Scientific discoveries of the 19th century. Scientific works of James Maxwell

History of the air Terentyev Mikhail Vasilievich

4.3. James Clerk Maxwell (1831-1879)

Maxwell was born in the year Faraday discovered electromagnetic induction, and died in the year Albert Einstein was born. The significance of what he did in science was expressed by R. Feynman in the emotional statement we cited in the preface.

James Clerk Maxwell (1831-1879)

It is interesting to talk about Maxwell not only because he made a great discovery. He is James Clerk Maxwell - among the few people who managed to live life purely, without withdrawing into themselves, without withdrawing from social activity; to live, unfortunately, a short but harmonious life, filled as much with love for science as with love for people - relatives, women, friends, colleagues. He lived a life inseparable from nature. He had the highest light religiosity, which did not require ritualism and asceticism. As he himself said, his faith is too deep to be reduced to any specific system. Maxwell died of cancer, as did his mother. In the last year of his life, he knew that he was dying. The physical suffering he endured without complaint was excruciating, but his greatness was also evident in the courage with which he accepted his death.

One could consider Maxwell the absolute ideal of a scientist and a person if such a characteristic did not conjure up a schematic image. Maxwell, on the contrary, was the embodiment of life. A good illustration of what has been said can be his own words, spoken in his youth: “In order to enjoy life and enjoy freedom, he (a person) must constantly have before his eyes what needs to be done today. Not what needed to be done yesterday - if he does not want to fall into despair, and not what needs to be done tomorrow - if he does not want to be a projector... Happy is the person who sees in the work of today a logical part of the work of his whole life " These are not specific rules for ordering life that every organized person formulates for himself. The words were spoken in connection with general reflections on the place of personality in history, on the possibility of having power only over the moment of the present and precisely through this, to realize the unity of the infinite with the finite, without neglecting one’s momentary existence.

What is most surprising about Maxwell’s life is the contradiction between the apparent ease and naturalness with which, as if casually, his main works were completed, and their colossal weight in the history of science.

The chronology of Maxwell's life is as follows. He was born on June 13, 1831 in Edinburgh in Scotland. He spent his childhood in Glenleir, his father's estate. In 1841 he entered the classical grammar school in Edinburgh, and in 1847 he entered the University of Edinburgh. In 1850, Maxwell transferred to Cambridge, first to St. Peter's College, and then to Trinity College (Newton studied and worked there). He graduated from college in 1854 and a year later became its employee. But soon he received the chair of natural philosophy at Marischal College in the Scottish city of Aberdeen. Since 1860, Maxwell has been professor of physics at King's College, University of London. In 1859 he wrote a classic paper calculating the distribution of velocities of gas molecules. In the period from 1855 to 1865 he did major work on the theory of the electromagnetic field. Since 1865, he stopped his scientific and teaching activities for five years and went to Glenlair to engage in agriculture and write books. There his famous “Treatise on Electricity and Magnetism” was created, which was published in 1873. In 1870, Maxwell returned to Cambridge and became director of the Cavendish Laboratory. In 1879, he prepared for publication an edition of Cavendish's works. That same year, Maxwell died at the age of 48. Next we will try to comment on and enliven this dry list of biographical facts.

In one of the branches of the old Scottish family of Clerks there were two brothers - John and James. The elder brother John inherited the baronetcy and the rich estate of Penicuik, and the younger brother, James (Maxwell's grandfather) became a sailor. (In England, land is not divided by inheritance.) John died childless, and James had two sons. His eldest son, George, became heir to Penicuik, and his youngest son, John (names in the family are not very varied) went to university and became a lawyer. He inherited the small estate of Middleby, owned by the Maxwells, another branch of the Clerks family. So John Clerk became John Clerk-Maxwell. (In Scotland, it was common practice to assign a second surname when inheriting land.) He married the daughter of a judge, Frances Kay. This woman had intelligence, energy and a sense of humor. She was able to bring order to the disorderly lifestyle of John before his marriage, who was kind and talented, but did not find a suitable point of application in time. As an amateur, he was interested in technology and the natural sciences, went to meetings of the Edinburgh Philosophical Society, had learned friends, even published a short note on technology, which he was very proud of, loved conversations on scientific topics, but nothing more. After marriage, his life took a new direction. Together with Frances, he began to expand and improve his estate. It was in the spirit of the times. The estate was given a new name - Glenleir (“Den in the Narrow Valley”). Construction of the house began, and the parents moved their newly born son, James Clerk-Maxwell, the future great physicist, into the building, which was not yet completely finished. The house has been preserved - it was built firmly in Scotland.

