Category Archives: Mathematical Instruments

John Smeaton

John Smeaton (1724—1792) was the first to use ‘Civil Engineer’ as a title. He is now most famous for his rebuilding of the Eddystone Ligthhouse after it burned down in 1755. However, Smeaton was an incredibly industrious man, racking up a huge number of projects of a bewildering variety. It is exhausting just reading about his activities.

John Smeaton was born in 1724 at Austhorpe, near Leeds, in Yorkshire. His father was a lawyer and intended John, his eldest son, to follow in his path. At a young age John Smeaton found a great mechanical aptitude and interest, making his own tools as necessary for his work. While still a teenager, he met and formed a close friendship with nearby clockmaker Henry Hindley (1701—1771). Smeaton’s father sent him to London to study for the law, but it did not last, although Smeaton retained a careful and precise way of writing reports and memos for his clients that lasted his whole career.

Abandoning formal legal training, Smeaton returned to Austhorpe and, presumably taught by Henry Hindley, trained as a philosophical instrument maker. By his mid-twenties he had set up shop in London, started moving in scientific circles in the capital, and soon began publishing papers in the Philosophical Transactions of the Royal Society. Around 1752 he began his investigations into water- and wind-mill power, studying efficiency of under- and over-shot water-wheels and the effects of varying the shape and angle of windmill sails. On the strength of his work in philosophical instruments he was elected Fellow of the Royal Society in 1753, and when he finally published his paper on wind and water power to great acclaim in 1759, he was awarded the Society’s prestigious Copley Medal.

His first mill was built in 1753. In 1755 he went on a tour of the Low Countries for five weeks, closely observing mills, locks, canals, and harbors. His diary records his detailed observations of hydraulic works, but matters not directly related to engineering get short shrift. I don’t think he ever mentions what he ate, for example. Smeaton was an excellent engineering draughtsman, and hundreds of his careful drawings survive, but he was less interested in non-practical art. His diary for June 22, in Bruges, records:

I see the 2 Great churches for the service of the town, in which were such a numbers of Altars, Crucifixes, Priests, Painting &c., as it would be endless to describe: among the paintings I see many that pleased me, but none that struck me sufficiently to make me remember them. (Diary, 15)

The Eddystone Lighthouse burned down in December 1755 and in February 1756, Smeaton was appointed to rebuild it, a task which occupied much of his time until October 1759. He married Ann Jenkinson in June 1756, but she can’t have seen much of him in the early years of their marriage. They had two daughters who reached adulthood, Ann and Mary; Mary married Jeremiah Dixon.

After the completion of the lighthouse, he moved his base to Austhorpe, making trips to London and wherever his commissions took him as necessary. In the early 1760s, he designed and built the Calder navigation, involving 26 locks in 24 miles. He consulted on several large drainage projects, designed pumping engines, and planned the Forth and Clyde Canal. He also designed the lovely Coldstream Bridge.

All this was the work of just five years or so, and he kept up this pace including a steady flow of technical innovations for the rest of his working life.

He was painted several times, including this portrait from around 1759, now in the collection of the Royal Society.

Another of Smeaton’s commissions was a water pump for Kew in 1761 which raised water from a deep well for the lake. It is presumably this project that brought him into contact with Joshua Kirby, then Clerk of the Works at Kew, and probably explains Smeaton’s support for Kirby’s FRS candidacy.



Skempton, A.W., ed. John Smeaton, FRS. London: Thomas Telford Limited, 1981.

Smeaton’s DNB entry.

Smeaton, J. John Smeaton’s Diary of his Journey to the Low Countries 1755. Leamington Spa: The Newcomen Society, 1938.

No Mathematics!

Trouble erupted at the meeting of the Chapter House Philosophical Society in January 1785 when one of its members proposed reading a paper on astronomy. The club had been formed in 1780 to discuss ‘Natural Philosophy in its most extensive signification’, but the issue of whether ‘natural philosophy’ a.k.a. science extended as far as mathematical topics had never arisen. The Chair of the Society argued that discussion of topics that might lead to ‘mathematical disquisition’ were unconstitutional. The founding documents of the society were sent for, and finding that they did not exclude exact sciences, the chair next argued that the society should be governed by custom rather than law. Finally a resolution was introduced to ban astronomy in the future. The mathematical instrument maker George Adams Jr., who had just been elected a member of the society at the same meeting, must have wondered what kind of a club he had joined.

I thought this was interesting in light of Sorrenson‘s point about the lack of interest in mathematics at the Royal Society.

This account is taken from the delightful description of events in Millburn (2000), pp. 188-189.


Millburn, John R. (2000). Adams of Fleet Street. Instrument Makers to King George III. Aldershot: Ashgate.

Henry Baker

Henry Baker, FRS (1698—1774) was an interesting person. His father, a Clerk in Chancery, died when he was young, and he was largely brought up by his grandmother. He was apprenticed as a bookseller, later declaring his apprenticeship ‘as agreeable a Part of Life as any I have ever known’. Not that he became a bookseller. At the end of his apprenticeship, he went off to visit some relatives and ended up staying for nine years. What caught his interest was the 8-year-old daughter of his host, John Forster, who had been born deaf. Baker undertook to teach Jane and her two younger siblings, also born deaf, to read, write and lip-read, a task in which he was successful and instructing the deaf became his main source of income. He charged high prices and a lucrative practice. He also swore his pupils to secrecy and never revealed the details of his procedure, although it was doubtless based on that devised by the mathematician John Wallis.

