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of being "Portuguese settlements," are three kingdoms governed by native princes, totally independent of Portuguese authority. The remainder of the extract identifies the Cape of Good Hope, Caffraria, and the country of the Hottentots; but the fact is, that the nearest part of Caffraria is almost nine degrees of longitude east of the Cape; and is the country of the Caffres and not of the Hottentots-who are the original inhabitants of the colony and the regions north of it.

Chapter 28th commences with a brief dissertation on the objects, use, importance and history of Mathematics. This is followed by a short history of Arithmetic, and a statement of its importance to other branches of science, and an account of the principal works on that subject, which it will be proper for the student to peruse. The next chapter contains the history, definitions, and symbols of Algebra, with an account of the chief modern treatises on the subject. The same plan is extended to Geometry, Trigonometry, and Conic Sections. In the enumeration of books, we think that the authors have here been too diffuse, and that they would have benefited the student more if they had made greater use of their privilege of selection. Mr. Leybourn's Mathematical Repository, as mentioned at page 475, is the old series of that work: the new series of which has for several years been publishing in octavo. It is curious, however, to see the article on Geometry terminate in the following manner. After recommending "Hutton's or Barlam's Dictionary, or Nicholson's British Encyclopedia," to the mathematical student, it is added, "or, above all, the great national work of the Rev. Dr. Rees, entitled, the New Cyclopedia,' of which nearly sixty parts are before the public." On this recommendation there is no. need of comment-to either publishers or preachers.

Conic Sections are succeeded by Fluxions. Here, however, our authors remind us of men in a foreign country, making use of a language with which they are but imperfectly acquainted. After explaining the nature of the subject, by an extract from Simpson's Fluxions, and having mentioned its induction by Sir Isaac Newton, they add,

"We shall just give our reader an insight into the science, by shewing. in a few of the simplest cases, which the young algebraist will readily understand, how fluxions are adapted for determining the maxima and minima of bodies- for drawing tangents to curves, &c. by which he will readily understand in what way the science may be made to extend to the investigation of the most abstruse and difficult problems in the vari-· ous branches of mathematics and natural philosophy."

This is certainly promising a great deal; but how is it accomplished? Having explained in what sense the "early” and latter" letters of the alphabet are to be used, they give the

Rule for finding the fluxion of a given fluent (no explanation or the term fluent has been given), in which there is but one variable quantity. This rule applies only when the variable quantity is of the first power. The Rule for finding the fluxion of the product of two or more quantities is then given; and also that for the fluxion of a fraction. "The application of fluxions to the solution of problems de maximis et minimis, and to the drawing of tangents to curves," is then shown by the following well-known examples. 1. To divide a right line into two parts, such that their product shall be a maximum. 2. To determine the greatest rectangle that can be inscribed in a given circle. 3. To draw a tangent to a circle and also to a parabola. Each of these solutions requires the fluxion of a compound quantity to be found, one term of which contains the second power of the variable quantity; but no Rule has been previously given either for the compound quantity or the power. This last arises from their having made the first rule partial instead of general:-It should have been given for finding the fluxion of any power of a flowing quan

tity, as x. They also promised to show the adaptation of fluxions for "determining the maxima and minima of bodies." Do they call a right line or a rectangle a body? or have they written the word body instead of quantity? the latter we think has been the case.

In naming books on this subject, they have, contrary to their usual custom, been sparing. In addition to Sir Isaac Newton's method of fluxions, they have added the names of Rowe, Vince, Simpson, and Maclaurin. If they chose to omit those of Emerson and Holyday; we cannot perceive any reason why they should have left out that of Mr. Dealtry, whose work on that subject, published within a few years, is certainly as well adapted to promote the progress of the student as any of those they have mentioned. We will just cite another inadvertency here for the sake of having it corrected in the next edition.

"The great work on Astronomy, so regarded by the mathematicians and philosophers of all countries, is that entitled "Philosophiæ Naturalis Principia Mathematica, auctore Isaaco Newtono." Thi, however, can only be read by mathematicians of the highest order. As introductory to it, we have "A view of Sir Isaac Newton's Philosophy by Henry PemLerton," 410: and which is by much the better work." Vol. II. p. 136. It is this part in Italics that requires correction or expla

nation.

Our limits prevent us from pursuing this analysis any further; we can therefore only say that in most of the other' chapters, we have found much to commend. The multiplicity of subjects included in the work, (and we think there is not one too many) has necessarily imposed on its authors a brevity that confines them

to an outline of each; and even in some instances, the space that can be allowed is insufficient to render that outline complete. The enlargement of the plan, by the addition of another vo lume on the occasion of a second edition, would be desirable, and could hardly fail of meeting with public approbation. Upon the whole, the work is well calculated to convey information on a great variety of subjects, to those for whose use it is designed; the language in general is perspicuous, and with the exception of a few quaint phrases and inadvertencies, especially in the definitions, is well fitted for the purposes of instruc

tion.

Their directions for studying a particular subject often bear the stamp of experience; and their remarks on the pleasure and utility resulting from that study not unusually deserve the most serious attention of the student. The subjects of science are illustrated by eight outline plates.

