Robert Hooke

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Robert_Hooke 

 

Robert Hooke
Born	28 July 1635 Freshwater, Isle of Wight, England
Died	3 March 1703 (aged 67) London, England
Nationality	English
Alma mater	Wadham College, Oxford
Known for	Hooke's law Microscopy Coining the term 'cell'
Scientific career
Fields	Physics and chemistry
Institutions	Oxford University
Academic advisors	Robert Boyle
Influences	Richard Busby
Signature

Robert Hooke FRS (/hʊk/; 28 July [O.S. 18 July] 1635 – 3 March 1703) was an English natural philosopher, architect and polymath. As a young adult, he was a financially impoverished scientific inquirer, but came into wealth and good reputation following his actions as Surveyor to the City of London after the great fire of 1666 (in which he appears to have performed more than half of all the surveys after the fire). At that time, he was also the curator of experiments of the Royal Society, and a member of its council, Gresham Professor of Geometry. He was also an important architect of his time—though few of his buildings now survive and some of those are generally misattributed—and was instrumental in devising a set of planning controls for London, the influence of which remains today. Allan Chapman has characterised him as "England's Leonardo".

Hooke studied at Wadham College, Oxford, during the Protectorate where he became one of a tightly knit group of ardent Royalists led by John Wilkins. Here he was employed as an assistant to Thomas Willis and to Robert Boyle, for whom he built the vacuum pumps used in Boyle's gas law experiments, and conducted the experiments themselves. He built some of the earliest Gregorian telescopes and observed the rotations of Mars and Jupiter. In 1665 he inspired the use of microscopes for scientific exploration with his book, Micrographia. Based on his microscopic observations of fossils, Hooke was an early proponent of biological evolution. He investigated the phenomenon of refraction, deducing the wave theory of light, and was the first to suggest that matter expands when heated and that air is made of small particles separated by relatively large distances. He proposed that heat was the manifestation of faster movement of the particles of matter.

He performed pioneering work in the field of surveying and map-making and was involved in the work that led to the first modern plan-form map, though his plan for London on a grid system was rejected in favour of rebuilding along the existing routes. He also came near to an experimental proof that gravity follows an inverse square law, and first hypothesised that such a relation governs the motions of the planets, an idea which was developed by Isaac Newton, and formed part of a dispute between the two which caused Newton to try to erase Hooke's legacy. He originated the terraqueous globe theory of geology, disputed the literal Biblical account of the age of the Earth, hypothesised the idea of extinction, and wrote numerous times of the likelihood that fossils on hill and mountain tops had been raised there by "earthquakes", a general term of the time for geological processes. Much of Hooke's scientific work was conducted in his capacity as curator of experiments of the Royal Society, a post he held from 1662, or as part of the household of Robert Boyle.

In later life, Hooke became party to jealous intellectual disputes, which may have contributed to his relative historical obscurity outside of his association with Newton in particular.

Life and works

Hooke's microscope, from an engraving in Micrographia

Much of what is known of Hooke's early life comes from an autobiography that he commenced in 1696 but never completed. Richard Waller mentions it in his introduction to The Posthumous Works of Robert Hooke, M.D. S.R.S., printed in 1705. In the chapter Of Dr. Dee's Book of Spirits, Hooke argues that John Dee made use of Trithemian steganography, to conceal his communication with Queen Elizabeth I. The work of Waller, along with John Ward's Lives of the Gresham Professors (with a list of his major works) and John Aubrey's Brief Lives, form the major near-contemporaneous biographical accounts of Hooke.

Early life

Robert Hooke was born in 1635 in Freshwater on the Isle of Wight to John Hooke and Cecily Gyles. Robert was the last of four children, two boys and two girls, and there was an age difference of seven years between him and the next youngest. Their father John was a Church of England priest, the curate of Freshwater's Church of All Saints, and his two brothers (Robert's uncles) were also ministers. Robert Hooke was expected to succeed in his education and join the Church. John Hooke also was in charge of a local school, and so was able to teach Robert, at least partly at home perhaps due to the boy's frail health. He was a Royalist and almost certainly a member of a group who went to pay their respects to Charles I when he escaped to the Isle of Wight. Robert, too, grew up to be a staunch monarchist.

As a youth, Robert Hooke was fascinated by observation, mechanical works, and drawing, interests that he would pursue in various ways throughout his life. He dismantled a brass clock and built a wooden replica that, by all accounts, worked "well enough", and he learned to draw, making his own materials from coal, chalk and ruddle (iron ore).

