Yesterday, we took a look at some of the many portraits of Isaac Newton the second Lucasian professor of mathematics at Cambridge, today, we are turning our attention to a nineteenth century occupant of that honourable chair, Charles Babbage (1791–1871).
Although Babbage came from a very wealthy family with a high social status there are no know childhood portraits. The earliest portraits seem to be from 1833, when he was already forty-two years old and Lucasian Professor. There is a stippled engraving made by the English engraver John Linnell (1792–1863). The son of a carver and guilder he had contact with several painters as a pupil before being admitted to the Royal Academy in 1805. He was only sixteen when left the Academy and went on to long and successful career as painter and engraver.
Self-portrait of John Linnell c. 1860Linnell’s portrait of Babbage
There is a second stippled engraving of Babbage from 1833 as Lucasian Professor by Richard Roffe (fl. 1805–1827) about who very little is known.
Roffe’s portrait of Babbage
There is an early painted portrait of unknown date and by an unknow artist, now in the National Trust’s collection.
British (English) School; Charles Babbage (1792-1871) ; National Trust
There is a painted portrait in the National Portrait gallery from 1876 by Samuel Lawrence (1812–1884) a British portrait painter, who painted the cream of the mid Victorian society, ncluding the polymath William Whewell, a student friend of Babbage’s.
Samuel Lawrence attributed to Sir Anthony Coningham Sterling, salt print, late 1840sSamuel Lawrence portrait of Babbage
There is lithographic portrait from 1841 now in the Wellcome Collection by D. Castellini after the pencil drawing Carlo Ernesto Liverati (1805–1844). I can find nothing on either Liverati or Castellini.
L0020480 Charles Babbage Credit: Wellcome Library, London. Wellcome Images Portrait bust of Charles Babbage with facsimile Lithograph By: D. Castellini after: Liverati, C.E.Published: –
Babbage was a man of his times and a major technology fan so we naturally have quite a lot of photographic portraits. There is a daguerreotype from around 1850 made by the French photographer and artist Antoine François Jean Claudet (1797–1867).
Antoine Claudet in 1850Claudet’s daguerreotype of Babbage
Claudet was active in the Victorian scientific community and was working with Charles Babbage on photographic experiments around the time this compelling portrait of him was made. In it, the pattern of embellished fabric on the side table is picked up in Babbage’s waistcoat. (National Portrait Gallery).
Claudet also took one of the only two surviving photographs of Ada Lovelace in c. 1843 or 1850
Claudet’s daguerreotype of Ada Lovelace
There is a seated photographic portrait of Babbage:
Half-length portrait of Babbage, seated, body turned to the left as viewed, Babbage looking to camera. The image is embossed “J M MACKIE PHOTO”. The reverse has two inscriptions. Top, in ink: “For my dear Aunt Fanny from her affectionate nephew B Herschel Babbage”. [Benjamin Herschel Babbage (1815-1878)]. Below “Copied from a negative taken for the Statistical Society about 1864. Charles Babbage was elected a Fellow of the Royal Society in 1816. (Royal Society)
There is another undated seated photographic portrait of an elder Babbage with the caption,” Charles Babbage (1792-1871). English mathematician and mechanical genius.”
The Illustrated London News published an obituary portrait of Babbage
Obituary portrait of Charles Babbage (1791-1871). The caption is The late Mr Babbage. Illustration for The Illustrated London News, 4 November 1871. This portrait was derived from a photograph of Babbage taken at the Fourth International Statistical Congress which took place in London in July 1860. (Science Museum)
Most of the images shown here were used multiple times in writings about Babbage-.
Humans are strongly guided by their visual perception. Naturally the other senses—smell, hearing, taste, touch—play a role but seeing is predominant. This is reflected in everyday speech. When we want to draw somebody’s attention to something or emphasise a point we often say “Look!” or “Look here!” even when we are only going to say rather than show something. We use the word “see” to signal understanding, “I see” or “do you see”.
Visual perception also played a strong role in the early evolution of science. People developed theories to try and explain what they could see. This was particularly true in astrology-astronomy where the only empirical evidence available was visual. It is significant that the period that most people believe is the nativity of modern science, the early seventeenth century, saw the invention of both the telescope and the microscope, the first instruments to extend the perception of one of the senses, namely vision, allowing researchers to see and examine things that were previously hidden from their sight.
Visual presentation plays an increasing role in the presentation of the history of science with historians examining and interpreting visual representation from times past. One thing that interests people, and not just historians, is what did a given scientist look like. Unfortunately, in popular presentations the portraits or photographs used tend to be those of said scientist as a dignified senior citizen, maybe when receiving that Nobel Prize or the tenth honorary doctorate, rather than as a young researcher when they were actually doing the work for which they were honoured. The further back we go the real difficulty is knowing whether the visual representation is real, i.e. true to life, or some artists ideal of the person in question.
Over the next three days I going to be taking a look at the surviving portraits of the three scholars, who make up my Christmas Trilogy every year—Isaac Newton, Charles Babbage, and Johannes Kepler.
Newton’s family were not by any means poor, when he inherited the family estates they provided him with an income of £600 p.a. at a time when the income of the Astronomer Royal was £100 p.a., but they were relatively simple puritan farmers so, there are no youthful portraits of Isaac, as a child. This, of course, all changed when he became the most famous natural philosopher and from the later part of his life we have quite a lot of portraits which documents his advancing age.
There is however one engraved portrait from 1677 on which the caption reads “Sir Isaac Newton. when Bachelor of Arts in Trinity College, Cambridge. Engraved by B. Reading from a Head painted by Sir Peter Lily in the Possession of the Right Honorable Lord Viscount Cremorne.”
Source: National Portrait Galery vis Wikimedia Commons
Sir Peter Lely was actually Pieter van der Faes, a Dutch portrait painter, who became a master of the Guild of St Luke, the city guild for painters, in Haarlem in 1637.
Peter Lely self-portrait c. 1660 Source: Wikimedia Commons
He moved to London in 1643 and succeeded Anthony van Dyck (1599–1641) as London’s most fashionable portrait painter going on to paint portraits of the rich, powerful, and famous including both Charles I and Oliver Cromwell, as well as Charles’ most famous mistress Nell Gwynne.
Peter Lely: long-time mistress of Charles II of England, Nell Gwynne as Venus, with her son, Charles Beauclerk, as Cupid.
Interestingly when Robert Hooke first came to London it was an apprentice to Lely but he then attended Westminster school instead.
Probably the most well-known portraits of Newton are those painted by Sir Godfrey Kneller (1646–1723). Kneller like Lely, whom he succeeded as London’s most fashionable portrait painter, was like him not English.
He was born Gottfried Kniller in Lübeck the son of Zacharias Kniller a portrait painter. He first studied in Leiden but then became a pupil of Ferdinand Bol (1616–1680) a pupil of Rembrandt Harmenszoon van Rijn (1606–1669) and of Rembrandt himself. Together with his brother Johann Zacharias Kniller (1642–1702) he spent the early 1670s painting in Rome and Venice before the two moved to London in 1676 and Godfrey inherited Lely’s crown as the in portrait painter. Kneller set up a portrait studio and specialised almost exclusively in painting portraits. His production rate was almost unbelievable and he achieved it by a streamlined work process. At sittings he only made sketches of the face of the sitter and then filled in the rest without reference to the sitter. We don’t know if his Newton portraits were done in this manner.
Godfrey Kneller portrait of Isaac Newton 1689 Source: Wikimedia CommonsGodfrey Kneller portrait of Isaac Newton 1702 Source: Wikimedia Commons
There are a series of four formal portraits of Newton in his eighties as the President of the Royal Society. These were painted by John Vanderbank (1694–1739), this time an English born painter but the son of the Huguenot refugee from Paris, John Vanderbank Snr. well-to-do proprietor of the Soho Tapestry Manufactory and Yeoman Arras-maker to the Great Wardrobe, supplying the royal family with tapestries from his premises in Great Queen Street, Covent Garden.
John Vanderbank self-portrait drawing c. 1720 Source: Wikimedia Commons
John Vanderbank studied composition and painting first under his father and then the painter Jonathan Richardson (1667–1745) before becoming a pupil of Godfrey Kneller in 1711 at his art academy in Great Queen Street, Covent Garden next door to his father’s tapestry workshop. Like Kneller, Vanderbank became a renowned portrait painter.
Vanderbank, John; Isaac Newton ,1725 Fellow, Source: Trinity College, Cambridge; Vanderbank, John; Isaac Newton 1726; Source: The Royal SocietyVanderbank, John; Isaac Newton 1727, Source: Trinity College, Cambridge; Vanderbank, John; Isaac Newton not dated; Source: The Royal Society;
There is a single, oft reproduced, portrait of Newton by the Irish painter Charles Jervas (c. 1675–1739) who was another pupil of and assistant to Godfrey Kneller and succeeded Kneller as Principle Painter in Ordinary to George I in 1723.
Self Portrait aged fifty, 1725 (oil on canvas) by Jervas, Charles (1675-1739) oil on canvas Newton portrait by Charles Jervas Source: Royal Society
John Smith (c. 1652–c. 1742), a very prolific English mezzotint engraver, was also a member of Godfrey Kneller’s circle and, as to be expected, he also produced an engraved portrait of Newton.
John Smith the Engraver 1696 painted by Sir Godfrey Kneller 1646-1723 Source: Tate GalleryJohn Smith’s engraved portrait of Newton
Also from the Godfrey Kneller’s circle was the English engraver George Vertue (1684–1756), who produced an engraving of a Vanderbank portrait.
George Vertue, portrait by Jonathan Richardson (1733) Source: Wikimedia CommonsGeorge Vertue’s portrait of Newton Source: Royal Society
There is a single portrait of Newton by Enoch Seeman the Younger (1689–1745), who was born in Gdańsk and was brought to London by his father Enoch Seeman the Elder, also a painter, in around 1704. He also painted in the style of Godfrey Kneller.
Self-portrait of Enoch Seeman Source: Wikimedia CommonsEnoch Seeman the Younger; Isaac Newton (1642-1727), Trinity College Cambridge
There is a portrait of Newton painted in 1712 by the English artist James Thornhill (1675/6–1734)
Self-portrait James Thornhill
Purchased for the Newton family home of Woolsthorpe Manor. It is a rare depiction of the great man without a wig.
Woolsthorpe Manor portrait of Newton by James Thornhill
There is a second Thornhill portrait, also without wig, in Trinity College Cambridge
James Thornhill; Isaac Newton Trinity College, University of Cambridge;
Trinity College Cambridge, Newton’s college has a full sized marble statue of Newton produced by the French sculptor Louis-François Roubillac (1702–1762), who moved to London in 1730. This was presented to the college by the mathematician and Master of Trinity Robert Smith (1690–1768) in 1755 and cost £3000, a vast sum in those days.
Louis-François Roubillac marble statue of Isaac Newton, Trinity College Cambridge Source: Wikimedia Commons
Posthumously Newton rose to the status of a scientific god so, there are many engraved portrait from the later eighteenth and the nineteenth century often based on the Kneller portraits. Due to his fame and status, especially in later life, there are many portraits of Isaac Newton and I’m sure I’ve missed one or the other but the selection above should give you an impression of what England’s most famous scientist looked like.
