Part 4

From the extreme points of the right line A, B, with radii less than the length of the line describe two arcs intersecting each other at C and D, and through the points of their intersection draw the line, which will be perpendicular to the given right line at the middle.

In this way, too, may any line be divided into too equal parts with facility and exactness.

PROBLEM III. _To erect a perpendicular at or near the end of a given right line._

Take any point, D, on the given right line A, B, as a centre, and to the required point C, as a radius, and describe an arc C, E, F. Take a portion of this arc, say E, and make from C, E, equal to E, F. Join F and C. Now with E, C, for a radius, describe the arc G, E, H, and make from E to H equal to from E to G. Then through H from C draw the perpendicular required.

There are other methods of accomplishing this, but we will not introduce them here, as the one now given is sufficient.

We will now proceed to the formation of geometrical figures which enclose space.

That which is bounded by one line is called a _circle_; and a right line dividing it into two equal parts is called its _diameter_; from the centre of which to either end is called the _radius_: and the boundary line is termed the _circumference_ from the Latin words _circum_, around, and _fero_ to carry. That is: a line carried around. Thus we see an area or space is enclosed by one line. An area may be enclosed by two lines; but one, or both of them, must be curved; as two right lines cannot enclose a space. But three can; and the figure is called a _triangle_.

PROBLEM IV. _In a given circle to construct a Triangle._

Take the radius of the circle, and with it mark off six points on the circumference. Take two of these lengths of the radius and join their extreme points A and B, which will be the base. Now take this base as a radius and describe alternately two arcs cutting each other at C. Join A, C, and B, C, and a triangle is formed, whose sides being equal is termed an _equilateral triangle_.

In order to ensure its being upright, erect a perpendicular at the centre, and let the two sides A, C, and B, C, meet that perpendicular where it intersects the circumferences. Or, begin the triangle at this point, and mark off two lengths of the radius, joining the extreme points as before; and do this at each side of the perpendicular; finally connecting the distant extremities of the two sides for a base.

PROBLEM V. _To construct an upright square in a given circle._

Let fall a perpendicular, I, E, from the centre to the circumference, and with that as a radius and E as a centre, cut the circumference at A, B, C, and D, and join the points. The four-sided figure called a square is thus formed.

PROBLEM VI. _On a given right line_, A, B, _to construct a pentagon, or five-sided figure_.

Draw B, F, perpendicular and equal to the half of A, B. Produce A, F, to G, making F, G, equal to F, B. From the points A and B, with the radius B, G, describe arcs cutting each other at I. From I, with the radius I, B, describe a circle. Inscribe the successive chords A, E; E, D; D, C; C, B, which with the base A, B, completes the pentagon.

If the circle be given, and a pentagon to be inscribed in it, the following is as simple as it is practical. From the centre erect a perpendicular, which shall meet the circumference at D. At each side of this point divide the circumference into five equal parts, and connect every two of them from D to E, from E to A, and from D to C, C to B. Now connect A and B and the pentagon is formed.

PROBLEM VII. _On a given line_ A, B, _to construct a hexagon, or six-sided figure_.

Take the length of the radius I, G, and lay it off from F to A, A to B, B to C, C to D, D to E, and E to F.

PROBLEM VIII. _To form an octagon, or eight-sided figure._

Refer back to _Fig. 5_. Draw the radius I, E, till it meets the circumference at E. Join the points E, A, and E, B. Repeat this at each of the four sides, and the octagon is formed.

PROBLEM IX. _To form a decagon, or ten-sided figure._

Refer to _Fig. 6_, and proceed as in the preceding problem.

PROBLEM X. _To construct a duo-decagon, or twelve-sided figure._

Refer to _Fig. 7_, and duplicate the chords, as already shown.

We do not present 7, 9, or 11 sided figures, because they seldom or ever come into practice. Our object being to give what is useful and not overburden the memory unnecessarily.