On his father's death in 1648, Robert was left a sum of forty pounds that enabled him to buy an apprenticeship; with his poor health throughout his life but evident mechanical facility his father had it in mind that he might become a watchmaker or limner (a decorator of illuminated manuscripts), though Hooke was also interested in painting. Hooke was an apt student, so although he went to London to take up an apprenticeship, and studied briefly with Samuel Cowper and Peter Lely, he was soon able to enter Westminster School in London, under Dr. Richard Busby. Hooke quickly mastered Latin and Greek, made some study of Hebrew, and mastered Euclid's Elements. Here, too, he embarked on his lifelong study of mechanics. 

It appears that Hooke was one of a group of students whom Busby educated in parallel to the main work of the school. Contemporary accounts say he was "not much seen" in the school, and this appears to be true of others in a similar position. Busby, an ardent and outspoken Royalist (he had the school observe a fast-day on the anniversary of the King's beheading), was by all accounts trying to preserve the nascent spirit of scientific inquiry that had begun to flourish in Carolean England but which was at odds with the literal Biblical teachings of the Protectorate. To Busby and his select students the Anglican Church was a framework to support the spirit of inquiry into God's work, those who were able were destined by God to explore and study His creation, and the priesthood functioned as teachers to explain it to those who were less able. This was exemplified in the person of George Hooper, the Bishop of Bath and Wells, whom Busby described as "the best scholar, the finest gentleman and will make the completest bishop that ever was educated at Westminster School".

Oxford

Robert Boyle by Johann Kerseboom, at Gawthorpe Hall, Lancashire

In 1653, Hooke (who had also undertaken a course of twenty lessons on the organ) secured a chorister's place at Christ Church, Oxford. He was employed as a "chemical assistant" to Dr Thomas Willis, for whom Hooke developed a great admiration. There he met the natural philosopher Robert Boyle, and gained employment as his assistant from about 1655 to 1662, constructing, operating, and demonstrating Boyle's "machina Boyleana" or air pump. It was not until 1662 or 1663 that was awarded a Master of Arts degree. In 1659 Hooke described some elements of a method of heavier-than-air flight to Wilkins, but concluded that human muscles were insufficient to the task.

Hooke himself characterised his Oxford days as the foundation of his lifelong passion for science, and the friends he made there were of paramount importance to him throughout his career, particularly Christopher Wren. Wadham was then under the guidance of John Wilkins, who had a profound impact on Hooke and those around him. Wilkins was also a Royalist, and acutely conscious of the turmoil and uncertainty of the times. There was a sense of urgency in preserving the scientific work which they perceived as being threatened by the Protectorate. Wilkins' "philosophical meetings" in his study were clearly important, though few records survive except for the experiments Boyle conducted in 1658 and published in 1660. This group went on to form the nucleus of the Royal Society. Hooke developed an air pump for Boyle's experiments based on the pump of Ralph Greatorex, which was considered, in Hooke's words, "too gross to perform any great matter." It is known that Hooke had a particularly keen eye, and was an adept mathematician, neither of which applied to Boyle. It has been suggested that Hooke probably made the observations and may well have developed the mathematics of Boyle's law. Regardless, it is clear that Hooke was a valued assistant to Boyle and the two retained a mutual high regard.

A chance surviving copy of Willis' pioneering De anima brutorum, a gift from the author, was chosen by Hooke from Wilkins' library on his death as a memento at John Tillotson's invitation. This book is now in the Wellcome Library. The book and its inscription in Hooke's hand are a testament to the lasting influence of Wilkins and his circle on the young Hooke.

Royal Society

The Royal Society was founded in 1660, and in April 1661 the society debated a short tract on the rising of water in slender glass pipes, in which Hooke reported that the height water rose was related to the bore of the pipe (due to what is now termed capillary action). His explanation of this phenomenon was subsequently published in Micrography Observ. issue 6, in which he also explored the nature of "the fluidity of gravity". On 5 November 1661, Sir Robert Moray proposed that a Curator be appointed to furnish the society with Experiments, and this was unanimously passed with Hooke being named. His appointment was made on 12 November, with thanks recorded to Dr. Boyle for releasing him to the Society's employment.

In 1664, Sir John Cutler settled an annual gratuity of fifty pounds on the Society for the founding of a Mechanick Lecture, and the Fellows appointed Hooke to this task. On 27 June 1664 he was confirmed to the office, and on 11 January 1665 was named Curator by Office for life with an additional salary of £30 to Cutler's annuity.

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, the implosion of glass bubbles which had been sealed with comprehensive hot air, and demonstrating that the Pabulum vitae and flammae were one and the same. He also demonstrated that a dog could be kept alive with its thorax opened, provided air was pumped in and out of its lungs, and noting the difference between venous and arterial blood. There were also experiments on the subject of gravity, the falling of objects, the weighing of bodies and measuring of barometric pressure at different heights, and pendulums up to 200 ft long (61 m).