Glenlair became his father's home for Maxwell in the deepest sense - he never broke with him spiritually, and at turning points in his life he always returned there, first to his father, and then, together with his wife, as a new owner.

Maxwell's childhood, despite the early death of his mother, was happy. My father did everything he could for this. On the whole, his subsequent life was prosperous. It is clear that deprivation and unsettled life are not necessary for successful scientific work. Ambition, from which Maxwell was also free, is not necessary for her. His personality was shaped to the greatest extent by the first ten years of his life, freely spent communicating with a wise and loving man who made the child a participant in all his economic and technical hobbies. Maxwell's personality is also determined by his constant connection with living nature both in childhood and throughout his subsequent life.

Scotland is a beautiful small country with a population of several million people, whose contribution to world culture is disproportionate to its size. This is a country of great poets and artists, but it is also the birthplace of higher technical education - the universities of Edinburgh and Glasgow pioneered the teaching of engineering sciences. Scotland has given the world a galaxy of brilliant engineers and scientists. Among them are V. Thomson, V. Rankin, V. Ramsay, E. Rutherford, D. Dewar and many others. The Scots are stubborn, determined, cautious and skeptical, they have no external sophistication, but there is strength and a deep sense of unity with nature. Perhaps these qualities are really associated with the constant uncertainty of the climate - this idea has been repeatedly expressed. Maxwell as a physicist belongs to all humanity, but as an individual he is a true Scotsman, conscious of his roots.

Maxwell began studying at the age of 10 at a school bearing the pompous name of Edinburgh Academy. He left his father and Glenleir with great reluctance, lived in Edinburgh with his aunt Miss Kay, and at first, apart from some dullness and shyness, he did not show himself to be anything special in his studies. His abilities (along with his interest in physics and mathematics) awaken around the age of 15, and then some mysterious mechanism turns on, producing extraordinary spiritual activity that does not weaken for 30 years.

After his son enters the University of Edinburgh, his father sets up a physics laboratory in Glenlair so that James does not get bored during the holidays. At the age of 19, Maxwell reported his first serious scientific work at the Royal Society of Edinburgh: “On the equilibrium of elastic bodies.” His reading range at this time was wide - the Greeks, Newton, Lucretius, Cicero, Herodotus, Kant, Hobbes, Jung, Fourier, and later, at Cambridge, Tacitus and Demosthenes were added. Despite all this, teachers are unable to saturate him with additional tasks in mathematics. Maxwell's extraordinary abilities are completely obvious to those around him, and in the fall of 1850 his father decides to alienate him and send him to Cambridge. This was normal practice for the best Scottish students - the level of teaching physics and mathematics at Cambridge was higher.

The basis of English universities are colleges, which usually arose in the Middle Ages from church schools. The University of Cambridge received its status in 1318. By 1850 it consisted of several colleges. The most famous are St. Peter's College (Peterhouse), founded in 1284, and Trinity College, founded in 1546, the place where Newton studied and worked.

Maxwell first entered Peterhouse, but after a few weeks he transferred to Trinity College, where he found the environment more pleasant and upon graduation there were more opportunities for work in areas related to physics and mathematics. The time from 1851 to graduation from college in 1854 is a period of intense study for Maxwell, and as often happens with young, talented people, his development occurs with great redundancy - the individual generously spends energy, as if testing his capabilities, “playing with strength.” All aspects of Trinity's life captivate Maxwell at this time - from science, philosophy, morality to whist and chess.

Maxwell's college tutor was Mr. W. Hopkins, who had previously tutored William Thomson (1824-1907) and George Stokes (1819-1903). (“Tutor” is literally a mentor - a position somewhat corresponding to our class teacher.)

During the period described, Stoke taught at the college, heading the Lucasian chair (at one time it was occupied by Newton). The field of mathematics and physics to which Stokes made fundamental contributions would later be used by Maxwell to describe electromagnetic phenomena. In this regard, we were all lucky - Maxwell was taught by the very people who were supposed to do it.

Subsequently, Hopkins formulated his impression of Maxwell as follows: “He was the most extraordinary person I have ever seen. He was organically incapable of thinking about physics incorrectly.”

The testimony of Maxwell's college friends is interesting. In particular, Mr. Lawson recalls the party where they met: “Maxwell, as usual, showed himself to be an expert on all the subjects to which the discussion turned. I've never met such people. I think there is no topic on which he could not speak - and speak well - expressing surprising and unconventional opinions." Lauzon talks about another funny episode when Maxwell, as usual, ran into his room in the morning to chat about various topics. It was difficult to stop him, and Lauson had not yet prepared for the test, having unsuccessfully spent the previous day and most of the night solving the problems posed by Mr. Hopkins. Maxwell comes to his senses half an hour before the test: “Well, that’s enough, I have to go do the problems that old Gop gave us.” Needless to say, by the time the test began, he had solved all the problems correctly.

