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LESSONS IN GEOMETRY.—XV.

intersect cd in F. The point F is the centre from which the

arc AC B has been described. PROBLEM XXXV.-To find the centre of any given circle, or of Now let A E B in Fig. 53 be the arc of which it is required to any given arc of a circle.

find the centre. Join A B as before; bisect A B in D. Draw Let A B C (Fig. 53) be the given circle of which it is required D E perpendicular to A B, and join A E. Produce e d indefinitely to find the centre. First, draw any straight line, A B, dividing towards c, and at the point A in the straight line E A, make the the circle into two unequal segments. Bisect A B in D, and angle E AF equal to the angle A E F, producing the leg A F of through the point o draw the straight line E c at right angles the angle E AF, if necessary, far enough to intersect E D proto AB. Bisect Ec in F. The point F is the centre of the circle duced in the point F. This point, as before, is the centre from ABC.

which the arc A E B has been described. There are other methods by which the centre of the circle In the first of these two cases it will be noticed that the aro A B C may be found, although the one that has just been described of which the centre is required is greater than half the circumis perhaps the most simple. For instance, we might have drawn ference of the circle of which it is an arc, but in the second it is the straight lines G H, KL as tangents to the circle A B C, through less than half the circumference. If the arc were half the

the points A and B, and at circumference, it is plain that to find its centre all we have to FR, H

the points of contact, A and do is to join its extremities, and biseot the chord that joins

B, drawn the straight lines them.
M

AN, B 0, at right angles to On further inspection of Fig. 53 it will be noticed that the
the straight lines G H, KL, straight lines GH, KL, which were drawn as tangents to the
and intersecting each other circle ABC through the points A and B, have their points of
in the point F; from which intersection m in the straight line ce obtained by producing
we learn that if any two CE in an upward direction; and the angle A M C is equal to the
points be taken in the cir- angle BMC. This leads to another mode of finding the centre
cumference of a circle, which of the circle A B C, which is as follows:
are not the opposite extremi. Through any two points, A and B, in the circumference of the
ties of a diameter of that given circle A B C, draw the tangents G H, K L, intersecting each
circle, and tangents to the other in the point M. Bisect the angle A M B by the straight

circle be drawn through line M E, and produce it to cut the circumference of the circle K these points, the straight in c. Bisect c E in F. The point F, as before, is the centre of

lines drawn at right angles the circle A BC.
to the tangents through the PROBLEM XXXVI.—To describe a circle through any three
points of contact shall inter- given points which are not in the same

sect each other, if produced straight line.
Fig. 53,

far enough, in the centre of Let A, B, C(Fig.55), be the three given
the circle.

points through which it is required This method is useful when we wish to find the centre from to describe a circle, or rather the cirwhich an arc or part of the circumference of a circle of very cumference of a circle. Join A B, AC, great extent has been described. The following is a third and bisect these straight lines respecmethod of finding the centre of a given circle or the given arc of tively in the points D and E. Through any circle. Let us suppose, as before, that ABC in Fig. 53 D draw the straight line D F of inde

к represents the given circle. Set off along any part of the cir- finite length, perpendicular to AB, cumference three equal arcs, BE, E A, and AP. Then from the and through E draw the straight line B points P and E as centres, with any radius greater than the EG, also of an indefinite length, perradius of the given circle, describe two arcs intersecting each pendicular to a C. The point of inother in the point n; and from the points A and B as centres, tersection, H, of the straight lines D F,

Fig. 55. with any radius greater than the radius of the given circle, EG, is the centre from which a circle describe two arcs intersecting each other in the point Q. Join may be described with a radius, 1 A, that shall pass through AN, EQ. The point F in which these lines intersect each other the other two given points, A, B, and c. The same result would is the centre of the circle A B C.

be obtained by joining the straight lines A B, B C, or A C, C B, Our figures, as we have said before, sometimes appear compli- bisecting them, and drawing perpendiculars through the points cated from the necessity that there is of saving as much space of bisection as shown in the figure.

