William Frederick Durand
Aerodynamic Theory
A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
William Frederick Durand
Aerodynamic Theory
A General Review of Progress Under a Grant of the Guggenheim Fund for the Promotion of Aeronautics
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
- Artikelnr. des Verlages: 978-3-642-89632-3
- 1934
- Seitenzahl: 420
- Erscheinungstermin: 1. Januar 1934
- Deutsch
- Abmessung: 235mm x 155mm x 23mm
- Gewicht: 640g
- ISBN-13: 9783642896323
- ISBN-10: 3642896324
- Artikelnr.: 39562940
- Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
- Artikelnr. des Verlages: 978-3-642-89632-3
- 1934
- Seitenzahl: 420
- Erscheinungstermin: 1. Januar 1934
- Deutsch
- Abmessung: 235mm x 155mm x 23mm
- Gewicht: 640g
- ISBN-13: 9783642896323
- ISBN-10: 3642896324
- Artikelnr.: 39562940
Division A Mathematical Aids.- Preface.- I. The Complex Variable (x + iy).- 1. Introductory.- 2. Properties of the Functions ? and ?.- 3. The Inverse Relation z = F (w).- 4. The Complex x + iy as the Location of a Point in a Plane.- 5. Results Growing Out of the Expression of the Complex Variable in the Exponential and Circular Function Forms.- 6. The Integration of Functions of a Complex Variable.- 7. Influence of Singularities.- 8. Cauchy's Theorem.- 9. Cauchy's Integral Formula.- 10. Hyperbolic Functions.- 11. Hyperbolic Functions of Imaginaries and Complexes.- 12. Inverse Relations.- 13. Derivatives of Hyperbolic Functions.- 14. Illustrations of Complex Functions.- II. Integration of Partial Derivative Expressions.- III. Fourier Series.- 1. Fourier Series.- 2. Fourier Series Continued.- IV. Theory of Dimensions.- 1. Introductory.- 2. Kinematic Similitude.- 3. The II Theorem.- 4. Non-Dimensional Coefficients.- V. Vector Algebra: Two-Dimensional Vectors.- 1. Definition of Vector and Scalar.- 2. Algebraic Representation of a Vector.- 3. Representation by Rectangular Components.- 4. Exponential Representation of a Vector.- 5. Addition of Vectors.- 6. Subtraction of Vectors.- 7. Multiplication of a Vector by a Scalar.- 8. Multiplication of a Vector by a Vector.- 9. Division of a Vector by a Vector.- 10. Powers and Roots of a Vector.- 11. Vector Equations of Common Curves.- 12. Differentiation of a Vector.- VI. Vector Fields.- 1. Introductory.- 2. Vector Components.- 3. Line Integral.- 4. Line Integral in Two Dimensions.- 5. Vector Flux.- 6. Vector Flux through a Volume.- 7. Vector Flux in Two Dimensions.- 8. Rotational and Irrotational Motion.- 9. Rotational and Irrotational Motion in Three Dimensions.- VII. Potential.- 1. Potential.- 2. Addition Theorem for Velocity Potentials.- 3. Conditions in Order that a Potential ? may Exist.- 4. Conditions for the Existence of a Velocity Potential in a Two-Dimensional Vector Field.- 5. The Functions ? and ? of Chapter I as Potential Functions for a Two-Dimensional Field.- 6. Given the Function w, Required to Find the Remaining Functions and the Field.- 7. Given the Function ? or ?, Required to Find the Remaining Functions and the Field.- 8. Given a Field of Velocity Distribution as Determined by u and v, to Find ?, ? and w.- 9. Illustrations of 6, 7, 8.- VIII. Potential-Continued.- 1. Interpretation of ?.- 2. Interpretation of ?.- 3. Reciprocal Relations of ? and ? to a Vector Field.- 4. Geometrical Relation Between Derivatives of the Functions ? and ?p.- 5. Velocity Relations in an Orthogonal Field of ? and ?.- IX. Special Theorems.- 1. Gauss' Theorem.- 2. Green's Theorem.- 3. Stokes' Theorem.- X. Conformal Transformation.- 1. Introductory.- 2. Application of Vectors to the Problem of Conformal Transformation.- 3. Typical Forms which the Transforming Function May Take.- 4. Illustrative Transformations.- 5. Transformation of a Field of Lines.- 6. Illustrative Field Transformations.- 7. Special Conditions.- 8. Singular Points.- Division B Fluid Mechanics, Part I.