ページの画像
PDF
ePub

66

To establish the conviction which this letter must produce, concerning the worthy Dr.'s" repugnance" to flattery, it would only be necessary to cite the twenty second letter, which refers to a very elegant version from Horace" by the young Lord, and assures him and the public that part of it is" particularly beautiful, uniting "ease and elegance with closeness and fidelity." As if this right honourable mode of advertising Lord John's poetical gifts could need to be dignified by an exhibition of literary talent, or as if the public could think of requiring a specimen of the Doctor's acumen before they re-echoed his applause on juvenile exercises which are carefully withheld from their inspection, he has favoured us with a scrap of classical criticism. The subject of it is the following distich:

Quod si me lyricis, vatibus inseres,
Sublimi feriam sidera vertice."

He tells us it would be" illogical" and "nonsensical bombast" of the Poet to say, "If you will insert me amongst the lyric poets, I shall strike the stars with my lofty head;" he therefore maintains that inseres belongs not to the verb insero, inserui, but to insero, insevi, to graft, proposing to translate the words thus, "But if you engraft me on the lyric poets, I shall shoot out so vigorously that my top will soon reach the stars." This we must confess is worthy of Ruperti or Grævius himself; it is in the true spirit of commentation, "the rage of critics, for illustrating themselves and obscuring their author." For our part, as we have never been scandalized at so familiar an exaggeration as "sublimi feriam sidera vertice," a proverbial metaphor for expressing great elation of mind, we despair of discerning any Horatian elegance in the notion of grafting one poet on a great many other poets, to enable this poet to send out branches, and those branches to reach the stars. Dr. C.'s etymological correction in the following page, corresponds with his critical elucidation; "the diph thong" in Macenas, he says, "should be in the second syllable, as thus, Mecenas. Its etymology is Mm xavos, literally in English, Uncommon." p. 174. As there is no good authority. for this spelling, which is exploded by Gessner, (vide Thesaur. sub voc. Mæcenas, Manyas) and the critics, in general, we presume Dr. C.'s fancied etymon will not be deemed singly sufficient to establish it. At any rate he spells the name improperly, as his own etymology requires it to be

Mecœnas.

In writing his next letters to a young nobleman, we recommend Dr. C. to consult the Epistles of Pliny, instead of the Panegyric; and admonish him, when he assumes the office of "Critic," not to enact the character of "Puff."

Art. XVII. Mathematical Tables, Containing the Logarithms of Numbers, Logarithmic Sines, Tangents, and Secants, and a Traverse Table; To which are prefixed, Logarithmical Arithmetic, and Plane Trigonometry, also Examples on the Mensuration of Heights and Distances. For the Use of Schools. By J. Brown, Mathematician. 2nd Edition, corrected, improved, and enlarged, &c. &c. 8vo. pp. 80 of Introduction, and 86 of Tables. Price 78. Edinburgh, P. Hill; Longman and Co. 1808,

THESE Tables, though inferior in some respects to those of Hutton, of Callet, and of Taylor, are yet printed of such a size and price, and with such correctness, as will render them highly useful to those who are frequently engaged in logarithmic or trigonometrical computations, and are unwilling to encumber themselves with a less portable volume. They are judiciously arranged, and printed with a handsome type; but unfortunately the delicate Thinness of the paper, while it renders the volume commodious, gives many of the pages an indistinct appearance. Beside the tables mentioned in the above extract from the title-page, there are tables of Natural Sines, of Compound Interest, of the Probabilities of Life, and of Annuities on Single and on two Joint Lives. The introductory part treats of the binomial theorem, the nature of logarithms, the deduction of logarithmic series, computations by logarithms, the calculation of sines, tangents, secants, &c., plane trigonometry, mensuration of heights and distances, computation of interest and annuities, with reversions, &c.; rules for working by traverse tables, and for the admeasurement of heights by the barometer and thermometer.

