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87-400: The word Pithoprakta translates to "actions through probability". This relates to Jacob Bernoulli 's law of large numbers which states that as the number of occurrences of a chance event increases, the average outcome approaches a determinate end. The piece is based on the statistical mechanics of gases, Gauss's law , or Brownian motion . Each instrument is conceived as a molecule obeying

174-481: A compound microscope that he designed. Hooke was an impoverished scientific inquirer in young adulthood who went on to become one of the most important scientists of his time. After the Great Fire of London in 1666, Hooke (as a surveyor and architect) attained wealth and esteem by performing more than half of the property line surveys and assisting with the city's rapid reconstruction. Often vilified by writers in

261-415: A logarithmic spiral and the motto Eadem mutata resurgo ('Although changed, I rise again the same') engraved on his tombstone. He wrote that the self-similar spiral "may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self". Bernoulli died in 1705, but an Archimedean spiral

348-548: A balance-controlled watch before the Royal Society, may support Hooke's claim to priority for the idea. Nevertheless, it is Huygens who is credited with building the first watch to use a balance spring. Hooke's announcement of his law of elasticity using an anagram was a method scientists, such as Hooke, Huygens and Galileo , sometimes used to establish priority for a discovery without revealing details. Hooke used mechanical analogues to understand fundamental processes such as

435-591: A brass clock dismantled, he built a wooden replica that "would go". Hooke's father died in October 1648, leaving £40 in his will to Robert (plus another £10 held over from his grandmother). At the age of 13, he took this to London to become an apprentice to the celebrated painter Peter Lely . Hooke also had "some instruction in drawing" from the limner Samuel Cowper but "the smell of the Oil Colours did not agree with his Constitution, increasing his Head-ache to which he

522-494: A curator to furnish the society with experiments, and this was unanimously passed and Hooke was named on Boyle's recommendation. The Society did not have a reliable income to fully fund the post of Curator of Experiments but in 1664, John Cutler settled an annual gratuity of £50 on the Society to found a "Mechanick" lectureship at Gresham College on the understanding the Society would appoint Hooke to this task. On 27 June 1664, Hooke

609-421: A disgruntled, selfish, anti-social curmudgeon. For example, Arthur Berry said Hooke "claimed credit for most of the scientific discoveries of the time". Sullivan wrote he was "positively unscrupulous" and had an "uneasy apprehensive vanity" in dealings with Newton. Manuel described Hooke as "cantankerous, envious, vengeful". According to More, Hooke had both a "cynical temperament" and a "caustic tongue". Andrade

696-485: A dog could be kept alive with its thorax opened, provided air was pumped in and out of its lungs. He noted the difference between venous and arterial blood, and thus demonstrated that the Pabulum vitae ("food of life") and flammae [flames] were the same thing. There were also experiments on gravity, the falling of objects, the weighing of bodies, the measurement of barometric pressure at different heights, and

783-491: A finite limit less than 2. Euler was the first to find the limit of this series in 1737. Bernoulli also studied the exponential series which came out of examining compound interest. In May 1690, in a paper published in Acta Eruditorum , Jacob Bernoulli showed that the problem of determining the isochrone is equivalent to solving a first-order nonlinear differential equation. The isochrone, or curve of constant descent,

870-601: A limit (the force of interest ) for more and smaller compounding intervals. Compounding weekly yields $ 2.692597..., while compounding daily yields $ 2.714567..., just two cents more. Using n as the number of compounding intervals, with interest of 100% / n in each interval, the limit for large n is the number that Euler later named e ; with continuous compounding, the account value will reach $ 2.7182818.... More generally, an account that starts at $ 1, and yields (1+ R ) dollars at compound interest , will yield e dollars with continuous compounding. Bernoulli wanted

957-580: A mechanism that improved the regularity of pendulum clocks used for astronomical time-keeping. Hooke characterised his Oxford days as the foundation of his lifelong passion for science. The friends he made there, particularly Christopher Wren , were important to him throughout his career. Willis introduced Hooke to Robert Boyle , who the Club sought to attract to Oxford. In 1655, Boyle moved to Oxford and Hooke became nominally his assistant but in practice his co-experimenter. Boyle had been working on gas pressures;

