Ohm, Founder of Mathematical Electricity

A Guest Post by James Joseph Walsh

I wrote about Ohm last year, focusing on the place of Ohm’s Law in Maxwell’s original equations and the struggle Ohm had getting his ideas accepted.

Ohm had a difficult but inspiring life, and James Joseph Walsh (1865–1942) is about to tell you all about it. Walsh was an accomplished physician and author. He wrote such excellent popular nonfiction as The Thirteenth, Greatest of Centuries, Makers of Modern Medicine, and The Popes and Science. Collaborating with Brother Potamian (Dr Michael O’Reilly, 1845-1917), he also wrote Makers of Electricity, from which I extracted this chapter on Ohm. Makers of Electricity is also available from Project Gutenberg and Archive.org.

Ohm, the Founder of Mathematical Electricity.

Lord Kelvin, himself one of the greatest of the electrical scientists of the nineteenth century, in commenting some years ago on Ohm's law, said that it was such an extremely simple expression of a great truth in electricity, that its significance is probably not confined to that department of physical phenomena, but that it is a law of nature in some much broader way. Re-echoing this expression of his colleague, Professor George Chrystal, of Edinburgh, in his article on electricity in the Encyclopedia Britannica (IX. edition), says that Ohm's law "must now be allowed to rank with the law of gravitation and the elementary laws of statical electricity as a law of nature in the strictest sense." In a word, to these leaders and teachers in physical science of the generation after his, though within a comparatively short time after Ohm's death, there has come the complete realization of the absolutely fundamental character of the discovery made by George Simon Ohm, when he promulgated the principle that a current of electricity is to be measured by the electromotive force, divided by the resistance in the circuit. The very simplicity of this expression is its supreme title to represent a great discovery in natural science. It is the men who reach such absolutely simple formulæ for great fundamental truths that humanity has come, and rightly, to consider as representing its greatest men in science.

Like most of the distinguished discoverers in science who have displayed marked originality, Ohm came from what is usually called the lower classes, his ancestors having had to work for their living for as long as the history of the family can be traced. His father was a locksmith, and succeeded his father at the trade. The head of the family for many generations had been engaged at this handicraft. The first of them of whom there is any definite record was Ohm's great-grandfather, Wilhelm Ohm, who was a locksmith at Westerholt, not far from Münster, in Westphalia. Wilhelm Ohm's son, Johann Vincent, the grandfather of the great electrician, during his years as a journeyman locksmith had spent some time in France, and subsequently settled down in Kadolzburg, a small suburb of Erlangen, in Bavaria. In 1764, he obtained the position of locksmith to the University of Erlangen, and became a citizen of that municipality. Both of his sons followed the trade of their father.

The elder of these, Johann Wolfgang, worked at his trade as a journeyman in a number of the small cities of Germany, and only after ten years of absence in what, because of the independent condition of the States now known as the German Empire, were then considered foreign parts, did he wander back to his native place. On his return he received the mastership in his craft, and shortly after, about 1786, married a young woman named Beck. George Simon Ohm, the electrical scientist, was the first child of this marriage, and was born March 16th, 1789. A second son, born three years later, also became distinguished in after-life for his mathematical ability. This younger brother, after having filled a number of teaching positions in various German educational institutions, was called as professor of mathematics to Berlin, where he died in 1862.

While their father, Johann Wolfgang Ohm, followed his trade of locksmith for a living, like many another handicraftsman, he had many mental interests which he cultivated in leisure hours, and doubtless dwelt on while his hands were occupied with the mere routine work of his trade. It is curiously interesting to find that he devoted himself, during the hours he could spare from his occupation, to two such diverse intellectual occupations as mathematics and Kant's philosophy; but they had no newspapers in those days, and a man, even of the artisan class, had some time for serious mental occupation. It might be thought, under these circumstances, that he would be but the most passing of amateurs in either of these subjects, and have a very superficial knowledge of them. This probably was true for his philosophy fad, for there are not many who have ever thought themselves more than amateurs in Kantism, and even Kant himself, I believe, thought that only one scholar ever really understood his system, and subsequently said he had some doubts even about that one; but in mathematics, the elder Ohm seems to have attained noteworthy success.

Hofrath Langsdorff, who was the professor of mathematics at Erlangen during the last decade of the eighteenth century, and who was called to Heidelberg in 1804, a fact that would seem quite enough to set beyond all question that his opinion in this matter may be taken as that of a competent judge, declared that the elder Ohm's mathematical knowledge was far above the ordinary, and that he knew much more than the elements even of the higher mathematics. Under these circumstances, it is not surprising that the father should have tried to encourage in both his boys a taste for mathematics, nor that he should have taken their mathematical instruction into his own hands and succeeded in making excellent mathematicians of them, even in their early years. He was so successful in this, indeed, that Langsdorff, after a five-hour examination of the brothers when they were respectively 12 and 15, did not hesitate to declare that the Erlangen locksmith's family was likely to be remembered as containing a pair of brothers who, for success in mathematics, might rival the famous Bernoulli brothers, so well known at that time.

This might be thought only a bit of neighborly praise, meant to warm a father's heart, yet it seems indeed to have been given quite seriously. Certainly the event justified the prophecy. It is not surprising that, with such a forecast to encourage him, the father should have been ready to make every sacrifice to enable both his sons to prepare for the university.

He continued his instruction of them, then, in mathematics, though he insisted at the same time that they should continue to keep up their occupation of locksmiths. In spite of his enthusiasm for mathematics, the old gentleman seems to have cherished no illusions with regard to the likelihood of pure mathematics ever serving them as a lucrative means of livelihood. It was a very satisfying intellectual interest, but a good trade was much more apt to prove their constant and substantial standby, unless, of course, the boys should actually prove to be the geniuses foretold. He seems to have realized to the full, Coleridge's idea that, like the literary man, the mathematician should have some other occupation, though he might not go to the extent of following Oliver Wendell Holmes' well-known addition to Coleridge's formula, that he should, as far as possible, confine himself to the other occupation. The boys were given the opportunity to attend the gymnasium of Erlangen, and seem to have had excellent success in their general studies besides mathematics.^[23]

In 1805, when George, the subject of our sketch, was sixteen years of age, he was graduated from the gymnasium and was ready for the university. On May 3d, 1805, he took his matriculation examination before the faculty of Erlangen, electing the course of mathematics, physics and philosophy. Later in life he told his friends that it was his deep love for the mathematics of these studies, and his persuasion that in them the student was brought in contact with the most important factors for absolute intellectual cultivation, that tempted him to take them up. To this he did not hesitate to add that there seemed to him to be some call of a higher voice, as if he had a vocation to dedicate himself to the cultivation and extension of these important subjects.

