One morn a boy who lov'd to roam, Along the meadows took his way, The vagrant wander'd far from home, And playful pass'd the joyous day. As near a hedge he sauntering stroll'd, He saw a Nightshade blooming gay, And fruit that flam'd the ruby's ray. And eat the fruit, and smelt the flowers; The fatal berries' subtle powers. By his example warnd, beware, Lest you the same sad fate should meet; Pursuing pleasure, dread the snare, That's spread to catch thy wareless feet. REFLECTIONS ON SEEING A LAMB THAT WAS FATTENING FOR SLAUGHTER. WANDERING through the mazy wild, In life's gay morn, what joys are ours ! Though I nor fear, nor wish to die, 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, Flaming on the verge of heav'n, I. X. HUMANITY. Ah me! how little knows the human heart The pleasing task of soft'ning others' woe; Stranger to joys that pity can impart, 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, . The glare and pride of pomp be, grandeur, thine : To wipe from misery's eye the falling tear, : And soothe th' oppressed orphan's woe be mine. Be mine the blush of modest worth to spare, To change to smiles affliction's rising sigh: The kindred warmth of charity to share, Till joy shall sparkle from the tear-fill'd eye. Can the loud laugh, the mirth-inspiring bowl, The dance, or choral song, or jocund glee, M. P. mathematical Department. MATHEMATICAL QUESTIONS IN NO, V. ANSWERED. 1. Qu. (56) Answered by Mr. E. Webster, Armley Mills. LET X?, 25x2, and 49x2, be the numbers required; then by the question, their common diff. 24.x? is to be a cube number, let nx be its root, then 24x2 = *3 n, and x 2; if n= 2, we find x = 3, consequently 9,225 and 441 are the numbers required. 24 It was answered exactly in the same manner by Messrs. Gawthorp, Hirst, Rylanılo, and Whitley; and nearly so by Messrs. Baines, Brooke, Butterworth, Cattrall, Cummins, Dunn, Eyres, W. Harrison, Burton Pidsea, Hine, Maffett, Nesbit, Putsey, Tomlinson, and 2. Qu. (57) Answered by Messrs. Baines, Brooke, and Whitley. Let za denote the required number, then its square, cube, and biquadrate roots are respectively mo, xf, and I!, and by the question, wo to = 224; hence r - 2x + 1=0. One root of this equation is evidently 1, and dividing by <-- 1, we have x + x-1=0, therefore 1=45 , and the number required is (V/5=?)"= 2 161–7275, whose square root is 9 - 475, its cube rootpot 7375 and its biquadrate root „5–2. These roots form an arithmetical progression whose common diff : 55 11 2 . And thus nearly it was answered by Messss. 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. Put x for the perpendicular, y the hypothenuse, and g= 165 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 y2 = gtx, and the base is = v(gter ---- 2x2). But the sum of the sides less the hypotheneuse is equal to the diameter of the inscribed circle; that is n (gtr — **) Vigtx +- x = 4;-when t=1", we have (gx-2) - gx + x = 4, from whence x = 14.52, then ys 15.2816, and the base = 4.7622. |