Open main menu

Popular Science Monthly/Volume 81/August 1912/Notes on Gauss and his American Descendants

THE

POPULAR SCIENCE

MONTHLY

 

AUGUST, 1912




NOTES ON GAUSS AND HIS AMERICAN DESCENDANTS
By Professor FLORIAN CAJORI

COLORADO COLLEGE

UPON the Hohehagen, the highest mountain summit in the vicinity of Göttingen, there was dedicated on the twenty-ninth of July, 1911, an observation tower which commands an imposing and picturesque view of the university town of Göttingen, as well as of the ruins of proud medieval castles upon the mountain ridges beyond. This observation tower on the Hohehagen, now becoming a favorite objective point for excursionists, bears the name of a great scientist who made Göttingen famous. It is called the "Gaussturm" or "Gauss tower." Rising to a height of 120 feet, it overlooks all surrounding trees and objects. Within this tower is a room, called the "Gausszimmer," the chief ornament of which is a large marble bust of the great scientist, designed by the sculptor Eberlein. Another interesting exhibit is a reproduction of the Gauss-Weber electro-magnetic telegraph. It is well known that Gauss and Weber in 1833 had a crude telegraphic line between the observatory and the physical laboratory in Göttingen, a distance of 9,000 feet. This was eleven years before Morse sent his message from Washington to Baltimore, "What hath God wrought." Gauss and Weber employed, in signaling, the deflection of a galvanometer needle moving to the right or left. Henry and Morse in this country produced signals by an electro-magnet attracting an armature. While the Morse instrument is widely used in land telegraphy, the galvanometer needle found early application in ocean telegraphy. Germany has always prided itself on the Gaussian telegraph. On the Potsdamer bridge in Berlin there is a statue representing Gauss in a sitting position, watching with keen interest the deflection of the needle of a telegraphic instrument before him. By his side there is a youthful allegorical figure stretching a telegraphic wire around the globe.

PSM V81 D112 Carl Friedrich Gauss.png

Professor Eberlein's Bust of C. F. Gauss., recently placed in the Gauss Tower on the Hohehagen.

The Gauss tower on the Hohehagen indicates the exact location of a corner of a geodetic triangle in a survey established by Gauss. This triangle is classic in the history of geodesy. It was on that survey that the now famous instrument, invented by Gauss, called the "heliotrope," was used for the first time. It reflects the rays of the sun from one station to another many miles distant so that directions can be measured accurately and signals sent from station to station.

The high esteem in which Gauss is held in Germany is shown also by the recent dedication of another "Gauss room" in the town of Braunschweig. The house at No. 30 Wilhelmsstrasse, bears a tablet with the inscription: "In this house was born Carl Friedrich Gauss on April 30, 1777." The plan to establish in this house a "Gausszimmer" was carried out by the Historical Union of the Herzogtum Braunschweig. All sorts of Gauss relics have been gathered and are exhibited here. Photographs are shown of near relatives and the immediate descendants of Gauss, among whom are several Americans. Braunschweig has always been proud of its illustrious son. There is a statue of him in that city, on one side of which the close observer will notice a regular polygon. This geometric figure recalls Gauss's first mathematical research, the discovery of a method of inscribing a regular 17-sided polygon into a circle by means of a ruler and a pair of compasses. On the Gauss bridge in Braunschweig a bronze celestial globe exhibiting the planet Ceres reminds passers-by of another great achievement of Gauss. Among astronomers his name first became known through his determination of the elements of the orbit of this planet Ceres from the observations on it made in 1801 by Piazzi in Italy. These observations were such that its orbit could not well be calculated by the old methods, and it remained for the genius of Gauss to devise a method of computing elliptic orbits which was free from the assumption of a small eccentricity and inclination. With the aid of Gauss's data the new planet was rediscovered by Olbers in Germany. Later Gauss gave much attention to modes of computing planetary and cometary orbits.

