Gustav Robert Kirchhoff
(12 Mar 1824 - 17 Oct 1887)
A Memoir of Gustav Robert Kirchhoff
By Robert Von Helmholtz.
Translated from the Deutsche Rundschau (1888).
[p.527] On the 20th day of October of the past year (1887) we bade our last farewells to Gustav R. Kirchhoff in St. Matthew’s Cemetery at Berlin. Natural science has lost one of its mightiest promoters, Germany is bereft of one of her keenest thinkers, the youth lament their honored, brilliant master, and his friends mourn over a man who belonged to the best, in the true meaning of this word. While Kirchhoff’s works made his name immortal, so that wherever physics is taught he will be mentioned, such were his modesty and simplicity that his own person was hidden behind the object to which he devoted his life, and if we except his colleagues and those who had the fortune to be near him, there were very few who knew more than that Kirchhoff was the illustrious discoverer of spectrum analysis. Let one of his students be permitted to attempt to do what he would never have undertaken himself and what even would have been painful to him while he lived,—to draw a picture of his work not in its pure, abstract form, destitute of all earthly vesture, as he produced it, but rather in connection with his personal life, and as a fruit of his personal genius.
Gustav R.Kirchhoff was a professor of mathematical physics. I mention this first, not because it is the main fact which would stand first in a biographical dictionary, but because mathematical physics is a science of which only he who was born to it can become an adept. There are vocations in life, there are branches of science that do not allow us to infer what spirit animates their adepts. In certain regions of abstract science however, whoever wants to penetrate into them, must have faculties and dispositions of definite nature and bias, otherwise he will not even cross the threshold that leads to them.
Pure mathematics is such a science. Everyday experience teaches us that only a small proportion of students are endowed with a genius for it. It is more difficult to say on what powers of the human mind such a genius rests. Mathematics is logic applied to numbers and extensive magnitudes. It requires accordingly a great power of abstraction and the faculty of intuitive perception of relations of magnitudes. At any [p.528] rate, just because the technics of pure logical thinking have to be developed to a great extent, the perceptive faculty of a mathematician, his judgment and his representation of things are of a peculiar kind.
The natural philosopher requires however another faculty still, I mean the faculty of observation. Every one whose work rests on observation is a student of nature in the widest meaning of this word; the physician, the traveller, the collector. To observe is to notice, and to collect what you have noticed. In proportion however as the collecting of things is done according to higher and higher standards, observation comes nearer to thinking, collecting approaches interpretation, and natural history verges into exact study of nature. The adepts of natural science work not only through the senses by means of observation, but also by means of the logical faculty of drawing inference. They differ from mathematicians chiefly in the material for their thinking being given in the external world and that they must have the talent to find it there, while the foundations of mathematics seem to be given a priori. Mathematics is the most convenient instrument in the exact science of nature because it is the tongue in which the latter can express its conclusions in the quickest and most precise way. That is why the exact study of nature becomes more and more mathematical; physics, after astronomy, has made the most progress in this direction; chemistry is about to follow it. Speaking generally, the greatest physicist nowadays will be he who is endowed equally with the gifts of observation and with logical precision of thinking, and has mastered experiment as well as mathematics. According to the pre-eminence of the one or the other faculty the place of each investigator will be nearer to the observers of nature or to the thinkers about nature. Both kinds are necessary, the latter is more seldom met with, there are more good observers than good thinkers. Gustav R. Kirchhoff belongs rather, according to his nature, to the great thinkers, and still his greatest and most celebrated discovery is a discovery of observation. He was one of the greatest natural philosophers just because he was a mathematical physicist in the above-mentioned sense.
The life of Kirchhoff was that of a thinker, too. He did not travel all over the world to see nature in the splendid attire of her multifarious productions, like Humboldt or Darwin; he did not work his way to theory through a school of purely practical life, like Faraday or Siemens. No more did he pass his life in the whirlpool of historical or social events. He accomplished his work quietly in the externally serene, but internally the more active, abodes of science,—in the lecture-rooms and laboratories of several German universities. Whoever wants to know him must follow him thither into spheres of thought that lie afar off from the interests of the day.