He had been but some two years at the university, when for a time his studies had to be interrupted, partly for lack of means to pursue them, but partly because to his father, at least, the university course was not the source of such satisfaction as he had anticipated from his son's ability in mathematics. While Ohm took his studies seriously, he was not by any means a mere "grind," and, indeed, the reputation which he acquired at the university for many of the qualities which make for a student's popularity among his fellows, was not such as would be likely to appeal to a very serious-minded father. Ohm had acquired the fame of being one of the best dancers in the university; he was a brilliant billiard player and an unrivalled skater; all of which indicates that as a young man he had the physical development and acuteness of sense so necessary to enable him to gain prestige in all these sports.

His father, in spite of his desire for his son's university career, was quite willing, then, at the end of September, 1808, to have him take up a position as teacher of mathematics in the school kept by Pastor Zehnder, in the Canton Berne, in Switzerland. His very youthful appearance (he was only 18 years of age at the time, quite boyish looking and not even large for his years) caused the head of this institution no little surprise when he came with letters of introduction showing that he was to be the new teacher in mathematics. He could scarcely believe his eyes for a time. Within a few months, however, he was convinced of the ability and the capacity for work of his new addition to the faculty, who seems to have given, from the very beginning, excellent satisfaction in his rather important position.

Ohm remained there some three years and a half and then moved to Neunberg, where, independent of any educational institution, he set himself up as a private tutor in mathematics. His reason for so doing, as he himself tells, was that he wished to devote himself to the study of pure mathematics more than was possible in a regular teaching position. For this same reason also he refused a number of offers of positions as teacher of mathematics, which would ordinarily be considered quite flattering to a young man of only 21. Another reason for refusing these offers was that he wished to perfect himself in French, and he had an excellent opportunity afforded him for conversation in this language in the conditions in which he was placed in Neunberg. This last may seem an unusual reason, but it is characteristic of Ohm's determination always to add to his power of understanding and expression.

Most young men in Ohm's circumstances are so occupied with the thought of immediate success in life, that every possible abbreviation of their studies which will bring them nearer the opportunity to make their own living is likely to be heartily welcomed. Ohm, however, realized that his own intellectual development was more important, especially at this time, even than getting on in the world; and for this reason his life has an added interest, not only for students themselves, but especially for those who have the best interests of students at heart and wish to be able to cite examples of how a little delay in getting at one's actual life-work, or, still more, at a remunerative occupation, may serve the very useful purpose of preparing a man so much the better to bring out his best intellectual possibilities when he does settle down to his work.

At Easter, 1811, Ohm returned to Erlangen, after having spent nearly two years perfecting himself in mathematics. He then finished his studies at the university, which seems not to have had the rule of requiring attendance for a definite period before coming up for its degree, but permitted him to take the examinations for the doctorate of philosophy on the strength of the work he had done, and gave him his degree on the 25th of October of the same year. With the drawing tighter of the bands of red tape in educational institutions in more recent years, Ohm would have found it difficult to get his degree thus readily, though it was the university rather than the graduate who was eventually to be honored by it. After this, he became privatdocent in mathematics at the university, and taught for three semesters. He met with marked success and became very popular with the students. After a year and a half, however, he gave up his university position to accept the professorship of mathematics at the Realschule of Bamberg.

While Ohm was here, the spirit of young Germany awoke at the news of Napoleon's unfortunate Moscow campaign, in which his good fortune seemed to have definitely abandoned the great Emperor of the French. Most of the students of the universities of Germany were deeply aroused by it, and those who know Körner's and Uhland's songs will have some idea of the depth of patriotic feeling that was stirred in thousands of young German hearts, who thought that now the opportunity for the fatherland to throw off the hated foreign yoke forever, had come at last. Ohm debated with himself whether he should volunteer with the crowds of young men who were so bravely giving up everything, that the fatherland might be free. Two things deterred him. If he went as a soldier, the material assistance he was able to give his father, and which, as the old man was now advancing in years and had spent most of his little savings upon his sons, was needed, would have to be given up. The other motive that kept him at home was, according to his German biographer in the Allgemeine Deutsche Biographie, which we have been following for most of these details, because he felt that what he might be able to accomplish in other fields besides those of battle would eventually prove more beneficial for his fatherland, and indeed for the whole of humanity, than anything he could do as a soldier, even with the patriotic motive to help his country to throw off the yoke of the foreign usurper, which had proven so hard to bear. As we have already seen, it was a characteristic trait of Ohm all through life, that he cherished the idea, which acquired almost the force of a premonition, that he was destined for great things.

Ohm continued his work as a teacher, then, instead of volunteering for the army; but, as might be expected, found the monotonous work of drilling young students in mathematics extremely unsatisfactory after a time. At the end of a year and a half of service at Bamberg, he asked for a change in the conditions of his teaching position. Instead of this, he received a transfer to the Bamberg pro-gymnasium, where he was to teach Latin until a regular teacher was appointed. In spite of his representations that the teaching position offered him was utterly at variance with his talents and his inclinations, he was compelled to accept this occupation for a time, though after some delay there came the assurance that, just as soon as possible, he would be assigned to a position as teacher of mathematics.

In spite of his unfortunate circumstances, which would ordinarily be thought quite enough to keep him from serious work until he was settled in a position more suited to his tastes, he devoted himself to the writing of his first book during this time, and it was published by Enke, in Erlangen, in the spring of 1817. Its title was, "Outlines of the Study of Geometry as a Means of Intellectual Culture." It comprised nearly two hundred pages, and gives the best possible insight into the ability and intelligence of the author, then a young man of only twenty-eight. As a sort of appendix, he gives a short sketch of his father, evidently introduced, not quite so much for the purpose of filially confessing his obligations to the old locksmith mathematician, nor with the idea of repaying some of his immeasurable debt for all the opportunities which the sacrifices of paternal affection had brought into the life of his sons, as to emphasize the excellent educational influence which his father's mathematical training had had upon his boys, and thus prove his thesis as to the value of mathematical studies in education. Few filial tributes were ever more deserved or given more convincingly or with less suggestion of the conventional attitude of son to father.

