humidity varies with the wind; hence, we have dry winds and
moist winds. In the middle of Germany, the driest wind is
the east; the most humid, the north. These winds change
their character in the different seasons of the year. In winter,
the east is the most humid, and the west the driest. In sum-
mer, on the contrary, the west is the most humid, and the
east the driest. These differences affect the temperature of
the winds; the most humid are the coldest.

Prob. 5. Given 4x-2y= 20, and 4x+2y= 100; to find the values of x and y. Ans. 15 and 20. Prob. 6. Given 5x+8=7y, and 5y + 327x; to find the values of x and y. Ans. 11 and 9.

Now, the first member of each of the equations is x, and the second member of each is equal to x. But according to the Axiom that quantities which are respectively equal to another quantity, are equal to each other; therefore we have 2+y=14-y; whence, y = 6.

Prob. 7. To find two numbers such, that their sum shall be 24; and the greater shall be equal to five times the less. Here, let x be the greater; and y the less.

Lastly, by substituting the value of y in the 1st equation, we have x+6=14; and x=8. Therefore, 8 and 6 are the values of x and y.

In solving the preceding problem, it will be observed that we first found the value of the unknown quantity a, in each equation; and then, by making one of the expressions denoting the value of x, equal to the other, we formed a new equation, which contained only the other unknown quantity y. This process is called extermination or elimination.

In the resolution of equations, there are three methods of extermination, viz. by comparison, by substitution, and by addition and subtraction.

From this equation, by separating the left hand member into

Case I. To exterminate one of the two unknown quantities by factors, we have comparison.

RULE.-Find the value of one of the unknown quantities in each of the equations, and form a new equation by making one of these values equal to the other. Find the value of the unknown quantity in this equation, by the rules formerly given. Then substitute this value of the one unknown quantity in either of the other equations, and resolving it by the same rules, the other unknown quantity will be found.

Prob. 1. Given x + y = 36, and x − y = 12; to find the
values of x and y.

Transposing y in the first equation, gives
Transposing y in the second equation,,,
Making these values of x equal

Transposing, etc.,

Substituting the value of y,

y

x=36
x=12+ y

--

12+y=36
y= 12
x=12+12= 24.

Hence, 24 and 12 are the values required.
Prob. 2. Given 2x+3y=28, and 3x+2y=27; to find
the values of x and y. Ans, 5 and 6.

Prob. 3. Given 4x+y=43, and 5x+2y= 56; to find
the values of x and y. Ans. 10 and 3.

Prob. 4. Given 4x-2y=16, and 6x 9y; to find the values of x and y. Ans. 6 and 4.

The rule given above may be generally applied for the exwhich other methods will be found more expeditious. termination of unknown quantities. But there are cases in

Prob. 10. Given x=hy, and ax + bx=y2; to find the values of x and y.

As in the first of these equations, x is equal to hy, we may in the second equation substitute this value of x for z itself. The second equation will then become, any+bhy = y2.

The equality of the two sides is not affected by this alteration, because we only change one quantity for another which contains only one unknown quantity. Whence, y=ah+ble, is equal to it. By this means we obtain an equation which and xah2 + bh2.

This process is called extermination by substitution.

Case II. To exterminate an unknown quantity by su stitution.

Prob. 12. Given 8x+y=42, and 2x + 4y = 18; to find the values of x and y. Ans. 5 and 2.

Prob. 13. Given 2x+8y = 84, and 4x+6y=68; to find the values of x and y. Ans. 2 and 10.

Prob. 14. Given 3x + 3y = 72, and 4x + 5y = 116; to find the values of x and y. Ans. 4 and 20. Prob. 15. Given x + 10y= 124, and 2x+9y=124; to find the values of x and y. Ans. 8 and 12. Prob. 16. A privateer in chase of a ship 20 miles distant, sails 8 miles, while the ship sails 7. How far will each sail before the privateer will overtake the ship? Ans. 160 and 140 miles.

