Robert Hooke, Early Science and Surveying - Professor Michael Cooper

Thank you, Tim. Yes, I'm the one with the first lecture after lunch. At least I shall do my best to stay awake for 20 minutes. I have a script here to keep me going. Robert Hooke's life could be described as one of hyperactive curiosity. His scientific ambitions were so wide-ranging that they were generally unattainable. But his passion to understand the natural world stayed with him until the last year of his life. In the short time available, I would like to look at another side of Hooke's life that was orderly and meticulously recorded by him, his work as city surveyor after the Great Fire of London. Measurements were essential in his surveying and in his science. So I shall discuss Hooke's approach to measurement in both activities and draw some conclusions about his achievements. First of all, his science. From the time of his childhood at Freshwater in the Isle of Wight, Hooke had an exceptional intuitive understanding of mechanical devices. You've seen this Wilkins picture before, but not in this context. You will notice that on the left he is said to be the Bishop of Chester, but the time of publication of the book on the right predates that. The bookseller who sold it to me assured me that the portrait was put in later during a rebinding and that the wormholes in the right are in fact authentic. I took his word for it. When John Wilkins, warden of Wadham College, met Hooke, a pupil at Westminster School, he was so impressed by Hooke's ingenuity and knowledge of Euclid's geometry that he gave him a copy of his book Mathematical Magic. Despite its title, Wilkins wrote the book to show that virtue and wisdom can be found in methodical study and practice of mechanics, an unfashionable idea at the time and still unfashionable today to some extent. This was a lesson that Hooke learned and put to good use for most of his life. He left Westminster School in 1653 with a choral scholarship and followed the well-trodden path to Christchurch, Oxford. He was employed by the formative members of the Royal Society led by Wilkins at Wadham College. They needed Hooke's ingenuity to make mechanical contrivances and instruments for their observations. Around 1657 Robert Boyle employed Hooke to assist him with his experiments on the properties of air in Boyle's private laboratory in Broad Street, Oxford. In 1660 Boyle published what would become known as Boyle's Law. The pressure on a quantity of air at constant temperature is inversely proportional to the volume of the air. Contrary to common belief, Hooke's famous air pump was not used in the experiments that led directly to Boyle's Law. For those experiments Hooke made a very large J-shaped glass tube. Here, squeezed into a plate in micrographia, Hooke was quite parsimonious with his diagrams. He forced as many onto a printing plate as possible. The shorter arm, about 300 millimetres long, was closed at the end. That's just to be seen on the right there with some mercury at the bottom. The other arm, about four metres long, was open at the top. The tube was set upright in the stairwell of Boyle's laboratory. Small amounts of mercury were poured one after the other into the longer tube. At each stage the position of the top of the mercury in each arm was recorded relative to scales marked out on strips of paper pasted to the outside of the glass tube. These scale readings gave the volume and pressure of the air trapped in the smaller, closed arm of the J-tube at each stage. After the experiment had been reported in 1660, some objections were made as to its validity. In 1662 Boyle published a riposte to the objections. This time he included a table of measurements presented in a way that was unprecedented but is now commonplace. For each one of the pairs of measurements he produced two figures shown in this table here. The one on the left at the end, the D, is the measured pressure and the figures on the column headed E are the hypothetical pressures, the pressures that would be expected if Boyle's law was true. Readers were invited to consider the differences between each pair of values and decide for themselves whether or not to accept Boyle's law. Well, here's the evidence you can do that yourself. Are they close enough to be acceptable or not? Details of the experimental procedure were published so that anyone could carry out new experiments and report their own findings. No further serious objections were made at the time, although Boyle's law has been modified since to make it more general. Soon after Boyle's riposte was published, Hooke was appointed the Royal Society's first curator of experiments. Hooke was a Baconian. In Micrographia, and even in his diary, he refers to Francis Bacon in respectful terms such as the Great Verulum. The Royal Society was formed as an image of Bacon's Solomon's House, a fable in which mankind benefits from increased understanding of the natural world by experiment and observation, backed up by rational debate and the keeping of records. Hooke was an ardent seeker after truth about the natural world, but he knew he could never achieve it. Professor Briggs this morning told us about truth. In Wren's inaugural lecture to Gresham College, he said, I paraphrase, the only truth we can know is mathematical truth. What he didn't say, and might have done, was that the reason for that is that we invent mathematics so we know what is true. We didn't invent the natural world, I'm told. Hooke was an ardent seeker after truth, but he knew he could never achieve it. He wrote, Wherever the reader finds that I have ventured at any small conjectures at the causes of the things that I have observed, I beseech him to look upon them only as doubtful problems and uncertain guesses, and not as unquestionable conclusions or matters of unconfutable science. Hooke spent most of his life making better guesses at the causes of natural phenomena, painstaking measurements often failed to justify his intuitive understanding because the materials he worked with were imperfect and his senses and reasoning inadequate. Again he wrote, All the uncertainty and mistakes of human actions proceed either from the narrowness and wandering of our senses, from the slipperiness or delusion of our memory, from the confinement or rashness of our understanding, so that it is no wonder that our power over