In practical astronomy, which along with theoretical astronomy was revolutionized at the beginning of the nineteenth century, little had been accomplished in Göttingen until the arrival of Gauss in 1807. The new observatory at this time consisted only of the foundation, although its completion had been planned. Due to the disturbed and distressing conditions of the times there seemed to be little hope of seeing the plans fully realized. Gauss therefore worked for some time at the old observatory, where Tobias Mayer had been active and had made some noteworthy contributions to astronomy. It was located in an old slate-covered tower which had served in the Middle Ages as a defense for the inner town wall. Until recently parts of it could be seen on Turmstrasse.
After a long delay the Westphalian government appropriated in 1810 the sum of 200,000 francs for the further construction of the observatory, which amount was to be distributed over a period of five years until the completion of the structure. After various architects had worked on the plans, it was finally built in the Doric style under the direction of a contractor named Müller, essentially according to the wishes of the astronomers.
In 1814 the exterior of the observatory was finished—with the interior work yet to be done. The two apartments were ready in 1816; Gauss with his family took the west, and Harding the east, wing. The new instruments did not arrive from Munich until 1819 and 1821. What was then usable from the old observatory included Bird’s six-foot wall quadrant, with which old Tobias Mayer had carried on his observations for his catalogue of fixed stars, and William Herschel’s ten-foot mirror telescope, which served Harding a long time in the comet observations. The other instruments ordered from Lilienthal were scarcely used, except to show the starry heavens to visitors. The great mirrors of the Schröter telescope demanded a large scaffold, and it was originally planned to set up this structure between the west wing and Geismar-Landstrasse; but when the new instruments arrived from Munich and required Gauss’ complete attention, the plan was forgotten, and only the two large metal mirrors of twenty-foot focal length are now extant. Wilhelm Schur found them in 1886 in a strongly oxidized condition and later had them set up in the west meridian hall on blocks of wood.
In 1814 the excellent Fraunhofer heliometer with an objective of 1,5-meter focal length and an aperture of 76 millimeters arrived in Göttingen. Gauss was very much interested in this instrument at first and made several observations with it, but along with other instruments of similar construction from Berlin, Breslau, and Gotha, it was not used until the transit of Venus on December 8, 1874 (on Auckland Island), and again in 1882. The instruments of Repsold were altered for this purpose and set up in a revolving tower on the terrace of the observatory. Here the heliometer was used regularly after 1886.
After the new observatory was completed in the fall of 1816 and Gauss had moved into his rooms, he made a trip to Munich in order to inspect the new instruments ordered there. Before they reached Göttingen, the observatory had already received the Repsold meridian circle.33 This instrument, the second oldest of all meridian circles, was previously at the private observatory of Johann Georg Repsold at Elbhöhe (Stintfang) in Hamburg near the place which was later the site of the German Oceanic Observatory. H. C. Schumacher used it in 1804 for the observation of circumpolar stars. When Repsold was compelled by war conditions to give up his observatory, the instrument remained several years in his workshop and was purchased by Gauss for the new Göttingen observatory at Schumacher’s suggestion, after Repsold had made several alterations, including a new triple objective constructed according to Gauss’ formula. The instrument was eagerly used by Gauss for the first two years in observing Polaris; later he gave a method for determining its elevation. However, when the two new meridian instruments arrived—the meridian circle and the passage instrument of Reichenbach (from Munich) —Gauss no longer used the Repsold. He turned it over to Harding to get positions on it for his star atlas, and occupied himself principally with the new meridian circle.
