Monthly Archives: November 2013

Sorrenson – Perfect Mechanics

Sorrenson, Richard, Perfect Mechanics. Instrument Makers at the Royal Society of London in the Eighteenth Century, Boston: Docent Press, 2013, ix+240 pp. Amazon link.

Perfect Mechanics looks at the connections, and tensions, between the Eighteenth-Century mathematical instrument makers and the Royal Society. In this highly-readable and well-researched adaptation of a Princeton Ph.D., Sorrenson blends together over-arching themes with detailed case studies.

If the Royal Society was an elite club for philosophical gentlemen, what were mere artisans doing there? Sorrenson shows that both halves of this thesis are flawed. Although a Royal Society, and chartered by Charles II, the Society was largely neglected by indifferent sovereigns. While an interest in the workings of the society and sufficiently high rank was a guarantee of membership, the remainder of the fellows formed a more diverse group than might be imagined. While social status was an advantage, membership could be achieved through diligent study, patient observation, and significant contribution to the body of knowledge, regardless of class. While the Society depended for its continued existence on a group of (largely) landed gentry who paid their dues and took their copies of the Society’s journal of record, the Philosophical Transactions, but played little active part in the working of the organization, the active Fellows spanned a range of social class.

The Society’s mission was exploration of the modern experimental and natural philosophies, but in outlook they were more Baconian than Newtonian. Observation and experimentation were prized above abstract theorizing. “To the eighteenth-century Fellows of the Royal Society, the ideal scientific life was exemplified by those members who made careful observations of natural or artificial phenomena, gave them a mechanical explanation or demonstration where possible, avoided grand theory, and above all produced reliable and accurate facts” (35). Newton cast a long shadow. Sorrenson notes that pure mathematics makes up some 2% of all papers published in the Philosophical Transactions.

Behind the search for reliable and accurate facts lay the instruments, and the instrument makers. The eighteenth century saw the introduction of a host of observation instruments, and the refinement of others, from telescopes and microscopes, to vacuum pumps, barometers, hydrometers and clocks. Observations with these instruments greatly augmented natural human senses and as the facts became more accurate and precise, they uncovered new, unexpected phenomena. The gentlemen philosophers needed close interaction with the artisans, and here we come to the second part of Sorrenson’s analysis. While instrument makers for the regular trade could be seen just as craftsmen, working with their hands for commercial gain, those at the cutting edge of instrument design needed both a practical ability and theoretical background. A few instrument makers at the top of their profession made their own discoveries, published in the Philosophical Transactions, were awarded the Copley Medal, the Society’s highest honor, and were welcomed as Fellows. Sorrenson presents three case studies, for the early part of the century, the middle and the latter decades.

First is George Graham (1673—1751). Praised for the great mural quadrant he designed and made for Edmond Halley for the Greenwich Observatory, an instrument of unsurpassed accuracy, Graham regularly published his own astronomical observations in the Philosophical Transactions, and the great accuracy of his instruments allowed the discovery of the new phenomenon of the aberration of starlight, a discovery in which he himself played a significant part.

Graham also discovered the diurnal variation in the Earth’s magnetic field by the expedient of making a superbly accurate compass and taking careful measurements several times a day for two solid years. An exemplar of the governing philosophy of science. Graham had trained as a clockmaker under Thomas Tompion. The rate of a pendulum clock depends on the length of the pendulum, and this varies with temperature as the length of the pendulum increases in warmer weather and decreases in colder weather. Therefore a clock will not beat steady time over the year. Graham devised a way of attaching a mercury column to the pendulum to exactly counter this effect, and this is the instrument displayed behind him in the portrait above (from an engraving by J. Faber after Thomas Hudson).

