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Young–Laplace equation

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In physics , the Young–Laplace equation ( / l ə ˈ p l ɑː s / ) is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids , such as water and air , due to the phenomenon of surface tension or wall tension , although use of the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces . It is a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness): Δ p = − γ ∇ ⋅ n ^ = − 2 γ H f = − γ ( 1 R 1 + 1 R 2 ) {\displaystyle {\begin{aligned}\Delta p&=-\gamma \nabla \cdot {\hat {n}}\\&=-2\gamma H_{f}\\&=-\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)\end{aligned}}} where Δ p {\displaystyle \Delta p} is the Laplace pressure , the pressure difference across the fluid interface (the exterior pressure minus the interior pressure), γ {\displaystyle \gamma } is the surface tension (or wall tension ), n ^ {\displaystyle {\hat {n}}} is the unit normal pointing out of the surface, H f {\displaystyle H_{f}} is the mean curvature , and R 1 {\displaystyle R_{1}} and R 2 {\displaystyle R_{2}} are the principal radii of curvature . Note that only normal stress is considered, because a static interface is possible only in the absence of tangential stress.

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71-521: The equation is named after Thomas Young , who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young–Laplace–Gauss equation, as Carl Friedrich Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions using Johann Bernoulli 's virtual work principles. If

142-820: A 2 mm wide (1 mm radius) tube, the water would rise 14 mm. However, for a capillary tube with radius 0.1 mm, the water would rise 14 cm (about 6 inches ). In the general case, for a free surface and where there is an applied "over-pressure", Δ p , at the interface in equilibrium, there is a balance between the applied pressure, the hydrostatic pressure and the effects of surface tension. The Young–Laplace equation becomes: Δ p = ρ g h − γ ( 1 R 1 + 1 R 2 ) {\displaystyle \Delta p=\rho gh-\gamma \left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)} The equation can be non-dimensionalised in terms of its characteristic length-scale,

213-468: A chill arose between them. For many years they kept details of their work away from each other. Some of Young's conclusions appeared in the famous article "Egypt" he wrote for the 1818 edition of the Encyclopædia Britannica . When Champollion finally published a translation of the hieroglyphs and the key to the grammatical system in 1822, Young (and many others) praised his work. Nevertheless,

284-671: A cultural Christian Quaker. Hudson Gurney informed that before his marriage, Young had to join the Church of England , and was baptized later. Gurney stated that Young "retained a good deal of his old creed, and carried to his scriptural studies his habit of inquisition of languages and manners," rather than the habit of proselytism. Yet, the day before his death, Young participated in religious sacraments; as reported in David Brewster 's Edinburgh Journal of Science : "After some information concerning his affairs, and some instructions concerning

355-461: A fellow in 1794. He resigned his professorship in 1803, fearing that its duties would interfere with his medical practice. His lectures were published in 1807 in the Course of Lectures on Natural Philosophy and contain a number of anticipations of later theories. In 1811, Young became physician to St George's Hospital , and in 1814 he served on a committee appointed to consider the dangers involved in

426-653: A few details. Thomas Young (scientist) Thomas Young FRS (13 June 1773 – 10 May 1829) was a British polymath who made notable contributions to the fields of vision , light , solid mechanics , energy , physiology , language , musical harmony , and Egyptology . He was instrumental in the decipherment of Egyptian hieroglyphs , specifically the Rosetta Stone . Young has been described as " The Last Man Who Knew Everything ". His work influenced that of William Herschel , Hermann von Helmholtz , James Clerk Maxwell , and Albert Einstein . Young

497-412: A gravitational field of magnitude and orientation given by: where M {\displaystyle M} is the mass of the field source (larger), and r ^ {\displaystyle \mathbf {\hat {r}} } is a unit vector directed from the field source to the sample (smaller) mass. The negative sign indicates that the force is attractive (points backward, toward

