朱尔·安托瓦内·利萨茹Jules Antoine Lissajous

朱尔·安托瓦内·利萨茹于1841年进入巴黎高等师范学校。1847年，他成为圣路易中学的数学教授，担任此职直到1874年。1850年，他因一篇关于振动棒的学位论文获得博士学位，该论文使用克拉尼沙图法确定节点位置。1874年，利萨茹成为尚贝里科学院院长，次年又被任命为贝桑松科学院院长。

利萨茹对波感兴趣，并开发了一种研究振动的光学方法。他希望能够看到由振动产生的波，这些波通常以声音的形式表现。起初，他研究音叉与水接触时产生的波，研究由此引起的涟漪。基于这些想法，他发表了Sur la position des noeuds dans les lames qui vibrent transversalement Ⓣ（《论横向振动叶片中节点的位置》）（1850年）。1855年，他描述了一种通过将光束从附着在振动物体上的镜子反射到屏幕上来研究声振动的方法。他发表了Sur un cas particulier de stéréoscopie fourni par l'étude optique des mouvements vibratoires Ⓣ（《论振动运动的光学研究提供的立体视觉的一个特例》）（1856年），随后发表了他的主要著作Mémoire sur l'étude optique des mouvements vibratoires Ⓣ（《振动运动的光学研究学位论文》）（1857年），这是一篇85页的论文。次年，他发表了Sur les vibrations transversales des lames élastique Ⓣ（《论弹性叶片的横向振动》）。

让-马里·迪阿梅尔曾试图用机械连杆来演示这些振动，但利萨茹想避免连杆引起的问题。他通过依次将光从两个以直角振动的音叉上的镜子反射，获得了利萨茹图形。这些曲线之所以能被看到，仅仅是因为人眼的视觉暂留。利萨茹研究了当他的音叉频率略有不同时看到的拍，在这种情况下会看到一个旋转的椭圆。也许他最大的名声来自他讲座的质量，幸运的是，弗瑞兹·约翰 Tyndall详细描述了他的一次著名讲座，Tyndall于1853年被任命为皇家研究院自然哲学教授。下面的描述出自Taylor [3]，其中引用了Tyndall的话：-

[皇家研究院]周五晚间演讲的演讲者来自世界许多地方，值得记录一次特别令人难忘的夜晚，这次夜晚由约翰 Tyndall报道。那是利萨茹于1857年访问皇家研究院。

利萨茹曾在鼓励协会和法国皇帝[拿破仑三世]本人面前展示了他关于振荡组合的实验。Tyndall对这些演示很感兴趣，并计划重复它们，但当咨询利萨茹时，他提出自己来伦敦。Tyndall报道了讲座的细节，并记录说，在讲座开始时，利萨茹：“……祝贺观众有M Duboscq在场，他负责自己的电灯；这是这次使用的光源。”

演示开始时，一束光从灯投射到演讲者手中的镜子上；当他快速移动镜子时，他可以在天花板上产生一个光环和各种其他图形，从而说明视觉暂留，这是许多其余演示的一个基本特征。然后他进行了许多实验，展示了我们现在所知的‘利萨茹图形’。

例如，他把一面小镜子固定在一支音叉的一个叉股上，并安排一束光从这面镜子反射到手持的镜子上。

当用琴弓拉过音叉时，像便伸长成一条线。通过转动手中的镜子，屏幕上的像分解成一条明亮的蜿蜒轨迹，长达许多英尺。

接着他展示了各种振动组合，其中包括最常与他名字联系在一起的那种：光先落在一支音叉所附的镜子上，然后再落到第二支音叉所附的镜子上，第二支音叉的放置使光束所获得的振动与第一支所给的振动成直角。

他还演示了他的“phonoptomètre”。这是一台显微镜，其物镜固定在一支音叉上，因而可以沿某一特定方向振动。如果通过这台显微镜观察另一个振动物体，例如一根弦，使两种振动成直角，那么音叉的频率与受试物体频率之比就可以相当精确地确定。

在这一系列精彩的实验结束时——多亏了进行实验者的技巧，这些实验全部成功——经麦可·法拉第先生提议，与会者一致投票感谢利萨茹先生和迪博斯克，并由院长诺森伯兰公爵阁下转达给这两位先生。

协助利萨茹进行这次演示的迪博斯克自己发明了Bioscope，一种用于显示运动三维图片的观看器。十二对或更多对照片图像被放置在一个纸板圆盘周围，每对图像上下排列。这些图片可以通过两面成角度的小镜子观看。它的销量有限——事实上，已知只有一台观看器留存下来。利萨茹对这个仪器中包含的巧妙想法印象深刻，但怀疑它是否具有商业可行性：-