Instruments were devised to measure a second of arc in the movement of the sun or other stars, to measure the strength of gunpowder, and in particular an engine to cut teeth for watches, much finer than could be managed by hand, an invention which was, by Hooke's death, in constant use.

In 1663 and 1664, Hooke produced his microscopy observations, subsequently collated in Micrographia in 1665.

On 20 March 1664, Hooke succeeded Arthur Dacres as Gresham Professor of Geometry. Hooke received the degree of "Doctor of Physic" in December 1691.

Illustration from The posthumous works of Robert Hooke... published in Acta Eruditorum, 1707

Hooke and Newcomen

There is a widely reported but seemingly incorrect story that Dr Hooke corresponded with Thomas Newcomen in connection with Newcomen's invention of the steam engine. This story was discussed by Rhys Jenkins, a past President of the Newcomen Society, in 1936. Jenkins traced the origin of the story to an article "Steam Engines" by Dr. John Robison (1739–1805) in the third edition of the "Encyclopædia Britannica”, which says There are to be found among Hooke's papers, in the possession of the Royal Society, some notes of observations, for the use of Newcomen, his countryman, on Papin's boasted method of transmitting to a great distance the action of an mill by means of pipes, and that Hooke had dissuaded Newcomen from erecting a machine on this principle. Jenkins points out a number of errors in Robison's article, and questions whether the correspondent might in fact have been Newton, whom Hooke is known to have corresponded with, the name being misread as Newcomen. A search by Mr. H W Dickinson of Hooke's papers held by the Royal Society, which had been bound together in the middle of the 18th century, i.e. before Robison's time, and carefully preserved since, revealed no trace of any correspondence between Hooke and Newcomen. Jenkins concluded ... this story must be omitted from the history of the steam engine, at any rate until documentary evidence is forthcoming.

 

In the intervening years since 1936 no such evidence has been found, but the story persists. For instance, in a book published in 2011 it is said that in a letter dated 1703 Hooke did suggest that Newcomen use condensing steam to drive the piston.

Personality and disputes

Hooke was irascible, at least in later life, proud, and prone to take umbrage with intellectual competitors, though he was by all accounts also a staunch friend and ally and was loyal always to the circle of ardent Royalists with whom he had his early training at Wadham College, particularly Christopher Wren. His reputation suffered after his death and this is popularly attributed to a dispute with Isaac Newton over credit for his work on gravitation, the planets and to a lesser degree light. His dispute with Oldenburg about whether Oldenburg had leaked or passed on details of Hooke's watch escapement to others is another well-known example.

Newton, as President of the Royal Society, did much to obscure Hooke, including, it is said, destroying (or failing to preserve) the only known portrait of the man. It did not help that the first biography of Wren, Parentalia, was written by Wren's son, and tended to exaggerate Wren's work over all others. Hooke's reputation was revived during the twentieth century through studies by Robert Gunther and Margaret 'Espinasse. After a long period of relative obscurity he has now been recognised as one of the most important scientists of his age.

Hooke was apt to use ciphers and guard his ideas. As curator of Experiments to the Royal Society he was responsible for demonstrating many ideas sent in to the Society, and there is evidence that he would subsequently assume some credit for these ideas. Hooke also was immensely busy and thus unable—or in some cases unwilling, pending a way of profiting from the enterprise via letters patent—to develop all of his own ideas. This was a time of immense scientific progress, and numerous ideas were developed in several places simultaneously.

None of this should distract from Hooke's inventiveness, his remarkable experimental facility, and his capacity for hard work. His ideas about gravitation, and his claim of priority for the inverse square law, are outlined below. He was granted a large number of patents for inventions and refinements in the fields of elasticity, optics, and barometry. The Royal Society's Hooke papers (recently discovered after disappearing when Newton took over) will open up a modern reassessment.

Engraving of a louse from Hooke's Micrographia

Much has been written about the unpleasant side of Hooke's personality, starting with comments by his first biographer, Richard Waller, that Hooke was "in person, but despicable" and "melancholy, mistrustful, and jealous." Waller's comments influenced other writers for well over two centuries, so that a picture of Hooke as a disgruntled, selfish, anti-social curmudgeon dominates many older books and articles. For example, Arthur Berry said that Hooke "claimed credit for most of the scientific discoveries of the time." Sullivan wrote that Hooke was "positively unscrupulous" and possessing an "uneasy apprehensive vanity" in dealings with Newton. Manuel used the phrase "cantankerous, envious, vengeful" in his description. More described Hooke having both a "cynical temperament" and a "caustic tongue." Andrade was more sympathetic, but still used the adjectives "difficult", "suspicious", and "irritable" in describing Hooke.