Today at 15:03 UT (that’s GMT for all those still living in the past) the Sun on its apparent journey to the south will briefly stand still above the Tropic of Capricorn before turning and beginning its climb northwards up to the Tropic of Cancer. The brief still stand gives the moment its name Solstice from the Latin Solstitium, point at which the sun seems to stand still. A composite noun set together from sol the sun and past participle stem of sistere, stand still, take a stand; to set, place, cause to stand. Tropic comes from Latin tropicus pertaining to a turn, from Greek tropikos of or pertaining to a turn or change. This moment marks the winter solstice in the northern hemisphere and the summer solstice in the southern hemisphere.
As I note at this time every year, rejecting the purely arbitrary convention of midnight on 31 December marking the beginning of the New Year, here at the Renaissance Mathematicus my New Year is the winer solstice, the point in the astronomical calendar in the depth of winter, when the light begins to return.
I wish all of my readers a happy solstice and may you enjoy whatever seasonal events you participate in. I personally don’t celebrate any of them. I thank all of you for your engagement, for reading my verbal outpourings, for your comments and your criticisms and hope you will continue to do so in the year to come.
Philip Ball is one of the best English science writers and with certainty one of the most if not the most prolific. He churns out books and article, with radio programs thrown in along the way, at a rate that is absolutely mindboggling. We here at the Renaissance Mathematicus exposed the secret of his production rate several years ago. Like Santa, who had gnomes in his workshops at the North Pole producing all those toys, Ball has a team of gnomes chained to writing desks in the cellars of Ball mansion busily scribbling away at his next publications.
A couple of years back the gnomes embarked on the production of a series of history of science coffee table books, richly illustrated volumes explaining the history of science for the non-expert. If you are looking for a last minute Christmas present, perhaps for a teenager fascinated by science, or just somebody who would like to delve into the history of science, without doing battle with an academic text, then these volumes are highly recommended.
The first volume to make its way out the gnomes production centre was The Elements: A Visual History of Their Discovery (Thames & Hudson, 2021) a beautifully illustrated book that takes the reader from the story of the four classical elements of Ancient Greece down to the artificially created atomic elements of the twentieth century.
Telling the story of the discovery of each element or group of elements along the way. Unfortunately, I feel obliged to point out that this, otherwise wonderful book, has a flaw. It seems that somewhere during the editing phase, the story of the discovery of mercury slipped through a gap and failed to make it into the published work. However, despite this highly regrettable lapsus the book is a delight to read and highly informative.
In 2023, the gnomes turned their attention to the world of experimental science and delivered up Beautiful Experiments: An Illustrated History of Experimental Science (University of Chicago Press). This one truly delivers what the title promises.
The book has alternating chapters and interludes. The chapter looks at a set of historical experiments united by a common theme. For example, the theme of the first chapter is How Does the World Work and starts with Eratosthenes measuring the size of the world, followed by Foucault demonstrating diurnal rotation. Moving into modern physics we have Michelson and Morley attempting to detect the ether followed by Arthur Edington proving relativity. The first interlude asks the metaphysical questions, what is an experiment? and what makes a good experiment? We return to the world and the violation of parity, closing with the discovery of gravitational waves.
This pattern is repeated in What Makes Things Happen?, with the interlude The Impact of New Techniques. The third chapter asks What is The World Made From?, and its interlude questions the books title, What is a Beautiful Experiment? Chapter four is a theme from the history of science that is of particular interest to me, What is Light? and its interlude looks at The Art of Scientific Instrumentation. Moving on in chapter five we have the pregnant question, What is Life?, and an interlude about Thought Experiments. The book stays with the life sciences for the final chapter, How Do Organisms Behave, this time there is no interlude.
This book takes on a massive topic about which one could write a multi-volume encyclopaedia and masters it magnificently with a fine examples of classical experiments clearly explained and some intriguing metaphysical speculations about the nature of experimentation clearly expressed for the non-philosopher.
In 2025, the gnomes struck again with a truly magnificent volume, Alchemy: An Illustrated History of Elixirs, Experiments, and the Birth of Modern Science (Yale University Press).
All three books are beautifully illustrated but the alchemy volume takes the quality of the illustrations to a whole new level, which is due to the nature of the topic and the available pictures. On a general note, this is an excellent introduction to the history of alchemy. Despite the excellent work done by historians over the last half century explaining the rich and influential history of alchemy, there are still large numbers of people, who think that alchemy is just a bunch of crazies trying to turn lead into gold. This volume tells the real complex story of the discipline in non-academic terms for the lay reader.
There are chapters on the origins of alchemy in different period and cultures. Other chapters look at specific aspects of the topic such as chrysopoeia (the quest for gold) the uses of alchemy, the alchemical laboratory and others. In between are informative potted biographies of the leading figures in the history of alchemy. Towards the end the book handles the historically important transition from alchemy to chemistry, a topic that for far too long was swept under the carpet with the claim that the two had nothing to do with each other.
All three books have good indexes and a short but good list of suggestions for further reading. They are all excellently produced and are both pleasant to look at and to read. For the quality, all three are very reasonably priced and won’t require you to take out a second mortgage. Philip Ball is to be congratulated for having trained his gnomes to produce such desirable books.
As I have pointed out is a couple of earlier posts the work carried out by mathematical practitioners in England in the last third of the sixteenth century and on into the seventeenth into navigation was an integral part of the deep sea voyages that mariners were beginning to undertake in what is usually referred to as the age of discovery or as I prefer to call it the age of exploitation. To quote myself:
Finding new lands, until then comparatively unknown to Europeans, was only a secondary aim of these voyages, their primary aim was commerce. The expeditions were searching for commodities with which they could make a fortune for themselves and their investors. Metal ores–gold, silver, copper–fine materials such as silk, and above all spices. The expeditions of Vasco da Gama (c. 1460s–1524), Christopher Colombus (1541–1506), and Magellan (1480–1521) were all about breaking the Arabic hold on the overland spice trade between Asia and Europe. The later multiple searches for a North-East or North-West passage were about finding a shorter, more direct trade route between Europe and Asia.
Important on the political level were those who proposed and supported the setting up of a British Empire to rival those of Spain and Portugal. The earliest was John Dee (1527–c. 1608), in his 1570 manuscript Brytannicae reipublicae synopsis, pushing the idea of English colonies particularly in North America in his General and Rare Memorials pertayning to the Perfect Arte of Navigation (1576). He was often derided for his intense interest in the occult. However, he was actually a leading and highly influential mathematical practitioner and navigational advisor to several of the early attempts to find both the North-East Passage and the North-West passage. As a promotor of empire, more influential that Dee was the geographer Richard Hakluyt (1552?–1616) with his Divers Voyages Touching the Discoverie of America and the Ilands Adjacent unto the Same, Made First of all by our Englishmen and Afterwards by the Frenchmen and BritonsWith Two Mappes Annexed Hereunto published in London by Thomas Woodcocke in 1562. This was followed by his never published manuscript A Particuler Discourse Concerninge the Greate Necessitie and Manifolde Commodyties That Are Like to Growe to This Realme of Englande by the Westerne Discoueries Lately Attempted, Written in the Yere 1584, which was dedicated to Queen Elizabeth. Hakluyt continued to collect accounts of voyages of discovery, oft interviewing the mariners personally, and in 1589 he published in London the first edition of his monumental The principall navigations, voiages, and discoveries of the English nations : made by sea or over land to the most remote and farthest distant quarters of the earth at any time within the compasse of these 1500 years : divided into three several parts according to the positions of the regions whereunto they were directed; the first containing the personall travels of the English unto Indæa, Syria, Arabia … the second, comprehending the worthy discoveries of the English towards the north and northeast by sea, as of Lapland … the third and last, including the English valiant attempts in searching almost all the corners of the vaste and new world of America … whereunto is added the last most renowned English navigation round about the whole globe of the earth. This was followed by two further volumes were published in 1599 and 1600, all three volumes running to over 1,760,000 words in three folio volumes and about two thousand pages. The whole edifice is now regarded as one of the great works of English literature.
Hakluyt continued to collect accounts of voyages from 1600 until his death in 1616 but never produced a fourth volume of his masterpiece containing these new narratives, this task was taken up by the Anglican cleric Samuel Purchas (bap. 1577–1726).
by Henry Richard Cook stipple engraving, 1820 Source: National Portrait Gallery
Samuel Purchas was the sixth son of George Purchas a cloth trader in the village of Thaxted in North-West Essex and was baptised in 1577. He attended St John’s College Cambridge, which is just thirty miles from his birth place, graduating BA in 1597 and MA in 1600. He was ordained a Deacon in 1598 and a Priest in 1601. In 1604, James I & VI presented him to the vicarage of St. Laurence and All Saints, in Eastwood in South-East Essex.
St. Laurence and All Saints Chuch Eastwood
Eastwood is two miles from Leigh on Sea. Both Eastwood and Leigh are today parts of the city of Southend-on-Sea but in the early seventeenth century Leigh was a thriving port on the Thames estuary and was a meeting place for mariners. Here he began collecting accounts of voyages, travels and discovery.
In 1613 , Purchas published his first book, Purchas His Pilgrimage: or Relations of the World and the Religions observed in all Ages and Places discovered, from the Creation unto this Present. A folio volume with nine hundred pages, it aimed to catalogue the world’s religions and geographies from biblical creation to contemporary discoveries, reflecting Purchas’s clerical perspective on divine providence amid human exploration.
First Edition 1613
It was instantly popular and there were expanded second and third editions in 1614 and 1617.
Second Edition 1614
A fourth edition was published inn 1626 containing additional maps, treatises and expansions, which exceeded nineteen hundred pages.
Fourth Edition 1626Taken from the fourth edition the earliest known map of China based on Chinese sources Purchas records that he originally based his map on a Chinese one, captured by Captain Saris, an English merchant in the port of Bantam (in modern Indonesia). Interesting to note the portrait of Matteo Ricci on the left hand side
In 1614, he was appointed chaplain to Archbishop George Abbot (1562-1633), the Archbishop of Canterbury, and rector of St. Martin, Ludgate in the City of London. Meanwhile he had made the acquaintance of Richard Hukluyt.
Around 1610, Purchas scraped an acquaintance with an aging and ailing Hakluyt, who at the time was collecting narratives for a further edition of the Principal Navigations. The contacts and interactions between Hakluyt and Purchas are unclear, but Purchas talks in his introduction to the Pilgrimes [his third book, 1625] about being promised the legacy of Hakluyt’s unpublished papers upon the latter’s death. The apparent agreement was never put into writing and Purchas ended up having to purchase Hakluyt’s literary remains for an unspecified yet substantial sum in 1617.[1]
In 1619, Purchas published His second book, Purchas his Pilgrim or Microcosmus, or the Historie of Man. Relating the Wonders of his Generation, Vanities in his Degeneration, Necessities of his Regenerations, a meditation on the history of humanity, framed, like his first book, from a biblical perspective.
In 1625, Purchas published his most ambitious book the monumental Hakluytus Posthumus, or Purchas his Pilgrimes, Contayning a History of the World, in Sea Voyages, & Land Travels, by Englishmen and Others.
In Purchas his Pilgrimes, he tells us that he has never been “200 miles from Thaxted in Essex where I was borne.”
A four volume compendium of travel narratives, most of them concerning the journeys of English travellers in the Elizabethan and Jacobean periods. This is, as the title tells us, the utilisation of the unpublished papers he purchased following Hakluyt’s death:
Volume I explores ancient kings, beginning with Solomon, and records stories of circumnavigation around the African coast to the East Indies, China, and Japan.
Volume II is dedicated to Africa, Palestine, Persia, and Arabia.
Volume III provides history of the North-East and North-West passages and summaries of travels to Tartary, Russia, and China.
Volume IV deals with America and the West Indies.
