Foppl’s Vorlesungen

The influential vision of the turn-of-the-century Cambridge school of math­ematical physics, as Lamb, Love, and others presented it, stood in contrast to the German idea of technical mechanics. This body of work came out of the great system of German technical colleges or technische Hochschulen, such as that at Charlottenburg, or in Munich where Prandtl had studied, or Hanover where both Prandtl and Runge had taught before their call to Gottingen. A representative example of this style of work is provided by August Foppl’s influential lectures on technical mechanics. His multivolume and vastly pop­ular Vorlesungen uber technische Mechanik was published in many editions around the turn of the century. Foppl originally worked in industry and had spent a number of years teaching in a trade school. He later rose to become the professor of theoretical mechanics at the Munich Hochschule and the di­rector of their materials laboratory.47 A versatile mathematician, Foppl had written the first book introducing Maxwell’s work on electromagnetism into Germany. The book was later revised and coauthored with the experimental physicist Max Abraham, and it is known that one student who was influenced by it was the young Einstein.48 Foppl had been Prandtl’s teacher at Munich and had supervised his doctoral research on the buckling of loaded beams.49 In 1909 Prandtl married Foppl’s eldest daughter, Gertrud. In Prandtl’s biog­raphy, written by his own daughter, there is evidence of a certain tension between Prandtl and his father-in-law, occasioned by the older man’s au­thoritarian attitudes, but there was no lack of scientific respect.50 Ludwig Foppl, who, along with Abraham and von Karman, had been in the audience at Cambridge when Lamb spoke, was one of August Foppl’s two sons. The other son, Otto Foppl, worked with Prandtl on wind-tunnel experiments in Gottingen. Some of Otto Foppl’s work is discussed in a later chapter; for the moment, however, the concern is with August Foppl (fig. 5.5).

What did the many readers of Foppl’s published lectures on technische Mechanik learn about the status of their field as they imbibed its carefully graded and expertly presented content? First, they learned that mathematics was a means to an end, rather than an end in itself. In the introduction to the first volume, Foppl wrote that mechanics makes extensive use of mathematics, but as an auxiliary. Mathematical techniques, he said, were simply the clothing in which the body of knowledge was garbed. The point was reiterated at the beginning of the more mathematically demanding third volume, but this time with more stress on just how important, on occasion, these aids could be:

Analytische Entwicklungen betrachte ich immer nur als ein Mittel zur Er – kenntnis des inneren Zusammenhangs der Thatsachen. Wer auf sie verzichten wollte, wurde das scharfste und zuverlassigste Werkzeug zur Verarbeitung der Beobachtungsthatsachen aus der Hand geben. (1900a, viii)

I only consider analytical processes as a means for understanding the intimate interconnections of the facts. Those who want to renounce them are letting go of the sharpest and most dependable tools for working with the facts of observation.

Mathematics provided what Foppl called Hilfsmittel and Werkzeuge, “aids” and “instruments.” Foppl’s language is important here. There had been in-

figure 5.5. August Foppl (1854-1924) was a versatile mathematician and a professor at the technische Hochschule in Munich. He was the author of an extremely influential textbook on technical mechanics that was based on his Munich lectures. He was also the father-in-law of Ludwig Prandtl. Photograph from Baseler et al. 1924.

tense, not to say wearisome, debate in German academic circles over whether mathematics was to be seen as a Hilfswissenschaft or as a Grundwissenschaft with respect to technology.51 Was it an auxiliary to, or a foundation of, tech­nology? The debate was really a coded argument over the status of math­ematicians in the technical college system and their role in the education of engineers. Foppl was signaling that mathematicians had to earn their living by making themselves useful to engineers. The function of mathematics was to further technology and engineering.

The first chapter of volume 1 of the Vorlesungen was devoted to the ori­gin and goals of mechanics. Foppl acknowledged that mechanics was part of physics and, like all the sciences, was grounded in experience. To grasp experience, he argued, it was always necessary to work with simplified, easily imagined “pictures” (Bilder) of reality. The ideas of a point particle and a rigid body were two such pictures. Both were valuable and had their appropriate range of application, but they must not be mistaken for physical realities.52 Foppl also drew a distinction between the Naturforscher and the Techniker— the natural scientist and the engineer. His book was for the latter, not the former, and dealt with a mode of knowledge having special characteristics that differentiated it from natural science in general.

Bei der technischen Mechanik tritt als bestimmender Beweggrund fur ihre Fassung zu der Absicht einer Erforschung der Wirklichkeit. . . noch die an – dere Absicht, ihre Lehren nutzbringend in der Technik zu verwerthen. (11)

In the case of technical mechanics there is a definite motive for its approach over and above the intention to investigate reality. . . and that further inten­tion is that its theories be usefully applicable in technology.

