The success of Gauss and Weber with their telegraph aroused great attention at that time, at least in Germany. Steps were under way to use it on the railroad. Gauss and Weber both wrote memoranda on the subject to the directorate of the Leipzig-Dresden railroad then under construction. Weber wanted to use one rail for conducting the current and the other for its return, while Gauss proposed a copper wire of 1,6-millimeters or an iron wire of 3,8-millimeters strength for conducting and the rails for return. The railroad sent its expert to Göttingen, and after conference with them, he decided the lines would have to be underground. The plan was dropped because of its high cost. Thus Germany lost the honor of being the first to produce a practical telegraph. In a memorandum dated March, 1836, Weber recommended to the railroad Gauss’ principle of the needle telegraph, which however did not find practical application until five years later. Nevertheless, we know that Gauss and Weber were the first scientists to put electrical current in the service of communication. Lord Kelvin’s marine galvanometer of 1858 was nothing more than a Gauss-Weber needle telegraph.
The fact remains that in later years the invention of Gauss and Weber was almost forgotten, so that others claimed it. The reason for this is to be sought not merely in the personal vanity of competitors, in business interests, or in considerations of national prestige. Communication of reports on scientific work was poorly developed, and achievements of the first order were often made public in a foreign country only incompletely or at a very late date. Also, a widespread knowledge of the German language was lacking. Latin was still commonly used for scientific memoirs. Gauss and Weber had only 181 regular subscriptions to their journal on magnetism. Of these 30 went to the Prussian Academy of Sciences, 20 to the Bavarian, and 15 to the Russian.
It is almost incredible that Sir David Brewster wrote thus to Gauss on December 4, 1854:
DEAR MR. GAUSS,
I had lately a visit from our distinguished friend Mr. Robert Brown, who mentioned to me, when talking of the electric telegraph, that you had, many years ago, constructed and used one. As I am, at present, writing on the subject I would esteem it a particular favour if you would oblige me by a notice of what you have done, and of the time when you used it publicly.
The answer to this letter is probably one of the most interesting documents on the invention of the electric telegraph. It was the last letter written by Gauss, and several persons have made efforts to find it, but without success. There are two possible explanations for the loss of the letter. In leaving St. Andrews in February, 1859, and moving to Strathavon Lodge near Edinburgh, Sir David suffered an annoying and irreparable loss. He packed his carriage with valuable silverware, papers, and personal, treasured souvenirs. Through the carelessness of officials, his baggage was allowed to drop into the Firth of Forth, in the process of being transferred from the landing to the steamer. Some of the papers were destroyed and others badly defaced. Sir David married Juliet, younger daughter of James “Ossian” Macpherson, and in years after Brewster’s death most of his effects were kept at the Mansion House of Balavil estate, Kingussie, Scotland. On Christmas eve, 1903, a fire there destroyed many of Sir David’s personal papers, instruments, and other possessions. It is believed that one of these two events accounts for Gauss’ missing last letter.38
If the Gauss-Weber telegraph had been set up in a large city, it probably would have had more recognition. In those days Göttingen was a town of 9,968 inhabitants and 843 students; the railroad did not come through until 1854. Also, Gauss and Weber both shied away from priority disputes, placing their invention at the disposal of all, rather than trying to protect their rights. At the World’s Fair in Vienna (1873) and Chicago (1893) their telegraph was properly exhibited. In the Deutsches Museum at Munich and elsewhere it has “come into its own” in more recent years.
XIII
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Magnetism: Physics Dominant
Weber gave Gauss a great stimulus by searching for new phenomena, but Gauss was usually attempting to systematize and express in exact mathematical terms the experimental results obtained by others. A letter to Olbers shows that Gauss was deeply interested in the study of terrestrial magnetism as early as 1803. He urged Olbers to do something in this field. After his return from his American journey in 1804, Alexander von Humboldt began to encourage Gauss and his friends to take up research in magnetism. Olbers again tried to persuade Gauss to do some work in magnetism in 1820. The truth is that he was too busy with other subjects; it was not a lack of interest.
