purpose of humiliating the pride of the human understanding, as to serve, through succeeding generations, for a perpetual "cos ingenii." Should Providence, however, be so kind as to spare your life, until you complete your new system of navigation, with which, I am happy to learn, you are so rapidly progressing; I doubt not, from the idea which I now entertain of it, but it will prove a valuable succedaneum for the long sought-for discovery. I am, indeed, so well convinced of its utility, simplicity and superiority to all other systems of navigation, hitherto divulged; that I cannot but urge you, with the importunity of a friend, to accelerate the completion and publication of a work, the sterling excellence of which must secure you the respect of your cotemporaries, the gratitude of posterity, and entitle you, without vanity, to direct that your epitaph shall be extracted from the 30th ode of the 3d book of the immortal bard of Venusia.* With regard to your question, relative to the number seven, I will observe, that my vocational engagements have been so literally incessant, since the receipt of your favour, that I have not been able to give it that mature investigation, which, from its importance, and its curious bearing on numerical operations, it unquestionably deserves; the profound discoveries, the sage remarks, and the noli-me-tangere suggestions, of the erudite W. S. to the contrary, notwithstanding. However, from the little reflection, which I have been able to bestow on it, I have discovered one reason, why six equal digits will divide, exactly, by this remarkable and dignified number; I say dignified, because it expresses, ordinally, the day on which the Almighty Fabricator of the universe is said, in figurative language, to have "rested from his work." It is well known, that one number will exactly divide by another, when the first, or dividend, is a multiple of the second, or divisor. It is also known, that if a succession of dividends should leave remainders, whose sum amounts to a multiple of a divisor, the aggregate of the dividends will itself be a multiple of that identical divisor. Now, in the question proposed; if we take six units, they make, according to our notation, one hundred and eleven thousand, one hundred and eleven; which is only the aggregate sum of one, ten, one hundred, one thousand, ten thousand, and a hundred thousand. If we inquire, then, whether these numbers are, respectively, multiples of the septenary, we shall soon discover, that this property belongs to none of them; but we shall, at the same time perceive, that, on their being divided by the number seven, they will leave a set of remainders, whose sum is a multiple of the septenary; and, that therefore, the aggregate must be exactly divisible by that number. Now if this be true of six units, it must be true of six twos, of six threes, of six fours, and in fact, of any six equal digits; because every digit is a multiple of the unit. To substantiate the truth of this reasoning, I shall subjoin the following illustration. As we know that 111111 means the same thing as 1+10 + 100 + 1000 + 10000 + 100000; let the small . right hand square, in the annexed diagram, represent a unit; and let it be required to ascertain how often another square, of seven times its dimensions, is contained in it. It is obvious, that we shall have the remainder 4; or as seven will be a common denominator, we may say, that the remainder will be one. Let the second square, marked ten, be a superficies of ten times the contents of the first; and let it be required to ascertain how often that also contains the common measure seven; it is equally ob vious, that we shall have the remainder, or 3. Let then the contents of the succeeding squares be to each other in the same decuple ratio, as indicated by the numbers, which they enclose; and let the common measure seven be applied, 7[1]=1 successively, to them all; as they are all in- 7 [10] -= 3 commensurable, it is plain they will all leave remainders; and these, in the order of their evolution, will be found to 7 [100000] be one, three, two, six, 7 [100] 7 [1000] 7 [10000] 2 5 sum of remainders, = 21. four, and five.-Now, it is evident that 1+ 3 + 2 + 6 + 4 + 5 21, the sum of the remainders, amounts to a multiple of the septenary; and consequently, that the aggregate 111111 must divide, exactly, by, that number. Five equal digits will not do this; nor will seven; nor, in fact, will any other number that is not a multiple of six; and for this obvious reason; because the sum of their remainders will not be a multiple of the septenary. I would willingly make some further observations, on the curious properties of this digit; but my time will not permit; I have barely a sufficiency to add, should the publication of the Mathematical Correspondent be recommenced, you may count, with certainty, upon my most ardent wishes for its success, and my feeble exertions to contribute to its utility; if they can prove, in the smallest degree, auxiliary to so eminent a duumvirate of mathematicians, as Messrs. George Baron, of New-York, and Thomas Maughan, of Quebec.-I have the honour to be, my dear sir, with sentiments of respect and esteem, your friend and obedient humble servant, Newbern, N. C. April 29th, 1811. THOMAS P. IRVING. ORIGINAL POETRY.