CONTENTS. 



CHAPTER I. 



THE EQUATIONS OF MOTION. 

 ART. PAGE 



1 3. Fundamental assumptions . .... . ... ... 1 



4. Two forms of the equations 3 



5 11. The Eulerian form of the equations. Dynamical equations, equa 

 tion of continuity, surface conditions 8 



12 14. Second method. Flow of matter, momentum, energy ... 8 



15. Impulsive generation of motion 11 



16, 17. The Lagrangian form of the equations. Dynamical equations, 



equation of continuity 12 



18 21. Weber s Transformation 14 



Comparison of the Eulerian and Lagrangian methods. 



CHAPTER II. 



INTEGRATION OF THE EQUATIONS IN BPECIAL CASES. 



22 27. Velocity-Potential. Lagrange s Theorem. Equi-potential sur 

 faces. Physical interpretation of velocity potential . . 18 



2830. Steady Motion 22 



3187. Examples: Efflux of liquids and gases. The Vena Contracta. 



Rotating fluid . 25 



CHAPTER III. 



IRROTATIONAL MOTION. 



38 40. Analysis of the motion of a fluid element 32 



Circulation. 



41, 42. Irrotational motion in simply-connected spaces .... 37 



43 52. Particular case of a liquid. Properties of the velocity potential . 38 



53 59. Multiply-connected spaces 47 



Irrotational motion in such spaces. 