At the observatory in Göttingen, where Gauss carried on his great researches, there has been arranged in the rooms formerly occupied by

PSM V81 D113 The gauss tower on the hohenhagen.png

The Gauss Tower on the Hohehagen, near Göttingen, dedicated July 29, 1911.

him a Gauss archive, in which the manuscripts of Gauss and other interesting material have been deposited. In the town of Göttingen there is a statue of Gauss and his friend Weber, the physicist whom we have mentioned earlier. Gauss, in a sitting posture, and Weber, standing, appear engaged in a lively scientific discussion. Besides the telegraph, Gauss and Weber designed instruments which were used in the early determination of the magnetic elements of the earth's magnetism. Through Gauss's initiative there was established the German Magnetic

PSM V81 D114 Gauss birthplace in braunschweig.png

The House in the City of Braunschweig where C. F. Gauss was born and where Gauss Relics are now on Exhibition

Union, with the object of securing systematic and continuous observations. Important as were Gauss's achievements in geodesy and the earth's magnetism, his chief scientific researches were in mathematics and astronomy. During his labors at Göttingen, extending over nearly half a century, he made profound researches in the theory of numbers, which is one of the most subtle branches of mathematics. He greatly enriched by his investigations the theory of imaginary numbers, the theory of equations, the calculus of variations, the theory of probability, the geometry of surfaces, and the subject of infinite series. Like Sir Isaac Newton, he at times displayed a disinclination to enter upon a prompt publication of his scientific deductions. As a consequence of this, others rediscovered and published results which Gauss might have claimed for himself. Thus it is now known that some of the discoveries on elliptic functions made by Abel and Jacobi had been worked out by Gauss thirty years earlier but not published. According to Professor Felix Klein, some Gaussian manuscripts reveal a knowledge of the fundamental ideas of quaternions, a subject fully elaborated later by the genius of the Irish astronomer, Sir William Rowan Hamilton.[1] Perhaps the most striking case of loss of priority of discovery due to failure to place his results at the disposal of the general scientific public, is that of non-euclidean geometry. For many years Gauss permitted his mind to dwell upon the subtle subject of parallel lines, and he reached some exceedingly original results. But he did not write down in full what he had worked out in his mind, and nothing was published by him on this topic. Off and on he would touch upon this subject in letters to scientific friends. He expressed to them his intention not to allow any part of this research to reach the general public during his lifetime. On January 27, 1829, he wrote to Bessel: "Probably I shall not be ready for a long time yet, to prepare for publication my very extensive researches on this subject and perhaps this will not happen during my lifetime, for I would dread the clamor of the Boeotians, were I to speak out in full." Imagine his surprise when the Hungarian Wolfgang Bolyai, a close friend of his during their student days at the university, sent a printed document of twenty-six pages written by Wolfgang's son, John Bolyai, in which the young Bolyai had worked out with wonderful clearness and originality the fundamental propositions of non-euclidean geometry. Gauss saw at once that he had been anticipated. How did the world-renowned mathematician of Gottingen behave toward the young and unknown Hungarian? Students of scientific history know that on questions of priority of discovery many a bitter battle has been fought. Scientific men are only human, and they frequently fail to see the full merits of rival claimants. But Gauss showed himself as generous as a man as he was great as a scientist. After reading John Bolyai's published dissertation, he wrote to his friend Gerling as follows (February 1-4, 1832): "I consider this young geometer v. Bolyai a genius of the first rank." To his old friend Wolfgang Bolyai, Gauss wrote (March 6, 1832) in this manner:

Now about the work of your son. If I begin by saying that I dare not praise it, you will doubtless be startled for a moment. But I can not do otherwise. To praise it would be to praise myself, for the entire contents of the paper, the path which your son has pursued and the results which he has reached agree almost throughout with my own meditations, entertained by me in part since 30-35 years. By this I am surprised to the highest degree. It was my intention, during my lifetime to publish nothing of my own work, of which but little has thus far been put down on paper. Most people do not have the proper appreciation of the subject in hand and I have found only a few people who

PSM V81 D116 Statue of gauss on the potsdamer bridge in berlin.png

The Statue of Gauss on the Potsdamer Bridge in Berlin.

receive with interest the things I tell them. To be able to do so, one must have felt vividly what has been wanting, and on this point most people are quite in the dark. But it was my intention, some time to write down everything, so that it would not eventually perish with me. I am greatly surprised that I am saved this trouble and it is most pleasing to me that it is the son of my old friend who has anticipated me in such a remarkable way.

