APPENDIX

TO THE

THIRTEENTH VOLUME

OF THE

MONTHLY REVIEW

ENLARGED.

FOREIGN LITERATURE.

ART. I. Nova Acta Academiæ Scientiarum Imperialis Petropolitana, &t. i.e. New Tranfactions of the Imperial Academy of Sciences at Petersburgh, Vols. IV. and V. With the Hiftory of the Academy for the Years 1786 and 1787. 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 flowery paths of fcience, but is obliged to toil up the steep and rugged afcent of mathematical inveftigation; which, though it may not afford immediate pleafure, promifes folid advantage; because, when the fummit is once attained, we may enjoy a more enlarged and diftinct view of the works of nature, than we could otherwife have procured.

Omitting the account of the academical feffions, we shall proceed to the supplement of the historical part, which contains the memoirs prefented by correfpondents 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 eafily be perceived by ftating a particular example of the general propofition:

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

LI

Let

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 QA1Xa+QB2xb+QC2xc

AB X.

ab
a+b+c

ac

a+b+c

+BC2x

be
a+b+c

Concerning the Births, Marriages, and Deaths, in feveral of the Provinces and Cities of Ruffia. By M. B. F. HERMANN.

From this account, it is concluded that the population is doubled, in fome parts of Ruffia, in forty-five years; in others, in fifty and fifty-five; and, in others, in fixty years. From the tables of baptifms and funerals, it appears that, on an average, the former are to the latter as nineteen

to ten.

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

On the Loxodromic Curve. By the fame.

We now come to the memoirs, of which there are fix in the mathematical clafs; five by the late M. EULER, on the integration of various formulæ, and on the expreffion of roots and powers by feries: but these, and the remaining memoir by M. N. Fuss, on the rectification of curves by the inverse method of tangents, are so abftrufe, that no account which we could give of them would be interefting, except to those who are peculiarly fond of the moft difficult parts of the higher mathematics; and readers of this clafs must be referred to the work itfelf, in which they will find ample reason to admire the genius and refources of that great mathematician, whofe relics are here collected.

PHYSICO MATHEMATICAL CLASS.

On the Ofcillatory Motion of a Board fufpended on an Horizontal Axis, and impelled by the Wind. By M. L. EULER.

It has been difputed among mathematicians, whether the impulse of a fluid be proportional to the fine of the angle of incidence, or to the fquare of this fine. M. EULER inveftigates the general expreffion of this impulfe according to each of these hypothefes: but they lead him to equations that are not integrable; however, by examining particular cafes, in which the vibrations become ifochronous, he finds the expreffion for the time of each ofcillation, which appears to be greater on the former, than on the latter, of thefe fuppofitions. Hence, he obferves, it may be determined, by experiments, which of the two is erroneous.

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 Pitot applied to meafure the velocity of rivers. It consists of a fpiral tube opening at each end, in oppofite but horizontal directions, furrounding a vertical cylinder which must be made to revolve with great velocity, fo that the external water fhall exert a confiderable preffure 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 efpecially confiders thofe, the bore of which is cylindrical. In this cafe, the greatest effect, or quantity of water raifed, in proportion to the abfolute 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 to 1785. By M. KRAFFT.

From the tables here given, it appears that, in these five years, there were 6840 marriages, 29,445 births, and 25,810 deaths: thefe numbers increase 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 fame 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 perfons, who are married in a year, are to the whole number of inhabitants, as one to feventy; 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 fuppofes that the population of Petersburgh may be doubled in one hundred and eighty years.

PHYSICS.

On the Mufcular Fibres of the Heart; eighth Differtation. By M. C. F. WOLFF.

M. WOLFF here defcribes the middle ftratum of the fibres of the right ventricle. He obferves that the fibres of the external ftratum, which originate in the bafe and the lower margin of the feptum, and are inferted into the upper margin, converging in their course, are crofled by thofe of the middle ftratum, which arife from the lower margin of the feptum, diverge

as they proceed, and are inferted into the bafe and upper margin.

The fibres of this ftratum are distributed into twenty fafciculi, or muscles, which are here minutely defcribed, and illuftrated 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 incombuftible fubftance, which was invented by Dr. Faxe at Carlfcrone*. Attracted by the idea of its utility for preferving buildings from fire, M. GEORGI was refolved to difcover its compofition. For this purpose, he analyzed fome fpecimens 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 linfeed.

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 preffed and dried, an ounce of common glue, and four ounces of white bole. He diffolved the glue in a fmall quantity of water, and beat up the pulp with this to a paste, with which he mixed the bole. This he fpread out to a proper thickness in a mould; when dried, it was very hard, and the furface was remarkably fmooth. Some of these sheets he varnished with boiled linfeed oil, and, in order to compare them with the Swedish paper, he macerated a fquare inch of each, in cold water, during four months; that which he had not varnished was found to be a little fwelled in confequence of this operation but what had been varnished with the boiled oil ftood the trial fully as well as the Swedish, and was not at all altered.

He afterward laid the fame quantity of each on an iron fpatula, in the mouth of a well-heated furnace, and, with them, a piece of birch wood of the fame fize. After lying for fifteen minutes, the wood began to burn, and, in fifteen minutes more, was confumed to afhes. The pieces of paper-ftone were only fo heated as to occafion a hiffing 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 Swedish. Of both, the furface was blackened, and had fwelled up in little bubbles: but neither was at all burnt, nor even warped

* See Review, New Series, vol. viii. page 482. We now find that we then gave the inventor a wrong name, as we called him Faye In this we were missed by the Abbé Bertholon.

by

by the heat. The varnishing feemed to make no difference in the result of this and the following experiment, in which they were put on a red hot iron, and expofed to the hotteft 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 fcarcely altered in fhape and fize, and was only blackened and fcorched on the surface. It alfo refifted the inclemency of the weather equally well with the Swedish, but is not quite fo beautiful in its appearance. The cement, which Dr. Faxe recommends for filling up the crevices between the fheets, is made of boiled linfeed-oil, white lead, and chalk.

Defcription of the Charax Leucometopon. By M. BASIL ZUIEW. This fifh very much resembles the trout, but its teeth fhew that it belongs to the Characes; the furname of Leucometopon is given to it on account of its white head. It is defcribed from a specimen in the academical mufeum, which is feven inches long. We are not told where it was found.

Defcription of a new Species of the Echeneis. By the fame. Linné mentions only two fpecies of this clafs, the Remora, and the Neucrates; as the fifh here defcribed has a great affinity to the latter, our author calls it Neucratoides.

Obfervations on the Hypothefis that primary may be diftinguished from fecondary Mountains, by the Nature of the Metalliferous Ores, and by the Metals which they contain. By M. J. J. FERBER.

M. FERBER is of opinion that the hypothesis here mentioned is wholly groundless. He adduces the lead mines of Derbyshire, in order to refute the opinion, entertained by fome, that secondary mountains do not contain metallic veins; and that thefe are found in the highest parts of rocks of granite, he proves by the mines of Scharfenberg, Furftenberg, Saltzburg, and feveral others. He gives a number of inftances which fhew that these stones and minerals, which have been supposed to belong, exclufively, either to primary or to fecondary mountains, are often found in both; concluding that the only way of difcriminating them is by attending to the order of ftratifi cation.

The ASTRONOMICAL clafs contains only one memoir, (by M. S. ROUMOUSKY) on an eclipfe of the fun, obferved June the 15. N.S. 1787. The volume concludes, as ufual, with meteorological tables.