In 1820 Oerstedt discovered electromagnetism, and as a result the greatest scientific minds were occupied with this study in the following years. One need mention only the work of Biot and Savart 1820–1821, and the work of Ampère. Ohm’s law was enunciated in 1827. The memoir of George Green (1793–1841) on the theory of the potential appeared at Nottingham in 1828; it is uncertain whether Gauss was familiar with it. By far the most important contribution was Faraday’s discovery of induced currents in 1831. Fortunately it coincided with Weber’s arrival in Göttingen.
Humboldt had a little collection of magnetic instruments in his home, which he showed to Gauss during his visit there in 1828 and strongly urged him to give some time to magnetism. All these factors were enough to force Gauss definitely into the study of magnetism. He wrote Olbers in a letter dated October 12, 1829, about the visit of the Belgian physicist Quetelet:39 “The acquaintance of M. Quetelet has been very pleasant to me; in my yard we put on with his splendid apparatus various series of experiments on the intensity of magnetic force which granted an agreement scarcely expected by me.”
Quetelet’s visit stimulated Gauss on a point which was discussed in a paper of 1837, namely, the determination of the period of oscillation of a magnetic needle. He proposed to count the beginning of an oscillation at the point of greatest velocity instead of at the point of greatest elongation, as had been customary. Declinations of the magnetic needle were regularly made at the Göttingen Observatory as early as January, 1831. Sartorius von Waltershausen wrote that in the winter of 1832 he accidentally entered the observatory. Gauss picked up a small magnet and began to teach his friend; he showed that all the iron bars on the windows had become magnets through the effect of terrestrial magnetism. By January, 1832, he had thrown himself with all force into the investigation of magnetism, and by February of that year had succeeded in reducing the intensity of terrestrial magnetism to absolute units. The conception and theory were complete, and it was now a matter of making accurate measurements and refining the methods.
At this time Gauss had the idea of writing a major work on magnetism, but decided to publish separately a small part of it dealing with the intensity of terrestrial magnetism. In August, 1832, he began writing this memoir and on December 15 read it before the Royal Society of Göttingen. It was a memoir filling thirty-six pages, published in 1833 under the title Intensitas vis magneticae terrestris ad mensuram absolutam revocata, and may be found in Gauss’ Collected Works (V, 79). The German version appeared in Poggendorff’s Annalen (1833) and later as Number 53 of Ostwald’s Klassiker der exakten Wissenschaften. R. S. Woodward called this work “one of the most important papers of the century.” It reduces all magnetic measurements to three fundamental magnitudes: M or mass, l or length, and t or time. Mathematical and astronomical accuracy were thus brought to this part of physics: Gauss showed how absolute results could be obtained and not merely relative data based on observations with some particular needle. Coulomb’s law stated that the force of attraction or repulsion between two poles varies inversely as the square of the distance between them. Paragraph 21 of the Intensitas confirmed this law. Measurements of the intensity of magnetic force had been somewhat crude before the time of Gauss. He postulated that every magnetic body contains equal quantities of the two magnetic “fluids,” north, or positive, and south, or negative. He was the first person who recognized that such a determination is necessary if one is to arrive at a rational measurement of magne
tic quantities.
Gauss noted that magnetic forces depend on temperature and that it is necessary to determine experimentally the temperature influence in order to be able to reduce all observations to the same temperature. He then turned to the fact that the earth exerts magnetic force, discussed briefly the variations of declination, and emphasized that practically nothing was known on this subject. Then he proceeded to formulate this theory mathematically.
In Paragraph 25 of the Intensitas Gauss collected a series of numerical results on the absolute values of the horizontal intensity of terrestrial magnetism. He used as units the milligram, the millimeter, and the second; it is customary today to use the gram, the centimeter, and the second. He felt that more accurate results could be obtained by using heavier needles whose weight would be as high as two thousand or three thousand grams, and that this would help to reduce the influence of air currents.
But Gauss had more extensive plans; he desired to measure all magnetic elements (declination, inclination, variation) with the same accuracy as that achieved in measuring the horizontal intensity. In addition, he wanted to investigate the influence of temperature. He felt that terrestrial magnetism is the result of all polarized pieces of iron contained in the earth, both at the center and near the surface. Toward the end of 1832 he began to apply his methods to galvanism.
