THE MECHANIC'S, MACHINIST'S, AND ENGINEER'S PRACTICAL BOOK OF REFERENCE: CONTAINING TABLES AND FORMULE FOR USE IN SUPERFICIAL AND SOLID MENSURATION; STRENGTH AND WEIGHT OF MATERIALS; MECHANICS; MACHINERY: HYDRAULICS; CHEMISTRY; HYDRODYNAMICS; MARINE ENGINES; ADAPTED TO AND FOR THE USE OF ALL CLASSES OF PRACTICAL MECHANICS. EDITED BY CHARLES W. HACKLEY, Professor of Mathematics in Columbia College, N. . from A or F as centres, cut the former ares at r, or, and the fines Ar, Fr, will tend to the centre as required.qls 10. To describe an are, or segment of a circle, of large radii. Of any suitable material, construct a triangle, as ABC; make A B, BC, each equal in length to the chord of the are DE, and height, twice that of the arc Bb. At each end of the chord DE fix a pin, and at B, in the triangle, fix a tracer (as a pencil), move the triangle along the pins as guides; and the tracer will describe the are required. 11. Or otherwise. Draw the chord A CB; also draw the line HD I, parallel with the chord, and equal to the height of the segment; bisect the chord H 2 3 D 3 2 n A 1 2 3 C 3 2 1 B 3 2 1 in C, and erect the perpendicular C D join AD, DB; draw A H perpendicular to A D, and BI perpendicular to BD; erect also the perpendiculars An, B n; divide B and H I into any number of equal parts; draw the lines I 1, 33, &c.; likewise divide the lines An, B n, each into half the uber of equal parts; draw lines to D from each division in the 3 An, Bn, and, through where they intersect the former lines, Scribe a curve, which will be the arc or segment required. ar This t 2. To describe an ellipse, having the two diameters given. hat This "These 13" 39" (tha до also 'escribe an elliptic arch, the width and rise of span being 1. ha line at right angles the chord or span AB; erect the perpendicular A q, and draw the line qD equal and parallel to A C; bi sect AC and Aq in r and n; make Cl n equal to CD, and draw the line 1 rq; draw also the line n s D; bisect s D with aline at right angles, and meeting the line CD in g; draw the line gq, make CP equal to Ck, and draw the line gPi; then from g as a centre, with the radius g D, describe the are s Di; and from k and P as centres, with the ra S АК 3 dius Ak, describe the arcs A s and B i, which completes the arch as required. Or, sərgi A B 14. Bisect the chord AB, and fix at right angles any straight guide, as be; prepare, of any suitable material, a rod or staff, equal to half the chord's length, as def; from the end of the staff, equal to the height of the arch, fix a pin e, and at the extremity a tracer f; move the staff, keeping its end to the guide and the fixed pin to the chord, and the tracer will describe one half the arc required. 15. To describe a parabola, the dimensions being given. Let AB equal the length, and CD the breadth of the required parabola; divide CA, ČB into any number of equal parts; also divide the perpen diculars Aa and Bb into the same num ber of equal parts; 3 a 2 1 A. D 6 3 then from a and b draw lines meeting each division on the line ACB; and a curve line drawn through each intersection will form the parabola re quired. 16. To obtain by measurement the length of any direct line, though intercepted by some material object. Suppose the distance between A and B is required, but the right line is intercepted by the object C. On the point d, with any convenient radius, describe the arc cc, make the arc twice the radius in length, through which draw the line dce; and on e describe another d arc equal in length to once the radius, as eff; draw в the line e fr equal to e ƒ d; on r describe the are jj, in length twice the radius; continue the line through rj, which will be a right line, and de, or er, equal the distance between dr, by which the distance between A and B is obtained as required. " 17. A round piece of timber being given, out of which to cut a beam of strongest section. D C B B Divide into three equal parts any diameter in the circle, as Ad, e C; from d or e, erect a perpendicular meeting the circumference of the circle, as dB; draw AB and B C, also AD equal to BC, and D C equal to AB, and the rectangle will be a section of the beam as required. 18. To measure the distance between two objects, both being inaccessible. From any point C draw any line Cc, and bisect it in D; take any point E in the prolongation of A C, and draw the line Ee, making De equal to DE; in like manner take any point F in the prolongation of BC, and make Df equal to FD. Produce A D and ec till they meet in d, and also BD and fe till they meet in b; then ab equal AB, or the distance between the objects as required. 19. To ascertain the distance, geometrically, of any inaccessible object on an equal plane. Let it be required to find the distance between A and B, A being inaccessible; produce the line in the direction of A B to any point, as D; draw the line D d at any angle to the line A B; bisect the line Dd, through which draw the line B b, making cb equal to Be; draw the line db a a; also through c, in the direction c A, draw the line ac A, intersecting the line dba; then ba equal B A, the distance required. gotu pašina pia gior 20. Otherwise. Prolong A B to any point D, making BC equal to CD; draw the line Da at any angle with DA, and the line Cb similar to Be; draw also the line DE F, which intersects the line Ba; then ab equal BA, or the distance required. 21. To find the proper position for ansattune eccentric, in relation to the crank in a steam engine, the angle of eccentric rod, and tras AAN vel of the valve, being given. A if 2 Draw the right line A B, as the situation of the crank at commencement of the stroke; draw also the line Cd, as the proper given angle of eccentric rod with the crank; then from C as centre, describe a circle equal to the travel of the valve; draw the line ef at right angles to the line C a, draw also the lines 1 1, and 2 2, parallel to the line ef; and at a distance from ef on each side, equal to the lap and lead of the valve, draw the angular lines C1, C2, which are the angles of eccentric with the crank, for forward or backward motion, as may be required. e 2 B 22. The throw of an eccentric, and the travel of the valve in a steamengine, also the length of one lever for communicating motion to the valve, being given, to determine the proper length for the other. On any right line, as A B, describe a circle A D, equal to the throw of eccentric and travel of valve; then from C as a centre, with a radius equal to the length of lever given, cut the line A B, as at d, on which describe a circle, equal to the throw of eccentric or travel of valve, as may be line AB, and d B is the length of the lever as required. required; draw the tangents Ba, Ba, cutting each other in the the distance between the centres of formation and revolution, as Note.-The throw of an eccentric is equal to the sum of twice abor And steam openings, and the valve's excess of length more than just The travel of a valve is equal to the sum of the widths of the two sufficient to cover the openings. a b e d |