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and two inches apart. Any careful painter can prepare a board in this manner. The board should not be varnished. The red lines drawn on the board will interfere very little with the use of the board for ordinary purposes. The school should also be provided with one pair of chalk-crayon compasses, for the drawing of regular curves on the blackboard. Any ingenious carpenter can make a pair that will answer very well. One of the points may be hollowed out to receive the crayon, which may be tied in.

7. All the figures in a lesson, or on a page of the DrawingBooks, should be first copied by the pupils on the lined drawing-paper, and then the accompanying Problems should be drawn, and then the free-hand blackboard exercises, when such are suggested. The pupils should also explain the drawings fully-their measurements according to the scale given on the paper, and their real measures when. drawn on the blackboard. But if any of the pupils are too young to understand the few elementary principles of surface measurement that are given in Drawing-Book No. I., these principles may be passed over for the present, as they will come up again in a more extended exposition of the Drawing, Measurement, and Relations of Surfaces and Solids.

8. Although free-hand drawing can be carried out in the present series quite as extensively as in any other series, and perhaps with more effect than in any other, as the guide-lines at once detect all inaccuracies; and although this kind of preliminary practice is important for all designers in art, and especially for artists by profession, yet we would remind teachers and pupils that it is never relied on by architects, draughtsmen, and artisans for the drawing of working-patterns or designs for industrial purposes, and that most of the copies which are given in the drawing-books for practice in free-hand drawing are there executed, with elaborate care, by the aid of ruler and compass. Even the best of artists do not hesitate to resort to all possible mechanical appliances by which their work can be improved; and it would be strange, indeed, if we should deny to children those aids which we allow to age and ex

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perience. While, therefore, we recommend free-hand drawing in elementary exercises, and also in all portions of copies or original designs which can be well executed thereby, we would adyise advanced pupils to make use of all other aids that are essential to accuracy of result. Frequent directions are given throughout the work for freehand exercises in drawing on the blackboard.

9. For the purpose of getting the full effect of a drawing in diagonal Cabinet Perspective (Books II., III., and IV.), partially close the hand, and through the tubular opening thus formed look at the drawing from a position a little above and at the right of it. On thus viewing it intently for half a minute, the drawing will seem to stand out in bold relief from the paper; and if there are any inaccuracies in the perspective, they will be readily detected by the unnatural appearances which they will thus be made to present.

10. If the teacher should find some few slight inaccuracies in which the diagrams in the Drawing-Books do not fully come up to the descriptions of them, they must attribute it to the occasional want of care in the artists who copied them from the original drawings. The errors, however, are believed to be few, and of little importance; and the teacher who gets hold of the principles will easily correct them.

11. It should be remarked, also, that drawings in pencil and India ink, if well executed, and especially if made on the pink-ruled drawing-paper, will be clearer in shading, more distinct in outline, and will show to better advantage generally, than those in the Drawing-Books.

12. For convenience of adapting the explanations of drawings given in the Drawing-Books to those made on the blackboard, let it be understood that the lines on the blackboard are in all cases (unless otherwise directed) supposed to be drawn to the same scale as those assigned for the lines of the printed drawings.

II. STRAIGHT LINES AND PLANE SURFACES.

PAGE ONE.

LESSON I. Horizontal Parallel Lines.-A horizontal line is a line that has all its points equally high, or on a level with the horizon. Parallel lines are lines that extend in the same direction, and that are equally distant from one another, however far they may be extended. Thus, the lines that cross the paper from left to right are parallel lines, one eighth of an inch apart; and they are also horizontal lines when the paper lies flat upon the table, and also when it is raised to an upright position. All the lines in Lesson I. may be considered horizontal and parallel.

In drawing the copies on this page, use a No. 3 or No. 2 pencil, rounded at the point, and not sharp. Use no ruler. In figure No. 1, draw all the lines on the fine-ruled horizontal red lines seen on the drawing-paper-first tracing each line very lightly, carrying the pencil a part of the time from left to right, and a part of the time from right to left, so as to acquire a free command of the hand. Finish by drawing each line firm and distinct, and as true and even as possible. In the first column the lines are one eighth of an inch long; in the second column two eighths, or one quarter of an inch; and in the third column three eighths of an inch long. The printed vertical and horizontal lines in the DrawingBook, and also on the drawing-paper, are one eighth of an inch apart.

