respect to; además de, besides; a pesar de, in spite of, notwithstanding; cerca de, near to; frente á, or en frente de, opposite; en orden d, with regard to; junto á, adjoining; por el médio de, across; durante, during.

The preposition entre, between, when it comes before personal pronouns, does not govern them in the objective case in Spanish, but is followed by them in the nominative; as, entre tú y yo (and not entre ti y mi), between thee and me.

Prepositions, as in English, are placed before the word which they govern.

Care must be taken to distinguish the use of the same word in English, whether employed as a preposition or an adverb or conjunction. Thus in the phrases, after breakfast, before

ventana.

sobre la ciudad.

"Towards" is rendered by hácia; as,

Here comes towards us the lady of the house, aquí viene hacia nosotros la señora de la casa,

"Under" is rendered by debajo de or bajo; as,

Under the bridge, debajo del puente.
Under the table, bajo la mesa.

"Under" is rendered by so in the following phrases, so capa de, under cover of; so color de, under colour of; so pena de, under¡ penalty of; so pretexto de, under pretext of.

OF THE INTERJECTION.

¡Etelos que vienen! lo they come!

We-are covered with dust,

estamos cubiertos de polvo. We are-dying with cold, nos morimos de frío.

John killed him with a sabre

"Within" is rendered by dentro de; as

I-shall-need it within three days, lo necesitaré dentro de tres dias. "Without," meaning destitute of, with exemption from, is rendered by sin; and when it means outside of, or beyond, by fuera de; as,

To-buy without money, comprar sin dinero.

Treat me without ceremony, trúteme vind, sin ceremónia. They-cast him without the city, le echaron fuera de la ciudad. Sin in Spanish is regarded as a negative preposition, and is therefore often followed by a negative conjunction; as,

Sin otro fin ni motivo, without another end or (nor) motive.

There are other prepositions in Spanish, which, as they can be rendered in most cases by the corresponding English preposition, offer no difficulty to the learner. Such are para con, in

¡Ay de mi! alas for me! (or, woe to me!)

LESSONS IN TRIGONOMETRY.-No. VI.

TRIGONOMETRICAL FORMULE.

Whence,

We thus find the angle в and

R cos, a cos, x = cos. b cos, e cos. x + sin. b cos. c sin. ; or, dividing each term by cos. x, we obtain,

59° 16′ 46′′. 131° 28' 36".

R2 cos. α = ccs. b cos. c + sin. b cos. c tan. x.

But, by Theorem II., Cor. 2, we have,

R sin. b sin. c- R Cos. b cos.c—— Hence, by substitution, we obtain,

cos. la R

1:3 cos. (b+c).

B) cos. (sc) sin. B sin, c

(4)

and formula (2) becomes,

which formule enable us to compute the sides of a triangle when the three angles are known.

By means of the polar triangle, we derive from formula (1), R2 cos. A cos. a sin. B sin. c— cos. B cos. c. (6) Ex. 1. In a spherical triangle ABC, there are given a 130° 30′, B = 30° 50′, and c 32° 5. Required the three sides. Here half the sum of the angles is 96° 42′ 30′′ =s Also,

9.611435

9-631992

comp. 0290270 comp. 0-274781

Sum 19-S08478

9.904239

cos. b R

COS. (S A) cos. (S sin. A sin. c We thus find the side b— 40° 13′ 12′′,

=

c42° 0' 12".

Now if cos, a is greater than cos. b, the sign of the second member of this equation will be the same as that of cos. a. Hence cos. A and cos. a will have the same sign; or A and a will be of the same species when cos. a>cos. b, or sin. a<sin. b; that is,

If the sine of the side opposite to the required angle is less than the sine of the other given side, there will be but one triangle.

But if cos. a is less than cos. b, then whether the right-hand member be plus or minus will depend upon the magnitude of cos, c; or cos. c will have two values, corresponding to cos. A cos. A; hence,

and

from which it follows, as in the preceding case, that if cos. A is greater than cos. B, A and a will be of the same species. But if cos. A is less than cos. B, then c may be taken so as to render cos. a positive or negative. Hence, if the sine of the angle opposite to the required side is less than the sine of the other given angle, there will be but one triangle; but if the sine of the angle opposite to the required side be greater than the sine of the other given angle, there will be two triangles.

LESSONS IN READING AND ELOCUTION. No. XXX

THE SCHOLAR'S MISSION.

