Pray, brother is not practical geometry the proper introduction to perspective?

And pray, sister, did not the word alphabet once alarm you? and afterwards the words grammar, French, geography, gamut, etc.? Anticipation is as often erroncously awful as it is pleasing; possession is the test. Let the rudimental knowledge you already possess, teach you how to feel respecting the important addition we are endeavouring to make to your accomplishments.  
What say you to geometry, my brave John?

I do not intend to be alarmed at a word, I promise you. I suppose you will soon shew us the meaning of it: - What is Geometry?

Practically, it teaches the methods of drawing lines, polygons, circles, ovals, and all other measurable surfaces with truth, and proportionate to any scale you may find occasion to adopt. But it may be some considerable gratification to you to learn, that little more than the names of the genral figures, and drawing the usual practical problems, will be all that is requisite to our progress in perspective. There will be very few mathematical calculations; and I promise you great pleasure in the results of your studies. One attainment, very conducive to your success in perspective drawing will be, the acquiring a ready use of the instruments: at the same time you will be gaining a knowledge of, at least, the alphabet of a universal language; which geometry may be considered, its principles being invariably the same everywhere, and at all times. Do you know, John, where to find the case of instruments, and the parallel ruler?

Take the key, and bring them here; and I hope you will never forget that you found them clean and safe when you first began to learn the use of them; for if you let your intsruments get out of order, you will soon feel the inconvenience of it.

Here are the instruments, brother (fig. 1). - Are we all to have instruments and drawing boards?

Of course; and I must observe, that genius may be much retarded for want of the possession and knowledge of these simple keys to the doors of art. The framed drawing board (fig. 2.) is made of various sizes and may be had at the principal colour shops: it only requires attentive inspection to know how to put the paper on it. First, cut a piece of drawing paper,* about an inch longer and wider than the panel: pass a clean damp sponge all over the back of the paper (that side on which the maker's water - marks read backwards); then take out the panel, and place it evenly on the paper, lift up the paper and panel together; place them in the frame; press them well up to the front; replace the two bars behind; and, when dry, the paper is ready to draw on.

No; draftsmen paste or glue the edges of very large sheets, and lay them down on smooth boards; and this is the most usual method with architects and others for large drawings.

First, observe that you must damp the back of the paper, and let the moisture diffuse till the sheet is pliant; then paste (with strong paste, quickly) about half an inch of the edge of the paper. Some artists double back as much of the paper as they mean to paste or glue: but I think it best, when pasting, to lay a flat ruler as a barrier to the paste. If you want to use the paper instantly, you must glue the edge, as that will bear drying by the fire: the pasted edges will not, but must dry gradually. It is well to lay down paper for drawing on the evening previous to the day on which you wish to use it. Recollect to use glue quickly, and stick the part you glue to the board as you proceed; for glue will set, or chill, very quickly.

I must first exlplain the instruments, to which I beg you will pay great attention: now take the largest compasses (fig.3.) out of the case, and by unscrewing that little screw at a, you may take out the steel leg (take care of it): then take that instrument out of the case which has a lead pencil in it, b, the compasses where you took out the steel leg, and turn the screw tight again; - thus we are provided with the means of drawing the circular parts of geometrical drawing. Very highly finished instruments are made without the screw a, the parts being fitted to each other so nicely as to hold well together without its help.

That is very complete: will you tell me, brother, why there is a joint c, in the pencil leg you have fixed in the compasses, as there is not one in the steel leg which you first took out?

Were it not for the joint, the pencil, or drawing pen, would lean too much on its side when a large circle is required to be drawn, and the line would of course be broad with the pencil, and the pen would not mark; but by bending that knee or joint you can draw to the full extent of the compasses, with the point perpendicular to the paper: thus geometry rewards the igneuity of mechanincs. Try it, and prove it.

That is a steel drawing pen, to place in the compasses after the pencil outline is correct; and you are therewith enabled to ink in all the circular parts of your drawing.

Then is suppose this long steed pen which has no joint is to ink in the straight lines?

They are to take dimension with, and are called dividers, and are nicely adapted to set off any number of equal parts, etc.

Yo appear perplexed at this instruments: come, I shall soon relieve you; it is called the sector, and is particularly useful in many points of mathematical inquiry, but almost entirely useless in the practice of prespective: yet I hope you will find opportunity for learning the use of the lines on one side, and the line of polygons on the other, when you are far enough advanced in arithmetic.

