TRANSLATION AND IMITATION OF A LATIN POEM. Supplement, 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 flavour'd, 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, Surflect, May 11, 1811, TOL, H ADDRESS TO MY FIRST GRAY HAIR. BY MR. THELWALL. “ And thou hast chang'd thy hue, companion staid, Well! my firm mind, Hovering Winter, hail ! Oh! give me yet, The sheltering fence of competence, to guard mathematical Department. MATHEMATICAL QUESTIONS IN NO. IV. ANSWERED. 1. Qu. (31) answered by Mr. T. Ford, Owstwick. X-10 Put x = number of galions at first, then 3 what the officer seized ; and £9.185. €8. 2s. = £ 1. 16s. is their value; therefore, x : £9, 18s. ::-10 : £1.16s. Now multiply means and extremes, 3 by reduction r = 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. of r 2. Qu. (32) answered by Mr. W. Bruster, Donningtoe. By the nature of compound interest as 100:16) + 100+2x 2x ::1: -= the amount of 4 1. for one year. 100 100+2x 3r Consequently x x - the amour 100 100 - 2r pds. at 2x per cent. for 3r years, and x x 3r 10 -100 + 2x3 3x = 5x by the, question; hence - 2 = 5, 100 100 + 2x and extracting the cube root ) *4=1.709976, 100 from whence, by trial and error, x cmes out = 5.312728 = the principal sought. The same by Mr. J. Baines, jun. Hort, ry Bridge. By the question, (1 +.02x)** X X = it, or (i +.02x)** = 5, whence 3.x x log. (1 + .024', = .69897, and by approximation x = 5.3127. Other solutions were sent by Medrs. Anglicus, Dunn, Fori, Gawthrop, Hine, Hirst, Ma ett, Nesbit, Putsey, Rylindo, Tomlinson, and Winward. 3. Qu. (33) answered by Anglicus, and Mr. Bruster. Put the versed sine A E = 50 = a, and DE = x; then DA = A E с = the diameter. Now, by a mensuration and the question, 8 v(a + xo).- 2x = 160, and by B 3 reduction 60x1920x = 70400*from whence * x2 53.806525, and AB=a+ 107.90284265 is the diameter required. 0 = Otherwist Mr. Ford, ar Mr. J. Gawthrop. Put the chord suus g the given arc = 2x, 0 = 30, and a = 160; then by known rules 8V (r?_vo)—2x 3 9a’ — 6402 =u, whence x = + 100 x2 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. Win. ward. 60 4. Qu. (34) answered by Mr. Putsey, and Rylando. с Let D E F be a section of the given sphere, and ACB a section of the circumscribing cone. Put O D= r, and E CD=x; then CE=VCD X CF) = v(x - 2rr), and by similar tri. angles CE: EO :. ČD: DB= D by the ques✓(r? - 2rr) - 2rr 3 tion is a minimum, which in fluxions, and reduced, we get x = 4r; hence A B = 42, 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. rr Х 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=2 n D, or Dn= 2n F; therefore, 2 FD=8=CD, and CÉ =v(CO-EO) =V (36 - 4) = 5.6568542, which is also = A B, 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. Garthrop, Mr. Hine, Mr. Maffett, Mr. Tomlinson, and Mr. Winward. |