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that the feed is always reckoned by the males, and more the females of a family, and (that) the name in a father's house could only be preserved by the male descendants' in which relpect Jesus Christ was not a son of David: there, fore this connexion is destroyed.

“ The doctrines of christianity, especially the preceptive ones, taken from his own mouth, cannot to all appearance be affected by insisting on the character of David, whether good or bad ; right forry would this author be if they rested on any such dependance. The divine tendency of these doctrines is so manifeft; they are so refined in their own nature, that they will ever claim the most exalted reverence from mankind, to ihem and to their glorious publisher, independant on all foreign contingencies, on all `former narrow tenets, and superstitious rites; which he has fo totally superfeded among his professors : and that they ever may is the fincere prayer of this abused writer. He therefore hopes an acquittal from this part of his indictment.”

How far these professions are sincere, it would not become us to determine ; but we cannot help dissenting from this writer's opinion, that christianity cannot be affected by such controverfies as this, concerning the character of king David; as we are firmly persuaded, that the connection between the Old and New Testament is so inseparable, that whatever tends to weaken the authority of the one, muft infallibly impair the foundation of the other. However, on his owni fuppofition, we shall take leave of this writer with a hint of advice, viz. that as we have no mean opinion of his abilities (whatever may be thought of his learning) we should be glad to see them more usefully employed.

We are not sorry, therefore, to find himn concluding with the following sensible declaration, viz. “ Religious contest is most disagreeable of all other : since it has ever been lealt decisive ; and most incentive of those propensities which the genuine dietates of pure religion directly tend to suppress. The writer, therefore, at the same time that he drops this controversy, has no present intention ever more to engage in any of the like nature.”

Before we entirely close this article, it may not be improper to mention the Author's poft fcript, in which he has treated Dr. Patten's miserable vindication of David with becoming spirit and contempt; at the same time that he does justice to the candour of Mr. Harwood, author of the Conversion of a Deift: in the appendix to which, Mr. Harwood had inserted some Remarks on the History of the Man after God's own Heart.

Marbematics.

Mathematics. With Eleven Copper-plates. By the late Reta Mr. William West of Exeter. Revised by John Rowe.

3$, in boards. Richardson. T HIS small manual, of which every page thews the band

T of a master, is a posthumous work; and is published for the benefit of the Author's widow, by the ingenious Mr. Rowe, who some years fince obliged the world with An Introduction to the Doctrine of Fluxions * The Editor informs us; that the present publication was selected from several, inathematical papers, written at different times, few of which were finished, and none perhaps ever intended for public inspection.

The first five pages contain a short introduction to the fuxionary calculus; the following thirty-eight, respecting the application of that doctrine to the solution of problems de maximis et minimis ; in which Mr. West has rendered that useful and difficult branch of the mathematics plainer, and more easy to be understood, than we remember to have seen it done by any other Writer ; and, at the fame time, has demonstrated, in a very elegant manner, the common method of making the fluxion of a maximum or minimum = 0.

The other part of this frall performance confists of tweuty-four miscellaneous questions, with their solutions : feveral of these are very curious, and the solutions neat and elegant. But the twentieth propofition, which, from a note at the foot of the page, appears to have been written in the year 1746, is of so interesting a nature, that it deserves particular notice. It is a new method of constructing a sca-chart; in which the meridians, parallels of latitude, and rhumbs, are all truly and geometrically projected in strait lines.

It is well known, that every projection of the sphere will give true solutions to all nautical problems, but that only is properly adapted to the mariner's use, where the rhumb, or the path a fhip defcribes in failing, according to the direction of the compaís, is represented by a strait line, because there will then be no difficulty in determining exactly the bearing of any two places, or the true course that a Thip must fail from one to the other.

* See Review, Vol. XIX. p. 528. Rev. July, 1759.

This This rectilinearity of the rhumb-line is the chief property of Mercator's projection; and, to accomplish this very thing, employed the attention of the most celebrated navigators after the invention of the compass; but was never brought to any degree of perfection, till performed by our ingenious countryman, Mr. Edward Wright: whose invention will render his name famous to all posterity. : This projection Mr. Weft has now perfected by the following proposition, which we shall give in his own words.

" If a rectangular piece of paper be turned into the form of a right cylindrical tube, and a sphere be inscribed therein, so as that the axes of the fphere and cylinder coincide, or, that the equator be the line of contact between the said tube and sphere, and all the points of the spheric furface' be projected or tranferred to the concave surface of the tube, by right lines proceeding from the center of the sphere, and terminating in the said concave surface of the tube: and then, if the paper be opened and I tretched upon a plane, it will present a chart, in which the meridians, parallels of latitude, and rhumbs are all truly and geometrically projected in right lines. Quære the Demonstration ?

