De Forcrand Research Articles

A thermodynamic study of the (fluoromethane + water) system

A study of the (fluoromethane+water) system was conducted at temperatures between 255K and 298K, and pressures from 0.09 to 2.6MPa. The solubility of fluoromethane in liquid water was measured from 280K to 298K, at pressures up to the hydrate formation pressure. The p–T behavior of the liquid+hydrate+vapor (LHV) three-phase equilibrium was measured from 273K to 295K. The p–T behavior of the ice+hydrate+vapor (IHV) three-phase equilibrium was measured from 251K to 273K. The intersection of the LHV and IHV curves was used to find the lower quadruple point, Q1, at T=272.55K and p=0.2442MPa. Solubility-corrected enthalpies of dissociation were determined at the lower quadruple point using the Clapeyron equation. The de Forcrand method was used to determine the hydration number of the hydrate at Q1. The results show that not all of the cages in the SI hydrate structure are filled.

A thermodynamic study of the (difluoromethane + water) system

A study of the (difluoromethane + water) system was conducted at temperatures between (255 and 298) K, and pressures from (0.06 to 1.30) MPa. The solubility of difluoromethane in liquid water was measured from (280 to 298) K, at pressures up to the hydrate formation pressure. The ( p, T) behavior of the (liquid + hydrate + vapor) three-phase equilibrium was measured from (274 to 292) K. The ( p, T) behavior of the (ice + hydrate + vapor) three-phase equilibrium was measured from (257 to 273) K. Solubility-corrected enthalpies of dissociation were determined at the lower quadruple point ( Q1) using the Clapeyron equation. The de Forcrand method was used to determine the hydration number of the hydrate at Q1. The results show that not all of the cages in the SI hydrate structure are filled.

Another method to compute the thermodynamic Casimir force in lattice models

We discuss a method that allows us to compute the thermodynamic Casimir force at a given temperature in lattice models by performing a single Monte Carlo simulation. It is analogous to the one used by de Forcrand and co-workers in the study of 't Hooft loops and the interface tension in SU(N) lattice gauge models in four dimensions. We test the method at the example of thin films in the XY universality class. In particular we simulate the improved two-component phi4 model on the simple cubic lattice. This allows us to compare with our previous study, where we have computed the Casimir force by numerically integrating energy densities over the inverse temperature.

UA(1)anomaly in hot and dense QCD and the critical surface

We discuss the chiral phase transition in hot and dense QCD with three light flavors. Inspired by the well-known fact that the ${U}_{\mathrm{A}}(1)$ anomaly could induce first order phase transitions, we study the effect of the possible restoration of the ${U}_{\mathrm{A}}(1)$ symmetry at finite density. In particular, we explore the link between the ${U}_{\mathrm{A}}(1)$ restoration and the recent lattice QCD results of de Forcrand and Philipsen, in which the first order phase transition region near zero chemical potential ($\ensuremath{\mu}$) shrinks in the quark mass and $\ensuremath{\mu}$ space when $\ensuremath{\mu}$ is increased. Starting from the Ginzburg-Landau theory for general discussions, we then use the Nambu--Jona-Lasinio model for quantitative studies. With the partial ${U}_{\mathrm{A}}(1)$ restoration modeled by the density dependent 't Hooft interaction, we fit the shrinking of the first order region found in de Forcrand and Philipsen's lattice calculation at low $\ensuremath{\mu}$. At higher $\ensuremath{\mu}$, the first order region might shrink or expand, depending on the scenarios. This raises the possibility that despite the shrinking of the first order region at lower $\ensuremath{\mu}$, the QCD critical end point might still exist due to the expansion at higher $\ensuremath{\mu}$. In this case, very high precision lattice data will be needed to detect the recently observed backbending of the critical surface with the currently available analytic continuation or Taylor expansion approaches. Lattice computations could, however, test whether the ${U}_{\mathrm{A}}(1)$ restoration is responsible for the shrinking of the first order region by computing the ${\ensuremath{\eta}}^{\ensuremath{'}}$ mass or the topological susceptibility at small $\ensuremath{\mu}$.

