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As ccntinel, laid at his feet.

Poor Tray watch'd the flock on the plain; ,c

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,
Whose daring fancy took her flight,
On eagle-wing to huge Plinlimmon's height,
And, as above his snow-capt brow she soar'd,
The fall of Cambria's children dear!
The heavenly maid, in wild dismay,
With Hoel's harp deplor'd,
While from her eyelids gush'd the soul-asshaging tear!

And oft when caution penn'd the guarded, fold,
Wrapt in his train I took my lonely way,

And listen'd pensive as his "curfew tolPd
The dreary knell of the departed day!"

With ling'riug step, at midnight's awful noon,
I sought the death-bed of the lab'ring hind;

Explor'd with him the spot with grass o'ergrown,
And the rude stone which rustic skill designed.

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 COLDSMITH.

|(|ir. .t.t

Next hapless Auburn's friend my bosom cheers,
Whom Nature love?, and every muse reveres!
To him was given the high victorious art,
To gain a conquest o'er the human heart;
No party theme his generous bosom fir'd,
Far other strains his social soul inspir'd j , .
In thy bless'd cause, O Virtue he engag'd,
And 'gainst thy foes alone fierce war he wagM.
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 prosper'd most the
swains!

Poet belov'd! my vanquish'd heart is thine,
And beats with transport thus to call thee mine!

TO BURNS.

And whae is he that syngs sae weel,
And pens "Addresses to the Deil?"
Whae gies the sang syke bonny turns?
Daft Gowk! ye ken it's sonsie Burns!

His gabby tales I love to hear,
They please sae meikle, run sae clear;
That ilka time, good traith, I read,
l'se wiser baith i'heart an head.

I wad advise, when rankled care
Begins to mak ye glow'r and stare,
That ye wad furst turn ow'r his leaf,
'Twill mak ye suon forget yer grief!

And should auld mokie sorrow freeten,
He's blythsome tale yer hearts will leeten;
And suor I am, ye grief may banter,"
By looking ow'r his "Tam o'Shanter.'1-

.

And, while I breathe, whene'er Ise scant*
Of cheerfu friends,—and fynde a want
Of something blythe to cure my glumps,
And free me frae the doleful dumps,

I'll tak his beuk, and read awhile,
Until he mak me wear a smile 5
And, then, if I hae time to spare,
I'll learn his "Bonny banks of Ayr!"

mathematical Department.

MATHEMATICAL QUESTIONS

IN NO. VI. ANSWERED.

1. Qu. (75) Answered by Mr. Brewer, Private 2nd R. L. Militia.

The area of the garden is readily found = 3130320 inches; and putting x for the depth of the pond, its diam. will be 8 s, and by mensuration (48x + x2) X ,5236* = 25,6564x3 is its concavity; also 64 x' x ,7854 50,2656a2 is the'surface of the pond. Hence, 3136320 — 50,2656 x* ± 25,6564 a;3, from whence x is found = 48,98515 int hes = 4,0820954 feet, and 81, or the diameter, = 32,65676 feet.

Again, by Mr. B. Brooke.

Let 8 * and x denote the diam. and depth of the pond; then its capacity will be 25,6564x', and its surface ~ 50,2656i'; but by thequestion 25,6564a;5 + 50,2656i' 3136320 inches the area of the garden; whence z is 48,9848, therefore the diam. is 10,8855, and the depth 1,3607 yards.

In the same manner it was answered by Messrs. J. Baiues, Reading; J. Bamford, Holthead; IV. Bruster, Donington; J. Butterworth, Haggate; J. Cattrall, Ply. mouth; J. Cummins, Holbeck; W. Dunn, Broughton;

J. Ely, Doveridge; J. Gawthorp, Leeds; W. Harrison,
Burton; J. Hine, Plymouth; S. Jones, Liverpool; M.
Macann, Lutton; Jb. Maffett, Plymouth; A. Nesbit,
Farnley; Rylando; J. Smith, Alton Park; E. Webster,
Armley Mills; and J. Winuiard, Plymouth.
-•

2. Qu. (76) Answered by Messrs. Bamford, Cummins, and Ely.

By adding the given surfaces together, we hare 314,16 for the whole surface; from whence we find the diam. = 10, and the circumference = 31,416; then, by mensuration, G| 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.

Again, by Messrs. Brooke, Bruster, and Webster.

The diameter of the globe is = V -—'—

° 3,1410

209 44

= 10, hence •■,.'■ =64 is the height of the im

3,1416 x 10 3

.90—40 . 400 „„_

mersed segt. and x,52S6 x ~r = 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

10 x 2

have the height of the immersed segment = «^—5—,

10472 and its solid content ■ cubic inches, is the con

tent of the water displaced by the globe; therefore, by .

10472 hydrostatics, 1728 : 1000 :: -—-—: 224,4513 ounces,

is the weight, as before.

It was answered also by Messrs. Armitage, Barnes, Brewer, Cattrall, Gawthorp, Hine, Jones, Maffett, flesbit, Rylando, Tomlinson, and Winward.,

3. Qu. (77) Answered by Mr. J. Smith, Alton Park. -<'A

Let ABCD and ABK represent vertical sections of the conic frustum and the cone completed, EF the dividing section ; and drawLC parallel to GK. Then by sim. triangles LB = 2 : LC = 12 :: GB = 5 : GK = 30, therefore, IK = GK—GI = 18.

Put ,7854 sz n, then, by mensuration, AB2 x GKx; = 1000«, is the content of the cone ABK, and DC X IK X ^= 216w, is the solidity of DCK. Half the difference of these = 392n is the solidity of the frustum EFCD, which, added to 216n, gives 608ra for the solidity of the cone EFK. Now, the cones ABK, EFK, eing similar solids. we have 1000b, : ^60&n fins

:: GK = 30: HK = 3() J-fi— = 3 ^608 = 6 ^76 =

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 4/7S5,4 (= content of the whole cone) : 30 :: ^477,5232 (= the solidity of the top cone and half frustum) : £5,41494, 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, anc| $15,753.6 is the solidity of the frustum, whence "785,4 — 610,7536 = 169,6464 = solidity of DCK,

therefore, 169,6464 + - 477,5232 is the so

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