The investigations relating to these different subjects are perspicuously exhibited, and the practical precepts deduced from them are in the main enunciated clearly. There are some omissions, however, which the editor might have avoided by following a rather different method: we allude principally to the omission of the nature and use of the arithmetical compliment, of spherical trigonometry, and of the most useful problems in nautical astronomy; as well as of a few serieses in the theoretical part of the work. Thus, when speaking of the binomial theorem, the Editor should have given, n n(n+1) (a+1)"="x e"x (1+ n(n+1)(n+2) + a+1 1.2(a+1)'

+

[ocr errors]

1, 2. 3 (a + 1) + &c. as a series which always converges the more rapidly, the greater a is with respect to unity. Among the logarithmic series at p. 6. it might have been advantageously added, that when is any positive number greater than 2, we shall have Log.nmx((n − 1) —— § ( n − 1 ) 2+} (n−1 ) 3 — § (n−1)*+&c.) a series converging with considerable rapidity: and by sub

-

[blocks in formation]

2

3

Log. n = mx (Z+ (2)~(Z) 3 + &c. )

[ocr errors]

a good converging series when n is any positive number greater than . The modulus in both series being denoted by m. Again, when treating of the modulus, at p. 8, it might have been added, that in any system of logarithms, the modulus is al

1

[ocr errors]

1

+&c)

way's equal to the Log. of (1+1++ + + 2.3 2.3.4 2.3.4.5 These and other curious consequences might have been readily deduced, had the Editor adopted the ingenious method of investigating logarithmic series discovered by Lagrange, viz by making the number ya *(1+a-1)* =((1+a—1)′′ )#, expanding the latter expression into a series by the binomial theorem, and then simplifying the result by supposing no. Indeed, we are much surprised that this method, and La'grange's analogous process for finding the log. when the number is given, have not yet found their way into any of our English books.

Farther, we should have advised the Editor, when treating the subject of Annuities on Lives, &c. instead of referring solely to Demoivre who commonly reasons on a wrong hypothesis, to direct his readers to the valuable performances of Simpson, Price, and Morgan.

But the principal alteration we would beg to recommend in a new edition of this Introduction, is a farther deviation from the geometrical method than the Editor has yet ventured to adopt; we advise this, not on account of any dissatisfaction with geometrical demonstrations, but for the sake of gaining space; since more topics may be investigated with equal perspicuity in smaller compass by the analytical method, Thus, after it is demonstrated geometrically that,

(a + b) ===

+

sin. (a

sin. a cos. b

sin. b. cos. a.

+

[blocks in formation]

sin. a sin. b.

=

every thing else relative to the arithmetic of sines and tangents, the expressions for multiple arcs, &c. becomes a matter of pure analysis. In like manner, after deducing the property of plane triangles, that

sin. A

sin. B

[ocr errors][merged small][merged small][merged small]

(where a and b are the sides respectively opposite the angles.

A and B), the whole of plane trigonometry may be investigated analytically. And again, in spherics, having shewn geometrically that, cos. a = coś. b cos, c. + cos. A sin. b sin. cos.b cos. q cos. c+cos. B sin. a sin.

cos, c = cos, a cos. b+cos, C sin. a sin, b the remaining doctrine of spherical trigonometry follows easily, by a mere transformation, and substitution of equations.

[ocr errors]

The alterations here advised need not be avoided on the supposition that they will make the introduction too abstruse: on the contrary, we think the change will rather simplify its general appearance. None of the processes which we recommend to be adopted, is so difficult, either in reality or in appearance, as the method of deducing the logarithmic serieses now introduced; with these changes, the introduction would have a greater air of uniformity, and room would be gained .for the admission of much more useful matter into the same 'space. We have given these hints of improvements, not with. a view of cavilling, or expatiating on defects; but from a real desire to render more beneficial to the public, a work which, even in its present state, we consider as richly deserving encouragement.

