602 



INDEX. 



Energy, of long waves, 278 



of solid moving through liquid, 



130, 172 



of surface waves, 378 

 of vortex-systems, 239, 242 

 superficial, 442 



Equation of continuity, 5, 6, 15 



Equations of motion, 



of Motionless fluid, 3, 14 

 of a solid in a liquid, 171, 176, 192 

 of a viscous fluid, 514, 516 

 relation to moving axes, 322 



Equilibrium of rotating masses of 

 liquid, 580, 588 



Expansion, waves of, 464 



Fish-line problem, 455 



Flapping of sails and flags, 392 



Flow defined, 35, 39 



Flow of a viscous fluid through a 



crevice, 519 

 Flow of a viscous fluid through a pipe, 



520, 522 



Flux defined, 41 

 Forced oscillations, 269, 329 

 Fourier s theorem, 380, 395 



Generalized coordinates, 197 



Gerstner s waves, 412, 416 



Globe, oscillations of a liquid, 436 



tides on a rotating, 343 

 Globule, vibrations of a, 461 

 Green s theorem, 50, 



Lord Kelvin s extension of, 60 

 Group-velocity (of waves), 381, 401, 



445, 448 

 Gyrostatic system, 211, 503 



Harmonics, spherical, 117, 316 



conjugate property 

 of, 127 



ellipsoidal, 145, 155 



zonal, 121, 122 



sectorial, 126 



tesseral, 125 



Helicoid, motion of a, 191 

 Hydrokinetic symmetry, 181 

 Hypergeometric series, 121 



Ignoration of coordinates, 214 

 Image of a double-source, 138, 262 



Impulse defined, 169 

 theory of, 169, 173, 194 

 in vortex-motion, 237, 248 



Impulsive motion, 12 



Inertia of a solid, effect of fluid in 

 modifying, 130, 172, 192 



Instability of linear flow in a pipe, 573 



Irrotational motion defined, 38 



Jets, theory of, in two dimensions, 



103, 105 

 capillary phenomena of, 457, 459 



Kinematic coefficient of viscosity, 513 

 Kinetic energy of a solid in a liquid, 173 

 Kinetic stability, 327 



Lagrange s equations, 201, 207 

 Lagrange s (velocity-potential) theorem, 



18, 38 

 Lamina, impact of a stream on, 94, 



107, 109, 112 

 Laminar motion defined, 34 



in viscous fluid, 538, 



541, 545 



Laplace s tidal problem, 345 

 Limiting velocity, 24 

 Lines of motion, see stream-lines. 



Minimum energy, 51, 63 

 Modulus of decay, 497 



of water-waves, 545 



of sound-waves, 572 

 Multiple-connectivity, 53, 57 



Normal modes of oscillation, 268 



Oil, effect of a film of, on water- 

 waves, 552 



Orbits of particles (in wave-motion), 

 373, 376 



Ordinary stability, 327 



Orthogonal coordinates, 156 



Oscillations, see Small oscillations, and 

 Waves. 



Oscillatingplane,inviscousfluid,538,541 



Pendulum, oscillating in air, 490 



oscillating in viscous fluid, 568 

 Periodic motion of a viscous fluid, 

 538, 555, 559 