Now that mathematics has come to occupy probably even a less prominent place in education than it did in Ohm's time, though the burden of his complaint with regard to educational methods was that geometry was not used as a daily developmental subject as much as it should be, it may be interesting to recall some of the reasons which he advanced for urging its greater employment as an instrument for mental training. He thought that rational geometry should occupy a place of honor among our means of education. Its quality as a mode of pure reasoning, though so closely related to the senses, made easy the transition from sensation to thought, which is such an important element in education; while its eminently simple character, though combined with definite demands upon the constructive faculties, made it appropriate in a high degree for the education of the young out of the field of merely imitative use of the intellect, into that of independent thinking and following out of ideas. "Geometry," says Ohm, "when properly taught, not with the fruitless drilling usually employed in teaching it, but in such ways as to secure deep personal attention, must take rank above all other branches of education, in enabling the student to break down the barrier which separates mere understanding from personal investigation. It forces a man whose thoughts were, up to this time, only the repetition of others' thoughts, to think for himself and to light for himself in his own mind the torches which enable him to see things clearly for himself, and not merely in the dimness of the half light that is thrown on them by the explanations of others."

Geometrical methods always had a special fascination for Ohm, and practically all of his books and writings bear the impress of that close dependence of all parts on one another, that absolutely logical connection so characteristic of geometric accuracy of thought. His was the sort of mind likely to be benefited by mathematical training. Such minds are, however, comparatively few, for most men are not rational in any sense of the word, that would make them dependent on logical reasoning. Perhaps it is as well that they are not, for many of those lacking in logic or mathematical accuracy of thought and absoluteness of conclusion, still continue to accomplish much in the world of thought and do much valuable planning for the complexities of human affairs, where strict logic will not always solve the intricate yet incomplete problems that present themselves in human relations, where, indeed, individual unknown factors often make any but an approximate solution impossible.

The opinions of the critics as to Ohm's "Outlines of Geometry" were, as might be easily anticipated, not all flattering, since only a few of the critics were able to place themselves on the ideal standpoint of mathematical subjectivity from which he had written his book. King Frederick William III., of Prussia, is said to have read it with much interest, however, and the royal pleasure doubtless drew attention to Ohm's work, and may have contributed to the fact that, shortly after its publication, in September, 1817, Ohm was invited by the Royal Consistory of Cologne to take the position of head professor of mathematics and physics in the gymnasium of that city. This post was not only honorable, it was also highly remunerative, at least from the standpoint of teachers' wages as they were at that time, and Ohm eagerly accepted the position.

Lamont, who was the director of the Royal Observatory at Munich, has written a memorial of Ohm which contains much valuable information. The body of it is an address delivered at a meeting of the Faculty of the University of Munich in honor of Thaddeus Siber and George Simon Ohm, but its value has been much enhanced by notes added before publication. Siber was a Benedictine who was professor in the philosophical department at Munich, and died the same year as Ohm. Lamont says that he received his information as to intimate details of Ohm's life from his brother, Prof. Martin Ohm, of Berlin. His sketch is, therefore, absolutely authoritative. Lamont says with regard to this period of teaching at Cologne: "Ohm's first position of importance, in any way worthy of his talents, was the professorship of mathematics at the large Jesuit gymnasium in Cologne, in 1817, where the special gift that he possessed, of making the study of mathematics not only comprehensible but attractive to boys, brought him success and recognition."

For nearly ten years Ohm had the opportunity to put into practice in this Jesuit gymnasium of the Rhineland, the principles which he had so much at heart, for he was apparently given the full freedom of his department of teaching. He succeeded so well that he received wide and hearty recognition for his work. The mathematical studies of the Cologne gymnasium stood higher than had ever been the case before, and this was all Ohm's work. In the years before his teaching in the Rhenish city, those who were distinguished in mathematics at the University of Bonn had not come, as a rule, from Cologne, but from other places; but now nearly all the mathematical prize-takers of Bonn came from among Ohm's students, and the best of the candidates for teaching positions in physics and mathematics had also, as a rule, had the advantages of his training.

Among the best of his scholars at this time was the afterwards well-known mathematician, Lejeune-Dirichlet, who taught in Berlin with Jacobi and Steiner and succeeded Gauss in Göttingen. Another of his most distinguished pupils was the astronomer Heis, who occupied a modest position at the Munster Academy, but whose merits were above the post which he occupied, and who was distinguished for the excellency of his original work and his ability as a mathematician. One very interesting fact with regard to Ohm's teaching, was that he was successful in catching and holding the interest not only of those of his students who were later to specialize in mathematics, but also of those who took up mathematics only as a subject for mental development, that was to be applied to other purposes later in life, and who found Ohm's teaching of the greatest possible service. Among these, the well-known German literary man, Jacob Venedey, of Cologne, has expressed his affection and gratitude for his old teacher in a very striking way in his sketch of the cathedral at Cologne, written in the banishment that came to so many vigorous German thinkers after the failure of the revolution of '48. In sending a copy of this to Ohm, Venedey says: "Honored Sir:—It will perhaps be a source of wonder to you that a student who apparently learned so little from you and your colleagues that he must now earn his bread by writing, should continue to cherish for you the liveliest gratitude. It is not the fault of mathematics that only the dimmest recollection of them remains with me. I shall never forget the personality of my professor, however, nor his ways and methods of teaching. I frequently recount your way with us boys, and I have the liveliest remembrance of your influence as a teacher. There are seldom weeks, there never is a month, when I fail to recall you. This is no mere compliment that I am paying to you, since I know you too well to think that flattery would mean anything to you, as it would be unworthy of you, and I for my part am not one of those who like to bandy compliments. I have often wished to meet you again, and a hundred times I thought that I saw you because some one at a distance had something that recalled you. I may say to you that you accomplished something for me in those days of teaching that I would not have been able to accomplish for myself. I can only think of you, then, with the highest feelings of reverence approaching what might well be called love. It will be a happy day, indeed, for me if I am ever in a position to make an hour of existence happier for you in any way."

While Ohm so zealously continued his instruction in both the upper classes of the gymnasium, he never lost from sight that higher aim of original research and investigation to which his genius disposed him.

His choice of a subject for original investigation wavered for a long time between mathematics and physics, but, as he himself declared, his experience having shown him that authority was prone to play a large role in mathematics, while the field was more open for personal research and observation in physics, he resolved to take up that department for his special studies, consoled by the idea that physics cannot be properly pursued without mathematics. Looking around to select a subject that would serve as a striking preface to his work in this department, though resolved at the same time to avoid one where he would be without rivalry, he found it all ready to his hand in what one of his contemporaries called the enigmatic phenomena of the galvanic current. This was to prove a fortunate selection, indeed, both for himself and the opportunity afforded his genius as well as for the science of electricity itself.

