古斯塔夫·基尔霍夫Gustav Kirchhoff

古斯塔夫·基尔霍夫的父亲是Friedrich Kirchhoff，柯尼斯堡的一名法律顾问，对普鲁士国家有着强烈的责任感。基尔霍夫的母亲是Johanna Henriette Wittke。这个家庭是柯尼斯堡繁荣的知识界的一部分，而基尔霍夫，Friedrich和Johanna的孩子中最有能力的，从小就被教导为普鲁士服务是他唯一可走的道路。当时普鲁士的大学教授是公务员，因此基尔霍夫的父母认为，成为大学教授代表着学术能力高的人可以为普鲁士服务的合适职位。鉴于基尔霍夫在学校的学术能力，他未来的职业生涯自然随之而来。

基尔霍夫 在柯尼斯堡接受教育，他进入的是柯尼斯堡阿尔贝图斯大学，该校由普鲁士第一任公爵 亚伯拉罕·阿德里安·艾伯特 于1544年创办。恩斯特·弗朗茨·诺伊曼 和 卡尔·古斯塔夫·雅各布·雅可比 于1833年在柯尼斯堡共同建立了一个数学-物理讨论班，并用它向学生介绍研究方法。基尔霍夫 从1843年到1846年参加了 恩斯特·弗朗茨·诺伊曼-卡尔·古斯塔夫·雅各布·雅可比 讨论班。1843年正是 卡尔·古斯塔夫·雅各布·雅可比 身体不适的一年，因此是以非常积极的方式影响 基尔霍夫 的是 恩斯特·弗朗茨·诺伊曼。恩斯特·弗朗茨·诺伊曼 的兴趣当时坚定地在于数学物理，而当 基尔霍夫 开始在柯尼斯堡学习时，恩斯特·弗朗茨·诺伊曼 已经对电感产生了兴趣。事实上，恩斯特·弗朗茨·诺伊曼 在1845年发表了他关于电感的两篇主要论文中的第一篇，当时 基尔霍夫 正跟随他学习。基尔霍夫 在柯尼斯堡大学由弗里德里希·尤勒斯·里歇洛教授数学。

正是在跟随 恩斯特·弗朗茨·诺伊曼 学习期间，基尔霍夫 做出了他第一个与电流有关的杰出研究贡献。基尔霍夫 于1845年宣布的定律，使得可以计算具有多个回路的电路中的电流、电压和电阻，扩展了 格奥尔格·欧姆 的工作。基尔霍夫 考虑了一个由在网络节点处连接起来的回路组成的电网络，并给出了将每个回路中电流的计算归结为求解代数方程的定律。第一条定律指出，流入给定节点的电流之和等于流出该节点的电流之和。第二条定律指出，网络中一个回路内电动势之和等于该回路中各个电阻上的电势降或电压之和。

基尔霍夫 的定律可由应用 格奥尔格·欧姆 的定律得出，但他能够推广这些结果的方式显示出高超的数学技巧。在这个阶段，基尔霍夫 尚未意识到，格奥尔格·欧姆 关于热流与电流之间的类比——这一类比构成了当时对电流的公认理解——会导致对电流的不正确理解。由于在温度均匀的物体中没有热流动，人们便相信在导体中可以存在静态电流。基尔霍夫 的工作将在几年后使他认识到这一错误，并正确理解电流理论与静电学应当如何结合起来。

1847年对 基尔霍夫 来说是多变故的一年。他于当年从柯尼斯堡毕业，并于1847年迁往柏林，当时正值一个特别困难的时期，由于德意志邦联状况恶劣，那里的紧张局势十分严重。失业和歉收导致了不满和骚动，而1848年2月巴黎起义推翻路易-菲利普的消息又引发了麻烦。许多德意志邦国发生了革命，柏林也发生了战斗。共和主义和社会主义情绪意味着君主制陷入困境，但 基尔霍夫 处于特权地位，当他推进自己的事业时，并未受到周围事件的影响。

