Our historic person in the second article is Leonhard Euler whose 300th birthday was celebrated in September 2007 in Basel at a special congress, organized by SCNAT. Very impressive papers were presented about the person and the scientist Euler, but also to correct strange misunderstandings. While Euler is regarded everywhere as the great mathematician, some rather populist literature exist where the physicist Euler is considered as of secondary importance. This astonishes since latest publications about the modelling of turbulences directly relate to Euler's fundamental examinations [1]. A possible reason for this misjudgement was mentioned in the paper of Michael Eckert and will be presented in the following article. Our author is physics historian at the 'Deutsches Museum' in Munich and a recognized expert for fluidic mechanics. Without anticipating his contribution we will conclude that 'Risk management' would have been a need even 250 years ago. Physicists who often stand at the beginning of a technical value-added chain are well advised to control the subsequent engineering processes.

Bernhard Braunecker, SPS-Secretary


[1] ’Turbulenzübergänge’, B. Eckhardt, B. Hof, H. Faisst, Physik in unserer Zeit; 5/2006 (37) p.212. Some more impressive facts about the actuality of Euler’s work were presented on the conference about „Euler Equations: 250 Years On“, see www.oca.eu/etc7/EE250/.


Euler and the fiasco at Sanssouci

"I wanted to make a fountain in my Garden", Frederic the Great wrote to Voltaire on 25 January 1778. But the water-art project ended in a fiasco. When the King of Prussia looked from his castle at the fountain installation underneath in the Park of Sanssouci, his eyes were not enchanted by fountain jets. The fountain design was supposed to be executed according to the latest knowledge in hydraulics and should even surpass Versailles with its splendor. "Euler calculated the effort of the wheels for raising the water to a basin, from where it should fall down through canals, in order to form a fountain jet at Sans-Souci. My mill was constructed mathematically, and it could not raise one drop of water to a distance of fifty feet from the basin. Vanity of Vanities! Vanity of mathematics." [1]

Since then the fiasco at Sanssouci stands out as an example for the gulf between theory and practice. And Leonhard Euler, the mathematical genius from Basel, became a target of mockery and malicious joy. "The physical universe was an occasion for mathematics to Euler, scarcely a thing of much interest in itself; and if the universe failed to fit his analysis it was the universe which was in error," one reads in a popular book titled "Men of Mathematics". A historian of physics arrived at the lapidary conclusion: "The mathematical genius Euler was a second-rate physicist." In addition, there are speculations concerning the causes of his failure. "Unfortunately, he omitted the effects of friction, with embarrassing practical consequences," a physicist argued.

What has happened then in the Park at Sanssouci? A history of the constructions at Potsdam, authored by the King’s last architect, provides us with detailed information about these events. Frederic the Great wished that, besides a variety of fountains dispersed all over the Park, a 100 feet high fountain jet springs up in front of the castle—in a Park which could be fed on water only from the slowly flowing Havel about a mile away. The plan foresaw to lead the water from there via a canal to a pumping station in the Park from where it should be pumped through a pipeline into an elevated reservoir. The pump should be driven by a windmill. The reservoir was at a distance of about 3,000 feet away from the pumping station at the, a hill behind the castle. The height difference of about 150 feet between the reservoir and the level of the Park would be sufficient to provide the required pressure for the fountain jets.

The water-art project started in 1748, shortly after the constructions of the castle at Sanssouci were completed. At first everything proceeded according to the plan. The canal from the Havel to the Park, the reservoir up on the Höneberg, the windmill and the pump were accomplished within about a year. The tubes for the pipeline between the pump and the reservoir were made like wooden barrels, held together by iron bands. But when water was pumped up to the reservoir, the pipeline burst at the lower end long before the water arrived at the reservoir. Subsequently, the barrel-like tubes were replaced by entire drilled out trunks of trees. But these new tubes also burst. Now it was evident that wooden tubes would not withstand the high water pressure. A new pipeline was constructed from metal tubes. Although this pipeline did not burst, the flow rate to the reservoir was inefficient because the tubes had a too narrow inner diameter. The flawed pipeline constructions went on for years until 1756, when the Seven Years War caused a longer interruption. After the war the project was resumed for a short time, but finally the King lost patience and ordered that it was abandoned.

