The Author has followed the French text of Martin, whofe tranflation he has corrected in feveral places; and, as a knowledge of the order of time, and the dates of events, contributes greatly to throw light on the hiftorical part of holy fcripture, he has placed, throughout, at the head of each page, under the eye of the reader the year of the world, and the year before Chrift, which answer to the facts or events mentioned in the text. In this he has followed the chronology of USHER illuftrated and confirmed by the labours of Wells and Bedford. The preliminary discourses and prefaces that are placed at the head of each volume, are replete with ufeful knowledge, and are perfectly adapted to prepare the Reader for ftudying the fcriptures to the beft advantage;-and the differtations, chronological tables, and excellent maps with which this work is enriched, in the proper places, fhew that nothing has been neglected that might render it worthy of the esteem and approbation of the Public, and a valuable fource of improvement and inftruction for those whom the Author had principally in view, in compiling it.

The preceding volumes of this Commentary were published many years ago, at different times. The first contains the book of Genefis, the fecond thofe of Exodus and Leviticus, the third Numbers and Deuteronomy, the fourth the two books of Samuel and Ruth, and the fifth Joshua and Judges. The fixth volume, which is now before us, and which was published but a few months ago, contains the two books of Kings, and shews that the spirit of refearch and induftry, which diftinguishes this learned and judicious Commentator, has not been relaxed by the advanced age to which, we are informed, he has arrived. The preface, the chronological table, and a curious and learned differtation on the retrograde motion of the fhadow upon the dial of Ahaz, 2 Kings xx. 8-11, are manifeft proofs that Mr. CHAIS has availed himself of all the modern difcoveries and improvements, whether in criticism or philofophy, that could tend to throw new light upon the difficult paffages of holy writ.

One of the excellent things that we have remarked in this Commentary is, the uncommon evidence and fuccefs with which the Author defends, by found logic, or luminous criticifm, thofe paffages of fcripture which have given occafion to the malignant cavils, or fpecious objections, of unbelievers. We shall hereafter give fome fpecimens of the notes which occur of this kind; as alfo of the others that are defigned to enforce the duties of morality, or to illuftrate interesting points of erudition.

ART.

ART. XII.

Novi Commentarii Academica Scientiarum Imperialis Petropolitane, &c. -New Memoirs of the Imperial Academy of Sciences at Peterfburgh. Vol. XX. For the Year 1775. Petersburgh. Printed at the Prefs of the Academy. 1776.

THIS

HIS collection, which, for the future, fhall have a place in our Review, which its importance to the advancement of mathematical and natural fcience fo juftly claims, has been. carried on with the greateft reputation and fuccefs, by the uninterrupted labours of the celebrated Eulers and other eminent men, to the twentieth volume now before us. The Mathematical Memoirs contained in this volume are feven in number, of which we shall give little more than the titles. This will be fufficient for the geometrical reader, who will feek the farther inftruction he may defire in the work itself.

1. Analytical Refearches concerning continued Fractions. By. M. D. BERNOUILLI.

This learned Author, together with Euler and Le Grange, have given a new form to the theory of this kind of fractions, which had already made a confiderable progress in the last century. The principal defign of the Academician, in this Memoir, is to examine the cafe, in which infinite fractionary expreffions may be defined by a finite canon, whether algebraical or tranfcendental.

II. Farther Refearches concerning the Nature of continued Fractions. By the fame.

III. Solutions of certain Problems of Diophantes. By M. L. EULER.

IV. Analytical Speculations. By the fame. V. Concerning the Refolution of rectilinear Polygons.

LEXELL.

By M.

In a preceding Memoir this learned Academician had fhewn how equations may be found which furnish the refolution of any rectilinear figure, when it is confidered only with respect to its fides and the rules which conftitute its outline. At prefent he gives fome fpecimens of the manner of treating thefe equations, fo as to come at proper and easy folutions. For this purpose he indicates fourteen problems, which relate to the refolution of quadrilateral figures, and he undertakes to refolve them by the equations he has found.

VI. Obfervations on a new and fingular Kind of Series. By Mr. EULER.

The PHYSICO-MATHEMATICAL CLASS contains eight Memoirs on the following fubjects:

I. and II. General Canons for any Tranfpofition whatever of stiff Bodies. A new Method of determining the Motion of tiff Bodies. By Mr. EULER.

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III. Some

III. Some general Theorems relative to the Tranfpofition of stiff Bodies. By Mr. LEXELL.

IV. An eafy Rule by which a Judgment may be formed of the Soli dity of a Bridge, or of any ather Body of a fimilar Corftruction, from the Knowledge we have of the Solidity of its Model. By Mr. EULER.

This object of inquiry is (if we mistake not) new; but whether new or old it is an object of the utmost importance, and has an evident relation to public utility. It is well known how many mistakes and difappointments have been occafione by reafoning from the powers and effect of a small model to thofe of the machine, conftructed with the fame proportions, and upon the fame principles, but of a much larger fize. It has been a general notion that a bridge, or any work of that nature, will be fufficiently folid if the model, after which it has been built, is capable of bearing a weight, proportioned to that which the bridge is to fuftain; but this notion has been found, by experience, to be illufory. This, however, does not prove that we cannot reafon from the small model to the large work that is conftructed upon it, but only that the true method of rendering fuch reafoning juft, has not yet been fufficiently unfolded. It is the defign of the ingenious Author, in this Memoir, to render fuch reasoning more conclufive, by afcertaining the degree of folidity in the model of a bridge, which will give us a full affurance that the bridge built conformably to this model will have the requifite degree of folidity.