568-575: A liquid surface with a solid, and showed how from these two principles to deduce the phenomena of capillary action. In 1805, Pierre-Simon Laplace , the French philosopher, discovered the significance of meniscus radii with respect to capillary action. In 1830, Carl Friedrich Gauss , the German mathematician, unified the work of these two scientists to derive the Young–Laplace equation , the formula that describes

639-486: A method of tuning musical instruments. Later scholars and scientists have praised Young's work although they may know him only through achievements he made in their fields. His contemporary Sir John Herschel called him a "truly original genius". Albert Einstein praised him in the 1931 foreword to an edition of Isaac Newton 's Opticks . Other admirers include physicist Lord Rayleigh and Nobel Physics laureate Philip Anderson . Thomas Young's name has been adopted as

710-552: A physician at 48 Welbeck Street , London (now recorded with a blue plaque ). Young published many of his first academic articles anonymously to protect his reputation as a physician. In 1801, Young was appointed professor of natural philosophy (mainly physics ) at the Royal Institution . In two years, he delivered 91 lectures. In 1802, he was appointed foreign secretary of the Royal Society , of which he had been elected

781-505: A ratio of the original length); that is, stress = E × strain, for a uniaxially loaded specimen. Young's modulus is independent of the component under investigation; that is, it is an inherent material property (the term modulus refers to an inherent material property). Young's Modulus allowed, for the first time, prediction of the strain in a component subject to a known stress (and vice versa). Prior to Young's contribution, engineers were required to apply Hooke's F = kx relationship to identify

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852-555: A year later Young published an Account of the Recent Discoveries in Hieroglyphic Literature and Egyptian Antiquities , with the aim of having his own work recognised as the basis for Champollion's system. Young had correctly found the sound value of six hieroglyphic signs, but had not deduced the grammar of the language. Young himself acknowledged that he was somewhat at a disadvantage because Champollion's knowledge of

923-442: Is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other. The formula is: where m 1 {\displaystyle m_{1}} and m 2 {\displaystyle m_{2}} are any two masses, G {\displaystyle G} is the gravitational constant , and r {\displaystyle r}

994-654: Is credited with establishing Christiaan Huygens' wave theory of light , in contrast to the corpuscular theory of Isaac Newton . Young's work was subsequently supported by the work of Augustin-Jean Fresnel . Young belonged to a Quaker family of Milverton, Somerset , where he was born in 1773, the eldest of ten children. By the age of fourteen, Young had learned Greek , Latin , French , Italian , Syriac , Samaritan Hebrew , Arabic , Biblical Aramaic , Persian , Turkish , and Ge'ez . Young began to study medicine in London at St Bartholomew's Hospital in 1792, moved to

1065-581: Is much esteemed, it is too learned ... in short it is not understood." Young has also been called the founder of physiological optics. In 1793 he explained the mode in which the eye accommodates itself to vision at different distances as depending on change of the curvature of the crystalline lens ; in 1801 he was the first to describe astigmatism ; and in his lectures he presented the hypothesis, afterwards developed by Hermann von Helmholtz , (the Young–Helmholtz theory ), that colour perception depends on

1136-416: Is neglected. In Einstein's theory of general relativity , gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, masses distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. The gravitational force is a fictitious force . There is no gravitational acceleration, in that

1207-468: Is often referred to as the Law of Laplace , used in the context of cardiovascular physiology , and also respiratory physiology , though the latter use is often erroneous. Francis Hauksbee performed some of the earliest observations and experiments in 1709 and these were repeated in 1718 by James Jurin who observed that the height of fluid in a capillary column was a function only of the cross-sectional area at

1278-530: Is the gravitational acceleration . This is sometimes known as the Jurin's law or Jurin height after James Jurin who studied the effect in 1718. For a water-filled glass tube in air at sea level : and so the height of the water column is given by: h ≈ 1.4 × 10 − 5 m 2 a . {\displaystyle h\approx {{1.4\times 10^{-5}}\mathrm {m} ^{2} \over a}.} Thus for

