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Solutions to Mathematical Questions.


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Solutions to the foregoing, have, by y. Then, by the Question we have also been received from W. Turner, x - y = 1881 = a Bracken Hill, near Sheffield; S. T. of Saltash; and W. West, of Matomley,

and ya + xy = 324 = b Sheffield ; the latter of whom has also clear the last equation of fractions, sent a Solution to the second Ques- transpose yo and divide by y; then we tion.

Question 2d.-Let the numbers be shall have a = - 3y, whence represented by x, y, z, then per question we have

- 18b + 9 y.
xz + yz = 48300 = a
yx + 2x = 31500 = b

Substitute this value of xin the first xy + 2y = 38400 = 0

equation ; then will From the first of these equations subtract the second. Let the result

- 18 6 + 8 yo= a, be added to, and subtracted from the third, then by division we have or 9 h – 18 b y2 + 8 y* = a yo;

but by transposition 8 y - 18 6 y_ ay =-962 or 8 ye - (18Rb + a) y = - 9 *, for y put z, for (186 + a) put 8m, and divide the equation by 8: then will

z? — mz=- 62 a quadratic; Substitute these values of a and z, | whence z = in any of the original equations : sup-1" pose the first, then will

by restoring the numeral values of m ( * m) +y.” = a, and b, -= 144 = ?? or y = 12. which equation when properly reduced,

But x = 36 — 3 y, gives gjö = mn or y=( mn ) thatisx=(°12–36=) (81—36=)45.

.:. 12 and 45 will answer the condiwhence by restoring the numeral va- tions of the Question. lues of a, m, and n, y = 120, z = 230, and x = 90. So that 90, We have received answers to the 120, and 230, will answer the condi- two last Questions from J. Turner, and tions of the Question.

“ un campagnard” and Solutions from Question 3d.—Let the greater num-C-;W. Oakes, of Harlow ; W. Smith, ber be represented by x, and the less of Camborne; and J. J. Downes.

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Query.-Required the sums of the following series continued ad infinitum.

i 3 3.5 I 3.5.7 _ &c. &c. 1. 1+2.3 + 2.4.5 + 27.6.7 + *

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The Steam Engine.



Still men advance in talents, one and all,

Whether strong vice or weaker virtue call; A SATIRE.

The skilful thief can cheat the judge in chief,

My lord chief justice can harpoon the thief. Petere inde coronam

The laws, like fowler's nets, may catch the Unde prlus nulli velarunt tempora Muje.

brave, Εμοι δε ειη την αλιάν τρυπαν εν θεμιδος Or set like weasel traps, ensnare the knave;

No matter which, for perjury can kill,

| And, 'gainst all truth, grand juries find the bill.

But greater crimes and larger genius brought CONTENTS.

Reforming Bess, with mighty feelings fraught, Man in a state of barbarism-Origin of civil society. or

A sister queen to murder by her side, cities-Their good effects. Illustrated by a similitude

To wear silk stockings, and in coach to ride. Their corruption.-Insecurity of towns, on account of vice,

Why should the stranger to Crotona go? frand, rapine, and tyranny. Provoke Providence to disperse

Pythagoras instructs the shades below; mankind again-the Steam-Engine sent for that purpose how sent-described. Its effects. Citizens compelled to live

In his once crowded philosophic school, in the country-its new appearance.-The grove once sacred

Enormous vice now bears despotic rule. to Diana, now usurped by Venus. Men still vicious-but

Close on the borders of some lonely wood, less so than they would be in town. If the Steam Engine

Where late its mother and the shepherd were corrected, men might return to town-providentially

stood, prevented by the Queen's trial. The disorders of barbarism A poor forgotten lamb for pity bleats, gave rise to cities-their own vices destroy them.

Runs, stops, and runs, and oft his call repeats;

The waking wolf before the shepherd hears, TIME was, ere law and institute began,

And limb from limb the hapless victim tears. Of all the brutes that through the forest ran, From succour far, beset with treacheries, The wildest was ungovernable man.

