To find the area of a sector, very nearly, knowing the radius and the angle. Turn the angle into seconds, multiply by the square of the radius, and divide by 206265 × 2, or 412530. Mul 262. To find the solid content of a rectangular parallelopiped. tiply together three sides which meet: the result is the number of cubic units required. If the figure be not rectangular, multiply the area of one of its planes by the perpendicular distance between it and its opposite plane. To find the solid content of a pyramid. Multiply the area of the base by the perpendicular let fall from the vertex upon the base, and divide by 3. To find the solid content of a prism. Multiply the area of the base by the perpendicular distance between the opposite bases. 263. To find the surface of a sphere. Multiply 4 times the square of the radius by 3.1415927. To find the solid content of a sphere. Multiply the cube of the radius by 3'1415927 × 2, or 4-18879. 4 3' To find the surface of a right cone. Take half the product of the circumference of the base and slanting side. To find the solid content, take one-third of the product of the base and the altitude. To find the surface of a right cylinder. Multiply the circumference To find the solid content, multiply the area of the base by the altitude. of the base by the altitude. 264. The weight of a body may be found, when its solid content is known, if the weight of one cubic inch or foot of the body is known. But it is usual to form tables, not of the weights of a cubic unit of different bodies, but of the proportion which these weights bear to some one amongst them. The one chosen is usually distilled water, and the proportion just mentioned is called the specific gravity. Thus, the specific gravity of gold is 19.362, or a cubic foot of gold is 19.362 times as heavy as a cubic foot of distilled water. Suppose now the weight of a sphere of gold is required, whose radius is 4 inches. The content of this sphere is 4×4×4×4*1888, or 268.0832 cubic inches; and since, I by (217), each cubic inch of water weighs 252.458 grains, each cubic inch of gold weighs 252 458 × 19.362, or 4888.091 grains; so that 268 0832 cubic inches of gold weigh 268·0832 × 4888.091 grains, or 227pounds troy nearly. Tables of specific gravities may be found in most works of chemistry and practical mechanics. 2 The cubic foot of water is 908.8488 troy ounces, 75°7374 troy pounds, 997 1369691 averdupois ounces, and 62.3210606 averdupois pounds. For all rough purposes it will do to consider the cubic foot of water as being 1000 common ounces, which reduces tables of specific gravities to common terms in an obvious way. Thus, when we read of a substance which has the specific gravity 4'1172, we may take it that a cubic foot of the substance weighs 4117 ounces. For greater correctness, diminish this result by 3 parts out of a thousand. THE END. LONDON: PRINTED BY MOYES AND BARCLAY, CASTLE STREET, LEICESTER SQUARE. UNDER THE SUPERINTENDENCE OF THE SOCIETY FOR THE DIFFUSION OF USEFUL KNOWLEDGE. In Royal Duodecimo. REPRINT OF BARLOW'S TABLES OF SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, AND RECIPROCALS OF ALL INTEGER NUMBERS, FROM 1 TO 10,000. PRINTED FOR TAYLOR AND WALTON, BOOKSELLERS AND PUBLISHERS TO UNIVERSITY COLLEGE, UPPER GOWER STREET. IN 1814, MR. BARLOW, of the Royal Military Academy, published a more extensive table of the kind above described than had previously existed. At that time we believe no one table contained more than the first thousand numbers. The extent and accuracy of Mr. Barlow's performance gained for it a high reputation among mathematicians, which was enhanced by the additional Tables of Prime Numbers, Hyperbolic Logarithms, &c. &c. &c. These, however, though indispensable to the scientific calculator, are of little use to the practical engineer; and it may be that the mixture of the Tables, which are now reprinted, with others of a less general character, and with collections of mathematical formulæ, prevented practical men from seeing how great an accession of calculating power was within their reach. It must be added, that the type and paper were of the worst quality, and that a combination of circumstances kept the work out of sight; so that it was rarely to be met with, even among second-hand booksellers (though often asked for), at the very time when no inconsiderable portion of the original stock remained with the person who had succeeded to the rights of the publisher over the rest of the edition. An arrangement having been made, by which the copyright of the portion described in the above title has passed into the possession of Messrs. TAYLOR and WALTON, that part of the original work has been republished, in the same type, and with the same precautions for insuring accuracy, as used in the lately published Tables of Logarithms. To all who are aware that very many of the instances in which calculation is required by the engineer, architect, &c., arise out of the necessity of finding, either by direct computation or by logarithms, those results which will now be tabulated and obtained by inspection, nothing need be said in favour of the undertaking. To the actuary and money calculator the Table of Reciprocals will be found of the highest value. The work is accompanied by an explanation of the mode of using the tables. The subjoined specimen will shew the extent of the parts and the arrangement of the whole. 1901 361 38 or 1940 24 374 42 25 1937 375 19 69 1949 1950 | Cube. 6 869 835 701 7 301 384 000 | 43 6004587 12 3877959 5260389 39 |