海因里希·鲁道夫·赫兹Heinrich Hertz

海因里希·鲁道夫·赫兹的父母是Gustav Ferdinand Hertz和Anna Elisabeth Pfefferkorn。古斯塔夫·赫兹是一名改宗路德宗的犹太人。Anna是一位法兰克福医生的女儿，来自路德宗家庭，因此赫兹自幼按路德宗信仰抚养。他是父母五个孩子中的长子，有三个弟弟和一个妹妹。Gustav是汉堡的一名律师，后来升任Oberlandsgerichtsrat，最终于1887年成为参议员。我们注意到，赫兹的一个兄弟名叫赫兹，他有一个儿子也叫古斯塔夫·赫兹，此人在本档案中也有传记。

赫兹的正规教育始于六岁，当时他被送入由Richard Lange [1]开办的一所私立学校：-

……一位容不得错误的严师。赫兹的母亲密切关注他的功课，决心让他成为——而他也确实成为了——班上的第一名。

赫兹在Richard Lange的学校学习了十年。他展现出多方面的才能：他有相当强的动手能力，用别人给他的工具做木工，后来还用车床制作仪器来做实验。他也有出色的语言天赋，无论现代语言还是古典语言。1872年，他进入汉堡的Johanneum文理中学（Gymnasium），在那里他继续在众多科目上表现优异。他甚至请私人教师额外学习学校不提供的科目，如阿拉伯语和技术制图。他不仅擅长许多科目，而且喜欢这些科目，因此难以决定在大学里应该专攻什么。他应该学工程以发挥自己的动手能力，还是应该学习他同样热爱的自然科学？他在1875年春天参加了Abitur考试，决定以工程为职业后，他前往法兰克福积累实践经验。他做出了错误的决定。

赫兹在1875—76年间待在法兰克福，在那里他获得了建筑业的实践经验，也为工程学的国家考试而学习。在这个阶段他已经开始觉得工程学可能不是适合他的科目。他不喜欢那种工作环境，他太孤立了，他觉得这是由于在私营部门工作所致。他现在正艰难地接受自己做出了错误决定这一事实；他应该把花在这错误开端上的时间浪费掉并重新开始，还是应该将错就错坚持下去？他决定继续走工程这条路，1876年去德累斯顿理工学院短暂学习，随后离开去柏林服了一年兵役。在铁道团服完这一年兵役后，他去了慕尼黑，打算在那里的技术高等学校继续工程课程。此时他已非常清楚自己走错了路。方程中有几个新因素影响了这个问题，比如在消极方面，他对工程公司的工作环境感到不快，而在积极方面，他喜欢作为工程学习一部分而学到的数学。赫兹的父亲提供经济支持让他接受高等教育，所以如果他要改变方向，肯定需要父亲的同意。他向父亲解释了自己内心挣扎的问题，并问如果自己进入慕尼黑大学并以研究为职业，父亲是否会继续支持他。McCormmach写道[1]：-

对他而言，工程意味着业务、数据、公式——一种与装订书籍或木工相当的平凡生活——而他对此不感兴趣。虽然技术高等学校有一个很好的物理实验室，但在那里学习会导致国家考试，通常也通向一种实践性职业。相比之下，大学承诺一种永无止境的学习与研究生活，这适合赫兹的学术、理想主义品味；他首先知道自己想成为一名伟大的研究者。

这些论据说服了他的父亲，使他支持儿子改变方向。赫兹于1877年在慕尼黑大学注册入学，并在第一个学期补足了必要的数学基础。von Jolly建议他阅读约瑟夫·拉格朗日、皮埃尔·西蒙·拉普拉斯和西莫恩·德尼·泊松的著作[1]：-