ART. XX. The Maskers of Moorfields: a Vision. a Vision. By the late ANTHONY GRIFFENHOOF, Gent. 12mo. pp. 87. Miller. THE supposed editor of this vision is stated to be the brother of the deceased Anthony Griffenhoof, who, being left sole executor, was entrusted with several literary manuscripts, over which he was authorised to exercise a discretionary power. According to the author's advertisement," this work was produced in 1814, and consequently includes allusions to some occurrences in the preceding year, which the reader's discrimination must find out; but such is the poignancy of the satire, that the characters introduced as Masqueraders, cannot be mistaken.

Mr. Anthony Griffenhoof, being accustomed to indulge himself once a year in reading Horace, one of his favorite authors, was, during his last annual perusal, more than usually struck with the famous dialogue between the poet and Damasippus ; and the conclusion of this celebrated colloquy," that all men are actually mad," so worked upon the imagination of the author, that, during his reverie, he fell into a profound sleep. Though allegorical narratives abound under the title of visions, (some of them the productions of eminent authors) yet the idea, that the characters thus obtained are all mad, has some claim to originality. The scene of this vision, Moorfields, is happily chosen, and the Masquerade, at this time represented here, is supposed to take place one night in every year. The dreamer, surprised at the motley assembly, is con

ducted through the crowd by the genius of caprice, who explains to him the respective characters. Among these, are two famous Roman mimics, father and son, who wish to draw the attention of the company to an address written for the opening of this Masquerade. The following couplet

"When energising objects men pursue,

"What are the prodigies they cannot do?"

was delivered by the son with all the airs of a posture master, while his father accompanied him with the finest grimaces of an Italian fiddler. This, every reader must recollect, alludes to a certain Address, written for the opening of the New Drury Lane Theatre. Among the other well-known, and indeed entertaining characters, which form this group of masked Bedlamites, are the ghost of a Monk, who, being a sort of wholesale dealer in spectres, apparitions, &c, fancies himself a ghost, a bookseller, and publisher, who having the misfortune to be dubbed a knight, became in the end insolvent, and, wishing to pass off for a Pythagorean philosopher, wages eternal war against all animal food; an orator and poet, who, having a great genius for dramatic writing, forsook Thalia for Bacchus, &c. It would be an injury to this little work to diminish curiosity by further anticipation. The characters are admirably drawn, and the satire keen, without being offensive. A scene of uproar terminates the dream, and Mr. Griffenhoof's eyes open upon the following passage of Horace, which is prefixed as the motto

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ART. XXI. Lives of Caius Asinius Pollio, Marcus Terentius Varro, and Cneius Cornelius Gallus. With Notes and Illustrations. By the Rev. EDWARD BERWICK. Small 8vo. pp. 178.

PLUTARCH, the illustrious biographer of Cheronea, has not only gratified a laudable general curiosity, but blended the utile with the dulce. Instruction is the grand aim of biography; and greater instruction is to be derived from the lives of ancient than from those of modern heroes. Few, comparatively, have any knowledge of the former; and the knowledge which some possess of them may be beneficially encreased: but with those who have recently acted conspicuous parts on the stage of life, the world is already, in a great measure, acquainted,

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These three biographical sketches had been promised by Mr. Berwick when he published his lives of Messala, Corvinus, and Pomponius Atticus.

"Pollio, the subject of one of the sketches, was the most accomplished scholar of the age in which he lived, and was the first man who established a public library at Rome: and Terentius Varro, the most learned of the Romans, the subject of another sketch, was his particular friend; and his statue alone, of all living men, was deemed worthy of a place in that library."

The compiler seems to have explored the best documents, and to have properly availed himself of his researches; for he has detailed, with fidelity and impartiality (the best cha racteristics of a biographer) the chief events in the lives of these three ornaments of the Augustan age. The merits of Pollio, as a military character, poet, orator, historian, and critic, are faithfully discussed. He is well defended from the imputation of avarice, thrown upon him by Blackwell, who had asserted, "That he was resolute to make a fortune, cost what it would; and that, having great opportunities of doing it, he never lost the use which was to be made of them." Mr. Berwick observes in answer,

"When we consider the distracted state of the times, the conspicuous part borne in them by Pollio, the numberless forfeitures which were the natural effects of them, and above all, the success which finally attended the fortunes of his friends; when, I say, we consider the force of all these combined causes operating together, we need not be surprized at the great accession of property which attached to him. But to his credit let it not be forgotten, that, whatever fortune he amassed was converted to the most honorable uses, and the encouragement of learning and literary talents was among its richest fruits."

As a critic, our author also defends him from the severe censure of Dr. Stewart, who states him to be in that character "vain, arrogant, and capricious." Mr. Berwick shows the fallacy of Dr. Stewart's sources of information, and proves that other great men besides Pollio, had justly condemned the style of Sallust. The documents, which enabled our author to compile this life, and the former lives of Corvinus and Atticus, have no doubt assisted him in producing the other two sketches, particularly the life of Pollio's friend, Varro, pre-eminently characterised as the most learned of all the Romans. When upwards of 70 years of age, Varro's name appeared in the list of the proscribed.

"Though condemned to death as a friend to law and liberty, and consequently an enemy to the lawless usurpation of the triumvirate, there arose a degree of emulation among his old Cæsarian friends, which of them should have the honor of saving him. They disputed who should have the preference in supporting him in his disgrace; and Calenus obtained it, who carried him to his country house, where Anthony

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