M. WOLFF obferves that, as this fubftance lies between the parts which it connects, it becomes neceffary, in order to examine it, to separate them: but, in fo doing, this glutinous matter breaks into threads, which anatomifts have confidered as its natural state, and as conftituting its texture. He examined two contiguous muscles of the arm, covered and connected by this fubftance: their furface appeared as if they had been bare, only that the fibres were lefs diftinct, and the colour was lefs vivid but he could not difcern any filaments or lamellæ, nor any cells or pores. He then very gently feparated them a little, in order to fee what lay between them, and this be alfo found to be a smooth fubftance, exactly fimilar to the former :-but no fooner did he separate these muscles with greater force, than he faw the intermediate fubftance divide itfelf into filaments, which at first adhered to the parts that they covered, but afterward feparated, and became complete threads. When he brought the muscles together again, thefe filaments united and formed a fmooth furface.

In feparating the two parts which contain between them this fubftance, as it is almoft fluid and of confiderable tenacity, it will often happen that the external air penetrates into it, and thus produces a number of bubbles or vefficles. This has been confidered as a proof of its cellular texture, but our author afferts the contrary; because they are of various fizes; and becaufe, when examined by the microscope, they appear to be merely air-bubbles, and not organized cells communicating with each other: what has been taken for lamellæ, is, according to M. WOLFF, nothing elfe than the dried air vefficles. This fubftance, which is confidered as the cellular membrane, is faid to be white: but he affirms that, in its natural ftate, it is perfectly tranfparent, and has no colour; though, like other transparent substances, it appears white when its continuity is broken.

Concerning the Manner of making Steel from the Iron Ore of Siberia. By M. HERMANN.

Formerly, all the fteel manufactured in Ruffia was made by the fufion of iron bars: but it was deemed more advantageous to make it directly from the ore; and, with this defign, the direction of the forges near mount Oural was conferred on the author of this memoir; who defcribes the process adopted at the works at Pyfchminfk, near the river Pyfchma, about twenty-two werfts from Catharinenburg. Thefe works have furnished, from the year 1786 to 1789, about ten thousand pouds or 400,000 pounds of fteel, most of which is employed by the armorers at Toula. M. HERMANN obferves that, in order

order to obtain a good mafs of crude fteel, it is neceffary to heat it in a bottom of fand; for coal is apt to render it ferruginous, which he afcribes to the badnefs of the ore.

ASTRONOMY.

Concerning Two Aftronomical Problems.

By M. SCHUBERT.

This ingenious aftronomer proposes, in the former of these problems, a method by which a meridian line may at any time be afcertained without any obfervation of altitude, or any other inftrument than a watch, or time keeper. All that is required is to obferve the fame ftar three times fucceffively, fo as to have two azimuths, and the two correfponding horary angles; which may be done by means of three vertical threads, and a good watch. The general equation, by which the problem is refolved, is of the third degree: but the author takes notice of two particular cafes in which it becomes much more fimple, and which are, when the ftar is in the equator, and when the angles obferved are very small. The one or the other of these conditions is generally in the power of the observer.

The object of the fecond problem is to afcertain the latitude of a place by means of a watch and telescope fixed in a certain parallel of altitude, by which two or more ftars are to be obferved in the fame almacantar, each before and after its culmination. This method is analogous to that of equal altitudes.

Continuation of the Obfervations on the Lunar Tables inferted in the fifth Volume of thefe Tranfactions. By M. KRAFFT.

M. KRAFFT here proceeds in his transformation of the formulæ refulting from the theory of the moon's inequality of motion, and gives those which exprefs the latitude and the horizontal parallax of this planet.

On an Eclipfe of the Sun obferved June 4th, N. S. 1788. By M. STEPHEN RUMOUSKY.

We fhall not trouble our readers with any particulars of this memoir, as the refult of the author's obfervations did not coincide with those of his colleagues; and, though it appears that there was an error in the corrections applied in the calculation, their true value is not yet ascertained.

This volume, like the former, concludes with extracts from the Meteorological Journal kept by the academy during the year 1788; in which it appears that the thermometer fell on the 20th of January and the 23d of December, to 24 degrees of Réaumur's, or 23! below o, of Fahrenheit's feale on the 18th of July it rofe to 26 degrees of Réaumur's fcale, which is equal to 92% of Fahrenheit's.

APP. REV. VOL. XIII.

M m

In

In the hiftorical part of volume VII. we find a short account of the life of M. James Bernoulli, who died on the 3d of July 1789. He was born at Bafil in October 1759, and his family was remarkable for a, number of celebrated mathematicians. The names of his grand-father and grand-uncle, John and James Bernoulli, of his uncle Daniel, of his father John, and of his elder brother of the fame name, who still lives at Berlin, are well known in the republic of science. The gentleman to whom this article relates was educated, as moft of his relations had been, for the profeffion of law but his genius led him very early into the ftudy of mathematics; and, at twenty years of age, he read public lectures on experimental philofophy in the univerfity of Bafil, for his uncle Daniel Bernoulli, whom he hoped to have fucceeded as profeffor. Being disappointed in this view, he refolved to leave his native place, and to feek his fortune elsewhere; hence he accepted the office of fecretary to Count Breuner, the emperor's envoy to the republic of Venice; and in this city he remained till the year 1786, when, on the recommendation of his countryman M. Fufs, he was invited to Petersburgh to fucceed M. Lexell in the academy. Two months before his death, he was married to the youngest daughter of M. John Albert Euler.

