Vlll 



CONTENTS. 



ART. 

 6063. 

 64, 65. 



66, 67. 



Particular case of a liquid 



Green s Theorem 



Kinetic energy of a fluid. 



Thomson s extension of Green s Theorem 



PAGE. 

 , 54 

 , 57 



63 



CHAPTER IV. 



MOTION OP A LIQUID IN TWO DIMENSIONS. 



68, 69. The Stream-Function 66 



70 72. Irrotational motion. Kinetic energy 68 



73 79. Eelations between the velocity potential and the stream-function . 71 



Digression on the theory of functions of a complex variable. 



Logarithmic function. 



80 84. Examples. Special cases of motion . . f .80 



85 87. General formula for the velocity potential and the stream-function 84 



Motion of a circular cylinder in a liquid. 



88. Motion of translation of a solid through a liquid .... 87 

 Examples. 



89. Motion of rotation of a solid in a liquid 91 



Examples. 



90 93. Inverse complex functions . . . . . . . .94 



Kirchhoff s method. 



Examples. 

 94 98. Discontinuous Motions 98 



Helmholtz s and Kirchhoff s solutions. 



The Vena Contracta. 



Impact of a stream on a lamina. 



CHAPTER V. 



MOTION OF SOLIDS THROUGH A LIQUID. 



99 104. Kinematical investigations 



Examples. 

 105. Dynamical investigations 



Direct method. Application to a sphere. 

 106108. Indirect method 



Impulse. 



109. Equations of motion 



110 112. Kinetic energy. Momenta 



113, 114. Cases of steady motion 



115. Motion of a solid struck by an impulsive couple 



116. Expressions for the kinetic energy in certain cases. 



117. Motion of a solid of revolution in a particular case. 



118. Stability of a body moving parallel to an axis of symmetry 



119. Constraint necessary to produce any specified motion . 



110 

 118 

 120 



123 

 124 

 126 

 129 

 130 

 133 

 134 

 135 



