tides-Rigidity of the earth: probably greater on the whole

than that of a solid glass globe-Dynamic theory of tides

too imperfect to give any estimate of absolute values for

main phenomena: but not so for the fortnightly and semi-

annual tides-Amounts of fortnightly tide estimated on

various suppositions as to rigidity-Rigidity of the earth:

probably to be best learned from observations giving

amounts of fortnightly tides-Tide-gauges to be esta-

blished at ocean stations-Scantiness of information re-

garding fortnightly tides, hitherto drawn from observa-

tion

Advance in knowledge of tides since the first edition-The

theoretical value of the fortnightly and monthly elliptic

tides-Definition of symbols-Long-period tides-For-

mulæ for the longitude and R. A. of the intersection-

Evaluation of the function E-Theoretical expressions for

equilibrium value of fortnightly and monthly tides-Maxi-

mum and minimum values in British feet-Preparation

for reduction by least squares-Theoretical expression for

the tides when the earth yields bodily, and when there is

friction-Equations for reduction by least squares-Nu-

merical results of harmonic analysis of tidal observations

-Results of reduction-Tidal yielding of the earth's

mass. Rigidity about equal to or greater than that of

steel

SECTIONS

832-846

847, 848

APPENDIX C.-Equations of Equilibrium of an Elastic Solid deduced from

the Principle of Energy.

APPENDIX D.-On the Secular Cooling of the Earth.

APPENDIX E.-On the Age of the Sun's Heat.

APPENDIX F.-On the Size of Atoms.

APPENDIX G.-On Tidal Friction, by G. H. Darwin.

SCHEDULE OF ALTERATIONS AND ADDITIONS

IN PART I., VOL. I.

§ 198. Rewritten-degrees of freedom-geometrical slide (new).

§ 200. Small alterations.

§ 201. Slight alteration.

Appendix A. Laplace's equation in generalised co-ordinates (new).
Appendix B.

Examples of spherical harmonics-rewritten and much
extended (new).

§ 212. Slight addition.

§ 223. Units of length and time (new).

§ 225. Small addition.

§ 245. Part omitted.

§ 317. Small alteration.

§ 318. Old § 329 rewritten and extended.

§ 319. Old § 330-with considerable additions-ignoration of co-ordinates

(new).

§ 320 to § 324. Same as old § 331 to § 335.

§ 325. Extended from old § 336-addition to observed phenomena of fluid

motion.

§ 326 to § 336. Same as old § 318 to § 328, with some alterations-con-

siderable addition, to § 319 now § 327.

§ 337. Addition including slightly disturbed equilibrium (new).

§ 341. Extended to include old § 342 with addition.

§ 342. Same as non-mathematical portion of old § 343.

§ 343, a to p. On the motions of a cycloidal system rewritten and greatly

extended.

§ 345, i. to xxviii. Oscillations with friction-dissipation of energy-posi-

tional and motional forces-gyrostatics-stability (new).

§ 373 and § 374. Same as old § 373.

§ 374 to § 380.

§ 381 and § 382.

§ 383 to § 386.

Same as old § 375 to § 379, with alterations.

Same as old § 380.

Same as old §§ 381 to § 384. Old § 385 and § 386 omitted.

§ 398'. Harmonic analysis (new).

§ 401. Addition on calculating machines (new).

§ 405.

Foot-note quoted from old § 830; compare with new § 830.

§ 408. Slight alteration.

§ 409

$ 427}

Rewritten.

3429. Part rewritten.

SCHEDULE OF ALTERATIONS AND ADDITIONS

IN PART II., VOL. I.

§ 478 and § 479. Small addition.

§ 491 (f) and § 492. Slight alteration.

§ 493. Integral of normal attraction over a closed surface (new).

§ 494, a to q. Theory of potential-attraction of ellipsoids (new).

§ 495 (a), (b), & (c). Same as old §§ 493, 494, and 495.

§ 496. Small addition.

§ 519. Old § 520 rewritten, including part of § 519.

§ 520. Distribution of electricity on an ellipsoidal conductor (new).

Attraction of Homoeoids (new), including old § 523.

§ 521 to § 525.

§ 526 and § 527.

Attraction of ellipsoids (new), rewritten for old § 522.

§ 528 to § 530. Mathematical part of old § 519 rewritten.

§ 531. Old § 524 rewritten.

§ 532. Old § 521 rewritten.

§ 533. Same as old § 525 with small addition.

§ 534. Same as old § 526 and § 527.

§ 534 (a) to § 534 (g). Same as old § 528 to § 534.

§ 551 to § 557. Equilibrium of free and constrained rigid bodies, including

Theory of Screws (new)-old § 551 omitted.

§ 558 to § 559 (ƒ). Same as old § 552 to § 559, partly rewritten and slightly
altered.

§ 632. Slightly modified.

§ 686. Note on modulus of elasticity (new).

§ 688. Slightly modified.

§ 691, a to f. Theory of elasticity-wave propagation-resilience (new).

§ 812. Addition-lunar disturbance of gravity (new).

§ 818. Gravitational observatories (new, G. H. D.).

§ 824, 824'. Addition — ellipticity of internal strata of earth and other planets (new, G. H. D.).

§ 830. Entirely rewritten and extended (new, G. H. D.).

§ 832'. Rigidity and strength of materials of earth (new, G. H. D.).

§ 834.

Modification of analysis and correction (G. H. D.).

§ 835. Slight alteration.

§ 837. Small addition (G. H. D.).

§ 840'. Theory of elastic tides (new, G. H. D.).

§ 847 to end. Rigidity of earth deduced from tidal observations (new, G. H.D.)

-old § 847 to end entirely omitted.