159 Solutions to Mathematical Questions. 160 x2 — y2 = 1881 = a and y2 + 1 Solutions to the foregoing, have by y. Then, by the Question we have also been received from W. Turner, Bracken Hill, near Sheffield; S. T. of Saltash; and W. West, of Matomley, Sheffield; the latter of whom has also sent a Solution to the second Ques tion. y2 = whence by restoring the numeral values of a, m, and n, y = 120, z 230, and x = 90. So that 90, 120, and 230, will answer the conditions of the Question. xy324b Clear the last equation of fractions, transpose y' and divide by y; then we shall have a = 36 y 3y, whence 18b+9 y2. but by transposition or 8 y(18 b + a) y2 — — 9 b3, for y2 put z, for (186+a) put 8 m, and divide the equation by 8: then will 9b a quadratic; mz= whence z = by restoring the numeral values of m and b, z= 144y2 or y = 12. We have received answers to the two last Questions from J. Turner, and 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. QUERY.-Required the sums of the following series continued ad infinitum. A Question by J. B. Chivers, of Plunkett. To find two numbers such, that the sum of their squares may be a square number, and the difference of their squares a cube number. THE STEAM ENGINE. A SATIRE. Petere inde coronam Unde prlus nulli velarunt tempora Muzæ. Εμοι δε ειη την αλιᾶν τρυπαν εν θεμιδος οικω. CONTENTS. 162 Still men advance in talents, one and all, Or set like weasel traps, ensnare the knave; Man in a state of barbarism-Origin of civil society. Of Reforming Bess, with mighty feelings fraught, cities-Their good effects. Illustrated by a similitudeTheir corruption.-Insecurity of towns, on account of vice, fraud, rapine, and tyranny. Provoke Providence to disperse mankind again-the Steam-Engine sent for that purpose how sent-described.-Its effects. Citizens compelled to live in the country-its new appearance.-The grove once sacred to Diana, now usurped by Venus. Men still vicious--but less so than they would be in town. If the Steam Engine were corrected, men might return to town-providentially prevented by the Queen's trial. The disorders of barbarism gave rise to cities-their own vices destroy them. TIME was, ere law and institute began, Amphion next in bolder notes display'd pace, Tis death where'er he spreads his wat'ry veil. throne. E'en so the savage tribes in cities clos'd, That e'er content with poverty could stay. A sister queen to murder by her side, Close on the borders of some lonely wood, Where late its mother and the shepherd stood, A poor forgotten lamb for pity bleats, Where on the mart can honesty resort? Thus towns to infamies of savage life Bring back mankind, and none dares take a wife. Promiscuous love profanes our busiest streets, Sham'd wedlock hides her face from all she meets; Or else, with hair dishevelled, madly cries, 66 My oaths are sand; say where in secret lies, "The rank adulterer's devoted head?" 'Twere vain to seek him in a royal bed. Why should we marry, when in all distress, Friends, kindred, love us for our children less? E'en captious sycophants from those withdraw Whose wills are occupied by heirs at law. When it was seen that men before the flood, Like individuals, and provoking give teem; But now th'avenging angel is ordain'd, (To punish British cities, deeply stain'd With blasphemy, theft, murder, and base fraud,) To drop a monstrous engine from his cloud, The arsenal of torture for mankind, When sin excessive grows, and conseience blind. Just as Great Britain's thunder-bearers roll Through ocean's vast expanse to either pole, Chastising piracy, rebellions, crime, In isle, bay, continent, of every clime; So this stern spirit with Nemesian rod, Steers through the troublous air the storm of God; More than Egyptian plagues, dispensing far, Where giant crimes provoke th'unequal war. Not more astounded were the Lernian frogs, When great king Block descending shook their bogs, Than the proud citizens of London town, By monstrous huge Steam-engine thund'ring down: Boiling with heat, and belching fiery smoke, The monster stood, and brought beneath his yoke Th' immediate vicinage, who vainly fled; dew As light'ning swift, and fill'd th' avengers hand, 164 This engine sprung from so prodigious birth, With special murders terrified the earth. At noon the pestilence walks forth like night, With inky shroud defiling heavenly light. But yet these characters obscure express, To all who read phenomena, no less Than universal death, if they should dwell Where vengeance keeps the gloomy court of hell. As erst Achilles all the Trojan bands Dispers'd with armour-gleaming iron hands, Or Babel's clam'rous hoarse discordant tongues Spread through the world a flood of impious wrongs; So this dire monster emptied many a town, And cockney join'd in converse with the clown. Now men in fear from crowded streets withdraw, But not to live by simple food or law. Alcina's gardens, aromatic airs, Our painted ploughs and carts may haply shock The taste of lowing herd or bleating flock; The straw-built roof more snugly may invest The rural mouse, or sparrow in her nest. Their minds change not; but modern masonry Seems more commodious to the human eye. The country maids their dairy dress with care, And eke themselves with neatness due prepare. The rustic poets sing in courtly style Their love-sick idyls, and the maids beguile; Such seldom wait for blessing from above, But watch the coming gale with bosoms full of love. The grove was Dianas temple, chaste as snow The convict in adultery, rich and gay, fires, Yet softens and abates our wild desires; remove The antidote to towns, this Lemnian stove, 165 Night.-The Bards.