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1044-612: A medium for transmitting attraction and repulsion between separated celestial bodies, Hooke argued for an attracting principle of gravitation in Micrographia (1665). In a communication to the Royal Society in 1666, he wrote: I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having

1131-513: A new hypothesis from Paris about planetary motions, which he described at length; efforts to carry out or improve national surveys; and the difference of latitude between London and Cambridge. Newton's reply offered "a fansy of my own" about a terrestrial experiment rather than a proposal about celestial motions that might detect the Earth's motion; the experiment would use a body suspended in air and then dropped. Hooke wanted to discern how Newton thought

1218-496: A pamphlet on the parallels of logic and algebra published in 1685, work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines. By 1689, he had published important work on infinite series and published his law of large numbers in probability theory. Jacob Bernoulli published five treatises on infinite series between 1682 and 1704. The first two of these contained many results, such as

1305-432: A particularly keen eye and was an adept mathematician, neither of which applied to Boyle. Hooke taught Boyle Euclid's Elements and Descartes 's Principles of Philosophy ; it also caused them to recognise fire as a chemical reaction and not, as Aristotle taught, a fundamental element of nature. According to Henry Robinson, Librarian of The Royal Society in 1935: Without his weekly experiments and prolific work

1392-419: A place at Christ Church , Oxford , receiving free tuition and accommodation as an organist and a chorister , and a basic income as a servitor , despite the fact he did not officially matriculate until 1658. In 1662, Hooke was awarded a Master of Arts degree. While a student at Oxford, Hooke was also employed as an assistant to Dr Thomas Willis  – a physician, chemist and member of

1479-435: A simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it. ... Hooke's 1674 Gresham lecture, An Attempt to Prove

1566-620: A spinal deformity that was consistent with a diagnosis of Scheuermann's kyphosis , giving him in middle and later years a "thin and crooked body, over-large head and protruding eyes". Approaching these in a scientific spirit, he experimented with self-medication, diligently recording symptoms, substances and effects in his diary. He regularly used sal ammoniac , emetics, laxatives and opiates, which appear to have had an increasing effect on his physical and mental health over time. Hooke died in London on 3 March 1703, having been blind and bedridden during

1653-593: Is freely modulated and its speed-determined "temperature" varies. This piece was made into a ballet by George Balanchine , Metastaseis and Pithoprakta , along with the earlier Metastaseis . This article about a classical composition is a stub . You can help Misplaced Pages by expanding it . - Treble Jacob Bernoulli Jacob Bernoulli (also known as James in English or Jacques in French; 6 January 1655 [ O.S. 27 December 1654] – 16 August 1705)

1740-515: Is in fact e ): One example is an account that starts with $ 1.00 and pays 100 percent interest per year. If the interest is credited once, at the end of the year, the value is $ 2.00; but if the interest is computed and added twice in the year, the $ 1 is multiplied by 1.5 twice, yielding $ 1.00×1.5  = $ 2.25. Compounding quarterly yields $ 1.00×1.25  = $ 2.4414..., and compounding monthly yields $ 1.00×(1.0833...)  = $ 2.613035.... Bernoulli noticed that this sequence approaches

1827-494: Is known of Hooke's early life comes from an autobiography he commenced in 1696 but never completed; Richard Waller FRS mentions it in his introduction to The Posthumous Works of Robert Hooke, M.D. S.R.S. , which was printed in 1705. The work of Waller, along with John Ward 's Lives of the Gresham Professors , and John Aubrey 's Brief Lives form the major near-contemporaneous biographical accounts of his life. Hooke

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1914-414: Is subdivided into three, four, and five equal parts, allowing for fine differences in duration but also creating a steady pulse in each instrumental part, reducing the rhythm of the random walk to steady footsteps. Composer Simon Emmerson notes that this regularity is "impossible in reality and fails to use his ‘ stochastic ’ approach in this instance." Each part gets nowhere, but as a whole the mass's pitch

