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TO THE

THIRTEENTH VOLUME

OF THE

MONTHLY REVIEW

ENLARGE D.

FOREIGN LITERATURE. Art. I. Nova Atta Academic Scientiarum Imperialis Petropolitanæ, &t.

i... New Transactions of the Imperial Academy of Sciences at Petersburgh, Vols. IV. and V. With the History of the Academy for the Years 1786 and 1987. 4to. About 430 Pages in each

Volume. Petersburgh. 1789. THE HE character which we formerly gave of the publications of

this northern academy is confirmed by the volumes before us, in which the reader is not led through the smooth and Aowery paths of science, but is, obliged to toil up the steep and rugged ascent of mathematical investigation; which, though it may not afford immediate pleasure, promises solid advantage; because, when the summit is once attained, we may enjoy a more enlarged and distinct view of the works of nature, than we could otherwise have procured.

Omitting the account of the academical feffions, we thall proceed to the supplement of the historical part, which contains the memoirs presented by correspondents and approved by the Academy. These are as follow:

Demonftration of a Theorem" concerning Centres of Gravity. By M. LHUILIER.

The nature of this memoir prevents us from giving any abridged view of its contents : but the design of it will easily be perceived by stating a particular example of the general proposition:

Let A, B, C, be the centres of gravity of three bodies; a, b,c their respective masses, and Q their common centre of gravity. APP, REY. VOL, X111.

Let

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ac

a+b+c+

to ten.

Let right lines Q4, QB, QC, be drawn from the common centre to that of each body, and the latter be connected by right lines AB, AC, and BC; then QA Xa+QB’Xb+QC2Xc ab

be =AB2X- +AC:X +BC? X

a+b+c

a+b+c Concerning the Births, Marriages, and Deaths, in several of the Provinces and Cities of Russia. By M. B. F.HERMANN.

From this account, it is concluded that the population is doubled, in some parts of Russia, in forty-five years; in others, in fifty and fifty-five; and, in others, in fexry years. From the tables of baptisms and funerals, it appears thal, on an average, the former are to the latter as nineteen

Solution of a Problem in Spherics, viz. to find the greatest and least area of a spherical triangle, the base and altitude being given. By M.F.T. SCHUBERT

On the Loxodromic Curve. By the same.

We now come to the memoirs, of which there are fix in the mathematical class; five by the late M. EULER, on the integration of various formula, and on the expression of roots and powers by series : but there, and the remaining memoir by M. N. Fuss, on the rectification of curves by the inverse me thod of tangents, are so abstruse, that no account which we could give of them would be interesting, except to those who are peculiarly fond of the most difficult parts of the higher mathematics; and readers of this class must be referred to the work itself, in which they will find ample reason to admire che genius and resources of that great mathematician, whose relics are here collected.

PHYSICO MATHEMATICAL CLASS. On the Oscillatory Motion of a Board suspended on an Horizontal Axis, and impelled by the Wind. By M. L. EULER.

It has been disputed among mathematicians, whether the impulse of a Auid be proportional to the line of the angle of in. cidence, or to the square of this fine. M. EULER investigates the general expresion of this impulse according to each of these hypotheses: but they lead him to equations that are not integrable; however, by examining particular cales, in which the vibrations become ifochronous, he finds the expression for the time of each oscillation, which appears to be greater on the former, than on the latter, of these fuppofitions. Hence, he observes, it may be determined, by experiments, which of the two is erroneous.

Os

On a new Hydraulic Machine for raising Water. By M.JAMES BERNOULLI.

The machine, of which the powers are here mathematically investigated, is founded on the fame principle as the tube which Pilot applied to measure the velocity of rivers. It conlists of a spiral tube opening at each end, in opposite but horizontal dia rections, surrounding a vertical cylinder which must be made to revolve with great velocity, so that the external water shall exert a considerable pressure against that contained in the tube, which will be thus forced up and driven out at the upper opening. The formulæ here given are general, and may be applied to tubes of any particular form : but M. BernouLLI more especially considers those, the bore of which is cylindrical. In this case, the greatest effect, or quantity of water raised, in proportion to the absolute power, which is the moving force multiplied into its velocity, is as one to four.

Concerning the Registers of Births, Marriages, and Deaths in Petersburgh, from the Year 1781 70 1785. By mi. KRAFFT.

From the tables here given, it appears that, in these five years, there were 6840 marriages, 29,445 births, and 25,810 deaths: these numbers increale every year; for, in the year 1781, the number of marriages was 1207, of births 5540, and of deaths 5065; whereas, in 1785, there were 1471 marriages, 6109 births, and 5818 deaths. By an enumeration made by order of the government in the year 1784, it appears that the population of the city of Petersburgh, which contains 3840 houses, amounted to 126,827 males, and 65,619 females; in all, 192,446; that of Paris, in the same year, is faid, in the Memoirs of the Academy of Sciences, to have amounted to 593,070. Our author calculates that, in Petersburgh, the numbers of persons, who are married in a year, are to the whole number of inhabitants, as one to seventy; and that, on an average, from every ten marriages forty-three children are produced. From comparing the numbers of births and deaths during twenty years, M.KRAFFT supposes that the population of Petersburgh may be doubled in one hundred and eighty years.