The publication of Hooke's diary in 1935 revealed other sides of the man that 'Espinasse, in particular, has detailed carefully. She writes that "the picture which is usually painted of Hooke as a morose and envious recluse is completely false." Hooke interacted with noted craftsmen such as Thomas Tompion, the clockmaker, and Christopher Cocks (Cox), an instrument maker. Hooke often met Christopher Wren, with whom he shared many interests, and had a lasting friendship with John Aubrey. Hooke's diaries also make frequent reference to meetings at coffeehouses and taverns, and to dinners with Robert Boyle. He took tea on many occasions with his lab assistant, Harry Hunt. Within his family, Hooke took both a niece and a cousin into his home, teaching them mathematics.

Robert Hooke spent his life largely on the Isle of Wight, at Oxford, and in London. He never married, but his diary records that he had sexual relations with his niece, Grace, and several of his housekeepers. He at one point records that one of these housekeepers gave birth to a girl, but doesn't note the paternity of the child. On 3 March 1703, Hooke died in London, and a chest containing £8,000 in money and gold was found in his room at Gresham College. 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 an illiterate cousin, Elizabeth Stephens. He was buried at St Helen's Bishopsgate, but the precise location of his grave is unknown.

Science

Hooke's drawing of a flea

Mechanics

In 1660, Hooke discovered the law of elasticity which bears his name and which describes the linear variation of tension with extension in an elastic spring. He first described this discovery in the anagram "ceiiinosssttuv", whose solution he published in 1678 as "Ut tensio, sic vis" meaning "As the extension, so the force." Hooke's work on elasticity culminated, for practical purposes, in his development of 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 Hooke Folio (see External links below), describing a demonstration of a balance-controlled watch before the Royal Society, has been held to favour Hooke's claim.

Cell structure of cork by Hooke

It is interesting from a twentieth-century vantage point that Hooke first announced his law of elasticity as an anagram. This was a method sometimes used by scientists, such as Hooke, Huygens, Galileo, and others, to establish priority for a discovery without revealing details.

Hooke became Curator of Experiments in 1662 to the newly founded Royal Society, and took responsibility for experiments performed at its weekly meetings. This was a position he held for over 40 years. While this position kept him in the thick of science in Britain and beyond, it also led to some heated arguments with other scientists, such as Huygens (see above) and particularly with Isaac Newton and the Royal Society's Henry Oldenburg. In 1664 Hooke also was appointed Professor of Geometry at Gresham College in London and Cutlerian Lecturer in Mechanics.

On 8 July 1680, Hooke observed the nodal patterns associated with the modes of vibration of glass plates. He ran a bow along the edge of a glass plate covered with flour, and saw the nodal patterns emerge. In acoustics, in 1681 he showed the Royal Society that musical tones could be generated from spinning brass cogs cut with teeth in particular proportions.

Gravitation

While many of his contemporaries believed in the aether as a medium for transmitting attraction or repulsion between separated celestial bodies, Hooke argued for an attracting principle of gravitation in Micrographia (1665). Hooke's 1666 Royal Society lecture on gravity added two further principles: that all bodies move in straight lines till deflected by some force and that the attractive force is stronger for closer bodies. Dugald Stewart quoted Hooke's own words on his system of the world.

"I will explain," says Hooke, in a communication to the Royal Society in 1666, "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 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 1670 Gresham lecture explained that gravitation applied to "all celestial bodies" and added the principles that the gravitating power decreases with distance and that in the absence of any such power bodies move in straight lines.

Hooke published his ideas about the "System of the World" again in somewhat developed form in 1674, as an addition to "An Attempt to Prove the Motion of the Earth from Observations". Hooke clearly postulated mutual attractions between the Sun and planets, in a way that increased with nearness to the attracting body.

Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. Hooke also did not provide accompanying evidence or mathematical demonstration. On these two aspects, Hooke stated in 1674: "Now what these several degrees [of gravitational attraction] are I have not yet experimentally verified" (indicating that he did not yet know what law the gravitation might follow); and as to his whole proposal: "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 remarkable exchange of letters with Newton (of which the full text is now published). Hooke's ostensible purpose was to tell Newton that Hooke had been appointed to manage the Royal Society's correspondence. Hooke therefore wanted to hear from members about their researches, or their views about the researches of others; and as if to whet Newton's interest, he asked what Newton thought about various matters, giving a whole list, mentioning "compounding the celestial motions of the planetts of a direct motion by the tangent and an attractive motion towards the central body", and "my hypothesis of the lawes or causes of springinesse", and then a new hypothesis from Paris about planetary motions (which Hooke described at length), and then efforts to carry out or improve national surveys, the difference of latitude between London and Cambridge, and other items. Newton's reply offered "a fansy of my own" about a terrestrial experiment (not a proposal about celestial motions) which might detect the Earth's motion, by the use of a body first suspended in air and then dropped to let it fall. The main point was to indicate how Newton thought the falling body could experimentally reveal the Earth's motion by its direction of deviation from the vertical, but he 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 how the body would continue to move. A short further correspondence developed, and towards the end of it Hooke, writing on 6 January 1679|80 to Newton, communicated his "supposition ... that 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 was actually incorrect.)