The fourth edition of the Pilgrimage (published in 1626) is usually catalogued as the fifth volume of the Pilgrimes, but the two works are essentially distinct. Purchas himself said of the two volumes:
These brethren, holding much resemblance in name, nature and feature, yet differ in both the object and the subject. This [i.e. the Pilgrimage] being mine own in matter, though borrowed, and in form of words and method; whereas my Pilgrimes are the authors themselves. acting their own parts in their own words, only furnished by me with such necessities as that stage further required, and ordered according to my rules. (Wikipedia)
Purchas has been criticised for his sloppy and at time biased editing but many of the narratives that he and Hakluyt collected are the only accounts we have of important aspects of exploration during this period.
The emphasis in Purchas’ work on the religious and moral aspects of his narrative, contrasts strongly with Hakluyt’s goal of inspiring and interesting the nation in pursuing the project of exploration.
Purchas continued to be read down into the nineteenth century as one interesting anecdote from the history of English literature testifies. Kubla Kahn is one the romantic poet Samuel Taylor Coleridge’s most well know and loved poems, with its much quoted first stanza:
In Xanadu did Kubla Khan
A stately pleasure-dome decree:
Where Alph, the sacred river, ran
Through caverns measureless to man
Down to a sunless sea.
So twice five miles of fertile ground
With walls and towers were girdled round;
And there were gardens bright with sinuous rills,
Where blossomed many an incense-bearing tree;
And here were forests ancient as the hills,
Enfolding sunny spots of greenery.
Coleridge, himself tells to story of how he came to write the poem. Whilst reading he fell asleep under the influence of opium and dreamt to whole poem. Upon waking he immediately began to write it down but after a while he was disturbed by a visitor and had to take a break. Afterwards he could no longer remember the rest of the poem from his dream and so Kubla Kahn remained unfinished. The book he was reading when he fell asleep was Purchas His Pilgrimage.
The original passage from Purchas that inspired the drugged out poet was:
In Xamdu did Cubla Can build a stately Palace, encompassing sixteene miles of plaine ground with a wall, wherein are fertile Meddowes, pleasant Springs, delightful Streames, and all sorts of beasts of chase and game, and in the middest thereof a sumptuous house of pleasure.[2]
In his own account Coleridge names, the title of the false book by Purchas:
In the summer of the year 1797, the Author, then in ill health, had retired to a lonely farm-house between Porlock and Linton, on the Exmoor confines of Somerset and Devonshire. In consequence of a slight indisposition, an anodyne had been prescribed, from the effects of which he fell asleep in his chair at the moment that he was reading the following sentence, or words of the same substance, in ‘Purchas’s Pilgrimage’: ‘Here the Khan Kubla commanded a palace to be built, and a stately garden thereunto. And thus ten miles of fertile ground were inclosed with a wall.’
Some might find Coleridge’s reading matter strange for a poet but he was also a philosopher and deeply interested in the sciences. He was instrumental in introducing the continental Naturephilosophie of Friedrich Schelling (1775–1854) into England and was a passionate student of chemistry, optics, medicine and animal magnetism. It was also Coleridge (1772–1834) at the 1833 meeting of the British Association for the Advancement of Science who strongly objected to men of science using the term philosopher to describe themselves leading to Whilliam Whewell (1784–1866) coining the term scientist in imitation of the term artist.
[1] J. P. Helfers, The Explorer of the Pilgrim? Modern Critical Opinion and the Editorial Methods of Richard Hakluyt and Samuel Purchas, Studies in Philology, Vol. 94. No. 2 (Spring, 1997) pp160–186, p. 164
[2]Purchas his Pilgrimage: Lond. fol. 1626, Bk. IV, chap. xiii, p. 418.
In a previous post in this series I looked at the life of Christiaan Huygens (1629–1695) in general and his contribution to the development of optics in particular. In that post I emphasised that Huygens was a multi talent who built some of the best telescopes in the seventeenth century, he was an astronomer, who made important discoveries, and influential as a mathematician, and a physicist. Today I’m going to look at his contributions to hydrostatics and in particular his important contributions to mechanics.
Isaac Newton (1642–1728) is notorious for not having published the majority of his work. If we take mathematics for example, there were only two works published in his lifetime. The Arithmitica Universalis, basically a textbook, was edited and published by William Whiston (1667–1752), his successor as Lucasian professor, against Newton’s will and without his name. De analysi per aequationes numero terminorum infinitas (or On analysis by infinite series, On Analysis by Equations with an infinite number of terms, or On the Analysis by means of equations of an infinite number of terms) was written in 1669 and the manuscript was circulated amongst scholars in both England and abroad at the time at the time but was first published in 1711. However, The Mathematical Papers of Isaac Newton edited by D. T. Whiteside (1932–2008) run to eight, thick, large format volumes.
Whilst not as extreme as Newton, and not so prolific, Huygens seem to have shared this trait of not publishing scientific texts that he had spent years composing. We saw how, in in optics, he spent years researching a general text on his work only to abandon it and start a new more comprehension paper, of which after many years he only published the first of three parts. He also abandoned another work on both spherical and chromatic aberration. This pattern of behaviour repeated itself with his work on hydrostatics.
In his De iis quae liquido supernatant composed by 1650 but never published, Huygens, like others who worked on hydrostatics, starting with Archimedes, devotes much attention to the mathematical determination of centres of gravity and cubatures, as, for example, those of obliquely truncated paraboloids of revolution and of cones and cylinders. His hydrostatics has a single axiom, that a mechanical system is in equilibrium if its centre of gravity is in the lowest possible position with respect to its restraints. he derived the law of Archimedes from the basic axiom and proved that a floating body is in a position of equilibrium when the distance between the centre of gravity of the whole body and the centre of gravity of its submerged part is at a minimum. The stable position of a floating segment of a sphere is thereby determined, as are the conditions which the dimensions of right truncated paraboloids and cones must satisfy in order that these bodies may float in a vertical position.[1]
Illustration from De iis quae liquido supernatant as published in Huygens’ complete works
We saw in an earlier post that Descartes developed the laws of impact bodies. These were in fact wrong, and there is a certain irony that it was Huygens, a convinced Cartesian, showed that they were wrong and provided the correct laws of the collision of elastic bodies in his De motu corporum ex percussione in studies caried out between 1652 and 1656. Descartes work on the laws of collision had assumed an absolute measurability of velocity. Huygens rejected this and thought that the forces acting between colliding bodies depend only on their relative velocity. He incorporated this as hypothesis III in De motu corporum which asserts that all motion is measured against a framework that is only assumed to be at rest, so that the results of speculations about motion should not depend on whether this frame is at rest in any absolute sense. In 1661, Huygens conducted experiments on collision together with Christopher Wren (1632–1723). In 1668, The Royal Society launched an investigation into the topic and Huygens, Wren, and John Wallis (1616–1703) all submitted similar and correct solutions. Central to their solution was the conservation of momentum. Both Wren and Huygen’s papers confined their theory to perfectly elastic bodies (elastic collision), whereas Wallis also considered imperfectly elastic bodies (inelastic collision). Huygens published his De motu corporum in the Journal des Sçavans (Europe’s earliest academic journal established in 1665) in 1669.
De motu corporum ex percussione from his complete works
Huygens is, of course, well known as the man who produced the first functioning pendulum clock in 1657. His most important discovery was that, contrary to Galileo, a simple pendulum is not exactly tautochronous.
He tackled this problem by finding the curve down which a mass will slide under the influence of gravity in the same amount of time, regardless of its starting point; the so-called tautochrone problem. By geometrical methods which anticipated the calculus, Huygens showed it to be a cycloid rather than the circular arc of a pendulum’s bob, and therefore that pendulums needed to move on a cycloid path in order to be isochronous. (Wikipedia)
He solution to this problem was that the cheeks must also have the form of a cycloid, on a scale determined by the length of the pendulum.
Huygens’pendulum clock from Horologium Oscillatorium Source: Wikimedia Commons
Sixteen years after the invention of the pendulum clock, Huygens published a major work on horology, which was also his most important contribution to mechanics: Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (The Pendulum Clock: or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks). Although as contribution to the history of horology Huygens’ master piece is important, it is the studies of pendula leading to studies of gravity and the laws of fall that interest us here.
Sorce: Wikipedia Commons
The book is in five parts of which the first is purely a description of the design of his pendulum clock. The second part starts with three laws of motion, something that would be echoed by Newton in his Principia:
If there is no gravity, and the air offers no resistance to the motion of bodies, then any one of these bodies admits of a single motion to be continued with an equal velocity along a straight line.
Now truly this motion becomes, under the action of gravity and for whatever the direction of the uniform motion, a motion composed from that constant motion that a body now has or had previously, together with the motion due gravity downwards.
Also, either of these motions can be considered separately, neither one to be impeded by the other.
From these Huygens derives geometrically anew Galileo’s study of falling bodies including linear fall along an inclined plane and fall along a curved path. This leads to the fact that the cycloid is the solution to the tautochrone problem. The third part continues his study of the cycloid. Part four is a detailed study of the theory of the centre of oscillation. Part five contains a study of circular motion of a pendulum, It ends with It ends with thirteen propositions regarding bodies in uniform circular motion, without proofs, and states the laws of centrifugal force for uniform circular motion. These propositions were studied closely at the time, although their proofs were only published posthumously in the De Vi Centrifuga (1703).
The book was widely read and was highly influential. Newton acquired a copy, which he studied carefully. It’s influence can be inferred all over the first book of his Principia.
Newton’s first two laws of motion, the axioms on which his whole edifice is constructed, as presented in his Principia, are somewhat different to the modern versions presented in physics textbooks:
Law I Every body perseveres in its state of being at rest or of moving uniformly straight forward except in so far as it is compelled to change its state by forces impressed.
Law 2 A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.[2]
Cohen asks why Newton even need the first law, the principle of inertia, because it is already implied in the Definitions 3 & 4.[3]
Definition 3 Inherent force of matter is the power of resisting by which every body so far as it is able, perseveres in its state either of resting or of moving uniformly straight forward.[4]
Definition 4 Impressed force in the action exerted on a body to change its state either of resting or of moving uniformly straight forward.[5]
Cohen states:
No doubt another factor in Newton’s decision to have a separate law 1 and law 2 was the model he found in Huygens’s Horologium Ocillatorium of 1673, a work he knew well.[6]
Cohen goes on the explain how the two laws of the two authors actually differ.
All in all, Huygens with his correction of Descartes law of collision and is work on motion and force in his Horologium Ocillatorium had a significant impact on the future development of mechanics.
[1] H. J. M. Bos, Christiaan Huygens, Complete Dictionary of Scientific Biography
[2] Issac Newton The Principia Mathematical Principles of Natural Philosophy, A New Translation by I. Bernard Cohen and Anne Wilson assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia by I. Bernard Cohen p. 16
Anybody who has followed my meanderings over the years should be aware of the fact that I have a fondness for both polymaths and for scholars, who don’t conform to the usual expectations. This being the case, I was delighted to be asked if I would like a review copy of a new biography of the seventeenth-century anatomist, palaeologist, geologist, and religious convert, Nicolaus Steno /(1638–1686) I of course said, yes please. The book in question is Nuno Castel-Branco’s The Traveling Anatomist: Nicolaus Steno and the Intersection of Disciplines in Early Modern Science[1].
Castel-Branco has delivered up not just another run of the mill biography of a scientist but rather a master class in how to research, analyse and present the academic life journey of a complex and intriguing interdisciplinary scholar.