Sorrenson’s second case is the Dollond family, especially John Dollond (1706—1761). The Dollonds were opticians, and, along with spectacles, the main optical instrument of the mid-eighteenth century was the telescope. Telescopes are either reflecting (using mirrors) or refracting (using lenses). When light passes through a lens, the material bends, or refracts, the light. However, the amount the light is bent depends on the wavelength, with the blue and red bending through different angles. This is the phenomenon that allows a prism to split up white light. However, in a telescope, it means that white starlight gets smeared with colored fringes, a problem known as chromatic aberration that limits the accuracy of observations. John Dollond found a way two put two lenses of different types of glass together (crown and flint) to cancel out the effect. Not only did this immediately make refractive telescopes better (and sweep the market), but Isaac Newton had investigated the issue and stated flatly that it could not be solved. Dollond had bested Newton.

The third case is Jesse Ramsden (1735—1800), who married John Dollond’s daughter, Sarah. At the height of his career, Ramsden made the best instruments available. Orders poured in from observatories and kings across Europe. His extreme accuracy was matched only by his extreme dilatoriness. If you wanted a Ramsden instrument, you had to wait. He made enormous vertical circles, one seen in the background, used by astronomers to create improved star catalogs, and he designed and built the enormous theodolite used for the first Ordnance Survey of England. Ramsden’s other claim to fame, also shown in his portrait, is the dividing engine. This apparatus allowed and journeyman or apprentice, to divide a surveying instrument with the accuracy previously only available to the most skilled craftsmen. With this, he could produce cheaper and better sextants and other instruments for the insatiable navigational market, but the price for the profession was a loss of status. From experts mixing theoretical philosophy with practical mechanics, they became machine-tool users. The delicate social balance between gentlemen and instrument makers was being lost.

Sorrenson’s argument for how the instrument makers achieved social status, and how they lost it, is carefully made. The book contains a wealth of detail (and characters) not touched on here, all told with an ease that litle academic scholarship attains. Perfect Mechanics is an important account of a crucial period of development in British science and industry showing how philosophy, economics, social manners and technology blended together.

On the Road Again

Joshua Kirby had a deep and abiding interest in mathematical instruments, especially those connected with architectural and perspective drawing, and he had close relationships with several of the instrument makers in London, including John Bennet and George Adams. He designed several instruments and, indeed, wrote a book on a sector he designed. I have been digging into the world of the London instruments and instrument makers, which was going through something of a golden period when Kirby was involved, and I am giving a talk on the subject at the Canadian Mathematical Society Winter Meeting in Ottawa on December 7. Here’s my abstract:

DUNCAN MELVILLE, St. Lawrence University

Dividing to rule: Precision mathematical instruments in mid-18th century England

Development of mathematical sciences in the 18th century, especially in the interwoven strands of astronomy, navigation, and surveying, was driven by measurements of ever-increasing exactness. The mathematical instrument makers who designed and refined instruments of exquisite precision had to be experts in both theory and practice. In this talk I will explain some of the problems faced, and techniques used, by the leading practitioners of the day to produce such accurate measurements.

John Bevis

John Bevis (1695—1771) was a doctor and astronomer. He was a long-time friend of Edmund Halley, took a keen interest in John Harrison’s development of the chronometer, was a friend of the mathematical instrument maker George Graham and worked closely with Nevil Maskelyne, the Astronomer Royal.

Bevis went up to Christ Church Oxford in 1712, gaining his BA in 1715 and MA in 1718. He then travelled on the Continent and acquired his medical degree. He practiced as a doctor periodically, but it seems that his real love was astronomy. He was the first person to observe the Crab Nebula and last to see one planet occulting another when he witnessed Venus eclipse Mercury.

