four or five minutes with redoubled earnestness, sagely observed that "he had his doubts about the matter"-which in process of time gained him the character of a man slow in belief, and not easily imposed on.

The person of this illustrious old gentleman was as regularly formed and nobly proportioned as though it had been moulded by the hands of some cunning Dutch statuary, as a model of majesty and lordly grandeur. He was exactly five feet six inches in height, and six feet five inches in circumference. His head was a perfect sphere, and of such stupendous dimensions, that dame Nature, with all her sex's ingenuity, would have been puzzled to construct a neck capable of supporting it; wherefore she wisely declined the attempt, and settled it firmly on the top of his backbone, just between the shoulders. His body was of an oblong form, particularly capacious at bottom; which was wisely ordered by Providence, seeing that he was a man of sedentary habits, and very averse to the idle labour of walking. His legs, though exceeding short, were sturdy in proportion to the weight they had to sustain; so that, when ereet, he had not a little the appearance of a robustious beer-barrel standing on skids. His face, that infallible index of the mind, presented a vast expanse, perfectly unfurrowed or deformed by any of those lines and angles which disfigure the human countenance with what is termed expression. Two small grey eyes twinkled feebly in the midst, like two stars of lesser magnitude in the bazy firmament; and his full-fed cheeks, which seemed to have taken toll of everything that went into his mouth, were curiously mottled and streaked with dusky red, like a Spitzenberg apple.

His habits were as regular as his person. He daily took his four stated meals, appropriating exactly an hour to each; he smoked and doubted eight hours; and he slept the remaining twelve of the fourand-twenty. Such was the renowned Wouter Van Twiller-a true philosopher; for his mind was either elevated above or tranquilly settled below the cares and perplexities of this world. He had lived in it for years without feeling the least curiosity to know whether the sun revolved round it, or it round the sun; and he had watched for at least half a century the smoke curling from his pipe to the ceiling, without once troubling his head with any of those numerous theories by which the philosopher would have perplexed his brain, in account ing for its rising above the surrounding atmosphere.-Washington Irving.

III. THE CHILD OF THE TOMB: A STORY OF NEW BURYPORT. [The following fact is found in Knapp's "Life of Lord Dexter."]

Where WHITEFIELD sleeps, remembered, in the dust,
The lowly vault held once a double trust;

And PARSONS, reverend name, that quiet tomb
Possessed, to wait the day of weal and doom.
Another servant of the living God,

PRINCE, who (bereft of sight) his way had trod,
Unerringly and safe, life's journey through,
Now sought admittance to these slumberers too.
As earth receded, and the mansions blest
Rose on his vision,-"Let my body rest

With Whitefield's "-said he, yielding up his breath,
In life beloved, and not disjoined in death.
Obedient to his wish, in order then
Were all things done; the tomb was oped to ken
Of curious eyes,-made ready to enclose
Another tenant in its hushed repose:
And, lighted with a single lamp, whose ray
Fell dimly down upon the mouldering clay,
Was left, prepared, to silence as of night,
Till hour appointed for the funeral rite.

It chanced the plodding teacher of a school,-
A man of whim, bold, reckless, yet no fool,--

Deemed this an opportunity to test
How far the fears of spirits might infest

The bosom of a child. A "likely" boy,
The choicest of his flock, a mother's joy,
He took, unscrupulous of means, if he
His ends might gain, and solve the mystery.

Botn stood within the mansion of the dead,
And while the stripling mused, the teacher fled,
Leaving the child, where the dull cresset shone,
With the dumb relics and his God alone.
As the trap-door fell suddenly, the stroke,
Sullen and harsh, his solemn reverie broke.
Where is he?--Barred within the dreadful womb
Of the cold earth-the living in the tomb!
The opened coffins showed Death's doings, sad,-
The awful dust in damps and grave-mould clad,
Though near the haunt of busy, cheerful day,
He, to drear night and solitude the prey!
Must he be watcher with these corpses!-Who
Can tell what sights may rise? Will reason then be true?

Must he,-a blooming, laughter-loving child,-
Be mated thus ?-The thought was cruel, wild!
His knees together smote, as first, in fear,
He gazed around his prison;-then a tear
Sprang to his eyes in kind relief; and said
The little boy, "I will not be afraid.
Was ever spirit of the good man known
To injure children whom it found alone?"
And straight he taxed his memory, to supply
Stories and texts, to show he might rely
Most safely, humbly, on his Father's care,
Who hears a child's as well as prelate's prayer.
And thus he stood,- -on Whitefield's form his glance
In reverence fixed,-and hoped deliverance.

