Krayenhoff, Cornelis Rudolphus Theodorus

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Krayenhoff, Cornelis Rudolphus Theodorus

(b. Nijmegen, Netherlands, 2 June 1758; d. Nijmegen, 24 November 1840)

geodesy, engineering.

Krayenhoff was the son of C. J. Krayenhoff, a lieutenant colonel of engineers, and Clara Jacoba de Man. Sensitive to disappointments in his own military career, his father intended him for the bar. Thus, in 1777, after completing grammar school, Krayenhoff matriculated as a Jaw student at Harderwijk, but his interest in physics drew him to other faculties, where he took the not unusual two degrees, in science (1780) and in medicine (1784). He mounted the first lightning rod on a public building in the Netherlands, on the bell tower at Doesburg, near Arnhem, in 1782. The following year he published a Dutch elaboration of a French treatise on electricity.

During ten years of medical practice in Amsterdam, Krayenhoff continued his scientific pursuits, giving well-attended lectures on physical subjects. His profi. ciency impressed scientists, including Van Swinden, Paets van Troostwijk, and Van Marum. When the French army occupied, or liberated, Holland in 1795 the patriot Krayenhoff was persuaded to give up medicine for a military career. After commanding the forces in Amsterdam, he was appointed general of engineers. He became minister of war under King Louis Bonaparte, but he was relieved within the year and gladly returned to the more palpable tasks of engineering.

Krayenhoff zealously studied the arts of war, especially that of fortification. He strengthened to the utmost the defenses of Amsterdam until Napoleon ordered the king to cease further extensions. At the impending incorporation of Holland into the French empire, Krayenhoff urged using his forts for armed resistance, but the king had to clear the way for his imperial brother. In 1811 on a visit to Amsterdam, the third city of his empire, Napoleon severely rebuked Krayenhoff, who shouted at the emperor that he was responsible for his former conduct to nobody but King Louis. During a tour of inspection a week later, Napoleon admired Krayenhoff’s defense works and invited him to lunch in the fortress of Naarden. The general was later summoned to Paris to join the commission on fortifications, which, happily, also gave him time to visit each session of the Société des Sciences for “solid instruction” and to complete his Précis historique.

Under King William I, Krayenhoff was fully occupied with fortifications (for which he visited Curaçao in 1825) and with hydraulic engineering, regulating the great rivers and draining lakes. Pen. sioned in 1830, he devoted his lime fully to physics and astronomy. He was buried at Fort Krayenhoff near Nijmegen.

In 1798 it was decided to follow the French example and divide the “Republique Batave, une et indivisible”. into départements and arrondissements, for which purpose a committee with broad powers was installed. The first need was a suitable map of the whole terri. tory. All kinds of maps were collected, but their poor quality made it impossible to fit them together. Krayenhoff then wrung from the committee an order for effecting a triangulation, and during most of 1799 he measured, with a sextant, angles from and between church towers. In February 1800, with a specially forged chain, he measured a base on the ice of the Zuider Zee about 5.6 kilometers long. This survey enabled him to complete two of the nine sheets planned for the great map. On showing them to Van Swinden, then a member of the Directory, he was amply praised for having achieved so much by such simple means. All the same, it was to be regretted that this occasion had not been seized upon to obtain an extension of the triangulation done by Delambre and Méchain.

As a member of the committee for weights and measures (about 1796 to 1799), Van Swinden had had to recalculate the 115 triangles involved and thus was completely familiar with this famous endeavor. He explained to Krayenhoff the method and necessary instruments, and what precautions were needed. The general’s enthusiasm was boundless. His committee objected that with this new project all observations with the sextant would then be thrown to the winds, but Krayenhoff pleaded that these would be highly useful as a preliminary for the great undertaking. If the sextant work was not followed up, what a poor opinion the world would form of the state of science in the land of Huygens and Snellius!

Krayenhoff began by remeasuring fifteen of the twenty-two triangles observed in Flanders and Zeeland by the French astronomer J. Perny de Villeneuve. Some discrepancies, however, made him distrustful and he started again, taking as his base a side of the northernmost triangle determined by Delambre with its vertex at Dunkerque. Van Swinden put at his disposal an excellent repeating circle of Borda. Krayenhoff’s military duties caused frequent interruptions, once of two years in succession, but by 1811 the whole territory was covered by 162 triangles.