Gustav B. Kirchhoff, son of the lawyer, was born (1824), brought up, and educated at Konigsberg, the “City of Pure Reason.” According to a certificate from the Kueiphof High school, he wished to devote [p.529] himself to mathematics, and in fact he commenced the study of it under Richelot, and the elder Neumann. The latter, at first a mineralogist, and afterwards gradually becoming one of the great founders of the mathematical physics of our time, had a decisive influence on Kirchhoff. The student took to physics too, and helped to build up his master’s structure. While still a student, Kirchhoff wrote, in 1845, an excellent original paper (On the flow of electricity through a circular plate), and was granted a scholarship for a scientific journey to Paris. The disturbances of the year 1818, prevented him from going any farther than Berlin, however. He stopped there and qualified for a professorship in mathematical physics. Strange to say, the first course of lectures of a professor who afterwards attracted hundreds did not take place. Mathematical physics appeared at the time a very remote and abstract subject. In the year 1850, Kirchhoff went to Breslan in the quality of au adjunct professor, and in 1854, as a full professor to Heidelberg, so that he went through the usual career of a German professor.
The bloom of his life was the twenty years he lived and taught at Heidelberg. These years fell into the most brilliant period of the most beautiful of German universities, and Kirchhoff himself contributed much to the increase and preservation of Heidelberg’s fame.
Indeed, when Kirchhoff came to Heidelberg, the University of that town held an undisputed rank as the foremost of the German universities, through the renown of its teachers in law and history. A. v. Vangerow exercised an incomparable attraction through his celebrated lectures on the Pandects; at his side worked men like Wittermaier, Renaud, Mold; the historians Schlossen, Weber, Gervinus, Häusser have a worldwide renown. They raised the level not only of scientific —but even of social life to such a high standard that all who partook of it preserve forever the recollection of those days. A circle arose around Häusser in particular, which took its first beginning from political grounds, but became afterwards the seat of an enchanting and cheerful conviviality. Among the scientists, Kirchhoff s predecessor Jolly, the anatomist Henle, the clinical physician Pfeuffer, all belonged to this circle; and Bunsen, who was already famous when he came in 1852 to Heidelberg, was one of its foremost members.
Robert Bunsen, whose friendship with Kirchhoff became as eventful in the annals of German science as that of Gauss and Weber, made his acquaintance at Breslau. It was through Bunsen’s influence that Kirchhoff received a call to Heidelberg.
The large public knew nothing of Kirchhoff at the time his Berlin and Breslau papers could only be appreciated by his fellow-physicists. There was a great surprise at Heidelberg accordingly, when—heartily recommended by Bunsen—there came au unusually young, gentle, shy and modest North German. His fine, spirited talk, his amiable manners full of courtesy to every one, and his keen sense of wit and humor won the hearts of those who came nearer to him. Kirchhoff became accordingly [p.530] a favorite guest at the cheerful meetings of this circle at Häusser’s friends. But it was with Bunsen particularly that Kirchhoff came into a close connection in the first years of his sojourn at Heidelberg. Bunsen was his elder by thirteen years; strong, broad shouldered, of a more vivacious temper and of a more immediate influence, Bunsen struck with awe one and all by the plenitude of his powers. Thus the two men were in exterior very different from each other. It is a fact however that Bunsen and Kirchhoff not only accomplished together their great works, but even spent together their bachelor days as true friends. They took trips together to the magnificient environs of Heidelberg, they travelled together during the summer holidays, and even could often be seen together of an evening at the small Heidelberg theater, an amusement in which Kirchhoff particularly took a great delight from the days of his youth.
They did not part company, as is usually the case, even when Kirchhoff, towards the end of the sixth decade of our century, married the young and charming daughter of his Konigsberg Professor Riehelot. It was in fact during the years 1859-’62 that the two investigators, starting from a research of Bunsen, made and accomplished together the great discovery of spectrum analysis.
