Projection 49

Nov let the object he revolved around the edge of the base as an axis. In revolving in this way, it is evident that every point of the prism will move, except the edge which is the axis. A little thought will show that each corner that moves will move in a circle. For example, the corner d of the base will revolve in the arc of a circle the center of which is at point g, the radius of the circle being therefore The line is perpendicular to and must so remain as it revolves. This means that the line parallel to the V plane at first, will remain parallel; and the circle described by point din space will be parallel to V, and will be projected on V in its true size. The arc dvjvkv then represents the circle described by the motion of point d; and on H, this circle appears as the straight line dhj"kh, parallel to V.

In the same way, the other corners, a, b, and c, will each travel in a circle parallel to V. Then, if the prism be revolved through an angle of 45 degrees, each line of the elevation will simply revolve through this angle, with no change in length; and the resulting V projection will be the rectangle exactly the same size and shape as avbvfvdv, but inclined at 45 degrees with the horizontal. This rectangle will be the new V projection of the prism; and, remember ing that each point in revolving moves in a circle parallel to V, the new H projection may be found by dropping perpendiculars from cr and to meet parallels drawn from dh, a', bh, and c", thus determining the points dhi, ah1, i_hi, and These points, when joined in the proper order, give the new plan as shown by the dash lines in the figure.

64. The principles of such revolution may be explained as follows: (a) If any object, no matter how complex, be revolved about an axis perpendicular to V, the V projection will remain unchanged in shape and size, but will revolve to different positions with respect to the horizontal.

(b) The H projection, on the other hand, changing shape and size, will be found directly below (or above) the new V projection, and each point will be at the same distance from V as before revolving.

A similar statement will apply with merely an interchange of V for H, and H for V, in case an object be revolved about a vertical axis.

Fig. 54 shows the same prism as in Fig. 53; but in this figure, the new position has been moved a little to the right so as to clear the first position. Placing in this way takes more space, hut is clearer, and should always be used if the figure to be revolved is complicated. Notice

that in the plan of the second position, the upper end and the two upper sides are visible, while the lower end and the under side are invisible.

65. Third Plane of Projection or Profile Plane. Many times, the two views of an object as plan and elevation, are sufficient to describe the object completely; but in other cases a third view is required to give a satisfactory idea of the object in question. Sometimes, in addition, a sectional view may be necessary to show fully every detail.

The third view usually taken is in a direction perpendicular to that of the plan and the eleva tion. That is, for a rectangular object—as a cube or square prism—there may be the top view or plan; the front view or elevation, and the third, a profile view or end view. The direc tion of the profile view in comparison with the other two, is shown in Fig. 55, in which are rep resented the plan, elevation, and end or profile view of the outlines of a cabin. The end view is taken looking in the direction of the arrow.

It should be noted that the breadth of the end view is the same as that of the plan, while the height is equal to that of the elevation.

On comparing the three projections, it will be seen that the length is shown in plan and elevation, the width in plan and profile, the height in elevation and profile, and the slope of the roof in profile only. In making the three views, the profile or end view, in accordance with Article 59, should be drawn first.

66. Third-Angle Projection. Three views of a rectangular block, with parts of the top and bottom cut away, are shown in Fig. 56. In this figure, as in the preceding one, the arrangement customary in many drafting offices has been followed—of placing the plan above, the eleva tion beneath, and the end or profile view at one side. Where this custom is adopted, the view of the right-hand end is placed either at the right of the elevation, or of the plan; a view of the left-hand end is placed at the left; and so on. This is known as third-angle projection. Thus, in the figure, the end view is a view of the right hand end of the block.

This figure is an example of a case where the plan and elevation do not make the meaning of the drawing sufficiently clear and do not make the shape of the object apparent; hence the end view is required. The end view bears the letters A", BP, etc. The small p at the upper right-hand of the letter stands for profile, in the same way that a small v on the elevation means vertical, and a small h in plan means horizontal.