CONTENTS. xvii 



ART. PAGE 



284. Hypothesis that the stresses are linear functions of the 



rates of strain. Coefficient of viscosity . . . 511 



285. Boundary conditions. Question as to slipping of a fluid 



over a solid 514 



286. General equations of motion of a viscous fluid. Inter- 



pretation 514 



287. Dissipation of energy by viscosity. Expressions for the 



dissipation-function 517 



288-290. Problems of steady motion. Flow of a viscous liquid 



through a crevice, and through a tube of circular 



section ; Poiseuille's laws. Question as to slipping. 



Kesults for other forms of section . . . .519 

 291, 292. Steady rotation of a cylinder. Rotation of a sphere . 523 

 293-295. Motion of a viscous fluid when inertia is neglected. 



General solution in spherical harmonics. Steady 



motion of a sphere ; resistance ; terminal velocity. 



Limitations to the solution 526 



296. Steady motion of an ellipsoid 534 



297. General theorems of von Helmholtz and Korteweg . . 536 

 298-300. Periodic laminar motion. Oscillating plane. Periodic 



tidal force 538 



301, 302. Effect of viscosity on water-waves. Method of dissipation- 

 function. Direct method 544 



303. Effect of surface-forces. Generation and maintenance of 



waves by wind 549 



304. Calming effect of oil on water-waves 552 



305-309. Periodic motion with a spherical boundary. General 



solution in spherical harmonics. Applications. Decay 

 of motion in a spherical vessel. Torsional oscillations 

 of a shell containing liquid. Effect of viscosity on 

 the vibrations of a liquid globe. Torsional oscillations 

 of a sphere surrounded by liquid. Oscillations of a 



ball-pendulum 555 



310. Effect of viscosity on sound-waves 570 



311-312. Instability of linear flow when the velocities exceed certain 

 limits. Law of resistance in pipes. Reynolds' ex- 

 periments. Skin-resistance of ships. References to 

 theoretical investigations 572 