2001-405: Is the curve along which a particle will descend under gravity from any point to the bottom in exactly the same time, no matter what the starting point. It had been studied by Huygens in 1687 and Leibniz in 1689. After finding the differential equation, Bernoulli then solved it by what we now call separation of variables . Jacob Bernoulli's paper of 1690 is important for the history of calculus, since

2088-541: Is the first-recorded hypothesis of the cause of the expansion of matter by heat, of air's composition by small particles in constant motion that thus generate its pressure, and of heat as energy. In physics, Hooke inferred that gravity obeys an inverse square law and arguably was the first to hypothesise such a relation in planetary motion, a principle Isaac Newton furthered and formalised in Newton's law of universal gravitation . Priority over this insight contributed to

2175-565: Is usually painted of Hooke as a morose ... recluse is completely false". He interacted with noted artisans such as clock-maker Thomas Tompion and instrument-maker Christopher Cocks (Cox). Hooke often met Christopher Wren, with whom he shared many interests, and had a lasting friendship with John Aubrey. His diaries also make frequent reference to meetings at coffeehouses and taverns, as well as to dinners with Robert Boyle. On many occasions, Hooke took tea with his lab assistant Harry Hunt. Although he largely lived alone – apart from

2262-572: The Great Red Spot of Jupiter for two hours as it moved across the planet's face. In March 1665, he published his findings and from them, the Italian astronomer Giovanni Cassini calculated the rotation period of Jupiter to be nine hours and fifty-five minutes. One of the most-challenging problems Hooke investigated was the measurement of the distance from Earth to a star other than the Sun. Hooke selected

2349-459: The Maxwell–Boltzmann distribution law , with Gaussian distribution of temperature fluctuation. This theory states that "the temperature of a gas derives from the independent movement of its molecules." Xenakis drew an analogy between the movement of a gas molecule through space and that of a string instrument through its pitch range. To construct the seething movement of the piece, he governed

2436-663: The Oxford Philosophical Club . The Philosophical Club had been founded by John Wilkins , Warden of Wadham College , who led this important group of scientists who went on to form the nucleus of the Royal Society . In 1659, Hooke described to the Club some elements of a method of heavier-than-air flight but concluded human muscles were insufficient to the task. Through the Club, Hooke met Seth Ward (the University's Savilian Professor of Astronomy ) and developed for Ward

2523-413: The balance spring or hairspring, which for the first time enabled a portable timepiece – a watch – to keep time with reasonable accuracy. A bitter dispute between Hooke and Christiaan Huygens on the priority of this invention was to continue for centuries after the death of both but a note dated 23 June 1670 in the journals of the Royal Society, describing a demonstration of

2610-463: The logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob Bernoulli in 1694. In 1695, he investigated the drawbridge problem which seeks the curve required so that a weight sliding along the cable always keeps the drawbridge balanced. Bernoulli's most original work was Ars Conjectandi , published in Basel in 1713, eight years after his death. The work

2697-468: The vacuum pumps that were used in Boyle's experiments on gas law and also conducted experiments. In 1664, Hooke identified the rotations of Mars and Jupiter . Hooke's 1665 book Micrographia , in which he coined the term cell , encouraged microscopic investigations. Investigating optics  – specifically light refraction  – Hooke inferred a wave theory of light . His

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2784-598: The "notion" of "the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center". At the same time, according to Edmond Halley 's contemporaneous report, Hooke agreed "the Demonstration of the Curves generated thereby" was wholly Newton's. According to a 2002 assessment of the early history of the inverse square law: "by the late 1660s, the assumption of an 'inverse proportion between gravity and

2871-498: The 'molecules' according to a coherent sequence of imaginary temperatures and pressures. Brownian motion is a four-dimensional phenomenon (three spatial dimensions and time), and Xenakis created the score by first creating a two-dimensional graph, necessitating some simplifications. The abscissa ( x ) represents time at 5 cm = 26 MM , while the ordinates ( y ) represent pitch at 1 semitone = .25 cm, when transcribed into musical notation 5 cm = 1 measure. This length