In the Encyclopedias, or "Kerby's Dr. Brook Taylor's Perspective": there is also a cheap pamphlet on the use of the instruments.

And what use are we to make ofn this neat little thin rule, which has such a number of lines and figures on it? Will you please, indulgent master, to dispatch this intricate article as you did the sector?

Your request is granted, without any indulgence on my part; as you will only use is for a nice ruler. But I may tell you that the lines and figures are only proportionate scales; as, suppose you consider any one whole division on eihter of the lines, as an inch, foot, yard, pole, furlong, or mile, you will find the proportionate subdivisious at the end of that line; and on the other side is a line of inches, each divided by ten (or what is properly called decimally), and below that is decimal scale, which, by means of the diagonal divisions at each end, exhibits the smallest tenth part that a draftstman can distinguish practically by lines.

I think we shall not, hereafter, be alarmed at intricate appeances, since your explanations are so very intelligible.

Pardon, sisters! You know it cannot be long since I looked on these instruments with the same ideas of them as you seemed to entertain: there is nothing to pardon but a little impatience. Delibrate attention will render the whole as plain as that which I have already taught you.

It is called the protactor: it is used to find the number of degrees contained in an angle; thus: - Ann, draw a right line, and place the straight edge of the protractor truly on it; then make a mark on the paper, at the top of the protactor, at 90, and (without moving the protactor) make a mark on the line exactly at that little mark on the straight edge of the protactor, which divides it in half, and wich is the centre of its circular part: now take it off, and draw a right line trough the two marks you have made on the paper, and it will be exactly perpendicular to the line first drawn. From this you may remember that a right angle contains 90 degrees, or a quarter of a circle.

Not quite so clearly as you appear to do; but George will favour me with another example.

I will tell you, John, one advantage you have gained by it; you know you are very attentive to conversation: now suppose you had heard any one say that the sun was about 30 degrees above the horizon before I taught you this, could you have conceived what height the sun was?

I think a line draw from 30 on the protactor to the centre, would be in the same oblique direction from the level of the protactor, as the line my eye to the sun, when it is 30 degrees high, or above the horizon.

But the difference between a degree on this little instrument, and the vast extent of that circle which the sun is supposed to make to the earth, or rather the carth to it, seems to me to bear no comparison.

The observation is allowable at present; but you must henceforth remember, that the three hundred and sixtieth part of the smallest circle that can be drawn, or conceived, is as much one whole degree of such circle, as the three hundred and sixtieth part of the largest circle imaginable in the vast imensity of space; and 30 degrees on the one would form percisely the same angle at the centre as on the other! Now, Eliza, for proof; take a large sheet of paper, and draw an angle of 30 degrees (let the point, or centre, be near the middle of the paper): now place the steel leg of the pencil compasses on the point of the angle, and strike the largest circle the paper will admit; now strike the smallest possible, and two or three intermediate circles, and you will observe, that the space between the two lines which forms the angle of 30 degrees, will be found to be exactly one twelfth part of the circumference of each of the circles, where they cross these lines: and, consequetly, each is 30 degrees, because twelve times 30 is 360. You must each of you perform this experiment.

Now, brother, I understand how to conceive the sun's height when I hear the number of degrees mentioned; I love the instruments the more I know them: but I always thought them very difficult things till you began to explain them. Come, will you please to explain the parallel ruler?

(Fig. 2, c) It almost explains itself. Practice, with care and caution, will render it familiar to you. When you have drawn a line, and require another parallel to it, take care to keep the limb ofn the ruler, which you do not want to move, quite still, and firm to the paper with one hand, and move the other side, or limb of the ruler, upwards, or downwards, to the point required; then hold that firm to the paper while you draw the line: if this is not nicely attented to, you will lose the parallel, and confuse you drawing: indeed, the whole use of the instruments depends on precision, insomuch, that the words "geometrical precision", (strickly meaning, "mathematical,") are the terms made use of to convey an idea of the utmost correctness. There are made parellel rulers on rollers, and many other useful instruments; but I will now go on with Practical Geometry - demanding your whole attention for a short space of time; and then, John, I will teach you to draw in perspective: you must keep your eyes on the diagrams, while I explain each figure, or give what is termed.

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Concluding dialogue.  
Introduction.