1349-464: Is the distance between the two point-like masses. Using the integral form of Gauss's Law , this formula can be extended to any pair of objects of which one is far more massive than the other — like a planet relative to any man-scale artifact. The distances between planets and between the planets and the Sun are (by many orders of magnitude) larger than the sizes of the sun and the planets. In consequence both

1420-467: Is the steady gain in speed caused exclusively by gravitational attraction . All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; the measurement and analysis of these rates is known as gravimetry . At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation . At different points on Earth's surface,

1491-496: Is used to explain gravitational phenomena, such as the gravitational force field exerted on another massive body. It has dimension of acceleration (L/T ) and it is measured in units of newtons per kilogram (N/kg) or, equivalently, in meters per second squared (m/s ). In its original concept, gravity was a force between point masses . Following Isaac Newton , Pierre-Simon Laplace attempted to model gravity as some kind of radiation field or fluid , and since

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1562-934: The American Academy of Arts and Sciences in 1822. A few years before his death he became interested in life insurance , and in 1827 he was chosen as one of the eight foreign associates of the French Academy of Sciences . In the same year he became a first class corresponding member, living abroad, of the Royal Institute of the Netherlands . In 1828, he was elected a foreign member of the Royal Swedish Academy of Sciences . In 1804, Young married Eliza Maxwell. They had no children. Young died in his 56th year in London on 10 May 1829, having suffered recurrent attacks of "asthma". His autopsy revealed atherosclerosis of

1633-474: The University of Edinburgh Medical School in 1794, and a year later went to Göttingen , Lower Saxony, Germany, where he obtained the degree of doctor of medicine in 1796 from the University of Göttingen . In 1797 he entered Emmanuel College, Cambridge . In the same year he inherited the estate of his grand-uncle, Richard Brocklesby , which made him financially independent, and in 1799 he established himself as

1704-431: The capillary length is ~2 mm . The non-dimensional equation then becomes: h ∗ − Δ p ∗ = ( 1 R 1 ∗ + 1 R 2 ∗ ) . {\displaystyle h^{*}-\Delta p^{*}=\left({\frac {1}{{R_{1}}^{*}}}+{\frac {1}{{R_{2}}^{*}}}\right).} Thus,

1775-470: The capillary length : L c = γ ρ g , {\displaystyle L_{c}={\sqrt {\frac {\gamma }{\rho g}}},} and characteristic pressure p c = γ L c = γ ρ g . {\displaystyle p_{c}={\frac {\gamma }{L_{c}}}={\sqrt {\gamma \rho g}}.} For clean water at standard temperature and pressure ,

1846-416: The capillary pressure difference sustained across the interface between two static fluids. Young was the first to define the term "energy" in the modern sense. He also did work on the theory of tides paralleling that of Laplace and anticipating more well-known work by Airy . Young's equation describes the contact angle of a liquid drop on a plane solid surface as a function of the surface free energy,

1917-927: The hydrostatic Young–Laplace equations : r ″ ( 1 + r ′ 2 ) 3 / 2 − 1 r ( z ) 1 + r ′ 2 = z − Δ p ∗ {\displaystyle {\frac {r''}{(1+r'^{2})^{{3}/{2}}}}-{\frac {1}{r(z){\sqrt {1+r'^{2}}}}}=z-\Delta p^{*}} z ″ ( 1 + z ′ 2 ) 3 / 2 + z ′ r ( 1 + z ′ 2 ) 1 / 2 = Δ p ∗ − z ( r ) . {\displaystyle {\frac {z''}{(1+z'^{2})^{3/2}}}+{\frac {z'}{r(1+z'^{2})^{{1}/{2}}}}=\Delta p^{*}-z(r).} In medicine it

1988-421: The proper acceleration and hence four-acceleration of objects in free fall are zero. Rather than undergoing an acceleration, objects in free fall travel along straight lines ( geodesics ) on the curved spacetime. In physics , a gravitational field or gravitational acceleration field is a vector field used to explain the influences that a body extends into the space around itself. A gravitational field

