As centinel, laid at his feet, . Poor Tray watch'd the flock on the plain; And, pour'd from the thicket's retreat, Was heard the mellifluous strain. Suspended, his crook, on the tree, Hung ready his hand to receive; The ballad was plac'd on his knee, Which taught his fond bosom to heave, But broken is Corydon's reed, Ah! ne'er shall we hear it again! No longer his lambkins to feed, The shepherd shall traverse the plain. But though he to death is consign’d, And no more the lov'd bard shall we see, His song in a wreath is entwin'd, And that wreath forms a GARLAND for me! TO GRAY. Next see ethereal Gray, On eagle-wing to huge Plinlimmon's height, With Hoel's harp deplorid, Wrapt in his train I took my lonely way, And listen’u pensive as his “ curfew tolld The dreary knell of the departed day!” With ling'ring step, at midnight's awful noon, I sought the death-bed of the lab'ring hind; Explord with him the spot with grass o'ergrown, And the rude stone which rustic skill design'd. Oft shall his numbers soothe me to repose, Oft shall my bosom own their magic pow'r; His moral lay the hallow'd truth disclose, And oft beguile the solitary hour! TO GOLDSMITH. Next hapless AUBURN's friend my bosom cheers, Whom NATURE loves, and every muse reveres ! To him was given the high victorious art, To gain a conquest oʻer the human heart; No party theme his generous bosom fir'd, .. Far other strains his social soul inspir'd; .. In thy bless'd cause, O Virtue he engag'd, And 'gainst thy foes alone fierce war he wag'd. He saw oppression seize the poor man's soil, And bade the tyrant quit the impious spoil; With grief he saw the dome of pow'r arise, With shame he heard the hapless maiden's sighs! He saw the prince encompass'd by a train Of flatt'ring slaves, who spurn'd the harmless swain ; With weeping eye he view'd the lab’rer's lot, Driv'n like an exile, from his plunder'd' spot! Each realm he trac'd, recording in his strains, That land most bless'd—where prosperd most the swains! Poet belov'd! my vanquish'd heart is thine, And beats with transport thus to call thee mine! TO BURNS. And, while I breathe, whene'er Isè scánt," IN NO. VI. ANSWERED. ...1. Qu. (75) Answered by Mr. Brewer, Private and R. L. Militia. The area of the garden is readily found = 3136320 inches; and putting x for the depth of the pond, its diam. will be 8x, and by mensuration (48x + x2) x ,5236 x = 25,6564x3 is its concavity; also 64 x? x ,7854 = 50,2656 x? is the surface of the pond. Hence, 3136320 - 50,2656 x2 = 25,6564 23, from whence x is found = 48,98515 inches = 4,0820954 feet, and 8x, or the diameter, = 32,65676 feet.' Again, by Mr. B. Brooke. Let 8 x and x denote the diam. and depth of the pond; then its capacity will be 25,6564x', and its surface = 50,2656 r'; but by the question 25,6564x3 + 50,2656 r2 = 3136320 inches = the area of the gardeu; whence 1 = 48,9848, therefore the diam: is 10,8855, and the depth 1,3607 yards. . In the same manner it was answered by Messrs. J. Baines, Reading; J. Bamford, Holthead; W. Bruster, Donington; J. Butterworth, Haggate; J. Cattrall, Plymouth; J. Cummins, Holbeck; W. Dunn, Broughton; J. Ely, Doveridge; J. Gawthorp, Leeds; W. Harrison, and Ely. By adding the given surfaces together, we have 314,16 for the whole surface; from whence we find the diam. = 10, and the circumference = 31,416; then, by mensuration, 6 is the depth, and 4,713 the radius of the segment immersed'; therefore its solidity, 'or the quantity of water displaced, is 387,851; but, by the principles of hydrostatics, 1728 : 387,851 : : 1000 : : 14,028 lbs. = the weight of the globe. = 10, hence 3,1416 x 10=0 m Again, by Messrs. Brooke, Bruster, and Webster, / 209,44 + 104,72 The diameter of the globe is =V 3,1410 209,44 * =63 is the height of the im190—40 400 Esed segt, and 3 X 95236 x = 387,851 is its solidity. Therefore, by hydrostatics 1728 : 387,851 :: 1000 : 224.45 ounces the weight required. The same, by Messrs. Macann and J. Smith. Since the curve surface of the globe is given = 314.16. inches, its diam. is easily found = 10 in. and as the superficies of spherical segments are as their altitudes, we have the height of the immersed segment = 0 10 X 2 and its solid content="072 cubic inches, is the content of the water displaced by the globe; therefore, by 10472 hydrostatics, 1728 : 1000 :: 104 ostatics, 1728 : 1000 :: 27 : 224,4513 ounces, is the weight, as before. 1D It was answered also by Messrs. Armitage, Baines, Brewer, Cattrall, Gawthorp, Hine, Jones, Maffett, Nesbit, Rylando, Tomlinson, and Winward., 3. Qu. (77) Answered by Mr. J. Smith, Alton Park. 3 Let ABCD and ABK represent A GLB vertical sections of the conic frustum H 1Z and the cone completed, EF the dividing section; and draw LC parallel to GK. Then by sim. triangles LB = 2:LC = 12:: GB = 5: GK= 30, therefore, IK=GK-GI= 18. Put ,7854 = n, then, by mensuration, A B’ X = 1000n, is the content of the cone A BK, and DC-X 16n, is the solidity of DCK. Half the difference of these = 392n is the solidity of the frustum EFCD, which, added to 216 n, gives 608 n for the solidity of the cone EFK. Now, the cones ABK, EFK; , ping similar solids, we have 1000'n, : ~608n :: GK = 30:HK = 30 y 008 = 3 7608 =6776= 25.41494; therefore, HI = HK-IK= 7,41494 is the distance required. Again, by Mr. Armitage, Rochdale Academy. First, 10—6:12 :: 6.: 18 = what the cone wants in length to be complete, and 18+12=30 = length of the whole cone; then, by sim, solids, as 755,4 (= content of the whole cone) : 30 :: 477,5232 (= the solidity of the top cone and half frustum): 25,41494, and the distance from the bottom = 25,41494 – 18 = 7,41494, as before. Otherwise, by Mr. J. Cattrall, Fifer 2nd R. L. Militia. By similar triangles LB:LC:: BG:GK = 30; consequently, 785,4 is the solidity of the whole cone, and 615,7536 is the solidity of the frustym, whence, 785,4 - 615,7536 = 169,6464 = solidity of DCK, therefore, 169.6464 + 13,7630 = 477,5232 is the so |