Two Reviews and Two Perspectives

Glauert would have known that, however cogent he made his book, he could not meet all the demands of his intended audience. The diversity of interests that would inform the response would pull in opposing directions. The struc­tural tensions, present in British aerodynamics from the outset, were still at work. By its very nature, Glauert’s Elements of Aerofoil and Airscrew Theory could not satisfy the prejudices of both the practical engineer and the math­ematical physicist. Indeed, the book was designed to bring about a change of approach in both parties. Until it had worked its effect it was bound to be viewed with a certain reservation from both sides, even if, at the same time, its virtues were acknowledged.

The review that appeared in the Journal of the Royal Aeronautical Society was signed “A. R.L.” With its mixture of bluff praise and barbed comment, the review was such that no regular reader would have failed to recognize it as the work of Major A. R. Low.56 Glauert was identified as one (but only one) of the leading exponents of the Lanchester-Prandtl approach, and the Ele­ments was welcomed as (perhaps) the first full-length book on the subject in the English language. There was the hint that engineers might find Glauert’s discussion too advanced, and Low strongly recommended that students read a work by H. M. Martin “as an introduction to the volume under review, and, as well, for Mr. Martin’s mastery of elementary exposition” (167).57 Low simultaneously praised Glauert for the adequacy of his general references, which would “introduce the reader to the most important German work,” and criticized him for not citing Fuchs and Hopf’s Aerodynamik of 1922, which “quite evidently influenced the author, both as to selection and arrangement of materials” (168). The book by Fuchs and Hopf was broader in scope than the Elements, covering both lift and stability, and Low had reviewed it in the Aeroplane. While he had praised their treatment of lift, he had been scathing about their treatment of stability.58 Low acknowledged Glauert’s originality in using the method of images to arrive at a formula for tunnel interference effects in the case of rectangular (as distinct from circular) tunnels but quib­bled at an “unnecessary reference to Hobson’s Trigonometry” (168) to deal with a mathematical point that Low considered elementary.59 Low concluded his review by describing the Elements as “an important contribution to Eng­lish aerodynamic literature” and (high praise indeed) as a book that “should be of the greatest value to all designers of aircraft” (168).

Approaching the Elements from the direction of the mathematician rather than the engineer, R. V. Southwell reviewed it for the Mathematical Gazette.60 He praised Glauert’s “power of concise exposition” (394) and said the book gave “an admirable account of a fascinating theory.” It could be recommended as “indispensable to every student of modern aerodynamics” (395). But, as well as offering praise, it is clear that Southwell was taking care to locate Glauert’s achievement in a particular way. He began by noting that when Mr. Asquith first appointed the Advisory Committee for Aeronautics in 1909, “nothing seemed more certain than that aerodynamics must develop

as a purely empirical science” (394).61 Theoretical hydrodynamics was not sufficiently developed to take account of both inertial and viscous forces. Today, said Southwell, that “difficulty is not yet overcome, but it has been turned” (394). Prandtl’s wing theory is not “an exact theory,” but Prandtl “has supplied what for practice is almost as useful—a theory which can pre­dict” (394).

Southwell then clarified his distinction between exact and predictive theories. Consider Glauert’s chapter 8, which contained an account of skin friction and the origins of viscous drag. Southwell granted that Glauert’s brief treatment was appropriate given the limited purposes of the Elements but ex­pressed the hope that Glauert would produce a follow-up volume to expand the “somewhat slender outline” of the present chapter. The follow-up vol­ume would call for a “slightly altered arrangement” of the material. It appears to me, said Southwell, that

we ought to recognise not one “Prandtl theory,” but two. The first forms the main subject of the present work; its methods are those of the classical theory, and its assumptions, based on Lanchester’s picture of the flow pattern, are justified, ultimately, by its success in prediction. The second, which develops the notion of the “boundary layer” is more fundamental, more difficult, and (probably) less productive of concrete results than the first; its aim is to ex­plain the circulation round a lifting wing in terms of the known equations of viscous flow. (395)

The implication was that Glauert had adopted an “arrangement” of his material that did not adequately recognize the difference between the two theories. Glauert ran these two distinct theories together and aspired to a “combined” presentation. This may help the student, said Southwell, but it cannot do justice to either theory because “their methods are too distinct to permit a really satisfactory blend” (395). He did not believe that they could be combined in the way that Glauert wanted. “For the combined theory seeks to bring phenomena, in their very essence dependent on the viscosity of the fluid and its interaction with the solid boundary, within the scope of analysis which he knows is strictly applicable only to vortex motions existent through­out all time in a fluid devoid of all viscosity” (395). Southwell thus insisted on keeping apart what Glauert had sought to bring together. What the author had aspired to unify, the reviewer saw as incompatible. The themes invoked in Southwell’s review were familiar and characteristic of the British experts: there was the desire for a “fundamental” theory based on Stokes’ equations, a commitment to the “essential” difference between real and perfect fluids, and the appeal to the eternal character of vortices in a perfect fluid, that is, to Kel­

vin’s theorem. That Glauert, like Prandtl, was deliberately trying to overcome the idea that there is an “essential” difference between real and perfect fluids finds no recognition. Southwell acknowledged in Glauert’s unified presenta­tion not a principled methodological stance but a mere pedagogical expedi­ent, an “arrangement” of material to help students—and an arrangement that could not be sustained in the face of reality or in the pages of a more advanced treatise.