Would that all men of science could show the generosity toward rivals in matters of priority that Gauss showed toward John Bolyai. Gauss recognized the genius of Bolyai, gave him full credit for what he had done and gave up his own plans of preparing a paper on the new geometry.

Gauss lived nearly half a century at Göttingen in the midst of continuous work. In 1828 he attended a meeting of scientists in Berlin. After that he never left the vicinity of Göttingen, except in 1854, when a railroad was opened between Göttingen and Hanover. In the letter of August 7, 1852, which we print below in full, Gauss refers to his intention of going to Hanover, when the railroad is completed, and he says that he has not passed a night away from his own fireside since 1830. In marked contrast to this love of seclusion is the "Wanderungslust" of two of his sons, Eugen and Wilhelm. We shall see that both of them made their homes in the United States. A letter written by Wilhelm to his father in March, 1835 (kindly shown me by Mr. William T. Gauss, of Colorado Springs, Colo., a son of Wilhelm) discloses an intense longing to make his home in America, which country made uncontrollable appeals to his imagination. Wilhelm was then twenty-two years old and away from home. Here are fragments from the long letter on this subject:

Father, I pray you again, by every earthly consideration, let me come home and next fall or winter go to America! I have written you that I can secure a position at Potsdam. . . . If you command me to accept it, then of course I must obey, but I can not remain there permanently. I have no peace day or night and in everything I do, America stands before my eyes!. . . Let me come home and study the English language during the summer, let me make the necessary preparations, and start in September of this year by way of New Orleans for Missouri.

He remained in Germany two years longer, devoting himself mainly to the study of agriculture, in preparation for the life he expected to lead in America.

Gauss had four sons, one of whom died in infancy. We have already mentioned Eugen and Wilhelm. Joseph, the oldest, was an officer in the German army, later a director of the Hanoverian railroads. In the latter part of the 30's he visited this country as a representative of his government to investigate the American railway system, then in its infancy. He maintained his residence in Germany, where later he assisted his father in the triangulation of the kingdom of Hanover. He died in 1873. His son-Carl August Gauss, of Hameln, is the only grandchild of the mathematician who is living in Germany to-day. The United States now claims most of the descendants of Gauss. He had two daughters, who were married, but had no children. The older, Minna, married Ewald, the orientalist.

It is conceded that Eugen inherited more of his father's genius than did his brothers. Eugen left for this country as a boy of nineteen. Before coming he had been attending the University of Göttingen. While he was not more reckless than other students, he spent some of his time in fighting duels, enjoying the society of boon companions, and in doing whatever else made up the gay, yet not dissipated, life of a Göttingen student of those days. The accounts of Bismarck's career give a good idea of what this life was. Upon one occasion Eugen gave a dinner to some of his student friends. Instead of paying for the score himself, he sent the bill to his father. When his father rebuked him for this, he took violent offence. Without mentioning the matter to either of his parents, he made up his mind to leave home and go to the United States. A day or two after that incident he left for Bremen to take ship for New York. Upon learning of this, the father promptly did his utmost to induce Eugen to return home, and, when failing in his endeavor, offered him money for the journey. Eugen remained in New York until his money was spent. Then he enlisted in the army of the United States as a private soldier. He was transferred with other enlisted men to a post at St. Peters in Minnesota. He had been there but a short time, when the officers of the post discovered that he was an educated man and, desirous of relieving him of the more onerous duties, placed him in charge of a small library at the post. After having served five years in the army, Eugen entered the service of the American Fur Co. and for about four years spent most of his time at Fort Pierre in South Dakota. It was about this time that his brother Joseph Gauss came to the United States to examine American railways. He brought with him letters of introduction to General Scott and other prominent men. He wrote his brother, offering to use his influence to secure him a commission in the army. This offer Eugen declined, as he had other plans laid out for himself. Shortly after a visit in 1840 to his brother Wilhelm, who had by this time come to America, Eugen settled in St. Charles, Mo., where he engaged in business. In 1885 he removed to a farm near Columbia, Mo., where he died in 1896. Whatever estrangement may at first have existed between Eugen and his father on account of his departure from home against his father's will was not of long duration. One of the letters received by Eugen from his fisher in Göttingen was written shortly after Eugen informed him of his intention to marry. It was cordial and affectionate. The original of this letter is now in the Lick Observatory.[2]

