I purposely interrupted this letter for several days in order to write you in a really cool mood concerning your scientific communications: but how can I come to such! Every new day gives me new assurances of my happiness, new proofs of how much the good pure soul loves me. If anything could increase my happiness even more, it would be the discovery that she loved me first, even earlier than I loved her. Our first acquaintanceship in the summer of 1803 covered only a period of a few weeks (because I soon afterward left for Gotha) and was not renewed until April of this year. Although she had made such a favorable impression on me even at the beginning, I put off at that time any serious thought of marriage, partly because I had the opportunity of meeting her only a few times, and partly because of other conditions. In vain I have so often endeavored, therefore, to recall the day when I saw her for the first time. What a pleasant surprise for me, that she herself could tell me this and every following day when I saw her. Do think always of your friend, dear Bolyai, when he celebrates his happiest days on July 27 and November 22. On the latter day she became mine before God, when she will become mine before the world, certain other important conditions must determine. These will soon be decided, and I shall inform you immediately after our plans have matured.
On October 9, 1805, Gauss and Johanna were married at St. Katharine’s Church. They had their apartment at the time in Ritter’s house, where Gauss had been living as a bachelor, now Steinweg 22.
VI
—
Further Activity
In all his major writings Gauss is a notable representative of that type of scholar and investigator that Wilhelm Ostwald designated as Klassiker. In view of the general incomprehensibility of the Disquisitiones at the time of their publication, one may well imagine his pleased surprise three years later when he received a certain letter from Paris. He wrote to Olbers: “Recently I have had the joy of receiving a letter from a young Parisian geometer, Le Blanc, who is familiarizing himself enthusiastically with the higher arithmetic and gives proofs that he has penetrated deeply into my Disquis. Arith.” This word of recognition and praise is significant, since Gauss was conservative in such matters. His pleasure over this and following letters from the same correspondent would have been still greater if he had had an inkling that this “young geometer Le Blanc” who was offering additions to his own book was a woman.
In the late fall of 1806, when Brunswick was under French rule. Gauss apparently had planned to leave the city, but finally decided to remain. On November 27, a French officer named Chantel, chief of a batallion, entered the room where Gauss and his wife were. His general, Pernety, who was besieging Breslau and was busy with the encampment, sent him at the instance of “Demoiselle” Sophie Germain in Paris to inquire after Gauss’ health and if necessary to offer his protection. “Il me parut un peu confus,” Chantel reported to his general shortly after this scene. Of course Gauss was perplexed and astonished by this visitor, for he knew neither a General Pernety nor a “Demoiselle” Sophie Germain25 in Paris. In all Paris, he explained to the officer, he knew only one lady, Madame Lalande, the wife of the famous astronomer. When the officer asked further whether he wanted to write a letter to Sophie Germain in Paris and give it to him for forwarding. Gauss did not know whether to answer with yes or no. Under these circumstances he merely thanked the officer and his general for the kind attention shown him.
Not until three months later did Gauss discover through Denon who Sophie Germain really was. She saw fit to tell him herself. He wrote to Olbers, “That Le Blanc is a mere assumed name of a young lady, Sophie Germain, certainly amazes you as much as it does me.” Bolyai jokingly put these words in a letter of his to Gauss: “You once wrote me of a Sophie in Paris; if I were your wife, I would not be too pleased. Write me more of her.”
One of the fruits of Gauss’ sojourn in Helmstedt was the famous Easter formula. According to his own story his mother could not tell him the exact day on which he was born; she only knew that it was a Wednesday, eight days before Ascension Day. That started him on his search for the formula. His first article on this subject was published by von Zach in the Monatliche Correspondenz, II (August, 1800), 121. In this, the cyclic calculation of the Easter date is reduced to purely analytic processes. The simplicity of the method is extremely remarkable.