as we can by making one diagram serve as an PROBLEM XXXVII.—To draw a tangent to a given circle

illustration either to many methods of doing the through any given point either in the circumference of the circle & same thing, or to sequences that may arise out or without it.

of the consideration of the problem in question. The case in which the given point is in the circumference of Our readers are therefore in all cases when it is

the circle needs no illus. necessary recommended to study our problems

tration and very little with a piece of paper, a pair of compasses, and

R explanation, for it is a parallel ruler at hand, that they may construct

manifest that nothing Fig. 54. for themselves just so much of our diagram as

more is required than to is necessary for an illustration of the process in

o draw a straight line joincourse of description, disentangling it as it were from the

ing the centre of the figare that we have given as a means of explaining our direc

circle and the given point, tions. As an example of this, we give in Fig. 54, on a reduced S

and then through the scale, just so much as is absolutely necessary of Fig. 53 to

given point to draw a enable a reader to understand the first method that we have

straight line at right given of finding the centre of any given circle.

Fig. 56.

angles to the radius of Some of the methods that have been described for finding the

the circle thus obtained. centre of a given circle apply equally well, as it may have been The straight line drawn through the given point at right angles seen, to finding the centre from which any given art of a circle to the radius will be a tangent to the given circle. has been described ; but there is another method of finding the In the case in which the given point lies without the circum. centre of any given arc that we will now proceed to bring under ference of the circle, let A B C (Fig. 56) represent the given circle, the reader's notice.

and the given point without it. Find E, the centre of the First, let A CB in Fig. 53 be the art of which it is required to circle A B C, and join D E. Bisect DE in F, and from the point find the centre. Join A B; bisect AB in D; draw Dc at right r as centre, at the distance FE or FD as radius, describe the angles to A B, and join a c. Then at the point a in the straight circle DGH, cutting the circumference of the circle A B C in the line ca make the angle CAF equal to the angle A C F, and pro- points G, H. Join D G, D #, and produce them indefinitely duce the leg a r of the angle c A F, if necessary, far enough to l towards K and L respectively. The straight lines D K, D L are

A

D

Х

F

P

N

tangents to the circle A B C, and they are drawn from the given mysteries of devotion ; let me forget the world, and by the world be point D, without the circumference of the circle A BC, as forgotten, till the moment arrives in which the veil of eternity shall required.

fall, and I shall be found at the bar of the Almighty. From this problem we learn that from any point without a

Religion will grow up with you in youth, and grow old with you in circle two straight lines can be drawn which are tangents to age; it will attend you, with peculiar pleasure, to the hovels of the that circle, and that the angle formed by any pair of tangents closet, and watch by your béd, or walk with you, in gladsome union,

poor, or the chamber of the sick; it will retire with you to your drawn to a circle from a point without it is bisected by the to the house of God; it will follow you beyond the confines of the straight line which joins that point and the centre of the given world, and dwell with you for ever in heaven, as its native residence, circle. We also learn from this problem how, with a given radius, to

2. “Emphatic series." draw a circle touching two given straight lines. In Fig. 56, let

Assemble in your parishes, villages, and hamlets. Resolve, peti. LM, K N represent the two given straight lines, and x the tion, address. given radius of the circle that is required to be drawn, touching This monument will speak of patriotism and courage ; of civil and the given straight lines L M, KN. If necessary, produce the religious liberty; of free government; of the moral improvement and

straight lines 1 M, KN in the direction of m and N, and let elevation of mankind; and of the immortal memory of those who, with į them meet in D. Bisect the angle L D K by the straight line heroic devotion, have sacrificed their lives for their country. Do, and at any point, P, in the straight line D K draw PQ

I have roamed through the world, to find hearts nowhere warmer perpendicular to D K, and equal to the given radius x. Then

than those of New E'ngland, soldiers nowhere bråver, patriots nowhere through the point o draw the straight line R s of indefinite length, pèrer, wives and mothers nowhere trùer, maidens nowhere lovelier, parallel to D K, and intersecting the straight line do in the not be silent, when I hear her patriotism or her truth questioned with

green valleys and bright rivers nowhere greener or brighter; and I will point E. From the point E as centre, with a radius equal to so much as a whisper of detraction. the given radius x, describe the circle A H G. This circle touches the given straight lines L M, Kn, in the points I and G.