2059-519: The ripple tank he demonstrated the idea of interference in the context of water waves. With Young's interference experiment , the predecessor of the double-slit experiment , he demonstrated interference in the context of light as a wave. Young, speaking on 24 November 1803, to the Royal Society of London, began his now-classic description of the historic experiment: The experiments I am about to relate ... may be repeated with great ease, whenever

2130-458: The "enchorial" text of the Rosetta Stone (using a list with 86 demotic words), and then studied the hieroglyphic alphabet but initially failed to recognise that the demotic and hieroglyphic texts were paraphrases and not simple translations. There was considerable rivalry between Young and Jean-François Champollion while both were working on hieroglyphic decipherment. At first they briefly cooperated in their work, but later, from around 1815,

2201-399: The "far-field" gravitational acceleration associated with a massive body. When the dimensions of a body are not trivial compared to the distances of interest, the principle of superposition can be used for differential masses for an assumed density distribution throughout the body in order to get a more detailed model of the "near-field" gravitational acceleration. For satellites in orbit,

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2272-413: The 19th century, explanations for gravity in classical mechanics have usually been taught in terms of a field model, rather than a point attraction. It results from the spatial gradient of the gravitational potential field . In general relativity , rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as

2343-621: The Earth measuring differences in the distance between the two probes in order to more precisely determine the gravitational field around the Earth, and to track changes that occur over time. Similarly, the Gravity Recovery and Interior Laboratory mission from 2011 to 2012 consisted of two probes ("Ebb" and "Flow") in polar orbit around the Moon to more precisely determine the gravitational field for future navigational purposes, and to infer information about

2414-496: The Mechanical Arts (1807) he gives Grimaldi credit for first observing the fringes in the shadow of an object placed in a beam of light. Within ten years, much of Young's work was reproduced and then extended by Augustin-Jean Fresnel . Young described the characterization of elasticity that came to be known as Young's modulus, denoted as E , in 1807, and further described it in his Course of Lectures on Natural Philosophy and

2485-400: The Mechanical Arts . However, the first use of the concept of Young's modulus in experiments was by Giordano Riccati in 1782—predating Young by 25 years. Furthermore, the idea can be traced to a paper by Leonhard Euler published in 1727, some 80 years before Thomas Young's 1807 paper. The Young's modulus relates the stress (pressure) in a body to its associated strain (change in length as

2556-467: The Moon's physical makeup. The table below shows comparative gravitational accelerations at the surface of the Sun, the Earth's moon, each of the planets in the Solar System and their major moons, Ceres, Pluto, and Eris. For gaseous bodies, the "surface" is taken to mean visible surface: the cloud tops of the giant planets (Jupiter, Saturn, Uranus, and Neptune), and the Sun's photosphere . The values in

2627-599: The aorta. His body was buried in the graveyard of St. Giles Church at Farnborough , in the county of Kent . Westminster Abbey houses a white marble tablet in memory of Young, bearing an epitaph by Hudson Gurney : Sacred to the memory of Thomas Young, M.D., Fellow and Foreign Secretary of the Royal Society Member of the National Institute of France; a man alike eminent in almost every department of human learning. Patient of unintermitted labour, endowed with

2698-491: The container material with which the fluids in question are contacting/interfacing: R = a cos ⁡ θ {\displaystyle R={\frac {a}{\cos \theta }}} so that the pressure difference may be written as: Δ p = 2 γ cos ⁡ θ a . {\displaystyle \Delta p={\frac {2\gamma \cos \theta }{a}}.} In order to maintain hydrostatic equilibrium ,

2769-741: The decipherment. In the ensuing controversy, strongly motivated by the political tensions of that time, the British tended to champion Young, while the French mostly championed Champollion. Champollion did acknowledge some of Young's contribution, but rather sparingly. However, after 1826, when Champollion was a curator in the Louvre , he did offer Young access to demotic manuscripts. In England, while Sir George Lewis still doubted Champollion's achievement as late as 1862, others were more accepting. For example, Reginald Poole , and Sir Peter Le Page Renouf both defended Champollion. Young developed Young temperament ,

