26 

 LECTURE IV. 



ON DEFLECTIVE FORCES. 



IT has been shown that the velocity generated by an accelerating force, 

 is proportional to the time of its action, and the space described to the 

 square of the time. We are next to consider the more complicated cases of 

 the action of such forces. When they are directed to a certain point out of 

 the line of the motion which they affect, they become central forces, of 

 which we have an example in the force of gravitation, considered as it 

 governs the planetary motions ; and when this point becomes extremely 

 distant in comparison with the length of the body's path, so that the force 

 acts very nearly in parallel lines, the body comes under the denomination 

 of a projectile, as for instance a cannon ball projected horizontally or 

 obliquely. 



An accelerating force, therefore, tending to a point out of the line of 

 direction of a moving body,* deflects it from that line, and is then usually 

 called a centripetal force. And the natural tendency of the body to perse- 

 vere in its rectilinear motion, unless opposed by such a force, is sometimes 

 called a centrifugal force. How far the term force is properly applicable 

 to the perseverance of a body in its rectilinear motion, may perhaps be 

 liable to dispute. If we allow the propriety of the appellation, we must 

 . extend the definition of the term force to any change of the relative motion 

 of two points, and we must also allow the inertia of a body to be justly deno- 

 *; minated a force. The fact, however, is certain, that all bodies revolving 

 round a centre, have a tendency to recede from the centre in the direction 

 of the tangent, and when this force is counterbalanced an equal centrifugal 

 force must be exerted. 



The effects of a centrifugal force may be observed in the familiar instance 

 of a stone placed in a sling, which may be made to revolve in a vertical 

 direction, and even at the upper part of its orbit, may adhere, as it were, 

 notwithstanding its weight, to the sling which is above it, in consequence of 

 the excess of the centrifugal force above the force of gravitation. 



It is also a centrifugal force that is the foundation of the amusement of a 

 boy driving a hoop. A hoop at rest, placed on its edge, would very quickly 

 fall to the ground ; but when it is moving forwards, a slight inclination 

 towards either side causes the parts to acquire a motion towards that side, 

 those which are uppermost being most affected by it ; and this lateral 

 motion, assisted sometimes by the curvature of the surface of the hoop, 

 causes its path to deviate from a rectilinear direction ; so that instead of 

 moving straight forwards it turns to that side towards which it began to 

 incline ; and in this position its tendency to fall still further is counter- 

 acted by the centrifugal force, and it generally makes several complete 

 revolutions before it falls. The motion of a bowl, with its bias, is of a 

 similar nature ; the centrifugal force counteracting the tendency to curvi- 

 * Galileo, Dial. II. p. 147. 