-FOR THE PORT FOLIO. ORLANDO.-A POEM. CANTO II. MR. EDITOR, THE author of the poem called ORLANDO, at the request of several, has at length finished the second Canto, which he ventures to send to you for publication. Through the imprudence of a friend (in publishing the fi st canto) a youth, who has not yet attained his eighteenth year, was exposed to the harsh strictures of criticism. Many of the censures of the writer, who signs himself "Justice," might have been spared, not only as evincing little sensibility to the exquisite feelings of youth, but likewise as being unfounded. The author might say, with truth, that his heart is rather too proud to suffer him to become a wilful imitator; such a one too, as a person might suppose him to be, on reading the remarks of "Justice." He never imitated wilfully except the three several lines of Gray, Collins and Shakspeare. The following observations were made by a friend of his: whether they are just or not the public must determine. “Poets,” says he, "in reading the works of others, are frequently struck with ideas, which remain imprinted on the mind after the source whence they are derived is forgotten. Those being called into action by some circumstance, the person finding them floating on his brain, regards and uses them as his own offspring, whereas they are only his by adoption. This may account for some of the passages wherein you are thought guilty of plagiarism, as you inform me at the time you had not the Minstrel, and had read it but once. To proceed to the descriptive parts of the poem: France and Scotland both abound in savage mountains and delightful vales; therefore Nature does hold forth some resemblance in her grand outlines in either country; but when we descend to the particular scenery, the difference of climate is soon perceived. This similarity in outline, and dissonance in particularity, ought to be expected in two persons describing the different countries. Accordingly we find that Orlando and the Minstrel both describe hills and dales; but in the individual ideas which are imprinted on the mind by reading either, I defy the critic, with all his ingenuity, to discover any affinity scarcely: those he has pointed out are almost all verbal. "In those gloomy times in which the soene of both the Minstrel and Orlando is laid, the belief of the existence of ghosts was universally established; and a poet, pretending to delineate the feelings of a person who lived at such a period, would do wrong to omit this important cause of terror and delight. This is a sufficient reason why you should have introduced your twenty-fourth and fifth stanzas, although the imagery should be nearly the same as that employed by Beattie. But, in the particular ideas, I perceive no resemblance; the scenery that arises in my mind on reading both, is totally different. The visionary personages of the Minstrel are rather of a mild nature; those of Orlando are gloomy and terrific. "The critic falls into a very great absurdity, where he says the descriptions of the seashore are similar; no person of common sense, after reading the two, would say the one is an imitation of the other." Such are the observations of a friend. The author cannot judge of the justness of the remarks, because as Aristotle remarks “Has To oixelos epgov ayaraw." For those passages, where the critic condescends to praise him, the author feels the liveliest gratitude. He must confess, though upon the whole, the writer has treated him rather harshly, he has derived some benefit from his observations. He hopes this second Canto will prove it; he has taught him that after he has written he ought to make some research and observe whether other authors have not passages parallel with those he has penned. The critic in looking over it may, perhaps, find lines similar to those of preceding poets, but no imitations unmarked. The remarks of his friend, prefixed to the first Canto, where he says, "this poem is, perhaps, inferior to those of Chatterton," appear like those of a lunatic; as any attempt to equal that great but unfortunate poet, at such an age, would savour much of insanity. To discover the falsity of such criticism as the above, "Justice" was certainly right in coming forward; but he need not have maltreated the poet for the offences of his friend. However, since he has volunteered, we hope he will again present himself on the publication of this Canto, and "point out faults and beauties alike!" The three last stanzas may be deemed an excrescence; but the author could not repress the tribute of affection due to the place of his nativity. 1. AH! what a variegated scene is human life! Vain worm of earth, why dost thou not reflect: 2. But grieve not sore, at this thy common doom, Though prospects, sad, thy present landscape gloom, Fair Hope attends, like evening's beaming star, The cheer and solace of our devious way, Points happier views, advancing from afar, E'en o'er the mourner's face, reflects a sprightly ray. 3. But who can see, and yet not feel some gloom By one rash act, an early death obtain'd, Fled from a guilty world, all conscious of thy wrong. |