- Preface.- I. Fundamental Equations.- 1. Introductory, Characteristics of a Fluid.- 2. Physical Conditions, Notation.- 3. A Field of Fluid Flow as a Vector Field.- 4. The Equation of Continuity.- 5. The Equation of Force and Acceleration.- 6. Bernoulli's Equation.- 7. A Field of Flow; A Tube of Flow; Conditions of Equilibrium of a Field Within a Portion of a Tube of Flow; Momentum Theorem.- 8. Impulse and Impulsive Forces.- 9. Energy of the Field in Terms of Velocity Potential.- 10. Virtual Mass.- 11. Pressure at any Point in a Field Undergoing a Time Change.- II. Plane Irrotational Flow.- 1. Two-Dimensional Flow.- 2. Rotational and Irrotational Motion.- 3. Fields of Flow.- 4. Rectilinear Flow Parallel to Axis of X.- 5. Rectilinear Flow Parallel to Axis of Y.- 6. Rectilinear Flow Oblique to Axes.- 7. Sources and Sinks.- 8. Functions ? and ? for Source.- 9. Functions ? and ? for Sink.- III. Vortex Flow.- 1. Vortex Flow.- 2. Induced Velocity.- 3. Functions ? and ? for Plane Vortex Flow.- IV. Combination Fields of Flow.- 1. Combinations of Fields of Flow.- 2. Two Rectilinear Fields, One Parallel to X and One Parallel to Y.- 3. Rectilinear Flow Combined with Source.- 4. Rectilinear Flow Combined with Sink.- 5. Two Sources of Equal Strength.- 6. Two Sinks of Equal Strength.- 7. Two Sources of Unequal Strength.- 8. Source and Sink of Equal Strength.- 9. Source and Sink of Unequal Strength.- 10. Doublet.- 11. Combination of Sources and Sinks Distributed Along a Line.- 12. Field of Flow for a Continuous Source and Sink Distribution Along a Line.- 13. Combination of Sources and Sinks Distributed in any Manner in a Plane.- V. Combination Fields of Flow Continued-Kutta-Jou-Kowski Theorem.- 1. Rectilinear Flow with Source and Sink of Equal Strength.- 2. Rectilinear Flow with Doublet-Infinite Flow About a Circle.- 3. Rectilinear Flow with Any of the Source and Sink Distributions of IV, 11, 12, 13.- 4. Indefinite Stream with Circular Obstacle Combined with Vortex Flow-Indefinite Flow with Circulation.- 5. Pressure on a Circular Boundary in the Field of 4.- 6. Change of Momentum within any Circular Boundary in the Field of 4.- 7. Total Resultant Force on any Body in Field of 4.- VI. Application of Conformal Transformation to Fields of Flow.- 1. The Application of Conformal Transformation to the Study of Fields of Fluid Motion.- 2. Velocity Relations between Fields of Flow on the z and Z Planes.- 3. Conformal Transformation of the Circle.- 4. Transformation of the Flow Along the Axis of X into the Flow about a Circle.- 5. Transformation of the Flow about a Circle into the Flow about a Straight Line at Right Angles to the Flow.- 6. Flow of Indefinite Field about any Inclined Line.- VII. Particle Paths, Fields of Flow Relative to Axes Fixed in Fluid.- 1. Relative Motions in a Field of Flow-Stream-Lines and Particle Paths.- 2. Path of a Particle Relative to Axes Fixed in the Fluid.- 3. Derivation of Velocity Potential and Stream Function for Fields of Motion Relative to Axes Fixed in the Fluid.- 4. Field of Flow for a Thin Circular Disk Moving in Its Own Plane in an Indefinite Fluid Field.- 5. Field of Flow Produced by a Circle Combined with Vortex Flow Moving in an Indefinite Fluid Field.- 6. Field of Flow for a Straight Line Moving at Right Angles to Itself in an Indefinite Fluid Field.- VIII. Derivation of Potentials by Indirect Methods.- 1. The Derivation of Velocity Potential and Stream Functions by Indirect Methods.- 2. Field of Flow through an Opening in an Infinite Rectilinear Barrier.- 3. Field Produced in an Indefinite Fluid Sheet by the Movement of a Thin Lamina in its Own Plane.- 4. Field of Flow Produced by an Elliptic Contour Moving in the Direction of its Axes.- IX. Three-Dimensional Fields of Flow.- 1. Stream and Velocity Potential Functions for Three-Dimensional Flow.- 2. Sources and Sinks-Three Dimensional Field.