To be sure that his plans for a heliotrope would be carried out. Gauss turned the work over to Philipp Rumpf, inspector and mechanic of the Göttingen observatory. Work began in the spring of 1821.
Gauss found that a mirror about the size of a calling card would suffice to reflect sunlight with the brightness of a star of the first magnitude, if one assumes mean atmospheric absorption. His first calculations on this were based on the work of Bouguer, and he was surprised at the smallness of the required mirror.
Meanwhile Gauss had written to Repsold in Hamburg and sent him a sketch of the planned heliotrope, requesting him to undertake the construction of one. In May, 1821, a Hamburg resident traveling through Göttingen told Gauss that one of the instruments was ready and the other one would be in production immediately. In July, 1821, Rumpf completed his first Gaussian heliotrope. An instrument of this form is now in the Geophysical Institute of Göttingen University. In the simple form, this instrument consists of a plane mirror, 4, 6, or 8 inches in diameter, which may be rotated about a horizontal or a vertical axis. This mirror is at the station to be observed, the sun’s rays reflected by it impinging on the distant observing telescope. To the observer it appears to be a star of the first or second magnitude. In later years an improved heliotrope was introduced by the geographer and engineer Bertram. Gauss’ friends were rather reticent in making suggestions to him out of their experience with the simple heliotrope. Before its completion Gauss made use of a makeshift instrument which he called the vice-heliotrope.
Encke came now from the Seeberg observatory, where he had become associate director; from July 19 to 29, 1821, he and Gauss made successful observations and experiments with the heliotrope, Encke was on the Inselsberg and Gauss on the Hohenhagen, a distance of eighty-five kilometers. As a theoretician Gauss was quite naturally enthusiastic about his first invention in the practical field; he even visualized its possibilities as a mode of signaling in time of war.
The actual triangulation covered the years 1821–1823. A large number of points were determined, the principal ones being Hohenhagen, Brocken, Inselsberg, and Hils. For practical reasons the city of Hanover was dropped as a main point of triangulation although its exact location was determined. Gauss’ measurements on the Hils occupied the time from August 7 to 27, 1821. Accompanied by Hartmann, Gauss went on September 2 to Brocken, the last triangle point covered in 1821, from which the bearings of Lichtenberg, Hils, Hohenhagen, and Inselsberg were to be taken. The signal tower on the Hohehagen had burnt; Hils had such a tower, but in view of the great distances heliotropes were used. The weather turned out to be so bad that light seldom came from Hohenhagen, and Inselsberg had sunshine only a quarter of an hour in fourteen days. No better weather was to be expected in October, hence Gauss returned on October 3 because of the expected arrival of the King, who planned to visit the library, the observatory, and the riding school. The field work had required five and a half months, and the relatively cool weather that summer had benefited Gauss’ health. From November 22 to December 14, 1821, Gauss was in Altona to get the Ramsden zenith sector; Rumpf accompanied him in order to look after the packing.
In June, 1821, Schumacher founded the Astronomische Nachrichten and invited Gauss to collaborate. He told Schumacher that he would, as much as circumstances allowed, but warned him never to expect long contributions. The paper of 1822 on the application of the calculus of probability to a problem in practical geometry was intended for Schumacher. In the letter accompanying this paper Gauss showed his condescension by remarking very bluntly that he thought it was trivial.
The survey reached its most difficult stage as it approached the Lüneburg Heath. There were almost no hills, and forests frequently obstructed the view. On April 28, 1822, Gauss again went out on reconnaissance. He found a usable point an hour and a half northeast of Celle on a plateau near Garssen, where a French signal tower had stood. This point could be connected not only with Deister, but also with Lichtenberg. Gauss turned to Falkenberg, from which he could see Deister, Garssen, and Lichtenberg. Movement north from Garssen and Falkenberg offered “unspeakable difficulties.” However, he did have the satisfaction of setting up two triangles in the heart of the heath: Wulfsode-Hauselberg-Wilsede and Wulfsode-Hauselberg-Falkenberg.
