til they approach the middle, when it may be increased a little more rapidly, and the lines made somewhat thinner.

By pursuing this system, the shade will be graduated in a similar manner from every shore, and perfect symmetry in the positions of the lines will be insured.

SECTION III.

PRINCIPLES OF PLAN DRAWING.

1. What are Geometrical Drawings?

Geometrical drawings are those which are made for the purpose of conveying to the mind, through the eye, a just idea of the true proportions and dimensions of objects.

2. What objects are generally represented in geometrical drawings?

The objects represented in geometrical drawings are generally solid bodies, with irregular or curved surfaces, such as houses, blocks of wood, chairs, tables, &c.

3. Can we generally conceive of their shape and dimensions from one single drawing or view?

We cannot. For instance, if we place ourselves in front of a house, or opposite to one end of it, or if we stand behind it, or look down upon it from some great height, such as the top of a lofty steeple, we shall in each case have a different view of it; so that, unless we take different drawings of it, from several points, it will not be possible to convey any just notion of its general appearance.

4. What is a horizontal plane?

It is any plane parallel to the water-level, such as the level ground, the floor of a house, &c.

5. What is a vertical plane?

It is a plane perpendicular to a horizontal plane; such as the front or ends of a house, or the face of a vertical wall.

6. How many kinds of geometrical drawings are necessary in order to represent the form and dimensions of an object? Three kinds only are necessary; viz., a PLAN, a SECTION, and an ELEVATION.

7. What is a plan?

A plan of an object merely resembles the appearance which it would present to the eye, when viewed from a point directly above it.

In order to illustrate this more clearly, let us proceed to draw the plan of a small building

In commencing a building, the first thing necessary is to have a GENERAL PLAN, or plan of the foundation.

Let us

suppose that the building to be represented is a cottage, with a door and window only.

First, having fixed upon the scale on which the drawing is to be made, say 30 feet to the inch, lay off the length of the cottage 30 feet, on the line ab, and the width 24 feet, on ac, and complete the rectangle to repre

C

a

sent the exterior dimensions of the cottage; that is to say, its length and breadth from out to out. Next, lay off from the same scale the thickness of the wall from a to b, and from a to c, and draw the interior rectangle, having its sides parallel, respectively, to those of the

outer one.

wall.

ba

This will represent the interior faces of the

We see that this figure has nearly the same appearance

as would be presented by the foundations of a small building, viewed from a point directly over them.

Doors and windows are generally

marked in a ground plan. In order
to distinguish them from each other,
the lines of the foundation walls,
which interfere with the doors, are
rubbed out.
will be marked accordingly.

The doors and windows

It

The complete PLAN of the cottage is now drawn. shows the size of the room, the thickness of the walls, and the width and position of the door and window.

By means of a plan, drawn according to a scale, it would be easy to lay out correctly, the foundations of a building and the doors and windows of the lower story. But after building a few courses, we should be obliged to stop for want of further directions, because the PLAN can neither explain the height of the doors or windows, nor the height of any other part of the building.

This proves what has already been stated, viz., that more than one kind of drawing of any object is always necessary in order to explain its form and dimensions. Before proceeding to the other kinds of geometrical drawings, mentioned above, we will add some further explanations and observations on the subject of PLANS.

8. The PLAN of any object is always supposed to be made on a horizontal plane or dead level. The necessity of following this rule will appear from the following considerations.

Suppose it were required to build a house on uneven ground, such, for example, as the side of a hill. Every one knows that in laying out the foundation, no reliance would be put on any oblique measurements made along the slope,

but that all the measurements would have to be made in horizontal lines. For instance, if you were to measure 30 feet obliquely, along the side of the hill, for the breadth of your proposed building, it would still be necessary to lay the first floor horizontally. After this was done, you might find the space which was laid out for the breadth of the building, reduced to 29 feet, to 28 feet, to 25 feet, or even to a less distance, according to the steepness of the slope of the hill. The plan of an uneven field, in which the dimensions were marked according to oblique measurements made upon the sloping or irregular surface of the ground, would therefore be of no use.

9. It is more difficult to draw the plan of any object having sloping or oblique lines, than to draw the plan of a building having only horizontal and vertical lines, because the oblique or sloping lines must all be reduced in a certain proportion.

10. The following are the rules for laying down truly, on a horizontal plane, the points and lines of all objects, any way situated, with respect to it.

11. The imaginary horizontal plane, on which the plan is made, and to which all points and lines are referred, is called the HORIZONTAL PLANE OF PROJECTION.

This plane may be so taken as to cut the object which is to be drawn upon it, or it may be taken directly above or below the object. But for learners, it is best to begin by supposing the horizontal plane to pass through the base, or lowest point of the given object.

In respect to such points of the object as stand upon the plane of projection, or coincide with it, there can be no difficulty, for such points are their own place or projections on the plane.