What is the most odious species of 1yranny ? That a handful of men, free themselves, should executo the most base and abominable despotism over millions of their fellow-créatures ; that innocence

should be the victim of oppression; that industry should toil for READING AND ELOCUTION.-XV. ràpine; that the harmless labourer should sweat, not for his own ANALYSIS OF THE VOICE (continued).

benefit, but for the luxury and rapacity of tyrannic depredation ;-in a [NOTE.—Those examples, in this and a former lesson, in which ordipary endowments of humanity, should groan under & system of

word, that thirty millions of men, gifted by Providence with the the accents are purposely omitted, are intended as exercises for despotism, unmatched in all the histories of the world. the student.]

3. “Poetic series.”
EXERCISES ON INFLECTIONS.
Simple Concluding Series.

He looks in boundless majesty abroad,

And sheds the shining day, that burnished plays It is a subject interesting alike to the old and to the young.

On rocks, and hills, and towers, and wandering streams, Nature, by the very disposition of her elements, has commanded,

High-gleaming from afàr. as it were, and imposed upon men, at moderate intervals, a general

Round thy beaming car, intermission of their toils, their occupations, and their pursuits. ,

High-seen, the Seasons lead, in sprightly dance The influence of true religion is mild, and soft, and noiseless, and

Harmonious knit, the rosy.fingered Hours, constant, as the descent of the evening dew on the tender herbage,

The Zephyrs floating loose, the timely Rains, nourishing and refreshing all the amiable and social virtues ; but

Of bloom ethereal, the light-footed Déws, enthusiasm is violent, sudden, rattling as a summer shower, rooting

And, softened into joy, the surly Stòrms.
up the fairest flowers, and washing away the richest mould, in the
pleasant garden of society.

Hear him compare his happier lot, with his
Compound Concluding Series.

Who bends his way across the wintry wolds,

A poor night-traveller, while the dismal snow The winter of the good man's age is cheered with pleasing reflections of the past, and bright hopes of the future.

Beats in his face, and dubious of his paths, It was a moment replete with joy, amazement, and anxiety.

He stops and thinks, in every lengthening blast, Nothing would tend more to remove apologies for inattention to

He hears some village mastiff's distant howl, religion than a fair, impartial, and full account of the education, the

And sees, far streaming, some lone cottage light; characters, the intellectual processes, and the dying moments of those

Then, undeceived, upturns his streaming eyes, who offer them.

And clasps his shivering hands, or, overpowered, Then it would be seen that they had gained by their scepticism no

Sinks on the frozen ground, weighed down with sleep, new pleasures, no tranquillity of mind, no peace of conscience during

From which the hapless wretch shall never wake. life, and no consolation in the hour of death,

There was neither tree, nor shrub, nor field, nor bouse, por living Well-doing is the cause of a just sense of elevation of character; it créatures, nor visible remnant of what human hands had reared. clears and strengthens the spirits; it gives higher riches of thought; I am charged with pride and ambition. The charge is true, and I it widens our benévolence, and makes the current of our peculiar affec- glory in its truth. Who ever achieved anything great in letters, art, tions swift and deep.

or arms, who was not ambitious ? Cæsar was not more ambitions A distant sail, gliding along the edge of the ocean, was sometimes

than Cicero. It was but in another way.

