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CONTENTS.
ARTS.
MECHANICS.
CHAPTER I.
1-8. DEFINITION of Force, Weight, Quantity of Matter, Density,
Measure of Force.
10. Pressure another name for Force in STATICS.
11. Definitions with respect to the action of Forces.
12. Forces properly represented by geometrical straight lines.
Questions on Chap. I.
CHAPTER II.-The Lever.
17. Definitions of a Plane, a Solid, Parallel Planes, a Prism, and a
Cylinder.
18. Definition of Lever.
19. AXIOMS.
20. PROP. I. A horizontal prism, or cylinder, of uniform density
will produce the same effect by its weight as if it were col-
lected at its middle point.
21. PROP. II. If two weights, acting perpendicularly on a straight
Lever on opposite sides of the fulcrum, balance each other,
they are inversely as their distances from the fulcrum; and
the pressure on the fulcrum is equal to their sum.
22. Converse of Prop. II.
23. PROP. III. If two forces, acting perpendicularly on a straight
Lever in opposite directions and on the same side of the ful-
crum, balance each other, they are inversely as their distances
from the fulcrum; and the pressure on the fulcrum is equal
to the difference of the forces.
25. PROP. IV. To explain the different kinds of Levers.
26. PROP. V. If two forces, acting perpendicularly at the extremi-
ties of the arms of any Lever, balance each other, they are
inversely as the arms.
27. PROP. VI. If two forces, acting at any angles on the arms of
any Lever, balance each other, they are inversely as the per-
pendiculars drawn from the fulcrum to the directions in
which the forces act.
28. Converse of Prop. VI.
29. PROP. VII. If two weights balance each other on a straight
Lever when it is horizontal, they will balance each other in
every position of the Lever.
Questions on Chap. II.
CHAPTER III.-Composition and Resolution of Forces.
30. Definition of Component and Resultant Forces.
31. PROP. VIII. If the adjacent sides of a parallelogram represent
the component forces in direction and magnitude, the diagonal
will represent the resultant force in direction and magnitude.
32. PROP. IX. If three forces, represented in magnitude and di-
rection by the sides of a triangle, act on a point, they will
keep it at rest.
Questions on Chap. III.
36.
37.
CHAPTER IV.—Mechanical Powers.
Definition of Wheel-and-Axle.
PROP. X. There is an equilibrium upon the Wheel-and-Axle,
when the power is to the weight as the radius of the axle to
the radius of the wheel.
40. Definition of Pulley.
41. PROP. XI. In the single moveable pulley, where the strings
are parallel, there is an equilibrium when the power is to the
weight as 1 to 2.
42. PROP. XII. In a system in which the same string passes round
any number of pulleys and the parts of it between the pulleys
are parallel, there is an equilibrium when Power (P): Weight
(W): 1 the number of strings at the lower block.
43. PROP. XIII. In a system in which each pulley hangs by a
separate string and the strings are parallel, there is an equi-
librium when P: W:: 1 : that power of 2 whose index is the
number of moveable pulleys.
45. PROP. XIV. The Weight (W) being on an Inclined Plane,
and the force (P) acting parallel to the plane, there is an
equilibrium when P: W:: the height of the plane its
length.
46. Definition of Velocity.
47. PROP. XV. Assuming that the arcs which subtend equal angles
at the centres of two circles are as the radii of the circles, to
shew that, if P and W balance each other on the Wheel-
and-Axle, and the whole be put in motion, P : W :: W's
velocity: P's velocity.
48. PROP. XVI. To shew that if P and W balance each other on
the machines described in Propositions XI, XII, XIII, and XIV,
and the whole be put in motion, P : W :: W's velocity in the
direction of gravity: P's velocity.
Questions on Chap. IV.
CHAPTER V.-The Centre of Gravity.
49. Definition of Centre of Gravity.
50. PROP. XVII. If a body balance itself on a line in all positions, the centre of gravity is in that line.
51. PROP. XVIII. To find the centre of gravity of two heavy
points; and to shew that the pressure at the centre of gravity
is equal to the sum of the weights in all positions.
52.
PROP. XIX. To find the centre of gravity of any number of
heavy points; and to shew that the pressure at the centre of
gravity is equal to the sum of the weights in all positions.
54. PROP. XX. To find the centre of gravity of a straight line.
55. PROP. XXI. To find the centre of gravity of a triangle.
56. PROP. XXII. When a body is placed on a horizontal plane, it
will stand or fall, according as the vertical line, drawn from
its centre of gravity, falls within or without its base.
57. PROP. XXIII. When a body is suspended from a point, it will
rest with its centre of gravity in the vertical line passing
through the point of suspension.
Questions on Chap. V.
HYDROSTATICS.
59. Definitions of Fluid; of elastic and non-elastic Fluids.
CHAPTER II.—Pressure of non-elastic Fluids.
60. PROP. I. Fluids press equally in all directions.
61. PROP. II. The pressure upon any particle of a fluid of uniform
density is proportional to its depth below the surface of the
fluid.
62. PROP. III. The surface of every fluid at rest is horizontal.
63. PROP. IV. If a vessel, the bottom of which is horizontal and
the sides vertical, be filled with fluid, the pressure upon the
bottom will be equal to the weight of the fluid.
61. The pressure of a fluid on any horizontal plane placed in it, is
equal to the weight of a column of the fluid whose base is the
area of the plane, and whose height is the depth of the plane
below the horizontal surface of the fluid.
66. PROP. V. To explain the Hydrostatic Paradox.
67. PROP. VI. If a body floats on a fluid, it displaces as much of
the fluid as is equal in weight to the weight of the body; and
it presses downwards, and is pressed upwards, with a force
equal to the weight of the fluid displaced.
Questions on Chaps. I. and II.