Critical surface in hot and dense QCD with the vector interaction

We discuss the chiral phase transition of hot and dense quark matter. We illustrate that the first-order phase transition is generally favored at high baryon density and the repulsive vector-vector interaction weakens the first-order phase transition. We use the Nambu--Jona-Lasinio model with the Polyakov loop coupling for concreteness. We locate the QCD critical surface on the quark mass plane for various values of the vector coupling constant. We find that, with increasing quark chemical potential, the first-order region in the quark mass plane could shrink for sufficiently large vector coupling. This may be a possible explanation for the recent lattice QCD results by de Forcrand and Philipsen.

Comparison of | Q|=1 and | Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge | Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of | Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our | Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an O(a 4) -improved gauge action chosen to have small but positive O(a 6) errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the O(a 4) -improved gauge-field action with an O(a 4) -improved action constructed from the square of an O(a 4) -improved lattice field-strength tensor, thus having different O(a 6) discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of | Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.

Topological susceptibility with the improved Asqtad action

Chiral perturbation theory predicts that in quantum chromodynamics light dynamical quarks suppress the topological (instanton) susceptibility. We investigate this suppression through direct numerical simulation using the Asqtad improved lattice fermion action. This action holds promise for carrying out nonperturbative simulations over a range of quark masses for which chiral perturbation theory is expected to converge. To test the effectiveness of the action in capturing instanton physics, we measure the topological susceptibility as a function of quark masses with $2+1$ dynamical flavors. Our results, when extrapolated to zero lattice spacing, are consistent with predictions of leading order chiral perturbation theory. Included in our study is a comparison of three methods for analyzing the topological susceptibility: (1) the Boulder hypercubic blocking technique with the Boulder topological charge operator, (2) the more traditional Wilson cooling method with the twisted plaquette topological charge operator and (3) the improved cooling method of de Forcrand, Perez, and Stamatescu and their improved topological charge operator. We show in one comparison at nonzero lattice spacing that the largest difference between methods (1) and (2) can be attributed to the operator, rather than the smoothing method.

An exact algorithm for three-flavor QCD with O( a)-improved Wilson fermions

We present an exact dynamical QCD simulation algorithm for the O( a)-improved Wilson fermion with odd number of flavors. Our algorithm is an extension of the non-Hermitian polynomials HMC algorithm proposed by Takaishi and de Forcrand previously. In our algorithm, the systematic errors caused by the polynomial approximation of the inverse of Dirac operator is removed by a noisy-Metropolis test. For one flavor quark it is achieved by taking the square root of the correction matrix explicitly. We test our algorithm for the case of N f = 1 + 1 on a moderately large lattice size (16 3 × 48). The N f = 2 + 1 case is also investigated.

Phase structure of one-flavour QCD

Abstract Phase structure of one-flavour QCD C. Alexanch-ou a, 1, A. Borici b, A. Feo a, Ph. de Forcrand c, A. Galli d, F. Jegerlehner e, T. Takaishi f a Department of Natural Sciences, Unh,ersity of Cyprns, CY-1678 Nicosia, Cypnls b Paul Scherrer Institute, CH-5232 Villigen, Switzerland c Swiss Center for Scientific Computing, ETH-Zentnml, CH-8092 Ziirich, Switzerland d ELCA b~formatique, Hofiviesen Str. 26, CH-8057 Ziirich, Switzerland e DESY-IfH Zeuthen, D-15738 Zeuthen, Germany f Hiroshbna University of Economics, 731-01 Hiroshhna, Japan We present a study of the deconfinement phase transition of one-flavour QCD, using the multiboson algorithm [1]. The mass of the Wilson fermions relevant for this study is moderately large and the non-Hermitian multiboson algorithm [2] is a very suitable simulation algorithm. Finite size scaling is studied on lattices of size 83 x 4, 123 x 4 and 163 x 4. For heavy quarks, the behaviour of observables that probe the phase change, such as the Polyakov loop susceptibility, transition. The first-order transition weakens as the quark mass decreases and turns into a crossover. Locating the end-point (/~ep,/¢ep) accurately requires very large lattice sizes, beyond our computer capabilities. We thus consider an effective model, in the same universality class as full QCD but cheaper to simulate. By simulating larger systems, we locate the end-point in the coupling plane of this model. Then we map this end-point back onto full QCD. We thus estimate the end point of the first-order phase transition to occur at a quark mass of about 1.4 GeV. © 1999 Elsevier Science B.V. All rights reserved.