In 1686, when the first book of Newton's Principia was presented to the Royal Society, Hooke claimed that he had given Newton 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 contemporary report) Hooke agreed that "the Demonstration of the Curves generated therby" was wholly Newton's.

A recent assessment about the early history of the inverse square law is that "by the late 1660s," the assumption of an "inverse proportion between gravity and the square of distance was rather common and had been advanced by a number of different people for different reasons". Newton himself had shown in the 1660s that for planetary motion under a circular assumption, force in the radial direction had an inverse-square relation with distance from the center. Newton, faced in May 1686 with Hooke's claim on the inverse square law, denied that Hooke was to be credited as author of the idea, giving reasons including the citation of prior work by others before Hooke. Newton also firmly claimed that even if it had happened that he had first heard of the inverse square proportion from Hooke, which it had not, he would still have some rights to it in view of his mathematical developments and demonstrations, which enabled observations to be relied on as evidence of its accuracy, while Hooke, without mathematical demonstrations and evidence in favour of the supposition, could only guess (according to Newton) that it was approximately valid "at great distances from the center".

On the other hand, Newton did accept and acknowledge, in all editions of the Principia, that Hooke (but not exclusively Hooke) had separately appreciated the inverse square law in the solar system. Newton acknowledged Wren, Hooke and Halley in this connection in the Scholium to Proposition 4 in Book 1. Newton also acknowledged to Halley that his correspondence with Hooke in 1679–80 had reawakened his dormant interest in astronomical matters, but that did not mean, according to Newton, that Hooke had told Newton anything new or original: "yet am I not beholden to him for any light into that business but only for 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."

One of the contrasts between the two men was that Newton was primarily a pioneer in mathematical analysis and its applications as well as optical experimentation, while Hooke was a creative experimenter of such great range, that it is not surprising to find that he left some of his ideas, such as those about gravitation, undeveloped. This in turn makes it understandable how in 1759, decades after the deaths of both Newton and Hooke, Alexis Clairaut, mathematical astronomer eminent in his own right in the field of gravitational studies, made his assessment after reviewing what Hooke had published on gravitation. "One must not think that this idea ... of Hooke diminishes Newton's glory", Clairaut wrote; "The example of Hooke" serves "to show what a distance there is between a truth that is glimpsed and a truth that is demonstrated".

Horology

Hooke made tremendously important contributions to the science of timekeeping, being intimately involved in the advances of his time; the introduction of the pendulum as a better regulator for clocks, the balance spring to improve the timekeeping of watches, and the proposal that a precise timekeeper could be used to find the longitude at sea.

Anchor escapement

Anchor escapement

In 1655, according to his autobiographical notes, Hooke began to acquaint himself with astronomy, through the good offices of John Ward. Hooke applied himself to the improvement of the pendulum and in 1657 or 1658, he began to improve on pendulum mechanisms, studying the work of Giovanni Riccioli, and going on to study both gravitation and the mechanics of timekeeping.

Henry Sully, writing in Paris in 1717, described the anchor escapement as an admirable invention of which Dr. Hooke, formerly professor of geometry in Gresham College at London, was the inventor. William Derham also attributes it to Hooke.

Watch balance spring

Christiaan Huygens by Caspar Netscher

Hooke recorded that he conceived of a way to determine longitude (then a critical problem for navigation), 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, fitted with a coil spring attached to the arbour of the balance. Hooke's ultimate failure to secure sufficiently lucrative terms for the exploitation of this idea resulted in its being shelved, and evidently caused him to become more jealous of his inventions.

Hooke developed the balance spring independently of and at least 5 years before Christiaan Huygens, who published his own work in Journal de Scavans in February 1675.

Microscopy

Hooke's microscope

In 1665 Hooke published Micrographia, a book describing observations made with microscopes and telescopes, as well as some original work in biology. Hooke coined the term cell for describing biological organisms, the term being suggested by the resemblance of plant cells to cells of a honeycomb. The hand-crafted, leather and gold-tooled microscope he used to make the observations for Micrographia, originally constructed by Christopher White in London, is on display at the National Museum of Health and Medicine in Maryland. 

Micrographia also contains Hooke's, or perhaps Boyle and Hooke's, ideas on combustion. Hooke's experiments led him to conclude that combustion involves a substance that is mixed with air, a statement with which modern scientists would agree, but that was not understood widely, if at all, in the seventeenth century. Hooke went on to conclude that respiration also involves a specific component of the air. Partington even goes so far as to claim that if "Hooke had continued his experiments on combustion it is probable that he would have discovered oxygen".