Towards the beginning of the seventh decade Kirchhoff moved, at the same time with my father, to the newly erected Frederick Hall, the first great institution in Germany devoted wholly to the furtherance of resources in natural science. It was an external manifestation of the fact that the center of gravity of the Heidelberg University gradually shifted from law and history to natural science and medicine. The philosopher Zeller, the mathematician Hesse, afterwards Köuigsberger, the chemist Kopp, the clinician Friedreich, my father as physiologist, all received calls to the institution. The Frederick Hall, became a kind of branch university. In this building I spent the days of my childhood; Kirchhoff’s apartments, as well as the apartments of my parents under them, and the whole Frederick Hall, coalesce into one image in my memory. Large lecture-rooms and museums, with enigmatical ——ological names, stuffed animals, chemical and anatomical smells, acoustic sounds, then crowds of students (Russian lady students among them) overfloodiug at regular intervals the passages and the yards, to the great annoyance of children, while going to hear lectures by their (the annoyed children’s) fathers,—these are the impressions that time has left me.
Kirchhoff spent there happy years. His name was already famous through his discovery of spectrum analysis, so that his laboratory and his lectures became the most frequented ones. With his wife, his four children, and his nearest friends, he led a happy life made cheerful through convivial intercourse.
Unfortunately these in every respect pleasant circumstances came to an end already towards the close of the seventh decade. In consequence [p.531] of a fall on the staircase, he suffered from a sore foot, which compelled him for a long time to move only on a rolling-chair or by means of crutches. It was only at Berlin that he acquired again, after many relapses, his power of locomotion, but even after that he enjoyed his complete health only occasionally. He lost his wife about the same time, so that his family life broke asunder. Some of his friends (Häusser, Vangerow) died; others, like Feller and my father, received calls to Berlin. But accidents to his person could endanger his life, not his work. He continued to perform his task as a teacher and an investigator under the most difficult circumstances and after most severe trials, with a stoical faithfulness to duty and with iron consistency. His own person and his science should have nothing to do with one another.
Afterwards Kirchhoff married, as a second wife, Louise Brömmel, at the time matron of the university clinical hospital for the diseases of the eye. His inexhaustibly cheerful and amiable temper made this second marriage a happy one too, notwithstanding his frequent ill health.
In the year 1875, Kirchhoff received and accepted a call to the University of Berlin, after having refused previously an invitation to become a director of the projected solar observatory at Potsdam.
Whether a life at Berlin is to be considered as an advantage for a scientist may be doubted. The teacher acquires a larger, richer held for his activity, but just so much more is there loss of time for the investigator. Kirchhoff, however, owing to his infirm health, suffered but little from the turmoil of the capital. He did his work as usual; he published, as he used to, a paper or so every year in the reports of the academy; he did experimental work too in the laboratory of his friend, G. Hanseraann. He it was who, after continuous separation from Bunsen, stood nearest to him as a co-worker and friend.
But the most favorite and admirable work of Kirchhoff at Berlin (in fact unique in its effect) was his course of lectures on mathematical physics. His delivery captivated one and all through its external finish and the precision of exposition. Not a word too little or too much; he never bungled, hesitated, or made himself guilty of a want of clearness. The terseness of his calculus was truly admirable,—a quality not easy to explain to an outsider. The whole subject rose before a hearer in the shape of a highly artistic, classically perfect frame-work, in which every part could be logically deduced from some other, so that it was even an aesthetic pleasure to follow Kirchhoff’s deductions. In fact Kirchhoff’s lectures though intrinsically they belong to the most difficult, ought to be intelligible to every one—even the less gifted—provided of course he is acquainted with the instrument used, the mathematical language. It may happen, and it happened often indeed, that one was not able to see the arrangement of what was put before him, could not understand why and to what purpose Kirchhoff made such and such a deduction, but to follow the train of his master’s thoughts, to think the whole over and to reproduce it afterwards was within reach of every one.
