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ARTS.

CHAPTER III. Composition and Resolution of Forces.

27. Definition of Component and Resultant Forces.

28. Prop. 8. If the adjacent sides of a parallelogram represent the com- ponent forces in direction and magnitude, the diagonal will represent the resultant force in direction and magnitude.

29. Prop. 9. If three forces, represented in magnitude and direction by

the sides of a triangle, act on a point, they will keep it at rest.

CHAPTER IV. Mechanical Powers.

31. Definition of Wheel and Axle.

31. Prop. 10. 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.

32. Definition of Pulley.

32. Prop. 11. 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.

33. Prop. 12. 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.

34. Prop. 13. In a system in which each pulley hangs by a separate

string and the strings are parallel, there is an equilibrium when

P: W:1 that power of 2 whose index is the number of move- able pulleys.

35. Prop. 14. The weight (W) being on an inclined plane and the force

(P) acting parallel to the plane, there is an equilibrium when

PW the height of the plane its length.

36. Definition of Velocity.

37. Prop. 15. Assuming that the arcs which subtend equal angles at the

centers 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.

38. Prop. 16. To shew that if P and W balance each other in the

machines described in Propositions 11, 12, 13 and 14, and the whole be

put in motion, P: W:: W's velocity in the direction of gravity: P's

velocity.

CHAPTER V. The Center of Gravity.

39. Definition of Center of Gravity.

40. Prop. 17. If a body balance itself on a line in all positions, the

center of gravity is in that line.

42. Prop. 18. To find the center of gravity of two heavy points; and

to shew that the pressure at the center of gravity is equal to the

sum of the weights in all positions.

43. Prop. 19. To find the center of gravity of any number of heavy

points; and to shew that the pressure at the center of gravity is

equal to the sum of the weights in all positions.

45.

46.

Prop. 20. To find the center of gravity of a straight line.

Prop. 21. To find the center of gravity of a triangle.

47. Prop. 22. When a body is placed on a horizontal plane, it will

stand or fall, according as the vertical line, drawn from its center of

gravity, falls within or without its base.

48. Prop. 23. When a body is suspended from a point, it will rest with

its center of gravity in the vertical line passing through the point of

suspension.

HYDROSTATICS.

CHAPTER I.

1-3. Definitions of Fluid; of elastic and non-elastic Fluids.

CHAPTER II.

Pressure of non-elastic Fluids.

4. Prop. 1. Fluids press equally in all directions.

5. Prop. 2. The pressure upon any particle of a fluid of uniform den-

sity is proportional to its depth below the surface of the fluid.

6. Prop. 3. The surface of every fluid at rest is horizontal.

7. Prop. 4. 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.

10. Prop. 5. To explain the hydrostatic paradox.

11. Prop. 6. 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.

CHAPTER III.

Specific Gravities.

13. Definition of Specific Gravity.

14. Prop. 7. If M be the magnitude of a body, S its specific gravity,

and W its weight, W = MS.

15. Prop. 8. When a body of uniform density floats on a fluid, the

part immersed the whole body: the specific gravity of the

body the specific gravity of the fluid.

:

16. Prop. 9. When a body is immersed in a fluid, the weight lost whole

weight of the body: the specific gravity of the fluid the specific

gravity of the body.

18. Prop. 10. To describe the hydrostatic balance, and to shew how to

find the specific gravity of a body by means of it, 1st, when its

specific gravity is greater than that of the fluid in which it is weighed ;

2dly, when it is less.

19. Prop. 11. To describe the common hydrometer and to shew how to compare the specific gravities of two fluids by means of it.

CHAPTER IV. Elastic Fluids.

20, Prop. 12. Air has weight.

21. Prop. 13. The elastic force of air at a given temperature varies as

the density.

22. Prop. 14. The elastic force of air is increased by an increase of

temperature.

24. Prop. 15. To describe the construction of the common air-pump

and its operation.

25. Prop. 16. To describe the construction of the condenser and its

operation.

26. Prop. 17. To explain the construction of the common barometer,

and to shew that the mercury is sustained in it by the pressure of

the air on the surface of the mercury in the basin.

27. Prop. 18. The pressure of the atmosphere is accurately measured

by the weight of the column of mercury in the barometer.

28. Prop. 19. To describe the construction of the common pump and

its operation.

29. Prop. 20. To describe the construction of the forcing-pump and its

30. Prop. 21. To explain the action of the siphon.

31. Prop. 22. To shew how to graduate a common thermometer.

32. Prop. 23. Having given the number of degrees on Fahrenheit's

thermometer, to find the corresponding number on the Centigrade

thermometer.