Bochkarev and de Forcrand reply.

Comments by Marchesoni are aknowledged. It is shown that the numerical results by Bochkarev and de Forcrand exhibit consistency with theoretical results.(AIP)

Systems containing hydrogen peroxide at high concentration communication 9. The ternary system LiOH-H2O2-H2O

1. The ternary system LiOH \3- H2O2 \3- H2O was studied by the solubility method at +10\dg, 0\dg, \t-10\dg, and \t-21\dg, and solubility isotherms and polytherms were plotted 2. A solubility study of the ternary system LiOH \3- H2O2 \3- H2O in which the compositions of solid phases were determined by the residue method has established the existence of the following peroxide compounds of lithium: Li2O2H2O2 \sd 3H2O, Li2O2 \sd H2O2 and Li2O2 \sd 2H2O2. 3. Cohen's assertion regarding the absence of the compound Li2O2 \sd H2O2 \sd 3H2O, previously found by de Forcrand, was not confirmed. The compound Li2O2 · H2O2 · 3H2O exists over a wide range of temperature and over a wide range of hydrogen peroxide concentrations (5.0–40.0% H2O2). 4. The existence of the previously unknown compound Li2O2 \sd 2H2O2 is at a hydrogen peroxide concentration in the liquid phase of 64.8% at +10\dg and 84.0% at \t-21\dg. 5. The solid phases isolated in the course of the study of this system were investigated by several physicochemical methods.

Some Properties of Mixed Paraffinic and Olefinic Hydrates

Abstract An experimental investigation was made of the effect of temperature upon thethree-phase pressure associated with the propane-water and propene-watersystems when hydrates were present. In addition, the characteristics of thepropane-propene-water system were established over a limited range oftemperatures under conditions such that hydrate was formed. The hydrate phasefor this system may be a solid solution and the distribution of propane andpropene in it is similar to that found in the coexisting hydrocarbon liquidphase. Introduction A knowledge of the characteristics of hydrates of the hydrocarbonsencountered in industrial practice is of importance in connection with thedesign of process equipment. Villard carried out early studies of hydrates, andde Forcrand considered the more probable compositions of the hydrates ofhydrocarbons. Hammerschmidt presented information about the propane-water andthe isobutane-water systems. Scheffer studied the hydrate of hydrogen sulfidein detail, and de Forcrand reported on the hydrates of krypton, argon, andxenon. Roberts and co-workers determined the nature of the hydrates formed in themethane-water and ethane-water systems. Carson and Katz studied themethane-propane-water, methane-pentane-water, and the methane-hexane-watersystems in the four-phase region. The results of this rather extensiveinvestigation indicated that the paraffinic hydrates formed solid solutions.The experimental evidence now available does not support the existence ofhydrates of the pentanes-and heavier hydrocarbons but it cannot be stated withcertainty that such hydrates are not formed. Stackelberg made extensive studiesof the crystal structure of paraffinic hydrate, by means of x-ray techniquesand found that hydrates posses, a definite structure and composition. Theexistence of such a structure does not preclude the formation of solidsolutions of hydrates in aqueous systems containing two or morehydrocarbons. Wilcox, Carson and Katz reviewed the information on the hydrates ofimportance in the processing of natural gas and presented data concerning theirformation from natural gas. Kobayashi and Katz made studies at high pressure ofthe hydrate of methane, and Unruh and Katz investigated hydrates in mixtures ofcarbon dioxide and methane. Frost and Deaton contributed to the knowledge of the composition of theparaffinic hydrates. The irregularities in the experimental results wereseveral times the expected uncertainties. This experience confirms the behaviorencountered by other investigators indicating that hydrates tend to occludewater during their formation, thus rendering difficult the direct measurementof their composition. T.P. 3376