The first thing that I learnt reading this excellent book was that Steno was, according to the definitions of the period in which he lived, not a polymath. Castel-Branco tells us:
In the early modern period, polymaths or polyhistors, were those who wanted to know all there was to know, an attitude closely related to encyclopedism. A classic example of a seventeenth century polymath is Athanasius Kircher, S.J. (1602–1680, whose pretentions to universal knowledge were widely known then. Another famous polymath in his time was Leibniz, whose main goal in life was to create a “general science [scientia generalis]”of everything. These cases resonate with the definition of polymathy provided by the German scholar Johann von Wower (c. 1574–1612) in his De polymathia tractatio (Treatise on Polymathy; Hamberg, 1603), the first book to have the word in its title. Polymathy was “the knowledge of various things … spreading itself very widely gathered from all kinds of studies” [ex omni genere studiorum collectam, latissimi sese effundentum ]. Wower also remarked that the most important feature of the polymath was his mastery of grammar, one of the seven liberal arts most closely related to reading. Since the read many books across a variety of fields, seventeenth-century polymaths used special note taking techniques to capture and absorb most of the information that came there way. Steno learnt these reading skills, which had a significant impact on his scientific career. He also shared interests with Kircher and Leibniz, both of whom he met in his travels. But unlike them, Steno did not aspire to know everything.
In short, from an early modern perspective, Nicolaus Steno was no polymath. He read broadly like polymaths but applied his knowledge to focused intellectual problems instead. He even complained when new questions pulled him away from his projects. He feared that distractions would lead him to produce superficial scientific work—a criticism that some scholars applied to the writings of Kircher and other polymaths. In this book, I interpret Steno’s work method as focussed interdisciplinarity.[2]
This is a quite long quote and we’re only on page 10 of three hundred plus! But don’t worry I’m not going to turn this into one of my notorious ten thousand word book reviews. I brought this for two reasons, firstly it illustrates nicely the depth of Castel-Branco’s research, these three hundred words of text have a total of seven footnotes, and these are anything but superficial. Secondly, in his book Castel-Branco systematically unwraps the statements contained here about Steno’s reading and note taking methods and how he then applied the insights he obtained thereby to the various field of his life’s work. Above all, here Castel-Branco introduces us to his concept of focussed interdisciplinarity, which he sees at the centre of all Steno’s scientific activities. He explains it thus:
Steno’s focussed interdisciplinarity was a response to specific intellectual problems of the early modern period. By the late 1650s several new systems had arisen that purported to explain natural phenomena, but that had certain core differences. For instance, the natural philosopher and Catholic priest Pierre Gassendi (1592–1655) believed in the existence of the vacuum, whereas René Descartes rejected it, Jesuit mathematicians adopted a geo-heliocentric astronomy, in contrast to Galileo’s heliocentrism. These theories explained the available observations, but they were often opposite to one another and thus could not all be true. Steno faced similar disagreements in anatomy and the origin of fossils and became obsessed with solving them through what I call a search for certainty. Certainty was not necessarily the absolute certitude of geometry, but rather that of reliable knowledge which, because of its compelling and accurate descriptions, convinced others of its truth. Steno thought that certainty could be achieved by using reason and observations not only from the discipline he was working on, but also from mathematics, mechanics hydrostatics, and chymistry.[3]
Steno was like others in the early modern period and itinerant scholar, whose life weaved its way around seventeenth century Europe and Castel-Branco’s biography follows his life path, roughly chronologically, along the way unpacking and illustrating the aspects of Steno’s scientific activities that follow the description from the above paragraph and does so in great depth and exacting detail.
The opening chapter deals with Steno’s upbringing and his time as a student at Copenhagen University. He describes how Steno’s lifelong interest in mathematics was awakened in the artisanal workshop of his goldsmith father. He also documents the extensive education that Steno enjoyed both at school and university. Fascinating is the main theme of the chapter that deals with the contents of the so-called “Chaos” manuscript that Steno carried with him throughout his life. The “Chaos” manuscript documents the excerpts he took and the notes he made from the wide range of books he read during the enforced yearlong break in his studies due to the Siege of Copenhagen by Swedish troops during 1658|9. Here the foundations of that focussed interdisciplinarity can be found.
In the subsequent chapter Castel-Branco follows Steno to the Netherlands, where he established his reputation as a cutting edge anatomist of the era, in particular displaying his academic acumen in a priority/plagiarism dispute.
I’ll let Castel-Branco describe the third chapter:
In chapter 3 I summarise Steno’s focused interdisciplinary research method by describing his increasing use of chymistry, mathematics, and mechanics in anatomical research. I argue that the people he met and the places he visited in the Low Countries strongly encouraged his eclectic approach to anatomy.
After a brief return to Copenhagen the fourth chapter takes us to Steno’s almost yearlong stay in Paris, where he impressed the intellectual community with his abilities and above all, as in the Netherlands, with his public and semi-public dissections in which he explained and demonstrated the functions of various body parts. Here Steno formed a friendship with the Dutch biologist and microscopist, Jan Swammerdam (1637–1680), a friendship that influenced the work of both men.
Chapter five sees Steno crossing boarders once again on his way to the Medici Court in Florence, where he would become a late member of the Accademia del Cimento (Academy of Experiment) founded by Leopoldo de’ Medici, if only for a very brief time before it dissolved. Here he became friends with the mathematician Vincenzo Viviani (1622–1703), who assisted him with his most mathematical book his, Elementorum myologiæ specimen seu musculi descriptio geometrica (A Specimen of the Elements of Myology or a Geometrical Description of the Muscle, Florence1667). The title is an obvious reference to the Elements of Euclid. Steno knew that Giovani Borelli (1608–1679) was already working on a mathematical description of muscles and had hope for cooperation but Borelli feared that Steno wanted to steal his ideas and so refused to cooperate. Borelli’s book De motu animalia (Rome, 1680–1681) is much more famous but Steno published more than ten years earlier and at the time his book was a major success.
It was, of course, in Florence that Steno made his famous turn from the study of anatomy to paleology and then geology and it is to this that we turn in chapter six. The standard story is that he became the head of a washed up great white shark to dissect, the books cover illustration. Throughout his career, Steno’s public dissection had often been of animal rather than humans. The story goes that during this dissection he realised the fossils known as tongue stones were in fact fossilised shark’s teeth. Castel-Branco debunks this as a myth, as he explains that in the account of the dissection there is no mention of this discovery. Castel-Branco outlines other proposed routes for Steno’s interest in fossils, which he also rejects. He sees Steno’s interest as an extension of his anatomical work, a thesis that he very carefully explicates and establishes based on a detailed examination of the sources. He brings the same level of analysis to Steno’s groundbreaking work on stratigraphy.
Perhaps more fascinating was Steno’s turn from the Lutheranism of his Danish upbringing to Catholicism. This was not just a lip service conversion. Steno entered the Catholic Church in 1667 at the age of twenty-nine, was ordained as a priest in 1675 and then elevated to bishop in 1677, before leaving Italy to serve as a missionary in Northern Germany. Castel-Branco gives an in depth analysis of that conversion. One thing he makes clear is that contrary to a widespread claim, Steno did not abandon his anatomical studies during this period, although he didn’t publish anything new.
Nicolaus Steno as bishop J. P. Trap 1868 derivative work: Source: Wikimedia Commons
The above is a mere sketch of the main theme of each chapter in Castel-Branco’s biography, if I were to go into depth in my descriptions this review would not become ten thousand words long but one hundred thousand. Castel-Branco tackles his subject with a breadth and a depth that is truly breath taking. He analyses every aspect of Steno’s life and work in minute detail supporting his interpretation of Steno’s motivations with a bewildering array of facts each of which is supported by solid sources. One thing that I found extremely well done was that Castel-Branco in no way treats Steno as an isolated figure but in every situation firmly embeds him in the scientific milieu in which he is living and working, the friendships, the rivalries, the supporters, the detractors, the teachers, the student. The book as a whole paints a vibrant picture of the greater scientific community in the middle of seventeen-century Europe. This is an academic masterpiece, but despite the highest levels of meticulous accuracy the book remains eminently readable. In fact, I really enjoyed reading it, which I can’t claim about a lot of deeply academic books.
In a twelve page epilogue, Castel-Branco rehashes his central arguments for his interpretation of the life and work of Nicolaus Steno.
The entire book bristles with footnote, often with a whole cluster of sources to back up the statement they refer to and there is a very extensive bibliography and an equally extensive index at the end of the book. At the front of the book after the detailed contents pages is a list of the forty or so figures and tables with which the book is illustrated in the form of greyscale prints.
Castel-Branco has delivered up, what is destined to become the definitive biography of a truly fascinating seventeenth-century interdisciplinary researcher, who made substantial contributions to the science of anatomy, as well as being a founding figure in the modern history of palaeontology and geology. I recommend this book to any and everyone with an interest in the history of those disciplines or who simply enjoys first class history of science. Another plus point is that the paperback is actually affordable.
If you don’t want to take my word for the quality of this book, below are the opinions in the back cover blurbs of Matthew Cobb and Anita Guerrini both of whom know something about writing first class history of science books.
[1] Nuno Castel-Branco, The Traveling Anatomist: Nicolaus Steno and the Intersection of Disciplines in Early Modern Science, The University of Chicago Press, 2025
The majority of the previous posts in this series have featured the contribution of an individual or a culture – the Pre-Socratics, the ancient Greeks in general, the Stoics, The Epicureans, Neoplatonists, medieval Islam, the Oxford Calculatores & the Paris Physicists – or one or other of the disciplines that would eventually contribute to or become part of modern physics – astronomy, theories of fall, mechanics, optics, hydrostatics, mathematics.
In this post, I’m going to feature something different, the development of groups of scholars in the seventeenth century, who came together to discuss, exchange views on, dispute, criticise the emerging new aspects of science, in which they shared a common interest.
The earliest such group was actually founded in the sixteenth century and was the Academia Secretorum Naturae known in Italian as the Accademia dei Segreti, the Academy of the Mysteries of Nature, and the members referred to themselves as the otiosi (men of leisure). It was founded by the polymath Giambattista della Porta (1535–1615) in 1560.
Giambattista della Porta Source: WelcomeInstitute via Wikimedia Commons
The academy met regularly in della Porta’s home and membership was open to all, but to become a member one had to present a new secret of nature that one had discovered. We know what some of those new secrets were, as della Porta included them in the twenty volume version of his Magia Naturalis. In 1578 della Porta was summoned to Rome and investigated by the Pope. We do not know the exact grounds for this summons but he was forced to shut down his academy on suspicion of sorcery.
Della Porta’ short lived Accademia dei Segreti served as an inspiration for the next such group, Accademia dei Lincei founded in 1603 by the, then youthful, Italian aristocrat, Federico Cesi (1585–1630) of which Galileo (1564–1642) famously became a member during his triumphal visit to Rome to celebrate his telescopic discoveries in 1611.
Portrait of Federico Angelo Cesi (1585-1630) by Pietro Fachetti Source: Wikimedia Commons
The four founding members chose the name “Lincei” (lynx) from dell Porta’s book Magia Naturalis, which had an illustration of the fabled cat on the cover and the words “…with lynx-like eyes, examining those things which manifest themselves, so that having observed them, he may zealously use them.” Della Porta had, in fact, become a member a year before Galileo, in 1610. Cesi was more interested in natural history that the physical science and interestingly, unlike Galileo, was a supporter of Kepler’s elliptical astronomy.