The method originally applied only to the Julian and Gregorian calendars but was presently extended to the Passover in the Jewish calendar. Gauss made note of this extension in his diary on April 1, 1801. It was published by von Zach in the Monatliche Correspondenz (May 5, 1802), p. 435. Chevalier Cisa Gresy gave the first proof of the Gaussian rule for the Jewish calendar in the Correspondance astronomique, I (1818), 556.
The involved process was designed to prevent Easter and the Passover from occurring at the same time.26 But since no cyclic calculation can accurately agree with the course of the moon, this is impossible. The event will recur for centuries; in the nineteenth century it took place in 1805 and 1825; in the present century this occurs in 1903, 1923, 1927, 1954, and 1981. The last occurrence will be in the year 7485.
Following is the original Gaussian method of calculating the date of Easter:
In the Julian calendar:
m = 15
n = 6
In the Gregorian calendar,
from 1700 to 1799:
m = 23
n = 3
from 1800 to 1899:
m = 23
n = 4
Divide the year by 19, and call the remainder
a
Divide the year by 4, and call the remainder
b
Divide the year by 7, and call the remainder
c
Divide (19a + m) by 30, and call the remainder
d
Divide (2b + 4c + 6d + n) by 7, and call the remainder
e
Hence, Easter Sunday is (22 + d + e) March. The fact that April 25 was Easter in 1734 and 1886 eluded the notice of Gauss, von Zach, and Delambre. Gauss published a second paper on the method in 1807 (September 12) in the Braunschweigisches Magazin. In 1816 he published a correction which applies to his method from 4200 on; Dr. P. Tittel, then in Göttingen, had called his attention to the need for this.
Gauss’ first major undertaking in the astronomical field is the working out of a theory of the moon, found among his papers in notebook form, and is printed in Volume VII of his Works (1906), pages 633 et seq. It dates from 1801, according to diary note 120 (“Theoriam motus Lunae aggressi sumus”).
Up to 1788 Mayer’s Lunar Tables were in use for the computation of the Nautical Almanac Ephemerides. Meanwhile, Mason of the Board of Longitude had been commissioned to correct them further. After 1789, therefore, the Mason Tables took the place of the original Mayer Tables. As the need of further correction made itself felt, the Paris academy in 1798 set up the prize question: “To determine from a large number of the best, reliable, old and new lunar observations, at least 500 in number, the epochs of the mean length of the apogee and of the ascending nodes of the moon’s orbit.”
Bürg worked over this task, using more than 3,000 observations, which he compared with the Mayer Lunar Tables, and in 1800 he received the prize (as did Bouvard, who had also worked out a paper). Bürg continued his researches on lunar motion, and Laplace also began to formulate his theory of the moon about this time. In 1800 the Paris academy set up a new prize for the fulfillment of the following conditions:
(1) To determine from the comparison of a large number of good observations the value of the coefficients of lunar disparity most accurately, to give more accurate and more complete formulas for the length, breadth, and parallax of this body, than those on which the previously used lunar tables are based.
(2) To devise lunar tables from these formulas with adequate ease and reliability for the calculation.
The division of the pr
ize was limited to no certain time.
Herein, perhaps, is to be sought the motive that led Gauss to take in hand the working out of lunar tables. He deduced as fundamental equations the differential equations of the reciprocal shortened radius vector, of the mean length (or time), and of the tangents of the breadth, and used the true length as the independent variable. His fundamental equations are, therefore, similar to those of Clairaut, d’Alembert, and those set up later by Laplace, Plana, and others, but not to those of Euler.
The integration is carried out by approximations, in which the developments progress according to powers of the eccentricity and the slope of the tangents. Gauss develops the divisors of integration according to powers of the ratio of the mean motions of the moon and earth. On that account the form given to the results agrees essentially with those of Plana’s later theory (1832). Gauss compared the result of the first approximation with the values of Tobias Mayer. Meanwhile he soon gave up the entire work again, finishing only the perturbations of the breadth. The sudden breaking off is explained in a letter to Schumacher dated January 23, 1842: “In the summer of 1801. I had just set myself the task of executing a similar work on the moon. But scarcely had I begun the preparatory theoretical work (for this it is, which is alluded to in the preface of my Theoria motus) when news of Piazzi’s Ceres observations drew me in an entirely different direction.”
