In very rapid divisions, ascending or descending the scale in notes of equal length, no regard is had to accents; and, though the execution may be neat and articulate, an Italian, fond of simplicity, would say of it, as of a shake misapplied; non dice niente, it says nothing. Without accent there is no more melody in song, than in the humming of a bee; and without the regular arrangement of long and short syllables, there can be no versification. There are as many different accents in music as in speech, or modes of enforcing or enfeebling the meaning of words. There is a yes that says no, and a no that says yes. There are accents of spirit and accents of violence, of tenderness and of friendship. The voice of a feeling singer can modulate all these shades, or affect the hearer on the side of intellect as well as of sense. Dionysius Halicarn. regards accent as the source of all music. Accents is a poetical name for verse itself.

Winds on your wings to heav'n her accents bear

Such words as heav'n alone is fit to hear.'

Passions and affections are the food of vocal music. Dryden's Virgil, past. iii.

"Give to the musician (says Rousseau) as many images and sentiments to express as possible; for the passions sing, the understanding only speak:.”

The theological and billical criticism is most meritoriously distinguished by the total absence of party spirit. From the temper and erudition which the articles uniformly display, we are at no loss in attributing them to the learned and in defatigable editor. The most curious and important of those in the present

volume are Acts of the Apostles, Acts of Pilate, Alexandrian Manuscript.

The limits of our plan will not allow tive to the present volume, and our reus to enter into more particulars rela

marks on the second must be deferred to a future opportunity: we cannot take our leave, however, without saying a few words concerning the plates. These, thirty in number, are of such superior merit in every respect, as to rank far above the very best of those which have ever illustrated similar works. Messrs. Lowry and Milton, the artists employed, have exerted their talents to the full, and have produced engravings worthy of the work, and of their own high re putation; the subjects of the plates are also, for the most part, new, and obviously taken from original drawings.

A work thus auspiciously begun must necessarily increase in correctness and value as it proceeds: the references from the leading articles to others of inferior consequence afford a convenient method of amending errors, and supplying defects the gentlemen engaged will become habituated to the mode of writing which is best adapted to secure the great end of the design; and we do not doubt, that it will prove, when finished, a magnificent repository of science, honourable not only to those personally concerned in its execution, but to the language in which it is written, and the nation by which it is patronized.

A WORK of this kind must, from its very nature, abound in errors. It is not worth the bookseller's while to employ more than one person in the compilation of it, and the wisest man that ever lived would show his wisdom rather in declining than accepting of such a proposal. As a specimen, take the following article.

"DREAMS. The physicians who have accurately examined the state of their patients in every particular circumstance, have not omitted at times to inquire into their dreams, in those hours of sleep which their ill state allows them; and partly from experience, partly from reason and analogy, have found that there are many presages of diseases to come, and many indications of

such as are present (but unperceived, at least not seen in their full extent), to be had from what the senses suffer in dreams. Indeed if dreams are different from what might be expected from the business of the day, or the turn of thought before, they may always be looked upon as signs of a more or less distempered state of body, and the true condi tion of that state may often be better learned from them than from any other means. What has been observed by physicians in regard to the prognostics from dreams, may be summed up in the following manner; to dream of fire indicates a redundance of yellow bile; to dream of fogs or smoke, indicates a predominance of black bile; to dream of seeing a fall of rain or snow, or a great quantity of ice, shows that there is a redundance of phlegm in the body; he who fancies

himself among offensive smells, may be assured that he harbours some putrid matter in his body; to have red things represented before you in sleep, denotes a redundance of blood; if the patient dreams of seeing the sun, moon, and stars, hurry on with prodigious swiftness, it indicates an approaching delirium; to dream of a turbid sea, indicates disorders of the belly; and to dream of sceing the earth overflowed with water, or of be

ing immerged in a pond or river, indicates a redundance of watery humours in the body; to dream of seeing the earth burnt or parched up, a sign of great heat and dryness; the appearance of monsters and frightful enemies, indicates deliriums in diseases; and to dream often of being thrown from some very high place, threatens approaching vertigo, or some other disorder of the head, as an epilepsy, apoplexy, or the like."

