At last I find time to entertain myself with my darlings. Oh, how I long to get word of you! We all arrived here safe and sound. The journey was very hard on me, for I was uncomfortable as long as the trip lasted. As soon as I left the coach I was as happy as a fish. All our personal effects were already unpacked through the kindness of Prof. Harding, so that on our arrival at about three o’clock in the afternoon a warm room and a cup of tea greeted us. Nevertheless such a trip with “sack and pack” is most frightful and tiresome, as one can imagine; I believed the packing job was wonderful, but since I arrived there in fine shape, I wished for die sake of the fun that you had seen this chaos.
The first five days there was no end of hay and straw, now finally I am in order—with our apartment we are nothing less than satisfied. It is all connected, to name one objection. Our living room is the most tolerable; little dirty halls, a smoky draughty kitchen, old phlegmatic landlords, these are incidentally several merits, and not very apt to make the stay here pleasant for me. In the first eight days I didn’t see a soul except Harding, because it was impossible for us to make visits before Friday, when we visited 50 or 60 different families in the space of an hour, to be sure, without having heard or seen anyone. O the ridiculous people! A week ago today in spite of the bad weather we began daily to visit one or two families in a more reasonable manner (with body and soul), we are received everywhere very politely, indeed by several very cordially (confidentially. Gauss seems to stand in great respect here), also we now have visits daily from all the different people, among whom many a one is very interesting. I haven’t been in high society yet, but the people here seem to me to be trustworthy; I haven’t yet been able to make close friendship with anyone. [Omitted here are several lines bewailing the absence of friends in Brunswick, and inquiring about the price of coffee and sugar.] We are all well, my Joseph is becoming a splendid chap. He has been running about alone since two days before our departure. But to be sure this always looks awfully perilous. He gladdens us, and is my idol.
Now farewell, beloved friend, and write soon and much to your ever loving friend
HANCHEN GAUSS.
The old observatory was located on the street Klein-Paris (now Turmstrasse) in an old fortification tower, and this apartment which Hanchen mentions in the letter has not been located. In April, 1808, the family moved to the large house on the corner of Turmstrasse and Kurzestrasse 15. As a student in Göttingen, Gauss had lived at Gothmarstrasse 11 and on Geismarstrasse at Volbaum’s. The last address at which he lived before he moved to the new observatory is not known. Many of the family letters of this period are filled with references to Joseph, their only child at the time.
Gauss had just settled in Göttingen and had not yet drawn a cent as director of the observatory when a war contribution was ordered by Napoleon in the form of a compulsory loan for the newly created kingdom of Westphalia. The burden on the university was very heavy and Gauss’ portion was set at two thousand francs. One day he received a letter from Olbers with this sum, but felt he should not accept it and sent the money back to Bremen. Shortly afterward came a letter from Laplace stating that he had paid in the two thousand francs direct at Paris. Later Gauss paid back the French mathematician, with interest on the money, from his own funds. From Frankfort on the Main he received an anonymous gift of a thousand florins,28 which in later years he learned was a gift of the prince primate. Baron Karl Theodor Anton Maria von Dalberg (1744–1817), grand duke of Frankfort. This sum he kept as coming from a public purse, a tribute to his work rather than to personal friendship.
Writing under date of December 24, 1807, Frau Johanna thanked her mother for sausage and Christmas gifts sent to little Joseph, who had been ill. His celebration was to be postponed one week because of this and also because a little table and chair were not yet ready. He had been walking for some time and knew everyone, but did not talk yet. A discussion of servant problems followed.
On January 6, 1808, Johanna wrote to Dorothea Köppe again, expressing her homesickness for Brunswick and begging Dorothea not to reveal to her mother how very ill Joseph had been. She mentioned having made friends with the family of Thomas Christian Tychsen (1758–1834), professor of theology and oriental languages in Göttingen, and being especially attracted to his twin daughters Cäcilie and Adelheid, aged fourteen; also the family of Arnold Hermann Ludwig Heeren (1770–1842), professor of history, and the wife of Friedrich Stromeyer (1776–1835), professor of medicine. She mentioned a thé dansant and a concert but had absented herself from these and other social affairs because of her pregnancy. She alluded to Gauss’ astronomical observations and said he usually came to bed at one o’clock in the morning.
