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Some Books Recently Received

Some Books Recently Received February , 1939 A I R C R A F T E N G I N E E R I N G 55 A New Work on Hydrodynamics for Students—A Recently Developed Tool for Mathematicians Theoretica l Hydrodynamics. By L. M. The free streamline theory originated by on the other. The present reviewer can only Kirchhoff and Rayleigh is given fully, perhaps speak as one of the latter, and he feels that Milne-Thomson. (Macmillan, 31s. 6d.) more fully than is warranted by its physical " to bring about a wider appreciation .. . of Professor Milne-Thomson's book is a valuable interest, as surfaces of discontinuity of velocity matrices " th e authors would have done better addition to the published literature on hydro­ in fluids are nearly always unstable. This t o depart further from the order and rigour dynamics. It is writte n primarily as a text-book work is primarily applicable to free surfaces of pure mathematics. The practical student for use in universities and is based on lectures such as overflows over weirs, and it has been is always anxious to see how a new method given by th e autho r a t th e Royal Naval College. applied with partial success to the problem works in practical problems; he therefore The treatment of the subject is very clear of the je t resistance of planing surfaces, which likes to sec th e early introduction of practical throughout and it can be thoroughly recom­ has applications to the take-off of seaplanes. examples, even though this may necessitate mended to students and lecturers in mathe­ Chapters on wave motion and on viscous th e postponement of certain proofs required matics ; many engineers will, however, find fluid flow are included. All the simple prob­ for a rigorous presentation. To such students the methods used rather difficult to follow. lems of wave motion in two dimensions are th e first four chapters of this book, though The greater part of the book is concerned discussed, though the wave resistance of ships admirable in their arrangement and often with the How of an inviscid incompressible is not considered. Viscous fluid flow is treated elegant in manner, may seem a difficult and fluid, and the principal departure from the rathe r indigestible introduction. It may be briefly and th e chapter ends, after a few para­ treatmen t given in Lamb's Hydrodynamics is tha t this desire for a quick practical approach graphs about the boundary layer, with the the consistent use of vector analysis for three- statemen t that the applications of boundary is premature; that until matrices have dimensional work and of th e complex variable layer theory have so far been tentative and entered into computation more generally the for two-dimensional work. This may make empirical. It is difficult to agree with this mode of presentation best suited to th e practical th e book difficult for readers unfamiliar with statement, and one suspects that the boundar y worker cannot be judged. If this is so, then vector analysis, though a careful reading of layer theory does not appeal to Professor this book should certainly form an excellent chapter II, in which the theory of vectors is Milne-Thomson because the equations do not base upon which to found in due course a described, will go some way to mak e the succeed­ lend themselves to treatment by means of more elementary practical text book. ing chapters easier. There is, however, no general theorems. A very welcome feature of the book is th e doub t that Professor Milne-Thomson has I t remains to ad d tha t numerous examples ar e numerical examples, which are well chosen adopted the right course in using vectors, as given at the end of each chapter ; these arc and clearly displayed. Even more examples th e modern tendency is to dispense with co­ mainly taken from university examination and fuller explanations might usefully be ordinate systems as far as possible. It is, of papers and add considerably to the value of incorporated in any future edition. Another course, necessary to introduce co-ordinate axes th e book. H. B. S. notable feature of the book, and one typical a t some stage in the solution of particular of the authors' work elsewhere, is the high problems, but, generally speaking, the late r this standar d of detailed accuracy and clarity Elementar y Matrices, and Some Appli­ is done the neater the solution is. English maintained throughout. The printing is, as cation s to Dynamics and Differential writers have been more conservative than usual with the publishers, well and carefully Equations . By R. A. Frazer, \V. J. scientists in other countries and slower to done. Duncan and A. R. Collar. (Cambridge adopt vector methods, but it will eventually An incidental but interesting point about University Press. 