约瑟夫·佩兹瓦尔Joseph Petzval

约瑟夫·佩兹瓦尔的名字有不同版本，除了这里给出的之外，他常被称为Jozef Maximilian Petzval，但他的姓氏有时写作Pecval、Peczival或Pecivál。在给出不同版本的同时，我们还要指出，他出生的城镇是Spisská Belá，有时写作Szepesbéla。佩兹瓦尔出生时，该镇属于匈牙利，但现在位于斯洛伐克。事实上，由于欧洲这一地区历史上经历过不同民族，所有名字都有多个不同版本，我们意识到在下面给出的名字中我们并不一致。

约瑟夫是校长约翰（扬）Friedrich Petzval及其妻子苏珊娜（祖扎娜）克罗伊茨曼的儿子。苏珊娜是佩兹瓦尔和苏珊娜·克罗伊茨曼的女儿，于1776年4月20日在斯皮什斯卡贝拉受洗。约翰于1775年7月4日出生在洛德尼采，在斯皮什斯卡贝拉的福音派学校任教，并[13]：-

……对佩兹瓦尔产生了巨大影响。约翰·弗里德里希是个多才多艺的人，是一位极具天赋的音乐家、作曲家和业余机械师。他为所在地区的教堂做出了持久的音乐贡献，但也制造钢琴，为匈牙利军队改进马鞍，甚至研究过Perpetuum——一种早期的飞行器。他以非常古怪而闻名，人们常常会发现他穿着睡衣指挥教堂唱诗班。

约泽夫是他父母的六个孩子之一（实际上是七个，但有一个在婴儿期夭折）。他有一个弟弟奥托Balthasar Petzval，生于1809年1月6日。注意这个巧合：两兄弟同一天出生，但更大的巧合是第三个兄弟扬只差一天，生于1月7日，也有人说也是1月6日。1月6日是基督教的主显节，三位国王梅尔基奥、卡斯帕和巴尔塔萨在这一天探望新生的耶稣，因此约瑟夫的弟弟被命名为奥托·巴尔塔萨。毫不奇怪，这三兄弟在家里被称为“三王”。在此阶段我们注意到，Otto Petzval也成为数学教授，并出版了Elementary mathematics（匈牙利文）（1856年）和Higher mathematics（匈牙利文）（1867年）。另外三个孩子是女孩，其中一个是玛丽亚·玛蒂尔达。

Johann因教堂问题不得不离开Spisská Belá，1815年全家搬到Késmárk。佩兹瓦尔在Késmárk（今斯洛伐克的Kežmarok）上小学，之后在Podolin（今Podolínec）上中学。他在Levoca完成学业，全家于1819年搬到那里。起初他最好的科目是拉丁语和宗教研究，而数学表现很差，对这门学科毫无兴趣。佩兹瓦尔的老师建议他父亲让他退学去学一门手艺，家里考虑让他去当鞋匠学徒。然而，他发现了一本有趣的数学书，即Mathias Hauser所著的Analytische Abhandlung der Anfangsgründe der Mathematik Ⓣ（《数学基础分析论》）（1807年）。他在整个夏天研读这本书，成绩显著提高，以至于秋天返校时他已是班上最好的数学学生。1823年离校后，他前往Košice（当时名为Kassa），在那里上过一段时间中学，但经济拮据，被迫做家庭教师挣钱维生。他跟Barlai教授——数学与哲学教授——学习了两年。完成学业后，他担任了Almássy伯爵家的家庭教师一年。

1826年，佩兹瓦尔进入佩斯大学（今厄特沃什·罗兰罗兰大学）的几何学院学习哲学和数学。后来，1872年，佩斯城与多瑙河对岸的布达城合并，形成了布达佩斯。当时大学的主要教学语言是德语，直到1860年匈牙利语才成为教学语言。在大学学习的两年里，他研读了西尔维斯特·佛朗索瓦·拉克鲁瓦、皮埃尔·西蒙·拉普拉斯和约瑟夫·拉格朗日的著作。他还在学生中因高超的击剑技艺而声名鹊起。1828年从大学获得工程学位后，佩兹瓦尔被任命为佩斯城的防洪和排水专家。他从事这项工作七年，在工作中展现出了真正的才能。