It was presumably through a shared interest in the education of the deaf that Baker met Daniel Defoe, whose youngest daughter Sophia he married. They had two sons. The elder, and more colorful one, David Erskine Baker translated Voltaire’s Metaphysics of Sir Isaac Newton into English when only seventeen, was trained as an engineer on account of his mathematical skill, and joined a troupe of travelling players. His brother Henry became a lawyer.

In his youth Baker wrote poetry. Together with Defoe he founded the Universal Spectator, and in the early 1740s he got interested in microscopes. His book on microscopes, about which we will write in a separate post, was much more successful than Benjamin Martin’s Micrographia Nova, selling out a first edition of 1000 copies in only a few months. Although primarily a popularizer rather than a researcher, he used the microscope to study both crystal growth and polyps, earning him a Fellowship in the Royal Society in 1741, and its Copley Medal in 1744.

Baker was an inveterate organizer, recorder and committee member, clearly relishing the organizational tasks involved with the Royal Society, the Society of Arts, the Society of Antiquaries, and the Society for the Encouragement of Arts, Manufactures and Commerce. With these organizations he was intersecting Kirby’s orbit as Kirby was a member of these groups, too.

Most of the information in this post comes from the delightful article on Henry Baker by Gerard L’Estrange Turner.


Turner, G.L’E, 1974. ‘Henry Baker, F.R.S.: Founder of the Bakerian Lecture’. Notes Rec. R. Soc. Lond. October 1, 1974 29 1 53-79.

Book Review: Benjamin Martin’s Micrographia Nova

When Benjamin Martin’s Micrographia Nova appeared in 1742, he was still an itinerant lecturer, and the book was published in Reading.

The early 1740s saw rising interest in microscopes and their use as a means of enhancing optical perception and there was an accompanying flurry of publications explaining their uses to readers and, importantly, trying to drum up sales. This was certainly the purpose of Martin’s treatise. Martin’s book contained two large plates illustrating the two types of microscope he had designed with detailed comments on their parts and usage. This portion of the book reads like an instruction manual. Oddly, the plates were engraved by Emanuel Bowen, much better known as a mapmaker.

Martin then has a section of exaggerated computation to impress upon the reader the ‘extreme minuteness of visible Animalculae’ that can be observed with the microscope. The rest of the treatise, some 40 pages or so, is devoted to a catalogue of objects worth looking at under a microscope. The catalog is impressive in its span and its testimony to Martin’s experience with the microscope if, indeed, he had observed all the items he lists, but it is short on significance. He opens with “Human hair; its bulbous Root; its long small Cylindric Form; the Substance, if black, opake; otherwise, transparent” and proceeds through parts of bodies, both human and animal with separate chapters for birds, fish, insects, and reptiles and serpents before tuning to plants and miscellaneous objects.

Martin’s descriptions can be quite vivid and colourful. Here he is on mould:

If that which we call the Vinew or Mould of any Subject be view’d, it will discover a most beautiful Scene of Vegetation of a peculiar kind; there you will discover Fields of standing Corn, i.e. Stamina, with globular Apices; and various other Plants sui Generis; and you will not rarely find those Fields and Meadows stocked with a Sort of nimble small Cattle and Herds, which skip sportively over the Lawns. You will also see their various Pursuits, Contests, and horrid Attacks and Engagements; with divers other diverting Incidents among the Inhabitants of this Terra invisa, or invisible Land.

If that isn’t enough to get you excited, Martin would have you look at snails:

Their Shells are many of them beautifully embellish’d and variegated with Colours, and curiously wrought. The Eyes of Snails are a remarkable Oddity, they are seated on the tops of their large Horns, by which means they can be drawn into the Head or thrust out at Pleasure. Their Teeth are another Microscopic Object, and it is very pretty to see ’em feed on Leaves, &c with this Instrument. This Animal is Hermaphrodite, and the parts of Generation are in the Neck, which in Coitu are easily examined by the Microscope. The Eggs of Snails are round and white, and, when hatch’d, the young tender Brood make a very pretty Scene in the Microscopic Theatre.

It is clear from the many descriptions he gives, that his aim is to encourage amateurs to explore the natural world, to revel in its complexity and to marvel at the previously hidden delights opened up by the new instrument. He does not view the microscope as a research tool. In this he is just reflecting what he does in his lectures – to instruct and delight the wealthier classes. As he says in his Preface, “I have oftentimes been requested by Gentlemen to give a Catalogue of Microscopic Objects, which I have here done, and I presume so compleat, that scarce any extraordinary Phaenomenon, which requires the Use of this Instrument, and within the Reach of a Person in private Life, will be found wanting in it”. The engraving of the microscope carries the note: “These Microscopes are Sold by J. Newbery Bookseller in Reading Berks”, emphasizing the commercial nature of the enterprise.

Of all the objects to be viewed under the microscope, Martin reserves his most fulsome praise for:

THE SEMEN; the infinitely small and numerous Animalculae in all Male Sperm are the most astonishing Spectacle, and as yet the highest Attainment of the Microscope; you cannot fail of seeing Millions of these in the smallest Quantity of the human Semen, if laid under the Microscope while warm, and view’s with the greatest Magnifier, and most strongly illuminated, by the Sun’s Light refracted and reflected upon it.

You can get your copy here.

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.