplicand in usual form: then place the feet of the multiplier under the lowest denomination of the multiplicand, and set the remaining parts of the multiplier off to the right in their natural order. 2. Multiply first with the right hand figure of all, place the first product figure under its multiplier, and proceed in order as in Compound Multiplication. 3. Go through with each denomination in the same manner, placing the first figure under its multiplier towards the left. NOTE. If there be no feet in the multiplier, supply their place with a cipher. EXAMPLE. If the surface of a stone be 8 ft. 6 in. 9 seconds in length, and 7 feet 3 inches 8 seconds in breadth, what is the superficial content? Answer, 62 ft. 6 in. 7" 9" What is the superficial content of a table 8 feet 9 inches 10 seconds, by 5 feet 6 inches 7 seconds? Answer, 48 ft. 11 in. 2" 8" 10" OPERATION. |