Laplace's Theory Research Articles

On the evolution of global ocean tides

We apply Laplace's tidal theory to the evolution of lunar and solar tides on the geologic timescale of Earth's rotation and study the tidal resonance. We study the global tide in the mid-ocean far away from continents. On the short timescale, a linear relationship of tidal height and Earth's rotation is obtained. On the long timescale, the tide is less than 1 metre at present but it was 5 metres in the past and will reach 8 metres in the future because of resonances of tidal wave and Earth's rotation. We conclude that the Earth–Moon orbital separation and the slowdown of Earth's rotation are faster than expected before.

On The Nineteenth-century Origins Of Significance Testing And P-hacking

This paper examines the development of Laplacean practical certainty from 1810, when Laplace proved his central limit theorem, to 1925, when Ronald A. Fisher published his Statistical Methods for Research Workers. Although Laplace's explanations of the applications of his theorem were accessible to only a few mathematicians, expositions published by Joseph Fourier in 1826 and 1829 made the simplest applications accessible to many statisticians. Fourier suggested an error probability of 1 in 20,000, but statisticians soon used less exigent standards. Abuses, including p-hacking, helped discredit Laplace's theory in France to the extent that it was practically forgotten there by the end of the 19th century, yet it survived elsewhere and served as the starting point for Karl Pearson's biometry. The probability that a normally distributed random variable is more than three probable errors from its mean is approximately 5%. When Fisher published his Statistical Methods, three probable errors was a common standard for likely significance. Because he wanted to enable research workers to use distributions other than the normal – the t distributions, for example – Fisher replaced three probable errors with 5%. The use of after Fisher differs from its use by Pearson before 1920. In Pearson's Biometrik}, a significant difference was an observed difference that signified a real difference. Biometrika's authors sometimes said that an observed difference is likely or very likely to be significant, but they never said that it is very significant, and they did not have levels of significance. Significance itself was not a matter of degree. What might this history teach us about proposals to curtail abuses of statistical testing by changing its current vocabulary (p-value, significance, etc.)? The fact that similar abuses arose before this vocabulary was introduced suggests that more substantive changes are needed.

Effect of temperature on the water retention properties of two high performance concretes

This contribution aims at (1) determining experimentally the first desorption isotherms of two high performance concretes (based on CEM I and CEM V cements), at three different temperature levels T=20, 50 and 80°C, and (2) showing whether these may be simply described by adsorption and capillarity.Results at 20°C compare well with recently published results; in particular, an important desorption is observed at high RH (≥98%). A simple pore network model, based on Kelvin–Laplace's capillary theory, is implemented, and shows the existence of two main de-saturation modes, one at high pore radii (capillary pores), the other for pore radii on the order of a few nanometers (C-S-H porosity), where desorption is shown to occur. A complementary drying mechanism is evidenced at 80°C, which is attributed to ettringite and/or C-S-H degradation. Finally, proper numerical fitting of all isotherm data is achieved using the well-known three-parameter BSB model.

A history of parametric statistical inference from Bernoulli to Fisher, 1713-1935

The Three Revolutions in Parametric Statistical Inference.- The Three Revolutions in Parametric Statistical Inference.- Binomial Statistical Inference.- James Bernoulli's Law of Large Numbers for the Binomial, 1713, and Its Generalization.- De Moivre's Normal Approximation to the Binomial, 1733, and Its Generalization.- Bayes's Posterior Distribution of the Binomial Parameter and His Rule for Inductive Inference, 1764.- Statistical Inference by Inverse Probability.- Laplace's Theory of Inverse Probability, 1774-1786.- A Nonprobabilistic Interlude: The Fitting of Equations to Data, 1750-1805.- Gauss's Derivation of the Normal Distribution and the Method of Least Squares, 1809.- Credibility and Confidence Intervals by Laplace and Gauss.- The Multivariate Posterior Distribution.- Edgeworth's Genuine Inverse Method and the Equivalence of Inverse and Direct Probability in Large Samples, 1908 and 1909.- Criticisms of Inverse Probability.- The Central Limit Theorem and Linear Minimum Variance Estimation by Laplace and Gauss.- Laplace's Central Limit Theorem and Linear Minimum Variance Estimation.- Gauss's Theory of Linear Minimum Variance Estimation.- Error Theory. Skew Distributions. Correlation. Sampling Distributions.- The Development of a Frequentist Error Theory.- Skew Distributions and the Method of Moments.- Normal Correlation and Regression.- Sampling Distributions Under Normality, 1876-1908.- The Fisherian Revolution, 1912-1935.- Fisher's Early Papers, 1912-1921.- The Revolutionary Paper, 1922.- Studentization, the F Distribution, and the Analysis of Variance, 1922-1925.- The Likelihood Function, Ancillarity, and Conditional Inference.