He then began a series of investigations, always experimental in character, and with the mathematical explanations of the phenomena observed carefully worked out. Accounts of these studies appeared from time to time in the year-book for Chemistry and Physics, issued by Schweigger. After some ten years, these were collected together, or at least the principal portions of them, and published in the second half of the year-book for the year 1826. The apparatus for his experiments was fortunately at command in the gymnasium at Cologne, but without his mechanical skill, obtained from his experience as a locksmith when a boy, it would have been impossible so to vary his experiments and modify his instruments as to bring out many of the phenomena that he succeeded in demonstrating. Nearly all of the great discoverers in science have been handy men possessed of mechanical skill, and this is as true for medicine, as I have shown in "Makers of Modern Medicine,"^[24] though it might perhaps not be expected, as it is here in electricity, where it seems very natural.

Ohm felt, in 1826, that he had succeeded in exhausting nearly all that he could learn for himself, and as he wished to have opportunities for further study, and especially for further reading, he asked for an academic furlough that would carry him over the next year. The work that he had already accomplished was beginning to be appreciated, and after discussion of the papers that he had published up to that time, the requested furlough was promptly granted; and in a letter in which the school authorities praised his school work as well as his original investigations, they allowed him to take the sabbatic year for the furtherance of science on one-half the usual salary, though with the condition also that more would be allowed to him in case this seemed necessary and the conditions justified it.

This furlough was perhaps the most important event in Ohm's life. He employed it in bringing to a focus the ideas with regard to electricity which had been gradually worked out in his mind during the past ten years. In May, 1827, within six months after the beginning of his exclusive devotion to the subject, Ohm's article on the mathematics of the galvanic current appeared. It proved a scientific achievement of the first rank, that was to be epoch-making in the domain of electricity. It settled the conditions under which electrical tension exists in various bodies, and made it clear that there is a fundamental law of electrical conduction which could be expressed by an easy, simple formula.

Ohm's preface to his little book, that was to work such a revolution in electricity and was to remain for all time one of the classics in this department of science, is typical of the man in many ways. Its modesty could not very well be exceeded. Its simplicity constitutes in itself an appeal to the reader's interest. I know nothing in the literature of the history of science quite like it in these regards, unless it be the preface of Auenbrugger's little book on percussion, in which he laid the foundation of modern clinical diagnosis.^[25] The two men have many more qualities in common than the authorship of modest prefaces to their books. Both of them were geniuses whose names the aftertime will not willingly let die, and both of them accomplished their work apart from the stream of university life in their time, and met with a like fate in the neglect, for some time at least, by their distinguished colleagues of the important discoveries that they had made. Ohm's preface deserves to be quoted because of its classic quality:

"I herewith present to the public a theory of galvanic electricity as a special part of electrical science in general, and shall successively, as time, inclination and means permit, arrange more such portions together into a whole, if this first essay shall in some degree repay the sacrifice it has cost me. The circumstances in which I have hitherto been placed have not been suitable either to encourage me in the pursuit of novelties or to enable me to become acquainted with works relating to the same department of literature throughout its whole extent. I have, therefore, chosen for my first attempt a department of science in which I have the least to apprehend competition.

"May the well-disposed reader accept whatever I have accomplished with the same love for science as that with which it is sent forth!

—The Author, Berlin, May 1st, 1827."

In his preface to the American edition of the "Galvanic Circuit Investigated Mathematically,"^[26] Mr. Thomas D. Lockwood, vice-president of the American Institute of Electrical Engineers, said of this masterpiece of Ohm's: "A sufficient reason for republishing an English translation of the wonderful book of Professor G. S. Ohm is the difficulty with which the only previous translation (that of Taylor's Scientific Memoirs) is procurable.

"Besides this, however, the intrinsic value of the book is so great that it should be read by all electricians who care for more than superficial knowledge.

"It is most remarkable to note, at this time, how completely Ohm stated his famous law that the electromotive force divided by the resistance is equal to the strength of the current."

With regard to the book as a whole, Mr. Lockwood says, after suggesting certain anticipations of Ohm's ideas which had been made in the preceding century:

"Ohm's work stands alone, and, reading it at the present time, one is filled with wonder at the prescience, respect for his patience and prophetic soul, and admiration of the immensity and variety of ground covered by his little book, which is indeed his best monument."

Like many another great discovery in physical science, Ohm's work failed to receive the immediate appreciation which it deserved. It cannot be said, however, that it failed to attract attention. It would be easier, indeed, to forgive the scientists of the day if this were true. Not long after its appearance, abstracts from it were made by Fechner in Leipzig, by Pfaff in Erlangen, and Poggendorff in Berlin, which showed that these scientists understood very clearly the significance and comprehended the wide application of Ohm's law as claimed by its author. From these men there was no question of hostile criticism. Professor Pohl, of the University of Berlin, however, in the Berlin "Year-book of Scientific Criticism," did not hesitate to express his utter disagreement, and declared that Ohm's work was fallacious and should be rejected. Other writers of the time treated Ohm's article more or less indifferently, as a merely conventional contribution to science.

Professor Pohl's opinion was taken to represent the conclusions of the faculty of the University of Berlin, especially noted for mathematical ability. This was to prove a serious hindrance to Ohm in the university career which he had planned for himself. At Berlin they had the ear of the Minister of Education, and it was not long before Ohm felt that the criticisms of his work were making themselves felt in a direction unfavorable to him. Not long after the appearance of his book, there came a disagreement between Ohm and the educational authorities. Ohm felt that this was due to failure to recognize the significance of his work, and that under the circumstances he could not hope for the appreciation that would provide him with the opportunities he deserved. He insisted on sending in his resignation as a teacher. Nothing could change his determination in the matter, not even the pleas of his former scholars, and his resignation had to be accepted.

Ohm had hoped for a teaching position in a university. The Minister of Education declared that, while his work as a teacher had been accomplished with careful industry and diligence and conscientious attention to duty, the ministry regretted that, in spite of thorough appreciation of him and admiration for his excellent work as a scientist, they could not find for him a position outside of the gymnasium. How utterly trivial the conventional expressions sound, now that we know that they brought about for the time being the interruption of one of the most brilliant scientific careers in Europe. Of course, the geese cannot be expected to appreciate the swans, and it was not the minister's fault, but that of some of Ohm's own colleagues. The next six years of his life, the precious years between 38 and 44, Ohm had to give up the idea of teaching in a university, and devote himself to some private tutoring in Berlin, with a stipend of about three hundred dollars a year, miserable enough, yet sufficient, as would appear, for Ohm's simple mode of life. This he owed to the kindness of Gen. Radowitz, who employed him to teach mathematics in a military school in Berlin.

