Category Archives: Books

Blanco on Simpson and Publishing

Mónica Blanco has a nice article in the current issue of Historia Mathematica on Thomas Simpson and mathematical publishing in mid-18th-century London.

Thomas Simpson (1710—1761), now mostly remembered for Simpson’s rule for approximating definite integrals, wrote two books on calculus. The first, A New Treatise of Fluxions, was published in 1737, and the second, a new book rather than a second edition of the first, The Doctrine and Application of Fluxions, in 1750.

Blanco traces Simpson’s background, particularly the influences of Edmund Stone (1695?—1768) and his 1730 re-working of L’Hopital’s text, and Simpson’s friend Francis Blake (1707/8—1780). All three were Fellows of the Royal Society.

The core of Blanco’s paper is a detailed comparison of the structure and contents of Simpson’s two works, and an exploration of the reasons for the differences. However, possibly of wider interest, she also includes some general remarks on mathematical publishing and the reception of mathematical works.

Simpson’s first book appears to have been supported by subscription, although there is no list of subscribers attached to the volume, and was published by Thomas Gardner, a printer “with a dubious reputation” (68). By the time the second work appeared, Simpson was a known and successful author (he published several other mathematical works in between the two calculus books), and the project was taken on by the prominent bookseller John Nourse, whose mathematical list included the likes of Newton, Maclaurin, and Brook Taylor, putting Simpson in distinguished company. Long after Simpson’s death, Nourse brought out a second edition.



Blanco, M. Thomas Simpson: Weaving fluxions in 18th-century London. Historia Mathematica
41 (1) (2014), 38—81.

Zoffany and Kirby

The German artist Johan Zoffany (1733—1810) had a colorful life. Raised in the court of the princes of Thurn und Taxis, he showed an early interest in drawing and studied art first in Germany, and then in Italy where he spent six or seven years at Rome from the time he was seventeen. When he returned to Regensburg, he was soon appointed court painter. His life took a dramatic turn when he made a sudden, unsuitable, and, indeed, unsuccessful marriage, abandoned Germany and went to London in 1760. The kind of art that was popular in Germany was not to the taste of patrons in London, and Zoffany re-invented himself as a portrait painter, a line in which he became very successful, his sitters soon extending as far as the Royal family. Doubtless he was helped by his court polish and German background. At some point in the 1760s he became friends with Joshua Kirby, but the details are elusive. Mary Webster, in her monumental book on Zoffany, repeatedly affirms their friendship, but does not mention when and how they met. However, the art world in London was small, and the art world at court even smaller, so Kirby and Zoffany would certainly have had many opportunities to meet.

In 1772, Zoffany had planned to go with Joseph Banks as an artist on Captain Cook’s second voyage to the South Seas, but the project foundered on Banks’ excessive requirements for men and equipment. Instead, Zoffany went to Italy with a commission from Queen Charlotte to paint the famous gallery in Florence. Zoffany spent seven years on the task, returning with a picture, and a bill, that did not please the King and Queen. Zoffany stayed in London for a few years before going out to India, where he was enormously successful and made a good fortune. However, life in India was not good for his health, and he returned to England in 1789 and was based there for the rest of his life. He died in 1810 and is buried in the churchyard of St. Anne’s at Kew, along with Gainsborough and Kirby.

One of Zoffany’s portraits from the late 1760s is the rather charming The Reverend Randall Burroughes and his Son Ellis of 1769. Burroughes was a wealthy clergyman from Norfolk and Ellis, his only son was born in 1764.

The book young Ellis is engaged with is Joshua Kirby’s Perspective of Architecture (1761). Zoffany’s copy of this book was auctioned off with the rest of his belongings when he left for Florence in 1772. Zoffany’s portraits were careful compositions arranged to present an idealistic view. In the case of the Burroughes, not only is the setting contrived, but even the representation of the book. Mary Webster notes, “With characteristic pictorial licence, Ellis is shown turning over the frontispiece, designed by Hogarth, but the engraved plate of an arch that can be seen beneath is in reality Plate IV of the second volume of Kirby’s work” (170).





Webster, M. (2011). Johan Zoffany. New Haven: Yale University Press.

Critiques of Analysis of Beauty

Paul Sandby didn’t have it all his own way in his attacks on William Hogarth in the wake of the publication of the Analysis of Beauty. Despite misgivings in some quarters about Hogarth’s pretensions in reducing art to the `line of beauty’, the book was generally well-received. Paulson devotes a chapter to its reception in his 3-volume biography of Hogarth, giving a long description of various reviews from lengthy treatments, including one possibly written by Samuel Johnson for the Gentleman’s Magazine, to short poetic squibs. Paulson’s summary of the immediate reception in London is that, “The reviews acknowledged both its originality and its usefulness for a variety of readers. But they also leave the impression that Hogarth had strong friends within the literary establishment, and that his enemies were a small group centered in the St. Martin’s Lane Academy” (Paulson iii, 142). In other words, literary reviews were as much about personalities and politics as they were about the content of the reviewed work. At the time there was a great deal of ferment in artistic London with a group attempting to form an Academy with professorships and closed membership, a move opposed by Hogarth.

Among the lighter responses to the publication of the Analysis of Beauty quoted by Paulson is the following verse, which Paulson cites as appearing in the London Evening Post of 7—9 February 1754, a couple of months after the book first appeared the previous December (Paulson iii, 144). However, the anonymous lines had seen print right at the beginning of the controversial reception, being published in the Public Advertiser of 18 December 1753, coincidentally the very same issue that carried the report of the death of John Kirby, Joshua’s father, on the 13th of December.


Tho’ Scriblers, Witlings, Connoisseurs revile,

Thy Book shall live an Honour to this Isle:

Exert, once more, thy Analysing Art,

And five the World the Beauty’s Counterpart:

Dissect the Passions which the Works create;

Delineate Envy, Ignorance, and Hate.




Paulson, R. (1991). Hogarth. New Brunswick: Rutgers University Press.

George Washington’s Mathematics

Fred Rickey has recently posted on his Academia page a nice joint paper with Theodore Crackel and Joel Silverberg on George Washington’s early mathematics education.

In the 18th-century, students would copy extracts from books and copies of carefully worked computations into their own copy-books that they could then use for study and reference.

Some of George Washington’s original copy or cypher-books are known and the authors work backwards to discover his sources. They show that George Washington learned decimals and some work with logarithms and trigonometry. They also show that he did not use this theory in his surveying problems, relying on measurement of accurate scale drawings rather than computations to find sides of triangles. In a nice turn of phrase, they say Washington “encountered” mathematics, setting aside the questions of how much he understood, let alone used.

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.

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.