MATHEMATICS.

Of the memoirs in this clafs feven are by the late M. EULER, and two by M. Fuss, which relate to the differential calculus. Concerning thefe we fhall not enter into any particulars, becaufe, though fome of them well deserve the attention of mathematicians, they are not eafily abridged; and because, however we might gratify our own tafte by entering into a detail of their contents, it would not perhaps be very interefting to the majority of our readers. Of the other memoirs, which are on fubjects lefs abftrufe, and the practical utility of which is more immediately obvious, we fhall give a short

account.

On the geographical projection of an elliptic fpheroid. By M.

SCHUBERT.

When a map is intended to reprefent no very extensive part of the earth's surface, it may be confidered as that of a cone unfolded, which will be a projection very nearly exact. The memoir before us contains the formulæ for calculating the point at which the axis of the cone interfects that of the earth, and for determining the feveral degrees of latitude and longitude. M. SCHUBERT alfo adds rules for laying down any given area in the fame proportion that takes place on the furface of the

10

elliptic

elliptic spheroid. In this projection, the meridians and parallels are right lines, which interfect each other at right angles : but the formulæ that exprefs the arcs of latitude, and which in a spherical projection are very fimple, are here rather com. plicated, being compofed of circular and logarithmetical quantities. He likewife fhews how the projection, invented by De L'Ifle, may be applied to the fpheroid, fo that the diftances of the places reprefented may be laid down in their juft proportion. In this method, the meridians are right lines, which meet in a point three degrees beyond the pole; and that point is the common centre of the parallel circles. Tables are added, calculated for every degree of the meridian, on the hypothefis of Sir Ifaac Newton, as well as on that of De la Caille, concerning the proportion between the equatorial and polar diameters of the earth.

On the method of finding the momenta of forces with relation to a given axis. By M. EULER.

In order to find the momentum of a force, acting in the direction of a given right line, which we may call the directrix, and with relation to a given axis, the common rule is to multiply the force by a perpendicular drawn to the axis, from any point affumed in the directrix, and by the fine of the inclination of the directrix to a plane paffing through the axis and perpendicular-but, in applying this rule to practice, and in determining by calculation the perpendicular and inclination which occur in this expreffion of the momentum, the formulæ become very complicated and intricate. In order to obviate this inconvenience, M. EULER obferves that, as the perpendicular to the axis may be drawn from any point of the directrix, this point ought to be fo taken that the perpendi cular may be the leaft poffible; by which means the process becomes eafy, and the expreffion of the momentum very fimple. This he proves in a fatisfactory manner, and applies the expreffion of the momentum, thus obtained, to the folution of the following problem in mechanics: the three momenta being known, which a force, acting in a given direction, exerts on three fixed axes perpendicular to each other, and all paffing through the fame point A, to find the momentum which the fame force will exert on a fourth axis, paffing through the fame point A. memoir concludes with a demonftration that, whatever be the forces which act on a body moving on an axis az, if the momen ta, with respect to the three other fixed axes, af, ag, and ah, perpendicular to each other, be P, Q, and R, the momentum, with relation to the axis az, will be f P+g Q+ h R ; in which expreffion, the letters, f, g, and b, denote the cofines of

M m 2

The

the

the inclinations of the axis az with the feveral fixed axes. In a fecond memoir on the fame fubject, M. EULER applies ftatical principles to the above propofitions; by which means they are refolved in a more fimple and elegant manner.

An account of the experiments made in Ruffia concerning the length of a pendulum which swings feconds. By M. KRafft.

Thefe experiments were made at different times, and in various parts of the Ruffian empire; M. KRAFFT has collected and compared them, with a view to inveftigate the confequences that may be deduced from them. Hence he concludes that the length of a pendulum which fwings feconds in any given latitude, and in a temperature of ten degrees of Réau mur's thermometer, may be determined by the following equation:

x=(439,178+2,321. fine x2) lines of a French foot. This expreffion agrees, very nearly, not only with all the experiments made on the pendulum in Ruffia, but alfo with those of Mr. Graham, and those of Mr. Lyons in 79° 50′ north latitude, where he found its length to be 441,38 lines. It alfo fhews the augmentation of gravity from the equator to the parallel of a given latitude λ: for, putting g for the gravity under the equator, G for that under the pole, and y for that under the latitude A, our author finds

y=(1+0,0052848. fine x2).g and confequently G=1,0052848. g. From this proportion of gravity under different latitudes, M. KRAFFT deduces that, on the hypothefis that the earth is a homogeneous ellipfoid, its oblateness must be ; inftead of 1, which ought to be the refult of this hypothefis: but, on adopting the fuppofition that the earth is a heterogeneous ellipfoid, he finds its oblatenefs, as deduced from thefe experiments, to be ; which agrees with that refulting from the measurement of degrees of the meridian. This confirms an obfervation of M. De la Place, that, if the hypothefis of the earth's homogeneity be given up, theory, the meafurement of degrees of latitude, and experiments with the pendulum, all agree in their refult with respect to the oblatenefs of the earth.

On the motion of a double cone, apparently afcending along an inclined plane. By M. A. KONONOFF.

In this memoir, which confifts of algebraical calculations, M. KONONOFF endeavours to determine the forces acting on a body of this form, whatever may be the angle of the inclined planes. Thefe theorems he applies to bodies compofed of two truncated cones, and of two cones joined at their apices.

PHYSICS.