佩兹瓦尔从1832年起在佩斯大学讲授力学和数学，并于1835年成为佩斯大学高等数学教授。两年后，他接受了维也纳大学的数学讲席。我们注意到，佩兹瓦尔离开佩斯大学后不久，他的兄弟Otto Petzval于1839年被任命为佩斯大学高等数学教授，一直担任此职直到1883年去世。

佩兹瓦尔一生大部分时间都在研究拉普拉斯变换。他受到约瑟夫·刘维尔工作的影响，撰写了一篇长论文和一部两卷本专著，论述皮埃尔·西蒙·拉普拉斯变换及其在常线性微分方程中的应用。他的研究很透彻，但并不完全令人满意，因为他无法使用围道积分来反演该变换。但若不是佩兹瓦尔的学生，我们今天可能会把皮埃尔·西蒙·拉普拉斯变换称为佩兹瓦尔变换。佩兹瓦尔与这个学生闹翻，后者随后指责佩兹瓦尔剽窃了皮埃尔·西蒙·拉普拉斯的工作。尽管这是不实的，但乔治·布尔和儒勒·昂利·庞加莱无疑受到这场争吵的影响，将该变换称为皮埃尔·西蒙·拉普拉斯变换。塞纳希写道[5]：-

……在[19]世纪，[匈牙利]科学家在微分方程理论方面取得了特别出色的成果。……必须特别提到约瑟夫·佩兹瓦尔，他在发表了一系列关于自己显著成果的文章之后，于[19]世纪中叶出版了一部两卷本微分方程专著，在很长一段时间内是该领域唯一的指南[《线性微分方程的积分》Ⓣ（Integration of linear differential equations）（第1卷，1853年；第2卷，1859年）]。几十年后，它仍将被视为主要文献来源。在他的原创成果中，最重要的是关于带复变量的线性微分方程的奇解。他在这方面的研究比波恩哈德·黎曼更深入，并在若干方面领先于儒勒·昂利·庞加莱。如今相当完整的雅各布·黎卡提微分方程理论在很大程度上归功于他。

佩兹瓦尔最为人所铭记的是他在19世纪40年代初关于光学透镜和透镜像差的工作（佩兹瓦尔曲率以他命名），这使得现代相机的制造成为可能。佩兹瓦尔生产了一种消色差人像镜头，远远优于当时使用的简单弯月透镜。在[11]中，他在光学方面的工作描述如下：-

[在维也纳大学]他详细研究了L M Daguerre的发明，即所谓的达盖尔银版法，并着手将其曝光时间从几分钟缩短到几秒。1840年，他非凡的数学才能使他能够评估并制造出一种光度提高六倍的无像散镜头。这种佩兹瓦尔高度明亮的早期照相镜头形式被富有进取心的维也纳光学家Voigtländer采用，他将其投入批量生产，并在巴黎世界博览会上赢得了银牌。佩兹瓦尔还完善了望远镜并设计了观剧镜。

这一描述实际上掩盖了佩兹瓦尔遇到的许多困难。在被任命为维也纳大学数学讲席后，他在维也纳森林的卡伦山租了一座废弃的修道院，并在那里建立了自己的玻璃工坊。他设计的肖像镜头是对先前镜头的巨大改进，佩兹瓦尔已于1840年5月完成了计算。他将设计交给了由Peter Wilhelm Friedrich Voigtländer（1812-1878）经营的Voigtländer & Sohn 公司，并为此获得了一小笔钱。Voigtländer的公司由其祖父Johann Christoph Voigtländer于1756年创立，于1841年推出了一款使用佩兹瓦尔镜头设计的相机，它彻底改变了肖像摄影。Voigtländer发了财，但佩兹瓦尔没有申请专利，也没有收到版税。他与Voigtländer闹翻，并试图在卡伦山的工坊里制造他的镜头。军事地理研究所找上门来，请他设计一款风景镜头。他照做了，并设计出一款再次大大改进了当时所用镜头的镜头。大约1854年，他与光学家Carl Dietzler合作讨论了将镜头推向市场的事宜。1856年，他在利奥波第那科学院的一次会议上展示了他的镜头，但是，尽管他的工作受到了极大的欢迎，Dietzler的公司还是在1862年破产了。Voigtländer再次利用佩兹瓦尔的设计来推销自己的相机，进一步加深了两人之间的敌意。