[p.532] Paradoxical as it may seem, it was not impossible, without ever having understood Kirchhoff, to write his lectures as a first-rate book by means of the notes alone. It is to this quality of Kirchhoff’s dialectics (absolute clearness and self comprehension), that he owed a large part of his success as a teacher. During nine years Kirchhoff was able to deliver his lectures at Berlin without interruption. But it became more and more apparent to us, his hearers, what exertion they required from him and how he was obliged to gather his last strength in order to keep himself on his feet. Nevertheless he was always punctual to the minute, and the excellence of his lectures remained unimpaired. At last (1884) he was prohibited lecturing by the physicians; he took up however this favorite occupation of his once again for a short time. It became apparent however that palsy made him unable to move, and Kirchhoff was reduced entirely to his own home, to the rolling chair, and to the care of his family. In the last two years of his life one would see him always cheeiful and amiable, sitting in his arm-chair aud preserving a vivid interest in all problems. Never, not even once, did a complaint escape his lips, though he must have been will aware of the decline of his forces. Death, which came unawares during his sleep, delivered him from worse suffering.
We lost in him a perfect example of the true German investigator. To search after truth in its purest shape and to give it utterance with almost an abstract self-forgetfulness, was the religion and the purpose of his life. He loved and furthered science only for her own sake; every embellishment exceeding the limits of what was logically proved, would appear to him as a profanation,—any admixture of personal motives, or grasping at honors or lucre, would seem to him worthy of blame. And in life as well as in science, he carried out what he considered his duty as a man, a citizen, or functionary, with a logical rigor divested of all personal motives. But the knowledge of good alone does not make a man a good one, not even the will or the power to execute it. It was only Kirchhoff’s kindness of heart and humaneness, which if not demonstrative and warm in the expression of feelings, were the more pure and genuine, that made of him a true friend, a self-forgetful coworker, the teacher ready to help, the judge ready to acknowledge the merits of others; in short, a man that all of us loved. I have a fine instance lying before me of how friendly and obliging he was, even toward the humblest of his fellow-men. A poor workman—many would have taken him to be insane—applies in a letter to Kirchhoff, for an explanation of pessimistic doubts that torture him. “No physician, no priest, or any other materialistic egotist can help me, but only a man of a truly scientific educational training, an investigator and thinker himself, who does not consider himself too much above any of his fellowmen, placed below him by birth and circumstances, to communicate his conviction free of any compromise. When people tell me I am a workman and must not trouble myself about such mattters, I answer that not [p.533] all men are alike; that in all classes of men are individuals that have not only material, but also spiritual wants. Not all sciences that are known were developed by scientists alone,” etc. Many a one would have simply laid aside the workman’s letter. Kirchhoff however wrote to him a well-considered reply, as the minute shows, where among other things we read: “That there are such limits to our knowledge of nature, must be borne with patience by every sound mind whether he be a scientist or a workman. I can only advise you to leave off all impossible aspirations and trying to conceive things that are beyond conception. This requires a struggle, but a struggle is the lot of many men of all professions. The best help is to devote one’s self to the task which has fallen to one’s lot, and to fulfill the duties of the position in which one is placed.” And, in fact, Kirchhoff fulfilled himself the duties of his position. He was really “the truly noble mind, free from all egotistic sham,” the workman was looking for. As for us, we are only inclined to ask which to admire more, the greatness of his mind or the strength of his will that lifted him so high above
“The vulgar, which we all, alas, obey!”
We have tried to portray Kirchhoff as he appeared to us, his contemporaries, as a man and as a teacher. His works will outlive him and will be appreciated according to their merit only by posterity. To us, his pupils, falls the task, even if we do not belong to physics, to make appareut what science owes to him. One is apt in such cases to lay the chief stress on the practical results of his works, to adduce their influence on technics and industry. While speaking of Kirchhoffs works one must however keep free from such a bias, first because the chief value of many of his papers lies not in the application but in the method; secondly such considerations would have been antipathetic to his own mind. Kirchhoff never asked himself “What is the use of thy brooding and searching?” What he had to expound he expounded in the way best suited to the thing itself, and in as general a manner as possible, without paying any attention to accessory purposes. “I think I have found such and such a thing, and I take the liberty of giving a demonstration of it in what follows.” Such is the beginning of the most of his papers. His writings are less voluminous than might have been expected. His forty papers—product of as many years—are collected into a volume of moderate dimensions. He published besides, a report on his “Researches on the solar spectrum and the spectra of the chemical elements” and a volume of lectures on mechanics, the latter his most mature and perfect work.