- 3. Stream and Velocity Potential Functions for a Source or Sink- Three-Dimensional Space.- 4. Combination of a Source and Sink of Equal Strength-Three-Dimensional Field.- 5. Combination of Two Sources of Equal Strength-Three-Dimensional Field.- 6. Combinations of Sources and Sinks of Unequal Strengths-Three-Dimensional Field.- 7. Doublet in Three-Dimensional Space.- 8. Combinations of Sources and Sinks Along a Straight Line-Three-Dimensional Space.- 9. Field for a Continuous Distribution of Sources and Sinks Along a Straight Line-Three-Dimensional Space.- 10. Combination of Source with Uniform Flow: Three-Dimensional Space.- 11. Combination of Space Doublet with Indefinite Flow Parallel to the Axis of X-Indefinite Flow About a Sphere.- 12. Field of Flow for a Sphere Moving in a Straight Line in an Indefinite Fluid Field.- 13. Rectilinear Flow with the Source and Sink Distributions of 8 and 9.- 14. Any Field of Flow as the Result of a Distributed System of Sources and Sinks or of Doublets.- X. Aerostatics: Structure of the Atmosphere.- 1. Buoyancy.- 2. Center of the System of Surface Pressures.- 3. Structure of the Atmosphere: Standard Atmosphere.- 4. Derivation of Formulae.- Division C Fluid Mechanics, Part II.- Preface.- I. Kinematics of Fluids.- 1. Velocity Field.- 2. Surface Integrals.- 3. Line Integral.- 4. Scalar Triple Vector Products.- 5. Vectorial Triple Vector Products.- 6. Helmholtz' First Theorem.- 7. Stream-lines.- 8. Dyadic Multiplication.- 9. The Derivation of a Vector Field.- 10. Acceleration of Fluid Particles.- 11. Boundary Conditions. Superposition.- II. Dynamics of Fluids.- 1. Pressure.- 2. Materiality of the Vortices.- 3. Irro-tational Flow.- 4. Bernoulli's Pressure Equation.- 5. Fictitious Flows.- 6. Physical Interpretation of the Velocity Potential.- III. Motion of Solids in a Fluid.- 1. The Velocity Distribution.- 2. Apparent Mass.- 3. Apparent Momentum.- 4. Momentum of a Surface of Revolution.- 5. Remarks on Lift.- IV. Sources and Vortices.- 1. Sources and Sinks.- 2. Superposition of Two Sources.- 3. Doublet.- 4. Polar Coordinates.- 5. Motion of a Sphere.- 6. Apparent Mass of the Sphere.- 7. Apparent Mass of Other Source Distributions.- 8. Vortices.- 9. Forces Between Sources and Vortices.- V. Fluid Motion with Axial Symmetry.- 1. Stream Function.- 2. Equation of Continuity.- 3. Zonal Spherical Harmonics.- 4. Differential Equation for Zonal Surface Harmonics.- 5. Superposition of Sources.- 6. Elongated Surfaces of Revolution.- VI. Lateral Motion of Surfaces of Revolution.- 1. Doublets.- 2. Equation of Continuity in Semi-Polar Coordinates.- 3. General Relations.- 4. Elongated Surfaces of Revolution.- 5. Equation of Continuity in Polar Coordinates.- 6. Tesseral Spherical Harmonics.- VII. Ellipsoids of Revolution.- 1. General.- 2. Ovary Semi-Elliptic Coordinates.- 3. Equation of Continuity in Ovary Semi-Elliptic Coordinates.- 4. Method of Obtaining Solutions.- 5. The Axial Motion of an Ovary Ellipsoid.- 6. Discussion of the Solution.- 7. Apparent Mass.- 8. The Stream Function.- 9. Lateral Motion of the Ovary Ellipsoid.- 10. Rotation of the Ovary Ellipsoid.- 11. Modification of the Method for Planetary Ellipsoids.- 12. Most General Motion of Ellipsoids of Revolution.- VIII. Ellipsoid with Three Unequal Axes.- 1. Remarks on Elliptical Coordinates.- 2. Equation of Continuity in Elliptical Coordinates.- 3. Solution for the Motion Parallel to a Principal Axis.- 4. Discussion of the Solution.- 5. Evaluation of the Constants.- 6. The Elliptic Disc.- 7. Rotation of an Ellipsoid.- 8. Concluding Remarks.- Division D Historical Sketch.- Preface.- I. Period of Early Thought: From Antiquity to the End of the XVII Century.- II. Period of Classic Hydrodynamics: From the End of the XVII Century to the End of the XIX Century.- III. Period of Modern Aerodynamics: From the End of the XIX Century Onward.