The learner should go over and work out each of the foregoing problems several times. In fact, until they are soundly secured in his memory, so that on any emergency he can apply them to a required practice. They are the simplest rudiments, but as practically useful as they are simple. The Architect, the builder, as well as the several trades of carpenter, joiner, carver, stone-cutter, mason, and in fact, all in any way concerned in the practice of construction will at some time or other wish to recall one of these useful problems. Therefore do we dwell on the necessity for committing them, understandingly, to memory, and likewise the advantage required in being able to draw them neatly and perfectly on paper. In order to do this with satisfaction to one’s self, it is desirable that a fine point be constantly maintained on the pencil, and that uniform nicety be preserved with the curved lines, as well as the right or straight lines. For nothing looks worse than undue thickness in the one or the other. All should be alike.

In theoretical geometry a line, whether right or curved, is but imaginary, not having any thickness whatever, and therefore no palpable existence. In practical geometry the line must be visible, but ought to be so uniformly fine as to occupy scarcely any perceptible thickness. And herein lies the greatest beauty in geometrical draughting. By strict attention to this apparently trifling matter, its advantages will show wherever minute angles occur. They will be clear and distinct, and always satisfactory.

The learner should keep his first attempts, however coarse, for they will by comparison hereafter, show the advance he has made. Nor should he be content to “let well enough alone.” There is no “well enough” in drawing. It is a progressive science, and the true artist never believes he has done his best. Go as near to perfection as you can, and do not turn aside from, or step over obstacles to reach the end you have in view. Whatever you have neglected in early study will surely haunt you through after years, and trouble you when you can least bear the annoyance.

We now conclude this primary lesson, hoping that our learners may profit by the hints we have thrown out, and will thoroughly prepare themselves for the advance in our next.

* * * * *

THE first brick house in Iowa was built by Judge Rerer, of Burlington, in 1839.

VINES FOR THE DECORATION OF COTTAGES.

THE GROUND NUT VINE.

A tourist riding a few miles in almost any New England city, would hardly fail to notice that a large number of the rural residences display a profusion of architectural embellishment, without wearing a cheerful, home-like look. He would pass cottage after cottage ornamented with slender porticoes, fanciful verandas, sculptured gables and deep bay windows, but situated in a pen-like looking enclosure, and surrounded with fixtures, dark and dismal; and with arbor vitæ hedges whose yellow cast clearly indicated that they had been planted in ungenial soil. In each narrow yard he would notice flower beds, containing many unhealthy looking plants, and most of these beds would exhibit the same arrangement and the same multifarious specimens of the odds and ends of Nature for miles. He would remark concerning these suburban seats that they were _pretty_; he would hardly say beautiful, certainly not charming. They were not satisfying to the eye—they were designed to impart an expression of exquisite rurality but failed. As the same tourist passed by some old-fashioned farm house, with its broad green lawns in front, shaded with green old elms; as he noticed the wood colored porch covered with luxuriant woodbine, the dove-cote with its glittering birds, the dark orchards beyond the yard, the pond in the meadow overhung with willows; or, as he descried some inexpensive cottage, removed from the road and half hidden from view by graceful arbors and vigorous native trees, he would ride slowly and express his satisfaction at each of these scenes of rural taste and beauty.

It is not the richness of art that gives to English cottages their picturesqueness and poetic expression, but the beauty of the grounds that surround them, and the vines that adorn them. It is not the fantastic gables, nor the latticed windows that so captivate the eye of the traveller, but the tasteful foliage that drapes them, and the lustrous vines that embower them. Denude these cottages of these embellishments, and many of them would appear as uninviting to the eye as the mouldering tower without the classic ivy.

Louis XIV had his Versailles, and his elegant queen her embowered Triannon; but the simple charms of Triannon proved more inviting to the cultivated minds of the court, than the gorgeous pile and artificial gardens at Versailles.

We devote too much time to the cultivation of exotics, and too lightly value the vines and shrubs of our native soil. Again, we sacrifice rich foliage that lasts for a season, to gaudy flowers that last only for a brief period. The double prairie rose is a very delightful sight—for a single week—and during the remaining season it is a miserable brier, commonly wormy and lousy. Yet the prairie rose is in common use as an ornament for the veranda, while the jessamine, the woodbine, the wisteria and the luxuriant honeysuckle are, put in less conspicuous places, or their cultivation wholly neglected.