Emblem of the Lincei
Apart from Cesi, Galileo, and della Porta other notable scientific members were Giovanni Demisiani (died 1614) a Greek theologian, chemist and mathematician, who coined the name telescope, Johannes van Heeck (1579–c. 1620) a Dutch physician, naturalist, alchemist and astrologer, Johann Faber (1574–1629) a German physician, and botanist, who coined the name microscope, Johann Schreck (1576–1630) a German physician and polymath, who left the Lincei, became a Jesuit and became an important member of the Jesuit mission to China, and Francesco Stelluti (1577–1652) an Italian mathematician, naturalist and astronomer, who together with Cesi published the first work of microscopic investigations Apiarium in 1625.
The vast majority of the scientific work of the Lincei was natural history. However, although Cesi supported Kepler’s work rather than Galileo’s. the Lincei paid for the publication of his Letters on Sunspots in 1613 and more significantly his Il saggiatore (The Assayer) in 1623. The title page of The Assayer shows the emblem of the Licei, as well as the crest of the Barberini family, featuring three busy bees and the book was dedicated to the newly elected Pope Urban VIII.
Source: Wikimedia Commons
The title page of the Apiarium, which was a study of bees, had also featured Barberini family emblem and was also dedicated to Maffeo Barberini (1568–1644) on his election to Pope in 1623.
Urban found great pleasure in Il saggiatore and granted Galileo a private audience. The two had actually been good friends for years. This led to Urban granting Galileo permission to write his Dialogo, with its unfortunate consequences.
The Lincei were also due to finance the publication of the Dialogo but Cesi’s death in 1630 put an end to this plan and also signalled the dissolution of the academy.
Within Italy the next scientific academy was the Accademia del Cimento (Academy of Experiment) founded by Leopoldo de’ Medici with the support of his brother Grand Duke Ferdinando II in 1657, to further the experimental science of Galileo.
Justus Sustermans – Portrait of Cardinal Leopoldo de’ Medici Source: Wikimedia Commons
I have already covered this in detail in the post on Giovanni Alfonso Borelli (1608–1679) so, I’m not going to go into great detail here. Despite the involvement of such scientific heavy weights such as Borelli, the anatomist Marcello Malpighi (1628–1694), the physicist and mathematician Vincenzo Viviani (1622–1703), the physician, naturalist and biologist, Francesco Redi (1626–1697), and the pioneering Danish, anatomist and geologist Niels Steensen, known better as Nicolas Steno (1638–1686) the society never really gelled and there were often disputes amongst its member, rather than being officially dissolved it just fizzled out, as the members drifted away.
Mersenne and Gassendi began to hold meetings in Mersenne’s monk’s cell with other natural philosophers, mathematicians, and other intellectuals in Paris. Sometime after 1633 these meetings became weekly and took place in rotation in the houses of the participants and acquired the name Academia Parisiensis. Many of the above named were at some point participants along with the Englishmen, Thomas Hobbes, Kenelm Digby (1603–1665), and the Cavendishes, when living in Paris. Those not living in Paris such as Isaac Beeckman(1588–1637), Jan Baptist van Helmont (1580–1644), Constantijn Huygens (1596–1687)and his son Christiaan (1629–1695), and not least Galileo Galilei by correspondence.
Pierre Gassendi Source: Wikimedia Commons
The participants were by no means in accord with each other concerning the new developments in the sciences and in fact Mersenne provoked vigorous debate on contentious theme, such as the existence of the vacuum. Following Mersenne’s death in 1684 the leadership of the academy was taken over by the mathematician and poet Jacques Le Pailleur (before 1623–1654) until his own death when it ceased to exist.
A second society grew out of the activities of Henri Louis Habert de Montmort (c. 1600–1679) a French scholar and man of letters who was Cartesian and a friend of both Mersenne and Gassendi. He gathered a salon of learned men and philosophers in his salon. These included the astronomer Adrien Auzout (1622–1692), the mathematician and engineer Girard Desargues (1591–1661), the philosopher, physicist, and mathematician Jacques Rohault (1618–1672), the mathematician Bernard Frénicle de Bessy (c. 1604–1674), astronomer, physicist, mathematician and instrument maker Pierre Petit (1594–1677), the mathematician Gilles Personne de Roberval (1602–1675) and astronomer, physicist, and mathematician Christiaan Huygens (1629–1695), as well as various physicians and men of letters. In 1657 this salon became the Académie Montmort, which however was dissolved again in 1664 due to disagreements amongst its members.
Portrait of Henri Louis Habert de Montmor by Nicolas de Plattemontagne, 1659 Source: Wikimedia Commons
Adrien Auzout suggested to Louis XIV in a letter the need for a public observatory and that there was a group ready to being work if it received royal sponsorship. A proposed constitution was circulated to former Academy members but numerous modifications were made before the French Minister of State, Jean-Baptiste Colbert (1619–1683) encouraged Louis XIV to set up the Académie des sciences in 1666, a state sponsored scientific society. Colbert was almost certainly also influenced by the Academia Parisiensis in his decision.
Portrait de Jean-Baptiste Colbert (1655) by Philippe de Champaigne Source: Wikimedia Commons
The earlier activities in Italy also had a knock on effect in the German Empire. the Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften the German National Academy of Sciences Leopoldina, was founded in 1652, based on the model of the Italian academic societies described above, as the Academia Naturae Curiosorum (Academy of the Curious as to Nature). In 1677, Emperor Leopold I (1640–1705) raised it to the status of an academy and then declared it an Imperial Academy in 1687, naming it Sacri Romani Imperii Academia Caesareo-Leopoldina Naturae Curiosorum.
Portrait of Leopold I by Benjamin von Block, c. 1672 Source: Wikimedia Commons
The Royal Society in London was founded six years before the Académie des sciences on 18 November 1660, at a meeting at Gresham College, when 12 natural philosophers decided to commence a Colledgefor the Promoting of Physico-Mathematicall Experimentall Learning. Amongst those founders were the mathematician, astronomer and physicist Christopher Wren (1632–1723), the chemist, physicist, and alchemist Robert Boyle (1627–1691), the natural philosopher John Wilkins (1614–1672), the mathematician William Brounker (c. 1620–1684), and the natural philosopher Robert Moray.
At the second meeting, Rober Moray announced that King Charles II approved of the gatherings, and a royal charter was signed on 15 July 1662 which created the “Royal Society of London”, with William Brounker serving as the first president. A second royal charter was signed on 23 April 1663, with King Charles noted as the founder and with the name of “the Royal Society of London for the Improvement of Natural Knowledge”; Robert Hooke (1635–1703) was appointed as Curator of Experiments in November.
A suitably regal first Royal Society President Portrait of William Brouncker, 2nd Viscount Brouncker after Peter Lely Source: Wikimedia Commons
Like its French counterpart, the Royal Society did not materialise out of this air but was preceded by several groups of scholars who came together to discuss, support and further the new developments of science. To some extent the Royal Society was seen as an embodiment of the fictional Solomon House from the book New Atlantis of Francis Bacon (1561–1626), which was published in 1624. A major promotor of the Solomon House concept was the German-Polish polymath Samuel Hartlib (c. 1600–1662), who lived in London and combined the theories of Bacon with the pedagogical theories of the Czech philosopher, pedagogue and theologian John Amos Comenius (Jan Amos Komeński) (1592–1670).
Hartlib promoted his theories through the Hartlib Circle a correspondence network set up in Western and Central Europe, which existed between 1630 and 1660 and in which education was central but which covered agriculture and horticulture, alchemy, chemistry, and mineralogy, finance, mathematics, medicine, pansophism, which came from Comenius, Protestantism, and the settlement of Ireland. Hartlib’s ideas were widely discussed and both Robert Boyle (1627–1691), who would later become a major voice in the Royal Society, and his sister Lady Katherine Ranelagh (1615–1691) were very active participants in the Circle.
Another group that played a significant role in the period leading up to the formation of the Royal Society was the so-called Oxford Philosophical Club or Oxford Circle, which held weekly meetings at Wadham College under the chambers of the Warden, John Wilkins (1614–1672) in the period from 1649 to 1660. The founder of statistics William Petty (1623–1687) and Robert Boyle from 1655/6 onwards, who were both active member of the Hartlib Circle were members as were many other notable scholars including Christopher Wren and Robert Hooke. When Wilkins moved to Cambridge in 1659, Robert Boyle took over hosting the meetings.
Portrait of John Wilkins (1614-1672), Warden of Wadham College, University of Oxford(1648-1659) attributed to John Greenhill Source: Wikimedia Commons
In his letters, Robert Boyle referred to “our invisible college” or “our philosophical college” and it is not clear to which group he was referring, the Hartlib Circle, the Oxford Philosophical Club or the similar group meeting regularly at Gresham College. The tradition of these meetings were started by Henry Briggs (1561–1630) the first Gresham Professor of Geometry, who held meetings of all those interested in the mathematical sciences in his rooms at Gresham College. A tradition that was continued by both his successors as professor for geometry as well as the holders of the Gresham professorship for astronomy. Christopher Wren, as noted a member of the Oxford Circle, was appointed Gresham Professor for Astronomy in 1659 and it was in his room that that the Colledge for the Promoting of Physico-Mathematicall Experimentall Learning was founded in the following year.
At the end of the sixteenth century, those that supported and promoted the new scientific developments, such as Galileo and Kepler were fairly isolated from the conservative mainstream. In one of his letters to Galileo, Kepler actually suggested that they should combine their forces and present a united front against their critics. Galileo, as usual not wishing to share the limelight, simply ignored the suggestion, although it didn’t stop him quoting Kepler’s support when it fitted his purpose to do so.
Gradually, beginning in Italy, small local groups of scholars, such as the Lincei and later the Accademia del Cimento, began to come together to jointly promote the new developments. In France, this took on a whole new dimension with the Academia Parisiensis, which through extensive correspondence was truly international. All of these were private initiatives but there existence led to the establishment of state sponsored societies first with theRoyal Society in London (1660), then the Académie des sciences in Paris (1666) and the Leopoldina in Germany (1677) all of which grew out of earlier private initiatives. By the beginning of the final quarter of the seventeenth century the new science had become firmly established.
The formal recognition of state supported platforms for the discussion of a new natural philosophy was a clear sign that the long established Aristotelian philosophy had finally been dethroned, although some would continue to fight a losing rearguard action. However, the question of which new natural philosophy was still open.
* It should be noted that this whole post is cobbled together from various sources predominantly from Wikipedia and earlier blog posts of mine.
In the world of scientific instrument making in late sixteenth and early seventeenth centuries London Augustine begat Charles and Charles begat Elias and thus the leading English scientific instrument maker in the seventeenth century came to be. Augustine was the engraver and instrument maker Augustine Ryther (fl. 1576–1593), who stood at the beginning of a of an impressive dynasty of scientific instrument makers in the Worshipful Company of Grocers stretching down into the eighteenth century. Charles was Charles Whitwell (c. 1586–1611), Ryther’s most prominent apprentice, who went on the make instruments for many of the leading mathematical practitioners of the period. By far and away Whitwell’s most prominent apprentice was Elias Allen (c. 1588–1653), who went on to become the most prominent scientific instrument maker in London in the seventeenth century.
