Again, let zu 12 ru 48 and xz=144 or 36 u±3, ±6, ±2, 4, 18, 36, 12, 24. The answers must be taken vertically, and considered either as all positive or all negative. It does not appear, whether Mr. Porson framed the equation by any rule or scheme in the established theory of numbers. Perhaps it was by reflection, and repeated trials, applied to the object in view, without any system by which similar equations may be constructed. NOTE V. referred to in page 312. Course of Study of Modern History. A FULL knowledge of the history of France and of the principal events in the history of the Continent,— I. From the destruction of the Roman empire till the reformation;-II. From the reformation, till the reign of Louis the fourteenth ;-and-III. From his reign till the present time ;-may be obtained by perusing the following works; all of them are interesting and instructive, and written with great elegance. I. "L'Histoire de Charlemagne, by M. Gaillard," 4 vols. 8vo.* conducts the reader from the beginning of the French history, till the house of Capet. The next event of importance in the history of France, is the repeated wars between her and England. The history of them is found in Hume, and all other writers of the general history of England; but it is told in a more agreeable manner by father d'Orleans, in the second and third volumes of his "Histoire des Révolutions d'Angleterre," 4 vols. 8vo. + While these wars were at their height, the Crusades began; an interesting history of them is to be found in the two first volumes of the "Histoire des Chevaliers de "Malthe, by the Abbé de Vertot," + 5 vols. 8vo. and the "Esprit de Croisades," 4 vols. 8vo. These are followed by the French invasion of Italy, In Hookham's Catalogue, No. 14,529. + Ib. 14,935... Ib. 14,595. excellently related by the abbé de Bos, in his "Histoire "de la Ligue de Cambrai," 3 vols. 4to.* Here it may be proper to rest; and to take a short view of the general state of France and Italy during the middle ages. This is given in three very interesting works, Mr. Berington's " Lives of Heloisa and Abelard,”+ in two thin quarto volumes ;-"La Conjuration de Rienzi, by Father Cerçeau, a jesuit," in 1 vol. 8vo. ‡ and the "Mémoires pour servir à la Vie de Pétrarque, by the Abbé "de la Sade," 4 vols. 4to. § 66 66 II. `66 Mr. Berington's History of Literature during the "Middle Ages," presents the best account in print of that important subject ||; and Mr. Roscoe's ||" Lives of Leo "the tenth and Lorenzo di Medici," contain an interesting account of the revival of literature. In reference to this period "Cardinal de Retz's Conjuration de Fiésque,"¶ should also be read. After which," L'Esprit de la Ligue," 3 vols. 8vo.** than which the continent has not produced a better history, and the“ Intrigues du Cabinet, by M. d'Anquétil,” 4 vols. 8vo. ++ should be perused. Those, whom quartos do not frighten, will be delighted in the highest degree by the thirteenth, fourteenth, and fifteenth volumes of "Father Daniel's Histoire de France;" they contain the life of Louis the thirteenth, by father Griffet; a most interesting history of a most interesting reign. Here the eyes should be again turned on the adjacent state of the continent, and "Vertot's Histoire de la Révo"lution de Portugal,”* and his " Histoire de la Révolution "de Suède, † each of them contained in one vol. 8vo. should be read: and here, perhaps, " Mr. Butler's Revolutions of the German Empire," ‡ may be usefully perused. III. The "Mémoires du Cardinal Retz," § 6 vols. 8vo. which give an account of the troubles in the early part of Louis the fourteenth's reign, are universally read; the principal events of that time are to be found in the “ Intrigues "du Cabinet," already mentioned. After which, the two following works,-" Voltaire's Siècle de Louis quatorze,|| 2 vols. 8vo. and the " Abbé d'Anquétil's Louis quatorze et sa Cour," ¶ bring us to the present time. It only remains to mention, the bible of French politicians, Histoire du Traité de Westphalie," 6 vols. 8vo. by Father Bougeant. It contains an account equally interesting and instructive, of the war of thirty years; and all the political negotiations of France, from the league to the peace of Westphalia. 66 If the reader is alarmed at Mr. Roscoe's quartos he will find the substance of them very agreeably told by Varillas in his "Anecdotes de Florence."** As a most interesting historical novel, for it deserves no better name, I beg leave to recommend the " Conjuration contre Venice of the Abbé de St. Real."++ * In Hookham's Catalogue, 16,851. These are not in Hookham's Catalogue, but are easily procured. At Hookham's, but not in his Catalogue. § In Hookham's Catalogue 15,689. || Ib. 16,405. ** Ib. 13,216. NOTE VI. referred to in p. 305. A Letter addressed to Mrs. Edward Jerningham, MADAM, I SIT down to perform my promise, of committing to paper, some observations on music. With this view, I shall have the honour to offer you some miscellaneous observations,-I. On the Greek and Roman music : II. On the music of the Middle Ages: in which, 1st, its notation; 2dly, the stave; 3dly, the gamut and hexachords of Guido; 4thly, the division of notes; 5thly, musical bars; and 6thly, music in parts, will be successively mentioned: III. Advancing to modern music, 1st, the Flemish,—2dly, the Italian,-3dly, the German, -and 4thly, the French schools of music will be noticed; -5thly, then the English school of music, adverting occasionally to the anthem, the serious glee, and the oratorio : IV. I shall then notice the attempts in this country to imitate the Italian style of singing:· V. And afterwards give some account of the Gregorian chaunt; here I shall mention its chief peculiarities; 1st, that it is confined to unison; 2dly, that it almost absolutely rejects adventitious sharps and flats; 3dly, that the tonic or final note of all its melodies is confined to four notes of the octave; 4thly, its division into eight ecclesiastic tones; 5thly, the peculiar nature of their respective dominant notes; 6thly, the want in each of some tone or semitone, which modern music would require in the series of notes nearest corresponding with it; 7thly, I shall then offer some general remarks: VI. And finish my letter with |