CONTENTS. 



XI 



CHAPTER XI. 

 Hydrodynamics. 



Art. Page 



186. Equations of Motion . . . 496 



187. Hamilton's Principle ... 499 



188. Equation of Activity . . . 501 



189. Steady Motion 503 



190. Circulation ...... 506 



191. Vortex Motion 509 



192. Vector Potential. Helm- 

 holtz's Theorem .... 511 



193. Velocity due to Vortex . . 514 



194. Kinetic Energy of Vortex . 515 



195. Straight parallel Vortices . 515 



196. Irrotational Motion 620 



Art. Page 



197. Uniplanar Motion 521 



198. Wave Motion 529 



199. Equilibrium Theory of the 

 Tides 535 



200. Tidal Waves in Canals . . 538 



201. Sound Waves 542 



202. Plane Waves 543 



203. Echo. Organ pipes . . . 545 



204. Spherical Waves .... 547 



205. Waves in a Solid .... 548 



206. Viscous Fluids . 549 



NOTES. 



Note I. Differential Equations 559 



II. Algebra of Indeterminate Multipliers 562 



III. Quadratic Differential Forms. Generalized Vectors 563 



IV. Axes of Central Quadric 567 



V. Transformation of Quadratic Forms 572 



INDEX 580 