He lived and worked in London, creating a thriving business – he was the first English instrument maker to support himself solely through the production of instruments – and teaching his skills to many apprentices who became the core of the trade during the latter part of the century.[1]
As is, unfortunately, the case with many of the supposed minor figure in the histories of science and technology in the Early Modern Period we know almost nothing of Allen’s early life or background. The inscription on his engraved portrait, to which we will return later, states that he was born near Tonbridge in Kent, (here spelt Tunnbridge) but exactly where is not known. There are some indications that he came from the parish of Ashurst as he made a brass horizontal sundial for the churchyard, which had the following inscription:
ELIAS ALLEN MADE THIS DIAL
AND GAVE IT TO THE PARISH OF
ASHURST ANO DOMINI 1634
A very high quality horizontal sundial, set out to show individual minutes and signed ‘Elias Allen fecit’. London, c.1630 (not the one from the church, which is now lost) Source: Clockmakers’ Museum
His date of birth is not known and intriguingly the portrait inscription includes the phrase, ‘died at the age of’, but leaves a blank where the number should have been. If one assumes that he was fourteen when he was first apprenticed in 1602, then he would have been born in 1588. The normal spread of ages when youths were apprenticed means he was most probably born sometime between 1585 and 1590. We do know that he died in London in 1653.
To the end of the sixteenth century Kent was one of the richest counties in England and held a major strategic position between London and the continent with major ports on the coast and along the Thames. The notable father and son duo of mathematical practitioners, Leonard and Thomas Digges were members of a prominent Kent family.
As already mentioned Allen was bound as an apprentice to Whitwell in 1602, information that is taken from his application for freedom from the Grocer’s Company on the 17th September 1611. Whitwell had died earlier in the year. Allen displayed his burgeoning talent early as there is a sundial of his making in the National Maritime Museum collection dating from 1606.
Horizontal pedestal dial for latitude 52° North. The dial has an octagonal bronze dial-plate with four screw holes. It has an hour-circle, within which is a minute-circle. The hour-lines radiate from a small circle around the base of the gnomon. The initials ‘I * B’ are engraved either side of the southern part of the meridian line. The gnomon is triangular with its vertical edge shaped into ogee curves (double S-shaped curves).
This dial, signed ‘Elias Allin fecit 1606’, was made during the time when Allen was still apprenticed to Charles Whitwell and is the earliest known example of his work. The initials (I.B.) are probably those of the original owner. Source: National Maritime Museum
He next appears in a reference in the Speculumtopographicum: or The topographicall glasse Containing the vse of the topographicall glasse … Newly set forth by Arthur Hopton Gentleman (1587/8–1614) stating ‘The Glasse is made in brasse, in Blacke Horse-ally, neere Fleetebridge, by Elias Allin’.
This implies that Allen had moved out of Whitwell’s workshop in The Strand and set up for himself before he was granted his freedom. His application for freedom is the first mention of his name in the records of the Grocer’s Company:
‘This day the humble suyte of Elias Allen for his freedom whoe allegeth to have served Charles Whitwell grocer deceassed (in his lieftime using tharte [sic] of a Mathematician) by the space of nine yeres by indenture of apprenticehood is bythis Corte referred to theaxamincon [sic] and Consideracon of the Wardens.’
The examination took ten months and he was first granted his freedom on the 7th of July in the following year.
We know a little bit about his private life during his apprenticeship from the church records of the baptisms and burials of his children. From these it can be deduced that he married his wife, Eizabeth, in about 1606.
By 1613, Allen had moved his workshop from Black Horse Alley back to the parish of St Clements and an advertisement in John Speidell’s Geometricall Extraction of 1616, Allen was living ‘ouer against St. Celements Church in the Strand’.
This would suggest that he had taken over Charles Whitwell’s workshop, where he had served his apprenticeship. He took on his first apprentices and from the beginning it seems that his business flourished. Interestingly he had no particular speciality as an instrument maker but over the next forty years seems to have produced any and every instrument that was made out of metal. During the early years, he and his wife had several more children but almost none of them lived more than a couple of years.
He quickly gained a good reputation and established links with the mathematicians living in London. As well as being recommended by Arthur Hopton (a surveyor) and John Spiedell (fl. 1600–1634) (a professional teacher of mathematics) he was recommended in the leading textbook on surveying, published at the time, The Surveyor in Foure Bookes (1616) by Aaron Rathborne (b. 1571/2; fl. 1605–1622),
‘the making of [all brass surveying instruments] are well known to M. ELIAS ALLEN in the Strand ‘.
It is obvious that Allen was becoming well established and over time his workshop became a meeting place for the diverse members of London’s mathematical community – mathematical practitioners, including surveyors and navigators, private teachers of mathematics, university educated mathematicians, and gentlemen mathematicians – uniting these groups in the common interest in mathematics, its applications, and its instruments. These people would meet up in Allen’s premises and discuss matters of mutual interest foreshadowing the coffee house scene that would develop in the scientific community in London later in the seventeenth century.
Circa 1740, A London coffee house. (Photo by Hulton Archive/Getty Images)
Most notable amongst Allen’s mathematical associates were Edmund Gunter (1581–1626) and William Oughtred (1574–1660) both of whom were very much leading lights in the English seventeenth century mathematical community. Edmund Gunter (1581–1626) was a protégé of Henry Briggs. An Oxford educated cleric with a passion for mathematics, he devoted much energy to devising new or much improved scientific instruments for mathematical practitioners. Briggs recommended Gunter as the successor to the first Gresham professor of astronomy, Edward Brerewood (c. 1556–1613) but he did not receive the post. When Brerewood’s successor Thomas Williams, about whom very little is known, resigned, Gunter, once again with Brigg’s support, reapplied and was appointed. He held the post until his death in 1626.
In 1619, Henry Savile (1549–1622) established England’s first university chairs for mathematics the Savilian chairs for geometry and astronomy at Oxford. Savile’s first choice for the chair of geometry was Edmund Gunter and he invited him to an interview, according to John Aubrey (1626–1697) relating a report from Seth Ward:
[Gunter] brought with him his sector and quadrant, and fell to resolving triangles and doing a great many fine things. Said the grave knight [Savile], “Do you call this reading of geometry? This is showing of tricks, man!”, and so dismissed him with scorn, and sent for Henry Briggs.
And so, Briggs not Gunter became the first Savilian professor for geometry.
In 1623, Gunter published one of the most important guides to the use of navigational instruments for seamen, his Description and Use of the Sector, the Crosse-staffe and other Instruments and it became something of a seventeenth century best seller in various forms. David Waters in his The Art of Navigation say this, ” Gunter’s De Sectore & Radio must rank with Eden’s translation of Cortes’s Arte de Navegar and Wright’s Certain Errors as one of the three most important English books ever published for the improvement of navigation.” [2]
Waters opposite page 360
Although, Gunter was probably the leading designer of instruments during this period. However, he didn’t make them himself. All of his instruments were made by Elias Allen this alone was enough to establish Allen as the leading instrument maker in London.
Another university educated cleric, Cambridge this time, was William Oughtred (1574-1660), an amateur mathematician, who, working as a private tutor, became one of the most important teachers of mathematics in seventeenth century England. Newton considered him, together with John Wallis (1616–1703), and Christopher Wren (1632–1723), one of the three most important English mathematicians, who preceded him. Wallis, Wren, Seth Ward (1617–1689), and Jonas Moore (1617–1679) all regarded themselves directly or indirectly as disciples of Oughtred.
William Oughtred engraving by Wenceslaus Hollar Source: Wikimedia Commons There are apparently no portraits of Briggs or Gunter
Oughtred was another friend and protégé of Henry Briggs and in 1618, when he visited Briggs in Gresham College, Briggs introduced him to Edmund Gunter. This was a marriage made in mathematical heaven. One of Gunter’s most famous instruments was his sector:
The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication and division, geometry, and trigonometry, and for computing various mathematical functions, such as square and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. (Wikipedia)
Gunter didn’t invent the sector; there had been earlier sectors from Fabrizio Mordente (1532–c. 1608), Galileo (1564–1642), who improved the instrument from Guidobaldo dal Monte (1545–1607), and in England from Thomas Hood (1556–1620). Gunter developed Hood’s instruments adding addition scales, including a scale for use with Mercator’s new projection of the sphere.
Water opposite page 361Water opposite page 361Gunter sector signed by Elias Allen Source:
Gunter’s most popular instrument was his scale. The Gunter scale or rule was a rule containing trigonometrical and logarithmic scales, which could be used with a pair of dividers to carry out calculations in astronomy and in particular navigations. The Gunter scale is basically a sector folded into a straight line without the hinge. Sailors simply referred to the rule as a Gunter. Both his sector and his rule were, of course manufactured by Allen.
Gunter scale front sideGunter scale back side
Oughtred, introduced to Gunter’s work, now came up with the idea of laying two Gunter scales next to each other to facilitate calculation by sliding the one scale up and down against the other eliminating the need for the dividers, thus inventing the slide rule, which would go on to be a primary quick calculation device for mathematician, scientist and engineers for several centuries, until replaced in the modern age by the pocket calculator.
Paper image of the first slide ruleDetail: What’s remarkable about the Cambridge UL rule – and the reason it’s in the UL at all – is that it’s made of paper. It is preserved along with a letter from Oughtred to the craftsman Elias Allen, sent on 20 August 1638 – part of the Macclesfield Collection. In the letter Oughtred describes the slide rule and says that he “would gladly see one of [the two parts of the instrument] when it is finished: wch yet I never have done”. So even though the letter itself dates from 1638, many years after he invented the slide rule, Oughtred had still not got around to having one made. We have to speculate about what happened next, certainly Allen made the two-foot rule, inked it up as if it were a printing plate and then printed an image of it. Was this to send to Oughtred as a prototype? Was this kept as a record for his workshop? Either way the brass instrument is long since lost but the paper version survives – a concrete record of the very first slide rule. Boris Jardine
Oughtred then invented a circular slide rule.
Oughtred’s circular slide rule with sundial on reverse, Elias Allen, London, c. 1633-1640 – Putnam Gallery – Harvard University – DSC07908 – PICRYL – Public Domain
Both instruments were, of course, made by Elias Allen. There was a major dispute when Richard Delamaine (before 1629–before 1645), an earlier pupil of Oughtred’s claimed that he and not Oughtred had invented the slide-rule. Allen, as the maker of the Oughtred’s instrument became embroiled.
Oughtred also designed an innovative sundial
This octagonal brass pedestal sundial is known as a double horizontal dial because it has two scales for reading the hours. The first is a standard scale, which is used with the polar edge of the gnomon. The second is formed by the vertical edge of the gnomon (set at the centre of the dial) and the lines of projection of the celestial sphere on to the plane of the horizon (the horizontal projection).
The double horizontal dial was designed by the 17th century English mathematician William Oughtred. Elias Allen was a friend of Oughtred and he produced several double horizontal dials. They were useful not only for telling the time but also for demonstrating the motion of the sun through the day and also through the year. A number of double horizontal dials survive from the 17th century but it appears that they were not produced much after 1700. Source
There is another connection between Oughtred and Allen concerning the portrait that I said I would return to. It was extremely unusual for an instrument maker in the Early Modern Period to have his portrait painted. Not only did Allen have a formal portrait but it was the work of two leading artists of the period. The engraving was by Wenceslaus Hollar (1607–1677) from a, now lost, portrait by Hendrick van der Borcht II (1614–1672).
Portrait etched by Hollar after an original by Jan Meyssens, c. 1649. Prague Castle is in the background. Source: Wikimedia CommonsEtching by Wenceslaus Hollar Source: Wikimedia Commons
Hollar, known in German as Wenzel Hollar and in Czech Václav Hollar, was a Bohemian graphic artist, originally from Prague, who in 1627 was apprenticed to the Swizz engraver Matthäus Merian der Ältere (1593–1650) in Frankfurt. In the 1630s he lived in Strasbourg, Mainz, Koblenz and Cologne producing engravings of towns, castles and landscapes and establishing a reputation. Hendrik van der Borcht II was a German Baroque painter who lived in Frankfurt. Hollar only produced three portraits of mathematicians, as well as Allen he produced the engraved portraits of Oughtred and the English mathematician, astronomer, cartographer, and gunner, Nathaniel Ny (1624–after 1647) born in Birmingham. Between Oughtred, Hollar, and van der Borcht there is a direct connection, they all had Thomas Howard, 14th Earl of Arundel (1585–1646) as a patron.