Prob. 17. The ages of two persons, A and B, are such that seven years ago, A was three times as old as B; and seven years hence, A will be twice as old as B. What is the age of each? Ans. 49 and 21 years.

Prob. 18. There are two numbers, of which the greater is to the less as 3 to 2; and their sum is the sixth part of their product. What are the numbers? Ans. 15 and 10.

There is a third method of exterminating an unknown quantity from an equation; which, in many cases, is preferable to either of the preceding.

Prob. 19. Given x + 3y = a, and x values of x and y.

-3y=b; to find the

that the sum of both is 21110; and twice the number in the Prob. 27. The numbers of two opposing armies are such, greater army, added to three times the number in the less, is 52219. What is the number in each army? Ans. 11111

and 9999.

Prob. 28. The sum of two numbers is 220, and if 3 times the less be taken from 4 times the greater, the remainder will be 180. What are the numbers? Ans. 120 and 100.

In the solution of the succeeding problems, either of the three rules for exterminating unknown quantities may be used at pleasure. That quantity which is the least involved should be the one chosen to be first exterminated.

The student will find it a useful exercise to solve each example by each of the several methods, and carefully to observe which is the most comprehensive, and the best adapted to different classes of problems.

Prob. 29. The mast of a ship consists of two parts; onethird of the lower part added to one-sixth of the upper part, is equal to 28 feet; and five times the lower part, diminished by six times the upper part, is equal to 12 feet. What is the height of the mast? Ans. 108 feet.

Prob. 30. To find a fraction such that, if a unit be added to Here, if we add together the first members of these two equa- be added to the denominator, the fraction will be equal to . the numerator, the fraction will be equal to ; but if a unit tions, and also the second members, we shall have Let x the numerator, and y = the denominator.

2x = a + b,

an equation which contains only the unknown quantity x.
The other, having equal co-efficients with contrary signs, has
disappeared. Still the equality of the sides is preserved, because
we have only added equal quantities to equal quantities.
Prob. 20. Given 3x+y=h, and 2x+y=d; to find the
values of x and y.

Here, if we subtract the second equation from the first, we
shall have xhd, where y is exterminated, without affect-
ing the equality of the sides. Whence, y3d-2h.
2y=a, and x + 4y = b; to find the

Prob. 21. Given xvalues of x and y.

Here, multiplying the first equation by 2, we have

to their sum as 2 to 3; and whose sum is to their product as 3 Prob. 31. What two numbers are those, whose difference is to 5? Ans. 10 and 2.

Prob. 32. To find two numbers such, that the product of their sum and difference shall be 5, and the product of the sum of their squares and the difference of their squares shall be 65. Ans. 3 and 2.

Prob. 33. To find two numbers whose sum is 32, and whose product is 240. Ans. 20 and 12.

Prob. 34. To find two numbers whose sum is 52, and the sub-sum of their squares 1424. Ans. 32 and 20.

Case III. To exterminate an unknown quantity by addition

and subtraction.

RULE.-Multiply or divide the equations, if necessary, by such factors that the term which contains one of the unknown quantities shall be the same in both equations. Then subtract one equation from the other, if the signs of this unknown quantity are alike, or add them together if the signs are unlike; the result will be an equation containing only one unknown quantity, which is to be resolved as before.

It must be kept in mind that both members of an equation

Prob. 35. A certain number consists of two digits or figures,

the sum of which is 8. If 36 be added to the number, the digits will be inverted. What is the number? Ans. 26.

Prob. 36. The united ages of A and B amount to a certain number of years, consisting of two digits, the sum of which is 9. If 27 years be subtracted from the amount of their ages, the digits will be inverted. What is the sum of their ages? Ans. 63.

Prob. 37. A merchant having mixed a quantity of brandy and gin, found if he had put in 6 gallons more of each, the 6 of gin; but if he had put in 6 gallons less of each, the pro compound would have contained 7 gallons of brandy for every

In the preceding examples of two unknown quantities, it will be perceived that the conditions of each problem have furnished two equations independent of each other. It often Prob 40. Given x+y+z = 12, x + 2y +32=20, and becomes necessary to introduce three or more unknown quanti-+by+6; to find the values of x, y and s. Ans. 6, ties into a calculation. In such cases, if the problem admits of a determinate answer, there will always arise from the conditions as many equations independent of each other, as there are unknown quantities.

