LECTURE V. 



ON CONFINED MOTION. 



\VE have hitherto considered the princiijal cases of motion, either undisturb- 

 ed, or simply subjected to the action of an accelerating, retarding, or deflec- 

 tive force. We now proceed to examine the effects of an additional modifica- 

 tion, which is introduced, when the motion is limited to a given line or surface 

 of any kind; the body either being supposed to slide on the surface of a solid 

 actually extended, or being confined to an imaginary surface by its attach- 

 ment to a thread, or still more narrowly restricted, by means of two threads, 

 which allow it to move only in a given line. Suspension is the most conveni- 

 ent mode of making experiments on confined motion ; but it is not always easy 

 to cause the body to remain in the surface that is required ; and to confine it in 

 this manner to a perfectly plane surfiice, is impossible. When we suffer a body 

 to slide along any surface, there is a loss of force from friction, from the pro- 

 duction of rotatory motion, or from both these causes combined. The effect 

 of friction is obvious and well known ; and we may be convinced of the re- 

 tardation attendant on the production of rotatory motion, by allowing two cy- 

 linders, of equal dimensions, to roll down an inclined plane ; the one being co- 

 vered with sheet lead, the other having an equal weight of lead in its axis, 

 <^nd being covered with paper; and both having similar projecting surfaces at 

 the ends, which come into contact with the plane : we may easily observe that 

 in the first cylinder, much more of the force is consumed in producing rotatory 

 motion, than in the second, and that it therefore descends much more slowly. 

 (Plate 11. Fig. 20.) 



When a body is placed on an inclined plane, the force urging it to de- 

 scend, in the direction of the plane, is to the whole force of gravity, as the 

 height of the plane is to its length. This is demonstrable from the principles 

 pf the composition of motion, and may also be shown experimentally with 



