THE LEVER AND WHEELWORK. 



251 



claw of the hammer is the shorter arm ; the resistance of the nail is the weight ; 

 and the hand applied to the handle the power. 



Fig. 7. 



When a beam rests on two props, A B, fig. 7, and supports at some interme- 

 diate place, C, a weight, W. this weight is distributed between the props in a 

 manner which may be determined by the principles already explained. If the 

 pressure on the prop B be considered as a power sustaining the weight W, by 

 means of the lever of the second kind, B A, then this power multiplied by B A 

 must be equal to the weight multiplied by C A. Hence the pressure on B will 

 be the same fraction of the weight as the part A C is of A B. In the same 

 manner it may be proved, that the pressure on A is the same fraction of the 

 weight as B C is of B A. Thus, if A C be one third, and therefore B C two 

 thirds of B A, the pressure on B will be one third of the weight, and the pres- 

 sure on A two thirds of the weight. 



It follows from this reasoning that, if the weight be in the middle, equally 

 distant from B and A, each prop will sustain half the weight. The effect of 

 the weight of the beam itself may be determined by considering it to be col- 

 lected at its centre of gravity. If this point, therefore, be equally distant from 

 the props, the weight of the beam will be equally distributed between them. 



According to these principles, the manner in which a load borne on poles 

 between two bearers is distributed between them may be ascertained. As the 

 efforts of the bearers and the direction of the weight are always parallel, the 

 position of the poles relatively to the horizon makes no difference in the distri- 

 bution of the weights between the bearers. Whether they ascend or descend, 

 or move on a level plane, the weight will be similarly shared between them. 



If the beam extend beyond the prop, as in fig. 8, and the weight be suspend- 



Fig. 8. 



ed at a point not placed between them, the props must be applied at different 

 sides of the beam. The pressures which they sustain may be calculated in 

 the same manner as in the former case. The pressure of the prop B may be 

 considered as a power sustaining the weight W by means of the lever B C. 

 Hence the pressure of B, multiplied by B A, must be equal to the weight W 

 multiplied by A C. Therefore the pressure on B bears the same proportion to 