Prob. 39. Given x + 5y + 6 = 53, x+3y+3z=30, and x + y + z = 12; to find the values of x, y and

Here, from these three equations in order to derive two containing only two unknown quantities,

Subtracting the second from the first, we have 2y+3x=23.

Subtracting the third from the second, we have
2y+2z 18.

Next, from these two, in order to derive one,
Subtracting the fifth from the fourth, we have

recorded in the Book of Life. If their steps were not accom- | The heavens and the earth had a beginning, and they will panied by a splendid train of ménials, legions of ministering have an end. The face of the world is changing, daily and angels had charge over them. Their palaces were houses hourly. All'animated things || grow old and die. The rocks not made with hands: their diadems, crowns of glory which should never fade away!

On the rich and the eloquent, on nobles and priests, they looked down with contempt; for they esteemed themselves rich in a more precious treasure, and eloquent in a more sublime language; nobles by the right of an earlier creation, and priests by the imposition of a mightier hand. The very meanest of them was a being to whose fate, a mystèrious and térrible importance belonged, on whose slightest action the spirits of light and darkness looked with anxious interest; who had been destined, before heaven and earth were created, to enjoy a felicity which should continue, when heaven and earth should have passed away.

crumble, the trees | full, the leaves | fade, and the grass | withers. The clouds are flying, and the waters are flowing awày from us.

The firmest works of man, too, are gradually giving way, the wy clings to the mouldering tower, the brier | hangs out from the shattered window, and the wall-flower | springs from the disjointed stones. The founders of these perishable works have shared the same fate | long ago. If we look back to the days of our ancestors, to the men as well as the dwellings | of former times, they become immediately associated in our imaginations, and only make the feeling of instability stronger and deeper than before. In the spacious domes, which once held our fathers, the serpent hisses, and the wild bird | screams. Events which shortsighted politicians ascribed to earthly The halls, which once were crowded with all that taste and causes, had been ordained on his account. For his sake, science and labour | could procure,-which resounded with empires had risen, and flourished, and decayed. For his sake, melody, and were lighted up with beauty, are buried by their the Almighty had proclaimed his will by the pen of the evan-own ruins, mocked by their own desolation. The voice of merrigelist and the harp of the prophet. He had been rescued by nó ment, and of wailing, the steps of the bùsy and the idle | have common deliverer, from the grasp of nò cómmon foe. He had ceased in the deserted courts, and the weeds | choke the entrances, been ransomed by the sweat of nó vulgar ágony, by the blood and the long grass || waves upon the hearth-stone. The works of of no earthly sacrifice. It was for him that the sun had been art, the forming hand, the tombs, the very ashes they contained, darkened, that the rocks had been rent, that the dead had are all gone. arisen, that all nature had shuddered at the sufferings of her expiring God.

Thus the Puritan was made up of two different mèn, the one all self-abasement, penitence, gratitude, passion; the other proud, calm, infléxible, sagacious. He próstrated himself in the dust before his Máker: but he set his foot on the neck of the king. In his devotional retirement, he prayed with convulsions, and groans, and tears. He was half-maddened by glorious or térrible illusions. He heard the lyres of angels, or the tempting whispers of fiènds. He caught a gleam of the beatific vision, or woke screaming from dreams of everlasting fire. Like Vane, he thought himself intrusted with the scèptre of the millennial year. Like Fleetwood, he cried in the bitterness of his soul, that God had hid his fàce from him. But when he took his seat in the council, or girt on his sword for war, these tempestuous workings of the soul had left no perceptible trace behind them. People who saw nothing of the godly but their uncouth visages, and heard nothing from them but their groans and their hymns, might laugh at them. But those had little reason to laugh, who encountered them in the had of debate, or in the field of battle.