A History of Mathematical Statistics from 1750 to 1930

DIRECT PROBABILITY 17501805. Some Results and Tools in Probability Theory (By Bernoulli, de Moivre, and Laplace). The Distribution of the Arithmetic Mean, 17561781. Chance or Design: Tests of Significance. Theory of Errors and Methods of Estimation. Fitting of Equations to Data, 17501805. INVERSE PROBABILITY BY BAYES AND LAPLACE, WITH COMMENTS ON LATER DEVELOPMENTS. Induction and Probability: The Philosophical Background. Bayes, Price, and the Essay, 17641765. Equiprobability, Equipossibility, and Inverse Probability. Laplace's Applications of the Principle of Inverse Probability in 1774. Laplace's General Theory of Inverse Probability. The Equiprobability Model and the Inverse Probability Model for Games of Chance. Laplace's Methods of Asymptotic Expansion, 1781 and 1785. Laplace's Analysis of Binomially Distributed Observations. Laplace's Theory of Statistical Prediction. Laplace's Sample Survey of the Population of France and the Distribution of the Ratio Estimator. THE NORMAL DISTRIBUTION, THE METHOD OF LEAST SQUARES, AND THE CENTRAL LIMIT THEOREM. GAUSS AND LAPLACE, 18091828. The Early History of the Central Limit Theorem, 18101853. Derivations of the Normal Distribution as a Law of Error. Gauss's Linear Normal Model and the Method of Least Squares, 1809 and 1811. Laplace's Large-Sample Theory of Linear Estimation, 18111827. Gauss's Theory of Linear Unbiased Minimum Variance Estimation, 18231828. SELECTED TOPICS IN ESTIMATION THEORY 18301930. On Error and Estimation Theory, 18301890. Bienaym?'s Proof of the Multivariate Central Limit Theorem and His Defense of Laplace's Theory of Linear Estimation, 1852 and 1853. Cauchy's Method for Determining the Number of Terms to be Included in the Linear Model and for Estimating the Parameters, 18351853. Orthogonalization and Polynomial Regression. Statistical Laws in the Social and Biological Sciences, Poisson, Quetelet, and Galton, 18301890. Sampling Distributions under Normality. Fisher's Theory of Estimation, 19121935, and His Immediate Precursors. References. Index.

The Tidal Problem for Simple Circulations

Simple wave-circulation systems on the rotating spherical surface are considered in the framework of Laplace's tidal theory. For solid body rotation of the shallow 1-layer system the comparison of tidal theory and β-plane concepts shows that Matsuno's approach provides a consistent approximation for divergent low-frequency waves, while the midlatitude β-plane captures fewer aspects of the system. Tidal theory suggests an alternative formalism for extratropical low-frequency waves. The geography of wave activity depends on internal physics of the circulation: on a mean flow with constant layer thickness low-frequency waves populate an equatorial belt, while a hydrostatically driven eastward mean flow with varying layer thickness confines divergence-free Rossby waves to the extratropics. Effects of stratification and vertical shear are considered for solid body rotation of bishallow water with constant layer thickness. Rotation and mean flow stabilize against Kelvin–Helmholtz instability and the equatorial Kelvin wave is the most unstable mode of this flow. However, observed vertical shears in the tropical ocean remain well below the instability threshold. Baroclinic instability does not occur. Wave geography and stability characteristics of this system capture major features of the oceanic large-scale circulation.

Approximate capacities of some toroidal condensers

It is shown that a variety of electrostatic problems involving toroidal condensers are solvable approximately by means of a certain type of transformation of Laplace's equation and perturbation theory. After a critique of previous theory of the toroidal condenser with concentric-circular section, this problem is resolved, followed by the problem of the elliptic-toroidal condenser. On the basis of these solutions, other problems are solved approximately by a double-perturbation approach; namely, the problem of a circular torus containing a laminar ring, and that of the circular-toroidal condenser for which the circular sections are eccentric.