So in our cities now the stranger dies. When tender Orpheus struck his awful lyre, Where on the mart can honesty resort? And taught religion with a prophet's fire, For cheated truth what corner of the court The sa vage tribes confess'd the power of song, Is now reserv'd ? the wealthy Jew prevails, And harmony prevented many a wrong. And poverty must sneak behind the rails. Then social kindness built her fost’ring nest, How should a judge, in ermine, pride, and lace, Of softest dove-down, in the human breast. | With patience look on rags and smutty face? Sons, to their fathers known, for virtue strove, « To prison with him, and to gallows soon, And wedlock sanctified the bands of love. “ Let not such ordure stink beneath the moon." Amphion next in bolder notes display'd

The lawyers quirk, the speaking traders fraud, The perfect bliss of Cities; undismay'd The faithless guards that nightly walk abroad, By raging lion's glare, or tiger's spring,

The griping magistrate, and starving poor, By snake's envenomed bite, or harpy's wing, Make life uneasy, and estate unsure. Shap'd by his voice to oblong, round, or square, Thus towns to infamies of savage life For temples, palaces, and columns fair, Bring back mankind, and none dares take a Fit fragments from their marble quarries rose, wife. And rested where the wise musician chose. Promiscuous love profanes our busiest streets, Each tree too sent his well-proportioned beam, Sham'd wedlock hides her face from all she (Perhaps ev'n then with secret aid of steam,)

meets; To lift the roofs, the stately walls to bind | Or else, with hair dishevelled, madly cries, Ease, safety, virtue, pleasure, bless mankind. 1 “ My oaths are sand; say where in secret lies,

See where the tyrant Rhone his poison flings “ The rank adulterer's devoted head?” From Alpine summit, and, corrosive, brings | 'Twere vain to seek him in a royal bed. A burning sand to Sion's frighted vale; ? Why should we marry, when in all distress, 'Tis death where'er he spreads his watry veil. Friends, kindred, love us for our children less ? See him on th' opening shore of Leman Lake, E'en captious sycophants from those withdraw Check'a by superior purity, to


Whose wills are occupied by heirs at law. His headlong rage; relent, with altered pace, When it was seen that men before the flood, And sinking low, conceal his mud-stain'd face. By living long in gross corruption stood, There in the throng of waters he may rest, Eternal wisdom, kind, abridg'd the date And purg'd, become a copy of the best. Of human life, and fix'd a narrower fate. Geneva pleas'd salutes the polish'd Rhone, Men, in society united, live Swift envoy from the nymphs to Neptune's Like individuals, and provoking give throne.

Vice to their heirs, full ripe and ready made ; E'en so the savage tribes in cities clos’d, E'en children now are masters of the trade. Beneath the shade of equity repos'd ;

The mother vulture to her young ones bears Refind their manners, and improv'd the arts, A living prey, and in their presence tears All virtues learnt that science fair imparts. The palpitating lamb, and groaning kid;

But, time proceeding, to mankind arose Sons learn to do whate'er their fathers did. A period new; for human fortune knows Nor do death's agonies less luscious seem, No stable footing ; nor the wisest son

Than the rich nourishment with which they Can claim the conquests which his father won.

teem; A curse attends on all improvements, which The callow young are murderers ere they fly, Makes poor men envious, and oppressors rich. And crimes on eagle wing insult the sky. So civil government makes civil war,

Hark! at the gate of heav'n shrill murder's Of some who riches guard, from those that are

screams, Keen on the watch to seize the destin'd prey. | Wake sleeping vengeance to appall the Thames. The poet's miracle, a moral lay,

In premium once, was to Loretto sent That'e'er content with poverty could stay. A holy house, where pilgrims duly went


The Steam Engine.


To hail the hallow'd shrine; and daily fell This engine sprung from so prodigious birth, On all the pure inhabitants that dwell

With special murders terrified the earth. Within the sacred precincts of the place, At noon the pestilence walks forth like night, A shower of worldly wealth and heavenly With inky shroud defiling heavenly light. grace.

But yet these characters obscure express, But now th’avenging angel is ordain’d,

To all who read phenomena, no less (To punish British cities, deeply stain'd | Than universal death, if they should dwell With blasphemy, theft,murder,and base fraud,) | Where vengeance keeps the gloomy court of To drop a monstrous engine from his cloud,

hell. The arsenal of torture for mankind,

As erst Achilles all the Trojan bands When sin excessive grows, and conseience Dispers'd with armour-gleaming iron hands, blind.