-Human Life. For men assembled struggle to excel, And all on them their private vices fling. We in amazement for the issue wait, NIGHT. BY M. G. OF LIVERPOOL. The sable empress of the darkling night, Had, with the orb of day its fountain, fled. Together vanish'd from the darken'd sight. She chang'd to blackness; and the aerial space eye; The verdant lowland's crystal winding stream, The beast to's grassy couch had slunk away; then The foes of peaceful silence all had fled. Not e'en a motion rustled 'mongst the boughs; 166 The gentle gales had fann'd themselves to sleep; For Cynthia, with her numerous glitt❜ring train, Reviv'd and cheer'd awaken'd nature's face. In hues more soft than when bright Sol was near. Transparent, smooth, the glassy ocean lay, SONNET.-HUMAN LIFE. I saw life's frail bark, on her stormy way, The moon had veil'd her silver light in And every star had quench'd its feeble ray.- No pause of fears and agony was given; Was hush'd, and through that fatal midnight gloom, One star shone bright, to guide me from the Now, in its blessed light, I may not weep; 167 On Conscience. On Conscience. MR. EDITOR, SIR,-Your correspondent, J. B. of London, in col. 834, solicits an answer to the question-" What is Conscience?" This question, I am persuaded, deserves a very serious attention, because Christians, in general, appeal to the decisions of conscience in order to justify their deportment, and to prove that the tenets of their respective creeds bear the stamp of Divine authority. And if its decisions are not compatible with the doctrines of divine revelation, (as it may very possibly be the case,) the consequences produced may be of a serious nature. Of all that I have read on the subject, my judgment leads me to give the preference to Dr. Adam Clarke's definition, and which I consider to be rational, clear, and scriptural.-The following paragraphs, extracted from his learned Commentary, will, I think, form a satisfactory reply" to J. B.'s ques 66 tion. Oct. 14. 1820. THEOLOGUS. "Conscience is defined by some to be 'that judgment which the rational soul passes on all her actions; and is said to be a faculty of the soul itself, and consequently natural to it. Others state, that it is a ray of divine light. Milton calls it God's umpire:' and Dr. Young calls it a 'god in man.' To me it seems to be no other than a faculty capable of receiving light and conviction from the Spirit of God: and answers the end, in spiritual matters, to the soul that the eye does to the body in the process of vision. The eye is not light in itself; nor is it capable of discerning any object, but by the instrumentality of solar or artificial light: but it has organs properly adapted to the reception of the rays of light, and the various images of the objects which they exhibit. When these are present to an eye, (the organs of which are perfect,) then there is a discernment of those objects which are within the sphere of vision; but when the light is absent, there is no perception of the shape, dimensions, size, or colour, of any object, howsoever entire or perfect the optic nerve and the different humours may be. "In the same manner, (comparing spiritual things with natural,) the Spirit of God enlightens that eye of the soul which we call conscience: it penetrates 168 it with its effulgence; and (speaking as human language will permit on the subject) it has powers properly adapted to the reception of the Spirit's emanations, which, when received, exhibit a real view of the situation, state, &c. of the soul, as it stands in reference to God and eternity. Thus, the Scripture says, 'The Spirit itself bears witness with our spirit, &c.' i. e. it shines into the conscience, and reflects throughout the soul a conviction (proportioned to the degree of light communicated) of condemnation or acquittance, according to the end of its coming. "Conscience is sometimes said to be good, bad, tender, seared, &c.—good, if it acquit or approve; bad, if it condemn or disapprove; tender, if it be alarmed at the least approach of evil, and severe in scrutinizing the actions of the mind or body; and seared, if it feel little alarm, &c. on the commission of guilt. But these epithets can scarcely belong to it, if the common definition of it be admitted; for, how can it be said there is a 'tender light,' a' dark or hardened light,' 'bad God,' &c. &c. But, on the other definition, these terms are easily understood, and are exceedingly proper: e. g. ' a good conscience is one to which the Spirit of God has brought intelligence of the pardon of all the sins of the soul, and its reconciliation to God through the blood of Christ; and this good conscience retained, implies God's continued approbation of such a person's conduct; see Acts xxiii. 1. 1 Tim. i. 5, 19; and here, Heb. xiii. 18. A bad, or evil, conscience,' supposes a charge of guilt brought against the soul by the Holy Spirit, for the breach of the Divine laws; and which He makes known to it by conscience, as a medium of conveying his own light to the mind, see Heb. x. 22. 1 Tim. iv. 2. Tit. i. 3. A tender conscience' implies one fully irradiated by the light of the Holy Ghost, which enables the soul to view the good as good, and the evil as evil, in every important respect; which leads it to abominate the latter, and cleave to the former; and, if at any time it act in the smallest measure opposite to these views, it is severe in its reprehensions, and bitter in its regret. A darkened or hardened conscience,' means one that has little or no selfreprehension for acts of transgression, but runs on in sin, and is not aware of the destruction that awaits it; heed |