On April 25 Gauss was informed that the heliotrope light of the Bremen tower had appeared on the Brüttendorf mountain. Although still quite exhausted, he traveled there at once and measured some good angles. On the way back on the road from Ottersberg to Zeven, five hundred paces from the spot where his Brüttendorf base stone stood, his coach turned over as the result of a deep rut. The box with the theodolite fell on his thigh, and in his side he felt pain. The coach was not moving fast, hence there were no serious consequences, and the pains began to disappear the next day. Even the instruments were not damaged, but Gauss felt an unprecedented discouragement. From May 6 to 8 Olbers visited Gauss in Zeven and gave his spirits a lift. Gauss left Zeven and went to Bremen on May 10; measurements kept him busy there until May 22, when he went again to Osterholz in order to observe in Garlste. Thick moor haze and one thundershower after another prevented results up until May 28; hence he spent the first days in calculating station observations.
On June 6, 1825, he journeyed to Bremerlehe, where from June 7 to 13 he completed these measurements. Poor lodging at a Frau Muhl’s again affected Gauss’ health, and he longed for Varel, where the lodging was said to be good. But in Varel the weather was not very favorable; his health improved only slowly in spite of cool weather and the use of warm sea baths in Dangart, which was one hour distant.
Gauss arrived at noon on June 27 in Langwarden and remained there until July 12, 1825. Here the connection was to be made with the Danish triangulation. These measurements tortured Gauss indescribably for a long time and almost drove him to distraction; they were such as had annoyed him nowhere else. There were troubles with the instrument, refraction, the wind, cramped space in a tower, and so forth. In Langwarden Gauss took zenith distances of the ocean’s surface at ebb tide and from various points on the dikes, which he determined by a small triangulation. He did this to deduce the Göttingen observatory’s elevation above sea level.
In Jever a platform was built on the tower in order to get a view in all directions. Gauss spent two days in Wangeroog, but dropped further plans in this area, particularly since he again felt weakened by the heat. He finished on July 19 and spent the night of July 23–24 with Olbers in Bremen. He now went to Gnarrenburg near Brillit, where he stayed from July 29 to August 2. He had left this place in the spring on account of moor haze, but now had the same thing again to contend with. There was another heat wave, and he felt unable to make further measurements, except for several in Zeven, which he completed on August 4 and 5; he then returned directly to Göttingen. Gauss had planned a continuation of his survey, but actually he was now at the end of it.
Frau Minna’s physician had prescribed mineral baths for her. In the early fall of 1825 she and Gauss took a trip to South Germany via Marburg and Mannheim to Baden-Baden and back via the Black Forest, the Murgtal, Tübingen, Stuttgart, Würzburg, and Gotha. Gauss again saw Gerling, Nicolai, and Lindenau; he made the acquaintance of Eckhardt, Bohnenberger, and Wurm. He was pleased to see that many heliotropes were in use in the Darmstadt, Baden, and Württemberg surveys.
The journey did not have a good effect on Gauss’ health, since it was a very hot summer, and he was ailing most of the following winter. In October he began again to carry on some of his research on curved surfaces, which was to form the basis of his projected work on higher geodesy. This extensive and difficult subject kept him away from other work, and in the mornings he felt strained in preparing for his lectures and then returning to his meditations. At night he was getting only one or two hours’ sleep, and Olbers compared Gauss’ complaints with the pangs attending the birth of a stately hero. He doubted whether he ought to separate the purely geometrical parts from the work and publish them in the proceedings of the Royal Society, so he decided to put everything on paper. Gauss confessed that during no other period of his life did he work so strenuously and reap so little.
In the summer of 1826 Gauss busied himself with preparations for observations on the zenith sector simultaneously with Schumacher. He began in the spring of 1827 the calculation of his triangle network, which contained 32 points, 51 triangles and 146 bearings. Next he undertook a check on Krayenhoff’s measurements in the interior of Holland. This work stimulated him to apply the method of least squares, taking as examples one of his own triangulations and one of Krayenhoff’s.