At the end of this time, when he was nearly 45 years of age, his unfortunate situation attracted the attention of King Ludwig I., of Bavaria, who offered him the chair of professor of physics at the Polytechnic School in Nuremberg, which had recently by royal rescript been raised to the status of a Royal Institute, with the same rank in educational circles as a lyceum for the study of humanities. Here Ohm's duties were shortly to be multiplied. He became the inspector of scientific instruction, after having occupied for some time the professorship of mathematics, and later became the rector of the Polytechnic School, a position which he held for some ten years, fulfilling its duties with the greatest conscientiousness and fidelity.

Ohm continued his work at Nuremberg for more than fifteen years. During this time, he succeeded in making his mark in every one of the departments of physics. He is usually considered as owing his reputation as an experimental and mathematical scientist to his researches in electricity. As a matter of fact, every branch of physics was illuminated by his work, and perhaps nothing shows the original genius of the man better than the fact that everything which he took up revealed new scientific aspects in his hands. The only wonder is that he should have remained so long in a subordinate position in the educational world at Nuremberg, and received his appointment as university professor of physics at Munich only in 1849.

In the midst of the administrative educational work that came to him at Nuremberg, Ohm did not neglect original investigation, but somehow succeeded in finding time for experiment and study. Having made a cardinal discovery in electricity, of the value of which surely no one was more aware than himself, Ohm might have been expected, as soon as his new post gave him the opportunity, to devote himself quite exclusively to this department of science. Instead, he turned for a time to the related subjects of sound, heat and light, devoting himself especially to their mathematics. He did this, as he said himself, to complete for his own satisfaction his knowledge of the scientific foundations of the imponderables, as heat, light and electricity were then called, but also because he wished, for the sake of his students, to get closely in touch with what had been accomplished by recent investigators in physics.

It is almost a universal rule in science, that no matter how distinguished an investigator may be, he makes but one cardinal discovery. Ohm, however, was destined, after having brilliantly illuminated electricity by the discovery of a great law, to throw nearly as bright a light on the domain of acoustics; and there is a law in this department of physics which is deservedly called by his name, though it is often associated with that of Helmholtz. Helmholtz himself was always most emphatic in his insistence on Ohm's priority in the matter, and constantly speaks of the law in question by Ohm's name.

Perhaps no better evidence of the breadth of Ohm's interest in science, his supreme faculty for experimentation, or the originality of his investigating genius, can be found than the fact that he thus discovered, by experimental and mathematical methods, the solution to important problems in two such distinct departments of physical science as electricity and acoustics. Before his time, the question of electrical resistance was absolutely insoluble. The problem in acoustics was not less obscure, as may be judged from the fact that, though some of the best physicists and mathematicians of Europe during the eighteenth century—and there were giants in those days, among others, Brook Taylor in England, D'Alembert in France, Johann Bernoulli and Euler in Germany, and finally, Daniel Bernoulli—had devoted themselves to its solution, it remained nevertheless unsolved. Here, as in electricity, the simplicity of the solution which Ohm found shows how direct were his methods of thinking and how thorough his modes of investigation. Perhaps the most striking feature of Ohm's work in acoustics, and, above all, his solution of an important problem in music, is the fact that he himself, unlike most of his German compatriots, had no ear for music and no liking for it.

In his address delivered at the public meeting of the Royal Bavarian Academy of Sciences at Munich, in March, 1889, the hundredth anniversary of the birth of Ohm, Eugene Lommel, in discussing the scientific work of Ohm, said:

Eugen Cornelius Joseph von Lommel (1837-1899)

"Inasmuch as his law in acoustics furnished the clearest insight into the hitherto incomprehensible nature of musical tones, it dominates the acoustics of to-day no less completely than Ohm's law of the electric current dominates the science of electricity."^[27]

This law concerns the resolution of tones into their constituents. The ideas laid down by Ohm were almost absolutely novel. They were so new that none of the workers in acoustics could think that Ohm had made a great discovery. His law states that the human ear perceives only pendulum-like vibration as a simple tone. Every other periodic motion it resolves into a collection of pendulum-like vibrations, which it then hears in the sound as a series of single tones, fundamentals and overtones. Ohm arrived at this law from mathematical considerations, making use of Fourier's series; for its experimental verification he was compelled to use the well-cultivated ear of a friend, inasmuch as he was himself, as we have said, quite devoid of musical appreciation.

Ohm's results were too distant from the accustomed ideas of investigators of sound at that time to be accepted by them. Seebeck, who was one of the most prominent scientists of the time in acoustics, did not hesitate to criticise severely, just as Pohl had made little of Ohm's law of the electric current. While, however, foreigners were to teach German scientists the value of the advance that their great colleague in electricity had made, the privilege of pointing out the significance of his work in sound was to be a compatriot's good fortune. It was nearly a score of years, however, before this vindication was to take place. Then Helmholtz, a decade after Ohm's death, furnished the experimental means which enabled even the unskilled ear to resolve a sound into its simple partial tones, and revolutionized the theory of music by his classic work, "The Science of the Perception of Sound," which is based entirely on Ohm's law of acoustics.

Hermann Ludwig Ferdinand von Helmholtz (1821–1894)

Ohm, in the appendix to his work, "The Galvanic Circuit treated mathematically," dared to suggest certain speculations with regard to the ultimate structure of matter. He said: "There are properties of space-filling matter which we are accustomed to look upon as belonging to it. There are other properties which heretofore we have been inclined to look upon as accidents or guests of matter, which abide with it from time to time. For these properties man has thought out causes, if not foreign, at least extrinsic, and they pass as immaterial independent phases of nature under the names light, heat, electricity, etc. It must be possible so to conceive the structure of physical bodies that, along with the properties of the first class, at the same time and necessarily those of the second shall be given."

Louis Pasteur (1822 – 1895)

It is all the more interesting to come upon Ohm's speculations on this subject of the ultimate constitution of matter, because within a few years of his time, Pasteur, then only a comparatively young man, had also been taken with the idea of getting at the constitution of matter by his observations upon dissymmetry, which he abandoned after a time, however, because he found other and more practical subjects to devote himself to, though he never gave up the thought that he might some time return to them and perhaps discover the underlying principles of matter from observations in this subject. It was not until the last five years of his life, when Ohm was already past sixty, that he was to enjoy the satisfaction of an ambition which he had cherished from his earliest years as a teacher, and which, in spite of untoward circumstances, had been a precious stimulus in his work. For some twenty years he had hoped some time to be able to devote himself to the investigation of the physical constitution of matter. Unfortunately, when the opportunity came, the manifold duties of his teaching position prevented the completion of his great work, and doubtless robbed his generation and ours of a precious heritage in the mathematics of the structure of matter, which would doubtless have been of the greatest possible value.