Capillarity before Laplace: Clairaut, Segner, Monge, Young

The first half of Laplace's theory of capillarity [1] was published several months after the publication of Thomas Young's Essay on the Cohesion of Fluids [2]. When, after a delay caused by the war, it finally reached England, Young naturally was upset by the emergence of a formidable rival. He could have admitted the superiority of the new doctrine and used his leisure to develop the latter, but he did not choose this alternative; presumably, his insufficient knowledge of the calculus was a factor in his decision. He preferred to attack Laplace, and, as so often happens, the offensive was two-pronged: many of Laplace's results were declared to be erroneous, and the correct findings were said to be not new. In a recent paper [3], I have discussed one of the former criticisms and shown it to be unjustified. Here I review the work of four of Laplace's predecessors, and I attempt to estimate the extent to which they anticipated him. Three of them, and also James Jurin (1684-1750), have been commented upon by Laplace in the second Supplement of the 10th book of his Mecanique celeste [4], but this discussion is very brief and its impartiality, naturally, may be suspected. Thus a new comparison appears to be in order.

Pulmonary and Respiratory Physiology ed. by J. H. Comroe, Jr. (review)

BOOK REVIEWS Pulmonary and Respiratory Physiology. Vols. 1 and 2. Edited by J. H. Comroe, Jr. Benchmark Papers in Human Physiology, vols. 5 and 6. Stroudsburg, Pa: Dowden, Hutchinson & Ross, 1976. Pp. 397 (vol. 1); 445 (vol. 2). $52.00. These volumes are classics of the classic literature of physiology! The Benchmark papers set out to print the classics of physiology, and Dr. Comroe has arranged some really exciting reading for everyone who has any interest in the development of pulmonary physiology. The Benchmark concept was publication in toto of original articles, but of 1 16 chosen for these volumes, only 44 are given completely and only excerpts from the other 72 are printed. This was an excellent decision. Part 1 is divided into sections on air, oxygen and carbon dioxide, mechanical properties of the lung and thorax, and the pulmonary circulation. Short commentaries by Comroe at the beginning of each section give excellent background and correlation for the articles chosen. A bit about the authors and their historical perspective makes each article more enjoyable. Where would you, the reader, begin to choose important articles pertaining to the development of respiratory knowledge? Comroe chose the discovery of carbon dioxide by van Helmont in 1662. Several well-known discoveries are related in ensuing chapters, and these enable one to appreciate the ingenuity and initiative that was shown by investigators who had to make their own equipment and chemicals without the benefit of supply houses. Later chapters of section 1, part 1, deal with articles that tell of discovery of laws that we now take for granted. The works of Toricelli, Boyle, Henry, Dalton, and Bert are most illuminating. Comroe states, "Throughout the early history of science, we come across giants who had little formal education; Dalton was one of these, although he taught in a village school at the age of 12!" Comments such as this arouse the reader's interest in the early pioneers. Section 2 includes Hooke's lecture on the spring, Poiseuille's experiments with fluids flowing through small tubes, Laplace's theory ofcapillary action, and leads up to the discovery of surfactant. Excerpts from two articles that appeared long before Harvey reported his experiments are found at the beginning of section 3. Harvey's work, as would be expected, is also included. Developments in measurement of pulmonary blood flow and pressure, right heart catheterization, and measurement of capillary wedge pressure are part of this section, which closes with some information about nonrespiratory functions of the lung. Part 2 consists of "Regulation of Breathing," "Pulmonary Function in Man," and "Oxygen and Carbon Dioxide: Measurement and Transport." Section 1 comprises concepts of central control of breathing including chemical influence as an integral part of the concept. Most of these studies involved sectioning the Perspectives in Biology and Medicine · Summer 1977 | 607 brain stem ofanimals. These reports are followed by 10 papers relating to reflex, that is, peripheral nervous regulation of respiration, and include the original work of Breuer and Hering and of Heymans. Section 2 describes efforts toward measuring lung volumes, dead space, distribution of gases, and diffusion of gases in the lungs. The original papers describing the nitrogen meter, whole body Plethysmograph, and methods for determining ventilation-perfusion relationships are reproduced. The introduction of carbon monoxide for measuring diffusion is reproduced in some detail, as is the use of radioactive gas to measure regional blood flow. The first five papers of section 3 describe methods for determination of blood gases, and the sixth tells about the infrared gas analyzer. In fact, in these two volumes together, 34 papers chiefly described new methods and 21 additional papers reported new discoveries which had to have some new methodology. The importance of methods cannot be overlooked, for advances in almost any scientific field are largely dependent on them. This section reprints original papers that describe the effects of temperature, buffers, hemoglobin, and carbonic anhydrase on carriage of gases by the blood. The last two chapters relate the relatively recent information concerning the role played by organic phosphates (DPG). These volumes were sent to me with the comment, "I think you will agree that masterful commentary on the genuine classics makes for 'Super...