All greatness is born of a theme of speculation. How interesting this fragment of a world,

ambition. Let the ambition be a noble one, and who shall blame it! hastening to rejoin the great mass of existence! What a glorious

I confess I did once aspire to be queen, not only of Palmyra, but of

the East. monument of håman invention, that has thus triumphed over wind

That I am.

Is it not av

I now aspire to remain so. and wave ; has brought the ends of the carth in communion ; has Ptolemies and of Cleopatra ? I am applauded by you all for what I

honourable ambition ? Does it not become a descendant of the established an interchange of blessings, pouring into the sterile regions have already done, You would not it should have been less, of the north all the luxuries of the south ;* diffused the light of know. ledgo, and the charities of cultivated life; and has thus bound together more criminal

? Is it fixed in nature that

the limits

of this empire

Is so much ambition praiseworthy, and those scattered portions of the human race, between which nature

should be Egypt on the one hand, the Hellespont and the Euxine on seems to have thrown an insurmountable barrier!

the other ? Were not Suez and Armenia more natural limits : 0x 1. “Disconnected series."

hath empire no natural limit, but is broad as the genius that can Youth, in the fulness of its spirits, defers religion to the sobriety Palmyra possess the East. Not that nature subscribes this and to

devise, and the power that can win ?

Rome has the West. Let of manhood; manhood, encumbered with cares, defers it to the leisure of old age ; old age, weak and hesitating, is unable to enter on an

The gods prospering, and I swear not that the Mediterranean untried mode of life.

shall hem me in upon the west, or Persia on the east. Longinus is
right: I would
that the world

were mine. I feel, within, the will and Let me prepare for the approach of eternity ; let me give up my the power to bless it, were it so. soul to meditation; Jet solitude and silence aoquaint me with the Are not my people happy? I look upon the past and the present

upon my nearer and remoter subjects, and ask nor fear the answer. • Accidental “falling" inflection, for contrast.

Whom have I wronged 3-what province have I oppressed :—what city

more.

pillaged 7—what region drained with taxes ?—whose life have I unjustly

Still, still, for ever aken, or estates coveted or robbed ?-whose honour have I wantonly

Better, though each man's life-blood were a river, assuiled ?—whose rights, though of the weakest and poorest, have I

That it should flow, and overflow, than creep trenched upon ? I dwell, where I would ever dwell, in the hearts of

Through thousand lazy channels in our véins, my people. It is written in your faces, that I reigr not more over you

Dammed, like the dull canal, with locks and cháins, than within you. The foundation of my throne is not more power

And moving, as a sick man in his sleep, than love.

Three paces, and then faltering ; better be
How shall I know thee in the sphere which keeps

Where the extinguished Spartans still are free,
The disembodied spirits of the dead,

In their proud charnel of Thermopylæ,
When all of thee that time could wither, sleeps,

Than staguant in our marsh."
And perishes among the dust we tread ?

Exception.-—“Emphatic negation."
For I shall feel the sting of ceaseless pain,

I'll keep them all;
If there I meet thy gentle presence not;

He shall not have a Scòt of them;
Nor hear the voice I love, nor read again

Nò, if a Scot would save his soul, he shall not,
In thy serenest eyes the tender thought.

Do not descend to your graves with the disgraceful censure, that
Will not thy own meek heart demand me there?

you suffered the liberties of your country to be taken away, and that That heart whose fondest throbs to me were given ?

you were mutes as well as odwards. Come forward, like mèn; protènt My name on earth was ever in thy prayer,

against this atrocious attempt. Shall it be banished from thy tongue in heaven ?

I am not sounding the trumpet of wår. There is no man who

more sincerely deprecatos its calamities than I do. In meadows fanned by heaven's life-breathing wind,

Rest assurod that, in any case, we shall not be willing to rank list In the resplendence of that glorious sphere,

in this generous contest. You may depend on us for whatever beart And larger movements of the unfettered mind,

or hand can do, in so doblo a cause. Wilt thou forget the love that joined us here?