2840-499: The deformation (x) of a body subject to a known load (F), where the constant (k) is a function of both the geometry and material under consideration. Finding k required physical testing for any new component, as the F = kx relationship is a function of both geometry and material. Young's Modulus depends only on the material, not its geometry, thus allowing a revolution in engineering strategies. Young's problems in sometimes not expressing himself clearly were shown by his own definition of

2911-404: The diffusion of molecules out of the smallest droplets in an emulsion and drives emulsion coarsening via Ostwald ripening . In a sufficiently narrow (i.e., low Bond number ) tube of circular cross-section (radius a ), the interface between two fluids forms a meniscus that is a portion of the surface of a sphere with radius R . The pressure jump across this surface is related to the radius and

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2982-518: The faculty of intuitive perception, who, bringing an equal mastery to the most abstruse investigations of letters and of science, first established the undulatory theory of light, and first penetrated the obscurity which had veiled for ages the hieroglyphs of Egypt. Endeared to his friends by his domestic virtues, honoured by the World for his unrivalled acquirements, he died in the hopes of the Resurrection of

3053-486: The far-field model is sufficient for rough calculations of altitude versus period , but not for precision estimation of future location after multiple orbits. The more detailed models include (among other things) the bulging at the equator for the Earth, and irregular mass concentrations (due to meteor impacts) for the Moon. The Gravity Recovery and Climate Experiment (GRACE) mission launched in 2002 consists of two probes, nicknamed "Tom" and "Jerry", in polar orbit around

3124-457: The free fall acceleration ranges from 9.764 to 9.834 m/s (32.03 to 32.26 ft/s ), depending on altitude , latitude , and longitude . A conventional standard value is defined exactly as 9.80665 m/s² (about 32.1740 ft/s²). Locations of significant variation from this value are known as gravity anomalies . This does not take into account other effects, such as buoyancy or drag. Newton's law of universal gravitation states that there

3195-516: The general introduction of gas for lighting into London. In 1816 he was secretary of a commission charged with ascertaining the precise length of the seconds pendulum (the length of a pendulum whose period is exactly 2 seconds), and in 1818 he became secretary to the Board of Longitude and superintendent of the HM Nautical Almanac Office . Young was elected a Foreign Honorary Member of

3266-462: The grammar and vocabulary of 400 languages. In a separate work in 1813, he introduced the term Indo-European languages , 165 years after the Dutch linguist and scholar Marcus Zuerius van Boxhorn proposed the grouping to which this term refers in 1647. Young made significant contributions to the decipherment of ancient Egyptian writing systems . He started his Egyptology work rather late, in 1813, when

3337-430: The gravitational source. It is a vector oriented toward the field source, of magnitude measured in acceleration units. The gravitational acceleration vector depends only on how massive the field source M {\displaystyle M} is and on the distance 'r' to the sample mass m {\displaystyle m} . It does not depend on the magnitude of the small sample mass. This model represents

3408-565: The hierographical papers in his hands, he said that, perfectly aware of his situation, he had taken the sacraments of the church on the day preceding. His religious sentiments were by himself stated to be liberal, though orthodox. He had extensively studied the Scriptures , of which the precepts were deeply impressed upon his mind from his earliest years; and he evidenced the faith which he professed; in an unbending course of usefulness and rectitude." In Young's own judgment, of his many achievements

3479-399: The induced capillary pressure is balanced by a change in height, h , which can be positive or negative, depending on whether the wetting angle is less than or greater than 90°. For a fluid of density ρ: ρ g h = 2 γ cos ⁡ θ a . {\displaystyle \rho gh={\frac {2\gamma \cos \theta }{a}}.} where g