THE wants of our time and country, the constitution of our modern society, our whole position,-personal and relative,forbid a life of mere scholarship or literary pursuits to the great majority of those who go out from our colleges. However it may have been in other times, and other lands, here and now, but few of our educated men are privileged

"From the loopholes of retreat

To look upon the world, to hear the sound Of the great Babel, and not feel its stir."

Full

Society has work for us, and we must forth to do it. early and hastily we must gird on the manly gown, gather up the loose leaves and scanty fragments of our youthful lore, and go out among men, to act with them and for them. It is a practical age; and our Wisdom, such as it is, "must strive and cry, and utter her voice in the streets, standing in the places of the paths, crying in the chief place of concourse, at the entry of the city, and the coming in at the doors."

This state of things, though not suited to the tastes and qualities of all, is not, on the whole, to be regretted by educated men as such. It is not in literary production only, or chiefly,. that educated mind finds fit expression, and fulfils its mission in honour and beneficence. In the great theatre of the world's affairs, there is a worthy and a sufficient sphere. Society needs the well-trained, enlarged, and cultivated intellect of the scholar in its midst; needs it, and welcomes it, and gives it a place, or, by its own capacity, it will take a place of honour, influence, and power. The youthful scholar has no occasion to deplore the fate that is soon to tear him from his studies, and cast him into the swelling tide of life and action. None of his disciplinary and enriching culture will be lost, or useless, even there. Every hour of study, every truth he has reached, and the toilsome process by which he reached it: the heightened

grace or vigour of thought or speech he has acquired,-all shall tell fully, nobly, if he will give heed to the conditions. And one condition, the prime one, is, that he be a true man, and recognise the obligation of a man, and go forth with heart and will, and every gift and acquirement dedicated, lovingly and resolutely, to the true and the right. These are the terms; which an ingenuous mind can desire, or which a sound and and apart from these there is no success, no influence to be had far-seeing mind would dare to seek.

to obtain a substantial success, and an abiding, influence, Indeed, it is not an easy thing, nay, it is not a possible thing, except on these terms. A factitious popularity, a transient notoriety, or, in the case of shining talents, the doom of a damning fame, may fall to bad men. But an honoured name, enduring influence, a sun brightening on through its circuit, more and more, even to its serene setting,-this boon of a true success goes never to intellectual qualities alone. It gravitates slowly but surely to weight of character, to intellectual ability rooted in principle.-George Putnam.

THE TREASURE THAT WAXETH NOT OLD.

Oh! I have loved, in youth's fair vernal moru,
To spread imagination's wildest wing,
The sober certainties of life to scorn,

And seek the visioned realms that poets sing,-
Where Nature blushes in perennial spring,

Where streams of earthly joy exhaustless rise,
Where Youth and Beauty tread the choral ring,

And shout their raptures to the cloudless skies,
While every jovial hour on downy pinion flies.
But, ah! those fairy scenes at once are fled,

Since stern experience waved her iron wand,
Broke the soft slumbers of my visioned head,
And bade me here of perfect bliss despond.
And oft have I the painful lesson conned;

When Disappointment mocked my wooing heart,
Still of its own delusion weakly fond,

And from forbidden pleasures loth to part,
Though shrinking oft beneath Correction's deepest smart.
And is there naught in mortal life, I cried,

Can soothe the sorrows of the labouring breast?
No kind recess where baffled hope may hide,
And weary nature lull her woes to rest?
Oh! grant me, pitying Heaven, this last request,—
Since I must every loftier wish resign,
Be my few days with peace and friendship blessed;
Nor will I at my humble lot repine,
Though neither wealth, nor fame, nor luxury be mine
Oh! give me yet, in some recluse abode,

Encircled with a faithful few, to dwell,
Where power cannot oppress, nor care corrode,
Nor venomed tongues the tale of slander tell;
Oh! bear me to some solitary cell,

Beyond the reach of every human eye; And let me bid a long and last farewell

To each alluring object 'neath the sky,

And there in peace await my hour,-in peace to die. "Ah, vain desire!" a still small voice replied,

"No place, no circumstance can Peace impart: She scorns the mansion of unvanquished Pride,-Sweet inmate of a pure and humble heart. Take then thy station,-act thy proper part;A Saviour's mercy seek,-his will perforin: His word has balm for sin's envenomed sinart, His love, diffused, thy shuddering breast shall warm, His power provide a shelter from the gathering storm." Oh! welcome hiding place! Oh! refuge meet

For fainting pilgrims, on this desert way! Oh! kind Conductor of these wandering feet

Through snares and darkness, to the realms of day! So did the Sun of Righteousness display

His healing beams; each gloomy cloud dispel: While on the parting mist, in colours grey, Truth's cheering bow of precious promise fell, And Mercy's silver voice soft whispered,-"All is well." D. Huntington.

