nently float. If a cylinder, (e. g.) having its specific gravity to that of the fluid on which it floats as 3 to 4, and its axis to the diameter of the base as 2 to 1, be placed on the fluid with its axis vertical, it will sink to a depth equal to a diameter and a half of the base; and while its axis is preserved in a vertical position by external force, the centres of gravity of the whole solid and of the immersed part will remain in the same vertical line-but, when the external force that sustained it is removed, it will decline from its upright position, and will permanently float with its axis horizontal. If the axis be supposed to be half of the diameter of the base, and be placed vertically, the solid will sink to the depth of 3ths of its diameter; and in that position it will float permanently. If the axis be made to incline to the vertical line, the solid will change its position until it settles permanently with the axis perpendicular to the horizon.

Whether, therefore, a solid floats permanently, or oversets when placed on the surface of a fluid, so that the centre of gravity of the solid and that of the part immersed shall be in the same vertical line, it is said to be in a position of equili brium; and of this equilibrium there are three species, viz. the equilibrium of stability, in which the solid floats permanently in a given position,the equilibrium of instability, in which the solid, though the two centres of gravity already mentioned are in the same vertical line, spontaneously oversets, unless supported by external force,-and the equilibrium of indifference, or the insensible equilibrium, in which the solid rests on the fluid indifferent to motion, without tendency to right itself when inclined, or to incline itself farther.

If a solid body floats permanently on the surface of a fluid, and external force be applied to incline it from its position, the resistance opposed to this inclination is termed the stability of floating. Among various floating bodies, some lose their quiescent position, and some gain it, after it has been interrupted, with greater facility and force than others.

Some ships at sea (e. g.) yield to a given impulse of the wind, and suffer a greater inclination from the perpendicular than others. As this resistance to keeling or pitching, duly regulated, has been deemed of importance in the construction of vessels, several eminent mathematicians have investigated rules for determining the stability of ships from their known dimensions and weight, without recurring to actual trial. To this class we may refer Bouguer, Euler, Fred. Chapman, and others; who have laid down theorems for this purpose, founded on a supposition that the inclinations of ships from their quiescent

quiescent positions are evanescent, or, in a practical sense, very small.

But ships at sea (says our ingenious author) are known to heel through angles of 10°, 20°, or even 30°, and therefore a doubt may arise how far the rules, demonstrated on the express condition that the angles of inclination are of evanescent magnitude, should be admitted as practically applicable in cases where the inclinations are so great. If we admit that the theory of statics can be applied with any effect to the practice of naval architecture, it seems to be necessary that the rules, investigated for determining the stability of vessels, should be extended to those cases in which the angles of inclination are of any magnitude likely to occur in the practice of navigation.'

A solid body placed on the surface of a lighter fluid, at the depth corresponding to the relative gravities, cannot change its position by the combined actions of its weight and the pressure of the fluid, except by revolving on some horizontal axis which passes through the centre of gravity: but, as many axes may be drawn through this point of the floating body in a direction parallel to the horizon, and the motion of the solid respects one axis only, this axis must be determined by the figure of the body and the particular nature of the case. se. When this axis of motion, as it is called, is determined, and the specific gravity of the solid is known, the positions of permanent floating will be obtained, first by finding the several positions of equilibrium through which the solid may be conceived to pass, while it revolves round the axis of motion; and secondly, by determining in which of those positions the equilibrium is permanent, and in which of them it is momentary and unstable.'

Such as we have now briefly stated are the general principles on which the author's investigations are founded. We cannot farther accompany him in his elucidation of them, in the problems to the solution of which they lead, and in the important practical purposes of naval, architecture to which they are referred. The whole paper, comprehending no less than 85 pages, is curious and valuable; it abounds with analytical and geometrical disquisitions of the most elaborate kind; and it serves to enlarge our acquaintance with a subject that is not only highly interesting to the speculative mathematician, but extremely useful in its practical application.

With this latter view, the author seems to have directed his attention to the various objects of inquiry which this article comprehends. They are such as intimately relate to the theory of naval architecture, so far as it depends on the pure laws of mechanics, and they contribute to extend and improve this theory. The union of those principles that are deduced from the laws of motion, with the knowlege which is derived from observation and experience, cannot fail to establish

the

the art of constructing vessels on its true basis, and gradually to lead to farther improvements of the greatest importance and utility. To this purpose, the author observes that

If the proportions and dimensions adopted in the construction ofindividual vessels are obtained by exact geometrical mensurations, and calculations founded on them, and observations are made on the performance of these vessels at sea; experiments of this kind, sufficiently diversified and extended, seem to be the proper grounds on which theory may be effectually applied in developing and reducing to system those intricate, subtile, and hitherto unperceived causes, which contribute to impart the greatest degree of excellence to vessels of every species and description. Since naval architecture is reckoned amongst the practical branches of science, every voyage may be considered as an experiment, or rather as a series of experiments, from which useful truths are to be inferred towards perfecting the art of constructing vessels: but inferences of this kind, consistently with the preceding remark, cannot well be obtained, except by acquiring a perfect knowledge of all the proportions and dimensions of each part of the ship; and secondly, by making and recording sufficiently numerous observations on the qualities of the vessel, in all the varieties of situation to which a ship is usually liable in the practice of naviga

tion.'

Of the remaining articles belonging to the class of Mathematics, &c. we can only subjoin the titles, viz. Mr. Jones's Computation of the Hyperbolic Logarithm of 10 improved: being a Transformation of the Series which he used in that Computation to others which converge by the powers of 80. To which is added a

Postscript, containing an Improvement of Mr. Emerson's Computation of the same Logarithm. By the Rev. John Hellins.→ Maniere elementaire d'obtenir les suites par lesquelles s'expriment les quantités exponentielles, et les fonctions trigonometriques des arcs circulaires. Par M. Simon L'Huilier, F. R. S. An Algebraical Demonstration of Newton's Binomial Theorem. By the Rev. W. Sewell, A. M.

