While perspective projection is the method of pictorial representation generally used by the architectural draftsman, he sometimes finds it desirable to draw a quick mechanical picture on which he can measure most distances directly. This can not be done on a perspective as most of the distances are more or less distorted as has already been seen.

To supply this need of an easily made picture upon which parts may be measured directly, we have a system of drawing called Isometric Drawing. Although the ability to measure distances on this kind of a picture is gained, there is somewhat of a loss in pictorial value, as the Isometric drawing does not show the object exactly as seen by the eye of the observer.

This system then is used where approximate pictorial effect is desired together with the advantage of measuring distances directly on the picture. Such drawings are found useful to the architect in making pictorial diagrams of piping systems, etc., where artistic appearance is not a factor. In these the walls and floors are imagined to have been removed showing only the boilers, tanks, radiators, etc., with the connecting pipe lines all in the proper relation to each other. The usual Orthographic Projection drawing would be inadequate to show clearly and comprehensively such a system as a whole.

PLATE 10. ISOMETRIC.

This pictorial method is seldom used to represent the building itself except that it is sometimes satisfactory for framing drawings. See Plate 46.

For an illustration of this method, the brick has again been used and is considered to be 8 inches long, 4 inches wide and 2 inches high, Fig. 56, Plate 10. First it is turned so that the 2 by 8-inch face and the 2 by 4-inch face make angles of 45 degrees with the picture plane, Fig. 57; then tilted up or down into either position shown in Fig. 58a or 58b so that edges A-B, A-C and A-D each make an angle of 120 degrees with the other. These lines are known as Isometric Axes and all lines parallel to them are Isometric Lines.

Of course edges A-B, A-C, etc., are foreshortened when the brick is turned into this position but since this distortion is not great, all isometric lines are drawn in their true length. Accurate measurements may be made only along or parallel to these isometric lines. Thus in Fig. 58a or 58b every visible edge of the object is shown in its true length just as in Fig. 56.

If A-D is drawn vertically, A-B and A-C will make angles of 30 degrees with the horizontal, either up as in Fig. 59a or down as in Fig. 59b.

Now to represent the brick in isometric projection, Fig. 60, first draw the isometric axes like Fig. 59a (if it is desired to look down toward the top of the brick) or like Fig. 59b (if a view from below is needed); then in Fig. 60 measure along A-D 2 inches to point 1, then along A-B 8 inches to point 2 and along A-C 4 inches to point 3. Draw lines 1-4 and 3-6 parallel to A-B with the 30 degree triangle and T-square; then draw 1-5 and 2-6 parallel to A-C. Draw 3-5 and 2-4 vertically and the isometric drawing will be completed. This is the method of drawing any rectangular prism or combination of rectangular prisms.

PLATE 11. ISOMETRIC AND OBLIQUE.

If an object is irregular, imagine a transparent rectangular box to be placed around it, the box then drawn in isometric and the object drawn in the box. This has been done in Fig. 61, Plate II, where the surrounding box is lettered A-B-C-D-E-F-G. Make the rectangular box touch as much of the object as possible; thus the base of this object touches the box all around and the top K-L-M-N lies in the top of the box making both of these easy to draw. Locate corner Q, which lies in the top of the base, by measuring from J to T the distance V-Q that point Q is from face A-D-E-F; then draw a 30-degree line from T and measure along it to Q the distance that Q is from the back face C-D-E of the box. Draw Q-P then P-0 with the 30-degree triangle and T-square, the length of each being measured directly as they are both isometric lines. Connect K, L and A7 with P, 0 and Q and the drawing will be completed.

An isometric circle may be made by first drawing a circle with the compass and putting it in a square, Fig. 62a, Plate 11, then drawing the isometric of the square and then the isometric circle by-means of coordinate lines in the isometric square. This has been done in Fig. 62b where the points A, D and G have been located by the lines A-B and A-C, D-E and D-F, G-H and G-I, all of which are isometric lines whose lengths were taken from Fig. 62a and laid off in Fig. 62b.

An approximate isometric circle may be drawn by first drawing the isometric square as before, then the perpendicular bisectors of each side as in Fig. 63a, b and c. It will be seen that these bisectors intersect at B, D, E and F. With B as a center and a radius B-G, draw the circle arc from G to H. With E as a center and a radius E-H draw a circle arc from H to I. Then with D and F as centers complete the isometric circle. Figure 63a is a horizontal circle while Figs. 63b and 63c are vertical circles.

## Oblique Drawing

In isometric drawing the objectionable foreshortening of lines which is found in perspective is eliminated, but the distortion of shape still remains. An object with an irregular or a circular face is rather difficult to draw in isometric just as in perspective. This is noticed in Fig. 62b. To escape this, the method called Oblique Projection may be used. Here the object is considered as having the front face in or parallel to the picture plane and the view taken from a point to one side and slightly above or below the object as in Fig. 64, Plate 11. That face which is parallel to the picture plane is drawn just the same as in orthographic projection and in this lies the value of the method, for circles may be drawn with the compass, etc. Thus face A-B-C-D-E, Fig. 64, Plate 11, is drawn in its true shape. Then the lines A-F, B-G, C-H, etc., are drawn toward the right or left and upward or downward, in any convenient direction, usually at 30 or 45 degrees with the horizontal, and are shown in their true length as in isometric.

The following reminders will serve as a guide to produce the best results:

Where there is an irregular face, place it parallel to the picture plane.

Place the long dimension of the object parallel to the picture plane.

Where the irregular face is the short side of the object, neglect the rule about the long dimension.