One morn a boy who lov'd to roam, And fruit that flam'd the ruby's ray. Joy seiz'd the youth, he pull'd them straight, By his example warn'd, beware, Lest you the same sad fate should meet; REFLECTIONS ON SEEING A LAMB THAT WAS FATTENING FOR SLAUGHTER. WANDERING through the mazy wild, Unmindful of impending fate, Thy present blessings make thee smile; In life's gay morn, what joys are ours! Though I nor fear, nor wish to die, My wayward thoughts will sometimes roam ;- Yet live, till thou shalt call me home. Boston, Feb. 1812. W. M. EPITAPH IN ALGARKIRK CHURCH, NEAR BOSTON, LINCOLNSHIRE, ON JOHN BERIDGE, M.B. OBIIT oct. 17, 1788. THESE hallow'd stones an English heart infold, WILLIAM HAYLEY. LINES WRITTEN ON THE SEA-COAST. SWIFT approaching to the main, See the sparkling northern crown; And Arcturus' frozen wain, The dark blue vault is hast'ning down. Flaming on the verge of heav'n, Luna half her course has run, See her lightly flitting beams From his wonted fall and flow, Hark! what sounds thus float on air? 'Tis the waves that breaking flow When such a scene before us lies, Leeds. I. X. HUMANITY. Aн me! how little knows the human heart And tears, sweet sympathy can teach to flow. Pity the man who hears the moving tale Unmov'd; to whom the heartfelt glow's unknown, On whom the widows' plaints could ne'er prevail, Nor made the good man's injur'd cause his own. The splendid dome, the vaulted roof to rear, And soothe th' oppressed orphan's woe be mine. Be mine the blush of modest worth to spare, Till joy shall sparkle from the tear-fill'd eye. Can the loud laugh, the mirth-inspiring bowl, Or warm the breast, HUMANITY, like thee? M. P. Mathematical Department. MATHEMATICAL QUESTIONS IN NO. V. ANSWERED. 1. Qu. (56) Answered by Mr. E. Webster, ArmleyMills. LET x2, 25x2, and 49x2, be the numbers required; then by the question, their common diff. 242 is to be a cube number, let nr be its root, then 24x2 — x3 n3, and x = 24 n3 ; if n=2, we find x 3, consequently 9,225 and 441 are the numbers required. It was answered exactly in the same manner by Messrs. Gawthorp, Hirst, Rylando, and Whitley; and nearly so by Messrs. Baines, Brooke, Butterworth, Cattrall, Cummins, Dunn, Eyres, W. Harrison, Burton Pidsea, Hine, Maffett, Nesbit, Putsey, Tomlinson, and Winward. 2. Qu. (57) Answered by Messrs. Baines, Brooke, and Whitley. Let a12 denote the required number, then its square, cube, and biquadrate roots are respectively x, xa, and a', and by the question, x+x3 2x; hence r3 −2x+ 10. One root of this equation is evidently 1, and dividing by x- 1, we have +x-1=0, therefore and the number required is(√571)»– x= 161 root 2 72/5, whose square root is 9 7-35 2 4/5, its cube and its biquadrate root /5—2. These roots form an arithmetical progression whose common And thus nearly it was answered by Messrs. Butterworth, Cattrall, Cummins, Eyres, Gawthorp, W. Harrison, Hine, Hirst, Maffett, Nesbit, Putsey, Rylando, Tomlinson, Webster, and Winward. 3. Qu. (58) Answered by Messrs. Cattrall, Cummins, Gawthorp, Hine, Maffett, Nesbitt, Rylando, and Winward. y Put x for the perpendicular, y the hypothenuse, and g16 feet: then by art. 300 Marrat's Mechanics, a body descending down y in the time t, will describe the space, which, in this case, is =y, therefore ygtr, and the base is (gt2x-x2). But the sum of the sides less the hypotheneuse is equal to the diameter of the inscribed circle; that is (gtx-x2) · √ gt2x + x = 4;—when t = 1", we have (gx—x2) ✔gx+x=4, from whence = 14.52, then y= 15.2816, and the base 4.7622. |