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 &amp;lt;. 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 ; Kankine s com 

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