6. Remarks on a mixed Species of Evidence in Mat ers of History. With an Eramination of a new historical Hypothesis, in the Memoires pour la Vie de Petrarque, by the Abbé de Sade. By ALEXANDER FRASER TYTLER, Esq. Judge Advocate of North Britain.

The Abbé de Sade, it seems, in his "Memoires sur la Vie de Petrarque," asserts, that Laura was a married wo man; and that the poet was her cicisbeo. Mr. Tytler, zealous for the honour of Petrarch and his mistress, enters into a formal analysis of the Abbé's hypothesis, and devotes sixty-eight quarto pages, to show that the affection of Petrarch for Laura was an honourable and virtuous flame." There are few persons, we imagine, who would not much rather accede to Mr. T's deduction, than read his paper.

7. Description of an Extra-Uterine Fatus. By Mr. THOMAS BLIZARD, F.R.S. Edinburgh, Lecturer on Anatomy and Surgery, and Surgeon to the London Hospital.

This case is marked with one or two curious circumstances. The subject of it was a woman who after having miscarried of her fifth child only five weeks before her death, was seized with violent pains in the lower part of the abdomen, and swelling of the belly, which proved fatal on the same evening. On dissection full two quarts of blood appeared extravasated into the pelvis, and in the middle of the left fallopian tube, a pouch

about the size of a pigeon's egg was found ruptured, the only apparent cause of the hemorrhage. The enlargement of the uterus, gelatinous effusion into its cavity, and closing of the mouth, indicated a state of pregnancy in some forwardness, which was confirmed by the traces of membranes (probably the chorion and amnios), in the bursten sac of the fallopian tube. The cause of the obstruction to the passage of the ovum, through this tube, does not clearly appear, since it remained readily pervious to mercury after death.

8. Meteorological Abstract, for the Years 1797, 1798, and 1799. Communicated by JOHN PLAYFAIR, F.R.S. and Professor of Mathematics in the University of Edinburgh.

That there was a real deficiency of crop in the year 1799, is at present, we believe, universally allowed; in confirmation of which we find the following interesting observation.

"The mean temperature of the whole year, is 46° 18', more than 1°5′ below the usual mean. But the mean temperature of the season of vegetation, computed from the 20th of March to the 20th of October, is no more than 51. 27, almost 5° below that of 1798. This deficiency of temperature may appear at first sight hardly adequate to that deficiency in the crop which is ascribed to it, But it should be considered that vegetation scarcely proceeds at all with a temperature under 40, so that this may not improperly be regarded as the point of heat at which ve getation begins, and the boundary, inasmuch at least as regards agriculture, between fruitfulness and sterility. Now 56° is the mean temperature of a good season in this country, therefore 16° of heat is the whole distance beas we know from the instance of 1798, and tween the mere germination of vegetables, and the fullest naturity they can attain in our climate. A deficiency of 5° therefore, which is nearly a third of the whole 10°,

must necessarily be accompanied with a great shortcoming in the maturity of all vegetable productions."

μ

9. A new and universal Solution of Kepler's Problem. By JAMES IVORY, Esq. Kepler's problem is solved in this paper by approximation. It is well known to propose the determination of the anomaly of the eccentric from the mean anomaly being given; and to do this, the writer takes unity for radius, m for the mean anomaly, for the anomaly of the eccentric, for the eccentricity, and then from a figure, in which it is evident that the difference of two circular sectors, whose bases are the mean and eccentric anomalies, is equal to the area of a triangle, whose base is the eccentricity, and one side radius, terminated by the extremity of the arc of eccentric anomaly, it appears that the perpendicular from the eccentric point let fall upon the radius produced, is equal tom-fe This perpendicular is made equal to x sin. μ. Therefore m-u

x sin. .