DEMONSTRATION. i " With regard to the meridians, it is evident, that they are all thrown into right lines in the tube, being all parallel to its axis : and as the parallels of latitude are all projected

in circles perpendicular to the said meridians; so, upon open· ing the tube, &c. as aforesaid, they must necessarily become *sight lines also. The only thing therefore that requires a

demonstration is, that the rhumbs or loxodromics become :right lines, when the paper tube is extended as above. In · order to this, let the eye be supposed to be placed in the center of the sphere when inscribed in the tube, then every rhumb will appear to run round the concave tube in the manner of a

bottle screw in infinitum; and the only thing to be proved is, . that it keeps a parallel direction to itself every-where; or,

that it makes the same angle with all the meridians; or, that

the projected rhumb makes the same angle with the projected - meridian, as the true rhumb makes with the true meridian · on the surface of the sphere. These two angles do apparently

coincide, with regard to the eye placed as aforesaid ; that is, they are apparently equal to the eye in that situation ; and that they are also really equal is evident from this lemma, viz.

That the real and apparent bignets of any angle are the same, when the eye is placed perpendicularly over either of its fides,

or

· or when a perpendicular, dropt from the eye to the plane of

the angle, falls upon either of its sides. Now this is the very case with regard to both the angles in question ;, for the perpendicular from the eye falls on the angular point of the angle on the sphere; and a perpendicular from the eye falls on the meridian, which is one lide of the angle on the tube : consequently, the real and apparent bigness of each of those angles is the same ; and therefore, as they appear equal, they are really so. Q. E. D.

SCOLIU.M.; i concorso • It does not appear, that Mercator, or Wright, ever thought of this projcetion; for the meridian line here is manifestly a line of tangents ; whereas, in their projection, it is a collection of secants. It may be added, that Mercator's or Wright's chart is very faulty in the bearing of places ; but in this it is as' true and correct as upon the globe itself. I shall therefore presume to say, that this naval planisphere, or sea-chart, is the most useful for the purposes of Navigation ever invented; it being better than Mercator's in one im: portant respect, and equal to it in all others. .:

“ There are three projections of the sphere, the orthographic, the stereographic, and the nautical; the two first of these are well known to mathematicians : the last was in-, vented for the purposes of navigation, though hitherto a very imperfect and defective invention. The errors of the plain chart are corrected, in a great measure, by Mercator's or Wright's chart; though this latter is not a true projection of the sphere in any shape; nor indeed is it pretended to be such by Mr. Wright, one of its inventors, who represents it rather to be an extension of the spherical furface upon the “inner side of the concave cylinder in, which it is inclofed. Suppose (e. g.) the globe to be to inscribed in a cylindrie tube, as to touch it every-where in the equator, and consequently the axes of the globe and cylinder to coincide; then fuppose the tube to be of hard and unvielding subítance, as of marble or the like, and the globe to be of a soft substance, as a blad, der, and to enlarge itself as that does when Hown, until the globular surface becomes a cylindrical one, by applying itself to the internal or concave surface of the cylinder, both ways towards cach pole; Mr. Wrighi supposes all the parts of the spherical surface to increase uniformly in this extenfion; or, so as that the degrees of longitude and latitude every-where Thall fill continue to bear the same just proportion to each other, i. e, as radius to secant of the latitude. Whereas, the true projection (and which, I apprehend, will inuch better answer the purposes of navigation than either the plain chart or Mr. Wright's) is this, viz. Let the sphere be inscribed in a cylindric tube, as above ; and let all the parts of the spheric furface be transferred to the concave cylindric surface, by right lines drawn from the center of the sphere : the confequence of which is, that, when the cylinder is opened and fpread upon a plane, the meridians, parallels, and loxodromics will be all projected in right lines, as in Mercator's or Wright's chart, but in different proportions. And I take upon me to assert, that this is the first chart, or representation of the terraqueous globe, ever yet invented, in which the meridians, parallels, and rhumbs, are juftly and truly projected in right lines; for the latter cannot be fo projected in Mercator.”

answer

This specimen of Mr. Welt's * knowlege of mathematical subjects, and of his manner of treating them, will, we doubt not, excite the curious to a perusal of the whole performance.

Te is to this gentleman the world is indebted for several sensible and pious Discourses, published some time ago, on the Lord's Prayero See Review, Vol. XIX. p. 227.

MONTHL Y CATALOGUE,

For JULY, 1762.

POLITICAL., Art. 1o A Letter to the Right Honourable the Earl of · E******t, on the prefent critical Situation of the British

Miniflry. 8vo. Is. Nicoll. O FFERS fome reasonable conjectures relating to the fatal war

U in Germany, the uripromising war in Portugal, the monstrous increase of the national debt, and the importance of our bchaving with a proper firmness, whenever we come to settle the terms for a future peace, “If you would be great and glorious in your adminiftration, says he, to Lord E- t, fly the iteps of the late

M r , and act according to your conscience. If our arms are attended with the greatest success, without the nation's reaping the benefit of it at a peace, your reputation, like his, will blaze like a meteor for a time, and then vanilh for ever. In fort, my Lord, Mr. P-'s maxim, in his negociation, was, to reflore; let yours be, loʻRETAIN.

Art.

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