CONTENTS. 



Art. Page 



132. Kelvin and Dirichlet's Prin- 

 ciple 376 



133. Green's Theorem in Ortho- 

 gonal Curvilinear Coor- 

 dinates 379 



134. Stokes's Theorem in Ortho- 

 gonal Curvilinear Coor- 

 dinates 381 



135. Laplace's Equation in Spheri- 

 cal and Cylindrical Coord. 383 



136. Logarithmic Potential . . 385 



137. Green's Theorem for a Plane 386 



138. Application to Logarithmic 

 Potential 387 



139. Green's Formula for Loga- 

 rithmic Potential .... 388 



140. Dirichlet's Problem for a 

 Circle. Trigonometric Series 388 



140 a. Development in Circular 



Harmonics 390 



141. Spherial Harmonics . . . 393 



142. Dirichlet's Problem for 

 Sphere 395 



143. Forms of Spherical Harmo- 

 nics 395 



144. Zonal Harmonics .... 397 



145. Harmonics in Spherical 

 Coordinates . 398 



Art. Page 



146. Development of Reciprocal 

 Distance 398 



147. Development in Spherical 

 Harmonics 400 



148. Development of the Potential 

 in Spherical Harmonics . . 



149. Applications to Geodesy. 

 Clairaut's Theorem . . . 



150. Potential of Tide - generating 

 Forces 



151. Ellipsoidal Homoeoids. New- 

 ton's Theorem 409 



152 Condition for Infinite Family 

 of Equipotentials ... 



153. Application to Elliptic Coord 



154. Chasles's Theorem . . . 



155. Maclaurin's Theorem . . 



156. Potential of Ellipsoid . 

 157.. Internal Point .... 



158. Verification by Differen- 

 tiation 419 



159. Ivory's Theorem .... 420 



160. Ellipsoids of Revolution . 421 



161. Development of Potential of 

 Ellipsoid of Revolution . . 424 



162. Energy of Distributions. 

 Gauss's theorem .... 425 



163. Energy in terms of Field . 426 



402 



404 



408 



410 

 411 

 413 

 414 

 415 

 418 



CHAPTER IX. 

 Dynamics of Deformdble Bodies. 



164. Kinematics. Homogeneous 

 Strain 427 



165. Self- conjugate Functions. 

 Pure Strain 430 



166. Rotation 435 



167. General Small Strain . . 436 



168. Simple Strains. Stretches 



and Shears 439 



168 a. Elongation and Compression 



Quadric ....... 441 



169. Heterogeneous Strain . . 444 



170. Stress . . - . 446 



171. Geometrical Representation 



of Stress 450 



171 a. Simple Stresses .... 451 



172. Work of Stress in producing 

 Strain 454 



173. Relations between Stress and 

 Strain 455 



174. Energy Function for Isotro- 



pic Bodies 457 



175. Stresses in Isotropic Bodies 460 



176. Physical Meaning of the 

 Constants . . 461 



CHAPTER X. 

 Statics of Deformable Bodies. 



111. Hydrostatics 463 



178. Height of the Atmosphere 465 



179. Rotating Mass of Fluid . . 467 



180. Gravitating, rotating Fluid 468 



181. Equilibrium of Floating 

 Body 471 



182. Solid hollow Sphere and 

 Cylinder under Pressure 



183. Problem of de Saint -Yenant 



184. Determination of Function 

 for particular Cases . . . 