It is of course idle to speculate as to what he might have accomplished if left to his original investigation. The problem which he now took up was much more difficult than any of his preceding tasks. It would have seemed, however, quite as hopeless to those who lived before Ohm's laws, to look for a single complete law of the resistance of the electrical current in the circuit or of the overtones in music, as it is to us to think of a simple mathematical formula for atomic relations. What Ohm accomplished in these other cases by his wonderful power of eliminating all the unnecessary factors in the problem, would surely have helped him here. The main power of genius, after all, is its faculty of eliminating the superfluous, which always obscures the real question at issue to such a degree for ordinary minds, that they are utterly unable to see even the possibility of a simple solution of it. Art has been defined as the elimination of the superfluous; discovery in science might well be defined in the same terms. Under the circumstances, we cannot help regretting that Ohm was not allowed the time and the opportunity to work out the thoughts with which he was engaged. It would have been even more satisfactory if the precious years of his ripe middle age had not been wasted in trivial, conventional tasks, so that he might have been permitted to devote his academic leisure, sooner than was actually the case, to the problem which had been so constantly in mind since he made his great generalization in the laws of electricity.

Unfortunately, most of Ohm's time had now to be taken up with his teaching duties. Only for his self-sacrifice in the matter, his success as a teacher would doubtless have been less marked. Science itself must have suffered, however, from this pre-occupation of mind with a round of conventional duties, since Ohm could no longer devote his time to original research. In the meantime, his great discovery was coming to its own. During these ten years since the publication of his book, a number of distinguished physicists in every country—Poggendorff, and especially Fechner, in Germany, Jacobi and Lenz in Russia, Henry in America, Rosenkoeld in Sweden, and De Heer in Holland—took up the problems of the current strength of electricity as set forth in Ohm's law, and confirmed his conclusion by their investigations along similar lines. The French physicist and member of the Academy of Sciences, Pouillet, applied Ohm's ideas to thermo-electricity and pyro-electricity, employing his terms and bringing his work to the notice of foreigners generally, so that a translation of Ohm's work was made into English.

Joseph Henry (1797–1878) and Heinrich Friedrich Emil Lenz (1804–1865)

Ohm's work at once attracted the attention that it deserved in England. The Royal Society conferred on him the Copley Medal, which had been founded as a reward for important discoveries in the domain of natural knowledge. Before Ohm's time only one other German scientist, Carl Friedrich Gauss, of Göttingen, had ever been thus honored. The words employed by the Royal Society in conferring this distinction showed how thoroughly the representatives of English science appreciated Ohm's work. They said that he had set forth the laws of the electric current very clearly, and thus accomplished the solution of a problem which was as important in the realm of applied science as it had hitherto been in the schools. Recognition now became the rule, and Ohm had the satisfaction of having all his colleagues in the physical sciences acknowledge the significance of his work.

Johann Carl Friedrich Gauss (1777–1855)

Ohm's recognition, then, came from foreigners first, and only afterwards from his fellow-countrymen. Immediate appreciation might have meant much for him, and even this tardy recognition gave him renewed courage and new strength to go on with his work. He gave effective expression at once to his gratitude and to the stimulus that had been afforded him by the dedication to the Royal Society of London of the great work, "Contributions to molecular Physics," which he planned.

The year after he received the Copley Medal, he was made a Foreign Associate of the Royal Society of England, and from this time on his discoveries began to find their way into text-books as fundamental doctrines in the science of electricity. German and foreign scientific bodies followed the English example so happily set for them, and began to give him their recognition as a physicist of the first rank. Ohm's further observations were, for a time, not accepted so readily as his first law. The reason for this was that Ohm was so far ahead of his times that there was not as yet in existence a suitable electroscope to test their truth. Finally, the invention of an exact electrometer by Dellman, and its application by Professor Kohlrausch, of Marburg, made the experimental confirmation of all his work quite as significant as for his law.

It is a striking reflection on Ohm's career, though not very encouraging for the discoverer in science, to realize that some important discoveries, which thus proved eventually quite as epoch-making as his law, had lain for practically ten years neglected, and their magnificently endowed author had been allowed to eke out a rather difficult existence in teaching, not in the important department of science in which he was so great a master, but in certain conventional phases of mathematics which might very well have been taught by almost anyone who knew the elements of higher mathematics. Ohm's case is not a solitary phenomenon in the history of science, however, but rather follows the rule, that a genuine novelty is seldom welcomed by the leaders of science at any given moment; but, on the contrary, rather decried, and its discoverer always frigidly put in his proper place by those who resent his audacity in presuming to teach them something new in their own science.

Having thus illuminated electricity and acoustics, Ohm turned his attention to the department of optics. His power to simplify difficulties and get at the heart of obscure problems is illustrated by his contribution to this subject, made while he was professor of physics in the University of Munich. Optics had early engaged his attention, and in 1840 he published a paper in Poggendorff's Annalen, bearing the title, "A Description of some simple and easily managed Arrangements for making the Experiment of the Interference of Light." With his usual faculty for simplifying things, he showed that the interference prisms which were made so carefully by the French could be constructed from common plate-glass. He was indeed able to demonstrate that a simple strip from the edge of a piece of such glass could be used for this purpose.

He pursued this absorbing subject until 1852-53, and then set himself the difficult task of developing a general theory of these phenomena of interference which are so rich in form and color. The problem was indeed alluring, but some of the best minds in nineteenth century science in Europe had been engaged at it, without bringing much order out of the chaos, and it would have looked quite unpromising to anyone but Ohm, to whom, the greater the difficulty of a subject, the more the attraction it possessed. With his wonderful power of synthesis and his capacity to discover a clue to the way through a maze of difficulties, Ohm succeeded in finding a formula of great simplicity and beauty and which covered all the individual colors. It was only after he had reached his conclusions and was actually publishing his results, that the German scientist found that he had been anticipated by Professor Langberg, of Christiania, in Norway, with regard to the principal points of his investigation, though not as to all its details. Professor Langberg^[28] had published his article in the Norwegian Magazine for Natural Sciences in 1841, and an abstract of it had appeared the following year in the first complementary volume (Erganzungsband) of Poggendorff's Annalen.

Christian Langberg (1810-1857)

Of this publication by Professor Langberg, Ohm had known absolutely nothing. He had even gone to some pains to find out, before undertaking his own investigation, whether anything had been published on the matter. At the sessions of the German Naturalists' Association, held in 1852, he had called the attention of many prominent physicists and mineralogists who were present at that meeting to the colored concentric ellipses which occur in connection with certain crystals used in the investigation of polarization. He asked whether these had ever been seen before, or whether anything had been written about them. All of those whom he consulted declared that they had not observed them, and that, so far as they knew, nothing had been published with regard to them. Accordingly, Ohm proceeded with his work, only to find, after its formal publication, that he had been almost entirely anticipated and that the merit of original discovery belonged to his Norwegian colleague.

