rods at right angles to a beam, CC, which is formed of two pieces of wood or whalebone with slips of cork, or other elastic matter, between the rods.

Figure 6 is a section of the beam, showing also the mode of connecting the rods to the ruler, by small joints of brass; and fig. 5 shows another view of the same connection.

The wedges, marked DD, of wood or ivory, are for tightening or releasing the rods in setting or altering the curve; they tighten the rods by pressing against the elastic slips of cork. Fig.7 shows the wedges, D, D, on a larger scale.

SETTING-OUT BUILDINGS.

23. To set out a building to a plan, and build it with accuracy, is a branch of the buildingart which few can perform with satisfaction to themselves, or to their employers, and chiefly from want of method. The great principle of setting-out well consists in providing the means of correcting the work as it proceeds; and for this purpose, there should be two or more principal lines laid down in such situations that they can be restored at any time, during the progress of the building. Hence, it is obvious that they should be distinct from the walls: but it will be desirable to make the principal or longest line parallel to the longest wall; and the position of the lines should be drawn on the plan.

In an ordinary-sized and simple building, two lines, at right angles to one another, through the central part of the building, will be sufficient; as AB, CD, fig. 8. The points A, B, C, D, being chosen so that they will not be disturbed during the progress of the building, and that lines can be stretched from point to point at any time.

To prove whether the lines AB, BC be at right angles or not, set off 40 feet on a C, and 30 feet on a B, and then be should be 50 feet, if the lines be square to one another. The same thing may be tried by rods, making it 4, 3, and 5 feet, instead of 40, 30, and 50; or 8, 6, and 10 feet.* The distance and parallelism of the walls from these lines are easily tried at any time. 24. In setting-out any door, window, or other part, the distance of its centre from each wall should be measured, and half the width set off on each side of that centre; otherwise, from want of accurate workmanship, it may be found much out of its place, if measured from one wall only.

25. In setting-out any complex figure, that mode of doing it should be chosen which depends least on the accuracy of performing the operation. We will give the usual mode of describing an octagon as an example. Suppose a square, IKML, (fig. 8,) to be set out on the angle E of a building, to find the sides of the octagon, it is common to make M1, M4, L2, L7, and so on, each equal to ME; then 1, 2, 3, 4, 5, 6, 7, and 8, are the angles of the octagon.

26. Better thus.-Construct the square IKLM, and make Ea, Ed, Ec, and Eb, each equal to EM; then, if a line be stretched from a to d, from d to c, from c to b, and from b to a, they will cut the sides of the square in the angles of the octagon.

If the figure has been truly set-out, abcd will be an exact square, and which is easily tried.

M

E

6

* If a triangle be drawn, so that its sides be any equi-multiple of the numbers 3, 4, and 5, one of its angles will be s right angle. Thus, if 2 be the multiplier, then the numbers will be 6, 8, and 10; if 3 be the multiplier, then they will be 9, 12, and 15, and so on.

WORKING DRAWINGS.

27. It has already been stated how much depends on a sound knowledge of the formation of working drawings. We now propose to exhibit the principles of forming them in detail, with occasional examples of application to render the object we treat on more clear, and to relieve the tediousness of the bare contemplation of lines and figures.

28. A Working Drawing is a representation of the whole or of some part of an object on a level plane; and is either a plan, an elevation, a section of the object, or its development.

29. The form of an object on the ground, or on some plane parallel to the ground, is called the Plan; as, for example, the plan of a house, the plan of the chamber-floor of a house, and the like.

30. The form of an object, as it would be seen if the eye could regard it every where, in a direction perpendicular to the plane it is drawn upon, is called an elevation. Therefore, in an elevation, those sides of an object which are parallel to the plane of the drawing, are the only ones which are represented of their real size; and the sole difficulty of representing an object in elevation, consists in finding the form of the parts which are oblique to the lane of the I drawing.

31. If an object be supposed to be cut by a plane, the form its parts would have, at the place where it is cut, is called a Section. It is by means of sections that the construction and internal forms and arrangements of objects are shown.

32. As an elevation does not show the exact form of any thing which is oblique to the plane of the drawing, it is sometimes an advantage to consider the whole surface of the body to be spread out flat upon the plane of the drawing; a surface spread out in this manner is called the development of the object.

The forms which occur in working drawings are chiefly portions of solids, sometimes of regular solids, and not unfrequently of irregular ones. Therefore, to give an example of each solid which occurs would be an endless task; and we must confine ourselves to a few of the most usual forms, and show methods which are applicable to any form of solid whatever.

33. The principles of drawing an elevation and a section are the same, and therefore we need not repeat them for both cases, but at once proceed to finding the sections of bodies, showing the application to elevations when they are likely to occur of the same form.