Palaeontology

Drawings of the Moon and the Pleiades from Hooke's Micrographia

One of the observations in Micrographia was of fossil wood, the microscopic structure of which he compared to 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 petrifying water laden with minerals. Hooke believed that such fossils provided reliable clues to the past 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.

Charles Lyell wrote the following in his Principles of Geology (1832).

'The Posthumous Works of Robert Hooke M.D.,'... appeared in 1705, containing 'A Discourse of Earthquakes'... 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. 'However trivial a thing,' he says, 'a rotten shell may appear to some, yet these monuments of nature are more certain tokens of antiquity than coins or medals, since the best of those may be counterfeited or made by art and design, as may also books, manuscripts, and inscriptions, as all the learned are now sufficiently satisfied has often been actually practised,' &c.; 'and though it must be granted that it is very difficult to read them and to raise a chronology out of them, and to state the intervals of the time wherein such or such catastrophes and mutations have happened, yet it is not impossible.

Astronomy

Hooke noted the shadows (a and b) cast by both the globe and the rings on each other in this drawing of Saturn.

One of the more-challenging problems tackled by Hooke was the measurement of the distance to a star (other than the Sun). The star chosen was Gamma Draconis and the method to be used was parallax determination. After several months of observing, in 1669, Hooke believed that the desired result had been achieved. It is now known that Hooke's equipment was far too imprecise to allow the measurement to succeed. Gamma Draconis was the same star James Bradley used in 1725 in discovering the aberration of light. 

Hooke's activities in astronomy extended beyond the study of stellar distance. His Micrographia contains illustrations of the Pleiades star cluster as well as of lunar craters. He performed experiments to study how such craters might have formed. Hooke also was an early observer of the rings of Saturn, and discovered one of the first observed double-star systems, Gamma Arietis, in 1664.

Memory

A lesser-known contribution, however one of the first of its kind, was Hooke's scientific model of human memory. Hooke in a 1682 lecture to the Royal Society proposed a mechanistic model of human memory, which would bear little resemblance to the mainly philosophical models before it. This model addressed the components of encoding, memory capacity, repetition, retrieval, and forgetting – some with surprising modern accuracy. This work, overlooked for nearly 200 years, shared a variety of similarities with Richard Semon's work of 1919/1923, both assuming memories were physical and located in the brain. The model's more interesting points are that it (1) allows for attention and other top-down influences on encoding; (2) it uses resonance to implement parallel, cue-dependent retrieval; (3) it explains memory for recency; (4) it offers a single-system account of repetition and priming, and (5) the power law of forgetting can be derived from the model's assumption in a straightforward way. This lecture would be published posthumously in 1705 as the memory model was unusually placed in a series of works on the nature of light. It has been speculated that this work saw little review as the printing was done in small batches in a post-Newtonian age of science and was most likely deemed out of date by the time it was published. Further interfering with its success was contemporary memory psychologists' rejection of immaterial souls, which Hooke invoked to some degree in regards to the processes of attention, encoding and retrieval.

Architecture

Church of St Mary Magdalene at Willen, Milton Keynes

Hooke was Surveyor to the City of London and chief assistant to Christopher Wren, in which capacity he helped Wren rebuild London after the Great Fire in 1666, and also worked on the design of London's Monument to the fire, the Royal Greenwich Observatory, Montagu House in Bloomsbury, and the Bethlem Royal Hospital (which became known as 'Bedlam'). Other buildings designed by Hooke include The Royal College of Physicians (1679), Ragley Hall in Warwickshire, Ramsbury Manor in Wiltshire and the parish church of St Mary Magdalene at Willen in Milton Keynes, Buckinghamshire. Hooke's collaboration with Christopher Wren also included St Paul's Cathedral, whose dome uses a method of construction conceived by Hooke. Hooke also participated in the design of the Pepys Library, which held the manuscripts of Samuel Pepys' diaries, the most frequently cited eyewitness account of the Great Fire of London.

Hooke and Wren both being keen astronomers, the Monument was designed to serve a scientific function as a telescope for observing transits, though Hooke's characteristically precise measurements after completion showed that the movement of the column in the wind made it unusable for this purpose. The legacy of this can be observed in the construction of the spiral staircase, which has no central column, and in the observation chamber which remains in place below ground level.

In the reconstruction after the Great Fire, Hooke proposed redesigning London's streets on a grid pattern with wide boulevards and arteries, a pattern subsequently used in the renovation of Paris, Liverpool, and many American cities. This proposal was thwarted by arguments over property rights, as property owners were surreptitiously shifting their boundaries. Hooke was in demand to settle many of these disputes, due to his competence as a surveyor and his tact as an arbitrator. 