In 1852, Maxwell was elected to the “Club of the Apostles” - the intellectual elite of Cambridge, a small circle of about 20 members founded by the mathematician and priest Frederick Maurice. Maurice believed that the main path to improving society lies in improving its culture. Maxwell shared this belief; in any case, for many years he systematically spent time giving popular lectures to workers and artisans. Here is an incomplete list of topics on which Maxwell prepared essays presented at club meetings:

"Determination",

"What is the nature of evidence of design"

"Idiotic sprouts (about the occult)",

“Is everything beautiful in the arts due to nature?”

"Morality",

"Language and Thought"

“Is an autobiography possible?” etc.

At the beginning of 1854, Maxwell took the final exam in physics and mathematics at Cambridge - "tripos". This is a serious three-stage competition that requires students to prepare for many months in advance. The winner received the title of “senior debater,” which was extremely highly valued. As practice has shown, the “second debater” who took second place met no less high criteria. There were also third, fourth, etc. “disputants.” The most recent one was nicknamed “the wooden spoon.” Throughout the life of a person who graduated from Cambridge, with all his official movements in the university environment, the holder of the title of first or second disputant enjoyed privileges as an extraordinary person. It is surprising that such a selection system has not been devalued for decades.

The senior debater at one time was J. Stokes, the second debater was W. Thomson. The second debater graduated from Cambridge and J.K. Maxwell. The first was E. Rauss (1831-1907). Rouss subsequently completed a number of important works in mechanics, he became a tutor at Trinity College and tutor of J. Rayleigh, J. Thomson, L. Larmore - outstanding physicists who, by the way, were also the first debaters in their issues. Maxwell shared with Rouss the first Smith Prize in the independent examination in mathematics, which involves independent research on a given topic. The level of this test can be imagined if J. Stoke proved the famous theorem in vector analysis that bears his name, performing research specifically for the Smith Prize.

Later, Maxwell, no longer working at Cambridge, like other best graduates, repeatedly participated in the “tripos”, coming specially from afar for this purpose. Is it not this desire to preserve traditions and ensure the decisive influence of outstanding people from the scientific community that is one of the main reasons for the extraordinary fruitfulness of the Cambridge university system?

The period from 1854 to 1856 is critical for Maxwell's entire future fate. For some time he has been trying, without much enthusiasm, to write a book on optics. In this field, he did work on color vision, designed an ophthalmoscope, and invented a three-color spinning top to demonstrate his theory of color fusion. But at the end of 1854, Maxwell abandoned the book unfinished and no longer wanted “...to have anything to do with optics.” He completely immerses himself in the study of electrodynamics.

At that time, it was not easy to navigate electrodynamics. Describing the situation as it seemed to a layman, F. Engels says in the article “Electricity”: “... in chemistry, especially thanks to Dalton’s discovery of atomic balances, we find order, the relative stability of the results achieved and a systematic, almost systematic attack on the as yet unconquered area, comparable to a proper siege of some fortress.

In the doctrine of electricity, we have before us a chaotic pile of old, unreliable experiments that have received neither final confirmation nor final refutation, some kind of uncertain wandering in the dark, unrelated studies and experiments of many individual scientists attacking an unknown area at random. , like a horde of nomadic riders. Indeed, in the field of electricity, a discovery like Dalton’s has yet to be made, a discovery that gives the whole science a focus and research a solid foundation.”

And this statement was made in 1882, about 20 years after the final theory of electromagnetic phenomena had already been created by Maxwell! (Moreover, chemistry was never allowed to rise to such a degree of rigor and simplicity.) But this theory has not yet been correctly appreciated by everyone and has not yet been reflected in an accessible form - in lectures, books. What can we say about the level of discrepancies in the early 50s!

At the beginning of 1854, Maxwell, in a letter to Thomson, still asked what and how to study electricity. In letters to his father in 1855, he complains about difficulties in understanding the works of difficult German authors (meaning Weber, Neumann, Helmholtz). But even earlier, on the advice of Thomson, he concentrates on Faraday's Experimental Investigations into Electricity and decides not to read anything until he thoroughly understands what Faraday says. At the end of 1854, he already informed Thomson about the emergence of a new understanding of the subject, which a year later would lead him to writing the work “On Faraday's Lines of Force.” It was there that a program began, consisting of translating Faraday into the language of vector analysis, which in a few years would end with the derivation of the famous equations. Maxwell writes: "...I have recently been rewarded by finding that a mass of confusion has begun to be cleared up under the influence of a few simple ideas." This means that at this time he found a still limited analogy between the laws of electricity and the movement of the incompressible ethereal medium.