Composition of Chlorine Hydrate

THE composition of chlorine hydrate has been the subject of much experimental work. Faraday, by analysis, found the composition to be Cl2.10H2O. The composition has also been determined analytically by Roozeboom1 who found Cl2.8H2O, Bouzat and Azinires2 who found Cl2.6H2O, and more recently by Anwar-Ullah3 who agreed with this last formula. De Forcrand4 used an empirical rule to calculate the number of molecules of water present. According to de Forcrand's rule, if b.Delta;H is the heat of dissociation of the hydrate into gaseous chlorine and ice, and T the temperature at which the dissociation pressure is 760 mm., then b.Delta;H/T is a constant the value of which is approximately 30. The value of T is known from the dissociation pressures determined experimentally by Roozeboom, and this gives a value ofb.Delta;H equal to 8,478 cal./gm. mol. Since de Forcrand's rule is only an approximation, this value of b.Delta;H is very inaccurate. De Forcrand determined the heat of dissociation of the hydrate into gaseous chlorine and water by measuring the heat of solution of the hydrate in water and obtained a value of 18,360 cal. /gm. mol. The number of molecules of water present in the hydrate is then given by n = 18, 360 8, 478/1,436 = 6. 88, the latent heat of fusion of ice being 1,436 cal./gm. mol. De Forcrand therefore assumed the composition to be Cl2.7H2O.

Societies and Academies

PARIS. Academy of Sciences, July 28.—M. Léon Guignard in the chair.—A. Laveran and G. Franchini: Some flagellas of insects obtained in a pure culture, and in particular Crithidia melophagi. Details of the technique for obtaining pure cultures are given, and proof of the pathogenic action on mice.—A. Rateau: The theory of aeroplanes: application to an example.—R. de Forcrand and F. Taboury: The stability of the sulphones formed by the iodides of sodium, rubidium, and cæsium. These compounds have the composition MI + 3SO2; their dissociation pressures have been measured at -22.5° C, 0° C, +9.65° C, and at 150 C, and the results are given in the form of curves.—N. E. Nörlund: . The polynomials of Euler.—Ch. Platrier: The elastic equilibrium of a homogeneous isotropic body of revolution submitted to radial forces either proportional or inversely proportional to the radius.—H. Abraham and E. Bloch: Recording galvanometers with movable needle.—E. Brylinski; The induction reaction of alternators.—E. Poirson: A method of secret telephony. The telephonic currents are deformed by periodic interruptions by mechanical means, and the message cannot then be understood. The distorted currents can be rectified, at the receiving end by a synchronised apparatus. Experiments have been carried out by this method with success over distances up to 600 km.—J. Lavaux: Electrolytic luminescence phenomena presented by certain metallic anodes.—Jh. Martinet: The indirubins.—Ch. Chavanne and L. J. Simon: The critical solution temperatures in aniline of mixtures of hydrocarbons. Application to the analyses of petrols.—H. Colin and O. Liévin: The spontaneous oxidation of complex organic compounds of cobalt. Alkaline solutions of glycerol or lactic acid containing cobalt absorb oxygen up to a maximum; of one atom of oxygen for one atom of cobalt. Other substances, such as mannitol, erythritol, and glucose, under similar conditions absorb oxygen continuously beyond this limit.—P. Russo: The Eocene containing phosphate at Oued Zem (western Morocco).—G. Reboul and L. Dunoyer: The utilisation of temperature for the prediction of barometric variations.—L. Blaringhem: Floral variations in the large marguerite, Leucanthemum vulgare.—Mme. E. Bloch: Anatomical modifications of roots by mechanical action. Compression causes important local modifications, but the general development of the plant is uninfluenced, flowers and fruit remaining normal.—H. Bierry: Food ration. The minimum requirements of sugar and of fat.—L. Vialleton: The epiphyses and cartilage of conjugation in mammals.—A. Paillot: The cytology of the blood of the caterpillars of the Macrolepidoptera.

