32 APPLIED SCIENCE 



Applying this rule to the above problem we have 



12 X 3 X 3 _ 3 

 12 X 12 



The answer is the same as before, and after a little thought it is 

 evident that the two steps in the first case have merely been put 

 together in one expression in the second case. If the weight, % 

 lb., on the long end of the second lever at P is known (see Fig. 14), 

 and the pressure or weight which would be needed at W is to be 

 found, the same rule will apply but will be expressed in this man- 

 ner: Multiply the weight by the continued product of the long arms 

 and divide this by the continued product of the short arms: 



3 12 X 12 



- X - - = 12 Ibs. 



4 3X3 



Regardless of how many levers there are working together, 

 the rule is applicable. In all leverage problems the first, 

 and the most importam, thing is to find and locate the ful- 

 crum, as the fulcrum is the point which determines the 

 moment arms from which the required answer is obtained. 

 The moment arm is always the perpendicular distance from 

 the force or weight to the fulcrum. 



36. Shapes of Levers. The fulcrum of levers used in 

 machinery is usually cylindrical in shape, made of soft 

 r metal, and supported in the in- 



terior of a cylindrical opening in 

 which the lever works, so as to 

 reduce the friction. The lever is 

 FIG. 15. A Bent Lever. not onl y oscillating or vibrating, 

 but where the motion is circular 

 the fulcrum becomes the axis of rotation. 



