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we are acquainted. This pressure it is which occasions the descent of falling bodies to the ground, and causes all bodies lying on the ground to press against it. More accurate experiments prove that every particle of matter, whether of metal, wood, earth, or of any other substance, is subject to this influence. And it can be shewn that the degree of this pressure exerted upon a given body never changes. Thus, let a spring AB have one end A firmly fixed in an immoveable block. Suspend a proposed substance P from the other end B, then the spring will be bent in the manner represented in fig. 1, the point B taking a position B'. If the experiment be again tried with the same body P after any interval of time, it will be found that the spring will be bent exactly as at first; thus shewing that the Earth exerts an unvarying pressure upon every body.

If the experiment be tried with the same spring and substance P at a place in another latitude, or on a hill, or in a pit, the bending of the spring is not found to be the same as before: but at the same place no variation is ever observed in the result.

9. We may easily find other substances P', P", P"... each of which being suspended from B will bend the spring exactly as P does. By suspending 2, 3, 4,... of these bodies at a time, and marking the spaces through which the spring is bent in each case, we may form a graduated scale, by means of which we can ascertain exactly the degree of pressure which the Earth exerts upon any proposed body whatever, as compared with the pressure which it exerts upon P. If this be done, it is usual to call the pressure on P the unit of pressure; and the pressure which is exerted upon another body, if it be W times the pressure on P, is said to be equal to W.

10. The pressure W which the Earth exerts upon a body, when measured in the manner just described, is called the weight of the body. How great soever be the pressure which any other force exerts upon a body, we can always

find (hypothetically at least) so many bodies P, P', P", P"... that the Earth shall exert upon them, taken all together, exactly as much pressure as the proposed force exerts upon the proposed body. Hence then, with the assumption in Art. 3, we perceive that every force may be measured, and therefore represented, by a weight.

11. To avoid circumlocution, when a body is prevented by an obstacle from moving, it is usual to say that the body exerts a pressure upon the obstacle, and that the obstacle exerts an equal pressure upon the body in the contrary direction. The fact however is, that the body is completely passive; and the reason why it remains in a state of rest is, that it is under the influence of two equal pressures exerted on it in opposite directions. By the same licence, if a body, which is under the influence of the Earth's action, be suspended by a string, it is often said that the string exerts a force or pressure upon the body; the fact however in this case is, that the string by being attached to the body, becomes a part of the body; and the whole remains in a state of rest, for the same reason as before. Hence it will be seen that, in the experiment described in Art. 8, the spring exerts a force equal to that exerted by the Earth upon P, though in the contrary direction. And hence we say, when two bodies are pressed together, that they act and react upon each other with equal forces.

12. It is sufficiently evident, that two equal pressures, acting in opposite directions upon the same point of a body, counteract each other: but it is conceivable that if several pressures be applied to a body, even though they be not two and two in opposite directions, nor all applied to the same point of the body, they may counteract each other. The science which teaches the relations necessarily existing between the magnitudes of forces, their directions, and their points of application, when they exactly counteract each other, is called STATICS.

13. If several forces acting upon a body counteract each other, the body is said to be in equilibrium : and the forces are said to balance each other.

14. If several forces acting upon a free particle do not balance each other, the particle will begin to move in some direction in a certain manner. It may be prevented from so moving by applying a proper force in the opposite direction to that in which there is a tendency to motion. This new force exactly counteracts the whole system of forces: but it might be itself counteracted by a single force equal to itself and acting in a contrary direction. A single force satisfying these conditions would be exactly equivalent to the whole of the original system of forces; and it is therefore called their resultant.

15. We thus learn that several forces, if they act upon a free particle, may be replaced by one force; and the converse is evidently true, viz., that one force may be replaced by a system of several forces. When one force is replaced by a system of several forces, they are called its components.

16. By reference to Art. 6, we see that the motions which a rigid body may take are of two distinct kinds and therefore the reasoning just stated respecting a free particle does not apply to rigid bodies. We shall hereafter shew that, corresponding to the three cases stated in the Article referred to, a system of forces acting on a rigid body may have

(1) A resultant for rotation only,

(2) A resultant for translation only,

(3) Two resultants, one for the rotation and one for the translation.

17. It is evident from the explanations above given, that a system of forces, acting on a free particle, cannot have more than one resultant: but we have just seen that the same is not necessarily true when they act on a rigid body. It is always true, however, that the same force may have different systems of components.

18. If a particle, or a rigid body, be in equilibrium under the action of several forces, we may add to the

system, or take away from it, any set of forces which balance

each other.

This principle is called the "superposition of equilibrium," and we shall hereafter have frequent instances of its utility.

19. It follows at once from this, that when a body. is in equilibrium under the action of a system of forces, they may be all increased, or all diminished in any proportion, without affecting the equilibrium.

20. It scarcely needs remarking, that if a set of forces balance each other, any one of them is equal to, and acts in an opposite direction to, the resultant of all the rest.

21. It is proved by experiment, that when a rigid body is in equilibrium, any point (of the body) in the line of the direction in which a force acts, may be taken for the point of application of the force, without affecting the equilibrium.

22. If a system of unbalancing forces acts upon the same point of a rigid body, they will have the same resultant as if they acted upon a free particle.



23. To find the resultant of several forces acting, in the same line, upon the same point of a rigid body.

If all the forces act in the same direction along the line, they will produce the same effect as a single force equal to their sum.


If some act in one direction and some in the opposite direction, then by the first case the resultant of each set will be equal to the sum of the forces of which it is composed and these two resultants, acting in opposite directions, will be equivalent to a single resultant equal to their difference. Hence then whether the original forces act in the same or in opposite directions, their resultant is equal to their algebraic sum.

In forming this sum, we are to account those forces positive which act in one direction, and those negative which act in the opposite direction; and the algebraic sign of the sum so formed will shew in what direction the resultant acts.

24. COR. If a number of forces act in the same line upon the same point of a rigid body, they will be in equilibrium when their algebraic sum is equal to zero, for in that case their resultant vanishes, and they produce no effect. Hence the condition of equilibrium of any number of forces acting in the same line and upon the same point of a rigid body is that their sum shall be equal to zero.

25. DEF. Lines are said to represent forces in magnitude and direction, when they are drawn parallel to the

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