For an extensive study of Hooke's architectural work, see the book by Cooper.

Likenesses

Portrait thought for a time to be Hooke, but almost certainly Jan Baptist van Helmont

No authenticated portrait of Robert Hooke exists. This situation has sometimes been attributed to the heated conflicts between Hooke and Newton, although Hooke's biographer Allan Chapman rejects as a myth the claims that Newton or his acolytes deliberately destroyed Hooke's portrait. German antiquarian and scholar Zacharias Conrad von Uffenbach visited the Royal Society in 1710 and his account of his visit specifically mentions him being shown the portraits of 'Boyle and Hoock' (which were said to be good likenesses), but while Boyle's portrait survives, Hooke's has evidently been lost. In Hooke's time, the Royal Society met at Gresham College, but within a few months of Hooke's death Newton became the Society's president and plans were laid for a new meeting place. When the move to new quarters finally was made a few years later, in 1710, Hooke's Royal Society portrait went missing, and has yet to be found. 

Two contemporary written descriptions of Hooke's appearance have survived. The first was recorded by his close friend John Aubrey, who described Hooke in middle age and at the height of his creative powers:

He is but of midling stature, something crooked, pale faced, and his face but little below, but his head is lardge, his eie full and popping, and not quick; a grey eie. He haz a delicate head of haire, browne, and of an excellent moist curle. He is and ever was temperate and moderate in dyet, etc.

The second is a rather unflattering description of Hooke as an old man, written by Richard Waller:

As to his Person he was but despicable, being very crooked, tho' I have heard from himself, and others, that he was strait till about 16 Years of Age when he first grew awry, by frequent practising, with a Turn-Lath ... He was always very pale and lean, and laterly nothing but Skin and Bone, with a Meagre Aspect, his Eyes grey and full, with a sharp ingenious Look whilst younger; his nose but thin, of a moderate height and length; his Mouth meanly wide, and upper lip thin; his Chin sharp, and Forehead large; his Head of a middle size. He wore his own Hair of a dark Brown colour, very long and hanging neglected over his Face uncut and lank...

Time magazine published a portrait, supposedly of Hooke, on 3 July 1939. However, when the source was traced by Ashley Montagu, it was found to lack a verifiable connection to Hooke. Moreover, Montagu found that two contemporary written descriptions of Hooke's appearance agreed with one another, but that neither matched the Time's portrait.

In 2003, historian Lisa Jardine claimed that a recently discovered portrait was of Hooke, but this claim was disproved by William Jensen of the University of Cincinnati. The portrait identified by Jardine depicts the Flemish scholar Jan Baptist van Helmont.

Other possible likenesses of Hooke include the following:

• A seal used by Hooke displays an unusual profile portrait of a man's head, which some have argued portrays Hooke.
• The engraved frontispiece to the 1728 edition of Chambers' Cyclopedia shows a drawing of a bust of Robert Hooke. The extent to which the drawing is based on an actual work of art is unknown.
• A memorial window existed at St Helen's Bishopsgate in London, but it was a formulaic rendering, not a likeness. The window was destroyed in the 1993 Bishopsgate bombing.

In 2003, amateur history painter Rita Greer embarked on a self-funded project to memorialise Hooke. Her project aimed to produce credible images of him, both painted and drawn, that she believes fit the descriptions of him by his contemporaries John Aubrey and Richard Waller. Greer's images of Hooke, his life and work have been used for TV programmes in UK and US, in books, magazines and for PR.

Commemorations

Hooke memorial plaque in Westminster Abbey

• 3514 Hooke, an asteroid (1971 UJ)
• Craters on the Moon and on Mars are named in his honour.
• The Hooke Medal
• Robert Hooke Science Centre, Westminster School, London
• List of new memorials to Robert Hooke 2005 – 2009
• The Boyle-Hooke plaque in Oxford

Works

• Micrographia full text at Project Gutenberg, with illustrations at Internet Archive
• Collection of Lectures: Physical, Mechanical, Geographical and Astronomical. London : Printed for John Martyn, printer to the Royal Society, at the Bell in S. Pauls Church-yard. 1679. includes An Attempt to prove the Annual Motion of the Earth, Animadversions on the Machina Coelestis of Mr. Hevelius, A Description of Helioscopes with other instruments, Mechanical Improvement of Lamps, Remarks about Comets 1677, Microscopium, Lectures on the Spring, etc.
• The Posthumous Works of Robert Hooke
• The posthumous works of Robert Hooke, M.D. S.R.S. Geom. Prof. Gresh. etc. containing his Cutlerian lectures, and other discourses, read at the meetings of the illustrious Royal Society... illustrated with sculptures. To these discourses is prefixt the author's life, giving an account of his studies and employments, with an enumeration of the many experiments, instruments, contrivances and inventions, by him made and produced as curator of experiments to the Royal Society published by Richard Waller, R.S. Secr.