佩兹瓦尔如今因其在光学方面的杰出工作而得到认可，但他对事情的结果如此失望，以至于放弃了所有光学方面的工作，甚至停止讲授这一学科。最后一根稻草出现在1859年，他的家被盗，他正在撰写的一部光学论著的手稿被毁。此后他转向声学研究，但他仍在1861年成为摄影学会的创始人，不过谢绝了会长一职，宁愿被授予荣誉会员资格。

佩兹瓦尔在与佩兹瓦尔的争论中似乎完全正确，但不幸的是，他也与克里斯蒂安·多普勒发生过争论，而在那场争论中他完全错了。问题的出现有若干原因。首先，⟦N3⟧把摄影视为肖像和风景的一种艺术形式，而不是科学研究的工具。其次，他坚信科学发现必须牢固地建立在数学基础之上，只有能够用微分方程描述的科学，对他来说才是真正的科学。正是这些信念导致他对克里斯蒂安·多普勒关于光的理论发起了完全错误的攻击。

Austrian Academy of Sciences于1846年在维也纳成立。克里斯蒂安·多普勒于1848年当选为科学院院士，佩兹瓦尔于1851年当选。两人之间首次出现麻烦的迹象是在1851年，在5月27日的会议上，克里斯蒂安·多普勒提议科学院为达盖尔照相法的改进设立奖项。佩兹瓦尔反对这一提议，此事便未再推进。佩兹瓦尔究竟反对什么，目前还不太清楚。也许他认为自己是这方面的专家，克里斯蒂安·多普勒不应涉足他的领域。也许他认为自己的工作已经超越了这项竞赛的基本前提。

佩兹瓦尔对克里斯蒂安·多普勒发起了另一次攻击，抨击克里斯蒂安·多普勒原理，该原理将光源的频率与其相对于观察者的速度联系起来。克里斯蒂安·多普勒在1842年的论文Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels Ⓣ（《论双星和天上其他一些星的彩色光》）中提出了这一原理。克里斯蒂安·多普勒用几行推导出了这一原理，将光和声分别视为以太和物质中的纵波。当然，尽管克里斯蒂安·多普勒原理是正确的，并且对天文学研究极其重要，但克里斯蒂安·多普勒论文中的许多内容是不正确的，特别是他认为克里斯蒂安·多普勒原理解释了双星的不同颜色。佩兹瓦尔的攻击发生在1852年1月15日奥地利科学院的会议上，他在会上宣读了他的论文Über die Unzukömmlichkeiten gewisser populärer Anschaungsweisen in der Undulationstheorie und ihre Unfähigkeit des Princip der Erhaltung der Schwingungsdauer zu ersetzen Ⓣ（《论某些流行的波动理论看法的不可取性及其无法取代波长保持原理》）。该文后来于1852年发表在Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Classe Ⓣ（《帝国科学院会议报告。数学与自然科学》）上。他的攻击基于这样一个事实：克里斯蒂安·多普勒仅用简单方程就在几行内推导出了该原理。佩兹瓦尔在他的论文中声称：-

不应用微分方程，就不可能进入伟大科学的领域。

Academy1852年1月15日会议的纪要写道[1]：-

……正式成员佩兹瓦尔教授作了题为“论某些流行的波动理论看法的不可取性及其无法取代波长保持原理”的演讲。他提交了会议报告的手稿。正式成员克里斯蒂安·多普勒教授随后宣读了一篇题为“关于论文：论波动理论的一般原理的评论”的短文，并将其提交给会议报告。正式成员主任van Ettingshausen也宣读了对所提及论文的一些评论，这些评论也拟用于报告。

Alec Eden 写道 [1]：-

在这些反对意见中，佩兹瓦尔混淆了两种完全不同的情况：一种是声源与听者之间存在相对运动，另一种是介质在运动而声源与听者静止。在第二种情况下，根据克里斯蒂安·多普勒原理，音调没有变化。事实上，佩兹瓦尔长期而激烈的攻击——在1852年5月21日由Andreas von Baumgartner主持的奥地利科学院会议上达到高潮——最终被证明是克里斯蒂安·多普勒理论的最佳数学证明。

1852年10月21日科学院的第三次会议再次见证了佩兹瓦尔攻击克里斯蒂安·多普勒，但此时克里斯蒂安·多普勒已病重无法为自己辩护，并已南下希望恢复健康。佩兹瓦尔的攻击是恶毒的（例如见[4]）：-