It may be cited as an evidence of improving taste in the rural art, that rustic work, which imparts to a place an expression of delightful rurality, is taking the place of images, porcelain vases, etc., that long have been conspicuous objects in almost every parterre. The perfection of beauty to which this work may be carried has been admirably illustrated in Central Park, New York City, and widely copied by gentlemen of taste. Few objects are more pleasing than rustic arbors or even rustic urns over-running with foliage.

Among the most pleasing vines for embellishment of rural seats are the honeysuckle (_Lonicera japonica_ and the trumpet vine), the woodbine, the jessamine and the American ivy. For adorning stone work, the English ivy is very rich, though it grows imperfectly in our Northern latitudes.

The woodbine forms a massive drapery for a cottage porch. It has a rich marine hue in summer, and it is very richly tinted in autumn after the early frosts. The Japan honeysuckle is deliciously fragrant, and it retains its dark lustrous foliage until mid-winter. Unlike many climbers this honeysuckle, together with the trumpet vine, is not liable to be infested with insects. The feathery _clematis_, known also by the names of the _virgin’s bower_ and the _traveller’s joy_, is a pretty creeper for walls and fences; and the common hop vine may be made to add beauty to the dove-cote and the martin boxes, when these are placed after the old English manner, upon poles.

The American ivy is one of the most prolific of foliage vines. The leaves when they are young are of a delicate pea-green color, but they become dark and lustrous as the season advances. They are very gorgeous after the early autumn frosts, displaying the richest tints of orange and vermillion. The ivy forms a sort of net-work for old crumbling walls, and it is indigenous to stormy places.

There is a slender vine very common in the Eastern States that is seldom used for ornamental purposes, to which we would especially invite the attention of the florists. It is called the ground nut, (_Apios tuberosa._) Its foliage is dark, thick, and very graceful. The flowers are remarkable. They are dark purple in color and present a peculiar waxy appearance, in dense predunculate, axillary racemes. Their odor is wonderfully sweet, and it is so powerful and inexhaustive as to fill perpetually the air. The vine entwines itself among low bushes in its native state. A florist of our acquaintance supplemented the charms of her trellises of roses by entwining these vines among the branches. Her rooms were filled with fragrance whenever the windows were thrown open during the whole of the hot season. The flowers of the ground nut vine last for a very long period. Remember this vine in your summer rambles.—_Working Farmer._

CLEAN THE CELLAR.—The Boston _Journal of Chemistry_ says: “Diptheria, typhoid, and scarlet fevers, and many other most serious illnesses, have their origin in cellars both in city and country; and we can do our readers no greater service than to urge them to see that at all times they are in a dry, sweet, wholesome condition. Why should farmers and farmer’s families, living in the country away from the pestilential vapors of the cities, be so subject to attacks of malignant diseases? There is a reason for it, and we can point it out. They arise from the indifference manifested to the observance of hygienic rules and the violation of sanitary laws. Cleanliness is essential to health, and it is just as necessary in the country as in the city. A family living over a foul cellar is more liable to be poisoned and afflicted with illness than a city family living in its polluted atmosphere, but without cellar or basement filled with fermenting roots and fruits. There is far more sickness in the country among husbandmen than there ought to be. With plenty of pure air, water, and exercise, the evil imp Disease ought to be kept at bay, and he would be better if an observance of certain hygienic conditions were maintained. Bad conditioned cellars, small, close sleeping rooms, stoves—these are all agents of evil, and are fast making the homes of farmers almost as unhealthy as those of the dwellers in cities. Are not these suggestions worthy of consideration?”

ON THE ART OF GARDENING.

BY THOMAS HOPE.

What was, in the earlier times, the origin of the garden? The wish that certain esculent plants and fruits, which in the waste field and the wide forest are scattered at great distances, in small quantities, intermixed with useless vegetables and fruits, precarious in their appearance, and stinted in their growth, difficult to collect, and scarce worth the gathering, might in a nearer, a smaller, and a more accessible spot, be better secured, more abundantly produced, kept clearer of the noxious herbs and weeds which destroy their nutriment and impede their growth. This was, in its origin, the sole object of the entire garden; this, to the present hour, continues to be the principal purpose of that essential portion of the garden, devoted to the uses of the kitchen and the table.

