In the hiftorical part of volume V. we find extracts of two letters to the fecretary; the first from M. FRIES, written from Ouftioug-velikoi, a town in the government of Vologhda, one thousand werfts from Petersburgh, in 60° 58' north latitude, giving an account of the very fevere cold obferved there. Some obfervations on this fubject may not, perhaps, be unacceptable to our readers. On the 14th of November 1786, N. S. in the morning, the mercury in Reaumur's thermometer had fallen to 30 degrees below the freezing point. M. FRIES then expofed fome purified mercury in a china cup to the open air, and found it frozen to the confiftence of a pafte the next morning at three o'clock, when the thermometer had fallen to 34°: but, in three hours' time, it rofe again to 30°, and the mercury, which had been frozen, regained its fluidity. On the 13th of December, from fix in the evening till three o'clock the next morning, the thermometer ftood at 51°. M. FRIES found the mercury, which he had expofed to the air, frozen fo as to be quite hard; he brought it into his apartment, and broke it into three pieces; in the room it thawed in two minutes: but the cold which he felt on handling it was almost insupportable. On expofing it again to the open air, it became fo folid in lefs than an hour, that it was perfectly malleable. During this exceffive cold, the weather was very calm, but foggy; the birds dropped down dead; and the dogs feemed to have a foreboding of it; for, before it came on, they ftretched themfelves out on the floor, and howled in a very unusual manner. On the 19th of January 1787, the mercury in the thermometer fell to 60°, and, foon after, funk entirely into the bulb, where it was frozen.

Hence it appears that mercury, expofed to the open air, is much fooner affected by the cold, than what is contained in the thermometer; which might indeed have been concluded à priori: but M. FRIES obferves that thermometers do not indicate the true temperature of the air, when it is below 30 degrees; unless it be of fuch duration that the inftrument can be entirely penetrated by the cold; as was the cafe in the laft experiment; and even then the tube must be warmed by the application of the hand, to prevent the mercury in it from freezing before it can fink into the bulb.

The other letter is from M. DE CAROSI, an officer in the Polifh fervice, and gives an account of an earthquake at Mogula near Cracovia, the 3d of December 1786. It lafted five feconds; its direction was from fouth to north, and the motion was ofcillatory.

The fupplement contains a paper by M. F. LowITZ, on what he terms the dephlogisticating power of charcoal, and its

utility

utility in various chemical operations. He found that charcoal has the property of purifying acids from the brown colour and empyreumatic odour, which they are apt to contract in their preparation. In this view, he experienced its utility in making the acid of tartar, the terra foliata tartari, the acetum vini, the alcobol aceti Weftendorfi, and the crematum frumenti. From an experiment performed by M. Leichtenftein, in confequence of these difcoveries, it appeared that the acid of nitre was not merely dephlogifticated, but deftroyed by the charcoal; and that the refiduum of the coal became foluble in water like a falt. Hence our author was induced to make the experiments here related, in order to determine whether charcoal had a fimilar effect on other acids: this it appeared to have on the muriatic acid, but not on acid of tartar, nor on diftilled vinegar. On mixing powder of charcoal with pieces of beef, which had been exposed to putrefaction, he found that it deprived them of their fetor, and left them only the odour of pure volatile alkali.

The MATHEMATICAL class of memoirs contains feven paper by the late M. EULER, most of which, relating to the integra tion of differential equations, we shall omit. One, however, which contains an application of Sir I. Newton's theorem for the evolution of binomial powers, to fractional exponents, deserves our attention, on account of its general utility, as well as its perfpicuity. For this purpofe, M. EULER ftates (1+x)=1+Ax+Bx2+Cx3+, &c. in which expreffion A, B, C, &c. are determined by the experiment n. If the exponent be increased by an unit, the feries may be thus expreffed: (1+x)+'=1+A ́x+B2x2+C ́x3+, &c. and, if the several terms of these feries be compared, they will be A'-A=1, B'-B-A, C-C-B, &c. thus N-N=M. Then if N=xn, N'a (n+1), and N'-N-M=a: but if Ma then neceffarily Nan. In the fame manner, it is demonftrated that if we make 2 aa, and Man, we fhall have Nan (n-1); and univerfally, if Man (n-1) (n−2)

....

(n-λ) then N=— an (n−1) (n—2).............. (n—λ—1);

but as M, and N, denote any two following terms in the feries A, B, C. &c. the general evolved equation may be applied to each of the equations already found. Thus, as A'-A=1, we have M1 and N=A=n. Then, becaufe B'—B=A=n, we have here M=n; and N, which, in this cafe, correfponds with B, in (n-1) &c.-Hence it is eafy to fee that the exB,=n ponent n is not neceffarily confined to whole numbers, but may be expreffive of fractions, and of irrational, or even imaginary quantities.

L14

The

The remaining memoir under this clafs is by M. SCHUBERT, On the Geographical Projection of an Elliptic Spheroid.

The intention of this paper is to inquire whether the error, refulting from projecting the furface of the globe as that of a fphere, be really of fuch importance that it ought not to be rejected; and whether the rules for the projection, according to the oblate figure of the earth, be fo very difficult as fome have imagined. M. SCHUBERT adopts the Newtonian hypothefis of elliptic meridians, and confiders the ftereographic projection of a parallel, and of a right sphere. In the former, the meridians are right lines, and the parallels concentric circles, the radii of which are fomething greater than they would be in the projection of a sphere. This difference, however, never exceeds 1 of the radius of the equator, and may therefore fafely be neglected. In the projection of the right sphere, the meridians and parallels are ellipfes, the axes of which are in the fame proportion, as are those of the oblate fpheroid; the axes of the meridians increase as they approach the middle of the projection, in the ratio of the fecants; and the axes of the parallels increase in the ratio of the tangents of their distance from the pole: but the greater axes will always be parallel to the equator. The rules, which our author gives for the conftruction of the parallels, and for the divifion of the map into degrees of latitude and longitude, are plain and easy.