赫兹认为，若正确把握，自然界的一切都是数学的；他在学生时代——正如在整个职业生涯中一样——主要对物理问题感兴趣，只是间接地对数学问题感兴趣。

他修读了物理学、动物学和天文学以及数学课程，第二学期同时在大学和工业学院上课。在慕尼黑一年后，他搬到柏林，并非因为对当时所做的事情不满，而是因为当时德国学生在机构之间流动是标准做法。在柏林，他师从赫尔曼·冯·亥姆霍兹和古斯塔夫·基尔霍夫。尽管只有一年的大学学习经历，赫兹立即想要开始研究。哲学系宣布了一个关于电惯性的实验问题的奖项，赫兹非常渴望参加。该奖项由赫尔曼·冯·亥姆霍兹提出，尽管赫兹缺乏经验，但他意识到自己的巨大潜力，并在他的物理研究所为赫兹提供了一个房间，并在指导赫兹阅读背景文献方面给予了相当大的支持。

赫兹知道自己在正确的道路上[1]：-

他写信回家说，他最大的满足在于寻求和传播关于自然的新真理。以任何其他方式忙碌，他都觉得自己是社会的一个无用成员；与研究工作相对的私人学习似乎是自私和放纵的。

1879年，他被授予哲学系奖和金牌。赫尔曼·冯·亥姆霍兹现在建议赫兹研究他提出的柏林科学院的奖项主题。这要求提供支持或反对詹姆斯·克拉克·麦克斯韦理论所依据的假设的实验证据。这对赫兹来说听起来很有趣，但他想在自己选择的领域迅速取得进展，并觉得自己不能开始一个可能需要大约三年的项目。他拒绝遵循赫尔曼·冯·亥姆霍兹的建议，而是写了一篇理论著作Über die Induction in rotirenden KugelnⓉ（关于旋转球体中的感应），关于电磁感应，并于1880年1月提交作为他的博士学位论文；他只用了三个月就完成了。赫兹关于与在平行于圆盘轴线的磁场中绕其对称轴旋转的圆盘相关的电磁场的工作在[7]中考虑。他在下个月参加了必要的口试，并被柏林大学以优异成绩授予博士学位。随后，他被聘为赫尔曼·冯·亥姆霍兹在柏林物理研究所的助手。

在1880至1883这三年间，赫兹在柏林物理研究所工作，撰写了十五篇涉及多种主题的论文。其中大多数与电学相关，两篇关于阴极射线，还有几篇涉及诸如新型电流计和新型湿度计这样的仪器。赫兹必须决定推进职业生涯的最佳方式。他已经身处进行物理学研究的最佳场所，并与赫尔曼·冯·亥姆霍兹合作，赫兹觉得后者是世界上最优秀的物理学家。然而，要在柏林成为privatdozent，他将与那里已经处于编外讲师职位的大量科学家竞争。他决定尝试利用数学物理学在德国各大学扩展的机会，尽管他真正的热爱在于实验，还是寻求一个数学物理学的编外讲师职位。基尔大学正好在寻找这一领域的人选，因此，在赫尔曼·冯·亥姆霍兹的强烈推荐下，他habilitated于基尔。

正是在基尔，赫兹首次展示了他作为讲师的优势。他故意选择了一所没有为研究配备物理实验室的大学的数学物理职位。因此，他进行了理论工作，在那里工作的两年中写了三篇论文。一篇关于气象学，一篇关于电磁单位，而第三篇最重要，因为它代表了他对詹姆斯·克拉克·麦克斯韦理论的第一项工作。两年后，他渴望回到一个具有强大实验声誉的机构，而卡尔斯鲁厄工业学院的特别教授职位似乎很理想。他接受了这个职位，并于1885年4月20日作了他的就职演讲On the energy balance of the Earth。（参见[24]，该演讲首次发表在那里。）卡尔斯鲁厄的工业学院今天是卡尔斯鲁厄大学，正是在这里，赫兹做出了他最重要的发现，即他的名字最常与之相关的发现，即他在1888年对长波长电磁波的著名发现。然而，当他第一次担任这个职位时，远不清楚他正处于伟大的边缘[1]：-

他的逗留开始得不顺利；有一段时间他感到孤独，不确定接下来该开始什么研究。

自1878年首次抵达柏林以来，他第一次因研究之外的事情分心。到达卡尔斯鲁厄后不久，他遇到了同事的女儿Elizabeth Doll，他们于1886年7月结婚；他们有两个女儿，Johanna和Mathilde。正是在1886年11月，他开始研究赫尔曼·冯·亥姆霍兹向柏林科学院提出并在1879年试图说服他参与的问题。然而，推迟开始这项工作可能是一个明智的决定，因为S D'Agostino [11]认为赫兹在1884年对詹姆斯·克拉克·麦克斯韦方程的推导构成了他现在进行的电波传播研究的重要结构背景。Doncel在[14]中考察了赫兹的思想。他写道：-

