102 Statics: 



Fig so ' knowing p, 7, &F, and the specific gravity of the lever DF, 

 we would determine the distance FD at which the power q must 

 be placed ; designating FD by ?/, BF by fe, we shall have sy for 

 the weight r\ and, accordingly, 



j> 6 -f I s # 2 = q y, 

 from which y is easily obtained. 



In figure 78, it is evident that the longer the lever is, the 

 more the power q is to be diminished, till it becomes zero, after 

 which it must act in a contrary direction to produce an equili- 

 brium. 



In figure 80, as the lever is increased in length, the power q 

 becomes at first less and less to a certain point bej^ond which it 

 begins to augment. This may be easily shown in several ways, 

 and among others by the equation 



pl> + isi/ 2 = gry, 

 which gives 



by which it will be seen, that when y = 0, q must be infinite ; 

 and that when y is infinite, q must also be infinite. Accordingly, 

 between these extremes the values of q must be finite, and there 

 must be some point where it will be the smallest possible. In 



Cal 44 or( ^ er to determine this point, we have merely to put equal to 

 zero the differential of the value of <?, taken by regarding y only 



Cal. 11. as variable ; we have thus 



whence 



sy 2 =pb + 

 and 



Therefore the value of the smallest power <?, which can be em- 

 ployed with a heavy lever, of the second kind, is 