3550-553: The interfacial free energy and the surface tension of the liquid. Young's equation was developed further some 60 years later by Dupré to account for thermodynamic effects, and this is known as the Young–Dupré equation. In physiology Young made an important contribution to haemodynamics in the Croonian lecture for 1808 on the "Functions of the Heart and Arteries," where he derived a formula for

3621-544: The just. —Born at Milverton, in Somersetshire, 13 June 1773. Died in Park Square, London, 10 May 1829, in the 56th year of his age. Young was highly regarded by his friends and colleagues. He was said never to impose his knowledge, but if asked was able to answer even the most difficult scientific question with ease. Although very learned he had a reputation for sometimes having difficulty in communicating his knowledge. It

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3692-533: The modulus: "The modulus of the elasticity of any substance is a column of the same substance, capable of producing a pressure on its base which is to the weight causing a certain degree of compression as the length of the substance is to the diminution of its length." When this explanation was put to the Lords of the Admiralty, their clerk wrote to Young saying "Though science is much respected by their Lordships and your paper

3763-459: The most important was to establish the wave theory of light set out by Christiaan Huygens in his Treatise on Light (1690). To do so, he had to overcome the century-old view, expressed in the venerable Newton's Opticks , that light is a particle. Nevertheless, in the early 19th century Young put forth a number of theoretical reasons supporting the wave theory of light, and he developed two enduring demonstrations to support this viewpoint. With

3834-529: The name of the London-based Thomas Young Centre , an alliance of academic research groups engaged in the theory and simulation of materials. Young Sound in eastern Greenland was named in his honour by William Scoresby (1789–1857). Works cited Gravitational acceleration In physics , gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag ). This

3905-413: The presence in the retina of three kinds of nerve fibres. This foreshadowed the modern understanding of colour vision , in particular the finding that the eye does indeed have three colour receptors which are sensitive to different wavelength ranges. In 1804, Young developed the theory of capillary phenomena on the principle of surface tension . He also observed the constancy of the angle of contact of

3976-423: The pressure difference is zero, as in a soap film without gravity, the interface will assume the shape of a minimal surface . The equation also explains the energy required to create an emulsion . To form the small, highly curved droplets of an emulsion, extra energy is required to overcome the large pressure that results from their small radius. The Laplace pressure, which is greater for smaller droplets, causes

4047-482: The relationship described earlier by Young. Laplace accepted the idea propounded by Hauksbee in his book Physico-mechanical Experiments (1709), that the phenomenon was due to a force of attraction that was insensible at sensible distances. The part which deals with the action of a solid on a liquid and the mutual action of two liquids was not worked out thoroughly, but ultimately was completed by Carl Friedrich Gauss . Franz Ernst Neumann (1798-1895) later filled in

4118-406: The relevant languages, such as Coptic, was much greater. Several scholars have suggested that Young's true contribution to Egyptology was his decipherment of the demotic script. He made the first major advances in this area; he also correctly identified demotic as being composed by both ideographic and phonetic signs. Subsequently, Young felt that Champollion was unwilling to share the credit for

4189-624: The sides of the card. He observed that placing another card in front or behind the narrow strip so as to prevent the light beam from striking one of its edges caused the fringes to disappear. This supported the contention that light is composed of waves . Young performed and analysed a number of experiments, including interference of light from reflection off nearby pairs of micrometre grooves, from reflection off thin films of soap and oil, and from Newton's rings . He also performed two important diffraction experiments using fibres and long narrow strips. In his Course of Lectures on Natural Philosophy and

4260-402: The solution will exist only for the pressure difference shown above. This is significant because there isn't another equation or law to specify the pressure difference; existence of solution for one specific value of the pressure difference prescribes it. The radius of the sphere will be a function only of the contact angle , θ, which in turn depends on the exact properties of the fluids and

4331-409: The source). Then the attraction force F {\displaystyle \mathbf {F} } vector onto a sample mass m {\displaystyle m} can be expressed as: Here g {\displaystyle \mathbf {g} } is the frictionless , free-fall acceleration sustained by the sampling mass m {\displaystyle m} under the attraction of

