XVI CONTENTS. 



CHAPTER X. 

 WAVES OF EXPANSION. 



ABT. PAGE 



254. Coefficient of cubic elasticity . . . . . 464 



255-258. Plane waves. Velocity of sound in liquids and gases ; 



Laplace's theory. Energy of plane waves . . . 464 



259-262. Waves of finite amplitude. Condition for permanency of 

 type. Change of type in progressive waves. In- 

 vestigations of Riemann, Earnshaw, and Rankine. 

 Question as to the possibility of waves of discon- 

 tinuity 470 



263, 264. Spherical waves. Determination of motion in terms of 



initial conditions 477 



265. General equation of sound-waves. Poisson's integral . 480 



266. Simple-harmonic vibrations. Case of symmetry ; radial 



vibrations in a spherical envelope ; simple source of 

 sound 483 



267-270. General solution in spherical harmonics. Vibrations of air 

 in spherical envelope. Waves in a spherical sheet of 

 air. Waves propagated outwards from a spherical 

 surface. Ball-pendulum ; correction for inertia, and 

 dissipation-coefficient ....... 484 



271, 272. Isothermal oscillations of an atmosphere of variable 



density. Plane waves 491 



273, 274. Atmospheric tides. References to further researches . 494 



CHAPTER XI. 



VISCOSITY. 



275, 276. General theory of dissipative forces. One degree of free- 

 dom. Periodic imposed force. Retardation or accele- 

 ration of phase 496 



277. Application to tides in equatorial canal. Tidal friction . 499 



278, 279. General theory resumed. Several degrees of freedom. 



Frictional and gyrostatic terms. Dissipation-function. 

 Oscillations of a dissipative system about a con- 

 figuration of absolute equilibrium .... 503 



280. Effect of gyrostatic terms. Two degrees of freedom; 



disturbance of long period 506 



281-283. Viscosity of fluids. Specification of stress. Formulae of 



transformation .... 508 



