Motion,

360. Components of Varied Motion,. 386

361. Uniformly-Varied Velocity, 386

364. Varying Deviation,

365. Resultant Rate of Variation,

366. Rates of Variation of Component

Velocities,

Page

387

387

388

388

388

367. Comparison of Varied Motions, 389

CHAPTER II.-MOTIONS OF RIGID Bodies.

382. Helical Motion.

383. To find the Motion of a Rigid

Body from the Motions of three

SECTION 1.-Rigid Bodies, and their

Translation.

368. Rigid Bodies-how understood, 390

369. Translation or Shifting,

SECTION 2.-Simple Rotation.

370. Rotation defined

-

Centre

Rotation,

371. Axis of Rotation,

tation,

373. Angular Velocity,

385. Rotation combined with Transla-

tion in the same Plane,

386. Rolling Cylinder-Trochoids,

387. Plane rolling on Cylinder-Spiral

384.

Special cases,

372. Plane of Rotation-Angle of Ro-

374. Uniform Rotation,

375. Rotation common to all parts of

body,

376. Right and Left-handed Rotation, 391

877. Relative Motion of a pair of Points

in a Rotating Body,

378. Cylindrical Surface of equal Ve-

locities,

392

392

393

379. Comparative Motions of two

Points relatively to an Axis,

389. Components of Velocity of a Point

in a Rotating Body,

393

SECTION 3.-Combined Rotations and

Translations.

381. Property of all Motions of Rigid

Bodies,

394

Paths,

388. Combined Parallel Rotations,

394

395

396

. 397

398

398

399

389. Cylinder rolling on Cylinder-

Epitrochoids,

390. Curvature of Epitrochoids,

391.

Equal and Opposite Parallel Ro-

tations combined,

392. Rotations about Intersecting Axes

combined,

393. Rolling Cones,

394. Analogy of Rotations and Single

Forces,

395. Comparative Motions in Com-
pound Rotations,

SECTION 4.- Varied Rotation.

. 406

396. Variation of Angular Velocity, . 406

397. Change of the Axis of Rotation, 407

398. Components of Varied Rotation, 407

CHAPTER III.-MOTIONS OF PLIABLE BODIES, AND OF FLUIDS.

SECTION 1.-Motions of Flexible Cords. 413. General Differential Equations of

399. Division of the Subject,

CONTENTS.

PART IV. THEORY OF MECHANISM.

CHAPTER I.-DEFINITIONS AND GENERAL PRINCIPLES.

Page

425. Theory of Pure Mechanism defined, 421 431. Elementary Combinations in Me-

426. General Problem of Mechanism

stated,

427. Frame-Moving Pieces - Con-

nectors,

428. Bearings,

chanism,

xi

Page

423

432. Line of Connection,

424

429. Motions of Primary Moving Pieces, 423

430. Motions of secondary Moving Pieces, 423

. 425

CHAPTER II.-ON ELEMENTARY COMBINATIONS AND TRAINS OF MECHANISM.

451. Teeth of Spur-Wheels and Racks

-General Principle,

452. Teeth described by rolling curves, 438

453. Sliding of a pair of Teeth (see

also 455, 458, 462a),

454. Arc of Contact on Pitch Lines, . 440

455. Length of a Tooth; Slidingof Teeth,440

456. Inside Gearing, .

457. Involute Teeth for Circular Wheels, 441

458. Sliding of Involute Teeth, .

459. Addendum for Involute Teeth,

460. Smallest Pinion with Involute

Teeth,

443

461. Epicycloidal Teeth-least Pinion, 444

462. Addendum for Epicycloidal Teeth, 445

462A. Sliding of Epicycloidal Teeth, 445

463. Approximate Epicycloidal Teeth, 445

464. Teeth of Wheel and Trundle,

465. Dimensions of Teeth,

466. Sang's process for Describing

Teeth.

467. Teeth of Bevel Wheels,

447

468. Teeth of Skew-Bevel Wheels, 449

469. Teeth of Non-Circular Wheels, . 449

487. Coupling of Parallel Axes,

488. Comparative Motion of Connected

Points,

489. Eccentric,

490. Length of Stroke,

491. Hooke's Universal Joint,

492. Double Hooke's Joint,

493. Click,

SECTION 5.-Reduplication of Cords.

495. Velocity-Ratio,

496. Velocity of any Ply,

497. White's Tackle,

SECTION 6.-Hydraulic Connection.

498. General Principle,

SECTION 7.-Trains of Mechanism.

502. Trains of Elementary Combina-
tions,

CHAPTER III.-ON AGGREGATE COMBINATIONS.

503. General Principles,

504. Differential Windlass,

505. Compound Screws,

465

486. Dead Points,

458

459

459

. 460

. 460

461

462

462

443

443

463

463

463

464

CHAPTER III.-ROTATIONS OF RIGID BODIES.

570. Motion of a Rigid Body in General,

SECTION 1.-On Moments of Inertia, | 576.

Radii of Gyration, Moments of Devia-

tion, and Centres of Percussion.

Moments of Inertia round Pa-

rallel Axes compared,

516

577.

578.

571. Moment of Inertia Defined, 514

572. Moment of Inertia of a System

of Physical Points, .

Combined Moments of Inertia, . 517

Examples of Moments of Iner-

tia and Radii of Gyration,

517

579.

514

Moments of Inertia found by

Division and Subtraction,

519

573. Moment of Inertia of a Rigid Body,514

574. Radius of Gyration,

580.

515

575. Components of Moments of In-

581.

Centre of Percussion-Centre of

ertia,

. 515

CHAPTER IV-MOTIONS OF PLIABLE BODIES.

608. Nature of the Subject-Vibration, 552 | 612. Vibrations not Isochronous,

609. Isochronous Vibration.-Condi-

CHAPTER V.-MOTIONS OF FLUIDS-HYDRODYNAMICS.

SECTION 1.-Motion of Liquids without | 639. Internal Fluid Friction,

. 572

. 576

. 576

PART VI.-THEORY OF MACHINES.

CHAPTER I.-WORK OF MACHINES WITH UNIFORM OR PERIODIC MOTION.

Consumption of Coal in Steam Engines, 643

Dimensions of Great Chimneys,

I. Table of the Resistance of Materials to

II. Table of the Resistance of Materials to Shearing and Distortion,

IV. Table of the Resistance of Materials to Breaking Across,

V. Comparative Table of French and British Measures,

VI. Table of Specific Gravities of Materials,