Meanwhile, the recreant teacher,-where was he?
Gone in effrontery to take his tea
With the lad's mother!-Supper done, he told
The feat that should display her son as bold.
With eye indignant, and with words of flame,
How showers that mother's scorn, rebuke, and shame,
And bids him haste! and hastes herself, to bring
Him from Death's realm, who knew not yet its sting:
And yet believed,--so well her son she knew,-
The noble boy would to himself be true:

He would sustain himself, and she would find
Him patient and possessed, she trusted well his mind.
The boy yet lives, and from that distant hour
Dates much of truth that on his heart hath power;
And chiefly this,-whate'er of wit is wed

To word of his,-to reverence the dead.

XIV. FOUNDATION OF NATIONAL CHARACTER.

In

[To be marked for Inflections by the student.] Mental energy has been equally diffused by sterner levellers than ever marched in the van of a revolution,-the nature of man and the providence of God. Native character, strength, and quickness of mind are not of the number of distinctions and accomplishments that human institutions ean monopolise within a city's walls. quiet times they remain and perish in the obscurity to which a false organisation of society consigns them. In dangerous, convulsed, and trying times, they spring up in the fields, in the village hamlets, and on the mountain tops, and teach the surprised favourites of human law, that bright eyes, skilful hands, quick perceptions, firm purpose, and brave hearts, are not the exclusive appanage of courts.

Our popular institutions are favourable to intellectual improvement, because their foundation is in dear nature. They do not consign the greater portion of the social frame to torpidity and mortification. They send out a vital nerve to every member of the community, by which its talent and power, great or small, are brought into living conjunction and strong sympathy with the kindred intellect of the nation; and every impression on every part vibrates, with electric rapidity, through the whole. They encourage nature to perfect her work; they make education, the soul's nutriment, cheap; they bring up remote and shrinking talent into the cheerful field of competition: in a thousand ways they provide an audience for lips which nature has touched with persuasion; they put a lyre into the hands of genius; they bestow on all who deserve it, or seek it, the only patronage worth having, the only patronage that ever struck out a spark of "celestial fire,”—the patronage of fair opportunity.

This is a day of improved education; new systems of teaching are devised; modes of instruction, choice of studies, adaptation of textbooks, the whole machinery of means, have been brought, in our day, under severe revision. But were I to attempt to point out the most efficacious and comprehensive improvement in education--the engine by which the greatest portion of mind could be brought and kept under cultivation, the discipline which would reach furthest, sink deepest, and cause the word of instruction not to spread over the surface, like an artificial hue, carefully laid on, but to penetrate to the heart and soul of its objects-it would be popular institutions. Give the people an object in promoting education, and the best methods will infallibly be suggested by that instinctive ingenuity of our nature, which provides means of great and precious ends. Give the people an object in promoting education, and the worn hand of labour will be opened to the last farthing, that its children may enjoy means denied to itself.-E. Everett.

the points a, b, etc., e, f, etc., and divide HF, KG also into five equal parts in the points k, l, etc., o, p, etc. Of course, when the curve is large, the greater the number of parts into which the double ordinate, FG, and the parallels, HF, KG, are divided, the more accurately the curve can be traced, care being taken to divide the parallels into the same number of equal parts as each half of the double ordinate, FG, is divided into. From the point A draw straight lines through the points F, a, b, etc., and from B draw straight lines through the points k, l, etc., o, p, etc., and through the points of intersection of

required.

the lines Aa, Bn, Ab, вm, etc., numbered 1, 2, etc., and the points F, B, and G, trace the curve FBG. This curve is the hyperbola Lest some of our readers may be tempted to inquire of what practical use it may be to be acquainted with the method of tracing parabolas and hyperbolas of different degrees of curvature, we may remind them that the parabola sometimes is used in forming an arch, while such articles as tazzas and wineglasses, and other pieces of useful and ornamental china-ware, may be formed by the revolution of an hyperbola about its axis, as may be seen by copying the curve in Fig. 94, so that the vertex, B, points downwards, and then adding a slender stem and foot to form a wine-glass.