On June 1, 1822, Gauss returned home, somewhat weakened by the summer heat and the rigors of field work, to postpone further activity until he had more personnel and better instruments. He then spent fourteen days in preparation and decided to use his son Joseph as third assistant. On June 17, 1822, Gauss arrived in Lichtenberg and began measurements which ended on July 8. A moor fire in the direction of Falkenberg caused some disturbance for a week.
This summer (1822) three heliotropes were always used, as well as a heliotrope-style mounted mirror for telegraphing. From July 6 to 16 Deister was the center of activity. Joseph gave signals from Garssen, while Hartmann made the other stations visible, Müller, by cutting through woods, opened the way from Falkenberg to Wilsede. On July 18 Gauss went to Garssen, from which Falkenberg could be seen. On August 4 he went in the direction of Falkenberg and took lodging in Bergen, being forced to remain there five weeks. By the last of August Gauss was heartily tired of the operation.
On September 7 Gauss left Falkenberg and went to Hauselberg. There he could not receive any mail, and in a letter to Schumacher he humorously described his living quarters at Barlhof near Wilsede:
The sojourn here is not quite as bad as I had feared, without comparison better than in Ober Ohe, from which I worked on Hauselberg and Breithom. A family lived there, whose head writes his name “Peter Hinrich von der Ohe zur Ohe” (in case he can write), whose property embraces perhaps one square mile, but whose children tend the pigs. Many conveniences are not known at all there, for example, a mirror, a toilet, and such. Thank God, that with the agreeable cool weather I have survived rather well the ten day sojourn there.
The line Hauselberg-Breithorn had to be opened. This involved cutting through a forest, but by strenuous work and with favorable weather all the measurements on Hauselberg were completed in six days, and a stone base was set on Breithorn. Stones were very scarce on the heath, and sometimes tombstones had to be brought a distance of several miles. At all triangle points a stone base about three and a half to four feet high was used to set up the heliotrope and the theodolite. The clearing from Breithorn to Scharnhorst through Haassel was largely completed. Timpenberg was chosen for a further continuation to the north; it could be connected with Wulfsode, Wilsede, and Hamburg. However, it had to be dropped, as Gauss found out there on September 22. Measurements in Wulfsode were completed on September 23 and 24. Numerous measurements in Wilsede were completed from September 26 to October 7. On one day in Wilsede with clear atmosphere Gauss measured 150 angles without the heliotrope, a record which he equaled on only two other occasions during the entire survey. Scharnhorst was the ninth and last station of 1822; he remained there three days and started home on October 13. The angle between Deister and Lichtenberg was to be measured the following year. Actually, this angle was not measured later.
During the winter 1822–1823 Gauss restricted his astronomical observations so as to conserve his health. Early in December he sent Schumacher a paper on the transformation of surfaces, a subject which he had attacked the previous winter as the solution of a prize question. In consequence of a misunderstanding of a notice in the Leipziger Literaturzeitung, according to which no papers handed in to the Royal Society of Copenhagen were deemed worthy of the prize. Gauss early in 1823 requested the immediate return of his paper. He had not kept a copy of it. Schumacher explained to him that the news item referred to an entirely different prize question. After a lapse of two years Gauss published in February, 1823, the second part of his Theoria combinationis. Two problems in it (Articles 35 and 26) are probably the direct result of geodetic work.
The measurements of 1822 had progressed more rapidly than Gauss had anticipated. He attributed this to the
use of the heliotrope and the additional aid rendered by his son Joseph, who enjoyed the work so much that he dropped his plan to study law and enrolled as a cadet in the Hanoverian artillery corps. His father felt that he had aptitude for practical work, but insufficient inclination to abstract speculation demanded of a professional mathematician.
On March 22, 1823, Gauss was thrown to the pavement by a horse which had not been properly broken in, and had a narrow escape. The injury was limited to a black eye, cuts on the arm and the nose, and a bruise under the right eye, which fortunately was not permanently affected. He reported a week later to Olbers that rainbow colors under the eye were the only reminder of the accident.
The authorities of Bremen became interested in Gauss’ survey and gave him as an assistant young Klüver, who had previously studied under him in Göttingen. An inspector of the waterworks named Blohm, and his brother, accompanied Klüver on a reconnaissance of the triangle Haverloh-Wilsede-Falkenberg. Gauss decided to go to Bremen on May 15, 1823. On the way he learned in Hanover that the ministry had approved his plans for an extension of the survey. On May 19 he went on to Bremen and Rothenburg near Bullerberg, where he remained until May 28. He observed the Bremen church towers while Müller made a reconnaissance between Bremen and Wilsede.
