QUESTION 3. Answered by Verus. The same was answered by Messrs. Baines and Godward. The general term being 2, the next term or increment of the sines is (x+1)=x+6x+15x+20x+15x+6x+1. To find the sum of the inte 6 6 grals, we have 5 4 3 2 Question 1. Answered by Messrs. J. Baines, and T. S. Davies. Let A and G represent the centres of the earth and moon, and P the point, in the line joining them, from which the sum of the visible surfaces is a maximum. Put AG=d, AI=AC=R, GH=AD=r, and AP=x. Draw the tangents PI, PH; the radii AI, GH; and let fall the perpendiculars IB, HF; then PG=d-x, and the triangles API, BAI, being similar, (Euclid, vi. 8) we have AP: AI::AI: AB= 2 in like manner FG is found= the sum of the visible surfaces is as (BO× AC)+(FD × GD), that is, as (d-x) 2, that is, R3. (d-x) rx, orx = R/R+TM√/r 3 2 2 Rd R Take the radius of the earth, or R=1, 7=26923,d 60: 1+26923/26923 7.3544 from the centre of the moon. Now because the force of attraction without the surface of a body is always proportional to the quantity of matter divided by the square of the distance from the centre, (Whiston's Theory of the Earth, Lem. 7 and 9,) and if the quantity of matter in the earth and moon be as 71 to 1, we shall have the force of attraction at the earth's surface to that at the required point between the earth and moon, 52.6456 radii of the earth from its centre, or 71 .. 1 592 52.6456 7.35472, or as 70.999713 0071287. Whence, as 70.99 9713 12 stones 0071287: 00120485 stones 26988 of an ounce, the weight of the man required. 3 Solve the equation 16x++16x3 +24x2+10x=50, by quadratics only. 2. By the same Gentleman. The sum of n terms of the series 1, 2, 5, 9, 15, 25, 45, &c. is 2.2"+n3. Required the proof 3. By A. B ཁ A ball being projected from the top of a tower 100 feet high, in a direction parallel to the horizon, and with the velocity of 1881 feet per second, how far from the point of projection will it meet the horizontal plane of the tower's base? Poiesia. This department embraces original poetical compositions, translations of ancient and modern poets, with occasional Essays and Criticisms illustrative of the metrical art in general. We shall be select in proportion to the liberality of our Correspondents.] TRANSLATIONS FROM METASTASIO AND GUARINI. [See the last No. of N. S. p. 209.] To the Editor of the Northern Star. THE few lines which your correspondent L. has prefixed to the beautiful verses of Italian poetry, which he transmitted to you for insertion in the poetical column of your Magazine for last month, are almost enough to deter any one from attempting, however much inclined he might otherwise be, to give them an English dress. "Remembering," he writes, "that Poeta nascitur non fit, (a poet is born, not made,) I have not attempted translations of them :" For the very same reason, the writer of this letter, and indeed all your poetical correspondents, might decline the task of translating them into English verse: for which of them would have the vanity to say, I am a poet born." In order, therefore, not to subject myself to the ridicule which would justly be excited against me by such an assertion, I deem it necessary to say, that I am too conscious of the defect of the following verses, to suppose that they can claim any other merit than that of expressing the scntiments, without the poetry, of the Italian lines. If, with this acknowledgment, you think that these versions will be acceptable to your readers, you are at full liberty to insert them in some obscure corner of your Magazine, where, if they serve no other purpose, they will display to advantage the brighter rays. which some happier genius shall diffuse over its pages, since the brilliancy of a star is never so conspicuous as on a gloomy night, when its light is contrasted with the surrounding darkness. The first piece of Italian poetry which your correspondent has transmitted to you, is from Metastasio, but from which of his works it is selected, or on what occasion it was composed, he has not mentioned. It is, however, necessary, in order to understand a passage, whether of poetry or prose, to know these circumstances; for it is impossible to perceive all its beauties without seeing its connection with the lines which have preceded it, or, if it constitutes a whole in itself, (as these lines from Metastasio seem to do,) without knowing for what purpose it was written. In the absence of this knowledge, a translator is liable to make very great mistakes, and I am not sure (since your correspondent has left me entirely in the dark on this subject) whether I may not, for this reason, have fallen into some. I suppose, that these beautiful verses were written on the death of some young lady, distinguished for her superior charms, and whom, therefore, the imagination of the poet happily represents under the image of A ROSE; on this supposition (which, if wrong, your correspondent will oblige me by correcting) I have thus translated, or rather imitated them.. VOL. III. PP O BEAUTEOUS Rose! whose unstain'd flow'rs And thus more beautiful and fair, At once heaven's ornament and care, In the original, the three last lines, literally translated, are" and placed under the care of a more faithful husbandman, thou wilt be able to unite, in a state of tranquil peace, eternal fragrance with eternal beauty"-which might be more beautifully rendered than in the preceding version: in justice to Metastasio, and the taste of your correspondent, I thought it proper to notice this variation from the original. I shall consider it a favour if any of your readers will point out any other difference in this or the following lines, in which the translator has departed from the sense of the original, and where, by such a departure, he has injured the beauty of the image or the delicacy of the sentiment. FROM GUARINI. How blest the happy youth, whose eyes Thy lovely charms delighted see, And yet more blest the youth who sighs E'en though he sighs in vain-for thee. But ah! most blest the favour'd boy, He sees those heav'nly charms of thine, I subscribe myself, yours, &c. Yes, as I gazed thy form upon, I thought of heav'n-but thou art gone! Some other hand thy hand shall press, And must I leave thee? Fare-thee-well! |