2958-646: The Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance". (Hooke's inference about the velocity is incorrect. ) In 1686, when the first book of Newton's Principia was presented to the Royal Society, Hooke said he had given Newton

3045-473: The Dutch scientist Antonie van Leeuwenhoek went on to develop increased magnification and so reveal protozoa , blood cells and spermatozoa . Micrographia also contains Hooke's, or perhaps Boyle's and Hooke's, ideas on combustion. Hooke's experiments led him to conclude combustion involves a component of air, a statement with which modern scientists would agree but that was not understood widely, if at all, in

3132-698: The Motion of the Earth by Observations (published 1679), said gravitation applies to "all celestial bodies" and restated these three propositions. Hooke's statements up to 1674 make no mention, however, that an inverse square law applies or might apply to these attractions. His model of gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. Hooke did not provide accompanying evidence or mathematical demonstration; he stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified", indicating he did not yet know what law

3219-427: The Royal Society's correspondence; Hooke therefore wanted to hear from members about their research or their views about the research of others. Hooke asked Newton's opinions about various matters. Among other items, Hooke mentioned "compounding the celestial motions of the planets of a direct motion by the tangent and an attractive motion towards the central body"; his "hypothesis of the lawes or causes of springinesse";

3306-509: The Society could scarcely have survived, or, at least, would have developed in a quite different way. It is scarcely an exaggeration to say that he was, historically, the creator of the Royal Society. The Royal Society for the Improvement of Natural Knowledge by Experiment was founded in 1660 and given its Royal Charter in July 1662. On 5 November 1661, Robert Moray proposed the appointment of

3393-450: The atmosphere of collaboration between the two brothers turned into rivalry as Johann's own mathematical genius began to mature, with both of them attacking each other in print, and posing difficult mathematical challenges to test each other's skills. By 1697, the relationship had completely broken down. The lunar crater Bernoulli is also named after him jointly with his brother Johann. Jacob Bernoulli's first important contributions were

3480-434: The centuries after his death, his reputation was restored at the end of the twentieth century and he has been called "England's Leonardo [da Vinci] ". Hooke was a Fellow of the Royal Society and from 1662, he was its first Curator of Experiments. From 1665 to 1703, he was also Professor of Geometry at Gresham College . Hooke began his scientific career as an assistant to the physical scientist Robert Boyle . Hooke built

3567-440: The deaths of both Newton and Hooke, Alexis Clairaut , mathematical astronomer eminent in his own right in the field of gravitational studies, reviewed Hooke's published work on gravitation. According to Stephen Peter Rigaud , Clairaut wrote: "The example of Hooke and that of Kepler [serves] to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated". I. Bernard Cohen said: "Hooke's claim to

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3654-558: The differential calculus in " Nova Methodus pro Maximis et Minimis " published in Acta Eruditorum . They also studied the publications of von Tschirnhaus . It must be understood that Leibniz's publications on the calculus were very obscure to mathematicians of that time and the Bernoullis were among the first to try to understand and apply Leibniz's theories. Jacob collaborated with his brother on various applications of calculus. However

3741-505: The diversion he gave me from my other studies to think on these things & for his dogmaticalness in writing as if he had found the motion in the Ellipsis, which inclined me to try it. Whilst Newton was primarily a pioneer in mathematical analysis and its applications, and optical experimentation, Hooke was a creative experimenter of such great range who left some of his ideas, such as those about gravitation, undeveloped. In 1759, decades after

3828-737: The earliest-recorded observation of a microorganism, the microfungus Mucor . Hooke coined the term " cell ", suggesting a resemblance between plant structures and honeycomb cells. The hand-crafted, leather-and-gold-tooled microscope he designed and used to make the observations for Micrographia , which Christopher Cock made for him in London, is on display at the National Museum of Health and Medicine in Maryland . Hooke's work developed from that of Henry Power , who published his microscopy work in Experimental Philosophy (1663); in turn,

