CONTENTS. 



XV11 



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 j ;. 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. 



Eesults 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 



