Queen Mary; Mellen's Bugle; Dawes's Spirit of Beauty; Pierpont's Airs of Palestine; and Longfellow's Voices of the Night; as worthy specimens of poetry, chiefly lyrical.

Of American descriptive, and didactic poetry, one of the oldest specimens is Folger's Looking Glass for the Times, written as early as 1676. Wigglesworth's Day of Doom, created a strong sensation; but Godfrey's Court of Fancy, attracted little notice. R. T. Paine's Invention of Letters; Linn's Powers of Genius, and Valerian; and Lathrop's Vision of Canonicus, are valuable works. Dr. Dwight's Greenfield Hill, is a beautiful poem of this class. Barlow's Hasty Pudding, and his Conspiracy of the Kings, are, we believe, of a satirical or political character. Livingston's Philosophical Solitude, has met with little notice. Trumbull's Progress of Dullness, and Dwight's Triumph of Infidelity, are satirical poems of a high character. Osborne's Thanksgiving, is a touching description of that social New England festival. Mrs. Sigourney's Zinzendorf, relates to a nobleman of that name who became a Moravian Missionary to the Indians. Hillhouse's Vision of Judgment, and Mellen's Martyr's Triumph, are sublime productions; and Bryant's Ages, exhibits the power and purity of its author. Percival's Voyage of Life, and Consumption, are also excellent. Lunt's poem on Life, and Bacon's on Man, are, we think, worthy of mention. Of Romantic poems, we would name Percival's Wreck, his Prometheus, and The Suicide; Halleck's Fanny and Alnwick Castle; Drake's Culprit Fay; Willis's Melanie; Dawes's Geraldine; Mitchell's Indecision; Miss Davidson's Amir Khan; and, we believe, Dana's Bucaneer, Whittier's Minstrel Girl, and Sand's Yamoyden. Everest's Babylon; Hill's Ruins of Athens; and Rees's Battle of Saratoga; are, we believe, descriptive poems. Several of Willis's scriptural poems, as Jephthah's Daughter, and Hagar in the Wilderness, are beautifully descriptive and didactic; and this character belongs generally to the poems of Mrs. Sigourney and Bryant.

Of American dramatic poetry, the first specimen was probably the Prince of Parthia, by Thomas Godfrey, Jr.; and next to it was Leecock's Disappointment, a comic opera, printed in 1767. Mrs. M. Warren, of Boston, wrote The Adulateur, The Group, The Blockheads, and The Motley Assembly; political plays, during the Revolution. Her tragedies, the Sack of Rome, and the Ladies of Castile, we believe, were written at a later date. W. Dunlap wrote or translated nearly fifty pieces, including The Archers of Switzerland, the Voice of Nature, and André, a tragedy, founded on the fate of Major André. Colonel Humphreys wrote the Widow of Malabar, a tragedy, from the French; and Rev. John Blair Linn wrote Bourville Castle, and we believe other dramatic pieces. We must not omit to notice Lathy's Reparation, a comedy; D. Everett's Daranzel; W. Jones's Independence; W. C. White's Clergyman's Daughter, and Poor Lodger; J. N. Baker's Marmion, and Superstition; C. J. Ingersoll's tragedies, Edwy and Elgiva, and Julian; and D. P. Brown's Sertorius, and Prophet of St. Paul's. Among other works of merit are Willis's Tortesa, the Usurer ;

Epes Sergeant's Velasco; and especially Dawes's Athenia of Damascus but the tragedies of Hillhouse, called Hadad, Percy's Masque, and Demetria, are perhaps the best which our country has yet produced.