人们不能确切地说克里斯蒂安·多普勒的理论毫无价值，因为它以一种绝对不正确的方式指出了某一现象的事实。相反，人们必须说它具有负面价值，因为它通过一种简单和清晰的幻觉，使许多对该科学感兴趣的人被误导，而这种幻觉不过是肤浅的，缺乏理解的深度。

所有这一切的结果是，Academy支持了佩兹瓦尔的信念，即克里斯蒂安·多普勒的理论是不正确的，尽管自首次提出以来它已被实验多次验证。

这场争论由Egon von Opplzer于1901年在维也纳大学克里斯蒂安·多普勒雕像揭幕仪式上的演讲中作了总结[1]：-

他的对手佩兹瓦尔在奥地利科学院上把“大科学”和“小科学”之类的说法挂在嘴边，认为伟大的真理不可能在几行字里、通过一个只有一个未知数的方程找到，至少需要一个微分方程——他以此认为自己已经证明了克里斯蒂安·多普勒原理的不正确性。谁若探究得稍深一些，就会在这些攻击中发现，其动机并非纯粹科学的，而是更为个人的目标。这是天才与才能之间古老的对立，当才能一方不理解直觉行动与个人才华时，这种对立必然导致斗争。对克里斯蒂安·多普勒来说，审视自己的原理，这是清楚确定的；而对他——一位真正的自然研究者——来说，对一条已经通过实验得到证实的定律的攻击是完全不可理解的。他以事实为据、果断地作了回应。

作为教师，佩兹瓦尔深受学生喜爱[15]：-

作为维也纳大学的数学教授，他以生动的讲课和令人难以置信的独特教学风格而闻名。他讲授光学、线性方程与微分方程、分析力学、声学、弹道学和机械振动。佩兹瓦尔对学术教学方法非常批判——这大概是他从自己童年所遇到的有限教学风格的经验中发展出来的。他非常直言不讳地反对自己的系和大学行政当局，并努力把想象力和创造力带入课堂。

1869年1月，佩兹瓦尔娶了他的管家Katarina Schlegl。他当时62岁，但我们未能查明Katarina的年龄。遗憾的是，她三年后去世了。1877年，年满70岁的佩兹瓦尔从维也纳大学的教授职位上退休。此后，他退居卡伦山，在那里度过了生命最后14年，基本上独自生活。他在卡伦山上唯一的陪伴似乎就是他的马。他去世时，葬礼上没有家庭成员，只有几个学生、两三个老朋友和一位维也纳大学的代表。1905年，维也纳市长回忆说，佩兹瓦尔曾是一位伟人和伟大的学者，为维也纳市带来荣耀，也为维也纳大学带来荣耀。市长说，因为他，维也纳成了世界摄影中心。然而，他说，尽管佩兹瓦尔在维也纳生活了54年，他仍然忠于自己的祖国，他仍然是匈牙利人。

佩兹瓦尔因其工作赢得了许多荣誉。除上述之外，他于1873年当选为匈牙利科学院成员，1881年成为捷克数学家和物理学家联合会荣誉成员，并获得了法国颁发的查尔斯·舍瓦利耶铂金奖章。维也纳有一条街道以他的名字命名，月球背面的一座环形山也是如此。

Szénássy写道[5]：-

学生们喜欢佩兹瓦尔，认为他是一位真正坚定而乐于助人的朋友，但他的同事们却因他的强烈批评而深受其苦。

There are different versions of Józeph Petzval's name, and, in addition to the one given here, he is often known as Jozef Maximilian Petzval but his family name sometimes appears as Pecval, Peczival or Pecivál. While giving different versions, let us also remark that the town of his birth is Spisská Belá which is sometimes written as Szepesbéla. This town was in Hungary when Petzval was born there but it is now in Slovakia. In fact since this area of Europe has seen different peoples over time all names have several different versions and we realise that we have not been consistent in the names we give below.

Jozef was the son of the schoolmaster Johann (Ján) Friedrich Petzval and his wife Susanna (Zuzana) Creutzman. Susanna, the daughter of Joseph and Susanna Creutzman, was baptised in Spisská Belá on 20 April 1776. Johann, born on 4 July 1775 in Lodenice, taught in the evangelical school in Spisská Belá and [13]:-

... was a great influence on Joseph. A well-rounded man, Johann Friedrich was an incredibly gifted musician, composer, and hobby mechanic. He made a lasting musical contribution to the churches in their district, but also made pianos, improved the riding saddle for the Hungarian military, and even worked on the Perpetuum - an early flying machine. He was known for being very eccentric and would often be found directing the church choir in his pyjamas.