What an immense amount of brain work is here condensed into the smallest space possible! Kirchhoff’s style, like his delivery, was a model of the most clear and concise diction, absolutely classical in the subject concerned. The words stand as if hewn in stone, each one at its place, the logical comprehension of each duly considered; we find here condensed into a few lines what would have taken others pages to [p.534] describe; only when the existing words seemed not precise enough, he uses circumlocutions and definitions, and that mostly in mathematical language. He held the highest rank among those who strove to remove from exact sciences all want of clearness, all subjective judgments, all phrases. The influence of such an endeavor will transcend the limits of his particular science.
The most popular of Kirchhoff’s works is his spectrum analysis. It had in fact most extraordinary consequences of the most palpable kind, and has become of the highest importance for all branches of natural science. It has excited the admiration and stimulated the fancy of men as hardly any other discovery has done, because it has permitted an insight into worlds that seemed forever veiled for us. It is accordingly the most celebrated of Kirchhoff’s discoveries.
But however wonderful the results, what seems to us more admirable still is the truly masterly work itself, the unusually keen and at the same time ingenious and diligent way in which Kirchhoff deduced from the outset, from an accidental observation, a general theoretical law and all the surprising inferences, and demonstrated them with full strictness and certainty. Great men had already held in their hand before him the threads of his discovery without being able to unravel them. The French as well as English brought forward and still produce claims of priority. Kirchhoff repelled them quietly but firmly. All had seen something, made guesses, considered as possible or probable (without Kirchhoff having been aware of it at the time, however). A solid basis, a rigorous demonstration had been given by nobody; it was reserved to the acuteness, thoroughness, and perseverance of a German searcher to elevate the lucky guess to the rank of a sure knowledge.
Spectrum analysis in the narrowest sense, i. e., the “analysis of the chemical elements by means of spectral observations,” is due, if we wish to make a distinction, to an idea and a suggestion of Bunsen’s. Among the most ingenious performances of Bunsen may be reckoned certain very simple physical methods of qualitative chemical analysis, i.e., the detection and the discrimination of chemical elements. A characteristic re-action of this kind he found to be the coloring of non-luminous flames. Each chemical element vaporized or burned in a non-luminous flame, for instance a blue-burning gas-flame, imparts to it a definite characteristic coloring. We should be able accordingly to recognize each substance by the light its incandescent vapor emits if our eyes had the power to distinguish as many differences of color as there are substances in nature. Kirchhoff and Bunsen helped the eyes however by decomposing the light of flames into its separate colors by means of a prism. This gives rise to the spectrum of the flame. The rainbow is a natural spectrum of the solar light made by the rain drops. But this spectrum, as well as the spectra of all glowing solid or liquid bodies, offers quite another aspect from the spectra of flames, i. e., incandescent gases. The first consist of known colors varying in a [p.535] continuous way from one to another; the second consist of different bright lines separated by dark spaces, which bright lines have not only characteristic colorings, but are placed in particular positions and at definite intervals. Just as we recognize the constellation by their configurations and different brightnesses of their stars so do we distinguish the spectrum of iron from the spectrum of copper by the respective distances and coloring of their lines. We could even do without colors; it would be sufficient to measure by means of a scale the intervals between different lines in order to recognize by means of Kirchhoff and Bunsen’s tables the element we have before us. It may seem amazing—but it is true—that a color-blind man could know with absolute certainty what colors a flame emits! The greatest advantage of a method in natural science, its independence of all subjective judgment, was bestowed on spectrum analysis by its discoverers. The main part of Kirchhoff and Bunsen’s work and their chief merit is however the demonstration of the validity of the method, viz, that the configuration of lines depends only on the chemical nature of the luminous incandescent vapor, not on its temperature or other elements with which it is combined, and not on the nature of the flame in which it glows or other accessory circumstances. Of this a carefully worked out experimental proof was given, and Bunsen was accordingly able long ago to make the perfectly safe assertion that he discovered by means of his spectrum analysis a new element, because the salt from a certain mineral