34. The solids usually forming the parts of building are prisms, pyramids, cones, cylinders, spheres, and rings.

A PRISM is a solid, bounded by plane surfaces, of which two are opposite, equal, and parallel. A PYRAMID is a solid, bounded by plane surfaces, all but one of which meet in one point.

A RIGHT CONE is a solid, described by the revolution of a right-angled triangle about one of its legs. The leg, or the line round which the triangle revolves, is called the axis of the cone; and the base of a cone is the circle described by the other leg of the triangle.

A CYLINDER is a solid, described by the revolution of a right-angled parallelogram about one of its sides. The side round which the parallelogram revolves is called the axis of the cylinder; and the circles described by the ends of the parallelogram are called the ends of the cylinder. A SPHERE, OF GLOBE, is a solid formed by the revolution of a semi-circle about its diameter as an axis.

A RING is a solid described by a circle revolving round a point without the circle, and in a direction perpendicular to the plane of the circle.

A species of wedge-formed figure is also sometimes used, and a variety of forms which are generated by Gothic curves.

35. When the body to be represented consists of only part of a known regular solid, it will generally be most convenient to complete the solid to obtain the representation.

Sections of Solids.

36. To find the section of a cone, ABC, through a line given in position, and passing through the axis.

Let ABC, (figures 1, 2, and 3, pl. IV,) be the elevation of the cone, and let DE be the line of section. Through the apex or top of the cone, C, draw CF, parallel to the base-line AB, and produce ED to meet AB in D, as in figure 2 and 3, or to meet AB produced in G, as in fig. 1, as also to meet CF in F. On AB describe a semi-circle, which will be equal to half In the semi-circle take any number of points, a, b, c, &c. Draw Dd, in

the base of the cone.

and Gd', in fig. 1, perpendicular to GF; From the points a, b, c, &c. draw lines

figure 2 and 3, and Gd in fig. 1, perpendicular to AB; as, also, Dd, figure 2 and 3, perpendicular to DF. ae, bf, cg, &c., cutting Gd (figure 1) and Dd (figure 2 and 3) in the points e, f, g, &c. In figure 1, make in Ge', Gƒ', Gg', &c. equal to Ge, Gf, Gg, &c.; and in Dd', (figure 2 and 3,) make De', Dƒ', Dg', &c. equal to De, Df, Dg, &c. Through the points e', f', g', &c. draw lines to F. From the points a, b, c, &c. draw lines perpendicular to AB; and from the points where these perpendiculars meet AB, draw lines to the vertex, C, of the cone, cutting the line of section, DE, in l, m, n, &c. Through the points l, m, n, &c., draw lh, mi nk, &c. perpendicular to DE; and through the points D, h, i, k, &c., in figure 1, or d', h, i, k, &c. figure 2 and 3, draw a curve, which will be the section required of the cone ABC.

37. Remarks. In the first of these figures, the line of section cuts both sides of the cone; in this case, the curve Dhik and E is an Ellipsis. In fig. 2, the line of section DE is parallel to the side AC of the cone; in this case, the curve d'hikE is a Parabola. In fig. 3, the line of section, DE, is not parallel to any side of the cone; but when both it and the sides of the cone are produced, if it meet one of these sides, as at B', then the curve d'hikE is a Hyperbola.

And it may also be remarked, that the line of section, DE, in fig. 3, is the same as that which has before (in Art. 17,) been called the height; the part EB', contained between the two sides of the section, is called the major axis; and the line Dd, perpendicular to DE, the base.

Hence the same section may be found by the method already shown in Art. 17; viz. by drawing any straight line deb', fig. 4: make de equal to DE, fig. 3, and eb', fig. 4, equal to EB', fig. 3. Through d, fig. 4, draw the straight line DD at right angles to do': make ɗD equal to Dd', fig. 3; then, with the major axis b'e, the height ed, and the base dD, on each side describe the curve of the hyperbola, which will be of the same species as that shown in fig. 3.

38. To describe the section of a cylinder, through a line given in position, upon the elevation, (fig. 5, pl. IV.)

This might be considered a particular case of the last problem. For a cone, having its apex at an infinite distance from its base; or, practically, at an immense distance from its base, approaches to a cylinder; and all the lines, for a short distance, would differ insensibly from parallel lines. This is the construction shown at fig. 5. But as the sention of a cylinder frequently occurs, a more practical description of it is desirable.

Let ABHI (fig. 5) be the elevation of a right cylinder; AB being the base, and let DE be the line of section. On AB describe a semi-circle; and, in the arc Ad, take any number of