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and by a simple process, we shall obtain an expression of this kind: (uv-i+V(1—02)"+1=0
bl.-I putting nz = circumference =
VEquating the possible and the impossible parts, expressions for the chords of }, \, &c. of the circumference will result.
We discern little in this memoir that intitles it in our opi. nion to the honor of insertion. If Euler (Analysis Infinitorum) and La Croix (Introduction, Calcul diff.) have not given the same method, they have suggested those which are very nearly related and similar to it ; and the same resulis may
be obtained without the aid of those symbols, on the legitimate use of which all mathematicians are not agreed.
MEDICINE, CHEMISTRY, NATURAL HISTORY, &C. It appears by the dates prefixed to these memoirs, that a considerable period bas elapsed since they were presented to the Institute ; and in most cases, either the whole of the papers or an abstract from them has already been given in some of the literary journals: so that, however valuable in themselves, their publication will afford little new information. On this: account, we shall be more than usually brief in our notice of them.
Memoir on the Sap of Plants, and particularly on that of the Vine and the Hornbeam, with an Analysis of this Fluid. By M. Deyeux.-- The most important fact ascertained in this paper is that the sap of the vine and hornbeam contains the acetate of lime, united to a quantity of vegeto animal matter, which appears to be similar to the gluten of wheat. The essay is well written, and must have been valuable when it was originally presented to the society, in the year 1796 : but it is now, in a great measure, superseded by the experiments of M. Vau. quelin.
Memoir on three different Species of Carbonated Hydrogenaus Gas, produced by different Processes, from Ether and Alcóhol. By M. M. BoxDT, DEIMAN, PAATS VAN TROOSTWYK, and LAUWEREN
BURG, of Amsterdam.—This very valuable paper contains an account of the discovery of the olifient gas. An ample abstract of it was afforded to the chemists of France, soon after it was presented to the Institute, in the 45th vol. of the Journal de Phy, sique, and has been laid before the English reader in some of our temporary publications.
Sketch of some Experiments respecting the Division which Cylinders of Camphor experience at the Surface of Water, and Reflections on the Motions which accompany this Division. By J. B. VENTURI, Professor of Natural Philosophy at Modena, &c.-An account of these experiments has already appeared in the 21st vol. of the Annales de Chimie.
Memoir on the Blood of Persons affected with Jaundice, considered with respect to its Chemical Relations. By M. Deveux.--A principal object of this paper is to ascertain whether the yellow tinge which the blood exhibits in Jaundice be, according to the common opinion, owing to the actual presence of bile in it. Having obtained a quantiry of this blood, M. Deveux permitted the crassamentum and serum to separate ; when, although the latter exhibited the deep yellow color, it had neither the odor nor the taste of bile ; nor was alcohol, by being digested on it, impregnated with any degree of bitterness. It was remarkable that the crassamentum was not reddened in the usual manner by exposure to the atmosphere, nor did the serum become solid by the application of heat to it. We zhink that the author is justified in his conclusion that, in this case, there was no proper bile in the blood. The facts stated in this paper are curious, and deserve the attentive consideration of the physiologist.
Observations on the Concrete Citric Acid. By M. Dizé.These remarks have already appeared in the Annales de Chimie, and in an English dress.
Memoir on the Filaments or Hairs which cover the Plant that produces the Cicer Arietinum; and a Chemical Examination of the Liquor which exudes from these Hairs: By M. Deveux. --The hairs with which this plant is so abundantly beset are observed, at particular periods, to be ripped with a minute drop of fluid ; of which the author contrived to collect a suf. ficient quantity to examine its nature, when he found it to consist of pure oxalic acid.
Meteorological Observations made at Cayenne, from the 1st Da. cember 1778, to the 30th November 1789. By M. MENTELLE, Geographical Engineer, &c.-The most remarkable circumstance in these observations is the great quantity of rain that falls at Cayenne, which on the average is nearly 98 inches annually ; in the year 1791 it was 116 inches. In the interior part of Guiana, the rain is said to fall in still larger quantity.
History of a Woman who had one of the Ovaries tranformed into Hydatids, and in whose Womb was found a very hard and very compact Bony Substance. By Dr. ODIER of Geneva.-An unmarried female, 70 years of age, after having enjoyed a good state of health, was hurt by a fall, and had afterward a number of complaints, which were referred to the stomach : but from some of the symptoms it was suspected that the pancreas was scirrhous. After death this was discovered to be the case; and on continuing the examination, one of the ovaries was found converted into a mass of Hydatids, and the uterus, although of its natural size, was completely filled by a mass of bone.
Collection of different Observations on Chemistry. By M. Proust.–Of this very interesting paper we have already (vol. 48. p. 458.) had an opportunity of giving an ample account, from the historical part of the last volume of the Memoirs of the Institute. We are happy to see it now published in its entire state.
Anatomical Observations on a Patient, on whom the Operation for Popliteal Aneurism had been performed, according to the Method of Hunter. By M. DESCHAMP.—The subject completely recovered from the operation, but, after the space of eight years, was carried off by a disease of the chest, when an opportunity occurred of examining the state of the limb. About 21 inches of the arterial trunk was found to be obliterated.