本文为重建赫兹从电动力学概念到场论概念的转变提供了新的要素，这一过程发生在1887年9月至1888年2月之间。……结论是，赫兹的“空气波”思想属于这一过程的最后阶段，并且主要是通过赫尔曼·冯·亥姆霍兹理论框架内发现的实验线索而获得的。

赫兹将他的发现仅仅视为深入理解詹姆斯·克拉克·麦克斯韦理论的一步。他当然没有预见到，在Marconi读了赫兹的论文并看到其实际应用之后，那些令人难以置信的应用将改变通信和娱乐。赫兹写道：-

我不认为我发现的无线波会有任何实际应用。

D'Agostino在[13]中进一步加深了对赫兹在电磁理论研究以及他对詹姆斯·克拉克·麦克斯韦实验的发展的理解。赫兹需要新的装置来证明詹姆斯·克拉克·麦克斯韦关于电磁波存在的理论，他为此努力，最终在1888年实现。在卡尔斯鲁厄的四年间，赫兹发表了九篇论文。他的名声现在已经相当大，吉森大学向他提出了一个有说服力的邀请。然而，他也被要求去柏林接替古斯塔夫·基尔霍夫。像往常一样，赫兹深入思考了接受这些职位的后果。他沉思道，柏林意味着一个责任重大的职位、相当多的行政职责，以及很少的研究时间。他觉得这在他职业生涯的后期会是一个好的研究举措，但他只有31岁，他想把大部分时间用于研究。赫尔曼·冯·亥姆霍兹告诉赫兹，他会确保他在柏林有一个顶级的实验室，但赫兹仍然觉得这不是正确的举措。然后他在1888年12月收到了波恩大学普通教授的聘书[1]：-

他欣然接受，更多是因为波恩在莱茵河畔美丽而宁静的环境，而不是因为其科学前景。

波恩的空缺是因为鲁道夫·克劳修斯于1888年8月去世而产生的。当赫兹于1889年春天搬到波恩时，他不仅接替了鲁道夫·克劳修斯的讲席，还搬进了他的房子。他对詹姆斯·克拉克·麦克斯韦的理论进行了更多研究，于1890年发表了两篇理论论文。他从詹姆斯·克拉克·麦克斯韦的方程出发，寻找电动力学的力学基础。正如他在Electric waves（1893年出版的他的部分论文的英译本）的导言中所写：-

麦克斯韦的理论就是詹姆斯·克拉克·麦克斯韦的方程组。

赫兹是以太的狂热信徒，在这项工作中他提出将自由空间中的电磁场等同于以太的极化。McCormmach写道[1]：-

赫兹为詹姆斯·克拉克·麦克斯韦的理论带来了无与伦比的清晰性，整理了其概念和形式体系，使其他人能够迅速超越他。

甚至在搬到波恩之前，赫兹就出现了严重健康问题的首批迹象。他已经抱怨过牙痛并接受过重大的牙科治疗。1889年，为了治愈这一顽疾，他拔掉了所有牙齿。然而，到1892年初，问题再次出现，这次是在他的喉咙和鼻子。疼痛变得如此剧烈，以至于他无法再工作。他接受了花粉症治疗，并前往疗养院试图寻找治愈方法。没有任何方法成功，这并不太令人惊讶，因为该病症是由恶性骨病引起的。1893年春天，他勇敢地重新开始教学，接受了多次手术，这些手术至少提供了短暂的缓解，但疾病的一个后果是他现在患上了抑郁症。他于1893年秋季开始了1893-94学年的讲座课程，并于12月3日将他Die Prinzipien der MechanikⓉ（力学原理）一书的手稿寄给了出版商。他在12月7日做了最后一次讲座。不到一个月后他就去世了。