Exhaustive reports on the progress of the researches of Laplace and Bürg are in the Monatliche Correspondenz (1800–1802) and this may have been the reason that Gauss did not later resume his own work. Laplace’s results appeared in 1802 in Book III of the Mécanique céleste; Bürg received in 1803 the new prize, while the printing of his lunar tables was postponed until 1806. In 1803 Gauss copied the results of Laplace’s investigations from Book III of Mécanique céleste and added a few notes, which seem to relate to the tables of Mason and the results of Burg’s researches then known.
The Duke had planned to have an observatory built in Brunswick for Gauss, and this plan would have been executed had it not been for the disturbing consequences of the French Revolution and the Napoleonic troubles, in which Carl Wilhelm Ferdinand was no indifferent onlooker.
Shortly after the rediscovery of Ceres under Gauss’ direction, there came another welcome opportunity to apply his method of planetary calculation and to add to his stature among specialists.
Olbers, while observing the constellation Virgo on March 28, 1802, had seen a star of about the seventh magnitude, which was not to be found on the star chart or in the star catalogue. He hoped that he had discovered a new planet. In order to be certain, he took a star chart and marked the exact location of this body in the heavens. The next day he awaited nightfall with great excitement, eager to ascertain whether or not this was a fixed star. The evening sky on March 29 was perfect for observing. He repeated the measurements exactly and convinced himself that the new celestial body was a planet. It had moved from its position and showed an advance of 10 minutes in right ascension and a difference of 19 minutes in declination. Before publishing this discovery he observed the star on April 3, the weather being very favorable, and had the joy of being more strongly convinced that he was dealing with a new planet.
Then Olbers wrote to von Zach in Seeberg. The letter arrived on the morning of April 4 and von Zach, by his own observation, convinced himself on the same day of the correctness of his friend’s discovery. Olbers continued his observation of the new body and sent the data to his young friend Gauss with the request that he calculate the orbit. Gauss had the problem finished on April 18; it is said that the actual calculation required three hours. Previously people had marveled when Euler performed such a feat in three weeks, when others required months. Gauss’ work was distinguished by accuracy as well as speed. The notable fact was revealed that the orbit of the body (like that of Ceres) lay between Mars and Jupiter, and that both planets possessed the same period of revolution. This new planet presented one peculiarity; while Mars and Jupiter remained near the ecliptic and did not go beyond the zodiac, this new body passed the old limit considerably.
Olbers, with the privilege accorded him as discoverer, named the planetoid Pallas and expressed the conviction that still others would be discovered. John Herschel was moved to stigmatize the hope thus: “This may serve as a specimen of the dreams in which astronomers, like other speculators, occasionally and harmlessly indulge.” Today the number of known planetoids is in excess of a thousand, and at least the first fifty were discovered under the supposition of Olbers that “the connected orbits would have their nodal points in Virgo and Pisces.”
Certain people of that day, not so well trained as John Herschel, felt themselves called upon to treat scientific activity with levity and scorn. Thus von Zach told in April, 1801, of receiving a letter from a far corner of the earth in which someone made sport of the versatile endeavors of the astronomers and gave the well-intended advice that it was now time to refrain from building of air castles. Concerning this utterance, as petty as it was senseless, von Zach wrote:
We cannot restrain ourselves from quoting here an excellent passage from a letter of our Dr. Gauss which indicated the noble qualities and attitude of this worthy scholar. “It is scarcely comprehensible,” writes Gauss, “how men of honor, priests of science, can reveal themselves in such a light. As for me, I look on such incidents only as tests of whether I work for my own sake, or for the sake of the subject concerned.” These are the onera of fame, and Gauss will experience more in the course of time since he is just entering upon his literary career. But with such a type of mind as his, with such a consciousness and striving to work only for science, these burdens will never oppress him; they will neither put him out of tune with his age, nor embitter his life. We admonished him, therefore, to persist and abide steadfastly in these noble maxims, which we also would do very well to remember, and to recall our always sprightly, happy, and worthy old patriarch and teacher in the following moral-political-mathematical calculus:
Résultat d’un Calcul mathematico-politique et moral, par le Citoyen La Lande, Doyen des Astronomes
Il y a mille millions d’habitants sur la surface de la terre.