On May 30, 1823, Gauss began the real work of the summer on the Timpenberg. Niendorf, the next station, could be reached from his lodging at Bäzendorf only by a difficult walk. A clearing in the woods was required to connect it with Timpenberg. On June 11 Gauss went to Lüneburg for further measurements and on June 24 he met Schumacher in Altona. On June 27 he went to Blankenese and took readings on twenty-seven points. On July 21 Frau Minna’s serious illness called Gauss home, but he stopped one day in the city of Hanover to measure one hundred positions of church towers and other points in the Hildesheim area.
On September 13, 1823, Gauss went to Brocken a second time, in order to repeat the defective measurements of 1821. In late 1823 connection was made with the Hessian triangulation, which was being carried out by C. L. Gerling, former student and close friend of Gauss. Gerling went to Inselsberg. The weather was very favorable, although at the beginning Gauss sat for three days in fog on the Brocken. On September 27 he left Brocken and from October 5 to 16 observed on the Hohenhagen, where he closed his work, which in 1823 had kept him away from Göttingen two and a half months.
Gauss’ plan of connecting Göttingen with Hamburg by a chain of large triangles had not been realized. On the contrary, the network of triangles was rather complicated. His work was thereby increased; at the stations he was often busy until midnight at his desk. There were twenty-six triangles, all of whose angles he had observed himself. In the late summer of 1824 he proposed the determination of the latitudes of the observatories in Altona and Göttingen. He wrote Schumacher that he did not like to observe in the early morning hours because his eyes seemed much weaker then; that he preferred to stay up until 2 a.m. rather than get up at 5 or 6 a.m. Gauss was unable to undertake this project at once owing to the illness of his wife and the necessity of teaching two courses. He did not succeed in carrying it out until January and February, 1824.
In July, 1823, Gauss received official notice that the prize of the Royal Society of Copenhagen had been awarded him. Frau Minna’s illness, with the resultant changes in his home, as well as some financial losses, caused him to request Schumacher to exchange the medal for cash.
On February 15, 1824, Count Münster’s rescript went in, and on March 8 Gauss was directed by the cabinet ministry to continue the survey. Since Müller and Hartmann could not leave the city of Hanover before the close of the military-school course, the beginning of the measurements was postponed until April 18. Klüver, who had been under consideration for the preparation of the new land registry in Bremen, was appointed to aid; he proved very useful to Gauss.
On May 18 Gauss went to Visselhövede in order to resume the observations of 1822 on the Falkenberg. Four heliotropes were used this year, and thus the work progressed more rapidly. By May 23 he had finished at Falkenberg and had begun on the new point Elmhorst. Moor haze delayed the completion of these observations until June 5. Tall trees made a forest path necessary in all directions. From June 7 to 18 Gauss observed on the Bullerberg.
Gauss retained his living quarters in Rothenburg when he had completed his measurements on the Bullerberg and began to observe on the Bottel, a mile and a half from Rothenburg; this work occupied his time from June 19 to 24. He went to Zeven on June 27 and found the forest path already open. In Zeven Gauss enjoyed the beautiful natural surroundings, the rather cool weather, the pure air and good living quarters in the “Posthaus” at first, and he often walked the four kilometers to his observation station in Brüttendorf. Soon however he was complaining about the sultry heat, and on July 10 when he had finished his observations in Brüttendorf and had gone to Bremen, the fatigue of the field work and mode of life in the city affected him to such an extent that he doubted his ability to continue his work.
Gauss found his friend Olbers, now sixty-six years old, in good health; he visited in Bremen for six weeks. Next he went to the Weser river near Vegesack. He took lodging in Osterholz, a mile southeast of his triangle point. On Sunday, August 22, 1824, he had procured an open coach in which he left at 1 p.m. for Garlste. The sun was shining, but suddenly rain set in when he was half way to his destination, and lasted the rest of the day. Gauss was drenched to the skin, saw nothing, and returned at half-past eight in the evening. Later he went on foot several, times from Gnarrenburg to Brillit.