William Thomson was seven years older than Maxwell, but since his serious scientific activity began almost from childhood, by 1854 he was already one of the most prominent figures in physics. (Thomson began publishing at the age of 15. Maxwell wrote his first scientific work at about the same age, but his subsequent development was slower.) In 1846 (at the age of 22), Thomson became professor of physics at the University of Glasgow and held this post in for 53 years. He lived a long life, during which he traveled widely and was the author of remarkable discoveries in physics and technology. It is enough to mention his establishment of the absolute temperature scale (Kelvin scale), the formulation of the second law of thermodynamics. He gained wide public fame thanks to his important contribution to the work on laying the transatlantic telegraph cable. In the eyes of his contemporaries in the 50s and 60s, he was the first British physicist. Thomson was given a peerage by Queen Victoria. After this, he became Lord Kelvin (the title was chosen after the name of the river on which the University of Glasgow stands).

Maxwell met Thomson in Cambridge, where he spent 1-2 months every year at the beginning of summer. These people were subsequently bound by strong friendships, unclouded by differences of opinion. It must be said that Thomson did not accept Maxwell’s electromagnetic theory until the end of his life.

If J. Stokes taught Maxwell mathematical techniques, then from Thomson comes the method of physical analogies, which Maxwell adopted and used with great skill. At the age of 17, Thomson wrote a paper in which the static distribution of forces in a region containing electrical charges was calculated by analogy with the distribution of heat in a solid body. The charges in such a problem were equivalent to heat sources, and the mathematical relations describing the electric long-range action in the standard interpretation of Coulomb and Poisson turned out to be the same as if they had been obtained using the heat transfer mechanism, where, as is known, the distribution is established locally - from point to point - and there is not even a hint of long-range action. Maxwell was well aware of this important paper and it is reasonable to assume that it stimulated his initial interest in the method of analogies in physics.

The concept of short-range action and the view of electrodynamics as the theory of a medium that fills the space between charges, magnets and currents - Maxwell took all this from the works of Faraday. European physics at that time professed Newtonian principles of long-range action. At the same time, Weber's electrodynamics perfectly described all experimental facts, but had to allow for the existence of forces between elementary magnets and charges, depending on velocities and, perhaps, higher derivatives of coordinates with respect to time. Let us emphasize that it was Thomson who gave Maxwell fruitful advice to begin with the study of Faraday.

Maxwell finished his article “On Faraday's lines of force” in 1856. Oddly enough, after this he did other things, and several years had to pass before the Faraday theme was developed. During this period, Maxwell had no “competitors” - no one in the context under consideration was engaged in electrodynamics. As already mentioned, the whole field seemed quite complex and confusing, and the microstructure of electromagnetic interactions since the time of Laplace was considered a problem “nebulous and belonging to the future of science.”

Maxwell spent about two years (1857-1859) on a competition paper on the theory of the rings of Saturn. He won the competition. The subtle understanding of continuum mechanics and molecular theory that he achieved in the process of solving this problem turned out to be important for his subsequent work. But Maxwell, of course, did not take up the rings of Saturn for this purpose - he does not yet realize his main goal. He needed to assert himself in a prestigious competition and strengthen his position in the scientific community.

Despite the fact that Maxwell, obviously, was in no hurry in his work, did not pursue any special ambitious goals, did not set any distant global goals for himself, but simply lived, worked and did what he could and what was interesting to him at the moment , nevertheless, in six years, from 1856 to 1861, he accomplished an amazing amount. In 1859, he reported a remarkable work on the dynamic theory of gases. Although a detailed account of it is not our task, we cannot fail to mention that this is where the history of statistical physics begins. At the same time, Maxwell thought about electromagnetism and in 1861 wrote his main article: “On physical lines of force,” where the famous equations first appeared. Subsequently, molecular theory and electromagnetism are his main topics, although in 1864, as if in passing, he wrote an article “On the calculation of the equilibrium and stiffness of trusses,” which featured Maxwell-Cremona diagrams, which students are now studying in the course of strength of materials.

In 1864-1865, the “Dynamic Theory of the Electromagnetic Field” appeared, where the previous work on lines of force was freed from the “scaffolding”, and the equations were derived without reference to a specific model of the ethereal medium. The process ends with the publication of “A Treatise on Electricity” (1873) - a book through which several generations of physicists will become familiar with the content of Maxwell’s field theory.