E

Now let m=212 μ=2», and consequently sin. = sin. 2›=2 sin. › × cos. ›, the following equation is obtained, "— X sin. x cos. v. Let e EXS then sin. (-)ex sin. x cos. v.

Now since the arches m and can never exceed 180°, the arches n and never exceed 90°,

For the first approximatione is made equal to , and this may with propriety be assumed for the maximum value of sin. × cos. v=1⁄2, and consequently n—, eX sin. x cos., can never exceed and being never greater than unity, - cannot in the extreme case of bc

2

ing unity, be greater than . Now the difference of two small arches, and the difference of their sines is nearly the (ny) same. Therefore ex sin.

nearly equal to s.

is

Hence from the equation sin. (n) =ex sin. x cos., we may obtain, the value of corresponding to this first value of e, which may be considered as a first approximation to half the arch of eccentric anomaly.

From this value we may proceed by the same method to other values, by substituting for, and making

(ド)

Then let be substi

X sin. tuted for e in the equation sin. (")= ex sin. x cos. », and let denote the corresponding value of, it will be a second approximation, and so on. Our limits do not permit us to enter into the ingenious proof that the series of approxi mations are alternately too small or too great, and that it converges to the true length of half the arch of eccentric anomaly with uncommon rapidity. These points being settled, the rule is investigated for computing the arc from the equation sin. (—)=ex sin. x cos., supposing and e to be given quantities: and to illustrate the method two instances are taken from Euler, the one to diameter of a semicircle, which shail didraw a chord from the extremity of the vide the semicircle into two equal parts; and the second, to draw from a given point, in the circumference of a circle,

two chords that shall divide the circle into three equal parts. Three approximations bring out very nearly the same conclusions with Euler in the first, as he makes one segment of the semicircle 4-* 39′ 12" 46"", our writer giving it 47° 39′ 12". In the second instance Euler makes one arch 30° 43′ 33′′, and by this method it is found to be after the second approximation 50° 44′ 11′′.

By applying this method to the planetary orbits, it is shewn that the error of the first approximation is of litcury, and some places of planets and tle account, except in the orbit of Mer

comets are determined.

The whole

forms a very valuable paper, which will be read with great pleasure by the profound geometrician, and be found of great practical utility to the astronomer.

10.

Description of some Improvements in the Arms and Accoutrements of Light Cavalry. Proposed by the Earl of ANCRAM, Col nel of the Mid-Lothian Regiment of Fex cible Cavalry, and F.R.S.

These proposed improvements might have been very properly laid before a board of general officers, but are entirely out of place in the transactions of a phi• losophical society.

11. A new Method of expressing the Coef cients of the Development of the algebrak Formula, (a+b2—2 ab. cos. ©)", by Means of the Perimeters of two Ellipses,

n

when ʼn denates the half of any odtl Number; together with an Appendix, containing the Investigation of a Formula for the Rec' fication of an Arch of an Ell pse. By Mr. W. WALLACE, assistant Teacher of the Mathematics, in the Academy of Perth.

This is a worthy companion to the last article but one. In the development of the proposed expression, namely A+ B cos. +C cos. 2+D cos. 3+, the degree of labour in calculating a competent number of terms is known to be very great; to obviate which, a method is devised in this paper, of effecting the solution by means of the perimeters of ellipses. This is shewn by a fluxionary process to be efficacious, for the two first coefficients of the series are made to depend on the rectification of an ellipse, and all the others are determined from them, by means of an infinite series. As the rectification of an ellipse is neces sary, the investigation of a formula for that purpose is considered in an appendix. The formula is not to be made intelligible in our limits, as it involves several fluxional equations, and various series, but it contains these advantages,

ART. IV. The Transactions of the THE great contributor to this volume, is the learned and excellent president, Mr. Kirwan, who has furnished eight papers; nor have his associates been wanting either in zeal or abilities; the present publication being, upon the whole, highly creditable to the institution. The first article is,