Physics. On the Muscular Fibres of the Heart; eighth Dissertation. By M. C.F.WOLFF.

M. WOLFF here describes the middle ftratum of the fibres of the right ventricle. He observes that the fibres of the external Stratum, which originate in the base and the lower margin of the septum, and are inserted into the upper margin, converging in their course, are crofled by those of the middle stratum, which arise from the lower margin of the septum, diverge LI 2

as

as they proceed, and are inserted into the base and upper margin.

The fibres of this ftratum are distributed into twenty fasciculi, or muscles, which are bere minutely described, and illustrated by plates.

Experiments performed with a Defign to imitate the Paper-Stone or Artificial Slate. By M. J. G. GEORGI.

In our Appendix to vol. viii. we mentioned this incombustible fubftance, which was invented by Dr. Faxe at Carlscrone. Attracted by the idea of its utility for preserving buildings from fire, M. GEORGI was resolved to discover its compofition. For this purpose, he analyzed some specimens procured from Sweden, and found that they confifted of two parts by weight of a martial bole mixed with a small quantity of calcareous earth; of one part of the vegetable pulp of which paper is made, and one of animal glue, with an oil, which feemed to be that of linseed.

In order to imitate this preparation, the author tried several mixtures: that which fucceeded beft was an ounce and a half of paper pulp, well presled and dried, an ounce of common glue, and four ounces of white bole. He diffolved the glue in a small quantity of water, and beat up the pulp with this to a paste, with which he mixed the bole. This be spread out to a proper thickness in a mould; when dried, it was very hard, and the surface was remarkably smooth. Some of these sheets he varnished with boiled linseed oil, and, in order to compare them with the Swedish paper, he macerated a square inch of cach, in cold water, during four months; that which he had not varnished was found to be a little swelled in consequence of this operation : but what had been varnished with the boiled oil stood the trial fully as well as the Swedish, and was not at all altered.

He afterward laid the same quantity of each on an iron spatula, in the mouth of a well-heated furnace, and, with them, a piece of birch wood of the same size. After lying for fifteen minutes, the wood began to burn, and, in fifteen minutes more, was consumed to ashes. The pieces of paper-Itone were only fo heated as to occafion a hifing when plunged into water. On examining the several specimens, he found that what he had made had not been more affected by the heat than the Swedilh. Of both, the surface was blackened, and had swelled up in fittle bubbles : but neither was at all burnt, nor even warped

* See Review, New Series, vol. viü. page 482. We now find that we then gave the inventor a wrong name, as we called him Faze In this wè were milled by the Abbé Bertboloz.

by

by the heat. The varnishing seemed to make no difference in the result of this and the following experiment, in which they were put on a red hot iron, and exposed to the hottest fire in the middle of the furnace, during a quarter of an hour. In this trial, the Swedish specimen caught fire, and emitted a thick smoky flame, which continued about five minutes; it afterward burned with a white heat, and, when taken out, appeared to be reduced to three friable cineritious lamina; whereas that made by our auther remained hard, was scarcely altered in shape and size, and was only blackened and scorched on the surface. lc also resisted the inclemency of the weather equally well with the Swedish, but is not quite so beautiful in its appearance. The cement, which Dr. Faxe recommends for filling up the crevices between the sheets, is made of boiled linseed-oil, white lead, and chalk.

Description of the Charax Leucometopon. By M. Basil ZUIEW.

This fish very much resembles the trout, but its teeth thew that it belongs to the Characes ; the surname of Leucometopon is given to it on account of its white head. It is described from a specimen in the academical museum, which is seven inches long. We are not told where it was found.

Description of a new Species of the Echeneis. By the same,

Linné mentions only two species of this class, the Remora, and the Neucrates; as the fish here described has a great affinity to the latter, our author calls it Neucratoides.

Observations on the Hypothesis that primary may be distinguished from secondary Mountains, by the Nature of the Metalliferous Ores, and by tbe Metals which they contain. By M. J. J. FERBER.

M. FERBER is of opinion that the hypothefis here mentioned is wholly groundless. He adduces the lead mines of DerbyThire, in order to refute the opinion, entertained by some, that secondary mountains do not contain metallic veins; and that these are found in the highest parts of rocks of granite, he proves by the mines of Scharfenberg, Furstenberg, Saltzburg, and several others. He gives a number of instances which thew that these stones and minerals, which have been supposed to belong, exclusively, either to primary or to secondary mountains, are often found in both; concluding that the only way of discriminating them is by attending to the order of stratifi cation.

The ASTRONOMICAL class contains only one memoir, (by M. S. ROUMOUSKY) on an eclipse of the sun, observed June the 15. N.S. 1787. The volume concludes, as usual, with meteorological tables,

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