In these parts of the garden then, which are destined immediately for the gratification, not of the eye, but merely of the palate, it is only in proportion as we more fully deviate from the desultory and confused dispositions of simple nature—firstly, by separating the different species of esculent plants, not only from their useless neighbors, but from each other; and secondly, by confining the vegetables thus classed in those symmetric and measured compartments, which enable us with greater ease to discover, to approach, and to improve each different species in the precise way, most congenial to its peculiar requisites, that we more fully attain that first of intellectual beauties, which, in every production, whether of nature or of art, resides in the exact correspondence between the end we propose and the means we employ. Nay, if it be true that contrast and variety of colors and of forms are amongst the most essential ingredients of visible beauty, we may say that even this species of sensible charm is greatly increased in the aspect of a country by the opposition to the more widely diffused, but more vague shades and outlines of the unsymmetrical surrounding landscape, offered by the more vivid hues and more distinct forms of the gay Mosaic work of nicely classed and symmetrized vegetables which clothe these select spots.

Even where the general unadorned scenery is as bold and majestic as in Switzerland, or as rich and luxuriant as in Sicily, the eye with rapture beholds the variety, and enjoys the relief from the vaster and sublimer features of rude Nature, offered by the professed art of a neat little patch of ground, whether field, orchard, or garden, symmetrically distributed. It looks like a small but rich gem—a topaz, an emerald, or a ruby, sparkling amidst vast heaps of ruder ore; or rather like a rich carpet, spread out over a corner of the valley. It appears thus incontrovertible, that in that part at least of the garden which is immediately intended for utility, we incidentally produce not only greater intellectual, but greater visible beauty, by not confining ourselves to the desultory forms of unguided Nature, but by admitting the more symmetric outlines of avowed art, and it therefore only remains to be inquired, whether in that other and different part of the artificial grounds, in later times added to the former, which is directly intended for beauty, and which we therefore call the pleasure-grounds, we shall really produce more beauty, intellectual or visible, or, in other words, more pleasure to the mind or eye, by only employing the powers of art in a covert and unavowed way; in still only preserving the closest resemblance to the interminable and irregular forms of mere nature, or by exhibiting her additional resources in a more open and avowed manner; in contrasting these more indeterminate and desultory features of pure nature, with some of those more determinate and compassed outlines, which, indeed, on a small scale, are already found in many of the spontaneous productions of Nature herself; but which on a more extended plan, are only displayed in the works of art. I say, more pleasures to the mind or eye; for the portion of the garden here alluded to, no less than the one before mentioned professes itself to be a piece of ground wrested from Nature’s dominion by the hand of man, for purposes to which Nature alone was inadequate; and thence contending that there is the least necessity or propriety in rendering this district, appropriated by art, a fac-simile of pure Nature, independent of any consideration of superior beauty which this imitation may offer to the eye or mind, and merely because, to form a garden, we use materials supplied by Nature—such as air, water, earth, and vegetables, would be absurd in the extreme. As well might we contend, that every house, built of stone should resemble a cavern, and every coat made of wool, a sheepskin. Every production of human industry whatsoever, must, if we trace it to its origin, arise out of one or more definite ingredients of pure nature; and unless, therefore, by the same rule, every production of human industry whatsoever be obliged everlastingly to continue wearing the less regular forms of those peculiar objects of nature, out of which it is wrought, we cannot with more justice arraign gardens in their capacity as aggregates of mere natural substances and productions, for assuming the artificial forms of a terrace or a _jet-d’eau_, an avenue or a _quincunx_, than we can condemn opera-dancers and figurantes, in their capacity of compounds of natural limbs and features, for exhibiting the artificial movements of the minuet and the gavot, the entrechat and the pas-grave.

If, then, the strict resemblance to the desultory forms of rude nature be not indispensably requisite in the artificial scenery of pleasure-grounds, on account of any invariable reasons of propriety or consistency, inherent in the very essence of such grounds, this resemblance of studious art to wild nature, in the gardens that adorn our habitations, can only be more eligible on account of some superior pleasure which it gives the eye and mind, either in consequence of certain general circumstances connected with the very nature of all imitation, or only in consequence of certain more restricted effects, solely and exclusively produced by this peculiar species of imitation; namely, of natural landscapes through artificial grounds.