LECTURE III. 



ON ACCELERATING FORCES. 



WE have hitherto only considered motion as already existing, without 

 any regard to its origin or alteration ; we have seen that all undisturbed 

 motions are equable and rectilinear ; and that two motions represented by 

 the sides of a parallelogram, cause a body to describe its diagonal by their 

 joint effect. We are now to examine the causes which produce or destroy 

 motion. Any cause of a change of the motion of a body with respect to a 

 quiescent space, is called a force ; that is, any cause which produces 

 motion in a body at rest, or which increases, diminishes, or modifies it in a 

 body which was before in motion. Thus the power of gravitation, which 

 causes a stone to fall to the ground, is called a force ; but when the stone, 

 after descending down a hill, rolls along a horizontal plane, it is no longer 

 impelled by any force, and its relative motion continues unaltered, until it is 

 gradually destroyed by the retarding force of friction. Its perseverance 

 in the state of motion or rest in consequence of the inertia of matter, has 

 sometimes been expressed by the term vis inertiae, or force of inertia ; but it 

 appears to be somewhat inaccurate to apply the term force to a property 

 which is never the cause of a change of motion in the body to which it 

 belongs. 



It is a necessary condition, in the definition of force, that it be the cause 

 of a change of motior<with respect to) a quiescent space. For if the change 

 were only in the relative motion of two points, it might happen without 

 the operation of any force : thus, if a body be moving without disturbance, 

 its motion with respect to another body, not in the line of its direction, 

 will be perpetually changed : and this change, considered alone, would 

 [appear to] indicate the existence of a repulsive force ; and, on the other 

 hand, two bodies may be subjected to the action of an attractive force, 

 while their distance remains unaltered, in consequence of the centrifugal 

 effect of a rotatory motion. (Plate I. Fig. 9.) 



The exertion of an animal, the unbending of a bow, and the communi- 

 cation of motion by impulse, are familiar instances of the actions of forces. 

 We must not imagine that the idea of force is naturally connected with 

 that of labour or difficulty ; this association is only derived from habit, 

 since our voluntary actions are in general attended with a certain effort, 

 which leaves an impression almost inseparable from that of the force that 

 it calls into action. 



It is natural to inquire in what immediate, manner>any force acts, so as 

 to produce motion ; for instance, by what means the earth causes a stone 

 to gravitate towards it. In some cases, indeed, we are disposed to imagine 

 that we understand better [tolerably well] the nature of the action of a 

 force, as, when a body in motion strikes another, we conceive that the 

 impenetrability of matter is a sufficient cause for the communication of 

 motion, since the first body cannot continue its course without displacing 