在力学中，赫兹追随古斯塔夫·基尔霍夫，只将长度、时间和质量视为基本实体，力是一个派生概念。在Die Prinzipien der MechanikⓉ（力学原理）中，赫兹希望根据力学以太来解释所有电磁现象[1]：-

赫兹在《原理》的导言中解释说，要构造一门能够说明可感知物体之间合乎规律的相互作用的力学，就必须在三个概念[长度、时间和质量]之外添加一个假设。这个假设是：除了可感知的质量之外，宇宙还包含由刚性约束彼此束缚的隐藏的运动质量。

在[18]中，Lützen讨论了赫兹对隐藏质量的引入。在[19]中，他谈到赫兹的力学进路有三个新颖之处：(1)一个哲学导言，(2)一种不把力作为基本概念引入的力学论述，(3)一种几何形式。事实上，在[26]中，Tougas声称Die Prinzipien der MechanikⓉ(Principles of mechanics)的哲学导言强烈影响了路德维希·维特根斯坦的Tractatus logico-philosophicusⓉ(Tract on philosophical logic)。（另见Barker[6]。Hamilton[15]和Kjaergaard[17]也讨论了赫兹的哲学。）对同一问题的另一个有趣进路是Wilson在[27]中给出的。他写道：-

在过去十五年中，若干学者试图通过考察路德维希·维特根斯坦科学教育中的哲学方面来更好地理解其早期思想。采取这一历史进路的学者几乎只关注路德维希·维特根斯坦的语言意义图像论与物理学家赫兹在其1894年出版的《Die Prinzipien der Mechanik》Ⓣ(Principles of mechanics)导言中发展的心理图像认识论之间的联系。他们很自然地以路德维希·维特根斯坦为线索，后者在《Tractatus logico-philosophicus》Ⓣ(Tract on philosophical logic)中两次提到赫兹的著作。除赫兹之外，他们也在小得多的程度上讨论了路德维希·玻尔兹曼的哲学著作在路德维希·维特根斯坦思想发展中所起的作用。……然而，在分析并强调赫兹对路德维希·维特根斯坦影响的重要性时，他们误解了赫兹的哲学与玻尔兹曼的哲学著作和思想之间的时间顺序和实质关系。这反过来又显著影响了当前对路德维希·维特根斯坦早期思想之起源与发展的理解。

Die Prinzipien der MechanikⓉ(Principles of mechanics)的英译本于1899年出版，并于1956年由Dover Publications重印。

赫兹去世后，他的一位朋友致悼词说：-

他是一位高尚的人，有着非凡的好运，赢得了许多仰慕者，却没有人恨他或嫉妒他；与他有过亲身接触的人都被他的谦逊所打动，被他的和蔼可亲所吸引。他对朋友是真正的朋友，对学生是受尊敬的老师——学生们已开始大量聚集在他周围，有些人从很远的地方前来；对家人则是充满爱意的丈夫和父亲。

Heinrich Hertz's parents were Gustav Ferdinand Hertz and Anna Elisabeth Pfefferkorn. Gustav Hertz was a Jew who converted to become a Lutheran. Anna, the daughter of a Frankfurt doctor, came from a Lutheran family, so Heinrich was brought up as a Lutheran. He was the oldest of his parents' five children, having three younger brothers and one younger sister. Gustav was a barrister in Hamburg, later moving to Oberlandsgerichtsrat, and finally in 1887 becoming a Senator. Let us note that one of Heinrich's brothers was named Gustav Hertz and he had a son, also named Gustav Hertz who also has a biography in this archive.

Heinrich's formal education began at the age of six when he was enrolled in a private school run by Richard Lange [1]:-

... a taskmaster who had no patience with error. [Heinrich's] mother watched closely over his lessons, determined that he should be - as he was - first in his class.

For ten years Hertz studied at Richard Lange's school. He showed a whole host of talents: he had considerable practical skills which he used in doing woodwork with tools he had been given, and later he used a lathe to make apparatus with which he carried out experiments. He also had great language skills, both with modern and classical languages. In 1872 he entered the Johanneum Gymnasium in Hamburg and there he continued to excel at a wide range of subjects. He even took additional subjects with a private tutor, such as Arabic and technical drawing, which were outside the range offered at the school. Not only was he good at many subjects but he also liked these topics and struggled to make decisions about which he should specialise in at university. Should he take engineering and use his practical skills, or should he study the natural sciences which he also loved? He took his Abitur examinations in the spring of 1875 and, having decided to make a career in engineering, he went to Frankfurt to gain practical experience. He had made the wrong decision.

