Ingenious machines for drawing curves: The Archives



A frequent comment made by viewers of the Iron Genie harmonograph in action, is that it reminds them of the Spirograph. Most of us are familiar with this childhood toy, which consists of a large ring-gear with internal teeth and a series of different sized gears which run inside it – when you insert a pen-tip into one of the holes of the interior gear and run it around within the annular gear, you get a fascinating spiraloid drawing. The drawings that can be achieved with a single gear can be varied quite dramatically by inserting the pen tip into different holes, and further variations are achieved by using different sized gears.

Spirographs and harmonographs are part of an interesting narrative of private obsession and ingenious inventiveness that took place throughout the nineteenth century. Once you delve into the relatively obscure archives of this story, a number of extraordinary gentlemen come to light – scientists, mathematicians, academics, watchmakers, engineers and sometimes clergymen – who pursued their interests in creating ever more intricate devices for drawing mathematical curves, almost as a recreational activity. They joined societies, held informal symposia (or “Conversazione” as they were called) shared ideas and published booklets about their research. Their bequest is a rich and curious history.

The Museum of the History of Science, Oxford posesses a fascinating archive of some of these stories. I was priveleged to have had the chance to see some of them, and to speak with the museum archivist Tony Simcock, a fount of knowledge on the subject. A large part of the museum’s archive on the subject was collected by Richard Inwards, who in the latter part of the 19th Century had developed a ‘Spiraloid Curve Machine’. Inwards made an album of drawings created by this machine; the album itself, measuring approximately 11 inches  by 9 inches is lovingly hand- made with brown-paper pages and a soft leather binding. Its title-page is neatly inscribed by hand within a spiraloid curve drawing: “SPIRALOID CURVES by RICHARD INWARDS 1893 – 1898” and it also bears a handwritten note: “Specimens of Curves made in the Spiraloid Curve Machine designed and constructed by Richard Inwards. The instrument is based on an earlier and simpler one by The Revd. Sherrard Beaumont Burnaby Vicar of Hampstead.”   The drawings vary in size, ranging from 3 inches to 6 inches, and there are 118 figures in all, every one different, each displaying intricate, complex geometries.

Inwards 3

1 – Spiraloid Curve, Richard Inwards, MS Museum 290

Inwards 2

2 – Spiraloid Curve, Richard Inwards, MS Museum 290












geometric chuck 1

Ibbetson’s Geometric Chuck at the Science Museum, Kenington

I have not yet seen any independent references to The Revd. Sherrard Beaumont Burnaby’s instrument, but there is a fine and early example of a similar machine displayed in the mathematics galleries at the Science Museum in Kensington, London. It is called a Geometric Chuck, designed very early in the 19th century by John Holt Ibbetson Esq. He had it made for him by Holtzappfel & Co., a precision engineering company that made lathes and scientific instruments, and operated in London between 1795 and 1928. Ibbetson published an explanatory booklet to go with the launch of his machine in 1833, entitled: “A brief account of Ibbetson’s Geometric Chuck, manufactured by Hotzappfel & Co., with a selection of specimens illustrative of some of its powers.” This text can be accessed at California Digital Library Internet Archives by clicking the title link. In his somewhat bombastic introduction (perhaps with reason!) Ibbetson refers to earlier ‘inferior’ inventions, such as that of  John Baptist Suardi. Suardi is credited with being the initial inventor of this class of instruments that creates drawings of compound curves,  sometime in the eighteenth century ( I have been unable to locate any dates as yet) His invention was called the ‘Geometric Pen” and was accompanied by his treatise “Nuovo Instrumenti per la Descrizzione di diverse Curve Antichi e Moderne”.

Title page of Ibbetson's booklet, 1833

Title page of Ibbetson’s booklet, 1833


" Dr. E W Alabone and his Geometric Chuck" Science Museum, Kensington

” Dr. E W Alabone and his Geometric Chuck” Science Museum, Kensington
















Henry Perigal. 1801 - 1898

Henry Perigal. 1801 – 1898

J H Ibbetson was evidently the early mentor of another 19th century luminary, Henry Perigal, who was in turn friend and mentor of Richard Inwards (of the ‘Spiraloid Curves’ above) to whom he bequeathed the bulk of his research papers, now housed in the Museum of the History of Science archives.  Perigal was a polymath, the archtypal Victorian amatuer gentleman scholar,  who was a member of several societies, such as the London Mathematical Society.  He absorbed himself in a variety of investigations, which included working with the lathe and making curve drawings. Amongst his papers in the museum’s archives is a beautifully bound book containing designs he made on a geometric chuck, and an album of exqiusitely rendered drawings that he made by hand with compasses.

The museum’s archive contains material from another brilliant 19th century personality, the forward-looking scientific instrument maker John Matthias Augustus Stroh (1828 – 1914). In addition to inventing a clockwork phonograph and working on prototype telegraph systems, he produced some extraordinary stereoscopic drawings on a harmonograph (below):

Stroh Stereo

Stereoscopic harmonograph by Augustus Stroh, 1893 Museum of the History of Science, Oxford

This is one of two drawings, wrapped in a slip of paper and inscribed (by Perigal?) on the reverse: Pendulum Curves arranged for the stereoscope drawn by A Stroh Esq. and given by him Feb 21 1893. Archivist Tony Simcock handed me an old stereoscopic viewer, of the sort that was more generally used to view stereoscopic photographs, and to my amazement, the drawings actually do work! An exquisitely abstract three-dimensional form shimmers before your eyes. You can try it yourself, if you download and print off the image above to the dimensions 14 cm by 7 cm.

Harmonograph by Newton & Co. - engraving from Harmoniv Vibrations c. 1909

Harmonograph by Newton & Co. – engraving from Harmonic Vibrations c. 1909

The pendulum curve instrument, or Harmonograph, was first explored by Hugh Blackburn, Professor of mathematics at Glasgow University 1849 – 1879. A spin-off from his investigations into pendulum movements, the first mention of its actual manufacture appears to be in a rare 1893 publication by Irwine Witty of the Norwich Gossip Club. He states that the harmonograph “was first constructed by Mr. Tisley, of the firm Tisley and Spiller, the well-known opticians…”

The ultimate study of the harmonograph and its history comes from a book entitled “Harmonic Vibrations and Vibration Figures” published circa 1909, edited by scientific instrument maker Herbert C. Newton. Newton commercially manufactured the instrument, which had by now become a popular diversion in middle-class homes.  There is one on display in the mathematics galleries at the Science Museum, Kensington.

For the sake of limiting the length of this post I shall cover some the material in this book and related matters in my next post. Meanwhile, please see my Harmonograph Resources page on my official website, and please feel free to comment or suggest further resources and archives.