On February 29, 1808, Gauss wrote his parents that his wife Johanna had given birth that morning at six o’clock to a daughter not as dainty and pretty as Joseph, but well formed, strong, and healthy. The garments which Joseph wore during his first six months fit her perfectly, but the caps which Johanna had knitted were all too small. He regretted that the child had only one birthday in four years. She was named Wilhelmine, in honor of Olbers, who had already promised to act as godfather. In the family she was always called Minna, and grew up to be the very image of her mother. The child was described as loving, clever, goodhearted, pure, open, and happy. Humboldt wrote to her father that she was beautiful.
The young mother was very ill for three weeks after the child’s birth. In describing the child, she admitted that the father thought it too fat and large for a girl baby.
On April 11, 1808, Johanna’s mother wrote from Brunswick to say that Gebhard, Gauss’ father, had been taken seriously ill on Wednesday, April 6, that he had given up all hope of recovery and had made his will. She also mentioned the fact that her intended visit to Göttingen was postponed because of high water.
Then came another letter dated April 14, 1808, saying that Gauss’ father had died that day at 11:30 a.m. at his home, Aegidienstrasse 5.
In a later letter to Dorothea Köppe, Johanna described some of the social functions which she and Gauss attended in Göttingen. But there always seemed to be a note of homesickness in her letters. She danced, but Gauss could not induce her to play cards, because, she said, she would rather devote that time to the children.
In the winter semester 1808–1809 Schumacher29 went to Göttingen to study astronomy under Gauss. He kept notes on their conversations together, which he called “Gaussiana.” These have been very useful to later scholars. The intimate friendship between Gauss and Schumacher continued up to the latter’s death in 1850. Their correspondence, published 1860–1865, fills six volumes. We shall have occasion to refer to Schumacher continually in connection with Gauss’ scientific work.
When Alexander von Humboldt returned to Paris in 1804 from his American voyage, he heard the name of Gauss highly praised in scientific circles. Their first exchange of letters began in 1807. He and his brother Wilhelm had studied in Göttingen earlier than Gauss, but the three later became lifelong friends, the correspondence continuing until the death of Gauss. Another friend was Johann Georg Repsold, born September 19, 1770, in Wremen on the Weser. He was fire chief in Hamburg, and in an old artillery building had equipped an observatory with instruments which he had built himself. Repsold was long a friend of both Gauss and Schumacher. In June, 1809, he visited Gauss in Göttingen. His correspondence with Gauss relates largely to the purchase of his meridian circle for the Göttingen observatory. Repsold died in 1830 while still active, and his sons developed the workshop into a well-known firm for astronomical instruments.
VIII
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Labor and Sorrow
Gauss was now ready to publish his second major work, and Olbers referred him to Friedrich Christoph Perthes (1772–1843) of Hamburg and Gotha, the best-known German publisher at that time. Perthes had written Olbers that he had exhausted available funds on Johann Müller’s Universal History; later, however, he was glad to contract for the Gaussian work. I
t would be interesting to know what the author received for this work, which was originally written in German but published in Latin at the request of Perthes under the title: Theoria motus corporum coelestium in sectionibus conicis solem ambientium.30
Florian Cajori thus described the Theoria motus: “. . . a classic of astronomy, which introduced the principle of curvilinear triangulation; containing a discussion of the problems arising in the determination of the movements of planets and comets from observations made on them under any circumstances. In it are found four formulae in spherical trigonometry, now usually called ‘Gauss’ Analogies.’ ”31
The discovery of Ceres had suggested to Gauss’ inventive mind a great variety of beautiful contrivances for computing the movement of a body revolving in a conic section in accordance with Kepler’s laws. In the Theoria motus the author gives a complete system of formulas and processes for computing the movement of a body revolving in a conic section and then explains a general method for determining the orbit of a planet or comet from three observed positions of the body. The work concludes with an exposition of the method of least squares. This work exhibits in a very remarkable degree the effects of Gauss’ severe system of revision, in the skillful adaptation and reduction of methods and formulas, and in the careful estimate of the circumstances under which they may be most advantageously employed. We find in it no evasion of difficulties, and no resort to methods of approximation only, when the means of accurate determination are at hand. His aim was in every instance to obtain results of the same order of correctness with the observations upon which they were founded.