Societies and Academies

PARIS. Academy of Sciences, September 30.—M. Bouquet de Grye in the chair.—The problem of the dissipation of heat in thick wall with radiating surface, by M. J. Boussinesq.—Remarks on the formation of acids in plants, by MM. Berthelot and Andre. It has been found, that there is no relation between the total amount of vegetable acids contained in a plant, in the free or combined state, and the amount of acid in the juice extracted from the various parts.—On the engraved and painted figures of the Pakolithic period found on the walls of the cave of La Mouthe (Dordogne), by M. Emile Riviere. A minute description of prehistoric drawings, the existence of which was first indicated in 1895 The cave is nearly filled up with débris of prehistoric man, who inhabited the cave at two distinct epochs, which are clearly distinguished by a stalagmitic layer which separates them. The drawings are of three kinds, simple line engravings, others filled with a brownish-red ochre, and third a kind of striation of the rock. All, with one exception, represent animals, the most perfect being complete figures of bison and of a kind oi antelope. The wild goat and reindeer are also recognisable.—On differential equations of the second order with algebraical coefficients, by M. Paul J. Suchar.—On the variable stte of currents, by M. A. Petot.—The calculation of the heat of volatilisation and heat of fusion of some elements, by M. de Forcrand. The relation (L + S)/T = (l+s)/T = 30 between the molecular weight M, the heat of fusion 5, the heats of volatiljsation and fusion L, I, and the temperature, is applied to the cases of phosphorus, arsenic and selenium.—Nitromannite and nitrocellulose, by MM. Leo Vignon and F. Germ. It has been previously shown by one of the authors that the various nitro-derivatives of cellulose energetically reduce an alkaline copper solution. It is now shown that penta- and hexa-nitromannite behave similarly. This reducing power is not altogether due to the formation of mannose. Nitromannite, reduced by ferrous chloride, gives a mannite devoid of reducing power. From this point of view it behaves differently from the nitro-celluloses.—The formation of an isatiri derivative of albumen, by M. Julius Gnezda. A substance giving the reactions of chlorisatin has been obtained from the products of the reaction between hypochlorous acid and peptone.—On the reproduction and development of Peripatopsis Blainvillei, by M. E. L. Bouvier.—On stolonisation in the hydroides, by M. Armand Billard.—The fibrovascular elements of the stem and frond of some Filicineacæ, by MM. C. Eg. Bertrand and F. Cornaille.—On the localisation and dissemination of antimony in the organism, by M. G. Pouchet. The toxic action of antimony and its localisation require doses of antimony much larger than with arsenic, the loalisation of antimony being different from that of arsenic. The toxic action of arsenic is not diminished by the presence of antimony, but, on the contrary, appears to be somewhat increased.