On January 29, 1833, Gauss sent an official memorandum to the university board, proposing the erection of a magnetic observatory. This proposal was immediately approved, and the building was ready for use in the fall of 1833. Gauss gave a description of it in the Gottingische gelehrte Anzeigen of August 9, 1834. Weber published a description of the equipment in 1836. Except for the side rooms, the building was a long rectangle oriented exactly in the geographical meridian, 32 feet long and 15 feet wide; all iron usually found in buildings was replaced by copper. The ceiling was 10 feet high; double doors and double windows eliminated all air currents. The observatory cost 797 thalers, a large proportion of which was occasioned by the replacement of iron by copper.
The observatory was equipped with a theodolite mounted on a special base, an astronomical clock, and a magnetometer with a cabinet. The observations in the observatory were the determination of the declination and its variation at various hours, months, and years. Readings were taken daily at 8 a.m. and 1 p.m., because the greatest variations occurred in Göttingen at this time. Gauss and Weber had seven assistants in observing, including Gauss’ son Wilhelm. On certain days in the year forty-four hours of uninterrupted observation of the variation in declination was carried out, in order to study the regular course of the variation and its frequent anomalies, such as the influence of the aurora borealis. The first such observations occurred in Göttingen March 20–21, May 4–5, June 21–22, 1834. Intervals of observation ranged from five to twenty minutes. Friends of Gauss now undertook observations in Berlin, Frankfurt, and Bavaria. In September, 1834, Leipzig, Brunswick, and Copenhagen were added to the list.
On March 21, 1834, Gauss urged Encke to come and inspect the observatory in Göttingen before setting up any equipment in Berlin. In another letter he reminded Encke that one of the main difficulties was the procurement of good mirrors. The magnetic research in Göttingen attracted wide attention, and many German as well as foreign scientists now visited Gauss in order to inspect the equipment. Among them were Oerstedt and Hansteen; Göttingen now became the center of magnetic research. Meyerstein in Bonn and Airy in Greenwich began to make observations, and in Russia this activity occurred as far away as Nertschinck. In 1836 Gauss published in Schumacher’s Jahrbuch a popular essay “Erdmagnetismus und Magnetometer” in which he reported that operations were beginning in Freiberg, The Hague, Halle, Munich, Upsala, Vienna, Dublin, Breslau, Cracow, Naples, and Kasan. Gaussian instruments were set up at more than twenty points.
A Magnetic Association was formed and Gauss and Weber decided to publish the research of its members in a special periodical. Humboldt used his great influence to persuade the British government to erect magnetic observatories at as many places as possible in the colonies. The first number of the periodical appeared in 1837 under the title Resultate aus den Beobachtungen des magnetischen Vereins im Jahre . . . edited by Carl Friedrich Gauss and Wilhelm Weber. Its six volumes covered reports of the years 1836–1841. A commercial publisher handled the venture, but from the start there were difficulties. There were only 181 subscribers, and 110 copies went to individuals. In the six volumes. Gauss published fifteen articles and Weber twenty-three, which together amounts to two-thirds of the entire content. Nevertheless, the periodical was important as a center for publication of research on terrestrial magnetism and related areas.
Airy and Christie in a report to the Royal Society of London m 1836 proposed the erection of magnetic stations at Newfoundland, Halifax, Gibraltar, the Ionian Isles, St. Helena, Paranatta, Mauritius, Madras, Ceylon, and Jamaica. Later (1839) Montreal, the Cape of Good Hope, Van Diemen’s Land, Bombay, and a point in the Himalayas were added. The fact that the apparatus and time of observations were in agreement with the German Magnetic Association shows the high esteem in which Gauss and Weber were held.