Of American Romance, in prose, the first production appears to have been The Foresters, by Dr. Belknap of Boston, first published in 1787, in the Columbian Magazine, Philadelphia. It relates to our colonial history, and may be regarded as a continuation of Arbuthnot's John Bull. Tyler's Algerine Captive, published in 1797, is a genuine novel, though founded on facts. The first professed novelist, Charles Brockden Brown, wrote Wieland, Ormond, Arthur Mervyn, Edgar Huntley, Clara Howard, and Jane Talbot; works of genius and merit, though not of the most recent school. Washington Irving's Knickerbocker's History of New York; and his Jonathan Oldstyle's Letters, Salmagundi, Sketch Book, Bracebridge Hall, Tales of a Traveller, and Alhambra, are also classed as works of fiction, and are unsurpassed in style and character. Wirt's Old Bachelor, and British Spy, are also standard works of this class. Dennie's Female Quixotism; Mrs. Foster's Boarding School, and Coquette; and Mrs. Rowson's Rebecca, and Sarah, have met with less notice. Cooper's novels, have been generally read and admired; particularly The Spy, The Pioneers, The Pilot, The Last of the Mohicans, The Prairie, and The Red Rover. We would also mention Paulding's Dutchman's Fireside, and Westward Ho! Flint's Francis Berrian; Kennedy's Swallow Barn, and Horseshoe Robinson; Bird's Hawks of Hawk Hollow, Calavar, and Peter Pilgrim; Ingraham's Southwest, Lafitte, and Burton; Simms's Yemassee, Guy Rivers, and Mellichamp; Fay's Norman Lesley, and Countess Ida; Tuckerman's Isabel or Sicily; and Longfellow's Hyperion; as worthy specimens of American romance, generally evincing talent and taste. Miss Sedgwick's New England Tale, Redwood, Hope Leslie, Clarence, and The Linwoods, are beautiful and natural; and her recent minor tales are fraught with excellent instruction. The Hobomok, Rebels, and Wilderness, of Mrs. Child, (formerly Miss Francis); as also Miss Leslie's Pencil Sketches, and Althea Vernon, are entertaining productions; the last of this class which we have room to name.

Among the best productions of American eloquence, it is to be regretted that most of the speeches of Patrick Henry, Edmund Randolph, James Otis, Samuel Adams, and other Revolutionary worthies, have not been written out and preserved. Those of Fisher Ames, Hamilton, and Jefferson, are, we believe, mostly published with their works. A selection from the numerous eulogies of Washing ton, by various orators, would of itself form an interesting volume. The speeches and addresses of Clay, Webster, and Everett, have been published in separate volumes, and are, we think, models of their kind.

THIRD PROVINCE;
PHYSICONOMY.

In the province of Physiconomy, we would include those studies which relate more immediately to the material world; its forms and structure; its agencies and changes; its composition and varied relations; including those of animal and vegetable life. The name is derived from the Greek quos, nature and vouos, law; signifying literally the Laws of Nature; using this term, as it is often used, to designate the world of matter, or material objects collectively considered. In this province we comprehend the departments of Mathematics, or the study of numbers and magnitudes; Acrophysics, or Natural Philosophy, relating chiefly to natural phenomena; Idiophysics, or Natural History, treating chiefly of natural productions; and Androphysics, or the Medical Sciences, relating chiefly to the human frame, that microcosm, or minor world, the last and highest material production of the great Creator. The reasons for arranging these departments in the above mentioned order, having already been stated, need not here be repeated. (See pp. 34 and 35.)

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IX. DEPARTMENT:

MATHEMATICS.

THE department of Mathematics, includes the study of numbers and magnitudes; and hence it is sometimes termed, the science of quantity. The name is from the Greek μavdavw, I learn and was applied to it, because the ancients considered this department, in reference to its various uses, as the basis of all learning. As it finds its highest applications in the investigation of the laws of nature, we have here considered it as chiefly introductory to their study; and as belonging to the same province of human knowledge. As the science of quantity, it is applicable to all quantities which can be measured by a standard unit, and thus expressed by numbers or magnitudes. There are objects, such as feeling or thought, which may vary in intensity, but which we have not the means of measuring. We cannot say that we love one person exactly twice as much as another; or that one man is four times as wise as another; since love and wisdom are not mathematical quantities. But we can measure time, by seconds, days, or years; space, by inches, yards, or miles; and motion, by the space passed over in a given unit of time. Such quantities, therefore, may be expressed by numbers, and subjected to Mathematical calculations.