1848年至1850年，他在柏林担任无薪职位，正是在柏林工作期间，他纠正了上文提到的关于电流和静电学的公认理解。1850年，他离开柏林前往布雷斯劳，被任命为那里的编外教授。在他抵达布雷斯劳的那一年，基尔霍夫解决了一个关于弹性板变形的问题。该理论的早期形式已由索菲·热尔曼和西莫恩·德尼·泊松发展出来，但几年后是克洛德-路易·纳维给出了正确的微分方程。然而，仍有一些问题存在，基尔霍夫使用变分法解决了这些问题。

基尔霍夫在布雷斯劳时遇到了本生，本生在1851-52学年待在那里；两人成为坚定而持久的朋友。1854年，在海德堡工作的本生鼓励并支持基尔霍夫搬到那里。基尔霍夫接受了物理学教授的任命，并开始与本生进行富有成果的合作。他分享了海德堡围绕赫尔曼·冯·亥姆霍兹的圈子所产生的学术和社会兴奋。1857年，他与克拉拉·里歇洛特结婚。她是弗里德里希·里歇洛特的女儿，弗里德里希·里歇洛特是他在柯尼斯堡的数学教授之一。

基尔霍夫并不是当时唯一研究电流的人。威廉·韦伯和鲁道夫·科尔劳施也在研究这种电流的性质，并在1857年左右发表了与基尔霍夫关于电流在高导电性导线中速度的类似结果。基尔霍夫和威廉·韦伯都发现速度与导线的性质无关，并且几乎完全等于光速。然而，他们两人都将其视为巧合而不予考虑，而不是像詹姆斯·克拉克·麦克斯韦五年后那样推断光是电磁现象。

基尔霍夫关于黑体辐射（他在1862年引入的术语）的基础工作对quantum theory的发展很重要。夫琅禾费观察到了火焰产生的光谱中的亮线，并注意到它们出现在与太阳光谱中某些暗线相似的频率上。然而，要取得进一步进展，需要纯形式的物质，因为如果存在杂质，那么这些杂质通过产生谱线而混淆了图像。基尔霍夫能够通过生产比以前更纯形式的物质而取得他的基础性突破。然后他能够在1859年看到每种元素都有独特的特征光谱。他提出了他的辐射定律，指出对于给定的原子或分子，发射和吸收频率是相同的。

基尔霍夫和本生在1861年继续检查太阳的光谱，并能够识别太阳大气中的化学元素。他们在研究过程中发现了两种新元素：铯和铷。基尔霍夫也许最为人所知的是首次解释了太阳光谱中的暗线是由于光穿过太阳大气中的气体时特定波长的吸收造成的。这项工作开启了天文学的新时代。

基尔霍夫与他的第一任妻子克拉拉育有三个儿子和两个女儿，1869年克拉拉去世时，他独自抚养他们。一种残疾使他一生中大部分时间不得不依靠拐杖或轮椅，这使情况更加艰难。他后来于1872年在海德堡与来自戈斯拉尔的露易丝·布勒梅尔结婚。基尔霍夫曾收到其他大学的邀请，但他在海德堡很快乐，拒绝了这些邀请。然而，随着他的健康开始恶化，他意识到这门学科的实验方面——他非常喜欢的一个方面——变得越来越困难。因此，1875年当他被提供柏林数学物理讲席时，他接受了，因为这使他能够继续对教学和理论研究做出强有力的贡献，而不会因健康状况不佳而在进行实验时遇到问题。他最著名的论著是在他担任柏林讲席后出版的，是四卷本杰作Vorlesungen über mathematische Physik Ⓣ（《数学物理讲义》）（1876-94）。

在[1]中，Rosenfeld总结了基尔霍夫的贡献：——

在科学视野不断扩展的时期，对新知识进行整理和逻辑分析的需要很快便会出现。在十九世纪的杰出物理学家中，基尔霍夫的性情最适合这项任务。在他所有的工作中，他都力求在经验的定量陈述中做到清晰和严谨，使用直接而坦率的方法和简单的观念。他的思维方式在他那些具有直接实用价值的贡献（电网络定律）中，与在他那些具有广泛影响的贡献（光谱分析方法）中一样显著。