The PHYSICO-MATHEMATICAL clafs contains three theoretical memoirs on the curves formed by the compound motion of cylindrical bodies, and on the vibration of elaftic lamina: but they are so very abftrufe, and have fo little immediate prac tical utility, that we fhall not detain our readers with them. PHYSICS.

On the Mufcular Fibres of the Heart. By M. WOLFF. This anatomift here inveftigates the action of the middle ftratum of fibres of the right ventricle, which he described in the preceding memoir; (p.483.)the general use of them is to contract the ventricle :-but, belide this general tendency, there are fome fafciculi, which appear formed to produce more particular effects. Among thefe are three muscles, to which M.WOLFF gives the appellation of adductores arteria pulmonalis, by which the arterious orifice and the pulmonary artery are drawn toward the ventricle, while the latter expels its blood into the artery; they ferve alfo to ftrengthen the pulmonary artery, and enable it to bear the action of the blood impelled with a force which otherwife might occafion fatal aneurifms. There are also two mufcles which our author calls the contractor interftitii valvularis, and the aorticus; and, we are told, they both ferve to contract

the

the interslitium valvulare, and to express the blood which gets to it, when the ventricle is full: thefe mufcles are alfo of ufe in clofing the venous orifice of the ventricle during its fyftole, and in preventing the blood from returning into the right finus. Another muscle, which is called the posterior pulmonalis, and is remarkably powerful, contracts the arterious cone, or that part of the ventricle out of which the blood is immediately poured into the pulmonary artery. The fituation and direction of these muscles cannot well be explained without the plates by which the differtation is illuftrated.

Two Obfervations. By M. N. SocOLOW.

The first part of this Memoir contains an account of a preparation for killing worms, or other infects, that are destructive to the produce of the garden and the field. It is composed of three parts of lime water, and two of a faturated folution of the fixed alkali in water; with which the author directs the plants and trees to be moiftened, afferting that, without injuring the vegetable, it will deftroy all the infects that prey on it. The remainder of the paper relates to the revivification of infects which had been apparently killed in fpirits of wine, by covering them with warm ashes.

Defcription of an Aorta extended to an unusual Size, ruptured and offified in feveral places. By M. WOLFF.

The cafe here related is that of a man about forty years of age, and apparently in perfect health, who died suddenly, with out any previous complaint. On opening the body, the pericardium was found fo extended as to appear like a large bladder, which entirely filled up the anterior part of the thorax, and had driven back the lungs into the pofterior. When it was opened, between three and four pounds of fluid blood ran out, and a pound and a half of coagulated blood remained in it. When this was removed, M. WOLFF discovered a rupture of the aorta, in a longitudinal direction, about two inches in length, which appeared like a wound made with a knife on the pofterior surface, clofe to the arterious orifice of the left ventricle. The whole of the aorta was vitiated, had loft its elafticity, and was extended to an uncommon magnitude in length, as well as in diameter: the part inclofed in the pericardium was seven inches and four lines in circumference; and the length, from its origin to the end of the flexure, where it proceeds in a right line along the vertebræ of the back, was twelve inches and a half. On opening the artery, a number of small pieces of bone were discovered between its two coats; the author counted thirty-eight, one of which was an inch long, and feveral were half an inch in diameter: they were of various

fhapes,

fhapes, but all had very fharp edges; and to their action on its coats, the dilated state of the aorta, and its fatal rupture, are afcribed.

Defcription of a new Species of Gymnotus. By M. ZUIEW. This fifh was fuppofed, by Gronovius, and after him by Linné, to be a variety of the Carapo: but M. ZUIEW maintains that it is a diftinct species; from its colour, he calls it Gymnotus albus, but he obferves that it ought to be diftinguished from the albifrons, defcribed by M. Pallas. It is less than the carapo, and its lower jaw is longer than the upper.

A Chemical Examination of an Obfervation of M. de Caref concerning the Tranfmutation of Gypfe into Chalcedony. By M. J. G. GEORGI.

From a variety of foffils and petrifactions collected in the neighbourhood of Cracovia, M. De Carofi attempted to prove the tranfmutation of calcareous ftone into filex, of gypfe into chalcedony, and feveral fimilar changes of primary ftones. Some of thefe fpecimens were fent to the academy, and our author was commiffioned to examine them. Among them was fome gypfe, which M. De Carefi fuppofed to be advancing in its progress toward chalcedony: but, after keeping it during feveral years exposed to all the inclemency of the weather, and trying every method that art could fuggeft to accelerate its tranfmutation, it was found, by chemical analyfis, to have undergone no alteration.: fo that the hypothefis appears to be, as moft philofophers have believed, without any foundation.

ASTRONOMY.

Effay on M. Euler's Lunar Tables, with the Defign of giving them under a new Form, which shall confiderably shorten the Calcu lation of the Moon's Place. By M. KRAFFT.

The lunar tables published by M. Euler, in his laft work on the theory of the moon's motion, differ from thofe of Mayer, as they are calculated from formulæ immediately deduced from the univerfal principle of gravitation; as they give, instead of the longitudes and latitudes in arcs of a circle, the orthogonal co-ordinates of the moon's place, whence the tangents of these arcs are easily found; and as they lay down the arguments of particular equations folely from the mean motions of the fun and moon; whereas there are fome in Mayer's tables, which require that the true places of these heavenly bodies, the anomaly of the moon, and the place of its node, fhould be previously corrected by equations.

M. KRAFFT infifts on thefe advantages of Euler's tables over thofe of Mayer; he then propofes his method of rendering