98 Statics. 



D, acted by means of a blow or finite impression, it would raise 

 the weight p, however great it might be, at least during a certain 

 time, which, when p is very large, may be such that the eye can- 

 not distinguish it ; but the motion would not be the less real. 

 This subject will be placed in a clearer light hereafter, when we 

 come to treat of Collision. 



157. 169. By means of the ratio which we have established be- 

 tween the two powers/?, q, and the force exerted against the ful- 

 Fig. 68, crum F, we shall be able to solve this general question. Three 

 of these six things, namely, the two powers, the force exerted against 

 the fulcrum, and the three directions, being given, to find the three 

 others. When, however, the directions only are given, we 

 144. can merely find the ratio of the forces p, q, p. The solution in 

 this case is evident from what has been said. It may be easily 

 obtained also by geometrical construction, upon which we will 

 only observe, that when the directions are parallel, the question 

 is solved by articles 53, 160; and that, in general, if it is pro- 

 posed to determine the position of the fulcrum, when the powers 

 p and q, and their position are known, the question reduces itself 

 to finding, by article 38, the resultant of these two powers. 



170. The problem is different when more than two powers 

 are applied to the lever; in this case, as in that of the cords in 

 article 151, we can vary without end the ratio or the directions 

 of some of the powers, the others remaining the same, and yet 

 not destroy the equilibrium. There is, however, this difference, 

 between the lever and cords, that the condition of equilibrium in 

 the former is single, whereas in the latter there are as many 

 153. conditions of equilibrium as there are knots. It will suffice to 

 point out the condition of equilibrium in the lever, when three 

 powers are employed, to make it evident that the proposition will 

 hold true, for any greater number of powers. 



Fig. 77. 171. Let the three powers p, q, r, directed according to Bp, 

 E q, Dr, be in equilibrium by means of the lever BFD. The 

 power q may be considered as exerted in part against each of 

 the powers jo and ?,* and in part against the fulcrum F. Having 



* The power q cannot, strictly speaking, be considered as exerted 

 against r, since they both tend to turn the lever in the same direction 



