To find the convex surface and solidity To find the solidity or capacity of any To find the solid contents of a wedge To find the convex surface and solidity To find the convex surface and solidity To find the convex surface and solidity To determine the proper length of iron To determine the length of angle iron to form a ring of given diameter To find the diameter of a circle when any chord and versed sine are given To find the length of any given arc of a To find the area of the sector of a circle To find the area of a circular ring for angled iron hoops, from 6 inches to 6 feet in diameter; advancing by an eighth of an inch.-Angle outside Table containing the circumferences for angled iron hoops, from 6 inches to 6 feet in diameter; advancing by an eighth of an inch.-Angle inside 102 Table of the weight of flat bar iron Table showing the weight of a lineal foot of malleable rectangular or flat iron, from 1-8th of an inch to 3 inches thick; advancing by an eighth, and quarter of an inch, in Table showing the weight of a lineal foot of round bar iron, in avoirdu- Measure of squares, rectangles, &c. Measure of circles and polygons and F. Parallel Motions 20 22 206 260 G. Elevation and Section of an Overshot Water-Wheel constructed by Messrs. 241 H. Details 241 K. Boilers of the "Braganza" steam vessel, by Messrs. Bury, Curtis, and Kennedy 270 271 THE WORKSHOP COMPANION. PRACTICAL GEOMETRY. GEOMETRY is the science which investigates and demonstrates the properties of lines on surfaces and solids: hence, PRACTICAL GEOMETRY is the method of applying the rules of the science to practical purposes. 1. From any given point, in a straight line, to erect a perpendicular; or, to make a line at right angles with a given line. On each side of the point a from which the line is to be made, take equal distances, as A b, A c; and from b and c as centres, with any distance greater than b A, or c a, describe arcs cutting each other at d; join a d, which will be the perpendicular required. b 2. When a perpendicular is to be made at or near the end of a given line. Take any point n above a b, and with centre n and distance n A, describe a circle, cutting the given line at b; through b and the centre n, draw the diameter b n c, and join CA, which will be the perpendicular required. A 3. To do the same otherwise. From the given point a, with any convenient radius, describe the arc de b; with the same radius from d, cut the arc in c, and from c, cut the arc in b; also from c and b as centres, with the same or any other radius, describe arcs cutting each other in t; then will the line At be the perpendicular required. d A Note. When the three sides of a triangle are in the proportion of 3, 4, and 5 equal parts respectively, two of the sides form a right angle; and observe that in each of the preceding problems, the perpendiculars may be continued below the given lines, if necessarily required. 4. To bisect any given angle. From the point A as a centre, with any radius less than the extent of the angle, describe an arc, as c d; and from c and d as centres, describe arcs cutting each other at b; then will the line Ab bisect the angle as required. d 5. To find the centre of a circle that shall cut any three given points, not in a direct line. From the middle point b as a centre, with any radius, as b c, bd, describe a portion of a circle, as csd; and from and t as centres, with an equal radius, cut the portion of the circle in c, s and d, v; draw lines through where the arcs cut each other, and the |