In 1837 Gauss and Weber collaborated in the invention of the so-called bifilar magnetometer. They used the idea of measuring the magnetic force of direction by means of the direction force which a fixed body suspended by two cords experiences when it is diverted from its condition of equilibrium. In the same year they published in the Resultate a paper on the invention and use of the new instrument. It seems that Snow Harris in Britain had invented the instrument independently of Gauss and Weber, but that his work was unknown to them. Lloyd in Dublin used it independently of Gauss for magnetic measurements, but Gauss has generally been given credit for the instrument.
By 1832 Gauss possessed all the essential elements of a general theory of terrestrial magnetism, and was prevented from working out and publishing it only by the lack of experimental material. He did not carry out this plan until the winter of 1838. Finally his “Allgemeine Theorie des Erdmagnetismus” appeared in Volume III of the Resultate (April, 1839).40 He proceeds from the assumption that the cause of normal terrestrial magnetism is in the interior of the earth, while doubting this assumption for disturbances. He postulates further that terrestrial magnetism is the resultant of the action of all magnetic parts of the earth, regardless of whether one assumes two magnetic “fluids” or Ampère currents. Here the magnetic potential of the earth is developed mathematically. The two points at which the horizontal magnetic force is equal to zero (the whole magnetic force being directed vertically) he calls the magnetic poles of the earth.
Gauss now applied his theory to observations. The agreement between calculation and observation encouraged him to believe that he was near the truth. He was overjoyed in 1841 when an American, Captain Charles Wilkes, found the magnetic south pole at a point which deviated only slightly from his calculations. Captain Ross had found the magnetic north pole three degrees and thirty minutes to the south of the point indicated by Gauss’ calculation.
In closing the “Allgemeine Theorie” Gauss calculated the direction of the magnetic axis, that is, the direction of the magnetic moment of the earth, the magnitude of the moment, and the strength of magnetization of the earth. He found that the earth is very weakly magnetized in comparison with steel. His calculation of the moment was within 2 per cent of the correct value.
Of special importance at the close of the “Allgemeine Theorie” was a theorem which Gauss did not prove, but merely enunciated. It stated that instead of any desired distribution of magnetic fluids inside the space of a body there can be substituted a distribution on the surface of this body, so that the effect at every point of the outer space remains exactly the same, from which one easily concludes that one and the same effect in the whole external space is to be deduced from infinitely many different distributions of magnetic fluids in the interior. He raised the question whether one may assume that in every e
lement of volume there is an equal quantity of north and south magnetism, and thought this old assumption should be checked; also whether the seat of all normal terrestrial magnetism is in the earth’s interior. Modern research has shown that 94 per cent of the earth’s magnetic field comes from the interior and the remainder from external causes. This shows us that Gauss was correct in his theory, even though he did not have experimental facts to prove it. The cause of terrestrial magnetism and the fact that the direction of the earth’s magnetic moment almost coincides with the axis of rotation are not touched on. Gauss probably had private views on the subject, but never felt ready to give them to the public. It was the methods more than the results of earlier magnetic theories which Gauss criticized. He possessed the basis for his theory of terrestrial magnetism in 1806, but had to wait thirty years for the experimental data!
Gauss and Weber, assisted by C. W. B. Goldschmidt, published at Leipzig in 1840 an extensive Atlas des Erdmagnetismus, based on their theory. In later years it was out of print, and therefore Was reprinted in Volume XII of Gauss’ Collected Works (1929).
In a sense the close of Gauss’ work in magnetism was marked by the publication in the Resultate (1840) of his “Lehrsätze in Beziehung auf die im verkehrten Verhaltnisse des Quadrats der Entfernungen wirkenden Anziehungs- und Abstossungskräfte.” He was stimulated to write this paper by his work in magnetism. It is true that his measurements of inclination came after this time. In this paper the word “potential” as the name for a certain function occurs for the first time. He had used it previously in a note of October, 1839, which, however, was not published until after his death. George Green had used the name “potential function” for this function in 1828. Green’s paper remained almost unknown even in England, and there is no evidence that Gauss was acquainted with it. Probably both of them got the term from the vocabulary of medieval scholastic philosophy. As a matter of fact it is known today that Daniel Bernoulli used the name “potential” about a century earlier than Gauss or Green, although they certainly were unaware of it.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 19