30s.) be regarded as reactionary rather than con­ th e book is tha t it has been written with the servative to insist on using Cartesian co-ordin­ The authors of this book are well known specific encouragement of the Aeronautical ates. t o aeronautical engineers as in the forefront Research Committee. It may be surmised More than half the book is concerned with among workers on aeroplane flutter problems. tha t this encouragement expresses the Com­ Less generally known is th e fact that in dealing motion in two dimensions and this illustrates mittee's appreciation not only of the authors' with these problems th e authors ' mathematical th e relative difficulty of handling problems work, but also of the value of matrices as a in three dimensions. The reason for this is th e work has been signalised in recent years by mathematical implement for aeronautical in­ lack of a mathematical technique for three a frequent resort to matrices; and this book vestigations. The publication of this book dimensions corresponding with the use of the may be regarded as the outcome of their certainly presents aeronautical engineers with complex variable in two dimensions. As a experience in that field. Among books on an opportunity to acquire a tool bringing a broad generalisation, it might be said that any higher mathematics, therefore, this should be new power to bear on many practical mathe­ two-dimensional problem in inviscid fluid of more interest than most to aeronautical matical problems. engineers. motion is soluble approximately, if not exactly; A. G. P . whereas only a restricted class of three- I n their preface the authors state that the dimensional problems, mainly those associated book, which is believed to be the first to with spheres an d ellipsoids, is soluble. develop the subject of matrices with special reference to differential equations and classical An interesting original contribution of the TH E 1938 PARIS AERO SALON mechanics, is intended primarily for students author included in the book is th e application of applied mathematics with no previous know­ of conformal transformation to problems of I t is much regretted that, owing t o a printer's ledge of matrices; and they express the hope flow with axial symmetry. The method is no t error in the report of the Paris Exhibition, nearly so widely applicable as th e corresponding " tha t it will help to bring about a wider which appeared in the January issue of method in two dimensions, but it enables appreciation of the conciseness and power of AIRCRAF T ENGINEERING, it was made to appear matrices and of their convenience in compu­ solutions for th e flow past spheroids with their tha t the Bristol Blenheim bomber was fitted tation. " With these aims in mind, the first axes along the stream to be obtained without with V.D.M. instead of Rotol airscrews. four chapters of the book, amounting t o some using spherical harmonics. The paragraph in question (p. 5, column 3, 150 pages, arc devoted to an orderly exposition The theorems required are generally proved line 12 from the end) should have read : of the analytical and numerical properties of very neatly. For example, a simple derivation "Th e Rotol airscrews on the Blenheim and matrices that are required for use in the of Blasius's formula; for the lift and moment th e V.D.M. on the Do. 17 had metal blades, subsequent nine chapters on their applications. of an aerofoil is given ; these are obtained by . . . etc. " These applications refer mainly to differential integrating the pressure round the contour equations, and in particular to the equations of the aerofoil in term s of th e complex potential, A N ANNIVERSARY NUMBER of dynamics ; and many of th e examples given and the value of the contour integrals is then are concerned with aeronautical problems in shown, by Cauchy's theorem, to be independent Wit h its nex t issue, AIRCRAFT ENGINEERING which the authors have been specially in­ of the contour, thus avoiding the rather begins its eleventh year of publication, the terested. troublesome calculation of th e inflow of momen­ first number having appeared in March, 1929. tum into a. general contour. There appears to To mark the occasion a special enlarged issue By writing their book thus deliberately for will be published, containing a number of be a number of original proofs and contributions students of "applied " mathematics, th e authors articles written by specialists in various included in the book, but as ver y few references have — no doubt wittingly — lai d themselves are given it is no t possible to decide about the branches of aeronautics: aerodynamics, struc­ open t o attac k both b y "pure " mathematicians originality of some of the results. tures, production, etc. on the one han d and b y "practical " workers http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Aircraft Engineering and Aerospace Technology Emerald Publishing