spring showed unknown lines. Nowadays spectrum analysis is the most sensitive chemical method of decomposition. And nevertheless, what is still more astonishing is the further discovery made by Kirchhoff, by means of this method discovered jointly with Bunsen. Kirchhoff happened to let a solar ray pass through a flame colored with sodium and then through a prism, so that the spectrum of the sun and of the flame fell one upon another. It was to be expected that the well known yellow line of sodium would come out in the solar spectrum; but it was just the opposite that took place. On the spot where the bright line ought to have shown itself there appeared a dark line. To Kirchhoff this reversal of the sodium line appeared at once in the highest degree remarkable, and he suspected immediately that some fundamental law was lurking there. The fact had been noticed by others (as was proved afterwards), and that by men of the highest renown. It was reserved however to Kirchhoff’s genius to detect and to pick up the treasure of new truths that lay hidden there. Already on the day following the experiment he was able to deduce and to explain the phenomenon from a more general principle which, strange to say, belonged not to optics but to the theory of heat. From a proposition, very remote in appearance, that heat passes only from a body of a higher temperature to one of a lower and not inversely, he deduced by dint of purely logical inferences the fact of the reversal of the sodium line. The middle term in the syllogism was given by the celebrated Kirchhoff’s law on the [p.536] emission and absorption of light and heat by bodies, which says that all bodies absorb chiefly those rays, those colors they emit themselves, and that the ratio of the absorbed and the emitted amount of light is one and the same in all bodies however different. The paper where this law is proved is the most beautiful Kirchhoff ever composed, although there is the smallest amount of mathematics in it. The history of this law might serve as a model for the work of a student of nature; the law is vigorously deduced from well-known general propositions: but says itself something new; it gives the different particular inferences which are to be verified by experiment. It will be the lot of a few only to make such discoveries, but all ought to consider as a model to imitate, the diligence, the conclusiveness, and the care—and not less the great modesty—with which Kirchhoff communicates his discovery to the world: “On the occasion of a research made jointly with Bunsen on the spectra of colored flames, by means of which it became possible to us to recognize the qualitative composition of complex aggregates by inspection of their blow-pipe flames, I made some observations that give an unexpected disclosure as to origin of Fraunhofer’s lines, and justify the inference to be drawn from them as to the material constitution of the solar atmosphere, and perhaps of those of the brightest stars.” These words show that Kirchhoff himself made the wonderful application of his law. The Fraunhofer’s lines to which he alludes are, as is well known, fine dark bands that furrow the solar spectrum, such as it is, even without the help of a flame. The nature of these lines was at first very enigmatic. The just described experiment of Kirchhoff shows however that artificial Fraunhofer’s lines may be produced by means of a flame. The inference was near that the natural lines are produced by the same cause as the artificial ones, that they are reversed gas spectra, and that the light of the glowing solar body has already traversed somewhere incandescent gases, before it reached the earth. We may go further, however. When the artificial lines coincide with the Fraunhofer’s lines, as (for instance), Kirchhoff proved to be the case for iron, sodium, or nickel, one may conclude—taking one’s stand on the joint research of Kirchhoff and Bunsen—that these chemical elements are found in those hypothetical incandesceut gases. The fact that the sun consists of a glowing liquid nucleus, surrounded by an envelope of luminous vapors, and above all that these vapors contain the terrestrial substances whose line-spectra coincide with Fraunhofer’s lines, this fact was inferred,” with as much certainty,” says Kirchhoff, “as can be attained in natural science.”
It is a characteristic trait of Kirchhoff that he calculated numerically this certainty. It would be possible for the bright lines of iron, for instance, to coincide by mere chance with Fraunhofer’s lines; but the probability for such an event was found to be equal to 1/1,000,000,000,000 (one-billionth) [one million-millionth], an almost evanescent quantity. “There must be a cause that occasions these coincidences,” says Kirchhoff. “An adequate [p.537] cause can be produced; the observed fact may be explained if it be admitted that the rays of light that make the solar spectrum have traversed vapors of iron and suffered an absorption such as vapors of iron generally produce. It is at the same time the only cause that can be adduced; its adoption seems accordingly necessary.”