Sur ces mille millions de têtes
Que de méchants, de foux, de bêtes,
Mais nous ne pouvons les guérir,
Il faut les plaindre, et les servir.
The above verse was copied in his notebook by Gauss from the Monatliche Correspondenz under the heading “Cereri Ferdinandeae Sacrum” and shows that Gauss remembered with good humor those who felt themselves clever or ingenious enough to sneer at his scientific accomplishments. The book contains his calculations of Ceres’ orbit and comparisons with the observations of others.
In 1804 Olbers wrote to Gauss: “From a few lines in your last letter, I can almost believe that you are under the beneficent attraction of some beautiful star whose compelling force (to put it in a few words) could soon influence you to change your confirmed bachelorhood for the state of matrimony.” This obviously refers to Gauss’ future wife. Later we shall see the strange connection between these asteroids and Gauss’ family life.
On June 22, 1802, Gauss made his first visit to Bremen, where he remained for three weeks with Olbers. Together they visited Johann Hieronymus Schröter (August 31, 1745–August 29, 1796), who was an alumnus of Göttingen, 1764–1768, and an intimate friend of the Herschel family. Although very poor in his student days, Schröter set up a private observatory in Lilienthal in 1782. In April, 1800, Carl Ludwig Harding (September 29, 1765–August 31, 1834) of Lauenburg went to Lilienthal. He had already studied theology, and was now to act as tutor for Schröter’s ten-year-old son and also as astronomer at the observatory. On September 1, 1804, he discovered the asteroid Juno. It was on this Bremen visit in 1802 that Gauss became acquainted with him. A portraitist then in Bremen, named Schwarz, made the only picture of Gauss which we have of him in youth. It was a pastel crayon sketch and remained in th
e Olbers family. Olbers writes of it to Gauss on August 21, 1803: “Above all, my warmest, heartiest thanks for the priceless gift of your portrait, so attractive to me, which our Schwarz brought me. It is astonishingly good and strikes in the same way all who see it and have known you. Schwarz has outdone himself: not a one of your features is neglected.” Gauss received as return gift a portrait of Olbers in 1805, equally successful and executed by the same artist. This gift was indescribably dear to him all his life, and at his death it passed into the hands of his physician. Dr. Wilhelm Baum, then to Professor Ernst Schering, and in accordance with the latter’s request it became the property of the Göttingen observatory in 1897.
On November 8, 1802, Gauss observed with his meager instrument (a two-foot achromatic lens by Baumann) the solar transit of Mercury. When Juno was discovered by Harding in June, 1804, he observed it with a mirror telescope by Ahort.
On August 26, 1803, Gauss met with von Zach on the Brocken, where powder signals were given for the purpose of longitudinal determinations, and the first week of September the two went to Gotha, where Gauss wanted to perfect himself in practical astronomy. On December 7 he returned to Brunswick, and also spent some time with von Zach at the Seeberg observatory. The following year he had the pleasure of again seeing his friend Olbers at Bad Rehburg (near Hanover); the latter had written him on July 6, 1804: “I am going to Bad Rehburg on August 1 and will remain there fourteen days. In a single day you could come from Brunswick to Rehburg. What a satisfaction, what delight for me, if your good genius would persuade you about this time to refresh itself at this romantically attractive place.” For Gauss these three little trips were always among the happiest memories of his youth, especially since those years closed a rich epoch in his life.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 10