THE YOUNG MARINER'S DREAM.

In slumbers of midnight the sailor boy lay,

His hammock swung loose at the sport of the wind; But, watchworn and weary, his cares flew away,

And visions of happiness danced o'er his mind.
He dreamed of his home, of his dear native bowers,
And pleasures that waited on life's merry morn;
While memory each scene gaily covered with flowers,
And restored every rose, but secreted its thorn.
Then fancy her magical pinions spread wide,

And bade the young dreamer in ecstacy rise ;--
Now far, far behind him, the green waters glide,
And the cot of his forefathers blesses his eye.

The jessamine clambers, in flower, o'er the thatch;
And the swallow sings sweet from her nest in the wall;
All trembling with transport, he raises the latch;
And the voices of loved ones reply to his call.

A father bends o'er him with looks of delight;

His cheek is impearled with a mother's warm tear; And the lips of the boy in a love-kiss unite,

With those of the sister his bosom holds dear.

The heart of the sleeper beats high in his breast,

Joy quickens his pulses,-his hardships seem o'er; And a murmur of happiness steals through his rest,"O God! thou has blest me; I ask for no more.' Ah! whence is that flame which now bursts on his eye? Ah! what is that sound which now larums his ear? 'Tis the lightning's red glare, painting wrath on the sky! 'Tis the crashing of thunders, the groan of the sphere! He springs from his hammock,-he flies to the deck,--Amazement confronts him with images dire,Wild winds and mad waves drive the vessel a wreck,The masts fly in splinters,-the shrouds are on fire! Like mountains the billows tremendously swell:

In vain the lost wretch calls on mercy to save; Unseen hands of spirits are ringing his knell, And the death angel flaps his broad wing o'er the wave. O sailor boy! woe to thy dream of delight!

In darkness dissolves the gay frost-work of bliss: Where now is the picture that fancy touched bright, Thy parents' fond pressure, and love's honied kiss?

O sailor boy! sailor boy! never again

Shall home, love, or kindred, thy wishes repay; Unblessed, and unhonoured, down deep in the main, Full many a score fathom, thy frame shall decay. No tomb shall e'er plead to remembrance for thee,

Or redeem form or fame from the merciless surge; But the white foam of waves shall thy winding-sheet be, And winds, in the midnight of winter, thy dirge! On a bed of green sea-flower thy limbs shall be laid; Around thy white bones the red coral shall grow; Of thy fair yellow locks, threads of amber be made, And every part suit to thy mansion below. Days, months, years, and ages, shall circle away, And still the vast waters above thee shall roll: Earth loses thy pattern for ever and aye;O sailor boy! sailor boy! peace to thy soul!

Dimond.

THE VICTOR ANGELS.

Now when fair morn orient in Heaven appeared,
Up rose the victor Angels, and to arms
The matin trumpet sung: in arms they stood
Of golden panoply, refulgent host,

Soon banded; others from the dawning hills
Looked round, and scouts each coast light armed scour
Each quarter, to descry the distant foe,
Where lodged, or whither fled, or if for fight,
In motion or in halt: him soon they met
Under spread ensigns moving nigh, in slow
But firm battalion; back with speediest sail
Zophiel, of Cherubim the swiftest wing,
Came flying, and in mid air aloud thus cried;
ARM, Warriors, arm for fight,-the foe at hand,
Whom fled we thought, will save us long pursuit
This day; fear not his flight: so thick a cloud
He comes; and settled in his face I see
Sad resolution and secure: let each
His adamantine coat gird well, and each
Fit well his helm,-gripe fast his orbed shield,
Borne even or high; for this day will pour down,
If I conjecture aught, no drizzling shower,
But rattling storm of arrows barbed with fire.'

So warned he them, aware themselves, and soon In order, quit of all impediment;

Instant, without disturb, they took alarm,
And onward move, embattled: when behold!
Not distant far, with heavy pace the foe,
Approaching, gross and huge, in hollow cube,
Training his devilish enginery, impaled
On every side with shadowing squadrons deep,
To hide the fraud. At interview both stood
Awhile; but suddenly at head appeared
Satan, and thus was heard commanding loud:
"VANGUARD, to right and left the front unfold,
That all may see who hate us, how we seek
Peace and composure, and with open breast
Stand ready to receive them, if they like
Our overture, and turn not back perverse."

Milton.

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