Jozef was one of his parents' six children (actually seven but one died while a baby). He had a younger brother Otto Balthasar Petzval who was born on 6 January 1809. Note the coincidence that both brothers were born on the same day but an even greater coincidence is that the third brother Ján was only one day different, born on 7 January, or some say also on 6 January. The 6 January is the Christian festival of the Epiphany when the three Kings, Melchior, Caspar and Balthasar, visited the new born Jesus and hence the naming of Josef's brother as Otto Balthasar. Unsurprisingly the three brothers were known in their family as the "Three Kings". Let us note at this stage that Otto Petzval also became a professor of mathematics and published Elementary mathematics (Hungarian) (1856) and Higher mathematics (Hungarian) (1867). The other three children were girls, one of whom was Maria Mathilda.

Johann had to leave Spisská Belá because of problems in his church, and in 1815 the family moved to Késmárk. Joseph attended primary school in Késmárk (now Kezmarok in Slovakia) and, after that, the gymnasium at Podolin (now Podolinec). He completed his schooling in Levoca where the family moved in 1819. At first his best subjects were Latin and religious studies while he performed badly in mathematics having no interest in the topic. Petzval's teacher advised his father that he should leave school and take up a trade and the family considered having him become an apprentice to a cobbler. However, he found an interesting book on mathematics, namely Analytische Abhandlung der Anfangsgründe der Mathematik Ⓣ (1807) by Mathias Hauser. He studied this book over the summer and his performance improved markedly so that when he returned to school in the autumn he was now the best mathematics student in his class. After leaving school in 1823 he went to Košice (named Kassa at the time) where he attended the Lyceum for a while but he was financially poor and was forced to undertake work as a tutor to earn money to survive. He spent two years studying with Professor Barlai, the Professor of Mathematics and Philosophy. After completing his studies, he took a one-year position as a tutor employed by Count Almássy.

In 1826 Petzval entered the Institutum Geometricum of the University of Pest (today the Eötvös Loránd University) to study philosophy and mathematics. Later, in 1872, the town of Pest was to join with the town of Buda on the opposite bank of the Danube to form Budapest. The main language of instruction at the university at this time was German and not until 1860 did Hungarian become the language of instruction. During his two years at the university he studied the works of Lacroix, Laplace and Lagrange. He also made quite a reputation for himself in the student body as a highly skilled fencer. After graduating from the University with an engineering degree in 1828, Petzval was appointed to the city of Pest as an expert in flood prevention and drainage. He undertook this work for seven years and showed real talents in his job.

Petzval taught mechanics and mathematics at the University of Pest from 1832 and he became a professor in Higher Mathematics at the University of Pest in 1835. Then, two years later, he accepted a chair of mathematics at the University of Vienna. We note that soon after Petzval left the University of Pest, his brother Otto Petzval was appointed as a professor of Higher Mathematics at the University of Pest in 1839, a position he held until his death in 1883.

Petzval worked for much of his life on the Laplace transform. He was influenced by the work of Liouville and wrote both a long paper and a two volume treatise on the Laplace transform and its application to ordinary linear differential equations. His study is thorough but not entirely satisfactory since he was unable to use contour integration to invert the transform. But for a student of Petzval we might today call the Laplace transform the Petzval transform. Petzval fell out with this student who then accused Petzval of plagiarising Laplace's work. Although this was untrue, George Boole and Henri Poincaré, influenced no doubt by the quarrel, called the transformation the Laplace transform. Szénássy writes [5]:-

... in the [19th] century [Hungarian] scientists obtained particularly nice results in the theory of differential equations. ... special mention must be made of Józef Petzval who, after a whole range of articles on remarkable results of his own, around the middle of the [19th] century published a two-volume monograph on differential equations that was the only guide in the field for a long time [Integration der linearen Differentialgleichungen Ⓣ (Vol. 1, 1853; Vol. 2, 1859)]. Decades later it will still be referred to as a major source. Among his original results, the most important ones concern the singular solutions to linear differential equations with a complex variable. He went deeper into this subject than Riemann and was ahead of Poincaré in several respects. The nowadays fairly complete theory of Riccati's differential equations owes a lot to him.