On August 26 he went to Brillit and finished his observations there on August 30, although the atmosphere was very unfavorable. His assistant Baumann was using the heliotrope at a church tower in Bremen, but moor fires prevented success. A heat wave came and, as usual, affected Gauss, although the stay in Osterholz had benefited his health.
Olbers, Schumacher, and Repsold visited Gauss in Zeven; he reported that he never saw Olbers in a happier mood. On September 5, 1824, these measurements were finished; from September 17 to 24 measurements were made on the Steinberg. On September 25 Gauss again took measurements on the Bottel. The next day Gauss went to Apensen, a mile southwest of Buxtehude (where he boarded with a merchant named Köster). He was now 5,3 kilometers from his observation point Litberg, and wrote to Schumacher:
If your assistant prefers a worse but closer lodging to a somewhat better but more distant one, Sauensiek is only about 15 minutes (by foot) from Litberg. I myself have not yet been in Sauensiek, but Müller has lodged there, as well as Klüver and Baumann. I do not know whether the name comes from the fact that sows get sick there. But two breweries are there which also supply my lodging with their brew.
In Apensen Gauss could see the houses of Altona, from whose church tower the tent on the Litberg could be seen. On October 3 these measurements on the Litberg were completed, and he had to complete the measurements of 1822 at Wilsede. He boarded in Barl and enjoyed the place. Schumacher provided him with beer and wine, the latter being especially welcome. On October 17, 1824, he wrote Schumacher that he had not felt so well in years, as in the last three or four weeks—in spite of ten days of rainy weather. Schumacher had sent Gauss two sergeants to use the heliotrope; moreover. Gauss mentioned three artillery men who were aiding him. The names of two petty officers, Biester and Querfeld, are mentioned. In Barl, Gauss became acquainted with Thomas Clausen, who brought him a letter from Schumacher. Clausen seems to have aided him in proofreading the prize essay, which was now in press.
When Gauss returned home the last of October, he found out how serious Frau Minna’s illness in the summer months had been. Soon his home became the scene of disorder and worry when three of his children took the measles; his wife, weakened after two years of illness, also contracted measles and for a time hovered between life and death.
At this time strong efforts were being made to call Gauss to the University of Berlin. Soon after his return a letter ca
me from the ministry promising him a substantial raise in salary if he would reject the Berlin offer. He did not immediately agree to remain. However, the matter dragged on and he found out by the grapevine that a proposal for a liberal increment in his salary had been sent to the King in London. Soon the King’s approval arrived, and Gauss decided to remain in Göttingen although many of his friends urged him to accept the Berlin offer. His salary was raised to 2,500 thalers, and this at least in part can be attributed to satisfaction with his survey—which seemed important to Hanover.
Gauss soon overcame his disinclination to continue the survey. In March, 1825, he bought a new coach in the city of Hanover and decided to renew the triangulation early that year. He invited Schumacher and Bessel to visit him at his station Zeven, where he was also expecting Olbers. On April 18 or 19 he traveled via Hanover, Walsrode, and Rothenburg, reaching Zeven at noon April 25. In Hanover, where he stopped several days on business, he met, in the Hotel Hasenschenke, Encke, who was returning from Hamburg to Seeberg. At this time Schumacher, his guest Thune, professor of astronomy in Copenhagen, Bessel, Hansen, and Repsold went to Bremen. Schumacher, Bessel, and Hansen made some determinations of the latitude and longitude of Bremen. On Sunday, April 24, they accidentally met Gauss in Rothenburg. Upon his arrival in Ellermann’s Inn Gauss was more surprised than pleased when he first saw Thune and then the entire group. Rumpf in Göttingen was sick; this meant that during his last days at home Gauss had been forced to take apart and clean the instruments himself. The rigors of the trip and the running of errands in Hanover had left him tired. He had wanted to talk over privately with Bessel the call to Berlin. Bessel had first met Gauss in 1807 at Lilienthal. He also regretted this unsatisfactory visit with Gauss after such a long time. He thought that Gauss looked quite well.
Carl Friedrich Gauss, Titan of Science_A Study of His Life and Work Page 16