PROBLEM LXVI.-To describe the curve called the cycloid. The term cycloid, derived from the Greek KUKλotions (ku-kloi'-dees), like a circle, is a name given to the curve traced by any point in the circumference of a circle during the complete revolution of the circle while rolling along a straight line. For example, as a carriage is drawn along on a road or railroad, the end of any spoke in one of its wheels, or a nail in the tire, describes a succession of curves, similar to the curve resembling half of an ellipse in Fig. 95. That the reader may understand how the curve is traced, let A B C D represent a circle, having two diameters, AC, BD, intersecting each other at right angles, and let the circle be standing on a straight line, X Y, of indefinite length, so that the diameter A c is at right angles to XY, which is a tangent to the circle A B C D, the circle touching it only in the point A. Suppose the circle to roll slowly along the straight line x Y, in the direction of x, and pass into the position A' B' C' D'. has now performed a quarter of a complete revolution, and the point A in ascending into the position A' has traced a path represented by the curve A A'. In the next quarter of a revolution the point A is brought to the top in the position A", and when a complete revolution of the circle has been made it has passed from A" to A" and A, having traced in its passage from A to A the curve A A' A"A" A"". Practically, the cycloid may be traced by causing a thin disc of metal, ivory, or even cardboard, having a slight nick in its circumference to receive a pencil point, to travel slowly along the edge of a ruler until a

It

during the revolution. It is evident that, as every point of the circumference of the circle in succession touches the straight line A c during the revolution, A C, which we may call the base of the cycloid, is equal in length to the circumference of the circle B K D. If the circle be caused to return to its position in the centre of the cycloid when B is at its highest position, as in the figure, and straight lines, such as M H, N F, be drawn through the circle parallel to the base and terminating both ways in the curve of the cycloid, these straight lines pass through opposite points in the circumference of the circle B K D, at equal distances from the diameter B D, which is perpendicular to the base, G L being equal to G O, and E K to E P. It will be found that LH is equal to the arc B L, and that the arc BH is equal to twice the chord B L, and so on for the other points, M, N, F, in the curve of the cycloid, through which straight lines have been drawn parallel to the base. The arc BC will therefore be equal to twice BD, the diameter of the generating circle, and the whole curve A B C consequently equal to four times B D. This curve is said to have been discovered and its properties first investigated by Galileo. PROBLEM LXVII.-To describe a spiral.

drawn. Draw a horizontal straight line, X Y, of indefinite length Take any point, ▲ (Fig. 97), as the centre of the spiral to be through A, and from A as centre, with any distance, A B, describe the semicircle B D C. Then from the point B as centre, with the distance B C, describe the semicircle C E F on the opposite side of A B. Next, from A as centre, with the distance A F, describe x. the semicircle F G H, and then from B and A, in alternation as centres, at the

distances BH, A L, etc. etc., in succession as describe as many semicircles may be

N

L

M

Fig. 97.

required. A spiral of any given number of turns may be described on a given straight line by dividing the given straight line into as many equal parts as there are turns required, and bisecting the central division if the number of turns be odd, or the division on the right or The centres to be fixed in describing the semicircles must be left of the centre of the line if the number of turns be even. the point of bisection, and either of the points of division immediately contiguous to it if the number of turns be odd, or the point of bisection and the centre of the divided line if the number of turns be even. Thus, in Fig. 97, if it be required to describe a spiral of eight turns or semicircles on the given straight line RT, divide R T into eight equal parts, in the points N, H, C, B, F, L, P, and bisect BC, or B F, in A for the centre of the spiral. Then from the points A and B, in alternation, describe the semicircles BDC, CEF, etc. etc. PROBLEM LXVIII.-Any two straight lines being given, to determine a curve

by which they shall

be connected.

E

B

Let A B, C D (Fig. 98) be any two straight lines which it is required to connect by a curve. Produce A B, C D in the direction of B and C, until they meet in E. Bisect the angle BEC by the straight line E F. From the extremities B and c of the straight lines A B, C D, draw B F, C F perpendicular to A B and cn respectively, and intersecting each other and the straight line EF in the point F. From F as centre, with the distance F B or Fc, describe the arc BC. This arc connects the straight lines A B, CD. The same process is followed when the given straight lines are at right angles to each other, as AB, G II, which are connected by a curve, B G, struck from K as centre,

Fig. 98.

of

intersection of the perpendiculars B K, G K, drawn, as before, at right angles to the extremities, B and G, of the given straight lines A B, G H.