Experiments on the Influence of Light on Vegetables. By A. P. DECANDOLLE.--We have here an account of the comparative effects produced on plants, by being kept in a dark chamber, and in one lighted by lamps, to a certain degree of intensity. It was found that plants, which had been blanched in the dark chamber, were rendered green when removed into the Other : but the light of the lamps did not appear adequate to detach oxygenous gas from them. M. DECANDOLLE observed the effects of different degrees of light on what has been called the sleep of plants : but the results of his experiments do not seem sufficiently satisfactory to enable us to draw any important conclusion from them. Memoir on the Pores of the Bark. By the Same.
When the epidermis is removed from a leaf, a' net work is discovered, from the fibres of which arise a number of small pores. The use of these bodies has not been accurately ascertained : but from observing on what kinds of plants and on what particular parts of them they existed in the greatest number, the author concludes that their principal office is to carry on the insensible transpiration.
Memoir on the Vegetation of Misletse. By the Same. It was found that, by inserting the cut end of a branch which contained misletöe into a red infusion, the coloring matter passed into the vessels of the plant; and that the infusion was also capable of being transmitted from the misletoe into the branch.
Outline of a Plan for establishing Experimental Farms, and for fixing ihe Principles of Agricultural Improvements. By Sir John Sinclair, Bart. M. P. and founder of the British Board of Articulture. We learn that this paper was presented to the Institute by M. Otto, in the year 8, (1799) but it is for the most part ihe same with Essay X. in an 8vo. volume, on miscellaneous subjects, which Sir John S. published in London in 1802, and of which we gave some account in M. R. vol. xl. N. S. p. 289. The English essay is intitled “ Proposals for establishing by subscription a new Institution to be called the Plough: or Joint Stock Farming and Experimental Society, &c. Though the author seemed seriously to discuss the objections which would probably be urged against his scheme, we did not suppose that he was so sanguine as to cherish the idea of ever seeing it carried into effect. By offering it also to the French, however, it may be concluded that he did not consider the plan as altogether theoretical. He has here stated the outlines, but has deemed it prudent not to anticipate objections. In the Report suhjoined, it is admitted by our ene. mies that their resources for the execution of projects of this nature are very different from those which we enjoy in England; and that though the'scheme may appear to involve nothing extraordinary in the contemplation of the author's own countrymen, it mus' without doubt strike the French as gigantic,
Three plates accompany this communication; the first represents the divisions of an experimental farm, with the crops in each field for one year; the second, the ground plan and elevation of the circular cottages proposed to be erected for the labouring peasants; and the third, a plan and view of a village.
Observations on the Births, Marriages, and Deaths which occur. red at Montpellier in the course of twenty one Years, from 1772 to 1792 inclusive, and the Calculations which result from them respecting the Probabilities of Life. by M. J. A. MOURGUE.— The facts here stated are that during the above mentioned period the number of births at Montpellier was 25,064, viz. 12,919
males, and 12,145 females :--that the excess of males above females was 774:- that the anual average of births was 1193, or 615 males, and 578 females ;--that though in the whole of these i wenty-one years the births of males exceeded those of the females, yet in 1776, 178.4, and 1792, or about every eighth year, the number of female births surpasied that of the males ;-and that of the 25,054 biridis, 2735 were illegiti. mate, amounting to about of the whole
For the purpose of ascertaining the influence of the seasons on the production of the human species, M. MOURGUE placed in separate columns the births which happened between the autumnal and the vernal equinox, and those between the vernal and the autumnal. The result was in.at he found the births in the cold half year to exceed hy one seventh those of the six summer months, or to be as 13,490 to 11,574; the former surpassing the latter by 1916. The quarterly account stands thus : for January, February and March, the whole number was 6594 ; for April, May and June, 5388 ; for July, Aug. and Sept. 6186; and for Oct. Nov. and Dec. 6896: whence it follows that the three autumnal months give more births by one fourth than the three spring months. The author remarks, however, that, if we carry our view backwards for nine months from the birth, we shall find that these calculations will demonstrate the month of May to be most propitious to love.
Having compared the first five years of the above named 21 with the last five, or the period from 1972 to 1776 inclusively with that from 1788 to 1792, the writer discovered a considerable increase of population, not withstarding that the latter period included the first years of the revolution. According to an exact enumeration made in 1793, the city of Montpellier contained 32,897 inhabitants.
Under the head of Marriag-s, we are informed that, in the course of these twenty-one years, 5926 took place, or about 282 yearly. By comporing the annual number of marriages with that of the whole population, it appears that only one Marriage occurs in 117 persons. 11, moreover, we oppose the mean number of birihs (1193) to that of marriages (282,) it will be seen that only a little more than a quarter t of those who are born reach the married state.
* The author adds that, from observations made in other places, he is inclined to believe that this proportion of illegitimate to legitimate births will apply to all the great towns in France.
† This quarter should be about half, because 2oz Darriages must make 564 persoils.