In No. I., the pencil lines are drawn on the ruled lines, one eighth of an inch apart; in No. II., they are first drawn the same as in No. I., and then a line is drawn between every two; in No. III., two lines are drawn equally distant between every two lines first drawn as in No. I. No. III. represents coarse shading. Let the pupil imitate the foregoing with free-hand drawing on the red-lined blackboard, and tell the lengths of the lines, thus drawn-as two inches four inches, six inches, etc.; and their distances apart.

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LESSON II. Vertical Parallel Lines. ·A vertical line is one that is exactly upright in position-such a line as that which is formed by suspending a weight by a string. The lines in Lesson II. represent vertical lines; but they are really vertical only when the paper is placed in an upright position, and with the heading of the page upward. These vertical lines are parallel, for the same reason that those in Lesson I. are parallel.

Draw the lines in Lesson II. from the top downward, first going over each line lightly, once or twice; and, when the line is accurately traced from point to point, finish by marking it firmly.

What are the respective lengths of the lines in No. 1? In No. 3? In No. 4?

In Nos. 2 and 3 the lines are drawn at the same distances apart as in the corresponding numbers of Lesson I. In No. 4, three lines are drawn equidistant between the ruled lines. No. 2 represents coarse shading; No. 3, ordinary shading; and No. 4, fine shading.

Free-hand exercises on the blackboard, similar to those directed for Lesson I.

LESSON III. Angles, and Plane Figures. —No. 1 represents two right angles, x, x, formed by one line meeting another. An angle is the opening between two lines that meet.

When one straight line (a b) falls upon another straight line (cd), so as to make the adjacent angles (x, x) equal, the two angles thus formed are right angles. The angle at x, No. 2, is also a right angle.

An acute angle (e) is an angle that is less than a right angle; an obtuse angle (n) is an angle that is greater than a right angle.

A plane is a surface, on which, if any two points be taken, the straight line which joins them touches the surface in its whole length.

Nos. 3, 4, and 5 are plane figures called squares.

A rectilinear plane figure is a plane figure bounded by straight lines.

A square is a plane figure that has four equal sides and

four right angles. Nos. 3, 4, and 5 are squares. They are also called erect squares, because two of the sides of each are erect, or vertical.

A rectangle is a four-sided figure having only right angles. The term is generally applied to those rectangular (right-angled) figures which are not squares. Nos. 6, 7, and 8 are rectangles. Nos. 9 and 10 may be divided into rectangles.

Principles of Surface Measurement.

We will suppose that throughout Drawing-Book No. I. the direct distance from one line to another on the ruled paper is one inch, unless otherwise directed.

Then, how much space will one of the small ruled squares contain? (One square inch.) How much will four of them contain? (Four square inches.) As a standard of measurement, each of the small squares formed by the ruling of the paper is called a primary erect square.

How large is No. 3? (One inch square.) How much area, or surface, does it contain? (One square inch.)

How large is No. 4? (Two inches square. That is, it measures two inches on each side.) How much area, or surface, does it contain? (Four square inches, as may be seen by counting the primary squares within it.)

How large is No. 5? (Four inches square.) How much area, or surface, does it contain? (Sixteen square inches.) How large is No. 6? (Two inches by three inches.) How much area, or surface, does it contain? (Six square inches.) How large is No. 7, and what is its area? How large is No. 8, and what is its area?

Hence,

To find the area or surface measurement of any rectangle :

RULE I.—Multiply the length by the breadth, and the product will be the area.

PROBLEMS FOR PRACTICE.

1. Draw a square of three inches to a side.

What is its area?

2. Draw a square of nine inches to a side. What is its area?

Ans. 9 square inches.

Ans. 81 square inches.

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