CONTEXTS. 



IX 



ART. 



120, 121. Case of a perforated solid. Cyclic motion. 



122, 123. Motion of a ring 



124. Case of two or more solids 



125. Case of two spheres .... 



PAGB 



136 

 140 

 141 

 142 



CHAPTER VI. 



VORTEX MOTION. 



126,127. Definitions. Strength of a vortex .... 



128 131. Determination of motion in terms of expansion and rotation 

 Interpretation. Electromagnetic analogy. 



132. Vortex-Sheet 



133. Velocity-Potential due to a vortex 



134. Dynamical theorems . . 

 135 137. Kinetic Energy . . . . -. 



138, 139. Rectilinear vortices ^ ... . . 

 Examples. 



140 144. Circular vortices 



145. Conditions for steady motion 



146 

 149 



154 

 156 

 157 

 159 

 162 



167 



172 



CHAPTER VII. 



WAVES IX LIQUIDS. 



146 152. Waves of small vertical displacement . 



Waves in canals. 

 153 155. Small disturbing forces 



Canal theory of the tides. 



156 160. Waves in deep water 



161 163. Wave-propagation in two dimensions. Examples 

 164. Free oscillations in an ocean of uniform depth. 



173 



182 



185 

 194 



197 



CHAPTER VIII. 



WAVES IN AIR. 



165, 166. Plane waves . . . . . 201 



167, 168. Spherical waves 203 



169, 170. General equations of sound waves. Integration .... 206 



171, 172. Solutions of the exact equations of motion of plane waves . . 208 



Methods of Earnshaw and Eiemann, 



Change of type. 



173. Condition for permanency of type . 213 