Societies and Academies

PARIS. Academy of Sciences, September 16.—M. Bouquet de la Grye in the chair.—Demonstration and use of the formuke relating to the refractometer, by M. A. Cornu.—Onthe elastic arch, by M. G. Poisson.—On the simultaneous employment of multiplex and ordinary telegraphy in the same circuit, by M. E. Mercadier.—On the molecular weight of chloral hydrate at the temperature of its boiling point, by M. de Forcrand. By a discussion of thermochemicaldata the author arrives at the conclusion that at the boiling point chloral hydrate is not totally, dissociated, from 4 to 5 per cent. remaining undissociated.—On dunite from Koswinsky-Kamen, in the Ural, by MM. K. Duparc and F. Pearce. The results of a microscopical and chemical study of the dunites from this district.—A new cave with drawings on its walls of the Palæolithic period, by MM. L. Capitan and H. Breuil. An account of the discovery of a cave situated at Combarelles, in Tayac (Dordogne), about two kilometres from the Mouthe cave. The cave is about 225 metres long, and about 119 metres from the entrance drawings can be seen on the walls, which continue to the end of the cave. They are engraved upon a cretaceous rock, but the greater number are covered with a stalagmitic deposit, which is sometimes so thick that the lines cannot be seen through it. No less than 109 figures can be clearly made out, including drawings of the horse, cow, bison, reindeer, mammoth, and wild goat. It would appear that these drawings, the antiquity of which cannot be doubted, could only have been executed by artists reproducing animals that they saw. Hence they are clearly Paæolithic, and go back to the epoch when the mammoth and the reindeer lived in France.—Luminous rays diverging at 180° from the sun, by M. Jean Mascart.

Societies and Academies

PARIS. Academy of Sciences, August 1.-M. de Lacaze-Duthiers in the chair.-On boron pentasulphide, by M. Moissan. If the tri-iodide of boron, instead of being treated with sulphur in the dry way at a low red heat, as in the preparation of boron tri-sulphide, be mixed with sulphur and dissolved in carbon bisulphide at the ordinary temperature, boron pentasulphide is obtained. It fuses at 390°, and does not pass through the pasty state. In contact with water it forms boric acid, sulphuretted hydrogen, and a precipitate of sulphur. Mercury and silver reduce it to the trisulphide, forming metallic sulphides. Heated to fusion in a vacuum it decomposes into sulphur and the trisulphide. Its density is 1 -85. It is very difficult to obtain free from iodine, but in all the preparations the ratio between the boron and the sulphur has indicated the formula B2S5.-On the stripped plants of autumn, and their utilization as green manure, by M. P. P. Deherain. It has been found that by planting the ground with vetch or mustard, and digging it in during the autumn, the amount of nitrogen retained in the soil was nearly doubled.-Remarks on alimentation in the- Ophidia, by M. Leon Vaillant.-A report on the great anaconda of Central America kept in the reptile menagerie. Since 1885 the snake has eaten on the average five times per annum, its nourishment consisting of goats, three rabbits, and one goose. The interval between two meals was in one instance 204 days.-On symmetric tetrahedral curves, by M. Alphonse Dumoulin.-On Stokes' law, its verification, and interpretation, by M. G. Salet.-A spectrum, given by a spectroscope with quartz prisms, is received on the fluorescent substance contained in a Soret eye-piece. It is then projected transversally on to the slit of a second spectroscope. Through this the diagonal spectrum of Stokes' classical experiment is seen with perfect definition, no ray exceeding the theoretical limit. The law thus verified can also be deduced from thermodynamic considerations. According to Stokes' law, “the rays emitted by a fluorescent substance always have a smaller refrangibility than the exciting rays.” If it were possible to transform yellow into violet light by fluorescence, many chemical reactions would become possible which only occur at the higher temperature at which violet appears in the spectrum. This would be equivalent to the passage of heat from a colder to a hotter body, in contradiction to the second law of thermodynamics.-Constitution of pyrogallol, by M. de Forcrand.- On Cascarine, by M. Leprince.-Physiological examination of four cyclists after a run of 397 km., by MM. Chibret et Huguet. This distance, which was covered by the youngest of the party, an Englishman of 18, in seventeen hours, was that between Paris and Clermont-Ferrand. It was found that the temperature was at the finish rather below than above the normal; that the coefficient of utilization of urinary nitrogen varied inversely as the degree of fatigue, and that therefore a decided waste of nitrogen is a concomitant of excessive fatigue. The nutriment taken during the course consisted of much alcohol, champagne, beef-tea, and Kola solution in the case of the Englishman. He and the next in speed both took Kola. The winner was extremely fatigued at the finish; the next man, a Frenchman of 28, not at all. His pulse was beating at 60, that of the former at 84. The coefficients of utilization of nitrogen were 76*32 and 58*27 per cent, respectively.-On the properties of the vapours of formol or formic aldehyde, by MM. F. Berlioz and A. Trillat.'-Subcutaneous grafting of the pancreas: its importance in the study of pancreatic diabetes, by M. E. Hédon.-On the habits of Clinus argenlatus Cuv. and Val., by M. Frédéric Guitel.-On a Permian Alga, with its structure preserved, found in the boghead of Autun: Pila Bibractensis, by MM. C. Eg. Bertrand and B. Renault.-The chalk of Chartres, by M. A. de Grossouvre.