He published numerous papers in the Philosophical Transactions of the Royal Society from 1737 until his death, starting with observations on a comet. He set up a personal observatory at Stoke Newington, outside London and in the late 1730s he had an intense period of observation, filling three folio notebooks with observations in one year. Bevis prepared Halley astronomical tables for publication in the late 1740s, while also working on his gorgeous, but ill-fated, star atlas, the Uranographia. The book had 51 high-quality engraved star charts, each dedicated to a notable personage (the Princess of Wales got Virgo, Nathaniel Bliss, Professor of Geometry at Oxford, got the Triangles). Alas, it was never published as the publisher went bankrupt. Some impression were taken of the plates and a few copies exist. The Linda Hall Library in Kansas City has a fine digital reproduction of their copy. The publisher had taken (expensive) subscriptions in for several years and the fact that nothing came of the project was a sore point for Bevis for the rest of his life.

After the famous Lisbon earthquake, he prepared a compendium on The History and Philosophy of Earthquakes, and in 1759 was one of only two people known to have observed Halley’s Comet on its first predicted return. In the 1760s, he was one of the people asked to do the computations related to the test of Harrison’s chronometer after its trip to Barbados, and in 1765 he was (finally) elected as a Fellow of the Royal Society, becoming its foreign secretary the following year. He was appointed to the Royal Society’s committee to plan for the Transit of Venus in 1769, and was a proponent of Captain Cook. He himself observed the transit from Joshua Kirby’s house in Kew with Kirby acting as time-keeper, publishing his observations in the Philosophical Transactions of the Royal Society. He is said to have died as a result of a fall from his telescope when checking the time after observing a transit.

See also:

Transits of Venus


Ashworth, W.B. “John Bevis and His “Uranographia” (ca. 1750)”, Proceedings of the American Philosophical Society 125 (1) (1981), 52—73.

Wallis, R. “John Bevis, M.D., F.R.S. (1695-1771): Astronomer Loyal”, Notes and Records of the Royal Society of London
36 (2) (1982), 211—225.

The Modern Druid

In the 18th century, Britain’s security and prosperity depended on ships; the Navy for security, and shipping trade for prosperity. Continuance of the fleets of shipping depended on adequate timber supply, and most especially, oak.

The English Oak had long been a symbol of rural strength and solidity, but now it was taking on a patriotic tinge as well. Taking 150 years to reach maturity, capable of living for a thousand years, towering to 125 feet, and providing shade and shelter under its widespread branches, the oak was a well-known and loved species. It was also a vital one. A new ship could consume 2000 trees.

The natural widespread growth of the oak not being particularly conducive to ship timber, there was a need to shape the growth of the trees for straightness and height. To the rescue in 1747 came James Wheeler, Gent, of Higham in Suffolk with “The Modern Druid, containing instructions founded on physical reasons, confirmed by long practice, and evidenced by precedents, for the much better culture of Young Oaks more particularly, than what they have been subject to by any late discipline: with various reflections interspersed on the occasion.” He addressed his book “To the nobility and the gentry of Great Britain, Proprietors of Woods, Chaces, Wasts, Parks, or Pastures, or any kindly Soils Productive of the OAK”

Wheeler waxed loquacious, even by eighteenth-century standards. Here is one sample sentence, from the opening of Chapter III:

The state and also intended manner of my proceeding being before intimated, it will not be improper to mention an experiment, to corroborate a very material article advanced in the foregoing Chapter: That I may leave no scruples behind unobviated; which otherwise may be brought in evidence of my weakness—instead of my displaying the wisdom of nature—Wherefore I attempted to make proof statically, whether those very Oaks last mentioned, by means of having had their bark-slit on bough debarking; did grow the more in their circumference, and latitudinal girt than otherwise they would have done.

It is a curious book, a mixture of careful and specific advice, philosophical ruminations, excessive disquisition on the subject of oak sap, and a paean to the oak as a way for landowners to preserve the value of their holdings. His main argument is that lopping off lower branches to encourage straight growth does terrible damage to a tree (at least in the case of the oak) and recommends bark-cutting (stripping off a couple of inches of bark from a branch to let it die off slowly) and bark slitting (cutting vertical slits in the bark of the trunk to relieve the excess sap).