We may insert here a story that Kirchhoff liked to relate himself. The question whether Fraunhofer’s lines reveal the presence of gold in the sun was being investigated. Kirchhoff’s banker remarked on this occasion: “What do I care for gold in the sun if 1 can not fetch it down here!” Shortly afterwards Kirchhoff received from England a medal for his discovery, and its value in gold. While handing it over to his banker, he observed: “Look here, I have succeeded at last in fetching some gold from the sun.” As to Kirchhoff’s own opinion of the importance of this law, it was quite indifferent to him, as stated above, whether the law admitted of any application to the investigation of the nature of the sun and fixed stars, or had only a theoretical interest. As a characteristic trait of him may be mentioned that in his theoretical lectures he never says a single word about the region to which access was gained through his discovery, and in his collected papers he grants it a place only near the end.
The other papers of Kirchhoff treat various subjects of mathematical physics. Those concerned with electricity are the most numerous. A whole series of them is devoted to the calculation of the paths the electrical current takes in bodies of different shape or in a net-work of conduction. There is a Kirchhoff’s law about it too, which is of fundamental importance for the investigation of the distribution of the flow of electricity in complicated conditions of conduction. Another series of papers treats of the distribution of static electricity and magnetism. These were in part celebrated problems on which the greatest of his predecessors (like Poisson), had already tried their forces and had not succeeded in mastering them so completely as Kirchhoff. He was the first to apply the so-called mechanical theory of heat to chemical processes, and by this application he bridged the way to the connection of different branches of natural science by means of mechanical principles. The basis of the mechanical theory of heat, the law of the permanency of work, as Kirchhoff styled it, is according to him undoubtedly the most important accession of knowledge gained in our century in the region of natural science.*
The brilliant, various, and apparently complicated phenomena of light, Kirchhoff deduced in his lectures on optics from the purely mechanical theory of an elastic body. That aether is such a body is a hypothesis which, though enunciated by Kirchhoff’s predecessors, was worked out by him in a particularly vigorous way. Nevertheless, all phenomena can not be explained by such a supposition. That Kirchhoff developed this hypothesis and this only, and contented himself with mentioning at [p.538] the end of his course what circumstances spoke against his hypothesis and, in this way, demolished before the eyes of the students the whole structure, is to be accounted for by his idea of the scope and the limits of the investigation and interpretation of nature.
On such occasions, I must confess, I asked myself many a time, “What for? Why develop a theory that leads to contradiction with experiment? Is the probing of nature, for Kirchhoff, only the greatest and the most interesting exercise in calculation!”
In answer to such doubts 1 shall adduce his own words in his discourse delivered in 1865, as rector of Heidelberg University “on the scope of the natural sciences.” He says there: “There is a science called mechanics, whose object is to determine the motion of bodies when the causes that occasion them are known. … Mechanics is a twin sister of geometry; both sciences are applications of pure mathematics; the propositions of both, as to their certainty, stand on the same level; we have just as much right to ascribe absolute certainty to mechanical theorems as to geometrical.” And further: “If we were acquainted with all the forces of nature and knew what is the state of matter at a certain moment of time, we should be able to deduce by means of mechanics its state at every subsequent moment, and to deduce how the various natural phenomena follow and accompany each other. The highest goal the natural sciences must strive to attain is the realization of the just mentioned suppostion, … viz, the reduction of all natural phenomena to mechanics. We shall never attain the goal of the natural sciences, but even the fact that it is recognized as such offers a certain satisfaction, and in approximating to it lies the highest pleasure; to be derived from the study of natural phenomena.”