Early in 1827 Gauss did not know whether he ought to regard his field work as complete or not. He regarded the determination of the difference in latitude between Altona and Göttingen as an urgent necessity. He was glad to learn that the Duke of Sussex had presented to the observatory a fine clock by Hardy. In October, 1827, Schumacher visited Gauss on the way to Munich, and also on the return trip. Gauss used the occasion to give Schumacher some instruction on the improved model of the heliotrope. Shortly thereafter Schumacher published in his journal an article on this subject by Gauss, who now began actual work on his third geodetic memoir.
In the spring of 1828 observations for determination of the difference in latitude between Altona and Göttingen began. A lieutenant of the engineers corps named von Nehus was sent at the expense of the Danish government as assistant to Gauss, who secured living quarters for him near the observatory. He would have preferred Schumacher himself. In the beginning the weather was very unfavorable, but by July 20 the measurements were finished in Altona, where Gauss had enjoyed the hospitality of Schumacher. In Göttingen and Altona together Gauss had made about nine hundred observations. The mean error of an observation was approximately the same as on the meridian circle. The observations were very strenuous and often lasted until 4 or 5 a.m. All of this had a bad effect on Gauss’ health; he was also disturbed about his son Joseph, who because of nearsightedness was having difficulty in entering an officer’s career.
Gauss had finished his memoir on curved surfaces in March, but did not present it to the Royal Society because no issue appeared at Easter. He presented it in October and published his own notice of it on November 5.
During the survey Gauss had a daily allowance of five thalers. Captain Müller four thalers. Lieutenant Hartmann and Joseph Gauss three thalers each; four assistants received only sixteen groschen each per day. After completion of the survey Gauss received a personal bonus of a thousand thalers in gold.
On March 25, 1828, King George IV decreed the extension of the triangulation over the whole Kingdom of Hanover under the direction of Gauss. The use of general staff officers was recommended, and costs were not to exceed five thousand thalers per year. Each spring Gauss presented a working plan for the summer and in the fall reported on progress made. The direction of these operations entailed extensive daily correspondence. After completion of the field work Gauss spent several weeks calculating the results, a task in which he had no assistance. The determinations of three thousand coordinates are contained in sixteen volumes, which are preserved. These coordinates formed the basis for maps in Papen’s Atlas. Completion of the calculation connected with the survey lasted as late as 1848.
The triangulation work lay in the hands of Hartmann, Müller, and Joseph Gauss. Only once did Gauss visit a station—September 7, 1828, on the Hohenhagen. He dated a historical report on the survey February 8, 1838, prepared as result of the separation of England and Hanover after the death of George IV in 1837.
In the summer of 1828 Schumacher, on his way to Königsberg to receive Bessel’s chronometer, visited Gauss for several days. On August 14, 1828, Gauss requested a leave of absence for reasons of health. Immediately after the visit to Hohenhagen just mentioned, he went to Berlin, where he attended a scientists’ convention and for three weeks was a guest of Alexander von Humboldt. There he became acquainted with Wilhelm Weber, who at that time was on the faculty at Halle and in 1831 was called to Göttingen as professor of physics. From the time of this visit to Berlin, Gauss did not spend a night away from Göttingen during the remainder of his life, except in 1854, when the railroad was opened. This journey marked a turning point in Gauss’ life and introduced t
he third epoch, when physics was dominant.
Gauss took on another burden when he was appointed member of a commission on weights and measures for Hanover. In March, 1829, he participated in a conference of this commission in the city of Hanover, and in May of the same year he journeyed there again to discuss that year’s triangulations. His son Joseph was his only field assistant that year, and Gauss was highly pleased with his work. Gauss devoted much time to processing the measurements of Hartmann and Joseph, amounting to two hundred pages each.