Royal Irish Academy, Vol. VIII. 4to. into complete fusion; and that by gradual cooling, the several ingredients will again separate according to their respective degrees of fusibility, yet that there still remain difficulties which cannot be overcome. Quartz is certainly by far the least fusible of the three, and therefore would concrete the first, and from being deposited in a fluid medium, ought to occupy the lowest parts and to be more or less crystallized, while the felspar, becoming solid by mere cool

Mr. Kirwan is a strenuous advocate for the aqueous formation of rocks and mountains; Sir James Hall, on the contrary, is induced to consider granite, porphyry, and all the rocks of trapformation, as owing their present appearance to the action of subterranean heat. With regard to the igneous origin of granite, Mr. K. objects, and in our opinion very justly, even allowing it to be a fact, which however has never been proved experimentally, that granite composed of quartz, felspar, and mica, in the usual proportions, may be brought

ing upon the quartz. This, however, is not agreeable to actual appearances; the quartz is mingled with the fel spar, and is not crystallized except when lining the inside of cavities, and in some instances is even impressed by the crystals of felspar; thus clearly shewing the latter to have been solid and completely formed while the former was in a fluid, or, at least, in a soft

state.

A much stronger argument, however, in favour of the volcanic origin of basalt and the other rocks of trap-formation, is deduced from the experiments

of Sir James Hall. It had been objected, that though these minerals are fusible at a moderate heat, not exceeding 55° Wedgewood, yet the result was a homogeneous glass possessing the vitreous fracture and other external characters belonging to this mode of aggregation; Sir James, however, discovered, that although a perfect glass was certainly the first result, yet by increasing the heat and cooling slowly, all the characters of vitrescence disappeared, and the mass assumed an earthy appearance with the rudiments of crystallization, bearing a near resemblance to the natural whins. Mr. Kirwan is inclined to attribute the

earthy appearance and fracture of the acknowledged lavas to their slow refrigeration, but maintains that this very interesting and important discovery of Sir James Hall's is not conclusive with regard to the igneous origin of the rocks of trap-formation, or as they are called in Scotland, whins; because, 1st, These contain frequently calcareous spar and zeolite, and as the former of these holds carbonic acid and the latter water, as an essential constituent part, it is not easy to conceive how they could have been vitrified or fused. 2nd. The natural whins lose by being heated to redness, about five per cent. of volatile matter, whereas even the most ancient lavas lose none in similar circumstances. 3d. The external characters and other properties of the artificial whins bear only a general similarity to the natural ones, but differ in various important particulars; and 4th. The college of Dublin is possessed of fragments of basaltic pillars, in which marine shells are imbedded.

2. An Illustration and Confirmation of same Facts, mentioned in an Essay on the priive State of the Globe. By RICHARD KIRWAN, Esq. c.

According to Buffon and other French theorists, the race of fishes existed previous to the emersion of any of the solid part of our globe above the primeval waters, which covered its surface. According to the Mosaic cosmogony, which Mr. Kirwan, in the essay alluded to, undertakes the defence of, the creation of fish was posterior to this event. Mr. K. has therefore asserted, that no remains of marine animals are found imbedded and incorporated in masses of

stone, at a greater height than 9000 feet above the actual level of the sea. But Den Ulloa found petrified shells on a mountain near Guancavelica, in Peru, at the height of 13,869 feet. The object of the president, in this memoir, is to shew that the altitude of this mountain is greatly overrated, which he does, first by pointing out the imperfections of the barometer at the time when Don Ulloa made his observations, and se condly, by shewing from the same au thor, that the mountain was every where habitable, and therefore could not be of the height supposed.

3. An Essay on the Declivities of Mountains.

By RICHARD KIRWAN, Esq.

This, like many of the papers of Mr. Kirwan, is incapable of analysis, on account of the quantity and condensation of the matter that it contains. The object of the author is to shew, that the south and south east sides of primitive mountains are steep, while their northern and western sides form a much more obtuse angle with the horizon, on account of the secondary strata by which they are covered. Numerous authorities are cited to prove the fact, and the explanation of it is referred to the particular direction of the tides and currents of the primeval ocean.