3915-482: The falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical but Hooke went on hypothetically to consider how its motion could continue if the solid Earth had not been in the way, on a spiral path to the centre. Hooke disagreed with Newton's idea of the body's continuing motion. A further short correspondence developed; towards the end of it, writing on 6 January 1680 to Newton, Hooke communicated his "supposition ... that

4002-465: The first practical Gregorian telescope that used a silvered glass mirror. In 1660, Hooke discovered the law of elasticity that bears his name and describes the linear variation of tension with extension in an elastic spring. Hooke first described this discovery in an anagram "ceiiinosssttuv", whose solution he published in 1678 as Ut tensio, sic vis ("As the extension, so the force"). His work on elasticity culminated in his development of

4089-471: The formation of these craters and concluded their existence meant the Moon must have its own gravity, a radical departure from the contemporaneous Aristotelian celestial model . He also was an early observer of the rings of Saturn , and discovered one of the first-observed double-star systems Gamma Arietis in 1664. To achieve these discoveries, Hooke needed better instruments than those that were available at

4176-482: The fundamental result that ∑ 1 n {\displaystyle \sum {\frac {1}{n}}} diverges, which Bernoulli believed were new but they had actually been proved by Pietro Mengoli 40 years earlier and was proved by Nicole Oresme in the 14th century already. Bernoulli could not find a closed form for ∑ 1 n 2 {\displaystyle \sum {\frac {1}{n^{2}}}} , but he did show that it converged to

4263-446: The gravitation might follow; and about his whole proposal, he said: "This I only hint at present ... having my self many other things in hand which I would first compleat, and therefore cannot so well attend it" (i.e. "prosecuting this Inquiry"). In November 1679, Hooke initiated a notable exchange of letters with Newton that was published in 1960. Hooke's ostensible purpose was to tell Newton he (Hooke) had been appointed to manage

4350-453: The history of life on Earth and, despite the objections of contemporary naturalists like John Ray  – who found the concept of extinction theologically unacceptable – that in some cases they might represent species that had become extinct through some geological disaster. In a series of lectures in 1668, Hooke proposed the then-heretical idea the Earth's surface had been formed by volcanoes and earthquakes, and that

4437-428: The invention was, by Hooke's death, in constant use among clock makers. Hooke announced he conceived a way to build a marine chronometer to determine longitude. and with the help of Boyle and others, he attempted to patent it. In the process, Hooke demonstrated a pocket-watch of his own devising that was fitted with a coil spring attached to the arbour of the balance. Hooke's refusal to accept an escape clause in

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4524-472: The inverse-square law has masked Newton's far more fundamental debt to him, the analysis of curvilinear orbital motion. In asking for too much credit, Hooke effectively denied to himself the credit due him for a seminal idea". Hooke made important contributions to the science of timekeeping and was intimately involved in the advances of his time; these included refinement of the pendulum as a better regulator for clocks, increased precision of clock mechanisms and

4611-406: The last part of the book, Bernoulli sketches many areas of mathematical probability , including probability as a measurable degree of certainty; necessity and chance; moral versus mathematical expectation; a priori an a posteriori probability; expectation of winning when players are divided according to dexterity; regard of all available arguments, their valuation, and their calculable evaluation; and

4698-473: The last year of his life. A chest containing £8,000 in money and gold was found in his room at Gresham College . His library contained over 3,000 books in Latin, French, Italian and English. Although he had talked of leaving a generous bequest to the Royal Society, which would have given his name to a library, laboratory and lectures, no will was found and the money passed to a cousin named Elizabeth Stephens. Hooke

4785-454: The latest discoveries in mathematics and the sciences under leading figures of the time. This included the work of Johannes Hudde , Robert Boyle , and Robert Hooke . During this time he also produced an incorrect theory of comets . Bernoulli returned to Switzerland, and began teaching mechanics at the University of Basel from 1683. His doctoral dissertation Solutionem tergemini problematis

4872-522: The latter were responsible for shell fossils being found far above sea level. In 1835, Charles Lyell , the Scottish geologist and associate of Charles Darwin , wrote of Hooke in Principles of Geology : "His treatise ... is the most philosophical production of that age, in regard to the causes of former changes in the organic and inorganic kingdoms of nature". Hooke's scientific model of human memory