The Theoria motus will always be classed among those great works the appearance of which forms an epoch in the history of the science to which they refer. The processes detailed in it are no less remarkable for originality and completeness than for the concise and elegant form in which the author has exhibited them. Indeed, it may be considered as the textbook from which have been chiefly derived those powerful and refined methods of investigation which characterize German astronomy and its representatives of the nineteenth century, Bessel, Hansen, Struve, Encke, and Gerling. It is a curious fact that the date of the preface to this immortal work is exactly two centuries later than the date of Kepler’s equally renowned work Praefatio de stella Martis (March 28, 1609–1809). A few numerical errors have been found in the calculations of the Theoria motus, but these were nearly all corrected in the authorized edition of Gauss’ Collected Works, (Vol. VII, 1906). The entire work, of course, is based on Newton’s law of universal gravitation. It was forty years before the methods of the Theoria motus became the common possession of all astronomers. About that time frequent discoveries of new celestial bodies compelled them to master its methods.
Of the numerous fundamental works on astronomy planned by Gauss, the Theoria motus is the only one he presented to his contemporaries. It treats exclusively the elliptical and hyperbolic motion in so far as it concerns the determination of an orbit from observations, which leads to the conjecture that he may have postponed further investigations on this subject with the idea that his friend Olbers had successfully solved the problem of parabolic orbital determination. In the Theoria motus he applies methods for determining a hyperbolic orbit similar to those for an elliptic orbit. But he gives in the Theoria motus a numerical example only for the calculation of the elements from two radii vectores, the included angle and the time between them. In a letter of January 3, 1806, he pointed out to Olbers a certain case where the latter’s method for a parabolic orbit is not applicable. Later, in 1813, he found a correction for the method and in 1815 finally busied himself intensively with the parabolic-orbit problem. He not only gave Lambert’s equation a different form, but also developed a series of other important relations. The determination of a circular orbit (which Gauss characterized as easy and simple) was given in 1871 by Klinkerfues, his pupil, in a textbook. Gauss used the method of least squares in making the corrections as given in Articles 175–186 of the Theoria motus.
The appearance of the Theoria motus soon aroused among savants recognition and admiration for its author. Prince Primate Dalberg, already warmly interested in Gauss, sent him a golden medal; another was sent by the Royal Society in London. Sartorius tells us that Gauss became a member of all learned societies “from the Arctic circle to the Tropics, from the Tajo to the Ural, including the American societies.”32
In the year 1810 Gauss received from the Institut de France a new distinction: la médaille fondée par Monsieur Lalande, pour le meilleur ouvrage ou l’observation astronomique la plus curieuse. This prize he never allowed to be paid, because he did not want to accept any money from France. Part of the money was used by Delambre, secretary of the institute, and Sophie Germain, in purchasing a pendulum clock which was sent to Gauss and used in his room for the remainder of his life.
On September 2, 1809, Gauss wrote to his friend Karl Köppe (1772–1837) in Brunswick that he had received a call to the University of Dorpat, but rejected it because of the climate and the precarious, disorderly conditions there. Efforts were also being made at this time to call Gauss to Leipzig.
For the third time, on September 10, 1809, Gauss became a father. This child was named Ludwig in honor of Harding, the discoverer of Juno, but was always called Louis in the family; the father’s phrase was der arme kleine Louis. Olbers sent his congratulations on September 20: “May heaven make little Ludwig, in future years, the equal of his father in mind and heart.” Neither of Olbers’ expressed wishes was fulfilled. Little Louis died suddenly on March 1, 1810, only five months of age. He was buried on the family lot in St. Albans cemetery in Göttingen. Even before this, however, the great scholar had a much heavier affliction.