The Puritans brought to civil and military affairs a coolness of judgment, and an immutability of purpose, which some writers have thought inconsistent with their religious zeal, but which were in fact the necessary effects of it. The intensity of their feelings on one subject, made them tranquil on every other. One overpowering sentiment had subjected to itself pity and hatred, ambition and fear. Death had lost its térrors, and pleasure its charms. They had their smiles and their tears, their raptures and their sorrows, but not for the things of this world. Enthusiasm had made them stoics, had cleared their minds from every vulgar passion and préjudice, and raised them above the influence of danger and of corruption.-Macaulay.

While we thus walk among the ruins of the past, a sad feeling of insecurity comes over us; and that feeling is by no means diminished when we arrive at home. If we turn to our friends, we can hardly speak to them before they bid us farewell. We see them for a few moments and in a few moments more, their countenances are changed, and they are sent away. It matters not how near and dear they are. The ties which bind us together are never too close to be parted, or too strong to be broken. Tears were never known to move the king of terrors; neither is it enough that we are compelled to surrender one, or two, or many of those we love; for though the price is so great, we buy no favour with it, and our hold on those who remain | is as slight as ever. The shadows || ah elude our grasp, and follow one another' down the valley, We gain no confidence, then, no feeling of security, by turning to our contemporaries and kindred. We know that the forms, which are breathing around us, are as shortlived and fleeting as those were, which have been dust for centuries. tion of vanity, uncertainty, and rúin, is equally strong, whether we muse on what has long been prostrate, or gaze on what is falling now, or will fall so soon.

1

1

The sensa

we

If every thing which comes under our notice || has endured for so short a time, and in so short a time will be no more, we cannot say that we receive the least assurance by thinking on ourselves. When a few more friends have left, a few more hopes | deceived, and a few more changes | mocked us, shall be brought to the grave, and shall remain in the tomb: the clods of the valley shall be sweet unto us, and every man shall follow us, as there are innumerable before us." All power' will have forsaken the strongest, and the loftiest will be laid low, and every eye will be closed, and every voice hushed, and every heart will have ceased its beating. And when we have gone ourselves, even our memories will not stay behind us long. A few of the near and dear will bear our likeness in their bosoms, till they too have arrived at the end of their journey, and entered the dark dwelling of unconsciousness. In the [Marked for Rhetorical Pauses, Emphasis, and Inflections.†] thoughts of others we shall live only till the last sound of the bell, which informs them of our departure, has ceased to vibrate We receive such repeated intimations of decay in the world in their cars. A stone, perhaps, may tell some wanderer when a through which we are passing;-decline | and change | and toss, we lie, when we came here, and when we went away; but even foto decline | and change | and loss | in such rapid succession, that will soon refuse to bear us record: "time's effacing fingers" that we can almost catch the sound of universal wasting, and will be busy on its surface, and at length will wear it hear the work of desolation going on busily around us. The smooth; and then the stone itself will sink, or crumble, and ntain falling cometh to nought, and the rock | is removed the wanderer of another age will pass, without a single call ut of his place. The waters | wear the stones, the things which upon his sympathy, over our unheeded graves.- Greenwood. grow out of the dust of the earth are washed away, and the hope of man is destroyed." Conscious of our own instability, we look about for something to rest on; but we look in vain.

IV. UNIVERSAL DECAY.

When an emphatic series causes, thus, a succession of falling inflection, the second one in each clause falls lower than the first.

V.-ETERNITY OF GOD.