I must mention besides the famous words with which Kirchhoff commences his Mechanics, published in 1875: “Mechanics is the science of motion; its object may be stated to be to describe in the most complete and simple way the motion that takes place in nature.” The difference between the first and the last definition of mechanics is worthy of notice. At the former time, and before the large public, Kirchhoff spoke of causes of motion. Now, and in a strictly mathematical book, the word and the notion of cause do not appear. The interpretation of nature is given up; the only thing looked for is the simplest possible description of nature. These introductory words of his Mechanics, and their working out in the book itself are the most consequent, far-reaching expression of Kirchhoff’s way of looking at nature. He makes no hypothesis as to the possibility of arriving at a knowledge of things in themselves. He wants only to portray the phenomena in a logically certain form. In relation to the sensible world (according to Kant) we have logical (that is to say, a priori) certainty only of the propositions of geometry and mechanics, the last distinguished from the first on account of their requiring, besides the three dimensions of space, the fourth one, time, and the notion of a mobile matter. With these three [p.539] fundamental notions of space, time, and matter, Kirchboff tries to make his way to the description of the facts of experience and goes beyond his predecessors by delineating by means of pure geometry the supposed logically fundamental notions of force and mass. Force is to him the acceleration (change of velocity) experienced by a material particle in a unit of time; the knowledge of all these accelerating forces in a given moment of time would suffice to describe the world; experience bas shown however that the description gains in simplicity, if we multiply the acceleration by a certain positive constant, called mass of the moving particle. I have mentioned this abstract train of thought because it is very characteristic of Kirchhoff. Tbe necessity of looking at natural forces as something really existing, or the mass as something really constant, remaining equal to itself, he does not recognize. It is only a fact of experience that the movements in nature hitherto observed have taken place in such a way that they seem to be represented in the simplest manner by making those suppositions. We can build up mechanical systems on quite different bases, but it would not help us to describe simply the real movements. The problem of mathematical physics will be solved when the observed phenomena will be described by means of the simplest possible supposition as to the nature of forces and distribution of matter. There is nothing impossible in it; it can be proved in fact that all that men can observe in finite time must be susceptible of being described mathematically.
Even an outsider will not fail to notice, I think, that something is not included in Kirchhoff’s programme. The simplest description can not produce the conviction that the phenomena, even in future time, shall run in accordance with the description; its equations are, so to say, not laws. There exists a stand-point differing somewhat from that of Kirchboff; it looks for what is in accordance with a law in the change of phenomena. Experience teaches us that nature acts according to laws; because without laws experience would be impossible. Experience is the collecting of what is similar in different particular perceptions. That the laws exist is accordingly an observed fact and not a hypothesis. We feel them acting at every moment independently of our will. We must ascribe to them the same reality as to our will; these two things are opposite to one another, power against power. We designate them accordingly by the names of forces, and forces as causes of motion; they have the same reality as the motion itself. Up to this point nature may be said to be intelligible. What a force is we know not; we can only say that it manifests itself in the acceleration it imparts to the mass, and de facto accordingly, we do not go beyond Kirchhoff’s description of nature. As to results, the search after a law and the endeavor after the simplest description of nature is one and the same thing; the difference lies only in the formulation of the problem and sometimes possibly in the way towards its solution. It follows for instance from Kirchhoff’s definition, that it must be permitted (not only [p.540] upon pedagogical but even upon philosophical grounds) to use hypotheses, even when they are recognized not to be sufficient in all cases, provided they are still the simplest. In fine, only that will appear to us simple which is logically true.
From what precedes one sees how near sometimes mathematical physics approaches to metaphysics. Kirchhoff gave to empiricism in the theory of cognition, its most precise and most consequent expression, and placed himself accordingly at the acme of the whole of modern mathematical physics.
Kirchhoff’s endeavor after clearness and truth appears also in his philosophical stand-point, and makes him prefer to give the definition of his own problem in the study of nature from a narrow view, rather than to suffer in it even a semblance of a proposition accepted on faith, as nature’s conformity to law possibly is. And still he analyzed nature not merely as a critical thinker. His greatest discovery shows that he possessed also the alert introspection, the sympathetic investigation, and the intuitive insight into the working of natural forces, without which no true student of nature can make investigations. We repeat, Kirchhoff was one of the greatest students of nature, because he was a mathematical physicist in the sense explained above.