Art. XVIII. The Nature and Importance of a Good Education, A Sermon preached January 14, 1808, at the Rev. Mr. Gaffee's Meeting, New Broad Street, before the Promoters of the Protestant Dissenters' Grammar-School, lately opened at Mill-Hill, Hendon, Middlesex. To which are annexed, the Regulations of the Society, and a List of the Subscribers, &c. By David Bogue, A. M. 8vo. pp. 40. Price 18. Conder,

1808.

A Combination of the noblest powers with the best intentions in human character, is the greatest benefit to the community, the highest condition of our nature, and the just object of pursuit in all systems of educa tion. To promote in some degree this illustrious and beneficent object, among society at large, is the paramount purpose of our own labours; every institution, therefore, which is avowedly intended and evidently adapted to advance it, has especial claims to our cordial approbation. We do not hesitate in applying this character to the recent academical institution among Protestant Dissenters. And if any thing can increase our satisfaction at the commencement of an undertaking so congenial with our own in the rectitude of its primary design, it is the consideration, that among the particular class of our countrymen, who are precluded by their conscientious opinions from resorting to the grand national Seminaries, an establishment for superior classical and mathematical tuition, has long been peculiarly desirable. A few sentences extracted from an Address which has been circulated by the Founders, and prefixed to this Sermon, will enable the reader to appreciate the principles they entertain." "

"Though the School takes its denomination from the class of Christians in which it originated, and in which literary advantages are confessedly

most wanting, it is not intended either to exclude all but the children of Protestant Dissenters, or to attempt making proselytes of such children as shall be sent thither from another community. The former would be illiberal, the latter disingenuous; and both would constitute a gross dereliction of that just, candid, and manly system, which Protestant Dissenters should, above all people, hold themselves bound to maintain, when they say, "Let every one be fully persuaded in his own mind."

The Committee have engaged a very commodious house at Mill-Hill, in the parish of Hendon, a situation peculiarly pleasant and salubrious, where they hope many of the rising generation will imbibe the elements of sound literature and the principles of evangelical religion, and thus become a credit to the Institution, the joy of their parents, and blessings in every relation of social life."

Let us hope that Patrons will not be wanted in support of an Institution so adapted to the exigency of the churches, and to which the public attention would not have been solicited, but from a full conviction that the design is calculated to promote, far beyond the precincts of a party, the spirit of that religion, which is at once the ornament and the hope of man." pp. v.-vii.

Mr. Bogue has ably discharged the two functions of advocate and counsellor. His discourse is replete with just views and manly sentiments ; it includes a forcible train of argument in favour of the Institution, and a judicious exposition of principles to be observed in conducting it. The text is Prov. x. 1. A wise son maketh a glad father. Having first developed the constituent parts of a good education, good principles, and literary acquisitions he next specifies its fruits, capacity for business-habits of vigorous application-qualification for public employments-means of innocent relaxation a higher susceptibility of future improvement-the increase of knowledge in society-the power of influencing the public opinion. ability to serve the church of Christ-the promotion of religion and the divine glory. The style is energetic, rather than elegant; but well adapted to a discourse which is not declamatory, but argumentative. We must be contented with inserting the following specimens. The utility of early grammatical instruction is neatly explained.

A boy at school, sitting down to learn a lesson in Virgil, with his grammar and his dictionary by his side, presents an object by no means beneath the notice of a philosopher. Invention, judgment, memory, are all called into exercise: to make out his task, they must often be exerted with patient attention and perseverance; and it is only after repeated trials, that he succeeds. Among other effects of such a manner of spending time, the faculties of the mind are strengthened, and the capacity for every useful employment in life considerably enlarged.' p. 10.

That the general sentiments of a country be good, is a matter of the highest importance. But this will always depend on two things-on the number of christians, and on the influence which by their talents they have acquired over the public mind. It is by a comparative few, that the tone is given. Hitherto, unhappily, in most countries, public opinions have not been on the side of truth, and piety, and goodness: but false ideas on re ligion, on morals, on public institutions, and on the happiness of communVol. IV, M m

« 前へ次へ »