4959-417: The law of large numbers. Bernoulli was one of the most significant promoters of the formal methods of higher analysis. Astuteness and elegance are seldom found in his method of presentation and expression, but there is a maximum of integrity. In 1683, Bernoulli discovered the constant e by studying a question about compound interest which required him to find the value of the following expression (which

5046-497: The love of his life, and he was devastated when she died in 1687. Inwood also mentions "The age difference between him and Grace was commonplace and would not have upset his contemporaries as it does us". The incestous relationship would nevertheless have been frowned upon and tried by an ecclesiastical court had it been discovered, it was not however a capital felony after 1660. Since childhood, Hooke suffered from migraine , tinnitus , dizziness and bouts of insomnia ; he also had

5133-507: The most ingenious book that ever I read in my life". One of the observations in Micrographia is of fossil wood , the microscopic structure of which Hooke compared to that of ordinary wood. This led him to conclude that fossilised objects like petrified wood and fossil shells such as ammonites were the remains of living things that had been soaked in mineral-laden petrifying water. He believed that such fossils provided reliable clues about

5220-556: The motion of a spherical pendulum and of a ball in a hollow cone, to demonstrate central force due to gravity, and a hanging chain net with point loads to provide the optimum shape for a dome with heavy cross on top. Despite continuing reports to the contrary, Hooke did not influence Thomas Newcomen 's invention of the steam engine ; this myth, which originated in an article in the third edition of " Encyclopædia Britannica ", has been found to be mistaken. While many of Hooke's contemporaries, such as Isaac Newton, believed in aether as

5307-440: The movement of pendulums up to 200 ft long (61 m). His biographer Margaret 'Espinasse described him as England's first meteorologist , in her description of his essay Method for making a history of the weather . (Hooke specifies that a thermometer, a hygrometer , a wind gauge and a record sheet be used for proper weather records. ) In May 1664, using a 12 ft (3.7 m) refracting telescope , Hooke observed

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5394-406: The possibility a vacuum might exist despite Aristotle 's maxim " Nature abhors a vacuum " had just begun to be considered . Hooke developed an air pump for Boyle's experiments rather than use Ralph Greatorex 's pump, which Hooke considered as "too gross to perform any great matter". Hooke's engine enabled the development of the eponymous law that was subsequently attributed to Boyle; Hooke had

5481-688: The proposed exclusive contract for the use of this idea resulted in its abandonment. Hooke developed the principle of the balance spring independently of Huygens and at least five years beforehand. Huygens published his own work in Journal de Scavans in February 1675 and built the first functioning watch to use a balance spring. In 1663 and 1664, Hooke made his microscopic, and some astronomic, observations, which he collated in Micrographia in 1665. His book, which describes observations with microscopes and telescopes, as well as original work in biology, contains

5568-466: The rivalry between Hooke and Newton. In geology and palaeontology , Hooke originated the theory of a terraqueous globe, thus disputing the Biblical view of the Earth's age; he also hypothesised the extinction of species, and argued hills and mountains had become elevated by geological processes. By identifying fossils of extinct species, Hooke presaged the theory of biological evolution . Much of what

5655-493: The servants who ran his home – his niece Grace Hooke and his cousin Tom Giles lived with him for some years as children. Hooke never married. According to his diary, Hooke had a sexual relationship with his niece Grace, after she had turned 16. Grace was in his custody since the age of 10. He also had sexual relations with several maids and housekeepers. Hooke's biographer Stephen Inwood considers Grace to have been

5742-467: The seventeenth century. He also concluded respiration and combustion involve a specific and limited component of air. According to Partington, if "Hooke had continued his experiments on combustion, it is probable that he would have discovered oxygen". Samuel Pepys wrote of the book in his diary on 21 January 16 ⁠ 64 / 65 ⁠ : "Before I went to bed I sat up till two o’clock in my chamber reading of Mr. Hooke's Microscopicall Observations,