Krayenhoff in his Précis historique gives a full account of the measured angles and of the reductions applied. The measurements are of the highest quality, and still more credit is due Krayenhoff as the first to adjust completely an extensive network of triangles. Here he made an original contribution by introducing“the rule of sines in a polygon” (Fig. 1). This elemen. tary proposition was in itself nothing new—Krayen. hoff states that he came upon it in Lazare Carnot’s Géométrie de position. But his demonstration of its easy and useful application in geodesy was a memo. rable feat.

The then standard triangulation method generally comprised simple chains of triangles, limited only by the obvious condition that the angles of a triangle must add up to 180° + έ (έ being the spherical excess, I″ for every 198 square kilometers of the triangle’s surface). In the network the angular tour of the horizon about a central point has to equal 360°. The

high accuracy obtained is most clearly shown by the minor difference in length Krayenhoff was confronted with when a common side of two triangles was cal. culated along two different paths through the network. Of the fifty-two sides involved, twenty-nine showed a difference of less than 2.10-5 and only five one of more than 5.10-5. For the determination of the azi. muth, Krayenhoff introduced a simple method consisting in a determination of the time when the sun is passing the vertical plane through the line of vision.

Krayenhoff’s work had been abundantly extolled in the first half of the nineteenth century, especially in Holland but also by Delambre. Then grudging, adverse criticism came forth from Dutch scientists. Their disapproval followed upon an unfair treatment by Gauss, who had taken as representative the two triangles with the largest errors out of the list of 162 triangles in Krayenhoff’s Précis historique, intimating in this way that the adjacent Dutch triangulation was of a yet poorer quality than his own work in Hannover (see Dictionary of Scientific Biography, V, 303). He must have considered the rule of sines in a polygon so elementary that he forgot to mention Krayenhoff’s priority. Since then Gauss’s overwhelming influence has thrust Krayenhoff into oblivion. In Holland, however, an active study of Krayenhoff’s achievements has been carried on by geodesists and astronomers.

Another example of Krayenhoff’s inventiveness is a contrivance for gauging average stream velocity. A hollow cylinder, partly emergent and held in a vertical position by disks of lead, will float along at mean velocity in a certain tract, when the adjusted load keeps its lower end just clear of the bottom.


I. Original Works. Krayenhoff’s works on geodesy include “Batavische, Schreiben des Oberst-Leutenant Krayenhoff an Freiherrn von Zach,” in Monatliche Correspondenz, 9 (Feb. (1804), 168, 264, with map; original Dutch text in Algemene Konst en Letterbode (Apr, 1804), pp. 225–240, with map; Instructie voor de Geographische Ingenieurs door Generael-Majoor Krayenhoff, Ministry of War (The Hague, 1808), with maps and drawings; Hydrographische en Topographische Waarnemingen in Holland door den Oud-minster van Oorlog V. R. T. Krayenhoff (Amsterdam, 1813).

Précis historique des opérations géodésiques et astronomiques, faites in Hollande, pour servir de base à la topographic de cet état, exécutées par le Lieutenant-Général Krauyenhoff (The Hague, 1815), with map scale 84:100,000,000; 2nd ed. (1827), with a report by Delambre; Chorotopographische Kaart der Noordelijke Provinciën.

An original written protocol of Krayenhoff’s observations, and of his calculations in 18 vols., is preserved at the University of Leiden, codex 241.

Krayenhoff;s autobiography is Levensbijzonderheden van den Leutenant-Generaal Baron Krayenhoff, door hem zelven in schift gesteld en op zijn verlangen in het licht gegeven door Mr. H. W. Tydeman prof. jur (Nijmegen, 1844).

II. Secondary Literature J. D. van der Plaats, “Overzicht van de Graadmetingen in Nederland,” in Tijdschrift voor Kadaster en Landmeetkunde, 5 (1889), 217–243, 257–306, with map, and 7 (1891), 65–101, 109–133; W. Koopmans, “De laatste arbeid van Krayenhoff,” in Geodesia (1962), pp. 144–147; N. van der Schraaf, “Historisch overzicht van het Nederlandse driehoeksnet,” in Nederlands geodetisch tijdschrift, no. 4 (1972); N. D. Haasbroek, Investigation of the Accuracy of Krayenhoff’s Triangulation 1802–1811 in Belgium, the Netherlands and a Part of North Western Germany, publication of the Netherlands Geodetie Commission (1973).

W. Nieuwenkamp

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Krayenhoff, Cornelis Rudolphus Theodorus

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