Foppl was just the sort of utilitarian, applied mathematician from whom Lamb and Love had distanced themselves. Indeed, Lamb’s typology might have been expressly contrived to ensure that the Cambridge school did not get caught in the cross-fire between the champions of mathematics as Hilfswis- senschaft and as Grundwissenschaft. Be this as it may, Foppl certainly didn’t have the Cambridge tone. His technical mechanics was not natural philoso­phy. Furthermore, Foppl differentiated technical mechanics from mechan­ics in general because there are many cases when the general doctrines of mechanics do not, or do not yet, provide rigorous answers to the questions that have to be confronted by the engineer. Natural scientists and engineers, he said, stand in a wholly different relationship to these cases: “solchen Fallen steht aber der Naturforscher anders gegenuber als der Techniker” (11). The engineer must produce an answer and must forge concepts to deal with the problem. The natural scientist can wait for inspiration or more information; the engineer cannot:

Der Techniker dagegen steht unter dem Zwange der Nothwendigkeit; er muss ohne Zogern handeln, wenn ihm irgend eine Erscheinung hemmend oder fordernd in den Weg tritt, und er muss sich daher unbedingt auf irgend eine Art, so gut es eben gehen will, eine theoretische Auffassung davon zurechtle – gen. (11-12)

The engineer, by contrast, is subject to the force of necessity. He must, with­out delay, deal with the matter when some phenomenon interferes and inter­poses itself in his path. He must, in some way or other, arrive at a theoretical understanding of it as best he can.

The demands of this enforced creativity may generate concepts that do not meet the logical demands of existing mechanics. Here, said Foppl, was the deep reason for separating out technical mechanics as a special branch of knowledge—“diese Absonderung der technischen Mechanik als eines besonderen Zweiges der Wissenschaft” (11). Its practitioners must have the freedom to develop concepts of their own, and these might be distinct from those acceptable in the more reflective and leisurely branches of knowledge. For example, the application of hydrodynamic theory to turbines developed by Prasil and H. Lorenz, depended on certain artifices or tricks (Kunstgriffe) involving the idea of “forced accelerations.”53 The approach had been con­troversial, but Foppl defended it. He went on to say that in such cases subse­quent developments in science might permit a reconciliation. The anomalous concepts, special to engineering and technical mechanics, might be absorbed back into the main body of knowledge. But this was an open question, some­thing for the unspecified future rather than the urgent present. His main concern was to emphasize the restless force running through the scientific life of modern technology, which was, he said, like the life force in a tree that continually generated new branches.

In the peroration rounding off the introductory chapter, however, Foppl suddenly changed the metaphor. The life force of a tree was replaced by an­other kind of force. Knowledge was power, said Foppl, the power of a mod­ern technological state. The bucolic image was replaced by a military one. Those who first possessed the right theory (“die richtige Theorie”) might be able to intervene in nature at will. In this way, said Foppl, science, put at the disposal of humanity and its peoples, is the most powerful of all weapons— “und darum ist die Wissenschaft die gewaltigste Waffe, die Menschen und Volkern zu Gebote steht” (12).

What did Foppl understand by the “right” theory? His normative stan­dards were predictably active and pragmatic. Like many in his position in the technische Hochschulen, Foppl was fighting a war on two fronts. On one side were “humanistic” critics. These were usually outside the technical col­lege system, or only passing through it on their way to posts in universities. In as far as they wanted mathematics at all, they wanted it “pure.” On the other side were critics, often from within the technical colleges, who placed all the emphasis on practicality and were suspicious of any form of higher mathematics.54 These were the counterpart of the “practical men” in Britain who were so hostile to the work of the Advisory Committee for Aeronautics. In responding to the local, German, variant, Foppl dismissed such people as mere Praktiker.55 He had no time for them or their slogans about the conflict between theory and practice—“dem Gegensatze zwischen Theorie und Praxis” (3:vii.). For Foppl there was no such conflict:

Diese Behauptung lasse ich aber auf dem Gebiete der technischen Mechanik durchaus nicht gelten; hier kann nur von einem Gegensatze zwischen falscher oder unvollstandiger Theorie und der richtigen Theorie die Rede sein. Die richtige Theorie ist immer in Ubereinstimmung mit der Praxis. (3:vii)

I do not admit this claim as having any validity in the realm of technical me­chanics. Here one can only speak of the conflict between false or incomplete theories and the right theory. The right theory is always in agreement with practice.

Did Foppl mean that a theory was practical because it was right, or that it counted as right because it worked in practice? Taken in isolation, his wording was ambiguous. If, however, we recall Foppl’s insistence on the overpower­ing, practical necessities that dominate the life of the engineer—the “Zwang der Nothwendigkeit”—then the formal ambiguity can be resolved. In Foppl’s world, practice was the effective criterion not of an abstract and future truth but of acceptability and viability for the pressing moment. In the colleges of Cambridge, if Lamb is to be believed, the pursuit of truth had an aesthetic character. In the colleges of technology a theory was counted as right if, and only if, it worked.