5829-446: The square of distance' was rather common and had been advanced by a number of different people for different reasons". In the 1660s, Newton had shown for planetary motion under a circular assumption, force in the radial direction had an inverse-square relation with distance from the centre. Newton, who in May 1686 was presented with Hooke's claim to priority on the inverse square law, denied he

5916-450: The star Gamma Draconis and chose the method of parallax determination. In 1669, after several months of observing, Hooke believed the desired result had been achieved. It is now known his equipment was far too imprecise to obtain an accurate measurement. Hooke's Micrographia contains illustrations of the Pleiades star cluster and lunar craters . He conducted experiments to investigate

6003-817: The supposition, could only guess it was approximately valid "at great distances from the centre". Newton did accept and acknowledge, in all editions of the Principia , Hooke and others had separately appreciated the inverse square law in the solar system. Newton acknowledged Wren, Hooke and Halley in this connection in his "Scholium to Proposition 4" in Book   1. In a letter to Halley, Newton also acknowledged his correspondence with Hooke in 1679–1680 had reawakened his dormant interest in astronomical matters but that did not mean, according to Newton, Hooke had told Newton anything new or original. Newton wrote: Yet am I not beholden to him for any light into that business ... but only for

6090-456: The term integral appears for the first time with its integration meaning. In 1696, Bernoulli solved the equation, now called the Bernoulli differential equation , Jacob Bernoulli also discovered a general method to determine evolutes of a curve as the envelope of its circles of curvature. He also investigated caustic curves and in particular he studied these associated curves of the parabola ,

6177-455: The time. Accordingly, he invented three new mechanisms: the Hooke joint , a sophisticated universal joint that allowed his instruments to smoothly follow the apparent motion of the observed body; the first clockwork drive to automate the process; and a micrometer screw that allowed him to achieve a precision of ten seconds of arc . Hooke was dissatisfied with refracting telescopes so he built

6264-432: The type in which he was involved seem almost to be the rule rather than the exception. And Hooke's reaction to such controversy involving his own discoveries and inventions seems mild in comparison to the behaviour of some of his contemporaries". The publication of Hooke's diary in 1935 revealed previously unknown details about his social and familial relationships. His biographer Margaret 'Espinasse said: "the picture which

6351-415: The use of the balance spring to improve the timekeeping of watches. Galileo had observed the regularity of a pendulum and Huygens first incorporated it in a clock; in 1668, Hooke demonstrated his new device to keep a pendulum swinging regularly in unsteady conditions. His invention of a tooth-cutting machine enabled a substantial improvement in the accuracy and precision of timepieces. Waller reported

6438-520: Was appointed its Joint Secretary. Although John Aubrey described Hooke as a person of "great virtue and goodness". much has been written about the unpleasant side of Hooke's personality. According to his first biographer Richard Waller, Hooke was "in person, but despicable", and "melancholy, mistrustful, and jealous". Waller's comments influenced other writers for more than 200 years such that many books and articles – especially biographies of Isaac Newton  – portray Hooke as

6525-439: Was between 1684 and 1689 that many of the results that were to make up Ars Conjectandi were discovered. People believe he was appointed professor of mathematics at the University of Basel in 1687, remaining in this position for the rest of his life. By that time, he had begun tutoring his brother Johann Bernoulli on mathematical topics. The two brothers began to study the calculus as presented by Leibniz in his 1684 paper on

6612-584: Was born in 1635 in Freshwater, Isle of Wight , to Cecily Gyles and the Anglican priest John Hooke, who was the curate of All Saints' Church, Freshwater . Robert was the youngest, by seven years, of four siblings (two boys and two girls); he was frail and not expected to live. Although his father gave him some instruction in English, (Latin) Grammar and Divinity , Robert's education was largely neglected. Left to his own devices, he made little mechanical toys; seeing

6699-467: Was buried at St Helen's Church, Bishopsgate , in the City of London but the precise location of his grave is unknown. Hooke's role at the Royal Society was to demonstrate experiments from his own methods or at the suggestion of members. Among his earliest demonstrations were discussions of the nature of air and the implosion of glass bubbles that had been sealed with enclosed hot air. He also demonstrated that

