Inclined Plane. 123 



If, the equilibrium will be possible ; and the ratio of the weight 

 p to the effort in the direction SF will be determined by the fore- 

 going rules. The ratio of the effort, in the direction F, to the 

 power <?, will be the same as in the moveable pulley. Thus if 

 the power q is exerted in a direction parallel to the plane, the 207. 

 weight p will be to the power </, as the length of the plane to 

 half its height ; that is, the power will be only one half of what 

 would be necessary without the aid of the pulley, or fixed point B. 



210. With respect to the whole pressure exerted upon the 

 plane, it will be easily determined by the ratios above establish- 

 ed. As to the particular pressure, however, that takes place 

 upon each of the points where the body rests upon the plane, it 

 is absolutely indeterminate, except in the case where the body 

 touches only in two points ; and in this case the whole pressure 



is divided between these two points in the inverse ratio of the 161. 

 distances of its direction from these points. In every other case 

 there are no other conditions for determining the several pres- 

 sures except (1.) That the sum of them must be equal to the 

 whole pressure. (2.) That the sum of their moments, taken with 

 respect to an axis perpendicular to the direction of the whole 

 pressure, is zero ; the same will be true of the sum of the mo- 

 ments with respect to another axis perpendicular to the first. 

 These two axes, moreover, pass through a point in the direc- 

 tion of the whole pressure. Thus, when a body rests upon a 

 plane by means of a plane surface, there is no reason for suppos- 

 ing that all the points upon which it rests should experience 

 equal pressures, except when it has the figure of a right prism 

 or a right cylinder. 



211. With respect to bodies which rest upon several planes 

 at once, either in virtue of a single force, or of several forces, 

 in which we comprehend their gravity, the general law of equi- 

 librium is, (1.) That the resultant of all these forces must admit 

 of being decomposed into as many forces as there are points on 

 which the body rests ; (2.) That these must be perpendicular to- 

 the plane touching the body at this point. 



Let a heavy body KGI be placed in equilibrium upon two 

 inclined planes; this state can contim-e only while the weight ofrig.116, 

 the body is destroyed by the resistance of the planes ; if there- 