作为教师，他的贡献是重大的：——

基尔霍夫作为教师的卓越可以从他讲义的印刷文本中推断出来（他生前只设法出版了力学讲义，其余的是在他去世后编辑出版的）。这些讲义为德国大学的经典理论物理教学树立了标准，而当时这些大学正在科学的发展中占据领先地位。

他撰写的文本也具有持久的价值，并在他去世后的四十年里促进了德国理论物理学的强劲发展。

Gustav Kirchhoff's father was Friedrich Kirchhoff, a law councillor in Königsberg with a strong sense of duty to the Prussian state. Gustav's mother was Johanna Henriette Wittke. The family were part of the flourishing intellectual community in Königsberg and Gustav, the most able of Friedrich and Johanna's children, was brought up to think that service to Prussia was the only course open to him. University professors were civil servants in Prussia at this time and so to be a university professor, Gustav's parents believed, represented the right position where someone of high academic abilities could serve Prussia. Given Gustav's academic abilities at school, his future career followed naturally.

Kirchhoff was educated in Königsberg where he entered the Albertus University of Königsberg which had been founded in 1544 by Albert, the first duke of Prussia. Franz Neumann and Jacobi had jointly set up a mathematics-physics seminar at Königsberg in 1833, and they used it to introduce their students to methods of research. Kirchhoff attended the Neumann-Jacobi seminar from 1843 to 1846. Now 1843 was the year in which Jacobi became unwell, so it was Neumann who influenced Kirchhoff in a very positive way. Neumann's interests were at this time firmly in mathematical physics and, at the time Kirchhoff began to study at Königsberg, Neumann had become interested in electrical induction. In fact Neumann published the first of his two major papers on electrical induction in 1845 while Kirchhoff was studying with him. Kirchhoff was taught mathematics at the University of Königsberg by Friedrich Jules Richelot.

It was while he was studying with Neumann that Kirchhoff made his first outstanding research contribution which related to electrical currents. Kirchhoff's laws, which he announced in 1845, allowed calculation of currents, voltages and resistances in electrical circuits with multiple loops, extending the work of Ohm. Kirchhoff considered an electrical network consisting of circuits joined at nodes of the network and gave laws which reduce the calculation of the currents in each loop to the solution of algebraic equations. The first law states that the sum of the currents into a given node equals the sum of the currents out of that node. The second law states that the sum of electromotive forces in a loop in the network equals the sum of potential drops, or voltages across each of the resistances, in the loop.

Kirchhoff's laws followed from applying Ohm's law but the way in which he was able to generalise the results showed great mathematical skills. At this stage Kirchhoff was unaware that Ohm's analogy between the flow of heat and the flow of electricity, which formed the accepted understanding of electrical currents at that time, led to an incorrect understanding of electrical currents. Since no heat flowed in a body at a uniform temperature, it was believed that a static current could exist in a conductor. Kirchhoff's work would, a couple of years later, lead to him to realise this error and to give a correct understanding of how the theory of electric currents and electrostatics should be combined.

The year 1847 was an eventful one for Kirchhoff. He graduated from Königsberg in that year and moved to Berlin in 1847 at a particularly difficult time when tensions there were high due to poor conditions in the German Confederation. Unemployment and crop failures had led to discontent and disturbances, and trouble was sparked by the news that Louis-Philippe had been overthrown by an uprising in Paris in February 1848. There were revolutions in many German states and fighting in Berlin. Republican and socialist feelings meant that the monarchy was in trouble, but Kirchhoff was in a privileged position and was unaffected by events around him as he pressed forward with his career.

He taught at Berlin in an unpaid post from 1848 to 1850, and it was while he was working in Berlin that he corrected the accepted understanding of electric currents and electrostatics which we referred to above. He left Berlin for Breslau in 1850 when he was appointed as extraordinary professor there. In the year that he arrived in Breslau, Kirchhoff solved a problem concerning the deformation of elastic plates. An early form of the theory had been developed by Germain and Poisson but it was Navier who gave the correct differential equation a few years later. Problems remained, however, which Kirchhoff solved using variational calculus.