[Marked for Rhetorical Pauses, Emphasis, and Inflections.] There is one Being to whom we can lock with a perfect conviction of finding that security, which nothing about us can give, and which nothing about us can take away. To this

The learner having been conducted through the application of the rules
Hady as, Emphasis, and Inflections, separately, will now be prepared to Being we can lift up our souls, and on Him we may rèst

and apply them in conjunction.

them, exclaiming | in the language of the monarch of Israel, | person of the subjunctive of the imperfect, which are alike, the "Before the mountains | were brought forth, or ever Thou personal pronouns, for the most part, ought to be used, to avoid hadst formed the earth and the world, even from everlasting to everlasting Thou art GòD." "Of old | hast Thou laid the foundations of the earth, and the heavens are the work of Thy hands. They shall perish, but Thou shalt endure; yea, all of them shall wax old like a garment, as a vèsturei shalt Thou change them, and they shall be changed; but Thou art the same, and Thy years | shall have no end."

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tions to inhabit them.

confusion, e. g., che i-o ab-bia, che tu ab-bia, ch' e-gli db-ba, that I may have, that thou mayest have, that he may have; se i-o 4-vés-si, se tu a-vés-si, if I had, if thou hadst; che i-o si-a, che tu sí-a, ch'e-gli si-a, that I may be, that thou mayest be, that he may be; se i-o fós-si, se tu fós-si, if I were, if thou wert, instead of che db-bia, se a-vés-si, che si-a, se fos-si, etc.

2. Like most of the modern languages derived from the Latin stock, the Italian has five preterite tenses, while the English language, like the German, Dutch, Danish, and Swedish, has only three, the imperfect, the perfect, and the pluperfect. The Italian conjugation, in this respect, has the advantage of a greater precision, and, in narrations, of a greater variety.

Here then is a support, which will never fail; here' is a foundation which can never be moved the everlasting Creator of countless worlds, "the high and lofty One | that inhabiteth eternity." What a SUBLIME CONCEPTION! HE INHABITS ETERNITY, occupies this inconceivable duration, PERVADES | and FILLS THROUGHOUT THIS BOUNDLESS DWE'LLING, Ages on ages before even the dust of which we are formed || was created, HE 3. The English conjugation has only two tenses formed had existed in infinite majesty, and ages on ages will roll away The other tenses, the perfect, pluperfect, and future, are without the aid of auxiliaries, the present and the imperfect. after we have all returned to the dust whence we were taken, and still HE will exist in infinite majesty, living in the merely periphrases. The Italian conjugation has four tenses eternity of his own nature, reigning in the plenitude of his own formed without the aid of auxiliaries, the present, the imperomnipotence, for ever sending forth the word, which forms, sup- and the future. The determinate preterite, the pluperfect, fect, the indeterminate preterite (pas-sa-to in-de-ter-mi-nd-to), ports, and governs all things, commanding new-created light to and the future past, are the only Italian tenses requiring the shine on new-created worlds, and raising up new-created genera- aid of the auxiliaries a-vé-re and ês-se-re, to have and to be. The contemplation of this glorious attribute of Góp, is fitted In this point, also, the Italian conjugation has the advanto excite in our minds the most animating and consoling tage of greater brevity, while in English the accumulation of reflections. Standing, as we are, amid the ruins of time, and auxiliaries, particularly in the future past, renders it more the wrecks of mortality, where every thing about us | is created difficult to avoid a drawling and heavy style, e. g., a-vrê-i and dependent, proceeding from nothing, and hastening to destruc-a-ma-to must be expressed by four words: I should have tion, we rejoice that something is presented to our view | which loved; sa-re-i stá-to fe-ri-to, by ice: I should have been has stood from everlasting, and will remain for ever. When we have looked on the pleasures of life, and they have vanished indicative than in English, where, for the most part, it 4. The Italian subjunctive is far more different from the awdy; when we have looked on the works of nature, and perceived that they were changing; on the monuments of art, and resembles it, and can only be known by the sense or by cerseen that they would not stand; on our friends, and they have tain conjunctions connected with it; e. g., (ind.) d-m, I'love, fled while we were gazing; on ourselves, and felt that we were loved, (subj.) a-más-si (if, etc.), I loved; (ind.) ho a-má-to, I (subj.) d-mi (unless, though, etc.), I love; (ind.) a-má-va, Į as fleeting as they; when we have looked on every object to have loved, (subj.) db bia a-ma-to (unless, though, etc.), I have which we could turn our anxious éyes, and they have all told us that they could give us no hope, nor support, because they were so feeble themselves; we can look to the THRONE of GO'D: change and decay have never reached THAT; the revolution of ages has never moved it; the waves of an eternity | have been rushing past it, but it has remained unshaken; the waves of another eternity are rushing toward it, but it is FIXED, and can NE'VER BE DISTURBED.-Greenwood.