Next, let the given straight lines A B, C D be parallel to one another. Through B and C (Fig. 99) draw F B X, CE, perpendicular to A B, C D respectively. Join в C, and having taken a point, K, in BF, so that BK shall be less than BC, draw KL through K, parallel to B C, and cutting C E in L; from L as centre, with the distance LC, which is equal to B K, describe the arc C M, meeting BC in M. Join LM, and produce it in the same straight line towards M, to meet FX in N. From N as centre, with the distance N Bor N M, describe the arc B M. The given straight lines A B, CD are connected by the curve B M C.

K

IF

If, however, the given straight lines are not parallel, but would meet if one or both were produced, as G H produced meets B A in A, forming the small angle HAB, draw, as before, F X and Go at right angles to A B and

G H respectively. Take any point, K, Bisect KP in

in BF; make GP equal to BK, and join K P. Q, and draw Q R perpendicular to K P, meeting FX in R. Join RP, and from P as centre, at the distance PG, describe the arc Gs, meeting R P in S. Then from the centre R, at the distance RB or RS, describe the arc B 8, completing the curve BS G, by which the given straight lines A B, G H are connected.

This problem exhibits a mode of construction useful to engineers in laying out the curves of a railway; to landscape gardeners, in laying out walks and roads; and to carpenters, in forming curves to connect the straight edges of a piece of wood by a curve, when they are either parallel to one another, or inclined to each other at a greater or less angle.

At this point we bring to a conclusion our Lessons in Geometry, in which we have explained, as clearly and as fully as possible, the leading principles of the science on which all the constructive arts are based. Of the practical value of geometry to the artisan and mechanic we have already given many proofs. It will not be too much to say that any one who has studied these lessons carefully, and understands them thoroughly, has not only rendered himself a scientific workman, but has advanced far on his way to become an architect or civil engineer, or to enter any profession in which a knowledge of geometry is an essential requisite. From these lessons the student will find it of the greatest advantage to turn to "Euclid's Elements of Geometry," in which he will find a conclusive proof of almost every construction that has been brought under his notice in the preceding problems.

LESSONS IN LATIN.-XXIII.
REGULAR VERBS.-THE FIRST CONJUGATION.
ACTIVE VOICE.

Example.-Amo, I love. Chief Parts: amo, amavi, amātum, amare. Characteristic letter, a.

PARTS WITH THE CORRESPONDING ENGLISH.

Ind. Pres.

Amo, I love,

Having in the above corresponding parts given the Latin as well as the English of several members of the verb, I need not repeat them. I supply in full what remains. As I write for young men and women rather than for children, I omit adding the English in all the details of the persons; for when you know what is the first person, you will readily supply the rest: thus, if the English of amaveram, the first person, is I had loved, you know that the English of amaveras, the second person, thou hadst loved; and of amaverat, the third person, he had loved; so also in the plural.

is

Instead of I might have loved, the sub. pluperf. may some times be rendered (put into English) by I would, I should, or I could have loved.

In the corresponding English words, I have given the nearest approach to the several Latin parts. The student will do well to adhere strictly to these meanings at first, though, as the correspondence between the several Latin and the several English parts is not entirely complete and constant, he will find occasions when his English will appear scarcely idiomatic, or strictly proper. He cannot, however, learn too soon, that few particulars are any two languages exactly correspondent. Accordingly, for amo, I have set down what may be termed three meanings-namely, I love, I do love, and I am loving. Here it is obvious that the English is more rich than the Latin, inasmuch as it has three forms of the present tense indicative mood, while the Latin has but one form. Having but one form, the Latin cannot by a form indicate the variations of the English present tense. Consequently, here is a want of strict corre spondence; and here also is a source of doubt; for we may ask, what is the English equivalent of amo? is it, I love, or I do love, or I am loving?

After these remarks the student will know that it is with some latitude that he is to take these

CORRESPONDING LATIN AND ENGLISH SIGNS.
Ind. Pres.
-0,

English. do.

Latin.

or

I was loving.)

Latin. English.

I do love, or I am loving.

Sub. Pres.

-em,

may.

-erim,

may have.

Ind. Perf. Sub. Perf.

Latin. -i, English, have.

Latin. English.

Latin.

I shall or will love.

Inf. Perf:-Latin, -isse;
Inf. Fut. Imp. 1 Sup.

-rum esse, ama, -um,

English. about to. do. in order to. to.

might have.

-are,

to.

Part. Pres. Fut. Pe 1 A

-ans,

-ing. on the point of