By the beginning of the 60s, Maxwell already had a name in science. But he is only one among a number of famous physicists, nothing more. His scientific career does not look triumphant at all. He becomes a member of Trinity College on his second attempt, a year after the “tripos”. At the age of 26, Maxwell, having not yet completed any of his main works, was elected a member of the Edinburgh Society of Physicists, and at the age of 29 (in 1860) - a member of the Royal Society of London, which included only a few dozen people (including foreigners). The Royal Society is famous for the fact that in its entire history (down to the present day) not a single really important person in science has been “forgotten”. However, scientists with modest scientific background sometimes became members of the Society. In 1860, the Society awarded Maxwell the Rumford Medal, not for his work on electricity and molecular theory, but for his achievements in the field of color vision (which are of little interest today). And these are all his academic differences throughout his life.

Since 1855, Maxwell has been a professor at the ancient but peripheral Marischal College in Aberdeen. (He seeks to move from Cambridge to Scotland to be closer to his father. Unfortunately, his father dies in the summer of 1855, when Maxwell had not yet taken office.) In 1860, the department of natural sciences at the college was abolished and Maxwell was left without a job. He loses the competition for a professorship in Edinburgh to his friend P. Tait, the author of several books and a good teacher. However, at the end of I860 he received a full professorship in the department of natural philosophy at King's College London. These are almost daily lectures for nine months of the year and, in addition, once a week evening readings for artisans.

Maxwell was not a good lecturer, despite the fact that he took teaching very seriously. The gap between the student audience, who had little interest in learning, and the brilliant personality of the lecturer, prone to fantasies, abstractions, and analogies, which, unfortunately, was understandable only to himself, was too great. However, he was a strict examiner.

In 1865, Maxwell suddenly left college and lived as a farmer in Glenlair. Six years later, the idea arose to build the Cavendish Laboratory in Cambridge, where, as expected, the main areas of research would be heat and electricity. V. Thomson is the first to receive an offer to take over the post of director. The next candidate was Hermann Helmholtz. Only after their refusal did the organizers make the same proposal to Maxwell, who fulfilled his role with full brilliance as the builder and first director of what is now one of the most famous laboratories in the world.

It is not surprising that contemporaries were not aware of the true greatness of this man - Maxwell will be understood and appreciated in the next generation. But it’s amazing how carefree he himself was about such things, how generously he gave his time to others...

In 1853, while visiting his friend's parents during his student holidays, Maxwell fell ill. The owners - the Taylor family - literally conquered him with warmth and care. Talking about this episode, Maxwell makes a characteristic statement: “Love is eternal, but knowledge is transitory.” This is said during the most intense period of his intellectual life, and it is important that these are not empty words.

In 1855, for several weeks, Maxwell spent the best hours of the day at the bedside of a sick friend. In 1860, he provided his home to his sick cousin and for a month, having moved to the attic, he nursed him like a real nurse. In 1867, he and his wife made the only trip in their lives to the mainland, visiting several European cities, but spending most of their time in Italy. In one of the southern cities, the Maxwell couple finds themselves in a cholera epidemic. At the risk of their health and life, they work as orderlies, helping people in trouble. In Glenlair, Maxwell usually visits every sick person in the village.

The last years of Maxwell's life were overshadowed by his wife's serious illness. He is on duty at her bedside and sometimes does not sleep in his own bed for months. It must be said that his wife, Katerina-Marina Devore, daughter of the rector of Marischal College, responded to him with the same dedication on all occasions. There is evidence that she was a “difficult” woman, but this probably only concerned outsiders. She lived James' life, helping him as best she could, although Maxwell failed to teach her physics, which in his youth he considered important for mutual understanding. Maxwell was never separated from his wife for more than three or four days, and even during such short departures he always wrote letters. They had no children.

It is very difficult to understand how Maxwell himself assessed his place in science. Beginning in 1865, from the moment he left for Glenlair (Maxwell is only 34!), it seems that the desire to solve new problems fades into the background for him. He now sees the goal as presenting everything that has been done in a systematic form. This kind of work required thought. Their fruit, in the tranquil surroundings of Glenlair, was the Treatise.

The reaction was restrained. V. Thomson and J. Stokes did not accept it. A few years later, A. Shuster was the first to teach a course in electrodynamics based on the Treatise. Only three students are listening to him. (Among them is J. J. Thomson, who would discover the electron and be Maxwell’s successor as director of the Cavendish Laboratory.) The French reaction: “a complex and far-fetched theory,” “lack of logic” (P. Duhem). Ludwig Boltzmann admires the beauty of the equations, but believes that they “cannot be understood.” Helmholtz's position turns out to be the most constructive; he stimulates Heinrich Hertz to study the structure of equations and verify the existence of electromagnetic waves, which are predicted by the theory.