I will cheerfully concede every reasonable demand, for the sake of
The love that lived through all the stormy past,

péace. But I will not submit to dictation,
And meekly with my harsher nature bore,
And deeper grew, and tenderer to the last,

Rule 2.-" Question and answer."
Shall it expire with life, and be no more ?

Do you think these yelle of hostility will be forgottenDo you
A happier lot than mine, and larger light,

suppose their echo will not reach the plains of my injured and insulted Await thee there; for thou hast bowed thy will

cóuntry, that they will not be whispered in her green valleys, and In cheerful homage to the rule of right,

heard from her lofty hills ? Oh! they will be heard there; yès, and And lovedst all, and renderedst good for ill.

they will not be forgotten.

I will say, what have any classes of you, in Ireland, to hope from For me, the sordid cares in which I dwell,

the French! Is it your property you wieh to preserve -Look to the Shrink and consume the heart, as heat the scroll;

oxample of Heiland; and see how that pation has preserved its property And wrath hath left its scar,—the fire of hell

by an alliance with the French ! Is it independence you court PHas left its frightful scar upon my soul.

Look to the example of unhappy Switzerland: see to what a stato of Yet, though thou wear'st the glory of the sky,

nervilo abasement that once manly territory has fallen, under Franco ! Wilt thou not keep the same beloved name,

Is it to the establishment of Catholícity that your hopes are directed ? The same fair thoughtful brow, and gentle eye,

The conduct of the First Consul, in subverting the power and antho Lovelier in heaven's sweet climate, yet the same ?

rity of the Pope, and cultivating the friendship of the Mussulman in

Egypt, under a boast of that subversion, proves the fallxoy of such a Shalt thou not teach me, in that calmer home,

reliance. Is it civil liberty you require ? Look to France itaəli, The wisdom that I learned so ill in this,

crouching under despotism, and groaning beneath a system of slavery, The wisdom which is love,-till I become

unparalleled by whaterer has disgraced or insulted iny nation. Thy fit companion in that land of bliss ?

Shall I be left forgotten, in the dust,

When Fate, relenting, lets the flower revive ?
Both Inflections, in connection.

Shall Nature's voice,-to man alone unjust, -
Rule 1.-"Negation opposed to affirmation."

Bid him, though doomed to perish, hope to live ?

Is it for this fair Virtue oft must strive It is not a parchment of pédigree,-it is not a name derived from the ashes of dead men, that make the only charter of a king. English

With disappointment, pénury, and páin? men were but slàves, if, in giving crown and sceptre to a mortal like

Nò: Heaven's immortal spring shall yet arrive,

And man's majestic beauty bloom again, ourselves, we ask not, in return, the kingly virtues.

Bright through the eternal year of Love's triumphant rùign. The true enjoyments of a reasonable being do not consist in unbounded indulgence,* or luxurious éase, in the tumult of pássions, Rule 3.—" Disjunctive 'Or.'" the languor of indolence, or the flutter of light amúsements. Yielding

Will you rise like men, and firmly assert your rights, or will you to immoral pleasures corrupts the mind; living to animal and trifling tamely submit to be tràmpled on ? ones, de bases it; both, in their degree, disqualify it for genuine good, nad consign it over to wretchedness.

Did the Romans, in their boasted introduction of civilisation, act

from a principle of humane interest in the welfare of the world ? Or What constitutes a state ?

did they not rather proceed on the greedy and selfish policy of aggranNot high-raised battlements, or laboured móund,

dising their own nation, and extending its dominion ? Thick wall, or moated gáte;

Do virtuous hábits, a high standard of morálity, proficiency in the Not cities proud, with spires and turrets crowned,

arts and embellishments of life, depend upon physical formátion, or Not bays and broad-armed ports,

the látitude in which we are placed ? Do they not depend upon the Where, laughing at the storm, proud návies ride;

civil and religious institutions which distinguish the country? Not starred and spangled courts, Where low-browed baseness wafts perfume to pride!