The youngest son, Wilhelm, came to America in 1837, with the consent and approval of his father. He went on a sailing vessel to New Orleans and from there traveled up the Mississippi to Missouri. Just before leaving Germany, he had married Louisa Aletta Fallenstein, a niece on her mother's side to the mathematician Bessel. In the published Gauss-Bessel correspondence mention of the young couple is frequently made. In 1855 he located permanently in the city of St. Louis, where he was engaged in the wholesale mercantile business until the year of his death, in 1879. He was recognized as one of the representative business men of St. Louis. He was a man of great warmth of heart and of fine intellectual gifts. It may be mentioned that, when he went to St. Louis to live, he brought home with him a family of his slaves, as house servants. Before the civil war he freed all of them, starting the father as a hack-driver on his own account, by giving him a pair of horses and a carriage. To be an independent hack-driver was the ambition of many a southern negro of that time.

At the present time there are three grandsons of Carl Friedrich Gauss living in Colorado, four living in Missouri, and one in California.

The following letter (hitherto unpublished and now in the possession of Mr. William T. Gauss, of Colorado Springs, Colo.), penned by the mathematician Gauss only three years before his death, is of interest, not only because of what he says of himself, but also because of the references to social conditions and to some of his scientific friends. It is dated August 7, 1852, and is written to his son Wilhelm.

Lieber Wilhelm.

Ich kann nicht unterlassen, Theresens Briefe auch einige Zeilen von mir beizufügen.

Dein Schreiben vom 16 Januar (empfangen 26 Februar) hat mir mehrern Beziehungen viele Freude gemaeht, ganz vorzüglich aber deswegen, weil daraus hervorgeht, dass Du in alien Deinen Verhältnissen mit Deiner Lage zufrieden bist. Wie wenige Menschen in Deutschland—oder soil ich sagen in Europa—können von sich dasselbe sagen! Inzwischen kann ieh nicht läugnen, dass ich mir doch von Eurer Lebensweise kein recht (be)anschauliches Bild machen kann. Manches dabei wird freilich wohl (unendlich viel mehr als in der alten Welt) in beständig fortschreitendem Wechsel begriffen und jetzt ganz anders sein als vor 14 Jahren. Reisebeschreibungen durch Nordamerika gehen selten so weit nach Westen und so schwebten für mich die dortigen Zustände wie in einem Nebel. So möchte ich z. B. gerne wissen, ob die cultivirten Grundbesitze dort noch sehr zerstreuet, oder schon enge an einander liegen, ob unter den Besitzern viele Deutsche, oder ob es grösstentheils nur geborne Amerikanef sind, welche letztere in ihrer treibenden Unruhe wie ich glaube gewöhnlich nicht gerne lange an einem Platze bleiben, ob unter Deinen Nachbarn manche sind, mit denen Du freundschaftliehen Verkehr unterhältst, ob von den vielen Auswürflingen der letztjährigen deutschen u. a. Revolutionen oder Aufstände sich auch welche bis in Eure Gegend verschlagen haben. Das Auswandern nach Amerika überhaupt scheint noch mit jedem Jahre zuzunehmen; auch aus Göttingen hat eine Anzahl ihren bevorstehenden Abgang im Woehenblatt angezeigt, meistens sind es so viel ich erfahren habe nichtsnutzige Subjecte.