The Meteorological Journal, as usual, closes Part I.; and Mr. Barker's Annual Register of the Weather, &c. makes its customary appearance in the second Part.

ART. VII. Mr. Wakefield's Edition of Virgil.
[Article concluded from the Rev. for March.]

Eneid 1.

V... W E think Heyne's punctuation better than that which Mr. Wakefield has adopted: yet perhaps we should not, with either, place a comma after cano. V. 2. Mr. W. has inserted Lavinia for Lavinaque: we deem the latter preferable.

Virgil

V.35.

Virgil is uncommonly partial to the conjunction que. Mr. W.'s punctuation, Vela dabant lati, is evidently just. V. 229. He adopts the reading of Heinsius and Bentley; Deorumque, for Deúmque: without necessity, in our opinion. V. 317. He prefers the old reading Hebrum to Eurum. The words are, without doubt, easily convertible: but which of the two was the original is another question; we prefer the former, but would have it written Ebrum.

En. II.

V. 120. Mr. W. is pleased with obstupuere animi. We are better pleased with animis; agreeably to Æn. ix. v. 123. Obstupuere animis Rutuli. V. 139. We cannot admire Mr. W.'s adoption of forsan for fors ad. Were we to change the common reading, it would be for that of the Venetian edition: Quos illi ad poenas, forsan, &c. V. 301. Mr. W. reads with the Cambridge MS. of Jesus Coll.: clarescit sonitus. Virgil uses both the singular and plural of sonitus; and it is our opinion that the plural is here more proper and poetical than the singular. If we wished to make any change, it would be that of crebrescunt for clarescunt. V. 546. He reads Ex summo, &c. Heyne had conjectured E. which he afterward found to be the reading of the Warsaw MS. V. 683. Mr. Wakefield had formerly contended for the reading molli: but he now is of a different opinion, and prefers mollis, i.e. molles. Second thoughts are sometimes best. V.697. We dislike not Mr.W.'s changing tum into dum: it certainly is more expressive.

Æn. III.

V.70. Mr. W. reads "Dant maria, et lene crepitans," &c. on the faith of Macrobius and Manilius. He might have added the authority of Euphony. V. 348. He reads thus: Et vultum lacrimis verba inter singula fundit.'-This is ingenious: but as Virgil never, elsewhere, uses fundo with this meaning, we prefer the common reading, and consider multum as a Græcism. V. 516. Mr. W. prefers the reading Pleiadasque to pluviasque: For, says he, Nihil obstat diphthongus, quam sequente vocali passim corripiunt Græcorum probatissimi-fa. cetus igitur habendus est cum sua crisi Heynius.

V. 91.

Æn. IV.

Lectionem conjecturalem (Clara for Cara) fidenter inserui; minus videtur convenire epithetum cara pari perpetuas rixas agitami. Quid, quod Virgilius patrem ejus [suum] subse quatur, ad Il. o. 184?

Ηρη με προεγκε, Διος κύδρη παρακοιτις.
E

REV. MAY, 1797.

We

We are inclined to be of Mr. W.'s opinion. V. 471. He adopts Markland's conjecture, pœnis for scenis.

Æn. V.

V. 163. He reads læva for lævas. We see no good reason for the alteration. V. 275. He justly prefers the reading saxi to saxo, but proposes another, which he thinks still more Virgilian: namely,

Aut gravis acto

Seminecem liquit saxo, lacerumque, viator.”

V. 487. He reads manus for manu, and has this note on it: Quis dubitet, nos locum ambiguum saltem, et nobis ineptum, reductâ literulâ, sanitati restituisse. Manus neæ pro ipso Ænea, figurâ solemni poetis.' - Notwithstanding all this, we doubt, and doubt very much, the propriety of this change. The present reading is neither ambiguous nor inept; and although manus Enea might poetically denote ipsum Æneam, yet we believe that manus alone, without the addition of the person to whom it belongs, is never equivalent to that person: no more than vis would denote Hercules, without the addition of Herculea. V. 706. Hac responsa dabat. “Salebrosa oratio, (says Heyne,) sequente imprimis isque his, &c. Malim Hic (Nautes) responsa dabat; i. e, dare solebat super iis que vel portenderet," &c. Mr. W. deems this emendation as clear as light, and admits it into the text.-We confess that we are of a very different opinion, and can see nothing hobbling nor difficult in the present reading. On the contrary, what sort of construction is this? Nautes, quem unum Pallas docuit et multa arte reddidit insignem-Hic responsa dabat, &c. V. 763. Here Mr.W. contrary to his usual custom, defends the common reading numen, and pities those editors who would substitute nomen.-Yet, were we to give an edition of Virgil, we would replace nomen. Nothing is more natural. Not only the sight, but the very name, of the sea was odious to those good matrons.

En. VI.

V. 361. He reads with the MS. of Jesus Coll. ignava for ignara: the former is certainly more elegant, and the change of letters was easily made.

V. 657. Pro lectione longè in ptissima, vescentis, non dubitavi substituere undequaque inculpabilem ex conjectura, vertantis. Sic Æn. vii. 784.

ad Homeri exemplum Il. s. 541. M. 49. Jam vero dictionem vertere sibi eundem usum vindicare in activa voce, tum noster Maro, Georg. ii. 33. .365. Æn. i. 103. satis probat cum multis aliis scriptoribus, tum res ipsa."'