The remaining rules on “inflection," as they are of less No!mìn,-high-minded MÈN,

frequent application, are thought to be sufficiently illustrated Men who their duties know,

by the examples appended to each rule. A repetition of these, But know their rights, and, knowing, dare maintàin,

however, may be useful to the student as an exercise in review. Note.—“Concession and unequal antithesis.” The clouds of adversity may darken over the Christian's páth; but he

LESSONS IN MUSIC.-VIII. can look up with filial trust to the guardian care of a beneficent Father. I admit that the Greeks excelled in acuteness and versatility of

MENTAL EFFECT OF NOTES. , mind. But, in the firm and manly traits of the Roman character, I We have now to treat of a most important subject, and one Bee something more noble, more worthy of admiration,

which should be thoroughly well anderstood by every pupil. We war agninst the leaders of evil-not against the helpless tóols: We refer to the mental effect of notes. Let us put the topic in we war against our opprèssors,-not against our misguided brethren. the form of a question. What is the principal source of a note's

power to affect the mind ? We observe, for instance, in one of The penultimate inflection falls, when a sentence ends with the Handel's songs, that a certain note produces a certain effect rising alide.

upon our minds. Why does it produce that offeet? Is there

KEY D

any law by which such mental effects are chiefly regulated ? | this second mental effect, and that no other note produces the To these questions we answer, that many circumstances may same effect, however you may quicken its rate of movement modify the mental effect of a note, but that it is mainly pro- There is still

, therefore, a law presiding even in this “ duplicity" duced by the principle of key-relationship, in connection with of mental effect. This note LAH (sixth above or " minor third” rate of movement. We believe that every note of the scale below the key-note) is now proved to possess twin mental effects, (whatever may be the pitch of the key-note) has a peculiar the one showing the grave, the other the gay side of a certain "mission" of its own to the human mind-a proper mental emotion. So is it with every note of the scale. “ Key-relationeffect, which circumstances of pitch, quality of voice, rhythmical ship” gives it a certain acceptance with the mind, and “ rate of arrangement, peculiarities of expression, etc., may modify, but movement” has a certain way of modifying that impression. To cannot efface. Let us take an example, and look at it in these prove, however, that the key-relation into which a note is thrown, various lights. It cannot be doubted that the last noto in the by the sounds which have been heard before it, is the principal following phrase, from Dr. Calcott's well-known glee, produces producing cause of mental effect, we must try another experia mental effect peculiarly appropriate to the word to which it is ment. Take the same sound, as to absolute pitch, and vary its set. That note we call LAH. It is the sixth above or the key-relationship. Strike the “chord" and scale of B, for instance, “minor third" below the key-note. The question is, How and then the note B, at length, noticing its mental effect. Nert comes that note to produce a sorrowful impression on the strike the chord and scale of A, followed by the same note B mind? What is the law, if there is one, by virtue of which the same in pitch), as a long note. Notice, now, its effect on that note possesses its power ? Let the pupil sing the phrase :- the mind. How changed ! Try, next, the chord and scale of

G, and observe the note, in the same way. How changed again! Try other keys, and you will find that every change of koy-relationship makes a change in the ception which the mind gives to that particular sound of unaltered pitch. If you

wish to prove this to an incredulous friend, tell him that you :d d :r m :S s.f:m.r 1:

are about to play to him, on the flute or piano, a number of long For give, blest shade, the

tri - bu - ta - ry tear. notes, and that, without looking at your playing, he is to tell Try first the various conditions of pitch. Take a higher you, as well as he can, what notes they are, and describe their sound, say G, for your key-note or Doh, and sing the phrase mental effect. Then play to him the following phrases, and ask again. You will notice that the mental effect is modified, but it him, at the close, whether the notes were the same, or, if not

