CONTENTS. 



CHAPTER I. 

 THE EQUATIONS OF MOTION. 



ART. PAGE 



I, 2. Fundamental property of a fluid 1 



3-8. 'Eulerian' form of the equations of motion. Dynamical 



equations, equation of continuity 3 



9. Physical equations 7 



10. Surface-conditions 8 



II. Equation of energy 10 



12. Impulsive generation of motion 12 



13, 14. 'Lagrangian' forms of the dynamical equations, and of the 



equation of continuity 14 



15. Weber's Transformation 15 



16, 17. Extension of the Lagrangian notation. Comparison of the 



two forms .......... 16 



CHAPTER II. 

 INTEGRATION OF THE EQUATIONS IN SPECIAL CASES. 



18. Velocity -potential. Lagrange's theorem 18 



19, 20. Physical meaning of 0. Geometrical properties . . .19 

 21. Integration of the equations when a velocity-potential exists ; 



pressure-equation . . . . . . . .21 



22-24. Steady motion. Deduction of the pressure-equation from 



the principle of energy. Limit to the velocity . . 22 



25. Efflux of liquids ; vena contracta ...... 26 



26. Efflux of gases 28 



27-30. Examples of rotating fluid : uniform rotation ; Rankine's ' com- 

 bined vortex ' ; electro-magnetic rotation .... 29 



