ISOMETRIC DRAWING,

FOR COMMON SCHOOLS.

[The following is the first of a series of articles which will extend through several numbers of the MONTHLY. They will constitute a progressive series, and will gradually introduce the higher mechanical drawing. We are confident that they will be appreciated by our readers, and prove a valuable addition to the course of study pursued in our common schools.-EDITOR.]

IN

Prefalory Remarks.

N most of our schools, there are many young men whose course of study begins and ends within the same walls, and whose acquirements, as they finish "schooling," are limited to the short list of primary English branches.

The majority of these pupils in after-life engage in pursuits more or less connected with the mechanic arts. To all such, some knowledge of drawing is indispensable; yet, having no time for the intricacies of perspective, and but slight inducements to acquire proficiency in free-hand drawing, the rudiments of graphic representation are left unlearned.

For such, the system of Isometric drawing is of undoubted value; requiring no previous knowledge of geometry, and involving but few technical terms, it may be acquired by any one who can draw parallel lines of a given length, and divide them by a scale.

It is designed that the following exercises be drawn upon the blackboard, with approximate correctness, or upon proper paper surface, exactly to scale. In either case, they afford valuable training for the pupil, and a good introduction to higher branches of drawing.

A good preliminary exercise for pupils of nine or ten years of age is that of drawing straight lines upon the board without a ruler, and at the same time of a given number of inches in length, or of the length of a stick or string held up by the instructor. This exercise is further varied by requiring lines to be drawn by the pupil, which make a given angle with each other-the angle may be expressed in degrees, or by exhibiting the angle cut from paper.

After much experience in the class-room, the author confidently recommends these exercises to the consideration of teachers, and hopes they may be found to afford a pleasant and profitable variety in the routine of school-labor.

The learner is referred to the first pages of any work on geometry for definitions of the few geometrical terms used in the following exercises.

CHAPTER I.

LESSON 1.-THE CUBE.

We will commence our work by drawing a circle; if you draw it upon the blackboard, let the radius be about six inches; the radius in Fig. 3 is one inch, which is sufficient for a drawing upon paper.

If you have no dividers, the circle may be drawn by a pencil tied near the point by a thread-a method which I need not describe more fully. When the circle is complete, keep the distance or radius carefully, and, beginning at the lowest point in Fig. 3, measure or lay off this distance about on the curve, making dots at the points where the measurement falls. There will be exactly six of these distances.

Now join these points by straight lines, as in Fig. 4.

Draw lines from the center, L, to A, to F, and to I, and rub out the circumference. Your drawing, now, should be like Fig. 5. It is called the isometric projection of the cube.

In the succeeding lessons, we shall make our drawings without any circle, but by the aid of rulers, such as are represented in Fig. 1. You should be provided with them before drawing the next exercise.

The rulers should be thin, of hard wood, and the angles of the triangles should be precisely 30°, 60°, and 90°. They are sold in the cities under the name of isometrical rulers. In the country, you can get them made by a carpenter, if you will furnish him a paper pattern, which you can make in the following manner :

Draw an isometrical cube, just as in this exercise, on a sheet of thick paper; but let the radius be about eight inches. When the cube is complete, draw a faint line from L to H, and another from I to F; the upper face of the cube will then be divided into four triangles, like each other, and of the exact shape of the isometrical ruler; either of these being cut out, forms a good pattern from which a carpenter or cabinetmaker can make you a suitable ruler. Its edges should be quite straight, it should be less than one-eighth of an inch thick, and when correctly made, the shortest side is exactly half the length of the longest.

The shortest ruler in Fig. 1 is marked off in inches divided to eighths; the longer one is a plain, straight, thin ruler, and for blackboard purposes should be about twenty inches long; for the drawing-book or paper, ten inches is sufficient.

The method of drawing parallel lines by the aid of the triangular ruler is shown in Fig. 2, and will be more particularly described in the next lesson. You will please observe that Fig. 5 is formed of nine straight lines, three of which are vertical, or perpendicular to the bottom of the page; three incline upward to the right, forming an angle of 60° with the vertical lines; and three incline to the left at the same angle. It will be a profitable exercise to practice drawing this figure without the aid of rulers.

THE

A FEW OF MY TROUBLES.