Southwell said that the views he expressed “imply no criticism” of Glau – ert’s book. The claim may look disingenuous but I think it should be accepted as authentic. The words would make sense if Southwell were reading Glau­ert’s book as an exercise in technology rather than physics. Once Prandtl’s wing theory was understood as no more than an instrument of prediction, as something that could be assessed using purely pragmatic criteria, then the real business of science could be thought of as proceeding in parallel to the technology. There would be no need for any quarrel between those engaged in the two distinct sorts of activity, provided they were kept apart and not confused with one another. Thus Southwell could honestly declare that he was not criticizing Glauert’s book but simply making it clear what manner of book it was, and what criteria were appropriate for its assessment.

This left just “one small detail” (395) that Southwell certainly wanted to criticize in an explicit way. He was worried about the imaginary roller bear­ings that Glauert interposed between a fluid and a material body or between two layers of fluid moving in different directions or with different speeds. References to roller bearings cropped up at a number of points in Glauert’s book, for example, on pages 95, 100, and 117, and were represented diagram­matically on page 131. Southwell thought such talk was misguided, and he implied that Glauert should know better. Vortices don’t behave like roller bearings, and it won’t help the beginner to understand “the purely math­ematical concept of vorticity” (395), that is, the technical definition of the rotation of a fluid element. Southwell’s point was that “vorticity,” as the term is used in fluid dynamics, can be present when nothing in the flow behaves like a “vortex,” as that term is used in common language, that is, nothing is swirling, rolling, or rotating. For example, mathematically, “vorticity” is pres­ent when two immediately adjacent layers of ideal fluid move horizontally with uniform but different speeds. All the fluid in the respective layers moves in straight lines, but for the mathematician, this phenomenon is equivalent to an infinitely thin sheet of vorticity between the layers. Talk of “roller bear­ings,” however, will produce an incorrect picture in the mind. The begin­ner “will misunderstand either the vortex sheet, or the action of roller bear­ings” (395). The harshest criticism was thus directed at Glauert’s engineering imagery. Southwell was not, in general, against visualization.62 The complaint was against the way that viscous processes and the viscous boundary layer were represented in nonviscous terms.63

Despite these reservations, the publication of Glauert’s Elements in 1926 represented the de facto victory of the circulation theory of lift among Brit­ish experts. The theory and references to Glauert’s exemplary account of it found their way into all subsequent treatises and textbooks, such as Lamb’s Hydrodynamics and Ramsey’s Treatise on Hydromechanics. The victory was, of course, underpinned by the steady accumulation of evidence from experi­mentalists such as Fage.64 The increasingly secure position of the circulation theory was, however, of a qualified kind. The victory was no simple rout of the opposition. The situation might be described with the use of political metaphors by saying that territory was conceded and new spheres of influ­ence agreed on. The power of the circulation theory had been demonstrated, and a certain zone of occupation was now recognized—though not the full legitimacy of what had taken place. The task now was to get on with life under the new dispensation. In the Great War, Germany may not have prevailed, but in the field of practical aerodynamics a new respect was accorded to the circulation theory and Prandtl’s wing theory. In 1927 Prandtl was invited to London to deliver the Wright Memorial Lecture to the Royal Aeronautical Society and to receive the Gold Medal of the society.65

There had been a previous suggestion that Prandtl might give a talk, which had been conveyed via Glauert in 1922. Prandtl had felt compelled to turn down the invitation, however, because of his lack of English.66 The Wright Lecture was a much grander affair, and Prandtl, who clearly appreciated the invitation, now felt better equipped to cope, though he still had some anxie­ties. In the preparatory exchange of letters with the chairman and the secre­tary of the society he fussed over what he should wear. Should he be in Frack, that is, tailed coat? In hesitant English he announced that “I have at this time English lessons and believe to be able up to the date of the lecture, to read the paper myself.”67 In the event, despite displaying the recommended tails, white tie, and white waistcoat, he only delivered the opening passages of the lecture and then called on the help of Major Low. Low, who had worked with Prandtl to translate the text, read the remainder.68

Those opening passages, however, touched on a matter of some delicacy. They concerned the origin of the theory of the aerofoil and the relative con­tributions of Prandtl and Lanchester. Who invented the theory and who should get the credit? Prandtl was diplomatic but forthright. He said that Lanchester had worked on the subject before he, Prandtl, had turned his at­tention to it and that Lanchester had independently obtained an important part of the theory. Prandtl insisted, however, that the ideas he used to build up his theory had occurred to him before he read Lanchester’s 1907 book. This prior understanding, he argued, may explain why “we in Germany were better able to understand Lanchester’s book when it appeared than you in England” (721). The truth, Prandtl went on, is that “Lanchester’s treatment is difficult to follow.” It makes “a very great demand on the reader’s intuitive perceptions,” and “only because we had been working on similar lines were we able to grasp Lanchester’s meaning at once” (721).

Is Prandtl here corroborating Glazebrook’s excuse for the British neglect of Lanchester? Surely not, though he certainly shared some of Glazebrook’s ideas about Lanchester’s work. Like Glazebrook, Prandtl did not countenance the possibility that it was the understanding of Lanchester, rather than the failure to understand him, that lay behind the British response. But, while go­ing along with part of Glazebrook’s story, Prandtl’s comments actually serve to accentuate the tensions between the different parts of Glazebrook’s excuse. They made it even more necessary to explain why the Germans were in a po­sition to grasp Lanchester’s meaning when, allegedly, the British had not been able to rise to the occasion. Glazebrook had excused one failure by citing another failure, and what Prandtl had to say aggravated rather than alleviated this logical weakness.69