When his attention was called to the publication, Ohm was perfectly ready to acknowledge the priority of Professor Langberg's claim and to give him all the credit that belonged to his discovery. At the beginning of the second part of his article, he said:

"I know not whether I should consider it lucky or unlucky that the extremely meritorious work of Langberg should have entirely escaped me and should have been lost to general recollection. Certain it is that, if I had had any knowledge of it before, my present investigations, which were occasioned by this elliptical system, would not have been made and I would have been spared a deal of work. In that case, however, a number of other and scarcely less important scientific principles would have remained hidden for the time being at least. Under the circumstances, the profound truth of the old proverb, 'Man proposes, but God disposes,' has been brought home to me again. What originally set me investigating this subject now proves to be without interest for science, since the problem has been solved before. On the other hand, a number of things of which I had no hint at all at the beginning of my researches, have come to take its place and compensate for it."

Perhaps nothing will show better than this, Ohm's disposition toward that Providence which overrules everything, and somehow, out of the mixture of good and evil in life, accomplishes things that make for the great purpose of creation. His eminently inquiring attitude towards science, which had on three occasions led him to tackle problems that had puzzled the greatest of experimental scientists, has been shown. He must have been, above all things, a man of a scientific turn of mind, in the sense that he was not ready to accept what had previously been accepted even by distinguished authorities in science, but was ready to look for new clews that would lead him to simpler explanations than any that had been offered before. In spite of this inquiring disposition, so eminently appropriate to the scientist, and constituting the basis of his success as an experimenter and scientific synthesist, he seems to have no doubts about the old explanation of the creation nor the all-wise directing power of a Divine Providence. This is all the more interesting, because already the materialistic view of things, which claims to know nothing except what can be learned from the matter around us, had begun to make its way in Europe, especially in scientific circles, but Ohm remained untouched by it.

Another example of this same state of mind in Ohm is to be found in the preface to his last great work, his contribution to molecular physics, in which he hoped to sum up all that he could discover and demonstrate mathematically with regard to the constitution of matter. He knew that he was taking up a work that would require many years and much laborious occupation of mind. He realized, too, that his duties as professor of physics and mathematics as well as the directorship of the museum and the consultancy to the department of telegraphs, left him comparatively little time for the work. He foresaw that he might not be able to finish it, yet hoped against hope that he would. In the preface to the first volume, he declared that he would devote himself to it at every possible opportunity, and that he hoped that God would spare him to complete it. This simplicity of confidence in the Almighty is indeed a striking characteristic of the man.

The work which Ohm began thus with such humble trust in God, was to contain his conclusions concerning the nature, size, form and mode of action of the atom, with the idea of being able to deduce, by the aid of analytical mechanics, all the phenomena of matter. Unfortunately, he was spared only to write the first, an introductory volume which bears the title, "Elements of the analytical geometry of space on a system of oblique co-ordinates." This did not touch, as he confesses, the ultimate problem he had in mind. The second volume was to have contained the dynamics of the structures of bodies, and a third and fourth were to be devoted to the physical investigation of the atom and its relation to other atoms and matter in general.

Ohm devoted himself, however, with too much ardor to his duties as teacher, to allow himself to give the time to his own work that would have enabled him to finish it. Among other things that he did for his students was to complete a text-book of physics. He confesses that he had always felt an aversion to working at a text-book, and yet was impelled to take up the task because he felt that in electricity, in sound and in optics, the only way in which his students would get his ideas, many of which were the result of his own work, was to have a text-book by himself, and he felt bound in duty to do this for them, as he had accepted the position of instructor. He succeeded in completing the book very rapidly by lithographing his lectures immediately after delivery and distributing copies to his classes.

It is almost needless to say that the work was, in its way, thoroughly original. It was accomplished with the ease with which he was always able to do things; but, unfortunately, the strain of the work told on him at his years much more than when, as a younger man, he was able to work without fatigue. He acknowledges, at the close of the preface, that the task has been too great, and that he should not have undertaken its accomplishment, and especially not in the hasty way in which it was done. This preface was dated Easter, 1854. Within a few months, Ohm's strength began to fail, and the end was not long in coming.

According to the translation of the address of Lommel, as it appeared in the Annual Report of the Smithsonian Institute for 1851, Ohm died as the result of repeated attacks of epilepsy, on July 6th, 1854. The date is correct; the mode of death, however, is surely reported under a misunderstanding. The physician who hears of epilepsy is prone at once to inquire as to its origin, and to wonder how long the patient had been suffering from it. There are no reports of previous attacks of epilepsy, and the sudden development of genuine epilepsy in fatal form at the age of 65 is quite unlikely.

His German biographer, Bauernfeind, who is quoted by Lommel as one of the authorities for the details of Ohm's life, and who was a pupil and intimate friend, gives quite a different account. Up to the very last day of his life, Ohm continued his lectures. His duties as professor appealed to his conscience as no others. On Thursday, July 6th, 1854, he delivered his last lecture. That night at ten o'clock he died. The cause of his death was given as a repeated apopleptic stroke. It is evidently because of the occurrence of more apopleptic seizures than one, that the assertion of epilepsy was introduced unto the account of his death.

For some days before his death, Ohm had been very weak, but had continued to fulfil every duty. To us in the modern time, it may seem surprising that there should be lectures in a university in July; but the second semester of the university year in Germany is not supposed to come to a close until the first of August, when the summer vacation begins, and lectures are continued until well on into July. The manner of Ohm's death, as told by his biographer friend, at once corrects the idea of epilepsy, and also shows that his passing came without any of the preliminary suffering that makes death a real misfortune. A half hour before his death, he had been entertaining some friends with lively recollections of the events of his early life in Cologne and Treves. He had been quite gay in the stories that he told, and almost boyishly happy in the recollections of those early days. For one for whom duty had meant so much in life, and who had always tried so faithfully to fulfil it, no happier call to higher things could possibly be imagined than that which came to Ohm.

On the following Sunday he was followed to the grave by numbers of friends, by all his colleagues and by most of the students of the Munich University. The university felt that it had suffered a great loss, and no signs of its grief were felt to be too much. Ohm was buried in the old Munich graveyard, where his bones still rest, beneath the simple memorial not unworthy of the modest scientist who did his work patiently and quietly, yet with never-failing persistency; who cared not for the applause of the multitude, and accomplished so much quite independently of any of the ordinary helps from others and from great educational institutions that are often supposed to be almost indispensably necessary for the accomplishment of original scientific work.

