xiv CONTENTS. 



LECTURE V. 

 ON CONFINED MOTION, 32. 



Motion limited by suspension, or by a smooth surface ; Effect of friction and of 

 rotatory motion, 32. Inclined plane; Descent in the chords of a circle; 

 Velocity of descent, 33. Ascending force ; Energy ; Cycloid ; Cycloidal pendulums, 

 34. Laws of pendulums ; Swiftest descent, 35. Circular pendulums ; Pendu- 

 lums with resistance; Revolving pendulums, 36. Composition of vibrations; 

 Regulator for steam engines; Circular road; Principle of the least action, 

 37, 38. 



LECTURE VI. 



ON THE MOTIONS OF SIMPLE MASSES, 38. 



Definition of a moveable body, without regard to its extension ; Inertia [gravity] ; 

 Centre of inertia, 39. Its properties ; Reciprocal forces ; Quantity of motion, 40. 

 Momentum; Centre of inertia of a system; Motion of the centre of inertia, 41. 

 Action and reaction, 42. Newton's illustrations ; Magnitude of reciprocal forces, 

 43. Fall of a feather and of a piece of gold ; Lucretius ; Relation between forces 

 and distances ; Displacement of the earth by the effect of a machine, 44. 



LECTURE VII. 



ON PRESSURE AND EQUILIBRIUM, 45. 



Pressure, a force counteracted ; Pressure and momentum incommensurable, 45. 

 Laws of pressure included in those of motion; Opposition of pressures, 46. 

 Equilibrium of mechanical powers ; Centre of gravity ; Stability of equilibrium, 

 47. Stability independent of equilibrium, 48. Situation and motions of the 

 centre of gravity of animals, 49. Levers of two kinds ; Fundamental property of 

 the lever, 50. Series of levers ; Bent levers ; Oblique levers ; Wheel and axis, 

 51. Wheels and pinions ; Double axis ; Pullies, 52. Blocks; Smeaton'spullies; 

 Oblique ropes, 53. Inclined plane ; Wedges, 54. Props, or shores ; Screws ; 

 Nuts ; Hunter's screw, 55. Determination of mechanical power from virtual 

 velocities, 56. 



LECTURE VIIL 

 ON COLLISION, 57. 



Motions of various bodies acting reciprocally ; Elastic bodies, 57. Nature of 

 repulsion ; Experiment on an ivory ball ; Apparatus for experiments on collision, 

 58. Inelastic bodies ; Energy, 59. Measure of force ; Relation of labour to 

 energy; Preservation of energy; or of ascending force, 60. Effect of a blow; 

 Rotation, 61. Billiards ; Reflection, 62. 



LECTURE IX. 



ON THE MOTIONS OF CONNECTED BODIES, 63. 



!> fTf,'", I 



Rotatory power; Consideration of the square of the velocity, 63. Smeaton's 

 apparatus; Centre of gyration ; Centre of percussion and of oscillation, 64. Free 

 rotation ; Motion of a stick broken by a blow, 65. Preponderance, 66. Greatest 