natural causes and effects is so slowly improved. Seeing we are not only to contend with the obscurity and difficulty of the things whereon we work and think, but even the forces of our own minds conspire to betray us. Hooke's aim fell short of knowing the mind of God. His many attempts to demonstrate the inverse squalor of gravitational attraction by timing bodies falling from different heights all failed for the reasons he stated above. He was both irritated and inspired by his failures. Incidentally the first successful demonstration of the law of terrestrial gravitational attraction did not take place until 1990 when nine scientists from four institutions used Hooke's method of timing falling bodies but they also used laser interferometry, rubidium clocks, servo motors, two mathematical models of the local geoid, a 300 meter high radio tower in Colorado and a research grant with a very long alphanumeric identification code. Boyle and Hooke made more measurements than were necessary to verify Boyle's law. A recent statistical analysis of their experimental data has shown that they measured the positions of the mercury meniscus against the paper scales with a standard deviation of about one and a half millimeters, a surprisingly high precision, even though we know that they used magnifying glasses. Incidentally the scientists who carried out the 1990 gravity experiment in Colorado used a slightly modified version of Boyle's law in their calculations and they reported their results in the same way as Boyle and Hooke did in 1662 but with added statistics and again left readers to draw their own conclusions. Hooke often used diagrams in his publications. Micrographia is a superb example. The astonishing detail in its engravings is itself scientific evidence from which uncertain guesses can be made about how and why a natural object appears as it does. Micrographia soon became a bestseller, an entertaining subject for discussion at smart London dinner tables but Hooke intended the illustrations to be looked at through the eye rather than with the eye. I turn now to Hooke's surveying instruments. When London was destroyed by the Great Fire in September 1666, Hooke was 31 years old, a pivotal figure in the Royal Society and well thought of by the merchants of London who had appointed him Gresham Professor of Geometry in 1665. Only a few days after the outbreak of the fire, Guildhall was in ruin. The Court of Alderman held an emergency meeting in the room in Gresham College where the Royal Society held their Wednesday meetings. I shall use the word the city in general here not only to mean the geographical place but also the administrators, London's Lord Mayor, sheriffs and the Court of Alderman. The city installed London's officials and clerks in Gresham College and ejected from their lodgings a few very peeved Gresham professors. Gresham College became a place where city merchants, master craftsmen and bureaucrats mingled with Royal Society courtiers, aristocrats and politicians. The country was at war, 80% of London was a smoking ruin. Sedition, fear and rumour were rife. Decisions of national importance had to be taken. Hooke, allowed to remain in his lodgings, was at the centre of affairs and in a position to make his fortune. In the two weeks following the Great Fire, six plans for a new city were presented. Three came from members of the Royal Society. Christopher Wren and John Evelyn showed their plans to the King and on the 19th September in Gresham College, Hooke showed his plan to the Royal Society. Sir John Lawrence, the former Lord Mayor, was at the meeting and told the society that the city preferred Hooke's plan to the one produced by their own surveyor. The Royal Society and the city agreed that Hooke's plan should be shown to the King for his approval. But all plans for building a new London were set aside. Parliament was unable to find money to pay for the second war against the Dutch as well as for a new city. Reluctantly, the King, Parliament and the city all accepted a middle way. Rebuilding would take place mainly on the old foundation. The Privy Council appointed Wren as one of the three King's Commissioners for rebuilding. The city followed by appointing Hooke as one of the three city surveyors for rebuilding. King's Commissioners and the city surveyors drafted new building regulations for Parliament. A tax on coal was levied to pay for new parish churches and public works. Plans were made for some new streets. Others were to be widened or made straight. Scantlings of three different kinds of houses were specified to be built of stone or brick. Spaces were set aside for markets. New water and sewage systems were planned. London's main sewer, the Fleet River, would be cleaned out and made navigable as far as Holborn. A new quay along the Thames was planned. The first major town planning legislation was passed by Parliament. But its enforcement would require constant monitoring and measurement of work in progress. Illness or private work distracted four of the original six men appointed to supervise the rebuilding of London, leaving Wren and Hooke effectively in charge. They soon formed an efficient working partnership. Their scientific interests shaped a common purpose to create a durable city that was orderly, clean and airy, more beautiful and more healthy than the ramshackle and chaotic medieval city lost in the flames. They trusted one another and each in turn was trusted by the court and the city. Wren designed grand public buildings fit for a European capital, using materials and methods that he and Hooke had studied as scientists. Hooke continued to give him Gresham lectures and make instruments for his Royal Society experiments. But his morning job was to work for the citizens of London. He staked out new streets to the width specified in the Rebuilding Act. He measured areas of land that were taken away from citizens for public use. He settled building disputes. He solved technical and managerial problems on construction sites. Supervised the work of craftsmen. Checked contractors' bills, quantities, their invoices, fees and standards of workmanship. Hardly anything was built without Hooke's supervision. Even, or perhaps especially, the locations of houses of common easement and lay stalls were determined by him. The mutual trust between Wren, Hooke and their respective patrons held, despite