Some Books Recently Received

Aircraft Engineering and Aerospace Technology , Volume 11 (2): 1 – Feb 1, 1939

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Publisher
Emerald Publishing
Copyright
Copyright © Emerald Group Publishing Limited
ISSN
0002-2667
DOI
10.1108/eb030437
Publisher site
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Abstract

February , 1939 A I R C R A F T E N G I N E E R I N G 55 A New Work on Hydrodynamics for Students—A Recently Developed Tool for Mathematicians Theoretica l Hydrodynamics. By L. M. The free streamline theory originated by on the other. The present reviewer can only Kirchhoff and Rayleigh is given fully, perhaps speak as one of the latter, and he feels that Milne-Thomson. (Macmillan, 31s. 6d.) more fully than is warranted by its physical " to bring about a wider appreciation .. . of Professor Milne-Thomson's book is a valuable interest, as surfaces of discontinuity of velocity matrices " th e authors would have done better addition to the published literature on hydro­ in fluids are nearly always unstable. This t o depart further from the order and rigour dynamics. It is writte n primarily as a text-book work is primarily applicable to free surfaces of pure mathematics. The practical student for use in universities and is based on lectures such as overflows over weirs, and it has been is always anxious to see how a new method given by th e autho r a t th e Royal Naval College. applied with partial success to the problem works in practical problems; he therefore The treatment of the subject is very clear of the je t resistance of planing surfaces, which likes to sec th e early introduction of practical throughout and it can be thoroughly recom­ has applications to the take-off of seaplanes. examples, even though this may necessitate mended to students and lecturers in mathe­ Chapters on wave motion and on viscous th e postponement of certain proofs required matics ; many engineers will, however, find fluid flow are included. All the simple prob­ for a rigorous presentation. To such students the methods used rather difficult to follow. lems of wave motion in two dimensions are th e first four chapters of this book, though The greater part of the book is concerned discussed, though the wave resistance of ships admirable in their arrangement and often with the How of an inviscid incompressible is not considered. Viscous fluid flow is treated elegant in manner, may seem a difficult and fluid, and the principal departure from the rathe r indigestible introduction. It may be briefly and th e chapter ends, after a few para­ treatmen t given in Lamb's Hydrodynamics is tha t this desire for a quick practical approach graphs about the boundary layer, with the the consistent use of vector analysis for three- statemen t that the applications of boundary is premature; that until matrices have dimensional work and of th e complex variable layer theory have so far been tentative and entered into computation more generally the for two-dimensional work. This may make empirical. It is difficult to agree with this mode of presentation best suited to th e practical th e book difficult for readers unfamiliar with statement, and one suspects that the boundar y worker cannot be judged. If this is so, then vector analysis, though a careful reading of layer theory does not appeal to Professor this book should certainly form an excellent chapter II, in which the theory of vectors is Milne-Thomson because the equations do not base upon which to found in due course a described, will go some way to mak e the succeed­ lend themselves to treatment by means of more elementary practical text book. ing chapters easier. There is, however, no general theorems. A very welcome feature of the book is th e doub t that Professor Milne-Thomson has I t remains to ad d tha t numerous examples ar e numerical examples, which are well chosen adopted the right course in using vectors, as given at the end of each chapter ; these arc and clearly displayed. Even more examples th e modern tendency is to dispense with co­ mainly taken from university examination and fuller explanations might usefully be ordinate systems as far as possible. It is, of papers and add considerably to the value of incorporated in any future edition. Another course, necessary to introduce co-ordinate axes th e book. H. B. S. notable feature of the book, and one typical a t some stage in the solution of particular of the authors' work elsewhere, is the high problems, but, generally speaking, the late r this standar d of detailed accuracy and clarity Elementar y Matrices, and Some Appli­ is done the neater the solution is. English maintained throughout. The printing is, as cation s to Dynamics and Differential writers have been more conservative than usual with the publishers, well and carefully Equations . By R. A. Frazer, \V. J. scientists in other countries and slower to done. Duncan and A. R. Collar. (Cambridge adopt vector methods, but it will eventually An incidental but interesting point about University Press. 