HERE are good reasons why I should present this subject. In the first place, if I do not give an account of my own troubles, it is very doubtful whether any one else will, as I have reason to think that no person in the world is so deeply interested in them as I am, or has bestowed so much time to the consideration of them. And then, I believe, seriously, that my troubles are not mine only. Haven't you, many a time, sat alone in your school-room after the day's duties were done, and looked drearily around at the rows of vacant seats-at the figures on the blackboards at the cobwebs in the further corner of the ceiling-at the cleanfaced clock that ticked unusually loud, now that the place was still, and the echoes of poorly enunciated English, that make the air ache six hours out of a day, were quiet at last?

Haven't you sat thus, with your tired head in your hands, and both elbows resting on the desk, while the silence brought to you thoughts of the day's work? Are you ever satisfied with it? Can you look at it, and say, "This is quite perfect, and satisfies me?" On the contrary, are you not filled with depressing doubts and misgivings, and oftentimes with a wretched sense of your own shortcomings, and the inadequacy of the work you are doing?

There is no use talking of this. Try to tell your confidential friend about it. "Nonsense," he cries. "You are a tip-top teacher-you've got a fit of the blues-all you want is fresh air."

There is truth in this; still, a whole skyfull of fresh air fails to wholly divest my mind of a subtle sense of unsatisfaction in the work I am doing. It is not because the work is not a good one. In my soul, I believe there is no higher or nobler work than that which is set before teachers. It is not because I find unusual difficulties in the way-nothing of the sort. My scholars are not insubordinate or dofiant; for the most part, they are dutiful, attentive, and diligent. And yet, I am greatly dissatisfied with the work I do for them. So you see that my troubles are rather indefinite; that they are subjective rather than objective. Yet, notwithstanding they are vague and intangible, and exist only in my own mind, they are real, and cast very real shadows.

:

To begin, then it gives me a sense of annoyance that our work is so very prosaic and commonplace. The work of education, when viewed as a grand, triumphal crusade against the powers of darkness, is indeed inspiring. "But above all," cries the clarion voice of one of the world's great teachers," above all, where thou findest ignorance, brute-mindedness, stupidity, attack it, I say. Smite wisely, unweariedly, and rest not while thou livest and it lives; but smite! smite in the name of God !" I suppose ignorance, stupidity, brute-mindedness rose before Carlyle in

serried and embattled ranks, where any gallantly accoutered knight might find worthy foe; and if I could encounter them in that guise, no one knows what a gallant charge I would make. But the warlike spirit dwindles perceptibly, when I meet the worthy trio closely leagued and strongly fortified in a little stolid-faced child who stands at my knee. However, I whet up my battle-axe-a very mild one-and begin the attack.

"George, what letter is that?

"A. Say A, George.

"Look at it again, so as to know it next time. Now, remember that is A.

Now, George, what is it? You don't know! Didn't I just tell you it was A? Try to remember it now, George."

"Ugh!"

But then, it is a glorious work! You have heard the popular and eloquent Mr. B., who is a man of veracity, say so. Surely, it is a glorious work to train immortal minds; to build a temple that shall stand when palaces have crumbled, and the adamantine hills have melted away; to kindle a light that shall shine on when the world is lost in ruin, and the stars and suns have ceased to be. It is very exhilarating to hear all this; but after all, you and I don't often see the Eternal temples. We daub away with untempered mortar at the wretched little bricks that form our every-day building material; what we pile up one day falls down the next, very likely, and we see no great architectural results.

Edward Everett has told us that," From the humblest village school there may go forth a teacher who, like Newton, shall bind his temples with Orion's belt; with Herschel, light up his cell with the beams of before undiscovered planets; with Franklin, grasp the lightning." And this encouraging statement is not without a certain air of probability, since it is altogether more likely such a teacher would go from the school than that he would continue in it; but, for all that, when we have been carried off into mid air by sublime words like these, and then have come down to the earth again, we find we are still the same ordinary mortals that we were before we went up, and that we are not likely to bind any thing upon our temples, except a wet towel for the headache; that we still burn kerosene in our cells, and find that high enough, without going as high as starlight; and, ignoble creatures, we have not the slightest desire to be burnt with lightning.

Truly, there seems to be a laughable incongruity between the lofty and inspiring words that men utter of this work, and the work as we find it day by day—dull, commonplace, absurd, and wearisome.

Is it because they have a higher stand-point than we, and can see further, while we grope with our eyes intent upon what is nearest and most obvious?