Toward the end of 1830 Gauss secured for his son Joseph a furlough of six weeks ending December 20, so that he could help his father in processing the measurements. At the time he was experiencing domestic trouble and grief, which will be touched on at another point in the story. He sought briefly some diversion in crystallography. In the following years the work was delayed by lack of assistants and also by the cholera epidemic.
Gauss did not publish the geodetic formulas he used in calculating coordinates. In later years his assistant Goldschmidt indicated, but did not develop, them. Goldschmidt became observer at Göttingen in 1835 after the death of Harding; in 1831 he solved the prize question of the philosophical faculty, dealing with the catenoid, which Gauss had set up in 1830.
At the instigation of Gauss, or at least with his cooperation, a trigonometric survey of the Duchy of Brunswick was begun in 1833 under the direction of Professor Friedrich Wilhelm Spehr (1799–1833), a pupil of Gauss and a professor at the Collegium Carolinum. After the sudden death of Spehr on April 24, 1833, the project bogged down. Gauss was happy to know that his native land was to be surveyed. Joseph Gauss did not have a high opinion of Spehr’s ability in field work.
In 1834 Gauss devoted four months of strenuous work to calculating measurements made in the Harz area. He did the same for measurements in the Lüneburg area, Westphalia, and the Weser region in 1836, but not with the same vigor. Captain Müller devoted himself in 1836 to the triangulation of the area on the Upper Weser between Uslar, Göttingen, and Münden and in 1837 made preparations for gathering of data in the Osnabrück area. He also reconnoitered the Aller area for future trigonometric measurements. Later Müller succeeded in connecting his points with those of the Hessian survey.
Gerling asked Gauss whether he considered a determination of longitude between Göttingen and Mannheim important. Gauss gladly promised his cooperation in observing powder signals. This determination of longitude materialized in 1837, after Gerling had ended the Hessian survey. The rooms of the Göttingen observatory had to be cleaned for the centennial jubilee, September 17–19, 1837, and this task was completed beforehand.
The signals lasted from August 22 to September 9. Besides powder signals, the heliotrope was used for sending 179 signals from Meissner and 58 from the Feldberg; at these points there were 92 and 83 powder signals, respectively. The receiving points were Göttingen, Frauenberg, and Mannheim.
In late 1838 Gauss was busy with the reduction of Müller’s measurements on the Aller. Müller then covered the western part of the area around Bremen in 1839 and in 1841 set up the network in eastern Frisia, which connected the North Sea islands with the mainland. After Müller’s death in 1843, the completion of the work fell to Joseph Gauss.
Gauss published in 1843 a memoir on topics in higher geodesy; it has been reprinted in Volume IV of his Collected Works (pp. 259–300). A second memoir in geodesy appeared in 1846 and is to be found on pages 301–340 of the same volume. He planned a major work in geodesy, but never got far with it. An outline for it, the introduction, and the early part of a first chapter were found in his papers after his death and published on page 401 of Volume IX of the Collected Works.
The last reference to a geodetic question is found in a letter addressed to General Baeyer date June 22, 1853, and printed on page 99 of Volume IX of the Collected Works. Gauss’ activity in geodesy was especially important for his measurement of a degree, which was to have been part of a measurement of the meridian. The value of his survey was lessened by the fact that except for several church towers and the like, a generation after his death the trigonometric points were no longer extant in nature. It is regrettable that so much of Gauss’ valuable time was taken up by the survey. He himself estimated that he used a million numbers in it. The great value of his work here lies in the revolutionizing of methods, especially the invention of the heliotrope and the process of angle measurement. The method of least squares found one of its richest applications in geodesy. The importance of this geodetic survey for Gauss’ work in surface theory must be discussed in another chapter. He was one of the first to show geodesy its real goal by defining the form of the earth and explaining the causes of its irregularities.
The birthplace of C. F. Gauss in Brunswick (picture taken 1884), which was destroyed in World War II.