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LESSONS IN ITALIAN GRAMMAR.-No. XXIV.
By CHARLES TAUSENAU, M.D.,

Of the University of Pavia, and Professor of the German and Italian
Languages at the Kensington Proprietary Grammar School.
AUXILIARY VERBS.

THE Conjugation of Italian verbs, compared with that of the
English, offers the following peculiarities:-

1. The personal pronouns i-o, I; tu, thou; e-gli, és-so, he; él-la, és-sa, she; nói, we; voi, you; and e-gli-no, és-si (m.) él-le-no, és-se (f.), they, may be omitted before the Italian verbs; because their persons, with an unmistakable clearness, are expressed by the difference of their terminations, e. g., d-mo, d-mi, d-ma, a-mia-mo, a-má-te, á-ma-no, I love, thou lovest, he (she) loves, we love, you love, they love, is equivalent to 1-0 d-mo, tu á-mi, é-gli (él-la) á-ma, nói a-mid-mo, vói a-ma-te, é-gli-no (él-le-no) d-ma-no. In English, for want of inflections, the personal pronouns are inseparable from the verbs; and in this respect the Italian language has the advantage of a greater brevity and variety of expression. In two cases, however, even before Italian verbs, the personal pronouns are indispensable. In the first place, when they are required by emphasis or contrast, e. g., i-o v'en-tre-rò dén-tro, I shall enter; nói er-rid-mo, nói giá-mo in-gan-nd-ti, e non với, we are mistaken, we are cheated, not you. In the second place, in the singular, before the three persons of the subjunctive of the present, and also in the singular before the first and second

When the falling inflection recurs, in succession, as above, it falls Ower at each repetition.

wounded.

loved.

5. The Italian language has several regular forms for the conjugation of its verbs. The English has but one. This simplicity no doubt is an advantage of the English conjugation, which, however, is counterbalanced by the greater variety of

the Italian.

From these peculiarities, taken together, the learning of the Italian conjugation offers great difficulties to the foreigner, and particularly to the English, difficulties which are considerably increased by the very great irregularities of numerous verbs, by the frequent varieties of termination in one and the same person of a verb; and, last not least, by the frequent abbreviations and contractions in the style of poetry. In short, the Italian verb is by far the most difficult part of the Italian grammar, and a profound and complete knowledge of this part of speech almost may be pronounced a science in itself. Fortunately a smaller amount of knowledge will suffice for the beginning of reading and conversation, and the rest may safely which a foreigner can never hope to acquire a perfect be left to time, perseverance, and studious practice, without acquaintance with any language, not even with the English, In the conjuga notwithstanding its remarkable simplicity. tion of the auxiliaries, and of the verbs, I shall present to the learner, not only their regular forms, to be committed to memory, but also, for the purpose of reference, some of their ancient, poetical, and erroneous variations, in the shape of notes,

or additional remarks.

És-se-re, to be.

INDEFINITE MOOD (Mô-do in-de-fi-gi-to) Present (têm-po pre-sên-te), ês-se-re, to be. Preterite (tem-po pas-sd-to), ês-se-re stá-to, to have been. (tem-po fu-tu-ro), és-se-re per és-se-re, or a-vé-re ad ês-se-re, to be about to be.

Future

This is the most irregular of the Italian verbs, and, like the Latin verb esse, from which it is derived, it appears originally to have been formed from the fragments of several other verbs, for só-no, e-ra, fui, are words taken from quite different roots. It has, moreover, many other forms used in poetry or in popular dialects. Generally speaking, the Italian verba have. more than those of any other language, such a variety of forms for one and the