, remains essentially the same. Again, while in the key of G, how they differed. Unless he takes care to keep singing the sing the phrase, taking the lower LAH, instead of the upper. noto B all through (which would be a physical rather than a The effect on the mind is more gloomy, but it is still the same

mental test), he is sure to suppose the notes different. Of course effect. It is not the mere height in pitch, then, that gives to you must be acquainted with some instrument to perform this the Law its peculiar characteristic of sorrowfulness. The differ- experiment. The violin will give it most accurately. once between the same tune set in a low and in a high key is andoubtedly great, but the special effect of each individual noto remains of the same kind. Next try the effect of what is called in French “ timbre," or different qualities of sound, upon this note. Let the phrase be sung by a rough voice, a clear voice, a hard voice, a mellow voice, eto, or let it be played first on a flrate, next on a trumpet, and again on a violin. Such changes

|d.r:m.f / s.d:t1.1, m: 1r : 10:-1will cortainly modify the mental effect. One voice or instru. ment may be better than the other, but they will all agree in expressing, on the note Lan, the sorrowful sentiment, and, if they sound the note correctly, they cannot help doing so. This mental effect is therefore independent of the mere qualities of sound, and is governed by some other law. Let the next experiment be in relation to interval, for some persons might imagine I d.r:m.fs.dtillfilm: that the " distance in pitch” between RAY and LAH, called a fifth, produces the mental effect. Therefore sing the word "tear," when you come to the close, thus :

KEY B.

KEY A.

KEY G.

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t :1 You will find that every change produces a modification of the idea, but the idea itself belonging to Lah remains still the same. Interval, therefore, is not the law which governs mental effect. In a similar way you may try whether singing the same sound to different words or syllables, or with different modes of “expression” (as loud, soft, etc.), will produce any material changes. And when you have found that none of these various conditions of the note can rob it of its own peculiarly emotional character, then try another and most important experiment. Vary the rate of movement. Instead of singing the phrase slowly, sing it as rapidly as though it were a jig. You will then understand why we said that key-relationship, in connection with rate of movement, was the chief cause of mental effect. The note seems, now, to express an abandonment to gaiety, instead of sorrovi. But notice that LAH, sung quickly, always produces

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KEY C.

present, as a mental element, with every single note that follows. In a similar manner, the effect of a given colour—the artist will tell us-is modified by the surrounding ones, or those on which the eye has just rested. This is a deeply interesting subjects

and deserves to be well studied and further explored, especially d'r':m!.fl s'd't.1 r: d' : t :-1-:- in connection with harmonic combinations and effects.

These mental effects of notes in key have often been noticed KEY B.

in books of science. Dr. Calcott refers to them in his “Musical Grammar.” M. Jeu de Berneval, Professor to the Royal Academy of Music, in his “ Music Simplified,” illustrates them very ingeniously and beautifully. Dr. Bryce introduces them into

his “ Rational Introduction.” It would seem surprising (did we | d.r:m.f/s.diti.1, si : Iti :

Id :-- not know how the old notation, with its attempted, but inaccu

rate, scale of fixed sounds, takes up the learner's time, and disWhy a note's standing at a particular interval from the key tracts attention from the real beauties of musical science) that note should give it a particular musical effect, we do not know. these interesting facts, so well calculated to aid the pupil, have We can only notice the fact, and make use of it in teaching. been so little used in elementary instruction. It is obvious that There must come to us, along with the actual sound itself, some the moment a pupil can recognise a certain musical property ir: mental association of the relationship of interval (indicated by any note, he will be able to produce the note with the greater preceding notes) which has been thrown around it. The memory accuracy and satisfaction. From extensive experience we have of notes just heard hovers around that which we now hear, and found that infants and persons with untrained voices are able gives it its character. Quick succession approaches in effect to to appreciate these points, and derive constant pleasure and co-existence, as is familiarly shown in reference to the eye by assistance from the knowledge of them. The teacher will the zoetrope and other optical toys. Thus when once the key is find himself well repaid by a most careful attention to this established by the opening notes of the tune, it is still felt to be subject.

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