Hertz spent the year 1875-76 in Frankfurt where he gained practical experience in the building industry and also studied for the state examinations in engineering. Already at this stage he began to feel that engineering might not be the right topic for him. He did not enjoy the work environment, he was too isolated and this he felt was due to working in the private sector. He was now struggling to come to terms with having made the wrong decision; should he waste the time spent on this false start and begin again or should he make to best of a bad job and persevere? He decided to continue to follow the engineering route, going to Dresden Polytechnic for a short while in 1876 before leaving to do military service for a year in Berlin. After completing this year in the railway regiment, he went to Munich with the intention of continuing his engineering course at the Technische Hochschule there. That he was on the wrong road was by now so clear to him. There were several new factors in the equation which affected the issue such as, on the negative side, his unhappiness with the working environment of engineering firms, and on the positive side, his enjoyment of the mathematics he had learnt as part of his engineering studies. Hertz's father was supplying the financial support to allow him to undertake higher education so if he were to change direction he would certainly need his father's approval. He explained his soul searching problems to his father and asked if he would continue to support him if he entered the University of Munich and aimed at a research career. McCormmach writes [1]:-

To him engineering meant business, data, formulas - an ordinary life on a par with bookbinding or wood working - and he was uninterested. Although the Technische Hochschule had a good physics laboratory, a course of study there led to state examinations and usually a practical career. The university by contrast promised a life of never-ending study and research, one that suited Hertz's scholarly, idealistic tastes; he knew above all he wanted to be a great investigator.

The arguments convinced his father that he should support his son's change of direction. Hertz matriculated at the University of Munich in 1877 and spent the first semester gaining the necessary background in mathematics. He was advised by von Jolly to read works of Lagrange, Laplace and Poisson [1]:-

Although Hertz thought that, when properly grasped, everything in nature is mathematical, he was in his student days - as throughout his career - interested primarily in physical and only indirectly in mathematical problems.

He took courses on physics, zoology and astronomy as well as on mathematics taking courses in the second semester both at the University and at the Technische Hochschule. After a year at Munich he moved to Berlin, not due to any unhappiness with what he was now doing but rather because it was the standard practice at the time for German students to move between institutions. At Berlin he studied under Helmholtz and Kirchhoff. Immediately, despite only one year of university study behind him, Hertz wanted to start research. A prize had been announced by the Philosophy Faculty for the solution of an experimental problem concerning electrical inertia and Hertz was very keen to enter. The prize had been proposed by Helmholtz and, despite Hertz's lack of experience, he realised his great potential and offered Hertz a room in his Physical Institute and considerable support in directing Hertz to the background literature.

Now Hertz knew he was on the right road [1]:-

He wrote home that his great satisfaction lay in seeking and communicating new truths about nature. Occupied any other way he felt a useless member of society; private study as opposed to research seemed selfish and indulgent.

He was awarded the Philosophy Faculty prize and gold medal in 1879. Helmholtz now suggested that Hertz work on the prize topic proposed by him for the Berlin Academy of Sciences. This asked for experimental evidence for or against the assumptions that underlied Maxwell's theory. This sounded interesting to Hertz yet wanted to progress rapidly in his chosen area and felt that he could not embark on a project likely to take around three years. He declined to follow Helmholtz's proposal, and instead wrote a theoretical work Über die Induction in rotirenden Kugeln Ⓣ on electromagnetic induction and submitted it for his doctorate in January 1880; it had only taken him three months to complete. Hertz's work on the electromagnetic fields associated with a circular disk turning about its axis of symmetry in a magnetic field parallel to the axis of the disk is considered in [7]. He took the necessary oral examination in the following month and was awarded his doctorate with distinction by the University of Berlin. He was then employed as an assistant to Helmholtz at the Berlin Physical Institute.