Today Petzval is best remembered for his work on optical lenses and lens aberration done in the early 1840's (Petzval curvature is named after him) which allowed the construction of modern cameras. Petzval produced an achromatic portrait lens that was vastly superior to the simple meniscus lens then in use. In [11] his work in optics is described as follows:-

[At the University of Vienna] he studied in detail L M Daguerre's invention, the so-called daguerreotype, and took on shortening its exposure time from minutes to seconds. In 1840, his extraordinary mathematical talent allowed him to assess and build an anastigmatic with six times greater luminosity. This Petzval highly luminous early form of photo lens was used by the enterprising Viennese optician Voigtländer, who launched its mass production and won a silver medal at the World's Exhibition Fair in Paris. Petzval also perfected the telescope and designed the opera glasses.

This description actually hides a lot of the difficulties that Petzval encountered. After he was appointed to the chair of mathematics at the University of Vienna he rented an abandoned monastery on the Kahlenberg mountain in the Vienna Woods and there set up his own glass workshop. The portrait lens he designed was a great improvement on previous lenses and Petzval had completed the calculations by May 1840. He handed the design over to the company Voigtländer & Sohn run by Peter Wilhelm Friedrich Voigtländer (1812-1878) and received a small sum for them. Voigtländer's company, which had been founded by his grandfather Johann Christoph Voigtländer in 1756, marketed a camera using Petzval's lens design in 1841 and it revolutionised portrait photography. Voigtländer made a fortune but Petzval had not taken out patents and received no royalties. He fell out with Voigtländer and attempted to construct his lens at his workshop on the Kahlenberg. He was approached by the Military Geographic Institute and they asked him to design a landscape lens. He did so and produced the design of a lens which again vastly improved on what was in current use. In collaboration with the optician Carl Dietzler they discussed marketing the lens around 1854. He presented his lens at a meeting of the Academy of Sciences Leopoldina in 1856, but, although his work was received with great enthusiasm, Dietzler's firm went bankrupt in 1862. Voigtländer again used Petzval's designs to market his own cameras, further increasing the enmity between the two men.

Although Petzval is now recognised for his remarkable work on optics, he was so disillusioned by how things turned out that he gave up all his work on optics and even stopped lecturing on the subject. The last straw came in 1859 when his home was burgled and the manuscript of a treatise on optics which he was writing was destroyed. After that he turned to research in acoustics but he still was a founder of the Photographische Gesellschaft in 1861 but declined the offer of the presidency, preferring instead to be awarded an honorary membership.

Petzval seems to have been entirely in the right over his arguments with Voigtländer but, unfortunately, he also had an argument with Christian Doppler where he was totally incorrect. The problems arose for a number of reasons. First Petzval considered photography as an art form for portraits and landscapes, not as a tool in scientific research. Secondly, he was a firm believer in scientific discoveries being firmly mathematically based and only if one could describe the science via differential equations was it, for him, proper science. It was these beliefs that led to his completely incorrect attack on Doppler's theories regarding light.

The Austrian Academy of Sciences was founded in Vienna in 1846. Christian Doppler was elected to the Academy in 1848 and Petzval in 1851. The first sign of trouble between the two occurred in 1851 when, at the 27 May meeting, Doppler proposed that the Academy offer a prize for improvements in the Daguerre photographic process. Petzval objected to this proposal and it was not taken further. It is a little unclear what Petzval objected to. Perhaps he considered he was the expert and Doppler should not stray into his area. Perhaps he considered that his work had already overtaken the basic premise of the competition.

Soon Petzval launched another attack on Doppler, attacking the Doppler principle which relates the frequency of a source to its velocity relative to an observer. Doppler had proposed this in his 1842 paper Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels Ⓣ. Doppler derived the principle in a few lines treating both light and sound as longitudinal waves in the ether and matter, respectively. Although, of course, the Doppler principle is correct and extremely important for astronomical research, nevertheless much of Doppler's paper is incorrect, in particular his belief that the Doppler principle explained the different colours of binary stars. Petzval's attack came at the meeting of the Austrian Academy of Sciences on 15 January 1852 where he presented his paper Über die Unzukömmlichkeiten gewisser populärer Anschaungsweisen in der Undulationstheorie und ihre Unfähigkeit des Princip der Erhaltung der Schwingungsdauer zu ersetzen Ⓣ. It was published later in 1852 in Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften. Mathematisch-Naturwissenschaftliche Classe Ⓣ. His attack was based on the fact that Doppler derived the principle in a few lines using only simple equations. Petzval claimed in his paper:-

Without the application of differential equations, it is not possible to enter the realms of great science.