Jacob Bernoulli

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Jacob_Bernoulli

Jacob Bernoulli
Jacob Bernoulli
Born	27 December 1654 Basel, Switzerland
Died	16 August 1705 (aged 50) Basel, Switzerland
Alma mater	University of Basel (D.Th., 1676; Dr. phil. hab., 1684)
Known for	Bernoulli differential equation Bernoulli numbers Bernoulli's formula Bernoulli polynomials Bernoulli map Bernoulli trial Bernoulli process Bernoulli scheme Bernoulli operator Hidden Bernoulli model Bernoulli sampling Bernoulli distribution Bernoulli random variable Bernoulli's Golden Theorem Bernoulli's inequality Lemniscate of Bernoulli
Scientific career
Fields	Mathematics, mechanics
Institutions	University of Basel
Theses	Primi et Secundi Adami Collatio (1676) Solutionem tergemini problematis arithmetici, geometrici et astronomici (Solutions to a triple problem in arithmetics, geometry and astronomy) (1684)
Doctoral advisor	Peter Werenfels (1676 thesis advisor)
Other academic advisors	Gottfried Wilhelm Leibniz (epistolary correspondent)
Doctoral students	Johann Bernoulli Jacob Hermann Nicolaus I Bernoulli
Influences	Nicolas Malebranche
Notes
Brother of Johann Bernoulli

Jacob Bernoulli (also known as James or Jacques; 6 January 1655 [O.S. 27 December 1654] – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy. He is known for his numerous contributions to calculus, and along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.

Biography

Jacob Bernoulli was born in Basel, Switzerland. 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 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.

Image from Acta Eruditorum (1682) wherein was published the critique of Bernoulli's Conamen novi systematis cometarum

Bernoulli returned to Switzerland, and began teaching mechanics at the University of Basel from 1683. His doctoral dissertation Solutionem tergemini problematis 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 was between 1684 and 1689 that many of the results that were to make up Ars Conjectandi were discovered. 

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 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 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.

Important works

Jacob Bernoulli's first important contributions were 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 the fundamental result that ${\displaystyle \sum {\frac {1}{n}}}$ diverges, which Bernoulli believed were new but they had actually been proved by Mengoli 40 years earlier. Bernoulli could not find a closed form for ${\displaystyle \sum {\frac {1}{n^{2}}}}$, but he did show that it converged to a finite limit less than 2. Euler was the first to find the sum 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, 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 the term integral appears for the first time with its integration meaning. In 1696 Bernoulli solved the equation, now called the Bernoulli differential equation,

${\displaystyle y'=p(x)y+q(x)y^{n}.}$

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, 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.

Ars conjectandi, 1713 (Milano, Fondazione Mansutti).

Jacob Bernoulli's most original work was Ars Conjectandi published in Basel in 1713, eight years after his death. The work was incomplete at the time of his death but it is still a work of the greatest significance in the theory of probability. In the book Bernoulli reviewed work of others on probability, in particular work by van Schooten, Leibniz, and Prestet. The Bernoulli numbers appear in the book in a discussion of the exponential series. Many examples are given on how much one would expect to win playing various games of chance. The term Bernoulli trial resulted from this work. There are interesting thoughts on what probability really is:

... 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; 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.

Discovery of the mathematical constant e

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 is in fact e):

${\displaystyle \lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}}$

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 $1.00×1.5² = $2.25. Compounding quarterly yields $1.00×1.25⁴ = $2.4414..., and compounding monthly yields $1.00×(1.0833...)¹² = $2.613035.... 

Bernoulli noticed that this sequence approaches 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^R dollars with continuous compounding.

Tombstone

Jacob Bernoulli's tombstone in Basel Münster

Bernoulli wanted 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 was engraved rather than a logarithmic one.

Translation of Latin inscription:

Jacob Bernoulli, the incomparable mathematician.

Professor at the University of Basel For more than 18 years;

member of the Royal Academies of Paris and Berlin; famous for his writings.

Of a chronic illness, of sound mind to the end;

succumbed in the year of grace 1705, the 16th of August, at the age of 50 years and 7 months, awaiting the resurrection.

Judith Stupanus,

his wife for 20 years,

and his two children have erected a monument to the husband and father they miss so much.

Works

De gravitate aetheris, 1683

• Conamen novi systematis cometarum (in Latin). Amstelaedami: apud Henr. Wetstenium. 1682.
• De gravitate aetheris (in Latin). Amstelaedami: apud Henricum Wetstenium. 1683.
• Ars conjectandi, opus posthumum, Basileae, impensis Thurnisiorum Fratrum, 1713.