The observatory in Göttingen lies to the south of the old town wall about five minutes’ walk from the Geismar-Tor34 and consists of a main building, 120 feet in length from east to west and 45 feet wide, on whose west and east ends two wings extend to the north, each with two-story apartments for the families of the professors. These two, together with the main building, form a court opening to the north. To the south, where the observatory presents a facade of beautiful Doric columns, three large double doors open on a terrace 200 by 40 feet, partly laid with concrete and elevated six feet above the yard. The apartments with their gardens join it at both ends. This terrace furnishes room for transportable instruments and also for two iron revolving towers with the Fraunhofer heliometer and little Merz refractor, and can also be used for teaching purposes. The view from the terrace has been cut down by the growth of the city beyond the limits of the old town fortification wall out to the horizon, yet it has been possible to keep free and open the view from the Reichenbach meridian circle. To the east a strip of the horizon is lost by the Hainberg, on whose slope the observatory lies. The main building contains in the middle a rotunda with two opposite portals opening on the court and on the terrace. At the north portal the staircase leads to the dome room over this hall. To the east and west one goes from the hall out into two equal-sized meridian halls of 30 feet in a north-south direction, 20 feet east-west, 25 feet high; then come two large halls on the east and west, one serving as a lecture room and the other as a library. These rooms have doors to the terrace and the apartments so that all rooms are connected with each other. The rotunda in the center of the entire structure was covered over at the construction of the observatory by a revolving dome made in Göttingen. Not until 1888 was a new dome, 30 feet in diameter, set up by Grubb of Dublin.
To the joy and surprise of astronomers the great comet of 1811 emerged unexpectedly from the blue sky. Gauss saw it for the first time on August 22, deep in the evening twilight. Actual observations could not be carried out until later, partly because of the cloudy weather and partly because the view from the north side of the old observatory was cut off by buildings. But in early August, when the result of the observations made by von Zach arrived. Gauss calculated the parabolic elements of the comet according to several of these data, and calculated its orbit. The comet’s reappearance proved these calculations to be entirely correct, as was also his prediction that it would exhibit greater brilliance after its transit through the solar region. The peoples of Europe saw in the comet only a chastisement of heaven, a prelude of the burning of Moscow and an omen of Napoleonic dominion.
Napoleon’s great army, however, soon lay buried in the icy fields of Smolensk and along the Beresina. Germany armed herself. Her ally, the Cossacks, for whom there was great sympathy, soon came to her aid. A Cossack officer was naive enough, after he had allowed Gauss to show him the observatory, to demand as a perpetual memento the only chronometer there, which had been presented by King Jérôme. After the fall of Napoleon when the “good old days” returned to the country. Gauss enjoyed at all times the good will of the kings and the governing board of the university. The new observatory, construction of which had been ratified by the Westphalian government, as stated, was soon completed after a fashion. It was in this provisional condition when the director moved into his apartment in the fall of 1816.
IX
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The Young Professor: A Decade of Discovery, 1812–1822
Gauss spent exactly four years of happiest married life with Johanna, whom he loved most passionately. That he married so soon after her death appeared strange to relatives and friends. The same sort of thing is to be found today; especially do relatives of the first wife have that feeling. Yet it is easy to understand why a bereaved husband takes such a step. It is a well-known fact that men who have had an unusually happy married life remarry in most cases soon after the death of the wife because the isolation is unbearable. Such was the case with Gauss. It was even worse for him, because he was robbed
of the serenity and peace of mind so necessary for successful scientific work. Moreover, the knowledge that he was compelled to give a new mother to his children, the real legacy of his youthful love, was dominant in his thought. They sorely needed a mother’s loving care and discipline.
His choice fell on Minna Waldeck, the youngest daughter of the Göttingen professor of law Johann Peter Waldeck (1751–1815) and his wife, Charlotte Augusta Wilhelmine Wyneken (1765–1848). Minna’s full name was Friederica Wilhelmine, although she always used the short form. She was born April 15, 1788, and, although eight years younger than Gauss’ first wife, had been her best friend in Göttingen. Just before Gauss courted her, she had broken off an engagement and was thus in a somewhat depressed mood. His courtship did not immediately remove this condition. It was not easy for a girl of her type to shift her affections quickly to another. When she finally did accept the offer of marriage, it was due in a considerable degree to parental influence. Gauss was very welcome as a son-in-law to the aristocratic Hofrat Waldeck and his wife.