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4402-586: The sum of 12 plus the child's age. In an appendix to his 1796 Göttingen dissertation De corporis hvmani viribvs conservatricibvs there are four pages added proposing a universal phonetic alphabet (so as 'not to leave these pages blank'; lit.: "Ne vacuae starent hae paginae, libuit e praelectione ante disputationem habenda tabellam literarum vniuersalem raptim describere"). It includes 16 "pure" vowel symbols, nasal vowels, various consonants, and examples of these, drawn primarily from French and English. In his Encyclopædia Britannica article "Languages", Young compared

4473-445: The sun and the planets can be considered as point masses and the same formula applied to planetary motions. (As planets and natural satellites form pairs of comparable mass, the distance 'r' is measured from the common centers of mass of each pair rather than the direct total distance between planet centers.) If one mass is much larger than the other, it is convenient to take it as observational reference and define it as source of

4544-402: The sun shines, and without any other apparatus than is at hand to every one. In his subsequent paper, titled Experiments and Calculations Relative to Physical Optics (1804), Young describes an experiment in which he placed a card measuring approximately 0.85 millimetres (0.033 in) in a beam of light from a single opening in a window and observed the fringes of colour in the shadow and to

4615-434: The surface shape is determined by only one parameter, the over pressure of the fluid, Δ p and the scale of the surface is given by the capillary length . The solution of the equation requires an initial condition for position, and the gradient of the surface at the start point. The (nondimensional) shape, r ( z ) of an axisymmetric surface can be found by substituting general expressions for principal curvatures to give

4686-459: The surface tension γ by Δ p = 2 γ R . {\displaystyle \Delta p={\frac {2\gamma }{R}}.} This may be shown by writing the Young–Laplace equation in spherical form with a contact angle boundary condition and also a prescribed height boundary condition at, say, the bottom of the meniscus. The solution is a portion of a sphere, and

4757-565: The surface, not of any other dimensions of the column. Thomas Young laid the foundations of the equation in his 1804 paper An Essay on the Cohesion of Fluids where he set out in descriptive terms the principles governing contact between fluids (along with many other aspects of fluid behaviour). Pierre Simon Laplace followed this up in Mécanique Céleste with the formal mathematical description given above, which reproduced in symbolic terms

4828-418: The table have not been de-rated for the centrifugal force effect of planet rotation (and cloud-top wind speeds for the giant planets) and therefore, generally speaking, are similar to the actual gravity that would be experienced near the poles. For reference, the time it would take an object to fall 100 metres (330 ft), the height of a skyscraper, is shown, along with the maximum speed reached. Air resistance

4899-421: The wave speed of the pulse and his medical writings included An Introduction to Medical Literature , including a System of Practical Nosology (1813) and A Practical and Historical Treatise on Consumptive Diseases (1815). Young devised a rule of thumb for determining a child's drug dosage. Young's Rule states that the child dosage is equal to the adult dosage multiplied by the child's age in years, divided by

4970-408: The work was already in progress among other researchers. He began by using an Egyptian demotic alphabet of 29 letters built up by Johan David Åkerblad in 1802 (14 turned out to be incorrect). Åkerblad was correct in stressing the importance of the demotic text in trying to read the inscriptions, but he wrongly believed that demotic was entirely alphabetic. By 1814 Young had completely translated

5041-826: Was said by one of his contemporaries that, "His words were not those in familiar use, and the arrangement of his ideas seldom the same as those he conversed with. He was therefore worse calculated than any man I ever knew for the communication of knowledge." Though he sometimes dealt with religious topics of history in Egypt and wrote about the history of Christianity in Nubia , not much is known about Young's personal religious views. On George Peacock 's account, Young never spoke to him about morals, metaphysics or religion, though according to Young's wife, his attitudes showed that "his Quaker upbringing had strongly influenced his religious practices." Authoritative sources have described Young in terms of

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