Division A Mathematical Aids.- Preface.- I. The Complex Variable (x + iy).- 1. Introductory.- 2. Properties of the Functions ? and ?.- 3. The Inverse Relation z = F (w).- 4. The Complex x + iy as the Location of a Point in a Plane.- 5. Results Growing Out of the Expression of the Complex Variable in the Exponential and Circular Function Forms.- 6. The Integration of Functions of a Complex Variable.- 7. Influence of Singularities.- 8. Cauchy's Theorem.- 9. Cauchy's Integral Formula.- 10. Hyperbolic Functions.- 11. Hyperbolic Functions of Imaginaries and Complexes.- 12. Inverse Relations.- 13. Derivatives of Hyperbolic Functions.- 14. Illustrations of Complex Functions.- II. Integration of Partial Derivative Expressions.- III. Fourier Series.- 1. Fourier Series.- 2. Fourier Series Continued.- IV. Theory of Dimensions.- 1. Introductory.- 2. Kinematic Similitude.- 3. The II Theorem.- 4. Non-Dimensional Coefficients.- V. Vector Algebra: Two-Dimensional Vectors.- 1. Definition of Vector and Scalar.- 2. Algebraic Representation of a Vector.- 3. Representation by Rectangular Components.- 4. Exponential Representation of a Vector.- 5. Addition of Vectors.- 6. Subtraction of Vectors.- 7. Multiplication of a Vector by a Scalar.- 8. Multiplication of a Vector by a Vector.- 9. Division of a Vector by a Vector.- 10. Powers and Roots of a Vector.- 11. Vector Equations of Common Curves.- 12. Differentiation of a Vector.- VI. Vector Fields.- 1. Introductory.- 2. Vector Components.- 3. Line Integral.- 4. Line Integral in Two Dimensions.- 5. Vector Flux.- 6. Vector Flux through a Volume.- 7. Vector Flux in Two Dimensions.- 8. Rotational and Irrotational Motion.- 9. Rotational and Irrotational Motion in Three Dimensions.- VII. Potential.- 1. Potential.- 2. Addition Theorem for Velocity Potentials.- 3. Conditions in Order that a Potential ? may Exist.- 4. Conditions for the Existence of a Velocity Potential in a Two-Dimensional Vector Field.- 5. The Functions ? and ? of Chapter I as Potential Functions for a Two-Dimensional Field.- 6. Given the Function w, Required to Find the Remaining Functions and the Field.- 7. Given the Function ? or ?, Required to Find the Remaining Functions and the Field.- 8. Given a Field of Velocity Distribution as Determined by u and v, to Find ?, ? and w.- 9. Illustrations of 6, 7, 8.- VIII. Potential-Continued.- 1. Interpretation of ?.- 2. Interpretation of ?.- 3. Reciprocal Relations of ? and ? to a Vector Field.- 4. Geometrical Relation Between Derivatives of the Functions ? and ?p.- 5. Velocity Relations in an Orthogonal Field of ? and ?.- IX. Special Theorems.- 1. Gauss' Theorem.- 2. Green's Theorem.- 3. Stokes' Theorem.- X. Conformal Transformation.- 1. Introductory.- 2. Application of Vectors to the Problem of Conformal Transformation.- 3. Typical Forms which the Transforming Function May Take.- 4. Illustrative Transformations.- 5. Transformation of a Field of Lines.- 6. Illustrative Field Transformations.- 7. Special Conditions.- 8. Singular Points.- Division B Fluid Mechanics, Part I.- Preface.- I. Fundamental Equations.- 1. Introductory, Characteristics of a Fluid.- 2. Physical Conditions, Notation.- 3. A Field of Fluid Flow as a Vector Field.- 4. The Equation of Continuity.- 5. The Equation of Force and Acceleration.- 6. Bernoulli's Equation.- 7. A Field of Flow; A Tube of Flow; Conditions of Equilibrium of a Field Within a Portion of a Tube of Flow; Momentum Theorem.- 8. Impulse and Impulsive Forces.- 9. Energy of the Field in Terms of Velocity Potential.- 10. Virtual Mass.- 11. Pressure at any Point in a Field Undergoing a Time Change.