**Jules Lissajous** was a French mathematician best known for the Lissajous figures produced from a pair of sine waves.

- In 1874 Lissajous became rector of the Academy at Chambéry, then in the following year he was appointed rector of the Academy at Besançon.
- Lissajous was interested in waves and developed an optical method for studying vibrations.
- Jean-Marie Duhamel had tried to demonstrate these vibrations with a mechanical linkage but Lissajous wanted to avoid the problems caused by the linkage.
- He obtained Lissajous figures by successively reflecting light from mirrors on two tuning forks vibrating at right angles.
- Lissajous studied beats seen when his tuning forks had slightly different frequencies, in this case a rotating ellipse is seen.
- It was a visit by Jules Antoine Lissajous to the Royal Institution in 1857.
- Tyndall was intrigued by the demonstrations and planned to repeat them, but when Lissajous was consulted he offered to come to London himself.
- Tyndall reported the details of the lecture and records that, at the beginning of the lecture, Lissajous: "...
- He then performed a number of experiments demonstrating what we now know as 'Lissajous figures'.
- At the conclusion of this beautiful series of experiments, which, thanks to the skill of those who performed them, were all successful, on the motion of Mr Faraday, the thanks of the meeting were unanimously voted to M M Lissajous and Duboscq and communicated to those gentlemen by his Grace the President, The Duke of Northumberland.
- Duboscq, who assisted Lissajous in this demonstration, himself invented the Bioscope, a viewer for showing moving 3-dimensional pictures.
- Actually the minimum number was 24 but perhaps there were 16 pairs in the only ones that Lissajous saw.
- Although Lissajous was right about this particular apparatus, of course the method of sequentially showing still pictures was adopted for motion pictures on film.
- Lissajous was praised by his contemporaries for his work and awarded the Lacaze Prize in 1873 for his optical observation of vibration and, in particular, "for his beautiful experiments".
- Perhaps it is entirely fair that "his beautiful experiments" were a major factor in the award of the prize since Lissajous figures had been investigated forty years earlier by Nathaniel Bowditch.
- He had produced them in 1815 with a compound pendulum and, because of this, sometimes the figures are referred to as Bowditch figures or Lissajous-Bowditch figures.
- We should note, however, that Lissajous' work was entirely independent of that of Bowditch.
- Quickly Lissajous figures became a standard topic in physics texts and demonstrations.
- We have noted above John Tyndall's discussion of Lissajous's experiments, and he described them in detail in his acoustics text.
- Lord Rayleigh also discussed Lissajous figures in his classical treatise on acoustics.
- Hermann von Helmholtz used Lissajous' instruments in his study of string vibrations.
- Perhaps today it is Australians are most familiar with Lissajous figures since the Australian Broadcasting Corporation (ABC) has used such a figure for its logo since 1965.
- If Lissajous had produced this logo in a demonstration he would have needed to use two tuning forks at right angles, one vibrating three time as rapidly as the other.

Born 4 March 1822, Versailles, France. Died 24 June 1880, Plombières, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive