though they commence at the base, do not reach the apex, and this deficiency is greater in the lower than in the upper strata. He enumerates fix ftrata of fibres in the left, and only three in the right, ventricle.

A Chemical Analysis of the Ruffian Pot-cfb, and of Birch Afhes. By M. J. G. GEORGI.

Pot-afh is fo important an article of Commerce in Ruffia, that above thirty five thoufand pouds of it are faid to be annually exported from Petersburgh. M. GEORGI diftributes the various kinds of it made in the empire under three claffes, the ardafch, or cineres non depurati; the pot-ath, or cineres ruditer depurati; and the pearl-ath, or cineres perlati. Each of thefe forts contains pure alkaline falt, vitriolated tartar, calcareous and vitrifiable earth mixed with fand, and fome martial particles. Birch afhes appeared to have a fmall quantity of white magnefia but the author could not difcover any manganese in them, of which, according to the Swedish chemifts, they contain a large proportion.

An Account of fome uncommon Mineral Productions. By M. J. J. FERBER.

The fpecimens here defcribed were collected by this gentle man in his travels through Saxony, Bohemia, and Hungary: they are feventy-four in number: the most curious are native vitriolated magnefia, a yellow quartz in rhomboidal chrystals, lead mineralized by the acid of falt, white antimony, and an ichtyolite in gyps.

An Account of two Petrifactions. By M. B. ZUYEw.

Thefe foffils were found in an iron mine in Siberia; the one is conjectured to be a fifh, and the other the horn of fome animal, but of what kind is not known.

ASTRONOMY.

Concerning the mean Result of Aftronomical Obfervations. By M. EULER.

M. EULER here fuppofes, that of any celeftial phenomenon, as the altitude of a ftar, different obfervations are taken; that of these a certain number, expreffed by the letter a, give the true altitude; that a number b make it a minute greater, and c obfervations a minute lefs, than the true; fo that the whole number of observations is N=a+b+c. He then afks, what is the probability that the fum of these results shall beo, or = 1, or = ± 2, or = ± 3, &c.?

This problem is reduced to the following: fuppofe that of N tickets a certain number a are marked with a cypher, b with

• A poud equals about thirty-fix pounds avoirdupoife.

+1, and c with -1; and that a number n of these tickets are drawn by lot, each ticket being returned into the ftock as foon as drawn; what is the probability that the fum of the figures on the tickets drawn fhall be o, or ± 1, or ±2, &c.? Of this problem, fome particular cafes, in which n = 1, n = 2, n=3, are first confidered; and then the general problem is folved, according to the known principles of the theory of combinations and the doctrine of chances, by the evolution of the power N=(a+b+c)", in which the general form of each term is Mabc; the fum of the exponents being a+e+y=n, and the coefficient

M=

1.2.3....XI.2.3....ẞx.1.2.3..

Thefe operations being very tedious, when performed in the ufual method, M. EULER fhews how the terms affected by the fame power a+B+y=n, may be found without having recourfe to this evolution. He makes N=a+b+c+d+, &c. obfervations, of which the number a have the error a, b the error B, c the error 7, &c.; and inquires into the probability, that the mean refult fhall be any particular number ; for this

purpofe, the power (ax
evolved, and the fum of

α

B

+ bx + cx2+, &c.)" must be all the terms affected by the power ^, being divided by N", will fhew the probability of the mean refult being

x

n

Determination of the Latitude and Longitude of Mofdok in Crim Tartary, from the Obfervations of THEODORE TSCHERNOI. By M. STEPH. RUMOUSKY.

According to thefe calculations, Mofdok is fituated in 43° 43′ 23′′ north latitude, and its longitude from the meridian of Paris is 41° 30'. On the 10th of October 1785, new ftyle, the variation of the magnetic needle was 60° 40' toward the weft.

Obfervations on a new Method of finding the Anomaly of the Centre, when the mean Anomaly is given. By M. Fuss.

The method here difcufled was propofed by M. Klugel, in the Ephemerides of Berlin: but M. Fuss juftly objects to it as inconvenient in practice, and recommends a very fimple approximating formula, difcovered above fifty years ago by M. Euler, and explained in a memoir, entitled Emendatio Ta bularum Aftronomicarum per Loca Planetarum Geocentrica, publifhed in the year 1740, in the twelfth volume of the Com

mentaries

mentaries of this academy. This formula is the following, in which is the mean anomaly, e the eccentricity, and v

"the approximating expreffions of the eccentric anomaly: then we fin. v: but if the eccentricity be a very small part of the greater axis of the orbit, which is the case with respect to the planets, we may put vw, and then = w — e fin. w: by fubftituting this expreffion for v, we have we fin. (we fin. w); by another fubftitution, the next approximation will be w -e fin. [we fin. (we fin. w)]; and thus the fubftitution may be continued, till the value expreffed be fufficiently exact. These approximations will have the following form:

w-e fin. w

After this general view of the feveral memoirs in this publication, by which we leave our readers to judge concerning the prefent state of the academy, we have only to add, that the volume concludes with meteorological tables for the year 1785, drawn up by M. JOHN ALBERT EULER.

Sow.