30s.) be regarded as reactionary rather than con­ th e book is tha t it has been written with the servative to insist on using Cartesian co-ordin­ The authors of this book are well known specific encouragement of the Aeronautical ates. t o aeronautical engineers as in the forefront Research Committee. It may be surmised More than half the book is concerned with among workers on aeroplane flutter problems. tha t this encouragement expresses the Com­ Less generally known is th e fact that in dealing motion in two dimensions and this illustrates mittee's appreciation not only of the authors' with these problems th e authors ' mathematical th e relative difficulty of handling problems work, but also of the value of matrices as a in three dimensions. The reason for this is th e work has been signalised in recent years by mathematical implement for aeronautical in­ lack of a mathematical technique for three a frequent resort to matrices; and this book vestigations. The publication of this book dimensions corresponding with the use of the may be regarded as the outcome of their certainly presents aeronautical engineers with complex variable in two dimensions. As a experience in that field. Among books on an opportunity to acquire a tool bringing a broad generalisation, it might be said that any higher mathematics, therefore, this should be new power to bear on many practical mathe­ two-dimensional problem in inviscid fluid of more interest than most to aeronautical matical problems. engineers. motion is soluble approximately, if not exactly; A. G. P . whereas only a restricted class of three- I n their preface the authors state that the dimensional problems, mainly those associated book, which is believed to be the first to with spheres an d ellipsoids, is soluble. develop the subject of matrices with special reference to differential equations and classical An interesting original contribution of the TH E 1938 PARIS AERO SALON mechanics, is intended primarily for students author included in the book is th e application of applied mathematics with no previous know­ of conformal transformation to problems of I t is much regretted that, owing t o a printer's ledge of matrices; and they express the hope flow with axial symmetry. The method is no t error in the report of the Paris Exhibition, nearly so widely applicable as th e corresponding " tha t it will help to bring about a wider which appeared in the January issue of method in two dimensions, but it enables appreciation of the conciseness and power of AIRCRAF T ENGINEERING, it was made to appear matrices and of their convenience in compu­ solutions for th e flow past spheroids with their tha t the Bristol Blenheim bomber was fitted tation. " With these aims in mind, the first axes along the stream to be obtained without with V.D.M. instead of Rotol airscrews. four chapters of the book, amounting t o some using spherical harmonics. The paragraph in question (p. 5, column 3, 150 pages, arc devoted to an orderly exposition The theorems required are generally proved line 12 from the end) should have read : of the analytical and numerical properties of very neatly. For example, a simple derivation "Th e Rotol airscrews on the Blenheim and matrices that are required for use in the of Blasius's formula; for the lift and moment th e V.D.M. on the Do. 17 had metal blades, subsequent nine chapters on their applications. of an aerofoil is given ; these are obtained by . . . etc. " These applications refer mainly to differential integrating the pressure round the contour equations, and in particular to the equations of the aerofoil in term s of th e complex potential, A N ANNIVERSARY NUMBER of dynamics ; and many of th e examples given and the value of the contour integrals is then are concerned with aeronautical problems in shown, by Cauchy's theorem, to be independent Wit h its nex t issue, AIRCRAFT ENGINEERING which the authors have been specially in­ of the contour, thus avoiding the rather begins its eleventh year of publication, the terested. troublesome calculation of th e inflow of momen­ first number having appeared in March, 1929. tum into a. general contour. There appears to To mark the occasion a special enlarged issue By writing their book thus deliberately for will be published, containing a number of be a number of original proofs and contributions students of "applied " mathematics, th e authors articles written by specialists in various included in the book, but as ver y few references have — no doubt wittingly — lai d themselves are given it is no t possible to decide about the branches of aeronautics: aerodynamics, struc­ open t o attac k both b y "pure " mathematicians originality of some of the results. tures, production, etc. on the one han d and b y "practical " workers

Journal

Aircraft Engineering and Aerospace TechnologyEmerald Publishing

Published: Feb 1, 1939

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