V. Concerning the two Methods of determining both the Equilibrium and the Motion of flexible Bodies, and the admirable Conformity that there is between thefe Methods. By Mr. EULER. VI. and VII. Concerning the Preffure of Cords with respect to the Bodies that are placed under them, and the Impediment which their Motion receives from Friction.

The principal defign of Mr. EULER, in thefe Memoirs, is to lay down a method of determining the motion of both flexible and elaffic bodies which are not fituated in the fame plane. VIII. Concerning the Force of Oars of a new Kind, as alfo a Com

parifon between them and ordinary Oars. By Mr. Kraft. The theory of ordinary oars has been placed in the fulleft light by Mefirs. Bouguer and Euler. The queftion alfo propofed by the Royal Academy of Sciences at Paris, in the year 1753. produ ed feveral interefting illuftrations of the manner of navigating veffels, efpecially large ones, without the affiftance of the wind. The new kind of oars proposed by the learned Daniel Bernouilli, whofe answer to the question obtained the prize, feemed preferable to the ordinary ones in many refpects; and, nevertheless, thefe new oars have never fince

that

that time been an object of difcuffion, experiment, or practice. Mr. KRAFT, judging the subject worthy to be treated anew, undertakes here to unfold fully the theory of this new kind of oars, and to deduce from the first principles of mechanics and of the analytical method, the effects that may be expected from them.

The Memoirs relative to Natural Philofophy are four in number. The firft, Concerning the Foramen Oval, or oval Orifice, and its Ufe in directing the Motion of the Blood, by Mr. WOLFF, contains a curious difcovery in anatomy, and therefore deferves particular notice. The fyftem of Galen, with respect to the circulation of the blood in the foetus, adopted by Hervey, is well known, and was generally received, until the celebrated Mery, Member of the Academy of Sciences at Paris, gave an account of this matter diametrically oppofite to that of Harvey. This ingenious French anatomift affirmed that the blood did not pals from the right auricle of the heart into the left, but directed its courfe from the left auricle to the right by the foramen ovale, or oval orifice. The most eminent anatomists of the French Academy, fuch as Verney, Rohault, and Winflow were divided on this fubject, and Winflow propofed an hypothefis of his own, by which he meant to reconcile the two jarring fyftems, affirming that the blood paffed indifcriminately from the one auricle into the other, and only mixed, together, its conftituent parts in these paffages. Thefe difputes continued during the space of twenty years, and though the Academy de cided the matter in favour of Mery's opinion, yet all the more eminent anatomifts and phyfiologifts returned afterwards to the ancient doctrine of Galen and Hervey.

The Author of the Memoir now before us beats down, at one bold stroke, all these different fyftems, maintains that no anatomist has, hitherto, traced the real courfe which the blood follows in its circulation through the foetus, and affirms that it neither does nor can pafs from the right auricle to the left, nor from the left to the right through the oval orifice. The fubftance of his reafoning in fupport of this affertion may be reduced to the following propofitions: that there is a fynchronifm in the motion of the auricles of the heart, the fyftole and diastole happening, precifely, at the fame point of time. Now, the force that is neceffary to make the blood pafs from the one auricle into the other, cannot exert itself during the fyftole, because the two auricles are equally and fimultaneously contracted and throw out the blood with which they are filled. Neither can this force be exerted during the diastole, fince then the two auricles are dilated, and receive an extraneous blood from whatever part it comes: the one therefore cannot, at the fame time, exprefs into the other the blood which it contains,

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and

and therefore there does not exift any point of time in which the blood can país from one auricle into the other.

But if this be the cafe, what does Mr. WOLFF (it will be afked) fubftitute in the place of the fyftems which he overthrows, and what part of the animal ftructure does he reserve for the circulation of the blood in the foetus ? A new difcovery has furnished him with an anfwer to this question. One day as he was examining the heart of a new-born child, without any previous doubt concerning the truth of Harvey's fyftem, he perceived that the structure of the organ of circulation was very different from what it is commonly imagined to be. An accurate knowledge of this ftructure will render it eafy to point out the courfe which the blood takes in the foetus.

To form a just idea of the difcovery of Mr. WOLFF, it must be obferved that, having diffected, in the ordinary manner, the heart of a new-born child, he was not a little furprized to find that the aperture, on the left fide of it, was very different from that on the right, the first being formed by what is commonly called by foreigners the arc of Vieuffens and the valve of Euftachius, while the fecond is derived from the fame are and the valve of the foramen ovale. He eafily perceived that unless (contrary to all probability) the valves were coherent, there never could be any communication between the auricles. After an accurate examination of this ftructure, and a careful disfection of the foramen ovale, it appeared evident that the auricles had, in fact, no communication with each other, but were feparated by the inferior trunk of the vena cava, the aperture, which is difcernible in the right auricle being nothing more than the orifice of the cava, which effectuates its inofculation into that auricle, while the aperture that is seen on the left fide, and which is what is called the foramen ovale, is alfo no more than another orifice of the fame vein, which has its anastomosis or inofculation in the left auricle. In this manner, indeed, both the auricles have a communication with the vena cava; but between the one and the other there is no communication.

Having thus removed the kind of veil, that concealed the arrangement of these parts, and exhibited them under a new afpect, M. WOLFF, moreover perceived, that the vena cava, when viewed externally, afcends not only towards the right auricle, but alfo towards the left;-nay, that its correfpondence with the latter was ftill greater than with the former, its principal part being inofculated in the left auricle, and the smalleft part of it entering into the right. On examining the heart in calves and other new-born animals, our Academician always obferved the fame arrangement, according to which the foramen ovale is nothing more than the left orifice of the inferiour