Societies and Academies

PARIS.Academy of Sciences, May 2.—M. d'Abbadie in the chair.—The movements of minute organisms analyzed by means of chronophotography, by M. Marey. Using an arrangement described in the Revue Générale des Sciences in November last, and in NATURE, vol. xlv. p. 228, M. Marey has obtained photographs of the movements of blood corpuscles in the capillaries, and has analyzed the movements of zoosphores in the cells of a Cladophora. Enlargements from these negatives have been presented to the Academy. By taking a series of pictures at intervals of about one-tenth of a second, and projecting them upon a screen at about the same rate, the effect of the real motions of the object can be reproduced. The arrangement for doing this will be described in a future communication.—Observations of Swift's, Denning's, and Winnecke's comets, made at Algiers Observatory with the coudé equatorial, by MM. Rambaud and Sy. Observations of position are given.—On the approximation of functions of very large numbers, by M. Maurice Hamy.—On the tautochronism in a material system, by M. Paul Appell.—On the laws of electrolysis, by M. A. Chassy. When a substance having the formula MpRq is electrolyzed, M designating an electro-positive and R an electro-negative radicle, one equivalent of the radicle R, and p/q equivalents of the radicle Mare disengaged when one equivalent of hydrogen is set free in a voltameter included in the circuit. Wiedemann and others have found exceptions to this law, for in the case of some salts, q/p equivalent of the radicle R and one equivalent of the other radicle are disengaged. M. Chassy proposes to substitute the following law for those previously enunciated, all cases being included in it: “Lorsqu' on électrolyse une substance quelconque il se dégage toujours l'equivalent d'hydrogène ou la quantité correspondante du radical électropositif.”—A new case of abnormal solution: saturated solutions, by M. F. Parmentier. The author finds that the solubility of ethyl bromide in ether decreases rapidly with increase of temperature.—The occurrence of fluorine in different varieties of natural phosphates, by M. Ad. Carnot. From the results of the analyses of a number of sedimentary phosphates it is concluded that in the sedimentary phosphates the proportion of fluorine is sensibly equal to that in apatites having an equal percentage of phosphorus. Phosphorites of fibrous, semi-crystalline structure have almost the same composition as crystallized apatites. Earthy or compact phosphorites contain a less proportion of fluorine. Concretionary, zoned, and mammillated phosphorites contain barely any fluorine.—Estimation of small quantities of carbon monoxide by means of cuprous chloride, by M. L. de Saint-Martin.—Thermal study of the value of the replacement of hydrogen in phenolic hydroxyl, by M. de Forcrand. C6H6O sol. + Na sol. = C6H5. ONa sol. + H gas. … + 39˙10 cal. This is practically the mean value for the replacement of H by Na in tertiary alcohols and acids, for.

Societies and Academies

Societies and Academies