Reason thus played a part in this marriage, more so in the case of Minna than in the case of Gauss. The engagement (April 1, 1810) was put to a hard test, but eventually the marriage proved to be a very happy one. It was easy for Gauss to win quickly the full love of Minna. He felt profound gratitude for her domestic qualities and her loving care of his children, as though they had been her own. The children in turn loved her—a proof of her desire to make her husband and stepchildren happy. However, it must be admitted that Minna did not possess that hearty, happy nature so characteristic of Johanna. Gauss consulted her parents before he addressed her. Encouraged by them, he wrote on March 27, 1810, to Minna:
With beating heart I write you this letter upon which the happiness of my life depends. When you receive it, you will already know my wishes. How will you, best one, receive this? Shall I not appear to you in a disadvantageous light, because not half a year after the loss of a mate so well loved, I already think of a new union? Will you therefore consider me fickle or even worse?
I hope you will not. How could I have the courage to seek your heart if I did not flatter myself that I stand too well in your opinion for you to think me capable of any motive for which I should have to blush.
I honor you too much to wish to conceal from you that I have only a divided heart to offer you, in which the image of the dear transfigured spirit will never be extinguished. But if you knew, you who are so good, how much the departed one loved and honored you, you would understand that in this important moment, when I ask you whether you can make up your mind to accept the place she has left, I see her vividly before me, smiling joyfully upon my wishes and wishing me and our children happiness and blessing.
But, dearest, I will not bribe you in the most serious affair of your life. That a departed one would look down upon the fulfillment of my wishes with sincere joy; that your mother, whom I have informed of it (she herself will tell you what has induced me to do so)—that your father, who through your mother knows of it, both approve of my intentions and hope for the happiness of us all from it; that I, to whom you were dear from the first moment when I made your acquaintance, should become supremely happy through it, all this I mention only for the purpose of begging you, of imploring you, to give this no consideration, but to consider only your own happiness and your own heart. You deserve a happiness completely pure, and you must not allow yourself to be influenced by any subordinate considerations which lie outside of my personality, of whatever kind they may be. Let me also confess to you quite frankly that however modest and easily satisfied I am in my claims on life otherwise, there can not be for me any halfway condition in the narrowest, closest, domestic relation, and there I must be either extremely happy or very unhappy; and even the union with you would not make me happy if through it you too would not become entirely so.
I probably have had for some time a share in your good wishes: ask yourself, my dearest, whether you are able to give me more. If you should find that you could not, do not hesitate to pronounce judgment over me. But I would not be able to find words to express my happiness if you allowed me to call myself by a still more beautiful name, than that of your warmest friend
carl friedrich gauss
The wedding is entered on the records of St. John’s Church in Göttingen under date of August 4, 1810. At this time Gauss desired his mother to live with him, but she did not do so until 1817. Minna belonged to an aristocratic family; her descendants still treasure the Waldeck crest. This new marital bliss was not of long duration. As early as 1818 Minna’s health began to fail. The same year she went to the spa in Pyrmont for treatment. In 1820 and 1824 she tried Ems. Letters of this period leave no doubt that she was suffering from consumption. There were short intervals of improvement, but the disease progressed almost incessantly. Minna bore Gauss three children: (1) Peter Samuel Marius Eugenius, always called Eugene, who was born July 29, 1811; (2) Wilhelm August Carl Matthias, always called Wilhelm, who was born October 23, 1813; and (3) Henriette Wilhelmine Caroline Therese, who was born June 9, 1816, The daughter was always called Therese. Later these children of the mathematician will enter our story more fully.