A radical turn occurs after the work of Hertz. No new understanding arose, but the waves were discovered experimentally, and the equations were noticeably simplified in their written form. The fact that the theory is correct and provides a complete description of electromagnetic phenomena - this can no longer be doubted after Hertz. But what lies behind it is another question. Let's listen to Hertz: “It is difficult to get rid of the feeling that these mathematical formulas live an independent life and have an intelligence of their own, that they are wiser than ourselves, wiser even than their discoverers, and that we extract from them more than was originally contained in them.” " As more and more attempts to derive equations from the mechanics of the ether failed, the mysterious theory aroused more and more admiration. So G. A. Lorenz will say: “The Treatise” made on me, perhaps, one of the most powerful impressions of my life.”

But let's return to Maxwell's biography. It can be assumed that there was another reason explaining the sudden departure to Glenlair. A completely extraneous, random event may have played a role in making the decision to which we owe the existence of the Treatise. In 1865, Maxwell suffered a head injury. He hit the branch of a tree, trying to cope with the horse, which had become out of control. In addition to a concussion, one of the consequences of this incident was severe erysipelas. The sudden departure to Glenlair could mean a loss of ability for original creative work. Two types of activity - solving new problems and writing books - place high, but different demands on a person. (What these differences are is very difficult to formulate, but apparently they are profound, as numerous examples show. It is in theoretical physics that one type of activity often completely excludes the other.)

Maxwell's subsequent life is consistent with this explanation. Having agreed in 1871 to become director of the Cavendish Laboratory, he returned to academic life, but not to scientific work - this is clear in advance. He faces a completely new and complex task, requiring organizational abilities and great common sense.

In the 40s, G. Magnus opened the first physical laboratory in Berlin, in the 50s, W. Thomson organized a laboratory in Glasgow, and in 1862 the Clarendon Laboratory was created in Oxford. But the Cambridge project differs from all previous ones in its scale and thoughtfulness in the smallest details. The building itself was designed with future precision experiments in mind - it provided shielding from external fields, insulation from shocks, and many other technical details. The laboratory opened on June 16, 1874. In the same year, Maxwell begins studying the legacy of the man after whom it is named.

Henry Cavendish (1731-1810) is a completely unusual person in science. A rich man, the son of Lord Charles Cavendish, during his long life he published only two articles, but left 20 folders of manuscripts on magnetic and electrical phenomena, which contain a number of remarkable results, later again obtained by other authors.

Bringing back the name of Cavendish to history is an important task, but Maxwell only has 5 years to live! He deciphers the notes, repeats all the experiments and prepares the book “On the Electrical Researches of the Honorable Henry Cavendish between 1771 and 1781.” The book is published in 1879. Maxwell reads proofs to terminally ill patients.

He created a standard essay on the history of physics, where every statement was reliably verified - a thing almost impossible in our time. It makes no sense to regret that Maxwell spent the last years of his short life this way and not otherwise. “How is your own research?” - friend and biographer L. Campbell asked him when meeting during this period, to which Maxwell replied with a sad but kind smile: “I had to give up so many things in life already...”.

In fact, he always strived to do everything well in life and it was not by chance that he chose one path or another. In a review of one book on physics (V. Grove “On the Correlation of Physical Forces”) Maxwell says: “It is not discoveries and their registration by learned societies alone that advance science. ... The real center of science is not volumes of scientific works, but the living mind of a person. And in order to advance science, it is necessary to direct human thought in the right direction. ... [This] requires that in any given era people not only think in general, but that they concentrate their thoughts on that part of the vast field of science which at that moment requires development. In history we often see thought-provoking books producing this effect...”

We see that Maxwell's main scientific achievements date back to the decade 1855-1865. At the same time, many other events occur in his life - repeated changes of job, marriage, death of his father. And Maxwell least of all looks like an aloof fanatic, lost in narrow scientific problems. With clear sobriety of mind, he clearly programs his life, focusing on the most durable: “... As for the material sciences, they seem to me to be the direct path to any truth... concerning metaphysics, one’s own thoughts or society. The sum of knowledge that exists in these subjects takes a large part of its value from ideas obtained by drawing analogies with the material sciences, and the remaining part, although important for humanity, is not scientific, but aphoristic. The main philosophical value of physics is that it gives the brain something specific to rely on. If you find yourself wrong somewhere, nature itself will say so... I discovered that all the scientists who advanced science with their works (such as J. Herschel, Faraday, Newton, Jung), although they were very different from each other by the nature of their mind, they had clarity in definitions and were completely free from the tyranny of words when dealing with issues of Order, Laws, etc. This can never be achieved by writers and people engaged only in reasoning.” And a little later (March 25, 1858) in a comic poem, he formulated his position, which he never changed:

Let in our terrible world

Life is work without meaning or use.