- II. Plane Irrotational Flow.- 1. Two-Dimensional Flow.- 2. Rotational and Irrotational Motion.- 3. Fields of Flow.- 4. Rectilinear Flow Parallel to Axis of X.- 5. Rectilinear Flow Parallel to Axis of Y.- 6. Rectilinear Flow Oblique to Axes.- 7. Sources and Sinks.- 8. Functions ? and ? for Source.- 9. Functions ? and ? for Sink.- III. Vortex Flow.- 1. Vortex Flow.- 2. Induced Velocity.- 3. Functions ? and ? for Plane Vortex Flow.- IV. Combination Fields of Flow.- 1. Combinations of Fields of Flow.- 2. Two Rectilinear Fields, One Parallel to X and One Parallel to Y.- 3. Rectilinear Flow Combined with Source.- 4. Rectilinear Flow Combined with Sink.- 5. Two Sources of Equal Strength.- 6. Two Sinks of Equal Strength.- 7. Two Sources of Unequal Strength.- 8. Source and Sink of Equal Strength.- 9. Source and Sink of Unequal Strength.- 10. Doublet.- 11. Combination of Sources and Sinks Distributed Along a Line.- 12. Field of Flow for a Continuous Source and Sink Distribution Along a Line.- 13. Combination of Sources and Sinks Distributed in any Manner in a Plane.- V. Combination Fields of Flow Continued-Kutta-Jou-Kowski Theorem.- 1. Rectilinear Flow with Source and Sink of Equal Strength.- 2. Rectilinear Flow with Doublet-Infinite Flow About a Circle.- 3. Rectilinear Flow with Any of the Source and Sink Distributions of IV, 11, 12, 13.- 4. Indefinite Stream with Circular Obstacle Combined with Vortex Flow-Indefinite Flow with Circulation.- 5. Pressure on a Circular Boundary in the Field of 4.- 6. Change of Momentum within any Circular Boundary in the Field of 4.- 7. Total Resultant Force on any Body in Field of 4.- VI. Application of Conformal Transformation to Fields of Flow.- 1. The Application of Conformal Transformation to the Study of Fields of Fluid Motion.- 2. Velocity Relations between Fields of Flow on the z and Z Planes.- 3. Conformal Transformation of the Circle.- 4. Transformation of the Flow Along the Axis of X into the Flow about a Circle.- 5. Transformation of the Flow about a Circle into the Flow about a Straight Line at Right Angles to the Flow.- 6. Flow of Indefinite Field about any Inclined Line.- VII. Particle Paths, Fields of Flow Relative to Axes Fixed in Fluid.- 1. Relative Motions in a Field of Flow-Stream-Lines and Particle Paths.- 2. Path of a Particle Relative to Axes Fixed in the Fluid.- 3. Derivation of Velocity Potential and Stream Function for Fields of Motion Relative to Axes Fixed in the Fluid.- 4. Field of Flow for a Thin Circular Disk Moving in Its Own Plane in an Indefinite Fluid Field.- 5. Field of Flow Produced by a Circle Combined with Vortex Flow Moving in an Indefinite Fluid Field.- 6. Field of Flow for a Straight Line Moving at Right Angles to Itself in an Indefinite Fluid Field.- VIII. Derivation of Potentials by Indirect Methods.- 1. The Derivation of Velocity Potential and Stream Functions by Indirect Methods.- 2. Field of Flow through an Opening in an Infinite Rectilinear Barrier.- 3. Field Produced in an Indefinite Fluid Sheet by the Movement of a Thin Lamina in its Own Plane.- 4. Field of Flow Produced by an Elliptic Contour Moving in the Direction of its Axes.- IX. Three-Dimensional Fields of Flow.- 1. Stream and Velocity Potential Functions for Three-Dimensional Flow.- 2. Sources and Sinks-Three Dimensional Field.- 3. Stream and Velocity Potential Functions for a Source or Sink- Three-Dimensional Space.- 4. Combination of a Source and Sink of Equal Strength-Three-Dimensional Field.- 5. Combination of Two Sources of Equal Strength-Three-Dimensional Field.