To find the Content of Hewn Timber in Cubic Feet: 353. Put the length, and a and b, the two dimensions of the end in inches. Then q× a × b × 12 is the content in cubic inches; and, as 1728 or 12 × 12 × 12 cubic inches make one cubic foot, it is plain that When the area of the end is 144 square inches, the length of the piece is its content in c. f. Let a piece of timber be 36 ft. long, and 16 in. by 12 on the end, then : яхахъ 12 × 12 36 X 16 X 12 12 x 12 3X1648 c. f., the content. Examples. 1. Required the content in cubic feet of the following pieces of timber: 20 ft., 12 by 12; 30 ft., 12 by 10; 18 ft., 10 by 9; 24 ft., 12 by 11; 36 ft., 14 by 10; 40 ft., 16 by 12; 32 ft., 18 by 16; 34 ft., 13 by 12; and the cost at $2,121 per ton of 50 c. f. Answer, 267 c. f., and the cost $11,343. 2. Required the content of the following pieces, namely: two pieces, each 40 ft., 16 by 14; 3 pieces, each 36 ft., 19 by 18; 4 pieces, each 20 ft., 12 by 11; 3 pieces, 28 ft., 16 by 14; and 2 pieces, each 18 ft., 12 by 10; and the cost at $3 per ton. Answer, 12 t. 15 c. ft., and the cost $36,90. 3. Required the cost of 100 pieces, each 20 ft., 10 by 9, at $2 per ton; 50 pieces, each 30 ft., 14 by 14, at $3 per ton, and 75 pieces, each 18 ft, 12 by 12, at $4,50 per ton. Answer, $306,50. METRICAL OR DECIMAL SYSTEM. (From Kelley's "Universal Cambist.") THE fundamental standard adopted in France for the metrical system of weights and measures, is a quadrant of the meridian; that is to say, the distance from the equator to the north pole. This quadrant is divided into ten millions of equal parts, and one of these parts or divisions is called the Metre, which is adopted as the unit of length, and from which, by decimal multiplication and division, all other measures are derived. The length of the quadrant has been ascertained by MM. Delambre and Mechain, by measuring an arc of the meridian between the parallels of Dunkirk and Barcelona, and has been found to contain 5130740 French toises. This number, divided by ten millions, gives 36,941328 French inches, which is the metre, the element of all the other measures, and which is equal to 39,371 English inches. In order to express the decimal proportions, the following vocabulary of names has been adopted: For multipliers, the word Deca prefixed means On the contrary, for divisors, the word Deci 10 times. 100 66 1000 "6 10,000 } 10th part. Centi.. 100th " It may assist the memory to observe that the terms for multiplying are Greek, and those for dividing, Latin. Thus, Deca-metre, means ten metres. Deci-metre, the 10th part of a metre. Centi-metre, the 100th part of a metre, and so on for The metre, as before stated, is the element of long measure, and 39,371 English inches. The are, which is a square deca-metre, (or 100 square metres,) is the element of superficial measures. It equals 3,955 English perches. The stere, which is a cubic metre, is the element of solid measures, and 35,317 cubic feet English. The Litre, which is the cubic deci-metre, is the element of all liquid measures, and of all other measures of capacity. It equals 0,26419 English gallons, and the hectolitre = 2,8379 Winchester bushels. Lastly, the gramme, which is the weight of a cubic centimetre of distilled water, of the temperature of melting ice, (the greatest condensation,) is the element of all weights, and equals 15,434 English grains, Troy. New Weights and Measures of France, compared with the old, and also with English Weights and Measures. The litre, which is the unit for measures of capacity, = 2,1135 English pints, wine measure; and, therefore, 1 hectolitre equals 26,41906 wine gallons, or 2,83796 Winchester bushels. Winchester bushel = = 35,236 litres. Hence 1 This measure is used for fire-wood, stone, &c. The stere is the same as the kilolitre in the preceding article. The above weights, as before stated, are deduced each from some decimal proportion of the metre. Thus the kilogramme corresponds with the contents of a cubic vessel of pure water at the lowest temperature, the side of which cube is the tenth part of a metre, (the decimetre,) and the gramme answers to the contents of a cubic vessel, the side of which is the hundredth part of the metre, (the centimetre;) for the contents of all cubic vessels are to each other in a triplicate ratio of their sides, (Euclid, 33, xi.) |