And yet I will work bravely,

Let them think I'm a fool...

And now we will tell you in more detail what Maxwell did in his three famous articles on electromagnetism. Unfortunately, a real understanding of this section, unlike the previous ones, will require training in physics and mathematics. What can you do - the material becomes more complicated due to the fact that we go deeper into the essence of the subject. A reader who does not have such preparation should calmly skip incomprehensible passages, since, in the end, it is not the formulas that are important to him, but the circumstances around them.

The first article is called “On Faraday lines of force.” It was read at two meetings of the Cambridge Philosophical Society on October 10, 1855 and January 11, 1856. The second article, “On Physical Lines of Force,” was published in the Philosophical Journal in March 1861. The third, "The Dynamic Theory of the Electromagnetic Field", was submitted to the Royal Society on October 27, 1864, and published in the CLX volume of the Society's Transactions.

In the Treatise on Electricity and Magnetism (1873), the content of these works was restated. Perhaps by the time the Treatise was written, Maxwell's views had undergone some evolution. In any case, the presentation in it fits more easily into the atmosphere of that time, when ideas of long-range action dominated.

The highest point in Maxwell's work, if we bear in mind the philosophical and methodological aspects of the matter, is the “Dynamic Theory”. This work, especially its third and sixth parts (“General Equations of the Electromagnetic Field” and “Electromagnetic Theory of Light”), is addressed directly to the 20th century. Undoubtedly, Maxwell always considered his equations as a theory of the ether, subject to mechanical laws, but in this article for the first time he works with the concept of a field as an independent reality and demonstrates that from a phenomenological point of view it is enough to have only equations for the field, and the ether is not needed. But he first arrived at his main results not in the third, but in the second article, which is of greatest interest for the history of physics. Our goal is to tell you about it in more detail. But the second article cannot be discussed without setting out the contents of the first. Therefore, there are no options - you will have to start from the very beginning.

In the first article (“On Faraday lines of force”) there were no fundamentally new physical statements. If the strict criteria of modern physics journals had existed in the last century, one can easily imagine a reviewer who would have rejected it “as not containing new results.” But from a methodological point of view, primarily for Maxwell himself, it was extremely important. Interestingly, Faraday, having read the text that Maxwell first sent him, was captivated by its mathematical power. (Admittedly, one must bear in mind Faraday's deep "innocence" in matters of mathematical technique.) The work arose entirely from Maxwell's reflections on Faraday's Experimental Investigations into Electricity and was an attempt to express mathematically what Faraday said in words. In it, Maxwell finds an adequate mathematical apparatus, which will later lead him to final success. The true value of the article can only be understood by knowing the subsequent development. In this sense, one should take the assessment of L. Boltzmann, expressed in 1898 in the notes to the German edition of Maxwell’s works: “... This first major work of Maxwell already contains an amazing amount...”.

Maxwell begins by formulating the basic principles by which a correct theory should be built. As the same L. Boltzmann later noted, “... subsequent researchers of the theory of knowledge developed all this in more detail, but... only after the development itself had taken place. Here they (principles) are given even before the development begins...”

It must be borne in mind that Maxwell is not engaged in abstract philosophy of knowledge. His statements relate to problems of a specific science in specific circumstances. He writes: “... for the successful development of theory it is necessary first of all to simplify the conclusions of previous research and bring them to a form where the mind can comprehend them. The results of such simplification can take the form of a purely mathematical formula or a physical hypothesis. In the first case we completely lose sight of the phenomena being explained and, although we can trace the consequences of established laws, we are unable to gain a broader view of the various manifestations of the subject under consideration.

If, on the other hand, we use physical hypotheses, we see phenomena only through a veil of prejudice and owe this to blindness to the facts and crude assumptions that imply only a partial explanation of reality.

We must, therefore, discover some method of investigation which enables the mind at every stage not to be detached from a clear physical concept, and not at the same time to be bound by any theory from which the concept is borrowed. Thanks to this, we will not be distracted from the subject by pursuing analytical subtleties and will not deviate from the truth, replacing it with a favorite hypothesis.

In order to develop physical ideas that have not yet accepted any specific physical theory, we must use the existence of physical analogies. By physical analogy I mean a partial similarity between the laws of one science and the laws of another, due to which each of them is an illustration for the other...”

