XVI CONTENTS. 



CHAPTER X. 



WAVES OF EXPANSION. 



ART. 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 