- 6. Combinations of Sources and Sinks of Unequal Strengths-Three-Dimensional Field.- 7. Doublet in Three-Dimensional Space.- 8. Combinations of Sources and Sinks Along a Straight Line-Three-Dimensional Space.- 9. Field for a Continuous Distribution of Sources and Sinks Along a Straight Line-Three-Dimensional Space.- 10. Combination of Source with Uniform Flow: Three-Dimensional Space.- 11. Combination of Space Doublet with Indefinite Flow Parallel to the Axis of X-Indefinite Flow About a Sphere.- 12. Field of Flow for a Sphere Moving in a Straight Line in an Indefinite Fluid Field.- 13. Rectilinear Flow with the Source and Sink Distributions of 8 and 9.- 14. Any Field of Flow as the Result of a Distributed System of Sources and Sinks or of Doublets.- X. Aerostatics: Structure of the Atmosphere.- 1. Buoyancy.- 2. Center of the System of Surface Pressures.- 3. Structure of the Atmosphere: Standard Atmosphere.- 4. Derivation of Formulae.- Division C Fluid Mechanics, Part II.- Preface.- I. Kinematics of Fluids.- 1. Velocity Field.- 2. Surface Integrals.- 3. Line Integral.- 4. Scalar Triple Vector Products.- 5. Vectorial Triple Vector Products.- 6. Helmholtz' First Theorem.- 7. Stream-lines.- 8. Dyadic Multiplication.- 9. The Derivation of a Vector Field.- 10. Acceleration of Fluid Particles.- 11. Boundary Conditions. Superposition.- II. Dynamics of Fluids.- 1. Pressure.- 2. Materiality of the Vortices.- 3. Irro-tational Flow.- 4. Bernoulli's Pressure Equation.- 5. Fictitious Flows.- 6. Physical Interpretation of the Velocity Potential.- III. Motion of Solids in a Fluid.- 1. The Velocity Distribution.- 2. Apparent Mass.- 3. Apparent Momentum.- 4. Momentum of a Surface of Revolution.- 5. Remarks on Lift.- IV. Sources and Vortices.- 1. Sources and Sinks.- 2. Superposition of Two Sources.- 3. Doublet.- 4. Polar Coordinates.- 5. Motion of a Sphere.- 6. Apparent Mass of the Sphere.- 7. Apparent Mass of Other Source Distributions.- 8. Vortices.- 9. Forces Between Sources and Vortices.- V. Fluid Motion with Axial Symmetry.- 1. Stream Function.- 2. Equation of Continuity.- 3. Zonal Spherical Harmonics.- 4. Differential Equation for Zonal Surface Harmonics.- 5. Superposition of Sources.- 6. Elongated Surfaces of Revolution.- VI. Lateral Motion of Surfaces of Revolution.- 1. Doublets.- 2. Equation of Continuity in Semi-Polar Coordinates.- 3. General Relations.- 4. Elongated Surfaces of Revolution.- 5. Equation of Continuity in Polar Coordinates.- 6. Tesseral Spherical Harmonics.- VII. Ellipsoids of Revolution.- 1. General.- 2. Ovary Semi-Elliptic Coordinates.- 3. Equation of Continuity in Ovary Semi-Elliptic Coordinates.- 4. Method of Obtaining Solutions.- 5. The Axial Motion of an Ovary Ellipsoid.- 6. Discussion of the Solution.- 7. Apparent Mass.- 8. The Stream Function.- 9. Lateral Motion of the Ovary Ellipsoid.- 10. Rotation of the Ovary Ellipsoid.- 11. Modification of the Method for Planetary Ellipsoids.- 12. Most General Motion of Ellipsoids of Revolution.- VIII. Ellipsoid with Three Unequal Axes.- 1. Remarks on Elliptical Coordinates.- 2. Equation of Continuity in Elliptical Coordinates.- 3. Solution for the Motion Parallel to a Principal Axis.- 4. Discussion of the Solution.- 5. Evaluation of the Constants.- 6. The Elliptic Disc.- 7. Rotation of an Ellipsoid.- 8. Concluding Remarks.- Division D Historical Sketch.- Preface.- I. Period of Early Thought: From Antiquity to the End of the XVII Century.- II. Period of Classic Hydrodynamics: From the End of the XVII Century to the End of the XIX Century.- III. Period of Modern Aerodynamics: From the End of the XIX Century Onward.