6786-436: Was confirmed to the office and on 11 January 1665, he was named Curator by Office for life with an annual salary of £80, which consisting of £30 from the Society and Cutler's £50 annuity. In June 1663, Hooke was elected a Fellow of the Royal Society (FRS). On 20 March 1665, he was also appointed Gresham Professor of Geometry . On 13 September 1667, Hooke became acting Secretary of the Society and on 19 December 1677, he

6873-445: Was engraved rather than a logarithmic one. Translation of Latin inscription: Robert Hooke Robert Hooke FRS ( / h ʊ k / ; 18 July 1635 – 3 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist and architect. He is credited as one of the first scientists to investigate living things at microscopic scale in 1665, using

6960-448: Was ever too much subject", and he became a pupil at Westminster School , living with its master Richard Busby . Hooke quickly mastered Latin, Greek and Euclid's Elements ; he also learnt to play the organ and began his lifelong study of mechanics. He remained an accomplished draughtsman, as he was later to demonstrate in his drawings that illustrate the work of Robert Boyle and Hooke's own Micrographia . In 1653, Hooke secured

7047-548: Was in the field of probability , where he derived the first version of the law of large numbers in his work Ars Conjectandi . Jacob Bernoulli was born in Basel in the Old Swiss Confederacy . Following his father's wish, he studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy . He traveled throughout Europe from 1676 to 1682, learning about

7134-540: Was incomplete at the time of his death but it is still a work of the greatest significance in the theory of probability. The book also covers other related subjects, including a review of combinatorics , in particular the work of van Schooten, Leibniz, and Prestet, as well as the use of Bernoulli numbers in a discussion of the exponential series. Inspired by Huygens' work, Bernoulli also gives many examples on how much one would expect to win playing various games of chance. The term Bernoulli trial resulted from this work. In

7221-480: Was more sympathetic but still described Hooke as "difficult", "suspicious" and "irritable". In October 1675, the Council of the Royal Society considered a motion to expel Hooke because of an attack he made on Christiaan Huygens over scientific priority in watch design but it did not pass. According to Hooke's biographer Ellen Drake: if one studies the intellectual milieu of the time, the controversies and rivalries of

7308-646: Was one of the first of its kind. In a 1682 lecture to the Royal Society, Hooke proposed a mechanical analogue model of human memory that bore little resemblance to the mainly philosophical models of earlier writers. This model addressed the components of encoding, memory capacity, repetition, retrieval, and forgetting – some with surprisingly modern accuracy. According to psychology professor Douglas Hintzman, Hooke's model's most-interesting points are that it allows for attention and other top-down influences on encoding; it uses resonance to implement parallel, cue-dependent retrieval; it explains memory for recency; it offers

7395-576: Was one of the many prominent mathematicians in the Swiss Bernoulli family . He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibnizian calculus , which he made numerous contributions to; along with his brother Johann , he was one of the founders of the calculus of variations . He also discovered the fundamental mathematical constant e . However, his most important contribution

7482-665: Was submitted in 1684. It appeared in print in 1687. In 1684, Bernoulli married Judith Stupanus; they had two children. During this decade, he also began a fertile research career. His travels allowed him to establish correspondence with many leading mathematicians and scientists of his era, which he maintained throughout his life. During this time, he studied the new discoveries in mathematics, including Christiaan Huygens 's De ratiociniis in aleae ludo , Descartes ' La Géométrie and Frans van Schooten 's supplements of it. He also studied Isaac Barrow and John Wallis , leading to his interest in infinitesimal geometry. Apart from these, it

7569-509: Was to be credited as author of the idea, giving reasons including the citation of prior work by others. Newton also said that, even if he had first heard of the inverse square proportion from Hooke (which Newton said he had not), he would still have some rights to it because of his mathematical developments and demonstrations. These, he said, enabled observations to be relied upon as evidence of its accuracy while according to Newton, Hooke, without mathematical demonstrations and evidence in favour of

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