The chronicler of the failed water-art project at Sanssouci had made himself painful experiences with constructions under Frederic the Great. He reported other instances in which the King’s extravagance collided with his stinginess when it came to the costs. He named all practitioners who were involved with the realization of the water-art project and criticised them for their bungling. If Euler would have been responsible for the failure, as the King stated in his letter to Voltaire, this would have certainly entered the construction report in some detail. But Euler is not even mentioned.

Fortunately we do not have to speculate about Euler’s involvement. Both his scientific work and his correspondence with the King and with Maupertuis, the president of the Berlin Academy, is available in a multi-volume edition. An evaluation of these sources leads to the conclusion that Euler was unjustly blamed for the fiasco at Sanssouci. To the contrary, his analysis founded the hydraulic theory on nonstationary pipe flow. When the water is set in motion, the pressure within the tube is bound to rise. This pressure increases with the amount of water in the pipeline, and it occurs even when there is no height difference. Euler calculated this dynamic pressure increase which escaped traditional hydrostatics, and he derived recommendations concerning the power of the pump and the dimensions of the pipeline. He even warned explicitly that the project was bound to fail if the bungling in the Park proceeded. But his advice was completely ignored.

Compared to the long duration of the Sanssouci project, Euler was involved only very shortly. Less than a month passed between his first letter, addressed to Maupertuis on 21 September 1749 about the Sanssouci affair, until his comprehensive analysis issued to the King on 17 October 1749. This explains why his name is missing in the account of the constructions which extended over more than a decade. But Euler’s analysis concerned the crucial problem of the entire affair. He demanded that the thickness of the walls of the lead tubes be determined from experiments. He assumed that such tubes would be used for the pipeline after the barrel-like tubes burst—but the practitioners in the Park continued unabated with wooden tubes. With regard to the critical question of the pressure Euler wrote: "I have made calculations about the first trials at which the wooden tubes burst, as soon as the water reached a height of 70 feet. I find that the tubes actually sustained a pressure corresponding to a 300 feet high water column. This is a certain indication that the machine is still far from its perfection." Concerning the dimensions of the pipeline he suggested "that at all costs one has to use larger tubes." This advice, too, was ignored.

Euler’s pipe flow theory which resulted from his involvement with the "machine de Sanssouci" was a prelude to his formulation of the general equations of motion for ideal (i. e. frictionless) fluids. It was left to the 19th century to extend these "Euler equations" to the "Navier-Stokes equations" which take friction into account and form the basis of modern fluid dynamics. Euler’s theory, of course, would not serve as a blueprint for modern hydraulic engineering because friction modifies the outcome of the calculations according to the chosen design and materials. But this cannot be used as an excuse for the bungling at Sanssouci. To account properly for friction remained a problem until the 20th century.

Why, then, became Euler the scapegoat for the fiasco at Sanssouci? When Frederic II called Euler to Berlin in 1740, there were high expectations at the Prussian court. The Berlin Academy was supposed to live up finally to the standards which had been set already by Leibniz at its foundation in 1700—but so far remained unfulfilled. Frederic wished that it was on a par with the famous academies in London and Paris. However, he did not count Euler among his favourite assets, like Maupertuis or other exponents of French esprit. When Maupertuis died in 1759, he rather assumed himself the presidency of the academy than trust Euler with this task. In 1766, Euler returned frustrated to St. Petersburg, where he had served as a member of the Russian academy already before 1740. When Frederic blamed Euler for the fiasco at Sanssouci in his letter to Voltaire, the events in the Park were already 30 years in the past. Only in the temporal distance of more than 200 years the King’s utterance appears authentic. But his contempt of Euler, combined with his lack of understanding for mathematics and science, render Frederic (who is still called “the Great”) an unreliable witness. It is a pity that until today many shared his judgement, although Euler’s work sufficiently belies the slander that he was a theorist without touch of practical concerns.

Michael Eckert, Deutsches Museum München



[1] A detailed review with correspoding sources of literature can be found in Michael Eckert: Euler and the Fountains of Sanssouci. Archive for History of Exact Sciences, 56, 2002, 451-468. An analysis of Euler's work with focus on his shortly thereafter acquired general theory of ideal fluids appears in Michael Eckert: Water-art problems at Sanssouci—Euler’s involvement in practical hydrodynamics on the eve of ideal flow theory, Physica D (2007), doi:10.1016/j.physd.2007.09.006.


[Released: July 2008]