The minute of the Academy's meeting of 15 January 1852 reads [1]:-

... the full member, Professor Petzval held a lecture 'On the unsuitability of certain popular ways of looking at the undulation theory and their inability to replace the principle of maintenance of the wavelength'. He presented the manuscript for the report on the meeting. The full member, Professor Doppler, hereupon read a note entitled 'Remarks on the essays: on a general principle of the undulation theory' and presented this for the report on the meeting. The full member Director van Ettingshausen also read some remarks on the essay referred to which are also intended for the report.

Alec Eden writes [1]:-

In these objections Petzval confused two completely different cases: one in which there is relative movement between the sound source and the listener, and the other in which the medium is in motion but the sound source and listener are stationary. In the second case there is, according to the Doppler principle, no change in tone. In fact, Petzval's protracted and hard attacks, which came to a head during the meeting of the Austrian Academy of Sciences under the presidency of Andreas von Baumgartner on 21 May 1852, were eventually shown to be the best mathematical proof of Doppler's theory.

A third meeting of the Academy on 21 October 1852 again saw Petzval attack Doppler but by this time Doppler was too ill to defend himself and had travelled south hoping to restore his health. Petzval's attack was vicious (see for example [4]):-

One cannot say exactly that Doppler's theory is of no value because it points to the facts of a phenomenon in a way that is definitely incorrect. On the contrary one has to say it has negative value because it has caused so many interested in that science to be misled through an illusion of simplicity and clarity which, however, is nothing more than superficial and lacks depth of understanding.

The result of all this was that the Academy supported Petzval belief that Doppler's theory was incorrect despite the fact that it had been verified experimentally many times since it was first proposed.

The dispute was summed up by Egon von Opplzer in 1901 at a speech he gave of the unveiling of a statue of Doppler in the University of Vienna [1]:-

His opponent [Petzval] bandied with such expressions as 'great science' and 'small science' in the Austrian Academy of Sciences, being of the opinion that great truths could not be found in a few lines and through an equation with only one unknown, and that at least one differential equation is necessary - and in this way he believes to have shown the incorrectness of the Doppler principle. Whoever probes somewhat deeper will find in these attacks, not a purely scientific motive, but a more personal goal. It is the old contradiction between genius and talent which must lead to a struggle when, on the side of the talent there is no understanding of intuitive action and individual brilliance. For Doppler, surveying his principle, it is of clear certainty, and for him - a true natural researcher - the attack on a law that has already been confirmed through experiments is completely incomprehensible. He responded in a factual and decisive manner.

As a teacher, Petzval was well-liked by his students [15]:-

As Professor of Mathematics at the University of Vienna, he was known for his lively lectures and incredibly unique teaching style. He lectured on optics, linear and differential equations, analytical mechanics, acoustics, ballistics and mechanical vibrations. Petzval was very critical of academic teaching methods - a feat he probably developed out of his own experience with the limited teaching styles which he encountered as a child. He was very outspoken against his department and the university administration and strove to bring imagination and creativity into his classes.

In January 1869 Petzval married his housekeeper Katarina Schlegl. He was 62 years old at this time but we have been unable to find out Katarina's age. Sadly, she died three years later. In 1877, on reaching the age of 70, Petzval retired from his professorship at the University of Vienna. After this, he retired to the Kahlenberg where he lived essentially alone for the final 14 years of his life. His only company on the Kahlenberg seems to have been his horse. When he died there were no family members at his funeral, only a few students, a couple of old friends and a representative of the University of Vienna. In 1905 the mayor of Vienna recalled that Petzval had been a great man and a great scholar who brought glory to the city of Vienna and glory to the University of Vienna. Because of him, said the mayor, Vienna had become a world centre for photography. However, he said that although Petzval had lived in Vienna for 54 years he had remained faithful to his native country, he remained Hungarian.

Petzval won many distinctions for his work. In addition to those mentioned above, he was elected a member of the Hungarian Academy of Sciences in 1873, an honorary member of the Union of Czech Mathematicians and Physicists in 1881, and he received the platinum medal of Charles Chevalier from France. A street in Vienna bears his name as does a crater on the far side of the Moon.

Szénássy writes [5]:-

Students liked Petzval and considered him a true firm and helpful friend, but his colleagues suffered much from his strong criticism.