crises of overspending on major works and difficulties with contractors. By 1674 most of London had been rebuilt and Hooke was exhausted. He had spent his mornings meeting citizens face to face on streets at a time when they had lost their homes and businesses. Nobody could begin to rebuild until the city surveyor had staked out, measured and certified the property boundary. Hooke provided this service to more than 3,000 of London's citizens. He also measured and certified for compensation more than 300 areas of ground taken away by the city. He heard evidence in more than 600 building disputes and wrote reports to the city on his judgement and the reasons for them. These tasks were a sort of street theatre, performed before an audience of property owners, neighbours and passers-by. Probably at least as critical a gathering as the audience at his Royal Society performances. Hooke used simple and traditional equipment for his survey measures. He recorded dates, citizens' names, places and dimensions in his survey book, which he had with him all the time. Later, in a coffeehouse or at Gresham College, he calculated areas of land for compensation using a formula that he knew would almost always give the wrong value. As city surveyor, he deliberately sacrificed accuracy for expediency, something that he went to great lengths to avoid in his scientific experiments. He could have found a more accurate value of an area of ground by taking additional measurements, using more complicated instruments and formulae. But he chose to be economical with the truth to save time. He has been criticised for not inventing new devices for the city surveyors, but there was no need to do so. On the contrary, citizens were reassured to see surveyors using the familiar measuring rods and tapes to determine the amount of compensation they would receive for the land taken from them. At a time when citizens were desperate to rebuild their houses and begin trading again, there were many opportunities for Hooke to give priority service in return for a favour. Although he received an annual salary of £150 from the city, paid regularly every quarter day, he was also paid fees by private individuals and institutions for his work. These fees were negotiable. They varied between five shillings and five guineas. Searches in the City of London archives have produced no evidence, so far, that Hooke was anything other than scrupulously fair in his dealings with the public. He took up his tasks more or less in the order in which the requests for them were registered in the city archives. His fees depended on the amount of work involved, not on the wealth of his clients. Most of his legacy of around £10,000 came in fees paid to him by the citizens and institutions of London. His income from the Royal Society was small and irregular, and he had to sue Sir John Cutler for his salary as Cutlerian lecturer. Now to some conclusions. When most of London had been rebuilt, Hooke convinced the city that they could administer London more efficiently if they had an accurate and detailed large-scale plan. He persuaded some independent land surveyors, here's one of them, who normally competed with one another, to cooperate in a new kind of measuring scheme he'd devised specifically for urban mapping. William Leybourne was one of the competitive land surveyors. An author, in the fourth edition of his book on land surveying, written just after the city had been rebuilt and Hooke had introduced his new way of surveying an urban area, he wrote one of the most toe-curlingly obsequious prefaces dedicated to Sir Thomas Player, the Chamberlain of London. His ingratiation with him, I think, did not really pay off. But he was one of these antagonistic, confident, determined land surveyors that Hooke persuaded to work together in producing a plan of London. Hooke engaged Wenceslas Holler to engrave the printing plates and he persuaded the city to commission the recently appointed royal cosmographer and former dancing instructor John Ogilvie to organise a lottery to cover the costs of surveying and map production. It is the first large-scale map of a British town or city which shows features drawn to scale instead of as a bird's eye view. The same part of London there, St Mary Somerset, just to the south-east of St Paul's. Thames Street runs along the bottom, so the Thames is a little further south. And the traditional urban mapping was as shown on the left, and after Hooke's mathematical orthographic projection true to scale we have on the right. Some people think the one on the left is charming. It is in a way. It looks more like a monopoly board to me than a map. The scale of Hooke's map was 1 in 1,200, which is one inch on the map represented 100 feet on the ground. It's become known as Ogilvie and Morgan's map of London. When the 20 separate map sheets are joined together, they cover an area of about 10 square metres. Bigger than the screen there. Hooke intended the map to be mounted on linen so that it could be folded and carried around, a sort of A to Z map of London restored, but no copies have been found in that state. Through my eyes this is more than an accurate map. Gresham College you can see there in the centre top between Broad Street to the west and Bishop's Gate Street to the east. And right at the eastern side, opposite Gresham College, is St Helen's Bishop's Gate, where Hooke was interred before being removed from there to Wanstead in the 19th century. Behind this map lie thousands of measurements, calculations and drawing office designs, hundreds of committee meetings and arguments about cost, encroachments on neighbours' properties and denials of their rights of access and of light. It is a result of the moral purpose in practical geometry that the schoolboy Hooke had learnt from Wilkins. Barnard's Inn there, just to the left, south of Holborn, home of present Gresham College. Through microscopes and telescopes, Hooke and Wren sought understanding of the order and beauty of nature. By their own designs and construction of London's new buildings and streets, they created a more orderly and beautiful city. In civic life, Hooke knew that the urgent needs of homeless and penurious citizens could be met only if he were economical with the truth. In meeting their needs, I suggest that he did not do so much compromise his principles as show civic virtue.