Portrait by Peter Paul Rubens, 1629-1630, National Gallery Source: Wikimedia Cooms
Howard was a magistrate, diplomat and courtier who moved in scholarly circles, amongst his friends were James Ussher (1581–1656), William Harvey (1578–1657), John Seldon (1584–1654), Francis Bacon (1561–1626), and Inigo Jones (1573–1652). In 1628, Howard appointed Oughtred as mathematics tutor to his son William Howard (1614–1680).
William Howard, 1st Viscount Stafford portrait by Anthony van Dyck
When in London, Oughtred resided in Arundel House. Oughtred most important book, which established his reputation as a mathematician was an algebra textbook, Arithemeticæ in Numeris et Speciebus Institutio, quae tum Logisticæ, tum Analyticæ, atque adeus totius Mathematicæ quasi Clavis est (The Foundation of Arithmetic in Numbers and Kinds, which is as it were the Key of the Logistic, then of the Analytic, and so of the whole Mathematics) written for and dedicated to William Howard and first published in 1631. It went through several editions over the decades both in Latin and in English.
Thomas Howard was also a great collector of art, both paintings and sculpture, and amassed a large collection during his travels as diplomate over the years, which was housed in Arundel House. The collection included drawings by Leonardo da Vinci, both the Holbeins, Raphael, Raphael Parmigiano, Hollar, and Dürer. During an important but unsuccessful diplomatic mission to the Holy Roman Emperor, Ferdinand II (1578–1637) in 1636, Thomas Howard collected both Hollar and van der Borcht, then only twenty two years old, in Frankfurth, took them with him to Vienna, Prague and Italy before taking them back to London and installing them both in Arundel House. Appointing van der Borcht as curator of his paintings. Arundel House lay between the Strand and the River Thames near St Clement Danes, just around the corner from Allen’s workshop. In fact, Oughtred used Allen’s work shop as his mail address when in London and residing at Arundel House.
Arundel House (viewed from the north), 1646 engraving by Adam Bierling after a drawing by its then occupant, Wenceslaus HollarMap of Arundel House, drawn by Ogilby and Morgan, c. 1676
In the 1630s Allen became involved in the early years of the Worshipful Company of Clockmakers. Early clockmaking was mostly turret clockmaking and involved working in ferrous metals so, the majority of clockmakers in the City of London were members of the Worshipful Company of Blacksmiths, which had received its royal charter in 1571. With the increasing number of clock and watchmakers in the early seventeenth century, groups of them tried to establish their own guild from about 1620 onwards. These attempts were blocked by the Blacksmiths Company. However, the clockmakers succeeded in obtaining a royal charter issued on 22 August 1631. It is thought that Allen became involved with the clockmakers in an attempt to raise his status in the city, because he had little chance as an instrument maker in doing so in the Grocers Company.
The Court of Clockmakers Company, which governed it, consisted of a master, three wardens, and ten or more assistants. The assistants, who were required to pay a fee of £6 13s 4d for the privilege but were appointed for life. The wardens and master were elected annually from the assistants and normally held their office for one year.
Elias AlIen became an assistant in the Clockmaker’s Company on 3rd October 1633, just two years after its creation. This was despite the fact that he appears never to have become an official member of the guild. On 18th January 1635 (OS) he took on the responsibilities of the Renter Warden or Treasurer and this was followed a year and a day later by promotion to the Mastership (a post which he in fact held for eighteen months, until 29th July 1638)[3].
This fast raise to the Mastership of the newly formed livery company demonstrates Allen’s importance in the city as a metal worker and an instrument maker.
During his long and distinguished career Allen trained a very large number of apprentices in his workshop. At least seven of his apprentices became master-craftsmen and plied their trade successfully for many years to come. These were John Blighton, John AlIen, Robert Davenport, Christopher Brooke(s), Ralph Greatorex, Withers Cheney and John Prujean. Of these, perhaps the most significant was Ralph Greatorix (c. 1625–1675) a member of the clockmakers company, who was bound as an apprentice 25 March 1639 was freed 25 November 1653 and probably took over Allen’s workshop following his death in that year.
Greatorex was a mathematician and instrument maker, who became an integral part of the growing natural philosophy community in London in the second half of the seventeenth century. He was friends with William Oughtred and had dealings with John Evelyn and Samual Pepys. He also work or corresponded with Samuel Hartlib, Christopher Wren, Robert Boyle, Edward Phillips and Jonas Moore. He attended meetings of the Royal Society and conducted horticultural experiments at Arundel House.
What follows are some of the other instruments made in Allen’s workshop that have survived and are now in major collections.
Another notable instrument designed by Edmund Gunter and made by Allen was his Horary Quadrant
Edmund Gunter’s De Sectore et Radio (1623) describes what came to be known of as a Gunter quadrant, a form that was extremely popular throughout the 17th century. The quadrant could be used to observe and measure astronomical phenomena, to perform the basic tasks of surveying, and to carry out astronomical calculations.
This particular instrument, made by Elias Allen, could also be used for telling the time both during the day and at night (the latter process employing the nocturnal on the reverse). SourceSun-and-moon dial made by Elias Allen between 1607 and 1653 at his workshop, near St. Clement’s Church, London. Engraved “Elias Allen fecit a Moone diall”. It is callibrated for use at the latitude 51 1/2. Sun-and-moon dials are time-reckoning devices that can be used in daylight as sundials and at night as moondials. This example was made by Elias Allen (active 1602-1653) at his workshop known as ‘The Bull’s Head’ which was situated near St. Clement’s Church, near the Strand in London. Also showing two Gunter Sectors, a Gunter Horary Dial, and a compendiumCompendium consisting of a sundial, companss and calendar indices made by Elias Allen between 1630 and 1653, near St. Clement’s Church close to the Strand, London. Inscribed: “Elias Allen fecit” and outer lid engraved with the royal coat of arms. A compendium is a multi-function instrument. This example consists of a sundial, compass and calendar indices and was made by Elias Allen between 1630 and 1653 at his workshop near St. Clement’s Church which was called ‘The Bull’s Head’. The sundial ring is inscribed: “Elias Allen fecit” and the outer lid is engraved with the royal coat of arms of either King James I or King Charles I, but the object has been attributed to the reign of King Charles I. Source:
[1] The quote is from the preface to Hester Katherine Higton’s excellent doctoral thesis, Elias Allen and the Role of Instruments in shaping the Mathematical Culture of Seventeenth-Century England, which I shamelessly plundered in writing this post. You can download it here.
[2] David Walters, The Art of Navigationin England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 359
In the history of science of the seventeenth century Christiaan Huygens (1629–1695) occupies a rather strange niche. On the basis of his scientific achievements and his influence there can be very little doubt that he in on a level with the big names Kepler, Galileo, Descartes, Leibniz, Newton and in fact can easily be ranked higher than two of these. However, in popular literature he is largely ignored or only mentioned in passing. In an earlier post I argued this is because unlike the others he never propagated any sort of grand philosophy of science. Christiaan Huygens built some of the best telescopes in the seventeenth century, he was an astronomer, who made important discoveries, and influential mathematician, and a physicist.
Portrait of Christiaan Huygens by Bernard Vaillant (1686) Source: Wikimedia Commons
Christiaan and his brother Constantijn were the third generation of prominent, aristocratic, politicians. Their father was the diplomat, musician, and poet, Sir Constantijn Huygens Snr., Lord of Zuilichem (1596–1687).
Constantijn Huygens, painted by Michiel Jansz van Mierevelt in 1641 Source: Wikimedia Commons
Constantijn Snr. was the second son of Christiaan Huygens Snr. (1551–1624), secretary of the Council, and Susanna Hoefnagel, niece of the Antwerp painter Joris Hoefnagel (1542–1601). Christiaan Huygens Snr. personally, oversaw the education of his sons, Constantijn and his older brother Maurits. Education provided partially by himself and partially by selected governors. They were given lessons in music, art and languages, Constantijn would become fluent in French, Latin, Greek and later Italian, German and English. They were also taught maths, law and logic. In 1616 the brothers went to study at Leiden University, mainly to help them build a social network. Constantijn returned home in 1617 and received six weeks of training with Antonis de Hubert, a lawyer in Zieriksee. All in all, Constantijn received a high level all round education. He would go on the become an important diplomat as well as a prominent musician, and a leading Dutch poet. However, Constantijn was not just dedicated to the fine arts but also took an active interest in the developing new science and mathematics. He was friends with both Mersenne and Descartes. In fact, it was he who first drew Mersenne’s attention to his son’s emerging mathematical talents and he also introduced him to Descartes.
Huygens and his children by Adriaen Hanneman, Mauritshuis, The Hague Source: Wikimedia Commons
Constantijn applied the same education programme to his son Christiaan and his brother Constantijn that his father had applied to him. Private education at home from himself and selected tutors until the age of sixteen. It was a broad based liberal education which included languages, music, history, geography, mathematics, logic and rhetoric, as well as dancing, fencing and horse riding. His mathematics tutor was Jan Jansz Stampioen (1610–1653) known for his work on spherical trigonometry. Earlier he had been mathematics tutor to the future Stadholder of Holland, Zeeland, Utrecht, Guelders, Overijssel and Groningen in the United Provinces of the Netherlands, Willem II (1626–1650) Prince of Orange.
From May 1645 to March 1647 Christiaan was enrolled in Leiden University studying law and mathematics. Here he and his brother Constantijn were, on the recommendation of Descartes privately tutored by Frans van Schooten Jr, (1615–1660), the author of the expanded Latin edition of Descartes’ La Géométrie and as a leading expert on the most up to date advances in mathematics introduced Christiaan to the works of Descartes, Fermat and Viète.
Frans van Schooten Jr. artist unknown Source Wikimedia Commons
From 1647 to 1649 Christiaan continued his studies at the Orange College in Breda, where his mathematics tutor was the English mathematician, John Pell (1611–1685).
John Pell by Godfrey Kneller Source: Wikimedia Commons
Having completed his education Christiaan took part as a diplomat on a mission with Louis Henry of Nassau-Dillenburg (1549–1662) followed by visits to Bentheim and Flensberg in German, Copenhagen and Helsingør in Denmark. He had hoped to visit Descartes in Stockholm but the Frenchman died before he could.
Huygens was now fully and excellently equipped to follow his father and grandfather into a life in politics and diplomacy, as well has having received to best education in mathematics available in Europe at the time. It became obvious that he was not really suited to become a diplomat and the collapse of the House of Orange ended his family’s role in politics and so Christiaan became in the widest possible sense a mathematician. Living at home in the family mansion and with a generous allowance from his father, he had no financial worries and no need to find employment and could then devote himself fulltime to his research.
Huygens made several significant contributions, which played an important role in the developments in mechanics which I will deal with in a future post but for now I will concentrate on his contributions to optics.