During the three years 1880-83 that Hertz worked at the Berlin Physical Institute, he wrote fifteen papers on a variety of topics. Most related to electricity, two were on cathode rays, and several were on instruments such as a new ammeter and new hygrometer. Hertz had to decide on the best way to progress his career. He was already in the best place to undertake research in physics and working with Helmholtz who, Hertz felt, was the best physicist in the world. However to become a privatdozent in Berlin would put him in competition with a large number of scientists who were already in privatdozent positions there. He made a decision to try to take advantage of the expansion of mathematical physics throughout German universities and, although his real love was in experimenting, to seek a privatdozent position in mathematical physics. The University of Kiel was seeking someone in exactly that area so, with strong recommendations from Helmholtz, he habilitated in Kiel.

It was in Kiel that Hertz first showed his strength as a lecturer. He had deliberately taken a position in mathematical physics at a university which had no physical laboratories fitted out for research. As a consequence he undertook theoretical work, writing three papers during the two years he worked there. One paper was on meteorology, one was on electric and magnetic units, while the third was the most important since it represented his first work on Maxwell's theories. After two years he was keen to return to an institution with a strong experimental reputation and the offer of an extraordinary professorship in the Technische Hochschule in Karlsruhe seemed ideal. He accepted the position and gave his inaugural lecture On the energy balance of the Earth on 20 April 1885. (See [24] where the lecture is published for the first time.) The Technische Hochschule in Karlsruhe is today the Universität Karlsruhe, and it was here that Hertz made his most important discovery, the one with which his name is mostly associated, namely his famous discovery of long-wavelength electromagnetic waves in 1888. However, when he first took up the post it was far from clear that he was on the verge of greatness [1]:-

His stay began inauspiciously; for a time he was lonely and uncertain about what research to begin next.

He was then distracted from research for the first time since he first arrived in Berlin in 1878. He met Elizabeth Doll, the daughter of one of his colleagues, soon after arriving in Karlsruhe and they married in July 1886; they had two daughters, Johanna and Mathilde. It was in November 1886 that he began work on the problem which Helmholtz had posed for the Berlin Academy of Sciences and had tried to persuade him to become involved with back in 1879. However, it may have been a wise decision to delay beginning the work as S D'Agostino [11] suggests that Hertz's derivation of Maxwell's equations in 1884 formed an important part of the structural background to his studies on the propagation of electric waves which he now carried out. Doncel examines Hertz's thinking in [14]. He writes:-

This paper provides new elements for reconstructing Heinrich Hertz's conversion from an electrodynamic concept to a concept of field theory, a process that took place between September 1887 and February 1888. ... It is concluded that Hertz's idea of 'air waves' belongs at the very end of this process, and was mainly attained through experimental hints found within Helmholtz's theoretical framework.

Now Hertz saw his discovery as merely a step towards a deeper understanding of Maxwell's theory. He certainly did not foresee the incredible applications which, after Marconi read Hertz's paper and saw its practical application, would transform communication and entertainment. Hertz wrote:-

I do not think that the wireless waves I have discovered will have any practical application.

D'Agostino in [13] adds more to understanding Hertz's research in electromagnetic theory and his development of Maxwell's experiments. Hertz needed new apparatus to prove Maxwell's theory of the existence of electromagnetic waves and he worked his way towards this which was finally achieved in 1888. During four years in Karlsruhe Hertz published nine papers. His fame was now considerable and he was approached by the University of Giessen with a persuasive offer. However he was also asked to go to Berlin as a replacement for Kirchhoff. As always, Hertz thought deeply about the consequences of accepting the positions. Berlin, he mused, would mean a position of high responsibility, considerable administrative duties, and little time for research. He felt that this would be a good research move later in his career, but he was only 31 years old and he wanted to devote most of his time to research. Helmholtz told Hertz that he would make sure he had a top quality laboratory in Berlin but still Hertz did not feel it was the right move. Then he received an offer of an ordinary professorship at the University of Bonn in December 1888 [1]:-

He gladly accepted, more for Bonn's beautiful and quiet setting on the Rhine than for its scientific prospects.