While Kirchhoff was in Breslau he met Bunsen who spent the academic year 1851-52 there; the two becoming firm and lasting friends. In 1854 Bunsen, who was working at Heidelberg, encouraged and supported Kirchhoff to move there. Kirchhoff accepted the offer of an appointment as professor of physics and he began a fruitful collaboration with Bunsen. He shared in the academic and social excitement generated in Heidelberg by the circle gathered around Helmholtz. In 1857 he married Clara Richelot. She was the daughter of Friedrich Richelot, one of his mathematics professors from Königsberg.

Kirchhoff was not the only one working at the time on electric currents. Wilhelm Weber and Rudolf Kohlrausch were also working on the nature of such currents and published similar results to that of Kirchhoff around 1857 on the velocity of a current in a highly conductive wire. Kirchhoff and Weber both discovered that the velocity was independent of the nature of the wire and was almost exactly equal to the velocity of light. However, they both dismissed this as a coincidence rather than making the step which Maxwell made five years later of inferring that light was an electromagnetic phenomenon.

Fundamental work by Kirchhoff on black body radiation (a term he introduced in 1862) was important in the development of quantum theory. Fraunhofer had observed bright lines in the spectrum produced by flames and noted that they appeared at similar frequencies to certain dark lines in the spectrum of the sun. To make further progress, however, required pure forms of substances, for if impurities were present then these confused the picture by producing lines. Kirchhoff was able to make his fundamental breakthrough by producing purer forms of substances than had been previously the case. He was then able to see, in 1859, that each element had a uniquely characteristic spectrum. He presented his law of radiation, stating that, for a given atom or molecule, the emission and absorption frequencies are the same.

Kirchhoff and Bunsen went on to examine the spectrum of the sun in 1861 and were able to identify the chemical elements in the sun's atmosphere. They discovered two new elements, caesium and rubidium in the course of their investigations. Kirchhoff is perhaps best known for being the first to explain the dark lines in the sun's spectrum as caused by absorption of particular wavelengths as the light passes through gases in the sun's atmosphere. This work started a new era in astronomy.

With Clara, his first wife, Kirchhoff had three sons and two daughters and he was left to bring them up on his own in 1869 when Clara died. This was made harder by a disability which caused him to spend much of his life on crutches or in a wheelchair. He later married Luise Brömmel, who was from Goslar, in Heidelberg in 1872. Kirchhoff had been made offers by other universities but he was happy in Heidelberg and turned down such offers. However as his health began to fail he realised that the experimental side of the subject, one which he greatly enjoyed, was becoming increasingly difficult. Therefore, in 1875 when he was offered the chair of mathematical physics at Berlin, he accepted since it allowed him to continue to make a strong contribution to teaching and theoretical research without the problems that his poor health was giving him in carrying out experiments. His best known treatise, published after he took up the chair in Berlin, is the four volume masterpiece Vorlesungen über mathematische Physik Ⓣ (1876-94).

In [1] Rosenfeld sums up Kirchhoff's contribution:-

In a period of expanding scientific horizons, the need soon arises for ordering and logical analysis of new knowledge. Among the leading physicists of the nineteenth century, it was Kirchhoff whose temperament was best suited to this task. In all his work he strove for clarity and rigour in the quantitative statement of experience, using a direct and straightforward approach and simple ideas. His mode of thinking is as conspicuous in his contributions of immediate practical value (the laws of electrical networks) as in those with wide implications (the method of spectral analysis).

As a teacher his contribution was substantial:-

The excellence of Kirchhoff as a teacher can be inferred from the printed text of his lectures (he managed to publish only those on mechanics, the others being edited posthumously). They set a standard for the teaching of classical theoretical physics in German universities, at a time when they were taking a leading position in the development of science.

The texts which he wrote also had a lasting value and they contributed to the strong development of theoretical physics in Germany in the forty years after his death.