ART. II. Hiftoire et Mémoires de l'Académie Royale des Sciences, &c.' i. e. The History and Memoirs of the Royal Academy of Sciences at Paris, for the Year 1787; extracted from the Registers of the Academy. 4to. pp. 692. Paris. 1789.

AMID the feveral philofophical publications which folicit our attention, it is always with peculiar fatisfaction that we enter on a review of the tranfactions of the Royal Academy at Paris, which feldom fail to reward our labour with a variety of interefting information. This is remarkably the cafe with respect to the volume before us; the principal contents of which we fhall therefore, without farther introduction, endeavour to communicate to our readers.

The first part of the volume contains, as ufual, the hiftory of the academy: but, as we find nothing in this part deferving of particular notice, we fhall proceed to the memoirs, which, though they follow each other without any claffical arrangement, we fhall diftribute under diftinct heads.

GENERAL PHYSICS.

A Fifth Memoir on Electricity. By M. COULOMB. With an electrometer, conftructed on the principles laid down in his former memoirs, M. COULOMB performed a va

riety of experiments, with a view to afcertain the manner in which the electric fluid is divided between two conducting bodies in contact with each other. The refult of these experiments appears to be, that the greater is the difference in surface between two metal globes, the more does the denfity of the electric fluid vary on the furface of the fmaller, between the point of contact and that diametrically oppofite, and the more uniform is it on the furface of the greater, on which it increases rapidly from the point of contact, where it is imperceptible, to a diftance of seven or eight degrees from it, after which it becomes uniformly diffused. Thus if two spheres, the one of two, and the other of eight, inches diameter, be in contact, the denfity of the electric fluid on the former is imperceptible from the point of contact to thirty degrees diftant from it; from forty-five to ninety degrees it increases in the proportion of one to four; and from ninety to an hundred and eighty, the increase is as ten to fourteen: but, on the greater fphere, the electricity is imperceptible within feven or eight degrees of the point of contact, and is uniformly diffufed over the remainder of its furface. In the theoretical part of the memoir, M. COULOMB endeavours to fhew, that these refults are consonant with the univerfal law of attraction, and that the action of the electric fluid is inversely as the fquares of its diftances. His experiments are certainly ingenious, and his reasoning is plausible: but we cannot help repeating our doubts with respect to the fundamental principles of his hypothefis *.

Concerning fome Phenomena of Attraction and Repulsion. By

M. MONGE.

It is here juftly observed, that when light bodies, floating on the furface of a fluid, appear to attract or repel each other, or to be attracted or repelled by the fides of the veffel, these phenomena are the refult, not of an attractive nor of a repulfive force of the bodies with refpect to each other, but of the unequal preffure of the fluid furrounding them: thus alfo, when two plates of glass, fufpended in water very near together, seem to be drawn into contact, it is not the effect of any immediate attraction between them, but of their action on the 'fluid with which they are moistened, in confequence of which they are preffed toward each other. This explanation, which is by no means new, M. MONGE applies to the phenomena of crystallization; and he maintains that the coherence of two elements. of a crystal is not effected by any immediate attraction of each other, but by their joint action on the fluid that had separated them.

* See Rev. vol. lxxxi. p. 6c4.

On

On Thermometers. By M. CHARLES.

The difficulty of reducing thermometrical obfervations to one common ftandard, by which they may be compared, arifes not only from the want of certainty refpecting the fixed points of temperature, but also from the dilatation of the glass; and it is this circumstance to which M. CHARLES directs our attention in the memoir before us.

When a thermometer is immersed in hot water, the dilatation of the bulb is evident, from the fudden fall of the mercury previous to its afcent in the tube: but its exact quantity is not eafily determined, because of the expanfion of the mercury, which takes place at the fame time. Its effect, however, is far from being inconfiderable: it is, fays our author, a wellknown rule among inftrument-makers, that, in a thermometer which is defigned to extend from twenty-two degrees below, to eighty-two degrees above, the freezing point, according to M. REAUMUR's fcale, the capacity of the bulb must be to that of the tube, as fifty to one: if then we fuppofe the dilatation of the bulb, in paffing from o to ten degrees, to be

8

I

1200

we

or : but this is no less

1200' 150

may conclude that, in a change of temperature from o to eighty degrees, it will be than the third part of the capacity of a tube extending to a hundred and four degrees, and amounts to above thirty-four degrees. The effect of this will depend on the proportion between the dilatation of the bulb, and that of the fluid, with which it is filled; and will therefore be four times as great in mercurial thermometers as in thofe made with fpirits of

wine.

Without repeating the experiments here related, we cannot pretend to judge concerning the accuracy of the method, propofed by M. CHARLES, for afcertaining the quantity of this dilatation: but as the fubject is both curious and useful, we shall endeavour, as briefly as poffible, to give our readers fome idea of this hypothefis; premifing that the fcale mentioned is always that of Réaumur.

Suppose A to be the volume of the mercury in a thermometer, when it has been immerfed, as far as its height in the tube, in a bath, fo as to acquire its temperature; then if a represent the fpecific gravity of the mercury in this degree of warmth, its weight will be expreffed by a A: let A+Z be its volume, including the dilatation of the glafs, when immerfed in a fecond bath, its fpecific gravity, and (A+Z) its weight. Then, as mercury is not found to alter in weight by paffing

5