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Art. 37. The Spirituality of the Divine Essence. Preached before the

Associated viinisters and Churches of Hampshire, September 24, 1806, and published at the united Request of the Minister and Congregation of Farehamn, where it was delivered. - By John Styles. 8vo. Williams and Co.

In speaking of the Divine Nature, we employ words with very inadequate notions. The text of this discourse, (John iv. 24.) though in the shape of a positive proposition, conveys only negative ideas; and it is thus contemplated by the sensible preacher. It asserts that God is not matter, but possesses in his nature properties infinitely superior to and distinct from it; or is an eternal, independent, infinite, almighty, immutable, holy, and good spirit, having neither a body, por parts of a body. This doctrine is established by the marks of intelligence observable in the universe, by the creation of inferior spiritual beings, and by the testimony of revelation. Hence is deduced the importance of religion, the folly of idolatry, and the nature of acceptable worship.

To this elaborate discourse is added a suitable improvement.

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CORRESPONDENCE.
To the Editor of the MONTHLY Review.

30 April, 1807. Is your Review for February, p. 221, you ask a question, which

I beg lçave to answer, as it may prove highly detrimental to Messrs. Dring and Fage, by obstructing the sale of an article, of which they are the proprietors. Clarke's hydrometer is the only one used, or allowed by Government, for estimating the strength of spirits either in the Custonis or Excise ; nor is ihere, as far as I can learn, the least intention of disusing it.

• Permit me to add, that I prefixed the word Genuine, to distinguish my book from another with a title nearly similar : and I trust the Reviewer will allow that spurious arts, and spurious practices, are sometimes adopted in many ihings: and that many, who may possibly have learned both decinal fractions, and the extraction of roots, when at school, have forgotten them too far to apply them when they set about gauging, without the assistance of some remembrancer. To a candid reader, too, I apprehend, noihing I have given will be found superfluous; though aly such a one cannot deem the whole of Euclid's Elements Decessary

! I am, Sir,
"Your obedient humble Servant,

• PETER JONAS.'

We have received a letter from Mr. Winter, in which he intimates a want of candour in our account of his Sermon on the endless Dura. tion of Future Punishment : (Rev. for March, p. 335.) but we are rather surprized at such a charge, when we studiously endeavoured to distinguish between the preacher and his argument . We allowed Mr. W. to be what we believe he is, a very amiable man, though we could not suffer his reasoning to pass without animadversion, when we regarded it as subversive of all our notions of the divine rectitude. We grant that theologians, who take his side of the question, are induced by the laudable motive of deterring sinners : but they seem not aware that their argument, by destroying the moral attributes of God, would tend, it duly considered, to annihilate our love and reve. rence for the Deity, and in course to annihilate the first principle of religion. Scripture should therefore be judiciously interpreted on this point. That the meaning of words is influenced by the con. nection in which they stand, and by the subject to which they are applied, is very evident. In the present case, would not Mr. Winter smile with contempt at a writer who should quote the expressions of Scripture, " (verlasting mountains,and “everlasting bills," as proofs of the eternal existence of the world ? It is of little consequence whether xdatu or oùebgan be used. The latter is, as we remarked, employed in the text of the sermon: but we readily acknowlege an oversight on this point, as stated by Mr. W. in his letter, and have to observe that in Matthew 25. 46, to which he refers at p. 18, as the strongest evidence on the subject, the word xon.com and not oefen will be found - While we combat the doctrine of eternal punishment in another world, we certainly shall not hesitate to exonerate Mr W. from temporary censu!e at our insignificant tribunal, when it appears to have been erroneously bestowed.

We know nothing of the work mentioned by W. H. in a letter dated Lincoln, July 18, 1807 : but perhaps our acquaintance with it may commence betore the arrival of the time thus anticipated.

J.W H. has our thanks for his polite communication, and for the justice which he renders to our feelings in supposing that it cannot be otherwise than acceptable to us as literary men. We are scarcely aware, however, to what use we can apply it, since we are ignorant of the book to which it refers, but which we suspect to be a perio. dical publication not cognizable by us.

Our friend S. G. mistakes the meaning of the passage on which he founds his inference. When we spoke of Surveyors, (see Rev. for March, p 308.} we quoted the term used by the writer of the work then befure ve, but certainly did not design to pass a censure on & chitects. We know that the words are at present 100 often con. founded: but we intended then, and do now wish, to protest against such indiscriminate language :-a title, which is applicable only to scientific and well educated artists, should not be conferred on 1922surers and builders : - the context, we think, might have illustrated our meaning. To what precie description of persons the author of the book meant to refer, it is more within bis power than ours to ascertain.

The SPINDIX to this lol. of the Revie iv will be published with the Muniber for May, o: the ist of June.