Laplace's theory of errors

The genesis and development of the theory of errors before Laplace have been considered in a series of my articles [69] -[74]. My present aim is to elucidate the relevant work of Laplace himself, which hitherto I have considered only in connection with finite random sums [72] *. Laplace's contributions divide naturally into the Theorie analytique des probabilites (hereafter called TAP), first published in 1812 (and its supplements published in 1820), and the writings prior to this. These writings2 are studied in §§ 2-5, and the relevant places of the TAP in §§ 6-9; §§ 10 and 12-13 are devoted to somewhat specific subjects related to my theme, while §11 is an attempt to describe the limitations of Laplace's theory of errors. Several facts must be noted in following the text below. 1. Laplace's notation for f(x)dx = P{x^C^x + dx} is f(x) = P{C = x}. 2. Laplace's expression le veritable instant or, more generally, "the true value", is now part of the classical error theory. The different viewpoint of mathematical statistics employs the concept of parameters (specifically, location parameters) of distribution laws.

P.S. Laplace's work on probability

Taken together with my previous articles [77], [80] devoted to the history of finite random sums and to Laplace's theory of errors, this paper sheds sufficient light on the whole work of Laplace in probability.

The historical origins of the Van der Waals equation

This paper studies J.D. van der Waals's thesis in the light of his own remark that he set out to determine the “molecular pressure” in Laplace's theory of capillarity. Van der Waals is reviwed as working in the tradition of mechanical explanation that goes back directly to Newton. The influence of Clausius is also traced, but emphasis is placed on the different uses to which Clausius and Van der Waals put the virial theorem. The status of molecular theory in 1873 is analyzed.

On the prior probability in the theory of sampling

1. If a class consists of n members of which r have the property φ, and we wish to estimate r by the process of sampling, the distribution of probability among values of r, given the composition of the sample, necessarily depends to some extent on our previous knowledge. This is expressed by saying that the prior probability of a particular value of r is f(r). According to Laplace's theory f(r) is constant. It is obvious that there are cases where the previous knowledge is such as to ensure that f(r) is not constant; but the question remains whether such cases should be considered the exception or the rule.

Societies and Academies

PARIS. Academy of Sciences, September 4.—M. Armand Gautier in the chair.—Kr. Birkeland: The electrical constitution of the sun. A development of views put forward in two earlier communications. The photosphere is regarded as a sea of electric arcs. The bearing of these views on Laplace's nebular hypothesis is discussed, since, if matter is radiated under the action of electrical forces, it is not necessary to assume that at one time the nebula extended to the orbit of Neptune, and this reduces the force of Moulton's objections to Laplace's theory.—M. Merlin: Some theorems of arithmetic and an enunciation which contains them. Henri Viliat: A mixed problem of the theory of harmonic functions in an annular area.—Ed. Griffon: A singular case of variation by budding in the peach tree. A description of the appearance of shoots of almond, bearing blossom, on a peach tree.—Marcel Baudouin: Human post-mortem actions on the human bones in the bone caves of the polished stone period.— Stanilas Meunier: An Egyptian meteorite recently presented to the museum. This meteorite appears to belong to a new lithological type, and will be described in detail in a later communication.

On the Solution of a Certain Differential Equation Which Presents Itself in Laplace's Kinetic Theory of Tides.

On the Solution of a Certain Differential Equation Which Presents Itself in Laplace's Kinetic Theory of Tides.

6. On Laplace's Theory of the Internal Pressure in Liquids

Laplace, assuming molecular force to be insensible at distances greater than a small quantity a, finds the resultant molecular force on a unit particle at a distance x within the (plane) surface. This being called X, the internal pressure iswhere p is the density of the liquid. But this is evidently the work required to take unit volume of the liquid (particle by particle) from the interior to the surface. And it is easily seen that to carry it from the surface beyond the range of the molecular forces requires just as much more work:—for the density of the surface-film is treated as equal to that of the rest of the liquid.

XLIII. On Laplace's theory of capillarity

(1883). XLIII. On Laplace's theory of capillarity. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science: Vol. 16, No. 100, pp. 309-315.

XLVII. On Laplace's theory of capillarity

XLVII. <i>On</i> Laplace's <i>theory of capillarity</i>

4. On the Linear Differential Equation of the Second Order

This paper contains the substance of investigations made for the most part many years ago, but recalled to me during last summer by a question started by Sir W. Thomson, connected with Laplace's theory of the tides.A comparison is instituted between the results of various processes employed to reduce the general linear differential equation of the second order to a non-linear equation of the first order. The relation between these equations seems to be most easily shown by the following obvious process, which I lit upon while seeking to integrate the reduced equation by finding how the arbitrary constant ought to be involved in its integral.

XXIII. On a controverted point in Laplace's theory of the tides

XXIII. <i>On a controverted point in</i> Laplace's <i>theory of the tides</i>