TRANSLATION AND IMITATION

OF A LATIN POEM.
Suppiement, Vol. IV. P. 320. Poetical Magazine.
On rural themes my muse delights to dwell,
Of sylvan gods and rustic honours tell;
Where shepherds gaily chant melodious strains,
And sweetly with their music cheer the plains.
Observe the fields with waving corn replete,
And orchards furnish a delicious treat;
With grapes high flavoured, lo! now teems the vine,
Busy the peasants, and the weather fine;
The warbling songsters make the groves resound,
And all is plenty and delight around.

But ah ! too soon will autumn quit the field,
And her blithe reign to dreary winter yield;
Boreas will bellow from the surly north,
And show'rs of hail and snow come rushing forth ;

The birds sit moping on the naked trees,
, Their plaintive wailings wafted on each breeze.

But, soon will spring in beauteous form appear,
That most delightful season of the year;
Yes, flow'ry spring will come with graceful mien,
And hill and dale be dress'd in living green ;
Sweet odours, borne on zephyr's silken wing,
Shall hail the first approach of welcome spring :
All hail! thy yearly honours shall be paid
By each blythe rustic swain, and village maid ;
Amid the roseate bow'r, with flutt'ring wing,
At dewy eve the nightingale shall sing ;
Sweet violets, lilies, roses smile around,
And a rich verdure clothe the fertile ground.
Whilst fortune smiles, enjoy, with thankful heart,
Spring's short-liv'd pleasures, which must soon depart;
Yes, pass the happy day devoid of sorrow,
Nor wish, too deep, to pry into the morrow.

: J. BROWN, . Surfleet, May 11, 1811,

ADDRESS TO MY FIRST GRAY HAIR.

BY MR. THELWALL. “ And thou hast chang’d thy hue, companion staid, Of forty varying years ; thy darkest brown Shifting to silvery whiteness. Be it so: It is not the first time that I have met An old acquaintance with an altered face, And 'twill again betide me: or the wheel Of ever giddy Fortune must forego Her old propension, and no more invert My oft deluded hopes. But, of thy kind, Not Fortune's steadiest favour, nor her hate, Can stay the destin'd course. Mute monitor! Thou art, indeed, but as the harbinger Of many a change approaching; that shall soon, To all thy numerous tribe impart thy hue : Dappling at first with many a wintry spot, Till all is equal snow.

Well! my firm mind, That many a less expected change hath borne, Can bear that also.

Hovering Winter, hail !
Hail to thy wrinkled front, and hoary brow!
Not from thy reverend aspect do I shrink,
Season of waning life! if that thy snows,
Incrusting all without, leave yet within
The genial warmth of friendship; or if thon bring
(So winter should) the calm and social joy,
Of dear affiance, and communion sweet,
With few congenial minds, and not with hold
Quiet and competence, respect and love,
And literary leisure: if o'er all,
Thou not refuse to them, my infant buds,
(The hope and promise of a future spring)
Kindly protection from the ruffian blasts
Might mar their tender germs.

Oh! give me yet,
Ere dull inaction freeze the torpid vein,
Or numbing languor cramp the vital powers
Of sedulous efforts ; give me yet, to rear

The sheltering fence of competence, to guard
These from the blight; and I will not repine,
That nature's wheel revolves ; I will not mourn,
My spring of storms, my summer overcast,
Or toils autumnal, that the wayward year
Strive to repair ; but the last wintry hour
Accept as nature's boon; and even then,
When thy dim twilight, o'er the studious eye
Steals darkling, and the tottering step foregoes
The pride of wonted firmness, will I bend
My unrepining weight; if haply propt
Upon the matron arm of her belov'd!
My faithful stay through every woe of life!
Or on the filial shoulder rest awhile
My waning strength, that each successive day
Counts by some new privation ; till at length,
(Each function and each duty all fulfill’d)
Pleas'd with the thought I have not liv'd in vain,
I lay me down; and on the quiet couch
Of unreproving conscience pillowing me,
Welcome my doom; and, smiling, sink to rest.”