Uber sonstige hiesige Verhaltnisse wird Dir ohne Zweifel Therese ausführlicher schreiben. Ich selbst fühle mit jedem Jahre mehr allerlei Altersbeschwerden; doch habe ich in Betracht meiner Lebensjahre eigentlich kein Recht zu besonderer Klage. Zu den traurigsten Folgen eines hohen Alters gehört, dass immer mehrere unsrer frühern Freunde einer nach dem andern abscheiden. Schon Ende 1850 starb Schumacher. Am 14 Februar 1851 ganz unerwartet Goldschmidt, der noch den Abend vorher wohl und vergnügt bei mir gewesen war. Dieser Verlust hat mir lange viele Sorge gemaeht, da mein eigner Gesundheitszustand mir wenig Theilnahme an den Beobachtungen in der Sternwarte erstattet. Ich habe jedoch für jetzt die Lücke recht gut wieder ersetzt, indem anstatt Eines Gehülfen jetzt zwei (in Goldsehm. Gehalt sieh theilend) angestellt sind. Es sind ein Paar geschickte für das Beobachten eifrige junge Leute. Der eine davon (Dr. Westphal) hat schon das Glück gehabt (am 24 Julius) einen Kometen zuerst zu entdecken. Meyerstein befindet sieh wohl, und hat mich ersucht gelegentlich Dich von ihm zu grüssen. Eben so Dr. Ruete, der seit mehrern Jahren hier Professor u. besonders als Augenartzt sehr gesucht ist. Er wird aber Göttingen nachsten Michaelis verlassen, da er einen glänzenden Ruf nach Leipzig angenommen hat. Die Aussicht, die Du mir machst, dass ich einmahl Lichtbilder von Deinen Kindern, oder einigen von ihnen (das jüngste wird wohl vorerst nieht so lange ruhig sitzen können) erhalten soil, erfreuet mich sehr. Einstweilen aber bitte ich Dich wenigstens die Geburtsjahre u. Tage aller Deiner Kinder mir zu schreiben. Ich weiss es bloss von dem letzten (1 Julius 1851) und dem Briefe Deiner lieben Frau an Theresen. Aus dem letztern sehe ich auch mit Bedauern, dass ein von meinem lieben ültesten Enkel an mich gerichteter Brief verloren gegangen sein muss, da ich einen solchen nicht erhalten habe. Wenn er in Deinen nachsten Brief einige Zeilen einlegen will, so soil es mich sehr freuen, und braucht er sieh mit der Sprache gar nicht zu geniren, ich empfange sie eben so gerne wenn er english schreiben will. An der Eisenbahn von Hannover nach Cassel wird recht thätig gearbeitet, auch in der unmittelbaren Nähe von Göttingen. Der Bahnhof wird vor das Gronerthor kommen nahe bei der Anatomic Erlebe ich die Vollendung (hoffentlich in etwa 2 Jahr) so mache ich wohl auch noch einmahl eine Reise nach Hannover; meinen dortigen (31/4 jährigen) Enkel habe ich auch noch nicht gesehen. Seit Sept. 1830 habe ich keine einzige Nacht ausserhalb meiner vier Pfähle zugebracht. Nun lebenwohl, mein lieber Sohn, mit Deiner ganzen Familie.

Stets Dein treuer Vater

C. F. Gauss

Göttingen den 7 August

1852

In the early part of the last century, when Gauss was still a young man, comparatively little attention was given to the mathematical sciences in Germany. In the words of a German scientist (Stern): "Germany of that day could say with the lioness in Æsop's fable: 'I have given birth to but one, but that one is a lion.'" Later in the century Germany could boast of many sons who command the lion's share of merit and distinction. The more recent German veneration for men of science and for matters pertaining to scholarship found expression in the remark once made by the Duke of Cambridge to Alexander v. Humboldt: "One frequently hears adverse criticisms of Göttingen, but as long as we have our library and Gauss, we can afford to let the heathen rage." Humboldt made the memorable reply: "I agree to this, but I must ask your Highness to interchange the order of the treasures and to give first place to the first mathematician of our time, the great astronomer, the genial physicist."

  1. Professor P. G. Tait declared that Klein is mistaken and that the Gaussian restricted forms of linear and vector operators do not constitute an invention of quaternions. Klein's article is in Math. Annalen, LI., 1898. A note by Tait appeared in Proc. of the Royal Soc. of Edinburgh, December 18, 1899.
  2. For a copy of this letter and for additional details relative to the life and intellectual qualities of Eugen Gauss, as well as information relating to other descendants of C. F. Gauss in America, see an article, "Carl Friedrich Gauss and his Children," in Science, N. S., Vol. IX., 1899, pp. 697-704.