I know almost nothing about Wheeler. In the book, he mentions his poor health, and, although he did not die until 1763, his will was written a full ten years earlier, and makes much of his maidservant for nursing him through his “several illnesses”. He left the bulk of his property to his “kinswoman” Elizabeth, wife of Thomas Doyly of Dedham in Essex, and makes particular note of the disposition of his woods and timber. Presumably he had no children of his own.

The text of the book is largely unrelieved by ornamentation, but it does have a fine frontispiece showing the oak as “The Glory and Protection of Britain”. The plate was engraved by James Mynde from a picture by Joshua Kirby.

Transits of Venus

A transit of Venus is a rare astronomical phenomenon where an observer on Earth sees the planet Venus pass across the face of the sun. Due to the inclination of the orbits of the Earth and Venus, these transits come in pairs, eight years apart, with the pairs separated by a little over a century. They also always happen in June of December. Of course, it also must be daytime where you are when Venus crosses the sun. Just like the more common lunar and solar eclipses, Venus transits are only observable from certain places.

In order to know when a transit is going to occur, you have to have a very good understanding of the orbital dynamics of Venus. In order to see it, you need a telescope. Before the eighteenth century, both these resources were in short supply.

In 1639, the 21-year old astronomer Jeremiah Horrocks was studying Kepler’s Rudolphine Tables and comparing Kepler’s predictions of the motion of Venus with his own observations. Kepler had thought that Venus would just miss the sun in December 1639; Horrocks realized Kepler had made a mistake. Venus would transit the sun, and part of the transit would be visible (if the weather was good) from Lancashire, where he lived. Fortunately, Horrocks had bought himself a good telescope the year before, and the weather held. Horrocks, and his fried William Crabtree whom he had alerted, became the first people in all of recorded history to observe the transit. They also appear to have been the only ones. The image below shows the path Horrocks saw, bearing in mind that sunset that day was at 15:53.

Horrocks wrote up his observations in a Latin treatise called Venus in sole visa, and made important contributions to lunar theory before dying in early 1741 at the age of 22.

Having missed the 1639 transit, astronomers had to wait until the next pair of transits came along, in 1761 and 1769.

Apart from the obvious thrill of witnessing a rare event, why would astronomers care? The answer lay in the state of astronomy in the middle of the eighteenth century, and was again due to Kepler. Kepler had realized that planetary orbits in a heliocentric system were best modeled as ellipses, and his third law of planetary motion said that the square of the orbital period is proportional to the cube of the mean distance of the planet from the sun. Since astronomers knew the periods of the planets well, they could compute the relative distances of each planet, that is, relative to the distance of the Earth from the sun. But they didn’t know how far away from the sun the Earth was.

Although he was not the first to have the idea, the notion that a transit of Venus could be used to find the distance to the sun was popularized among the scientific community by Edmond Halley (he of comet fame). Halley himself would not live to see the next transits as he died in 1742, but he urged other astronomers to prepare. The basic idea was that observers in different places on Earth would see Venus make slightly difference tracks across the sun. This phenomenon, called parallax is similar to the way that if you hold a pencil at arms length and look at it with just your left eye, it lines up with a different spot on a distant wall than if you look at it with your right eye. The astronomers would be using the width of the earth as the two eyes. To have the best chance of success, the observing parties should be as widely separated as possible (subject to being in positions where the transits could be seen).

The key observations were the exact time the rear edge of Venus separated from the edge of the sun on entry, and the time when the leading edge of Venus just touched the edge of the sun on exit. So, the astronomers needed to know the exact local time, and their exact position, so that the times could be coordinated. Determining exact position in latitude and longitude was a major challenge and the details were not known for many locations. The observations were right at the limit of 18th century technology; the computations were long and difficult, and the prize was the size of the solar system. Thus was born the greatest international scientific endeavor of the century.