Maxwell uses the image of an incompressible fluid filling space. There is no real physical model behind this, although for simplicity we will use the word “model” to refer to this image. His fluid is simply a collection of imaginary properties illustrating theorems of pure mathematics. Thus, he freely, without worrying about the possibility of a specific implementation, introduces the concept of resistance R, which an element of liquid experiences when moving in space, and believes that R is proportional to the speed of movement of this element and (i.e. R = ku). Its fluid has no inertia, i.e. The resistance force of the medium is much greater than the density. Under such conditions, the liquid moves if there is a pressure p - Maxwell introduces such a pressure. The flow lines of an imaginary fluid are continuous throughout space with the exception of individual points - “sources” and “sinks”. Constant pressure surfaces are always perpendicular to streamlines.

Let us imagine a point source of force S 0 in an isotropic medium, which is equivalent to the integer number S 0 of some individual sources. The flowing liquid will move as shown in Fig. 2.

Rice. 2

If the source operates long enough and the liquid distribution is established, then exactly as much liquid flows into each volume per unit time as flows out. In this case, as is easy to understand, the speed of a fluid element at a distance r from the source will be equal to u= S 0 /4?r 2 . Let us now imagine an imaginary liquid flow tube. It is intersected at each place by an imaginary perpendicular surface of equal pressure. So, in Fig. 3 at all points of surface 1 the pressure is equal to p 1, at points of surface 2 - pressure p 2, etc. Let us imagine in this picture a single cubic volume of liquid moving perpendicular to its faces? 1 and? 2 (see Fig. 4). Since the resistance experienced by such a volume is equal to R = ku, then the pressure difference on the faces?p is equal to -ku. It follows that the change in pressure per unit length along each streamline is given by:

Now, recalling the form of Coulomb’s law, we can identify the pressure p(r) with the potential?(r), the speed u(r) with the electric field strength (or electromotive force - emf) E, the source S0 - c electric charge, the coefficient k is naturally associated with the dielectric constant of the medium?. If there are many sources at different points in space, within the framework of the formulated analogy, the correct distribution of fields and potentials will be obtained. As a result, Maxwell reproduces the well-known laws of electrostatics using a mechanical (more precisely, hydrodynamic) model in which there is no long-range action.

Rice. 3

Rice. 4

All physics related to this range of issues is described by one equation:

where?(r) is the charge density, div is a standard differential operation that extracts from the vector field E the part associated with the divergence from the point. In the static case, when the field E does not depend on time, it is possible to write E in the form of a gradient of some scalar function (potential):

E = -grad ?(r). (1)

All this was already well known before Maxwell. Equation (A), where instead of the field E the potential according to formula (1) is introduced, is called the Poisson equation.

Moving on to the consideration of magnetic phenomena and the interaction of magnets and currents, Maxwell no longer finds such a simple analogy. He takes the path of translating existing empirical laws into the language of differential equations, suggesting that magnetic quantities, in the same sense as electrical ones, can somehow be interpreted in the future in terms of the hydrodynamics of a new magnetic fluid. But a specific image of this liquid has yet to be found.

In this work, a duality arises that will be constantly traced further. The desire for mechanical analogies binds Maxwell to his age - one cannot really write equations for an object that clearly has material manifestations, in particular, transfers energy, and on the other hand, there is “nothing”, emptiness. At the same time, the subject of the study somehow does not fit into the accepted mechanical picture, and Maxwell has to follow the logic of the equations themselves, abandoning the idea of ​​a material carrier and recognizing the incompleteness of analogies. Thus, what he said about the principles on which a correct theory should be built remains (fortunately?) an unattainable ideal.

Without connection with a specific model, Maxwell arrives at a differential formulation of Faraday's law of induction, but retains the hope that “by carefully studying the properties of elastic bodies and the motion of viscous liquids” he will be able to find the corresponding mechanical image. In the meantime, he introduces an abstract symbol A(x,t) - a vector potential in modern terminology - and calls it “electrotonic intensity”, i.e. a measure of the “electrotonic state”. This hypothetical state of matter was invented by Faraday. It manifests itself only through its changes in time and space. Now it seems a mystery how Faraday was able to see the heuristic value in such a strange action - the introduction of an unobservable characteristic. At first glance, it seems no less miraculous that it was at this point that Maxwell was able to give an unambiguous mathematical interpretation to Faraday’s vague reasoning. Maxwell postulates the law: “The total electrotonic intensity along the boundary of a surface element is a measure of the amount of magnetic induction passing through that element or, in other words, a measure of the number of lines of force penetrating the given element.” In differential form (for infinitesimal surface elements) this law is written as:

Chapter 4 The emergence of the concept of the electromagnetic field. M. Faraday, J. C. Maxwell 4.1. England in the 19th century It is impossible to find a direct connection between such events as Faraday's discovery of self-induction (1831), Maxwell's introduction of the displacement current (1867) and, say, parliamentary reform