Casks are not commonly constructed in exact conformity with any regular mathematical figure. By most writers, on this subject, however, they are considered as nearly coinciding with one of the following forms: and their contents in cubic inches may be found by the rules in men suration, for determining the solidity of these figures. To find the Contents of a Cask by four Dimensions. Rule.--Add together the squares of the bung and head diameter, and the square of double the diameter, taken in the middle between the bung and head; multiply the sum by the length of the cask, and the product by 1309. To find the Contents of a Cask in the form of the Middle Frustrum of a Spheroid. Rule. Add together the square of the head diameter and twice the square of the bung diameter; multiply the sum by of the length, and the product by 00355, for a wine gallon of New York standard measure, or 0034 for old English gallons. If D and d the two diameters, and the length, the capacity in inches × d2) × 1 × 7854. And by substituting 00355 for 7854, we have the capacity in wine gallons. = = = (2D2 Example.-What is the capacity of a cask of the second form, whose length is 30 inches its head diameter 18 inches, and its bung diameter 24? 14760 × 00355 52.39 wine gallons. Ans. To find the Contents of a Cask in the form of two equal Frustrums of a Cone. Rule. Add together the square of the head diameter, the square of the bung diameter, and the product of the two diameters; multiply the sum by of the length and the product by 00355 for New York wine gallons, or 0034 for old English gallons of 231 cubic inches. Example.--What is the capacity of a cask whose dimensions are as follows: 30 inches long, head diameter 18 inches, and bung diameter 24 inches? 18=324 24=576 Product of 2 diam. =432 1332 × 10 13320 ×·00355=46.286. Or (D2+d2+Dd) × ‡l × 00355. OF ARTIFICERS' WORK. Artificers compute the contents of their works by several different measures, viz.: 1. Glazing and mason work, by the foot. 2 Painting, plastering, paving, &c., by the yard. 3. Flooring, partitioning, roofing, &c., by the foot. 4. Brickwork, by the 1000, or cubic foot. BRICKLAYERS' WORK. Brickwork is estimated at the rate of a brick and a half thick. So that, if a wall be more or less than this standard thickness, it must be reduced to it, as follows: Rule.-Multiply the superficial contents of the wall by the number of half bricks in the thickness, and of that product will be the contents required. BRICKS AND LATIS. DIMENSIONS. 15 common bricks to a cubic foot of 8-inch wall when laid. Laths are to inches by 4 feet in length, are usually set of ar inch apart, and a bundle contains 100. Stourbridge fire-brick 91 by 4 by 2 inches. Example.-How many bricks will it require to build a house 30 feet square, 20 feet high, and 12 inches thick, above which is a triangular gable, rising 12 feet, and 8 inches thick? Masonry is the science of preparing and combining stones, so as to properly touch, indent, or lie on each other, and become masses of walling and arching for the purposes of building. In stone walling, the bedding joints ought each to be laid horizontally when the top of the wall is to terminate so. In building bridges and fence walls upon inclined surfaces, the bedding joints ought to follow the general direction of the work. A wal' which consists of unhewn stone, is called a rubble wall, whether or not mortar is used. This species of work is of two kinds-coursed and uncoursed. In the former, the stones are gauged and dressed by the hammer, and the masonry laid in horizontal courses, but not always confined to the same thickness. The uncourse rubble wall is formed by laying the stones in the wall as they come to hand, without any previous gauging or sorting. Walls, columns, blocks of stone or marble, &c., are measured by the cubic foot; and pavements, slabs, chimney-pieces, &c., by the superficial or square foot. Cubic or solid measure is used for the materials, and square measure for the workmanship. In the solid measure, the true length, breadth and thickness, are taken, and multiplied continually together. In the superficial, there must be taken the length and breadth of every part of the projection which is seen without the general upright face of the building. DIGGING. 24 cubic feet of loose sand, 17 cubic feet of clay, 18 cubic feet of earth, 13 cubic feet of chalk, equal 1 ton gross. 