Huygens’ interest in optics began with his construction of telescopes. Already in 1652 he began to compose a treatise on dioptrics, known as Tractatus, which contained a comprehensive and rigorous theory of the telescope. His work here was pioneering. He announced its imminent publication several times in his correspondence but in the end abandoned it for a much more comprehensive work, now under the name Dioptica, consisting of three sections. The first dealt with the general principle of refraction, the second with spherical and chromatic aberration, whilst the third dealt with the construction of telescopes and microscopes. Descartes in his dioptrics had only dealt with ideal, elliptical and hyperbolic lenses, which at the time could not be produced. Huygens, instead, confined his investigations to spherical lenses, which could be produced and were used in the construction of telescopes and microscopes.
Huygens began an extensive study of both spherical and chromatic aberration, although when he began, chromatic aberration wasn’t really understood. He dropped plans to publish this when Newton published his legendary paper first paper on the cause of chromatic aberration: A letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; containing his new theory about light and colors: sent by the author to the publisher from Cambridge, Febr. 6. 1671/72; in order to be communicated to the R. Society(Philosophical Transaction, No. 80).
Huygens discovered that he could reduce the effects of aberration by using long focal length objectives for his telescopes, which would eventually lead to his aerial telescope in around 1675. Together with his younger brother Constantijn, who was involved in all his lens grinding and telescope building endeavours, he eliminated the telescope tube entirely mounting the objective in a short tube on a stand and holding the eyepiece mounted in another short tube, the two lenses being connected by a string. He published the design of these arial telescope in his Astroscopia Compendiaria in 1684. Here he wrote that he and Constantijn had objectives 8 inch (200 mm) and 8.5 inch (220 mm) diameter and 170 and 210 ft (52 and 64 m) focal length, respectively. Constantijn Huygens, Jr. presented a 7.5 inch (190 mm) diameter 123 ft (37.5 m) focal length objective to the Royal Society in 1690.
An engraving of Huygens’s 210-foot aerial telescope showing the eyepiece and objective mounts and connecting string Source. Wikimedia Commons
Christiaan also developed one of the earliest multi-lens eyepieces for use with very long focal length objectives. It consists of consist of two plano-convex lenses with the plane sides towards the eye separated by an air gap. The lenses are called the eye lens and the field lens. The focal plane is located between the two lenses. The eyepiece, known as the Huygens-Eyepiece became obsolete with advent of aberration free short focal length telescope.
Huygens-Eyepiece Source: Wikimedia Commons
The one major work on optics that Christiaan published during his lifetime was his Traité de la Lumière(Treatise on Light) submitted to the Académie des sciences in Paris in 1678 but first published in 1690.
Source: Wikimedia Commons
This was originally the first section of the earlier Dioptica and contains his ground breaking wave theory of light. Huygens was, however, not the first to present a wave theory of light, that honour goes to the French Jesuit scientist Ignace-Gaston Pardies (1636–1673), who was one of those who strongly criticised Newton’s first paper on optics, from 1672, as did both Huygens and Robert Hooke (1635–1703)[1]. Pardis wrote a manuscript around 1670 entitled On the motion of undulations, which he later lent to Huygens but which was never published. In his 1673 treatise on statics, he included a short description of this work:
first to describe the undulations of water, a matter of game and entertainment for children, which can be the subject of a very deep meditation for the most skilled philosopher”; and then treat sound by analogy with these undulations, and light by analogy with sound.
However, a second Jesuit Pierre Ango (1640–1694) inherited Pardies’ manuscript and used it as the basis for the first section of his L`Optique (Optics) published in 1682 after Pardies’ death. Both Jesuits present this work as a defence of Aristotle’s views against the neo-atomism of Pierre Gassendi (1592–1655) and the French physicist Emmanuel Maignan (1601–1676).
Ango filtering Pardies presented a study of the behaviour of waves and wavefronts in water, They gave the correct explanation of the formation of a wave by the impact of a stone. They described the reflection of a wave from a solid surface and correctly described the superposition of the reflected and incoming waves and like Mersenne and Hooke noted that the waves crossed each other without mutual hinderance. They then applied this to the study of the propagation of sound and by analogy to light. They presented models for both reflection and refraction.
Ango/Pardies ReflectionAngo/Pardies Refraction
On the hotly debated question as to whether light was transmitted instantaneously, they believed that in the absence of matter the propagation was instantaneous becoming truly wave-like in the presence of air or some other transparent medium. “They believed that light propagated almost instantaneously until it reached the atmosphere and thereafter assumed a finite velocity decreasing as the density of the air increased.”
In his Treatise on Light, Huygens followed to same path of creating an analogy between sound and light but saw greater differences between the two than Pardies. He noted that “they differ in several respects namely: in the first production of motion that causes them, in the manner in which this motion is propagated, and in the manner in which it is communicated.” Like Pardies he noted that the media in which sound and light are propagated must differ as light passes through a vacuum, whereas sound doesn’t.
The Treatise is actually fairly short given the extensive material it covers, the English translation that I have is only 101 small quarto pages long. The first section is titled, On Rays Propagated in Straight Lines, and is a brief outline of the entire book followed by a discussion on the nature of light in which Huygens presents his wave theory contrasting it with Descartes’ theories. This contains the first empirical proof that the propagation of light is not instantaneous but that light has a finite speed, which was provided by the Danish, astronomer Ole Rømer (1644–1710), who worked as the assistant to Giovanni Domenico Cassini (1625–1712) at the Paris Observatory, observing the Moons Of Jupiter, which had first been published in 1676. Huygens writes:
But that which I employed only as a hypothesis, has recently received great seemingness as an established truth by the ingenious proof of Mr. Römer which I am going to relate, expecting himself to give all that is needed for its confirmation. It is founded as is the preceding argument on celestial observations, and proves not only that Light takes time for its passage, but also demonstrates how much time it takes, and that its velocity is even at least six times greater than that which I have just stated.
For this he makes use of the Eclipses, suffered by the little planets which revolve around Jupiter which often enter its shadow:
Huygens provides an illustration and a long technical explanation of Rømer’s discovery. Which put very simply showed that the point in time in which Jupiter eclipsed one of its moons varied according to which side of the Earth’s orbit the observation was made. The time difference corresponding to the difference in distance that the light had to travel.
Huygens’ diagram for Rømer’s observations. The large circle is the Earths orbit around the Sun. The small circle is the orbit of a Jupiter moon shown entering or leaving Jupiter’s shadow
Following on from Rømer’s breaking news, Huygens moves on to the basic creation and propagation of light waves.
Light waves emanating from a light sourceLight waves propagating from a source A
Having the raw material there now follow successive chapters on the explanation of reflection and refraction using the wave theory, in which Huygens corrects Pardies’ model for refraction that was wrong.
Reflection of wavesReflection of an objectRefraction of light wavesHuygens’ diagram for the deduction of the sine law of refraction
Chapter IV, On theRefraction of Air, finds Huygens explaining atmospheric refraction using his wave theory, a topic of great interest to astronomers, of which he was one.
Chapter V, actually by far the longest in this short book, introduces a second novum after Rømer’s determination of the speed of light, On the Strange Refraction of Iceland Crystal. In 1699, Rasmus Bartholin (1625–1698), a Danish physician and grammarian, was the first to discover that light rays passing though Iceland spar (optical calcite) undergoes double refraction. He published an accurate description of the phenomenon, but he was unable to explain it.
Rasmus Bartolin artist unknown Source: Wikimedia Commons
In his treatise, Huygens provided most of the explanation. Because Huygens’ wave theory was that the nature of light was a longitudinal wave, which only has a single polarization he couldn’t total explain the birefringence (double refraction).
Huygens’ short treatise ends with a chapter on image formation, On the Figures ofTransparent Bodies, in which he demonstrates how to determine the true form of an object from its reflected or refracted image.
Huygens did not consider there to be enough knowledge available to speculate on the nature of colour and so he does not address the topic in the Traité de la Lumière. One might perhaps regard this as strange as Newton published his famous first paper, containing his new theory about light and colors, six years before Huygens submitted his Traité de la Lumière, to the Académie des sciences in Paris. Huygens was very much aware of Newton’s paper because he criticised Newton’s corpuscular theory of the propagation of light. This led to an, at times, acrimonious dispute between Newton and the proponents of a wave theory, Pardies, Hooke, and Huygens. A dispute that was then decided in favour of Newton’s corpuscular theory, when he became, so to speak, the king of science following the publication of his Principia, in 1687 or at the latest following the publication of his Opticks in 1704, a much more substantial volume than the Traité de la Lumière. I will return to this dispute in a later post.
Quoting Darrigol:
Huygens acknowledge two weaknesses of his system: it did not encompass the color phenomena discovered by Newton, and it did not explain a “marvelous phenomenon, discovered after writing all the above.” [about Icelandic spar] Namely, the ordinary or extraordinary beam issuing from one spar crystal did not necessarily undergo double refraction when entering a second crystal. There were special orientations of the second crystal for which only one kind of refraction occurred. Huygens commented:
It seems that we are forced to conclude that the waves of light, for having past the first crystal, acquire a certain form or disposition, through which when encountering the material of the second crystal in a certain position, they can stir the two different matters that serve to the two different species of refraction: and when encountering the material in another position, they can move only one of theses matters. Regarding how this happens, I have not found anything that satisfies me.
Despite these short comings, Huygens’s theory became the most respected of the medium-based theories of light of the late seventeenth century. Plausible reasons for this preference are Huygens’s ability to predict new laws, his lucid elegant style, his geometrical virtuosity, and his well established authority as one of the three greatest natural philosophers of his time.[2]
Following his defeat in the contest of theories of light to Newton, Huygen’s theory disappeared from the stage only to surface again in the early nineteen century with the new approach to a wave theory. In 1803, the English polymath (1773–1829), Thomas Young, carried out his famous double slit experiment, published in 1807, which could not be explained with Newton’s corpuscular theory of light.
Thomas Young portrait by Henry Perronet Briggs, 1822 Source: Wikimedia CommonsModern illustration of the double-slit experiment Source: Wikimedia Commons
The Poisson Spot (also Argo or Fresnel Spot) was demonstrated by the French mathematician, physicist, and astronomer François Arago (1786-1853) around 1819, another optical phenomenon that a corpuscular theory couldn’t explain.
François Argo portrait by Charles de Steuben Source: Wikimedia CommonsPhoto of the Arago spot in a shadow of a 5.8 mm circular obstacle.
The French physicist, Augustin-Jean Fresnel (1788–1827),
Portrait of Augustin-Jean Fresnel, c. 1825, photo-mechanical copy of engraving by E Rosette after a painting by A Tardieu, copied from Plate II, Light and Colour, by RA Houstoun, 1903, and used in frontispiece of Fresnel’s, Oeuvres completes published after his death in 1866. Source: Wikimedia Commons
revived Huygens wave theory of light and what is known as the Huygen’s construction: every point reached by a luminous disturbance becomes a source of a spherical wave. The sum of these secondary waves determines the form of the wave at any subsequent time. Fresnel modified this and proposed the Huygens-Fresnel principle: every point on a wavefront is itself the source of spherical wavelets and that the secondary wavelets emanating from different points mutually interfere. In 1881 he demonstrated that with this he could explain both the rectilinear propagation of light and also diffraction effects. He also changed Huygens theory that light waves were longitudinal waves to the theory that light waves were transverse waves and could, unlike Huygens finally give a complete explanation of all of the aspects of birefringence with its double polarisation.
Although he had to wait a hundred plus years, Huygens wave theory of light was finally vindicated.
[1] The very brief sketches of the wave theories of light from Pardies and Huygens are largely extracted from Oliver Darrigol, A History of Optics: from Greek Antiquity to the Nineteenth Century, OUP, 212, pp. 60-77
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
The Renaissance Mathematicus 