OrBabel's clam'rous hoarse discordant tongues Just as Great Britain's thunder-bearers roll Spread through the world a flood of impious Through ocean's vast expanse to either pole,

wrongs; Chastising piracy, rebellions, crime,

So this dire monster emptied many a town, In isle, bay, continent, of every clime;

And cockney join'd in converse with the So this stern spirit with Nemesian rod,

clown. Steers through the troublous air the storm of Now men in fear from crowded streets withGod;

draw, More than Égyptian plagues, dispensing far, But not to live by simple food or law. Where giant crimes provoke th'unequal war. No acorns feed them, no thatch'd hovels hide

Not more astounded were the Lernian frogs, Their dainty limbs. Nor social, side by side, When great king Block descending shook their Do man and beast their common right defend, bogs,

Nor dress'd alike as best becomes a friend. Than the proud citizens of London town, Love has its livery, and most nations hold By monstrous huge Steam-engine thund'ring | Their own in war the boldest of the bold. down:

Adepts who travel turban'd Turks to see, Boiling with heat, and belching fiery smoke, Do wisely claim their hospitality, The monster stood, and brought beneath his With heads close shorn, and crowns of muslin yoke

tapestry: Th' immediate vicinage, who vainly fled ;

Alcina's gardens, aromatic airs, For all around he rears a ruthless head, From sweeter plants than rich Arabia bears, From block to hydra turn'd; affrighting Lud, Perfume their pygmy palaces and ground. With all bis croaking battlements of mud, Those seem to dance in gay confusion round And ships that ride on his imperial flood. The guilty suburbs. More advanc'd they try, For he e'en through the ocean can pursue, Like Galatea, through the wood to fly, O'ertake and punish each abandon'd crew. | Yet turn to ogle with lascivious eye. As Myrra's child, from aromatic tree,

Our painted ploughs and carts may haply Burst the hard rind, (for incest will be free,)

shock So from the side of Mongibello came,

The taste of lowing herd or bleating flock; Tais genuine son of hell's pernicious flame, The straw-built roof more snugly may invest Shot through the air by heav'n's supreme | The rural mouse, or sparrow in her nest. command,

Their minds change not; but modern masonry As light'ning swift, and fill'd th'avengers hand, Seems more commodious to the human eye. Who shook it off to plague this suff'ring land. The country maids their dairy dress with Sure proof of guilt; for when the viper hiss’d, care, And twining grasp'd the great apostle's wrist, And eke themselves with neatness due prepare. He back restor'd it to the hissing wood, The rustic poets sing in courtly style Because those islanders were kind and good. Their love-sick idyls, and the maids beguile; And with it came a genius of the fire,

Such seldom wait for blessing from above, Whose skill his entrails feeds with baneful ire, But watch the coming gale with bosoms full Augmenting heat dissolv'd to vapoury dew

of love. His bowel moisture, which in vigour grew, The grove was Dianas temple, chaste as snow Forcing impetuous way through every tube Or childish innocence, though Venus now Of his complex anatomy-the cube,

Usurp her arrows, cheating those who dream The valve, cylindric pump, relax, compress Of lunar radiance, with a hotter beam.. His native fury, and fierce restlessness. Once every crime that man's corrupted mind Thus toss'd and roaring like sulphureous storm, Could harbour or commit was duly fin'd. Rais'd by the fiend, it strikes in ev'ry form One now we legal deem, the state may sell, Of racks, and wheels, and whirling beams, that | And mortgage all the rights of heav'n and hell, cry,

Yet wisely keep it at a doubtful rate, With hacking, cutting, breaking, hammering | Like fruiterer at his stall, who bids you eat, minstrelsy..

Then names the rascal price. 'Tis just to give The iuward groanings shake contiguous walls, An equal power to both, as sons of Eve. And black defiling smoke before it falls, | The convict in adultery, rich and gay, Doth smut the face of heaven, recoil again, His lady's worth inquires, and what's to pay: And wrench their vital breath from sintul men. The country, not exempt from wand ring Adventurers profane, when not afraid,

fires, Would pry into his secrets : some were bray'd, | Yet softens and abates our wild desires ; Like traitor Mufti in his tinkling brass; | And emulation wanting in the race, And some by strange explosion of the mass, The vicious passions keep a milder pace. Bestrode the clouds. By splinter lightning When crimes are rife, 'twere dangerous

remove A few, like Capanens, their gore distill’d. | The antidote to towns, this Lemnian stove,

Or childish inrows, cheating ter beam., mind

us to

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Night.--The Bards.-Human Life.


For men assembled struggle to excel, | The gentle gales had fann'd themselves to sleep: In vice, if bad—if good, in doing well.