1 cubic yard of earth before digging will occupy about 1 cubic yards when dug, and contains 21 striked bushels, which is considered a single load, and double these quantities a double load. Weight of a Cubic Foot of various Substances in common use. Clay of common soil weighs 3037 lbs. 1 cubic yard of sand weighs 1 66 (See Table of Specific Gravities of Bodies.) HYDRAULIC CEMENT. To build a rod of brick work requires 1 cubic yards of chalk lime and 3 single loads or yards of drift: or 1 cubic yard of stone lime and 3 single loads of sand; or 36 bushels of cement and 36 bushels of sharp sand. A load of mortar is 27 cubic feet, and for its preparation requires 9 bushels of lime and 1 cubic yard of sand. Lime and sand lessens about when made into mortar; likewise cement and sand. Lime, or cement and sand, to make mortar, requires as much water as is equal to of their bulk, or about 5 barrels for each rod of brick work built with mortar. A barrel of cement is 5 struck bushels, and weighs 3 cwt. 1 yard, or 9 superficial feet of the standard thickness (1 brick thick), requires of cement about 24 bushels. 1 yard superficial of pointing to brick work in cement, requires about of a bushel. 1 yard of plastering in cement, requires of a bushel. 1 bushel of cement will cover 14 square yards at 1 inch thick. or 11 or 24 66 66 66 66 66 BROWN MORTAR. One-third Thomaston or Rhode Island lime, two-thirds sand, and a small quantity of hair. TABLE, Showing the capacity of Cisterns, Wells, &c., in Ale Gallons and Hogsheads, in proportion to their diameters and depths. 81 347.7 91 10 11 33. 38.6 44. 49.6 55.2 60.7 390. 37.1 433 49.4 55.7 61.9 68.1 434-3 41.3 48.2 55 62. 68.9 75.8 481. 45.8 53.4 61. 68.7 76.4 84. 583.3 55.5 64.8 74. 83-3 92.6 101.8 12 693. 66. 77. 88. 99 110 121. EXPLANATION.-Find the diameter in feet in the left-hand coluinn of the table; then move to the right on the same line till you come under the depth in feet, and you will have the answer sought for, in hogsheads. Thus, if the capacity of a cistern be required, whose diameter is 8 feet, and depth 10, we find opposite 8, and directly under 10, on the same line, 55 2 which is the true answer sought. NOTE. The above table will be found useful and convenient in the construction of public reservoirs, as well as private cisterns, as it will enable any one to determine at a glance the dimensions in diameter and depth to hold a given number of hogsheads. For a private dwelling, the capacity should not be less than 7 feet diameter by 8 or 9 feet deep. In the construction of reservoirs for the supply of tenders on railroads, the height should be double that of the diameter, in order to obtain head of water, and thus save time in replenishing the tender. The preceding table was computed in English ale gallons: although in the State of New York but one standard measure for all liquids exists. The following additional rules for computing liquids will be found useful, and often very convenient : APPROXIMATING RULES FOR CALCULATING LIQUIDS. To find the number of Gallons contained in any Square or Rectangular Cistern Rule.-Multiply the contents of the cistern in cubic feet, by 7812 (for ale 6:127), or the contents in cubic inches by 004521 (for ale 00353), and the product will be the number of gallons, nearly. Example.-A cistern that is 6 feet long, 4 feet wide, and 4 feet deep, required its contents in New York gallons. 6×45×4 108 cubic feet. And 108 × 7-812=843 69 gallons=13:39 hhds. Or, 6 feet 72 inches; 4 feet 54 inches; 4 feet 48 inches. And 186624 × 004521=843·72 gallons = 13:39 hhds. Any two dimensions of a Square or Rectangular Cistern being given, to find the third that shall contain any number of gallons (ale or wine) required. Rule.-Divide the number of gallons that the cistern is required to hold by the product of the two dimensions, multiplied by either of the multipliers as above, according as the dimensions are given in feet or inches, or whether ale or wine measure be required, and the quotient will be the third dimension of the cistern, nearly. Example-Required the depth of a cistern to contain 1260 gallons, the length being 6 feet, and width 44 feet? 6×45×7812=(210·92; and 1260÷210 92=5.97 feet deep. NOTE. For calculating the capacity of right cylinders, or cylinders of the figure of the frustrum of a cone, see Mensuration of the Cylinder, &c. CARPENTERS' AND JOINERS' WORK. To this branch belongs all the wood-work of a house, such as flooring, partitioning, roofing, &c. Large and plain articles are usually measured by the square foot or yard, &c.; but enriched moldings, and some other articles, are often estimated by running or lineal measures, and some things are rated by the piece. PLASTERERS' WORK. Plasterers' work is of two kinds, namely: ceiling, which is plastering upon laths, and rendering, which is plastering upon walls, which are measured separately. NOTE. The contents are estimated either by the foot or yard, or square of 100 feet. Enriched moldings, &c.. are rated by running or lineal measure. |