125 



Prop on an, inclined Plane. 



[April 



/ 



Now for No. I 



B E is perpendicular to A C the 

 direction of the weight ; and 

 A B perpendicular to B C the di- 

 rection of the power. 



p : w : : be ; ABjbut 



"">C m BE:AB :: BC ; AC by 



-.....^i^r^; similar triangles ; therefore 



P : W : ; B C : AC and 

 P X A C = W xBC when in equilibrium. 

 But now, leaving A C and W out of consideration, or con- 

 stant as it is termed, what will be the result if B C be reduc- 

 ed one half in value or weight ? Why its proportion to P, of 

 course, becomes changed to that extent, or P is relatively one 

 half greater. 



Thus 2 : 4 ; : 6 : 12 ) and 2X12 — 4 X 6 



£ or 2 = 4 X. 6 = 2. i>2 ©C 4X 6whenin 

 P .* W ;: BC : AC) ~iT~ IF" equili- 



brium. 



But now altering the 6 into 3 (this figure representing B C.) 

 °^ 121? =5 1 that is 2 has now a proportion to 1. 



or P is now double in power ; and so the more you reduce one 

 aide the greater becomes the other (not to preserve the 

 * equilibrium/ mind, for the very reverse is attempted to 

 make the power superior to the weight), and, when B C is a 

 minimum, P becomes a maximum. 



But a lever will at once illustrate this ; perhaps more 

 familiarly. 



The case here is similar, 



for, according to the pro- 

 perty of the lever, P xA 

 C = W x B C as before. 

 0 ^ Now if we reduce the 

 weight on the right hand 

 side, the left arm falls, 

 and P becomes so much 

 heavier in comparison ; or, which has the same effect, 

 if we shorten one arm the other is relatively longer, and soon. 

 The more we reduce B C the greater becomes the energy of 

 P ; and its effect is greatest, or a maximum, when B C is 

 shortest, or a minimum. 