Mathematics, as a general science, is often subdivided into Pure, and Mixed. Pure Mathematics, relates to numbers, figures, or magnitudes abstractly, and without any necessary reference to material or tangible objects: but Mixed Mathematics, is the application of the former to natural objects; as matter, space, time, motion, and the like, which, though subject to mathematical relations, involve other principles, depending on the laws of nature. Thus, Mechanics, Astronomy, Navigation, Music, and other sciences, are sometimes included under the name of Mathematics: but we would here restrict the term to the Pure Mathematics, with some occasional applications; as being sufficiently extensive and important to constitute one department of human knowledge. It should not be forgotten that new mathematical principles and problems have led to new discoveries in nature, or inventions in the arts; and these, in their turn, have led to other new principles and problems in Mathematics.

The question may here arise, into how many branches this department should be divided. The branches of Arithmetic, Algebra, and Geometry, are generally recognized as distinct and elementary; while Trigonometry is sometimes connected with the latter, and sometimes regarded as a distinct branch. Considering, however, that Trigonometry is an application of Algebra to certain Geometrical figures, we have no hesitation in associating it with Conic Sections, in the branch of Analytic Geometry. The study of Descriptive Geometry,

or the delineation of objects geometrically, as it involves no other principles than those of Elementary Geometry, and differs chiefly in the mode of applying those principles, we would include in the same branch, under the common name of Geometry. There remains only the science of Fluxions, as it was named by Newton, or the Differential and Integral Calculus, as it has been named by the French mathematicians, to complete the list of branches in this department.

The History of Mathematics, may, we think, be referred chiefly to that of its individual branches. The knowledge of the ancients, in this department, was evidently far inferior to that of the moderns. Although they reckoned by tens; a fact which is adduced, among others, as proving the common origin of the nations thus reckoning; yet they did not use, and probably were not acquainted with the decimal notation which has so greatly simplified our modern Arithmetic. In Elementary Geometry, and the Conic Sections deduced therefrom, the knowledge of the Greeks would bear a comparison with that of modern times; but in these branches only, of the Pure Mathematics. Some of their most learned works were destroyed in the Alexandrian Library, or during the dark ages; but others were preserved by the Arabians themselves, when a milder dynasty succeeded; and the Greek works collected and translated into Arabic, by order of the Caliph Al Mamun, have supplied much of the information which we now possess, concerning ancient science. (p. 289.)

To the Arabians, we are indebted, for the introduction of the Decimal Notation, and for the science of Algebra; which they appear to have transmitted rather than invented; as we shall have occasion to show, in treating of the individual branches. Their mathematics, being introduced by the Moors into Spain, was zealously cultivated by Alphonso of Castile; and from thence it was introduced into France, as early as A. D. 970, by Gerbert, who afterwards became Pope Sylvester II. It was disseminated in Italy, about A. D. 1228, by Camillus Leonard, a rich merchant of Pisa, who had travelled in the East; and at about the same time, John of Halifax, or Sacrobosco, of England, wrote a treatise on the Arithmetic of the Arabs. From that period to the present, the progress of mathematics has been continuous; and the greatest nations of Europe have been competitors for the honor of its new discoveries and inventions.

The invention of Analytic Geometry, by Descartes, and of Coördinates, by Maclaurin, has greatly extended our means of investigating curves, and curved surfaces in general, as well as their included solids. The invention of Logarithms, by Napier, has simplified, in a wonderful degree, the higher numerical calculations, which before were extremely tedious. The invention of Descriptive Geometry, by Monge, has given us a complete method of representing and measuring geometrical magnitudes, and forms; the applications of which are of great practical value. And especially, the invention of Fluxions, or the Calculus, almost simultaneously by Newton and Leibnitz, has opened the way to a new and wide range of mathematical investigation, quite beyond the reach of ancient science, and which has served, in skilful hands, to detect and explain various laws of nature that before seemed absurd or contradictory.