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Next, resolving parallel and perpendicular to the line of action of P, we 

 find that both components of R A vanish, and hence that R A 0. Thus the 

 original forces were in equilibrium. 



76. Clearly these methods of compounding forces can be 

 extended, so that any number of parallel forces can be compounded 

 into a single resultant force. We see at once, on reversing the 

 resultant and resolving, that the resultant is parallel to the lines 

 of action of the original forces, while its magnitude is equal to 

 their algebraic sum. 



This result is of importance in connection with the weights of 

 bodies. It shows that the effect of gravity on any rigid body 

 i.e. the resultant of the weights of the individual particles of which 

 the body is composed may be regarded as a single force acting 

 vertically along a single line. 



In the next chapter it will be shown that, whatever position the 

 rigid body is in, this line always passes through a definite point, 

 fixed relatively to the body, known as its center of gravity. 



77. Without assuming this, we can find the line of action in a 

 number of simple cases. Suppose, for instance, we are dealing with 

 a uniform rod. The weights of two equal particles equidistant from 

 the center may be compounded into a single force acting through 

 the middle point of the rod. Treating the weights of all the parti- 

 cles in this manner, we find that the weight of a uniform rod may 

 be supposed to act at its middle point. 



In the same way we can see that the weight of a circular disk, 

 of a circular ring, or of a sphere may be supposed to act at its 

 center ; the weight of a cube or a parallelepiped at the intersection 

 of its diagonals, and so on. 



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78. If we try to compound two parallel forces which are equal 

 in magnitude but opposite in sign, we obtain as the resultant a 

 force of zero amount of which the line of action is at infinity. 

 Although such a force is of zero amount, its effect cannot be 



