By the Slide Rule. Set the length in feet upon B to 144 upon A ; and against the square, or girth upon D), is the solid content in feet upon C. ExamPLE.—How many cubic feet is contained in a tree 28 feet long and 16 inches į girth ? Set 28 upon B to 144 upon A; and against 16 upon D is 49.9 feet upon C. To find the Transverse Section of the strongest Beam that can possibly be cut out of a round piece of Timber. Let A B C D be the piece of timber given, draw the diameter BD, and divide it into three equal parts, as B im D, erect the perpendicular m C, meeting the circle in C, draw D C and CB; then draw A B equal and parallel to D C, like. wise A D equal and parallel to B C, and the rectangle will be a section of the beam as re. quired. D с B ON THE STRENGTH OF MATERIALS. A knowledge of the strength of materials is one of the most important, at the same time one of the most difficult subjects that the practical mechanic has to contend with, owing chiefly to the very different qualities of bodies of the same name; hence arise some doubts in selecting experiments whereon to build a data, there being scarcely two experiments made producing the same results. However, the following tables and rules are founded upon a mean of Mr. Rennie, Mr. Barlow, and Mr. Telford's experiments, having found them to agree the best with practice, and my own experiments on similar bodies. ON THE COHESIVE STRENGTH OF BODIES. The cohesive strength of a body is that force with which it resists separation in the direction of its length, as in the case of ropes, &c; and no reason can be assigned why the strength should not vary directly as the section of fracture, and is totally independent of the length in position, except so far as the weight of the body may increase the force applied ;-neglecting this, and supposing the body uniform in all its parts, the strength of bodies exposed to strains in the direction of their length, is directly proportionate to their transverse area, whatever be their figure, length, or position. H The following Table contains the result of experiments on the cohesive strength of various bodies in avoirdupois pounds ; -also one-third of the ultimate strength of each body, this being considered sufficient in most cases, for a permanent load. To find the ultimate cohesive strength of square, round, and rectangular bars, of any of the various bodies, as specified in the table. Rule.-Multiply the strength of an inch bar (as in the table) of the body required, by the cross sectional area of square and rectangular bars, or by the square of the diameter of round bars; and the product will be the ultimate cohesive strength nearly. EXAMPLE 1.-A bar of cast iron being 11 inches square, required its cohesive power. 1.5 x 1.5 x 18656 = 41976 libs. nearly. ExamPLE 2.—Required the cohesive force of a bar of English wrought iron, 2 inches broad, and { of an inch in thickness. 2 x .375 x 55872 = 41904 libs. Example 3.—Required the ultimate cohesive strength of a round bar of wrought copper, $ of an inch in diameter. .752 X 26540 = 14928.75 libs. PROBLEM II. The weight of a body being given to find the cross sectional dimensions of a bar or rod capable of sustaining that weight. Rule.-For square and round bars,-Divide the weight given by one-third of the cohesive strength of an inch bar, (as specified in the table;) and the square root of the quotient will be the side of the square, or diameter of the bar in inches nearly. And if rectangular, divide the quotient by the breadth, and the result will be the thickness. EXAMPLE 1.- What must be the side of a square bar of Swedish iron to sustain a permanent weight of 18000 libs. 18000 = .86 or nearly ź of an inch square. 24021 EXAMPLE 2.-Required the diameter of a round rod of cast copper, to carry a weight of 6800 libs. ,6800 = 1.16 inches diameter nearly. 4993 Example 3.-A bar of English wrought iron, is to be applied to carry a weight of 2760 libs; required the thickness, the breadth being 2 inches 2760 = .142 = 2 =.071 of an inch in thickness 18624 A TABLE Showing the Circumference of a rope equal to a chain made of iron of a given diameter; and the weight in tons that each is proved to carry; also the weight of a foot of chain made from iron of that dimensions. The transverse strength of a body is that power which it exerts in opposing any force acting in a perpendicular direction to its length, as in the case of beams, levers, &c. for the fundamental principles of which observe the following: That the transverse strength of beams, &c. are inversely as their lengths, and directly as their breadths, and square of their depths; and if cylindrical, as the cubes of their diameters; that is, if a beam 6 feet long, 2 inches broad, and 4 inches deep, can carry 2000 libs; another beam of the same material, 12 feet long, 2 inches broad, and 4 inches deep, will only carry 1000, being inversely as their lengths.Again, if a beam 6 feet long, 2 inches broad, and 4 |