The Gauss coat-of-arms
Silhouette of Gauss in his youth
Bust of Gauss by Friedrich Künkler (1810)
The Collegium Carolinum in Brunswick
The Schwarz portrait of Gauss (1803)
Minna Waldeck, second wife of Gauss
Portrait of Gauss by S. Bendixen (1828)
A sketch of Gauss by his pupil J. B. Listing
The courtyard of the Göttingen observatory as it appeared in Gauss’ time
Gauss’ personal laboratory in the Göttingen observatory as he left it
The Gauss-Weber telegraph (Easter, 1833)
Gauss’ principal instrument, the Repsold meridian circle
Biermiller’s copy (1887) of the Jensen portrait of Gauss (1840)
Gauss and Weber
Ritmüller’s portrait of Gauss on the terrace of the observatory
Gauss in 1854
Gauss about 1850
Portrait of Wolfgang Bolyai by János Szabó
Johann Friedrich Pfaff
XI
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Alliance With Weber: Strenuous Years
On November 30, 1830, the chair of physics at Göttingen became vacant through the death of Tobias Mayer. The Hanoverian cabinet minister in charge of university affairs36 promptly asked Gauss for his views on filling the place. These were fully expressed in a confidential memorandum to the minister dated February 27, 1831. Gauss called attention to the fact that the University of Göttingen had always adhered to the viewpoint that it was not merely a school for the instruction of students and a preserver of scientific knowledge, but also a center for participation in the development and extension of the sciences as common property of humanity. He also called attention to the fact that the Royal Society of Sciences in Göttingen was established with the last-named purpose in view. In that way Göttingen assumed its proper rank as an institution of world importance, and as long as it remained loyal to this viewpoint, it could withstand the fluctuations to which its enrollment was subject in stormy times, but must always assume its former rank with the return of more peaceful times. Such was Gauss’ opinion.
He went on to state that the new physicist must lecture to students of varying background and preparation, that he must be able to illustrate his lectures by means of well-executed experiments, that he must be well versed in all parts of physics and that he must be well trained mathematically. Gauss felt that the degree of mathematical knowledge should not be a measure of one’s value as a physicist. On the contrary, he wrote that a physicist who was a mathematician of top rank might not be the best professor of physics, at least he might not meet the needs of his students. Gauss stressed the fact, however, that a thorough physicist in the full sense of the word must be well grounded in the higher branches of mathematics. He regretted to admit that few professors of physics at German universities in his day met these high requirements.
Further on in the memorandum attention was directed to the fact that some professors of physics did not claim to be mathematically or theoretically trained, but limited themse
lves to applied topics in the area of chemistry, electricity, and the like. Gauss then reminded the cabinet minister that certain others had superficial and defective mathematical knowledge, in which instances ridiculous things frequently happened. He expressed the hope that the Royal Society of Göttingen might be spared such danger.
Gauss then proceeded to name five physicists who in his opinion met these requirements: Bohnenberger in Tübingen, Brandes in Leipzig, Gerling in Marburg, Seeber in Freiburg, and Weber in Halle. The background, training, experience, and abilities of these men were very carefully compared and discussed. Gauss wrote that he was not on such safe ground in discussing the abilities of these men as teachers; he knew their scientific ability, but as to teaching he was reduced to a knowledge of their personalities, and was attempting to be as conscientious and objective as possible. He called attention to the great difference in their ages, especially to the fact that Weber was only twenty-seven years old, and that he was the only one of the five Gauss had actually heard lecture. Weber’s lecture at the convention of scientists in Berlin in 1828 impressed Gauss as being well organized and excellent in quality. In addition, Weber’s publications showed great promise, a fine research spirit, and talent in experimenting, according to Gauss.
The question, of administrative ability in connection with filling the place was next touched on, as well as membership in the academic senate. Gauss felt that all five were men of high character in every respect. We are especially interested in what he wrote of Weber: “Weber made on me the impression of a modest amiable character, who lives more in science than in the external world. In such characters the development for real life is wont to gain direction only through events which guide it to them.”
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 17