这个仪器特别引人注目，因为它代表了一个难题的解决方案，但不幸的是，它没有批量销售的机会，因为所需的图片数量非常多：至少需要32张图片。

实际上，最少数量是24张，但也许利萨茹所看到的唯一一套中有16对。尽管利萨茹对这个特定仪器的看法是正确的，当然，顺序显示静止图片的方法被采用于胶片电影。

利萨茹因其工作受到同时代人的赞扬，并于1873年因他对振动的光学观察，特别是“因他那些漂亮的实验”而获得Lacaze奖。也许“他那些漂亮的实验”成为获奖的一个主要因素是完全公平的，因为利萨茹图形早在四十年前就由纳撒尼尔·鲍迪奇研究过。他在1815年用复摆产生了这些图形，因此，这些图形有时被称为纳撒尼尔·鲍迪奇图形或利萨茹-纳撒尼尔·鲍迪奇图形。然而我们应当注意，利萨茹的工作与纳撒尼尔·鲍迪奇的工作完全无关。

利萨茹图形成为物理学教材和演示中的一个标准主题。这些实验在1867年的巴黎世界博览会上展出。我们在上文已经注意到约翰对利萨茹实验的讨论，他在自己的声学教材中详细描述了这些实验。瑞利在其经典的声学论著中也讨论了利萨茹图形。赫尔曼·冯·亥姆霍兹在研究弦振动时使用了利萨茹的仪器。

插图：ABC.gif ↗也许今天澳大利亚人对利萨茹图形最为熟悉，因为澳大利亚广播公司（ABC）自1965年以来一直使用这样的图形作为其标志。如果利萨茹在演示中制作出这个标志，他需要使用两个成直角的音叉，一个的振动频率是另一个的三倍。

Jules Lissajous entered the École Normale Supérieure in 1841. In 1847 he became professor of mathematics at the Lycée Saint-Louis, holding this position until 1874. He was awarded a doctorate in 1850 for a thesis on vibrating bars using Chladni's sand pattern method to determine nodal positions. 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. He wanted to be able to see the waves that were created by vibrations, usually expressed in the form of sound. At first he studied waves produced by a tuning fork in contact with water, studying the ripples that were caused. Working on these ideas, he published Sur la position des noeuds dans les lames qui vibrent transversalement Ⓣ (1850). In 1855 he described a way of studying acoustic vibrations by reflecting a light beam from a mirror attached to a vibrating object onto a screen. He published Sur un cas particulier de stéréoscopie fourni par l'étude optique des mouvements vibratoires Ⓣ (1856), then his major work Mémoire sur l'étude optique des mouvements vibratoires Ⓣ (1857) which is an 85 page paper. In the following year he published Sur les vibrations transversales des lames élastique Ⓣ.

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. The curves are only seen because of persistence of vision in the human eye. Lissajous studied beats seen when his tuning forks had slightly different frequencies, in this case a rotating ellipse is seen. Perhaps he gained greatest fame through the quality of his lectures and fortunately we have a detailed description of one of his famous lectures by John Tyndall who had been named as Professor of Natural Philosophy at the Royal Institution in 1853. The description below is by Taylor [3], with quotations from Tyndall:-

Lecturers at the Friday Evening Discourses [at the Royal Institution] come from many parts of the world and it is worth recording one particularly memorable evening that was reported by John Tyndall. It was a visit by Jules Antoine Lissajous to the Royal Institution in 1857.

Lissajous had exhibited his experiments on the combination of oscillations before the Societé d'Encouragement and before the French Emperor [Napoleon III] himself. 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: "... congratulated the audience on the presence of M Duboscq who took charge of his own electric lamp; this being the source of light made use of on this occasion."

The demonstration began with a 'sheaf of light' thrown from the lamp on to a mirror held in the lecturer's hand; when he moved the mirror quickly he could produce a ring of light on the ceiling and various other figures, thus illustrating the persistence of vision that is an essential feature of many of the remainder of the demonstrations. He then performed a number of experiments demonstrating what we now know as 'Lissajous figures'.

For example he attached a small mirror to one prong of a tuning fork and arranged for a beam of light to be reflected from this mirror on to the hand held mirror.

When a violin bow was drawn across the fork the image elongated itself to a line. By turning the mirror in the hand, the image upon the screen was resolved into a bright sinuous track many feet in length.

He then went on to show various combinations of oscillations including the one most commonly associated with his name in which the light falls first on a mirror attached to one tuning fork and then to a mirror on a second tuning fork placed so that the oscillation given to the light beam is at right angles to that given by the first.

He also demonstrated his 'phonoptomètre'. This was a microscope in which the objective was attached to a tuning fork so that it could be made to vibrate along a particular direction. If some other vibrating object, such as a string, was viewed through the microscope so that the two oscillations were at right angles, the frequency ratio between that of the fork and that of the object under test could be established with considerable precision.

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. Twelve or more pairs of photographic images were placed around a cardboard disc, the images of each pair arranged one above the other. The pictures could be viewed through two small angled mirrors. It had only a limited sale - in fact only one viewer is known to have survived. Lissajous was very impressed by the clever idea contained in this instrument but doubted that it was a commercial proposition:-

This apparatus which is particularly remarkable because it represents the solution to a difficult problem, has, unfortunately, no chance of being sold in quantity, since the number of pictures need is very considerable: not less than 32 pictures are required.

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. The experiments were exhibited at the Paris Universal Exhibition in 1867. 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.

插图：ABC.gif ↗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.