The leading scientific organizations of the day sought funds and volunteers, and there was a boom in instrument buying for the leading manufacturers, mostly in London. The French sent the Abbé Jean Chappe d’Auteroche to Siberia, Guillaume Joseph Hyacinthe Jean Baptiste Le Gentil de la Galasiere to Pondicherry in India and Alexandre-Guy Pingré to the island of Rodrigues in the Indian Ocean. The British dispatched Nevil Maskelyne to St. Helena and Charles Mason and Jeremiah Dixon to Sumatra. It wasn’t all plain sailing. 1761 was in the midst of the Seven Years’ War, with France and Britain on opposing sides. Before Le Gentil got to Pondicherry, it had fallen to the British, and Mason and Dixon’s ship was attacked by a French vessel shortly after leaving Plymouth. Badly damaged, it limped back into port for a refit that left the trip several weeks behind. In the end, Mason and Dixon only made it as far as the Cape of Good Hope, although they did make very good observations there.

As the reports trickled in from around the globe, it turned out there were problems despite the greatly improved instruments available. Good observations required accurate timing, but observers stationed at the same post reported the key events at different times, often by as much as 10 or 20 seconds. First, it turned out that Venus had an atmosphere and that blurred the image and so the timing; the second was that the separation and arrival of Venus at the edges of the sun were not clean simple events. Instead, Venus seemed to ‘stick’ to the sun for a while and again, that affected the timing of the separation. The observations did lead to improved estimates of the parallax and so the distance to the sun, but not to the level of accuracy that had been hoped for. It was time for the second push in 1769.

For the second transit, even larger and better equipped teams were sent to favorable locations. The Jesuit Father Maximilian Hell went to Vardø off the northern coast of Norway; Chappe swapped Siberia for (Spanish) California after months of tense diplomatic negotiations; William Wales was packed off to Hudson’s Bay; Le Gentil, who had failed to make any observations while stranded in the middle of the Indian Ocean in 1761 after the British captured his original destination in India, had spent the intervening time in and around the Indian Ocean before preparing an observatory in Manila although at the last minute the French sent him back to India; and Captain Cook was sent out to Tahiti.

(Maximillian Hell in Vardø)

Similar observational problems bedeviled the 1769 expeditions, but the results gave improved estimates of the solar parallax of around 8.7 to 8.8 arc-seconds, very close to the correct value. The solar system had been measured to an unprecedented degree of accuracy.

The stories of these expeditions make riveting reading. Sailing to the far ends of the earth meant absences for years in dangerous conditions; the Arctic observers had to overwinter in order to prepare for the observations the next year; the teams had to build their own observatories and contend with uncooperative locals; they had to make detailed observations over extended periods of time just to determine their exact locations. They were enormously dedicated, and years of effort could be wiped out by a single cloudy day. After 1769, none of them would ever have another chance.

The recent transits of 2006 and 2012 lead to a flurry of interest and there are a number of excellent websites with more information about the 18th century transits, and several books were published to coincide with the events. Two good ones are:
The Day The World Discovered The Sun, by Mark Anderson, and

Chasing Venus: The Race To Measure The Heavens, by Andrea Wulf, both from 2012.

Anderson’s book is a gripping read, with excellent use of primary sources to add spice to the narrative, and is particularly good on Father Hell. The description just of his trip from Prague to northern Norway takes 20 pages of colourful description. He is equally detailed in the other expeditions he focuses on, especially the two trips of Chappe, and Cook’s epic voyage to Tahiti. The price of the detail and focus is that he cannot include everyone. Wulf, on the other hand, goes for a more balanced approach, forgoing some of the detail to include many more expeditions. Hell leaves Vienna on p. 139 and arrives in Norway on the following page. Both books, however, will give you a good understanding of the motives of those involved and the perils, often mortal, they faced in search of a single more accurate number.

In case you would like to watch a transit yourself, the next one is due in December 2117, so you have plenty of time to get ready.

See also:

John Bevis