The wearied winds remember'd not to blow: And fate, perhaps, did kindly interpose, The gen'ral peace all things combin’d to keep; A fiery barrier, when the senate chose

Save that the streamlet play'd its lapsing flow. To strip Steam-engine of his stifling smoke,

But night's black empress did not long retain, And mitigate in part the tyrant's yoke.

O'er nature's wide extending works, her Strange, that the majesty of Britain's throne,

sway; Should now march forth in sackcloth to atone For Cynthia, with her numerous glitt'ring train. For general corruptions ; that the Queen,

Appearing drove her from the earth away. Should in fierce trial with the peers be seen; While deep-envenomed tongues assault the

ThenCynthia deck'd in all her splendours bright, King,

Mounted the aerial azure-vaulted space ; And all on them their private vices fling.

And with her glowing silver-floods of light, Like those two victims of the Jewish priest,

Reviv'd and cheer'd awaken'd nature's face. Where one was doom'd to bleed, and one The spacious landscape, late in darkness dress'd, dismiss’d.

With all its beauties did again appear: We in amazement for the issue wait,

Hills, vales, brooks, forests, on the vision Not knowing how to justify the State;

press'd, We blindly cringe to fate's superior doom, In hues more soft than when bright Sol was Till fiery pillar shall dispel the gloom.

pear. Mean time the steam his ravages extends, Transparent, smooth, the glassy ocean lay, Dispeopling towns, and separating friends. Reflecting, as a mirror, heav'n's expanse ; From chaos all things rose. Disorder built And as above it Cynthia climb'd her way, Those cities first, that now dissolve in guilt.

She did, with pleasure, at her shadow glance. Oct. 31, 1820.

She reign'd triumphant over ev'ry foe,

While subjugated nature smil'd, resign'd: NIGHT.

Rejoicing under Cynthia's silv'ry glow,

Till to Aurora's rosy sway consign'd.

Nov. 30, 1820.

The sable empress of the darkling night,

Her raven-colour'd mantle round her spread,
And reassum'd her sceptre, when the light

do | Whose hallowed tongue, and harp of golden

wire, Had, with the orb of day its fountain, fled.

First hymn’d the glory of the Eternal One ? She snatch'd away the lily's hue of snow; • Who chaunted forth the deeds of honour, The rose's blush departed with the light;

done The castle stately, and the cottage low, By patriot hands, through danger, flood, and Together vanish'd from the darken'd sight.

fire ? Th' aspiring mountain, and its russet brow, | And stampt them in their songs that ne'er The humble valley, and its flow'ry breast,

expire ? The blooming meadows to her mandates bow; The generous sons of fame, whose race is run

The furzy heath was black at her behest. From earth to heav'n, whence first their She caus'd an utter change on nature's face;

strains begun, The shining garment which had dress'd 'the Fann'd by the breath of their immortal sire. day,

| Yes, they have pour'd their spirit at his shrine; She chang'd to blackness; and the aerial space

And worship'd in his temple of the earth; WhereSol had shone, in gloom the thickest lay. | And sung of nature, in her source divine ;

Of love, and harmony, in holy mirth; The lanscape's tints did then no longer teem

And they inherit well that second birth, Their glowing brightness on the wandering | A deathles's fame, o'er mortal fate to shine.

eye; The verdant lowland's crystal winding stream, No longer gleam'd, nor show'd th' o'erhang SONNET.--HUMAN LIFE. ing sky.

| I saw life's frail bark, on her stormy way, The beast to’s grassy couch bad slank away; By winds and waves through clouds and The warbler rested in his downy nest;

tempests driven; The village swain in sleep's embraces lay,

The moon had veild 'her silver light in With peace, upon his homely pillow, blest.

heaven, Thep all was quiet; all had silent grown;

And every star had quench'd its feeble ray. Still as the habitation of the dead :

Darkness was round her, nor the hope of day... The clam'rous sounds of day were then

No pause of fears and agony was given ;

Her shatter'd sail, by wave and whirlwind unknown;

riven, The foes of peaceful silence all had fled.