Minna became practically a semi-invalid and thus could not take the social position to which she was entitled. The liberal allowance of money given to her was useless, as far as social life was concerned. Some of it was spent in collecting silverware; she had a cabinet in her room where she kept her rare pieces. Gauss took his coffee with Minna and (after 1817) his mother every afternoon, his daughter Therese sitting close to him. In 1848, the year Minna’s mother died, a number of her relics, as well as some pieces of the silver, were sent to Eugene and Wilhelm, who had migrated to the United States. Letters, family mementos, and some of Minna’s jewelry were also included. Unfortunately the ship sank and all these souvenirs were lost.
A gold medal issued to Gauss by George V of Hanover was in later years converted into spectacle rims by Eugene, who also unfortunately burned most of the letters his father had sent him. Wilhelm used to tell of King George’s visit to Gauss’ home. Great preparations were made for his entertainment. Two of the mathematician’s sons, dressed in black velvet suits, stood at the doorway as the king approached and dropped flowers in his path. The descendants treasure Gauss’ small cup and saucer bearing the inscription, Meinem guten Vater. They also have a tiny covered china dish decorated with dainty gold-painted china flowers, which served Gauss as a match box. They use under glass in a tray a piece of petit point embroidery which decorated a pillow in Gauss’ home. The bright reds, blues, and yellows of the gay design have remained fresh and attractive.
Minna died on September 12, 1831, at the age of forty-three. More must be said later concerning her death, which was undoubtedly hastened by grief over her son Eugene’s behavior and his sudden migration to America.
In April, 1810, Gauss had a call to the Royal Academy of Sciences in Berlin; this was engineered by Wilhelm von Humboldt. The marriage to Minna strengthened his ties in Göttingen and contributed much to his decision to reject the Berlin offer. This offer was renewed in 1821 and 1824; it hung fire until 1826. Yet in the beginning he did consider accepting, because in Berlin he would have had full time for research and observation—freedom from teaching duties. However, he enjoyed the companionship of young scholars, and in a sense felt well repaid for his teaching when he later saw substantial scientific accomplishment among his students. Their testimony refutes the charge that Gauss was not a good teacher.
On January 30, 1812, Gauss presented to the Royal Society of Sciences at Göttingen his “Disquisitiones generales circa seriem infinitam”:
This memoir was published in the Commentationes of the Royal Society, Vol. II (1813); the German translation by Dr. Heinrich Simon did not appear until 1888. The Latin text was published in Gauss’ Collected Works (Vol. III, 1866), however, and included a continuation found in his papers after his death. This memoir is important because
it founded a section of mathematical literature in which later such names as Kummer, Weierstrass, and Riemann were prominent. From the manuscript it appears that Gauss had originally intended to present this paper in November, 1811. Thus Gauss opened the critical or modern period of research on infinite series. Pfaff called this one the “hypergeometric series”; Euler had studied it, but Gauss was the first to master it. For the first time the convergence (validity) of an infinite series was adequately investigated.
This decade of his life was an especially productive one for Gauss. His work of this period covered a wide range of subjects in approximately two dozen memoirs. A number of them deal with difficult problems in mathematical physics, while others cover theoretical astronomy as well as observations, particularly of the asteroids and comets. Several papers had as a subject astronomical instruments recently acquired, and optical problems connected therewith. One finds also topics in the theory of numbers, and logarithms; he gave, too, a second and third proof of the fundamental theorem of algebra.
The years 1816 and 1817 mark the close of Gauss’ work in the field of theoretical astronomy. His later astronomical activity belongs to the area of observational and spherical astronomy, while the emphasis shifted to related domains. A fairly complete record of activity at the Göttingen University Observatory is given by the observation books still to be found in its library catalogue. This manuscript bears the title “Diary of Astronomical Observations at the Observatory in Göttingen.” It is in two volumes and a small quarto notebook in the Gauss papers. In it most results of observations are entered in chronological order. While the notebook covers only the time from January 1 to July 31, 1808, the first volume of the diary does not begin until November 3, 1808. With some gaps, this diary runs to April, 1822. After that date Gauss kept special records of his observations, mostly of comets and planets, on separate sheets of paper; these papers are not complete.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 13