S

mathematical Department.

MATHEMATICAL QUESTIONS

IN NO. IV. ANSWERED.
1. Qu. (31) answered by Mr. T. Ford, Owstwick.

X-10 Put x = number of gallons at first, then what the officer seized; and £9.185. — £8. 25. = o£ 1. 16s. is their value; therefore, x : £ 9. 188. ::: x-10

: £1.16s. Now multiply means and extremes, by reduction x = 22, and 9s. is the price per gallon.

True answers were also sent by Messrs. Anglicus, J. Baines, B. Brooke, W. Bruster, W. Dunn, J. Gawthrop, A. Hirst, W. Harrison, J. Hine, Lucinda, R. Maffett A. Nesbit, Philpot, Rylando, J. Tomlinson, and J. Win. ward.

2x :: 1:

2. Qu. (32) answered by Mr. W. Bruster, Donningtot. By the nature of compound interest as 100:16, +

+2*= the amount of £ 1. for one gear. Consequently = x (109421) + = the amourt of r pds. at 2x per cent. for 3r years, and « (100*-*)3r = 5x by the, question; hence ( and extracting the cube root (100.426) " '=1.709976, from whence, by trial and error, x cimes out =

/100 + 2x 3r
( 100 )

=

5,

100

5.312728 = the principal sought.

The same by Mr. J. Baines, jun. Hort,, ry Bridge. By the question, (1 +.02x)3* x x =iir, or (1 +.02x)3• = 5, whence 3.x x log. (1 + .022", = .69897, and by approximation x = 5.3127.

Other solutions were sent by Med rs. Anglicus, Dunn, Foril, Gawthrop, Hine, Hirst, Ma ett, Nesbit, Putsey, Rylundo, Tomlinson, and Winward.

- 3. Qu. (33) answered by Anglicus, and Mr. Bruster.

Put the versed sine A E = 50 = 1 a, and DE = r; then DA =

(AE+DE)=v(a' + x^). Also, A È = a:AD:: AD: AB = a + = the diameter. Now, by mensuration and the question, \ 8 (a + z).– 2x a

= 100, and by reduction 60x' - 1920x = 70400" from whence *= 53.806525, and A B = a = 107.90284265 is the diameter required.

Otherwist : Mr. Ford, ar Mr. J. Gawthrop. Put the chord suweng the given arc = 2x, 0 = 30, and a = 160; then by known rules

wh8V (r?_0)—20

= u, whence x = V(600 + 100) + = 53.806; whence to= 108 nearly.

In the same manner the question was answered by Mr. Baines, Mr. Dunn, Mr. Hine, Mr. Hirst, Mr. Maffett, Mr. Nesbit, Rylando, Mr. Tomlinson, and Mr. J. Winward.

4. Qu. (34) answered by Mr. Putsey, and Rylando.

Let D E F be a section of the given sphere, and ACB a section of the circumscribing cone. Put OD=r, and CD= x; then CE=VCD X CF) = V(x? — 2rr), and by similar tri. angles CE: EO :. ČD: DBA

Armor

Teore, i? — 2rc X 5 by the ques. tion is a minimum, which in fluxions, and reduced, we get x = 4r; hence A B = 472, and the solidity of the cone = 32 X 8 X .2618 = 67.0208, as required. Cor. The sphere is to its least circumscribing cone as 1 to 2.

v (r? — 2rx); therefore,

The same by. Messrs. Eruster., Dunn, Hirst, and Nesbit.

Let DEF be a section of the sphere, and A CB that of the cone, which will be the least when Cn = 2n D, or Dn= 2n F; therefore, 2FD=8=CD, and CE =V(CO’ — EO2) =(36 — 4) = 5.6568542, which is also = AB, the base of the cone; hence its solidity is easily found = 67.0208 ; whence it appears that the solidity of the cone is = twice that of the sphere. .

Answers to this question were sent also by Anglicus, Mr. Baines, Mr. Ford, Mr. Gawthrop, Mr. Hine, Mr. Maffett, Mr. Tomlinson, and Mr. Winward.