Xll CONTENTS. 



CHAPTER VI. 



ON THE MOTION OF SOLIDS THROUGH A LIQUID: 

 DYNAMICAL THEORY. 



ART. PAGE 



114, 115. Determination of < for the acyclic motion due to a single 



solid in an infinite liquid ; kinematical formulae . 167 



116. Theory of the 'impulse' 169 



117-120. Dynamical equations relative to moving axes. Expression 

 for the energy; coefficients of inertia. Formulae for 

 * impulse.' Reciprocal formulae. Impulsive pressures 

 of fluid on solid 170 



121. Equations of motion. Components of fluid pressure on 



moving solid. Three directions of permanent transla- 

 tion. Stability 176 



122. Steady motions. Case where the 'impulse' reduces to a 



couple 178 



123. Simplification of the expression for the energy in certain 



cases ' . . .181 



124-126. Motion of a solid of revolution with its axis in one plane ; 

 stability. Stability increased by rotation about axis. 

 Steady motion of a solid of revolution . . .184 



127. Motion of an 'isotropic helicoid' . . . . .191 



128. Motion of a hollow body filled with liquid . . .192 

 129-131. Motion of a perforated solid, when there is cyclic motion 



through the apertures. Meaning of ' impulse ' in 

 this case. Steady motion of a ring ; stability . . 192 

 132, 133. Equations of motion in generalized coordinates; Hanril- 



tonian principle. Derivation of Lagrange's equations 197 



134. Application to Hydrodynamics 201 



135, 136. Motion of a sphere near a plane boundary. Motion of 



two spheres in the line of centres .... 205 



137. Modification of Lagrange's equations in the case of cyclic 



motion 207 



138, 139. Alternative investigation ; flux-coordinates. Equations of 



motion of a 'gyrostatic system' 211 



140. Motion of a sphere in a cyclic region . . . .217 



141. Pressures on solids held at rest. Cases of thin cores, 



and tubes. Comparison with electro-magnetic pheno- 

 mena .... 218 