The vacancy at Bonn came about because Rudolf Clausius had died in August 1888. When Hertz moved to Bonn in the spring of 1889 not only did he move into Clausius's chair but he also moved into his house. He undertook more research into Maxwell's theories, publishing two theoretical papers in 1890. He searched for a mechanical basis for electrodynamics starting from Maxwell's equations. As he wrote in the Introduction to Electric waves (an English translation of some of his papers published in 1893):-

Maxwell's theory is Maxwell's system of equations.

Hertz was a fervent believer in the aether and during this work proposed identifying electromagnetic fields in free space with polarization of the aether. McCormmach writes [1]:-

Hertz brought an unparalleled clarity to Maxwell's theory, organising its concepts and its formalism so that others were able quickly to go beyond him.

Even before moving to Bonn, Hertz suffered the first signs of his serious health problems. He had already complained of toothache and had major dental treatment. In 1889 he had all his teeth removed in an attempt to cure the persistent condition. However, by early 1892 the problem returned, this time in his throat and nose. The pain became to intense that he could no longer work. He was given hay fever treatment and went to health clinics to try to find a cure. Nothing was successful, and this was not too surprising since the condition was caused by a malignant bone condition. Bravely he began teaching again in the spring of 1893, undergoing several operations which at least provided a short spell of respite but one consequence of the illness was that he now suffered from depression. He began his 1893-94 lecture courses in the autumn of 1893 and on 3 December he sent the manuscript of his book Die Prinzipien der Mechanik Ⓣ to the publisher. He gave his final lecture on 7 December. He died less than a month later.

In mechanics Hertz followed Kirchhoff and considered only length, time and mass as the fundamental entities, force being a derived concept. In Die Prinzipien der Mechanik Ⓣ Hertz hoped to explain all electromagnetic phenomena, in terms of a mechanical aether [1]:-

Hertz explained in the Introduction to the 'Principles' that to construct a mechanics capable of accounting for the lawful interaction of perceptible bodies it was necessary to add a hypothesis to the three concepts [length, time and mass]. The hypothesis was that in addition to perceptible masses the universe contained hidden, moving masses bound to one another by rigid constraints.

In [18] Lützen discusses Hertz's introduction of hidden mass. In [19] he talks about Hertz's approach to mechanics having three novelties: (1) a philosophical introduction, (2) an account of mechanics that does not introduce force as a basic concept, and (3) a geometric form. In fact in [26] Tougas claims that the philosophical introduction to Die Prinzipien der Mechanik Ⓣ strongly influenced Wittgenstein's Tractatus logico-philosophicus Ⓣ. (See also Barker [6]. Hamilton [15] and Kjaergaard [17] where Hertz's philosophy is discussed.) Another interesting approach to the same question is by Wilson in [27]. He writes:-

During the past decade and a half, several scholars have tried to gain a better understanding of Wittgenstein's early thought by examining the philosophical aspects of his scientific education. Those taking this historical approach have focused almost exclusively on the connection between Wittgenstein's picture theory of linguistic meaning and the epistemology of mental pictures developed by the physicist Heinrich Hertz in the introduction to his 'Die Prinzipien der Mechanik' Ⓣ, published in 1894. They have taken their cue, quite naturally, from Wittgenstein, who refers twice to Hertz's work in the 'Tractatus logico-philosophicus' Ⓣ. In addition to Hertz, but to a much lesser extent, they have also discussed the role played by Ludwig Boltzmann's philosophical writings in Wittgenstein's intellectual development. ... While analysing and stressing the importance of Hertz's influence on Wittgenstein, however, they have misconstrued the chronological and substantive relationship between Hertz's philosophy and the philosophical writings and ideas of Boltzmann. This, in turn, has significantly affected the current understanding of the genesis and development of Wittgenstein's early thought.

An English translation of Die Prinzipien der Mechanik Ⓣ was published in 1899, and reprinted by Dover Publications in 1956.

After Hertz died, one of his friends gave this eulogy:-

He was a noble man, who had the singular good fortune to find many admirers, but none to hate or envy him; those who came into personal contact with him were struck by his modesty and charmed by his amiability. He was a true friend to his friends, a respected teacher to his students, who had begun to gather around him in large numbers, some of the coming from great distances; and to his family a loving husband and father.