THE

A P P E N D I X

TO THE

FIFTY-SECOND VOLUME

OF THE

MONTHLY REVIEW

EN L A R G E D.

FOREIGN LITERATURE.

Art. I. Mémoires présentés à l'Institut, &c.; i.e. Memoirs pre

sented to the Institute of Sciences, Letters, and Arts, by seve ral learned Men, and read at the Meetings. --Mathematical and

Physical Sciences. Vol. I. 4to. Paris. Imported by De Boffe, To the

antient volumes of Memoirs of the Academy of Paris are annexed, as forming a supplementary work, eleven volumes, intitled like that which is now before us, Mémoires présentés, &c. In these repositories were inserted Memoirs communicated by foreigners, and by other philosophers who were not members of the Academy, and to that appendix the present corresponds, bearing a similar relation to the volumes of the Institute.

A preface details the causes which have hitherto delayed the publication of this volume : but they are uninteresting to the English reader.

Papers on MATHEMATICS, ASTRONOMY, &c. The brief Astronomical Memoirs, here inserted, are

Astronomical Observations made at the National Observatory of Paris, Year 4th. to determine the Opposition of Mars and Jupiter. By M. BOUVARD. Determination of the Orbits of some antient Comets.

some antient Comets. By J. C. BURCKHARDT. APP. REY. VOL. LII.

Memoir

Gg

Memoir on Micrometers. By J. C. BURCKHARDHT.

Theorems on Polyhedrometry. By Simon LHUILLIER, Professor of Mathematics at Geneva.-If we call the faces of a Polyhedron, A, B, C, D, &c. and the Inclination of two faces AB, ab, of AC, ac, &c. then it is easily shewn that

A= B. cos. ab + C. cos. ac + D. cos. ad + &c. (1) Similarly, B = A. cos. ab + C. cos. bc + &c.

(2) C= A. cos. ac + &c.

(3) These equations the Genevese Professor chiefly uses for deducing the properties of polyhedrons. His process, although not very compendious, is plain and direct, and is conducted by successive eliminations; thus from equations (1) (2), A may be eliminated ; also from equations (2) (3), &c.

In the latter part of his memoir, the author gives two theorems relative to the centre of gravity; in which the distance of the centre is determined by the sum of the products of cach body into the square of its distance from any point. The first theorem of this kind was proposed by La Grange in the Berlin Memoirs of 1783; and it has since been given by that learned author in his Fonct. Analyt, and by La Place in his Mecaniq. Céleste. If m, m', m", &c. denote the bodies d, d',"', &c. their distance from any point, P, , , &c. shews their mutual distances; then the distance of the centre of gravity from P= square root of this quantity:

md + m'd' + &c. mm'll + mm" d': +&c.
m+m' +&c.

(m + m' + &c.)" Memoir on Equations of mixed Differences. By M. BioT.-By an equation of mixed differences, is understood one that expresses a relation between the differential or fluxionary coefficients of y, and the differences of y; the quantity y being supposed to be a function of x.

For instance, if y, =yt Ay, then
dy

dy

dy dx

dx

dx or, in English notation,

gui

= -yis an equation of mixed differences.

Equations of this kind arise from such questions as the following. It is required to find curves possessed of this property, that if tangents be drawn to the points of which the coordinates are x, y, x, y, the angle formed by these tangents shall be constant. This problem, expressed in the notation appropriated to mixed differences, is

perty, sidered

(arc tang. =))

dx If the variation of x be such that x-xor Ax=1, then

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= ax + f (sin. 2 7 x, cos. 2 + x) = ax +o

dy

consequently

dx

=tan. (ax +o) and y=b+s dx. tan. (a x +) Again ; Euler's problems, solved by indirect methods, (in the Novi Commentarii, t. x.) belong to the theory of equations of mixed differences : for instance, this problem ; it is required to find curves possessing this property, that if from any one of their points a normal be drawn terminating in the axis, this normal shall be equal to the ordinate erected at its foot, and so on. These conditions, expressed analytically, are y = y2 +

d x2

ydy * = x +

dx since ydy is the value of the subnormal. The solutions of these equations are ya = wo? +

ydy

go? dy?

dx

w being a quantity of which the difference is 1, and Q and

! being arbitrary functions of sin. 2 nw, cos. 2 T W.

This is not the first time that M. Bior has presented to the public the fruit of his researches on this difficult part of analysis. The third volume of the Memoirs of the Institute contains similar inquiries.

The general and complete Integration of the Equations of the Propagation of Sound; the Air being considered as of three Di. mensions. By MARK ANTONY PARSEVAL.- The first problem relative to the propagation of sound was that which was sug. gested by the problem of vibrating chords. The air being conG g 2

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