It is readily seen that from this one projection, drawing, or view, no idea of the depth of the box is given, although the width and height are correctly shown. A top, or plan, view must now be made to show the depth of the box. Place another piece of ground glass a few inches above the box and, with the eye directly over each separate corner of the top, repeat the process of making the four dots, representing each top corner. Connect these four dots, and the figure thus formed represents the top projection, or plan view, of the box. Now, arrange the two pieces of glass, as shown in Fig. 99. The box being removed, the upper glass is simply lowered to the table, and the front glass is turned from the bottom forward and up, and laid directly below the upper glass.

This position of the figures represents the two projections - front elevation and plan - just as they would be drawn by a draftsman on a sheet of drawing paper. The width of the box is shown in both views, and being the same in each, the front elevation and plan are both of equal width, and therefore each point in the plan is directly over the corresponding point in the front elevation. In more complicated objects, where the complete idea cannot be obtained from the front elevation and plan views, an end view or both end views must be shown as in Fig. 100, which represents the projections of a box with a curved top. These end views are obtained by taking two or more pieces of ground glass, placing them one in front of each end, and then drawing the projections. This is done, as in the cases of the front elevation and plan, by making several dots for the shape of the top, and drawing a curved line through these dots. The two end views are placed as shown - the right-hand view at the right of the front view, and the left-hand view at the left. This gives the proper arrangement of the view as a draftsman would work them out on paper.

Fig. 99. Plan and Elevation of Box Shown in Fig. 98.

Fig. 100. Plan, Elevation, and End Views of a Box with a Curved Top.

Fig. 101. Six Views of Object Courtesy of Pennsylvania Railroad Company, Altoona, Pennsylvania.

In Fig. 101 is represented a practical case where the object is sufficiently complicated to require a view of each of its six faces. As will be seen in the figure, six views are shown - front, top, bottom, right side, left side, and rear. In Fig. 102 is represented the method of folding out the projection planes after the faces of the object have been projected on them, in order to have them all in one plane - that of the surface of the drawing paper, as shown in Fig. 101.

## Drawing The Projection On Paper

From the explanation just given, it will be seen that the projection views are all of the same size as the faces of the object they represent. They can, therefore, be drawn just as readily on a sheet of drawing paper without the use of the ground glass. For the front view, measure the four front edges of the object, and lay off on the paper a figure of the same shape as the front of the object. Repeat the process for the top of the object, obtaining the top view, or plan; and for each end of the object, obtaining the end view, or side views. The bottom and rear views can be placed in the same way. Draw the plan view with its four corners directly over the four corners of the front view, and the bottom view with its four corners directly under. Draw the right end, or side, view with its four corners directly to the right of the four corners of the front elevation, and the left end, or left side, view and rear view, with their corners directly to the left of the corners of the front view.

## Projection Lines

As each projected point of an object shown in plan view must be directly over the projection of the same point in the front elevation, a vertical dotted line will connect these points, as projected in pairs; and as each projected point in an end view must be directly opposite the projection of the same point in the front elevation, a horizontal dotted line will connect these points, as projected in pairs. These dotted lines are called projections or construction lines.

## Ground Line

Having the two planes at right angles on which the front elevation and plan are represented, when the top plane is turned up to bring the plan above the front elevation, as represented on the surface of the drawing paper, it revolves on the intersecting line of the two planes as an axis. This intersecting line xy in Fig. 103, is called the ground line, and this is usually abbreviated to GL. The projections may be placed at any convenient distance above or below the GL, unless these distances are given in any problem. In beginning all ordinary projection work, it is customary to show the GL as a horizontal line between the front elevation and plan views, and the projection of any pair of points in the front and plan views are always in a line perpendicular to the GL. This is evident from the fact that the points in the plan view are directly over the corresponding points in the front elevation. Although the ground line is usually used in learning the subject of projections, it is customary to omit it in practical work.

Fig. 103. Ground Line, xy, at Intersection of Horisontal and Vertical Planes.

Fig. 104. Typical Projections.

## Rules Of Projection

(1) If a surface is perpendicular to either plane of projection, its projection on that plane is simply a line - a straight line if the surface is plane, a curved line if the surface is curved.

(2) The projected view of any point of any object on a plane is in a perpendicular drawn to the plane through the point of the object.

(3) // a straight line is perpendicular to a plane, its projection on that plane is a point; and if the straight line is parallel to the plane, the projection is a line equal in length to the line itself and perpendicular to the ground line.

(4) All points on any object at the same height above its base must appear in the front elevation at the same distance below the ground line, and all points on an object at the same distance back of the front face must appear in the plan at the same distance above the ground line.

## Typical Examples Of Projection

Figs. 104 and 105 show clearly several ideas of plan and elevation. In such work as this, it is customary to call the vertical plane on which the front elevation is drawn V, and the horizontal plane on which the plan is drawn H.

Fig. 105. Typical Projections.

A= a point A" below H, and B" in front of V.

B= a square prism resting against V, two of its faces parallel to H.

C = a circular disk in space parallel to H.

D = a triangular card in space parallel to G.

E = a cone with its base resting against V.

F = a cylinder perpendicular to H, and with one end resting against H.

G = a line perpendicular to V.

H - a triangular pyramid back of V,with its base resting against H.