To death and horror seem'd an easy prey. The swarming city's din confus'd was hush’d; ( Have mercy, heaven !--When lo--the stormy No rustic's voice rebounded from the mead ;

deep No shrab was by the passing zephyr brush'd; Was hush'd, -and through that fatal midNor from the thicket did a chirp proceed.

night gloom, Echo herself enjoy'd a calm repose;

One star shone bright, to guide me from the For through the stagnant air no whisper

tomb. stray'd;

Now, in its blessed light, I may not weep ; Not e'en a motion rustled 'mongst the boughs ; | But still press onward with redoubled sail,

Nor did a breath the quiet air invade. To reach the Saviour-port that shall not fail.


On Conscience.


On Conscience.

| it with its effulgence; and (speaking MR. EDITOR,

as human language will permit on the SIR,—Your correspondent, J. B. of subject) it has powers properly adapted London, in col. 1834, solicits an an- to the reception of the Spirit's emanaswer to the question-“What is Con- tions, which, when received, exhibit a science?This question, I am per- real view of the situation, state, &c. of suaded, deserves a very serious atten- the soul, as it stands in reference to tion, because Christians, in general, God and eternity. Thus, the Scripture appeal to the decisions of conscience says, “The Spirit itself bears witness in order to justify their deportment, with our spirit, &c.'i. e. it shines into and to prove that the tenets of their the conscience, and reflects throughout respective creeds bear the stamp of the soul a conviction (proportioned to Divine authority. And if its decisions the degree of light communicated) of are not compatible with the doctrines condemnation or acquittance, according of divine revelation, (as it may very to the end of its coming. possibly be the case, the consequences “ Conscience is sometimes said to produced may be of a serious nature. be good, bad, tender, seared, &c.-good, Of all that I have read on the subject, if it acquit or approve; bad, if it conmy judgment leads me to give the pre-demn or disapprove; tender, if it be ference to Dr.Adam Clarke's definition, alarmed at the least approach of evil, and which I consider to be rational, and severe in scrutinizing the actions clear, and scriptural. The following of the mind or body; and seared, if it paragraphs, extracted from his learned feel little alarm, &c. on the commission Commentary, will, I think, form a of guilt. But these epithets can satisfactory reply” to J. B.'s ques- scarcely belong to it, if the common tion.

THEOLOGUS. | definition of it be admitted; for, how Oct. 14. 1820.

can it be said there is a 'tender light,'

a dark or hardened light,’ ‘bad God,' Conscience is defined by some to be &c. &c. But, on the other definition, 'that judgment which the rational soul these terms are easily understood, and passes on all her actions ;' and is said are exceedingly proper : e. g. ' a good to be a faculty of the soul itself, and conscience is one to wbich the Spirit consequently natural to it. Others of God has brought intelligence of the state, that it is a ray of divine light. pardon of all the sins of the soul, and Milton calls it “God's umpire:' and its reconciliation to God through the Dr. Young calls it a 'god in man.' To blood of Christ; and this good conme it seems to be no other than a science retained, implies God's contifaculty capable of receiving light and nued approbation of such a person's conviction from the Spirit of God: and conduct; see Acts xxiii. 1. 1 Tim. i. answers the end, in spiritual matters, 1 5, 19; and here, Heb, xiii, 18. 'Abad, to the soul that the eye does to the or evil, conscience,' supposes a charge body in the process of vision. The of guilt brought against the soul by the cye is not light in itself; nor is it capa- Holy Spirit, for the breach of the Dible of discerning any object, but by the vine laws; and which He makes known instrumentality of solar or artificial to it by conscience, as a medium of light: but it has organs properly conveying his own light to the mind, adapted to the reception of the rays of see Heb. x. 22. 1 Tim. iv. 2. Tit. 1.3. light, and the various images of the A tender conscience'implies one fully objects which they exhibit. When irradiated by the light of the Holy these are present to an eye, (the organs Ghost, which enables the soul to view of which are perfect,) then there is a | the good as good, and the evil as eoll, discernment of those objects which are in every important respect; which within the sphere of vision ; but when leads it to abominate the latter, and the light is absent, there is no percep-cleave to the former; and, if at any tion of the shape, dimensions, size, or time it act in the smallest measure opcolour, of any object, howsoever en- | posite to these views, it is severe in its tire or perfect the optic nerve and reprehensions, and bitter in its regret the different humours may be.

• A darkened or hardened conscience, “ In the same manner, (comparing means one that has little or no selfspiritual things with natural,) the Spirit reprehension for acts of transgression, of God enlightens that eye of the soul but runs on in sin, and is not aware which we call conscience: it penetrates the destruction that awaits it; hecus


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