The birth of Minna in 1808 had been difficult and caused Frau Johanna much suffering. As a result of the birth of Louis, she died on October 11, 1809. The grief-stricken husband wrote to Olbers: “Last night at eight o’clock I closed the angel eyes in which for five years I have found a heaven.” Johanna was buried on October 14 at the family lot in the St. Albans cemetery in Göttingen. Immediately thereafter. Gauss went on a trip to Olbers in Bremen and Schumacher in Altona, returning by way of Brunswick to be with old friends there.
In 1927, Carl August Gauss of Hamlin, Germany, found a lamentation for the deceased wife among his grandfather’s papers. There are actual traces of tears on the paper, and the writing covers two and one-half pages of folio paper. It is divided into two parts, the second being dated October 25, (Bremen). The first part is written with a coarser pen and darker ink than the second; the place where it was written is uncertain. This beautiful tribute shows Gauss to be a master of the German language, and it should be added that translation does not do it full justice:
Beloved spirit, do you see my tears? As long as I called you mine, you knew no pain but mine, and you needed for your happiness nothing more than to see me happy! Blessed days! I, poor fool, could look on such happiness as eternal, could blindly presume that you, O once incarnate and now again a newly transfigured angel, were destined to help me bear through my whole life all of its petty burdens. How could I have deserved you? You did not need earthly life in order to become better. You entered life only in order to be an example for us. Oh, I was the happy one whose dark path the Unsearchable allowed your presence, your love, your tenderest and purest love to illumine. Did I dare to consider myself your equal? Dear being, you yourself didn’t know how unique you were. With the meekness of an angel you bore my faults. Oh, if it is granted to the departed to wander about invisible but still near us poor creatures in life’s darkness, desert me not. Can your love be transitory? Can you take it away from the poor soul, whose highest good it was? O thou best one, remain near unto my spirit. Let your blessed tranquillity of mind, which helped you bear the departure from your dear ones, communicate itself to me; help me to be more and more worthy of you! Oh, for the dear pledges of our love, what can take the place of you, your motherly care, your traini
ng, only you can strengthen and ennoble me to live for them, and not to sink away in my sorrow.
25 October.—Lonesome, I sneak about among the happy people who surround me here. If for a few moments they make me forget my sorrow, it comes back later with double force. I am of no value among your happy faces. I could become hardened toward you, which you don’t deserve. Even the bright sky makes me sadder. Now, dear, you would have left your bed, now you would be walking at my arm, our darling at my hand, and you would be rejoicing in your recovery and our happiness, which we would each be reading in the mirror of the other’s eyes. We dreamed of a more beautiful future. An envious demon—no, not an envious demon, the Unsearchable, did not will it so. O Blessed One, already you see clearly now the mysterious purposes which are to be attained through the shattering of my happiness. Aren’t you permitted to infuse several drops of consolation and resignation into my desolate heart? Even in life you were so overrich in both. You loved me SO. You longed so much to stay with me! I should not yield too much to grief, were almost your last words. O, how am I to begin shaking it off? O, beseech the Eternal—could he refuse you anything?—only this one thing, that your infinite kindheartedness may always hover and float, living, before me, helping me, poor son of earth that I am, to struggle after you as best I can.
It is illustrative of Gauss’ character that in this period, so humiliating to Germany and so full of his own personal grief, he proved himself a genuine son of his native land. He guarded and cherished his native language and German science. With the fascination which mathematics held for Napoleon and the admiration which Laplace voiced concerning Gauss, he could have attained the greatest honors, distinctions, and material advantages possible at that time. Nevertheless he considered the chief purpose of his life to be the fulfillment of his scientific endeavors. The French were occupying Germany and seemed to have no desire to leave. It was therefore to their interest not to neglect the University of Göttingen in their new Kingdom of Westphalia. Doubtless for this reason Gauss was annoyed no further.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 12