66 FERGUSON'S LECTURES. 



LECT. 4. The fourth mechanical power is the inclines 

 ; and the advantage gained by it is as great as its 

 length exceeds its perpendicular height. Let A B be a 

 T1 e f c/iM - plane parallel to the horizon, 



ed plane- f 



and C D a plane inclined to 

 it; and suppose the whole 

 length C D to be three times 

 as great as the perpendicular 

 height Gf jp;in this case, the cylinder E will be sup- 

 ported upon the plane C D, and kept from rolling down 

 upon it, by a power equal to a third part of the 

 weight of the cylinder. Therefore a weight may 

 be rolled up this inclined plane with a third part of 

 the power which would be sufficient to draw it up by 

 the side of an upright wall. If the plane was four 

 times as long as high, a fourth part of the power would 

 be sufficient ; and so on in proportion. Or, if a pillar 

 was to be raised from a floor to the height G F. by 

 means of the machine A B D C, (which would then act 

 as a half wedge, where the the resistance gives way only 

 On one side) the machine and pillar would be in equilibria 

 when the power applied at G F was to the weight of 

 the pillar, as G Fio CD ; and if the power be increased, 

 so as to overcome the friction of the machine against 

 the floor and pillar, the machine will be driven, and 

 the pillar raised ; and when the machine has moved its 

 whole length upon the floor, the pillar will be raised 

 to the whole height from G to F. 



The force wherewith a rolling body descends upon 

 an inclined plane, is to the force of its absolute gravity, 

 by which it would descend perpendicularly in a free 

 space, as the height of the plane is to its length. For, 

 suppose the plane A B to be parallel to the horizon, the 

 cylinder C will keep at rest 

 upon any part of the plane ^ 



where it is laid. If the plane ^T \vA~_V nK 



be so elevated, that its perpen- \] 