Georg Simon Ohm (1789-1854)

Ohm's personal appearance will be of interest to many of those to whom his discoveries have made him appeal as one of the great original thinkers in modern science. He was almost small in stature, even below middle height; and those who remember Virchow, may get something of an idea of his appearance when told that those who saw Ohm and knew Virchow, considered that there was a certain reminder of each other in the two men. According to his intimate friend and biographer, he had a very expressive face, with a high, somewhat doubled forehead. His eyes were deep and full of intelligence. His mouth, very sharply defined, betrayed, at the first glance, at once the earnest thinker and the pleasant man of friendly disposition. He was always restful and never seemed to be distracted. He talked but little, but his conversation was always interesting, and, except when he was in some particularly serious mood, was always likely to have a vein of light humor in it. He did not hesitate to introduce a sparkle of wit now and then into his lectures, and especially knew how gently to make fun of mistakes made by his pupils, yet in such a way as not to hurt their feelings, but to make them realize the necessity for more careful thought before giving answers, and for appreciating principles before speculating on them. He was particularly careful not to do anything that would offend his students in any way, and it is to this care that the success of his method of teaching has been especially attributed.

His habits of life were from the beginning of his career simple, and they continued to be so until the end. He was never married, and he himself attributed this to the unfavorable condition of his material resources at the beginning of his career as a teacher, and the fact that the improvement in these did not really come until he was well past fifty years of age. He once confessed to a friend that he missed those modest pleasures of family life which do so much to give courage and strength for the greater as well as the lesser sufferings of life. Most of his years of teaching he spent in boarding houses. Only after his appointment to the professorship at Munich was he able to have a dwelling for himself, which was presided over by a near relative.

Ohm is remembered as a teacher rather than as an educational administrator. His pupils recall him as one who was able to be eminently suggestive, while at the same time he succeeded in making it easy to acquire the details of information. The didactic lecture, as a method of teaching, did not appeal to him, and his success was due to the application of quite other methods. He realized how much personal influence meant, and the peculiarity of his system of teaching was an almost uninterrupted lively personal intercourse with his pupils. Demonstrations and exercises at the board always occupied the first half of his two-hour lesson, and only the other half was devoted to the setting forth of new matter. In this way, Ohm succeeded not only in influencing each student according to his personal endowments, but he also began the training of future teachers by giving them a living example of what their work should be.

The success of Ohm as a teacher was recognized on all sides. His attitude towards his scholars was very different from that which was assumed by many teachers. Instead of being a mere conveyer of scientific information, he was himself "a high priest of science," as one of his pupils declared, supplying precious inspiration, and not merely pointing out the limits of lessons and finding out whether they were known, but making work productively interesting, while neglecting none of the details. His pupils became distinguished engineers, and as this is the period in which the state railroads were being built, there was plenty of opportunity for them to apply the instruction they had received. Not only were the reports of the Royal Commission of Inspection repeated evidence of Ohm's success as a teacher, but the technical schools which were under the care of Ohm's disciples soon came to be recognized as far above the average, and as representing not only the successful teaching of technics on his part, but also the influence that his example as a teacher had in forming others to carry on the work.

How much Ohm was beloved by those who knew him best can be properly appreciated from the following passage from the panegyric delivered in Munich in 1855, not long after his death, by Professor Lamont, who had known him intimately: "Nature," he said, "conferred upon Ohm goodness of heart and unselfishness to an unusual degree. These precious qualities formed the groundwork of all his intercourse with his fellows. Despite the underlying strength of his character, which kept him faithfully at work during all his career, whenever there was question of merely personal advantage to himself, he preferred to yield to pressure from without, rather than rouse himself to resistance, and he thus avoided all bitterness in life. The unfortunate events which forced him, during the early part of his career, from an advantageous position back into private life, did not produce any misanthropic feelings in him, and when later a brilliant recognition gave him that rank in the world of science which by right belonged to him, his simplicity of conduct was not in any way modified, nor was the modesty of his disposition at all altered." In a word, Ohm was one of those rare geniuses whose magnanimity placed him above the vicissitudes of fortune. His power to do original work was not disturbed by the opposition which a really new discoverer invariably meets, but his unfailing equanimity was just as little exalted into conceit and pretentiousness by the praise which so justly came to him once the real significance of his scientific work dawned upon the world.

With the realization of all that Ohm's Work meant in the department of electricity, it is easy to understand how his name deserves a place in the science for all time. In order permanently to honor his memory, the International Congress of Electricians, which met at Paris in 1881, confirmed the action of the British Association of 1861, by giving the name ohm to the unit of electrical resistance. This is an ideal monument to the great worker. It is as simple and modest a reward as even he would have wished, expressing as it does, the gratitude of succeeding generations of scientists for all time.

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FOOTNOTES:

[23] Ohm's brother, Martin Ohm, deserves a passing word, because his life is characteristically different in certain ways and because, above all, it represents academic success, while Ohm's was almost an academic failure. He finally received the professorship in mathematics at Berlin, and came to be considered as one of the greatest professors of the subject in Europe. Their careers form typical examples of the fact, often notable in history, that talent finds a ready welcome in the academic world, while genius is often neglected, and indeed may be, and often is, the target for bitter opposition. The younger Ohm's writings are mainly with regard to mathematics, but nearly always from some general rather than special standpoint, and very often with regard to the educational side of the subject. His first book was on Analytic and Higher Geometry in their Elements. He then wrote class text-books of mathematics and mechanics. One of his works, The Spirit of Mathematical Analysis and its Relation to a Logical System, because of its value as an educational document attracted widespread attention. This book, translated by Ellis into English, was published in London in 1845. One of Martin Ohm's earlier books should be of special interest to educators because of its subject. Its rather lengthy title is, "An Attempt to Formulate a Short, Fundamental, Clear Method to Enable Those without a Taste for Mathematics to Learn the Mathematics Necessary for the Higher and Technical Schools."

[24] Fordham University Press, 1907.

[25] Makers of Modern Medicine, Fordham University Press, New York, 1907.

[26] New York, Van Nostrand Company, 1891.

[27] Published in the Annual Report of the Smithsonian Institute for the year 1891, Washington, 1893.

[28]In the address on the scientific work of George Simon Ohm, published by the Smithsonian Institute in 1891, this name is translated Sangberg. In the article by Baurenfeind, in the Allegmeine Deutsche Biographie, the name is spelled Langberg. The form of the old German L may have suggested the letter S, or it may have slipped in as a typographical error.