Others in the field of applied mathematics in Germany may have made the case in different words, but Foppl’s general orientation toward engi­neering represented a widely held view. For example, in 1921 Richard von Mises started a new journal for applied mathematics—the Zeitschrift fur angewandte Mathematik und Mechanik. Prandtl and von Mises had been in correspondence after the war on new institutional arrangements for encour­aging applied mathematics. Prandtl mentioned that he and von Karman had been discussing the founding of a society to promote technical mechanics, “eine Vereinigung fur technische Mechanik,” and these exchanges were part of the process that culminated in the journal.56 On the first page of the new publication von Mises set out his conception of the task and goals of the dis­cipline and the role of the journal. He would have been conscious of stepping into a long-standing discussion about the role of mathematics in the German academic world but he had no desire to equivocate. He insisted that the core of the journal would be devoted to mechanics whose cultivation, he said, to­day lies almost exclusively in the hands of engineers, “deren Pflege heute fast ausschliefilich in den Handen der Ingenieure ruht.”57

Mathematics, said von Mises, covered a wide spectrum of activities so that the partition between pure and applied mathematics was a relative one, lo­cated differently by different practitioners. Each would count what was (so to speak) on their “left” as pure and what was on their “right” as applied. But there was not only this dimension to consider: the very content of mathemat­ics itself changed with time as new areas (for example, the concept of prob­ability) were brought within the scope of quantitative analysis. We must, said von Mises, accept this “two-fold relativity” in the identity of applied math­ematics. To overcome the definitional problems this created, he concluded that a practical, rather than a theoretical, specification of the field was called for. Applied mathematics and mechanics were to be defined as what was done, at that time, by scientifically oriented engineers. Thus,

Angesichts dieses Tatbestandes zweifacher Relativitat der Begriffsabgrenzung mussen wir nun eine praktische Erklarung dafur suchen, was wir hier im Fol – genden unter “Angewandter Mathematik” verstehen wollen. Es ist selbstver – standlich, dafi wir uns auf den Boden der Gegenwart stellen, und es sei hinzu – gefugt: auf den Standpunkt des wissenschaftlich arbeitenden Ingenieurs. (3)

Given the facts of this twofold relativity of the conceptual boundary, we must now seek for a practical explanation of what, in the following, we want to un­derstand by “applied mathematics.” It will be obvious that we take our stand on the basis of the present and, let it be added, on the standpoint of the scien­tific work of the engineer.

Clearly the two mathematical traditions that I have delineated had dif­ferent orientations: one more toward physics; the other more toward engi­neering. Obviously, Cambridge mathematical physics and German technical mechanics still had much in common. There were many respects in which they overlapped, and it was possible for results to be passed from the prac­titioners of one to those of the other. Prandtl’s early papers on elasticity and Foppl’s volume of the Vorlesungen devoted to the strength of materials were mentioned in Love’s treatise, while, in return, Foppl advised his more ad­vanced readers to consult Love’s work. Representatives of the two traditions attended the same conferences, even if this caused Lamb a touch of anxiety. Klein admired Cambridge pedagogy and tried, though without much suc­cess, to introduce it in Germany.58 Lamb’s Hydrodynamics was translated into German in 1907, again at Klein’s prompting, though later von Mises added a lengthy supplement to the book designed to build a bridge to the more tech­nical concerns and less formal orientation (“weniger formalen Richtung”) of German readers.59 Although G. H. Bryan evinced disdain for the intel­lectual level of the engineers in Joukowsky’s classes, he could write a respect­ful review of Foppl’s Vorlesungen in Nature saying, “Prof. Foppl’s treatises on technical mechanics are of a far more advanced character than the mechanics taught commonly to technical students in this country.”60 In his own way Bryan wanted to further the cause of applied mathematics in this country and was ready to hold up German efforts when it was expedient to do so. To this extent the acknowledgment of communality between British and German mathematical cultures was real enough.

Given this mixture of divergent tendencies and common ground, it is not surprising that the members of the respective traditions did not them­selves always have a clear awareness of the relations between them. This was epitomized in an exchange of letters that took place between G. I. Taylor and Ludwig Prandtl a number of years after the events described here. By the time the letters were written, in the 1930s, the magnitude of Prandtl’s contribu­tions had become known and widely admired. Taylor had written to say that he thought Prandtl deserved the Nobel Prize in physics. Prandtl’s response, in a letter of November 30, 1935, was not only becomingly modest but was also culturally revealing.61 He said that what he had done would not count as physics in Germany. Rather, it was a contribution to Mechanik.

Nach der in Deutschland ublichen Einteilung der Wissenschaften wenigstens wird die Mechanik heutzutage nicht mehr als ein Teil der Physik betrachtet, sondern steht als selbstandiges Gebiet zwischen der Mathematik und den Ingenieurwissenschaften.

At least according to the division of the sciences that is usual in Germany today, mechanics is no longer considered to be part of physics. Rather, it stands as an independent area between mathematics and the engineering sciences.

While Taylor now assimilated Prandtl’s work to physics, the Germans saw it as something distinct from physics and as standing between mathematics and engineering.62 The different stance toward engineering and its demands perhaps sheds light on why the circulation theory was actively resisted in Britain but accepted and developed in Germany. Before taking this argument further, however, I look at what Lanchester himself said to explain the rough ride given to his work. Lanchester’s account will give me an opportunity to look at another variable whose explanatory potential needs to be assessed, namely, the personalities of the main actors.