MECHANICS. 



B, the weights P' and P act at those 

 points, the pressure on the fulcrum C 

 will evidently be equal to the weight W 

 which was removed. But AV is equal 

 to the sum of P' and P, and in this case 

 the lever is one of the first kind. Hence, 

 in a lever of the first kind, the pressure 

 on the fulcrum is equal to the sum of 

 the power and weight. 



(24.) In (2-2) we supposed that the 

 bar which sustains the weight rests on 

 the props in a horizontal position. But 

 the conclusions which we have deduced 

 are equally true if the bar be inclined to 

 the horizon and the weight is distributed 

 between the props precisely in the same 

 proportion. For let A B (jig. 1 2.) be the 

 beam, and, as before, let the prop B be re- 

 placed by a weight P acting over a wheel, 

 and let the vertical line in which the string 



Fig. 12 



from B acts be B n, and let C W be 

 the direction of the weight. This is a 

 lever of the second kind, and by (14) it 

 follows that 



P : W : : A m : A n. 



But since C m and B n are parallel, it 



follows by the principles of geometry 



that A m : A n : : A C : A B. Hence 



P : W : : A C : A B 



or P = W x J 



which is the same value as we obtained 

 for the pressure on the prop B when we 

 supposed the beam A B to be hori- 

 zontal. 



Hence it appears that, whether the 

 beam be horizontal or inclined, the 

 weight is distributed between the props 

 in the same proportion. 



From what we have established in 

 (22) it follows, that when the weight is 

 placed at the middle point of the beam, 

 it is equally distributed between the 

 props, each prop bearing half of it. 



(25.) When two men bear a weight 

 on poles, the proportion sustained by 

 each is to be determined on the princi- 



ples which we have just established, and 

 when it is, as is usual, placed in the 

 centre between them, each bearer carries 

 half the load. If the centre of gravity 

 of the load be in the plane of the poles 

 which support it, this equal distribution 

 of the load continues whether the 

 bearers move on a level plane or on a 

 declivity. If, however, the centre of 

 gravity be above or below the poles, the 

 load is not equally distributed if the 

 bearers are on an ascent or descent. In 

 this case let G (Jg. 13.) be the centre of 



Fig. 13. 



fig. 14. 



gravity of the load below the poles A B, 

 and through G draw the vertical line G D. 

 Since the \veight acts as if it were col- 

 lected at the centre of gravity, it must 

 produce the same effect as if it were 

 suspended from D, and consequently is 

 distributed between the bearers A and 

 B in the proportion of B D to A D, and 

 consequently it presses more severely 

 on the upper bearer B. 



But if, on the other hand, the centre of 

 gravity be above the beam, the weight, 

 acting as if it were placed at D (Jig. 14.), 

 is distributed between the bearers A B in 

 the proportion B D to A D, and there- 

 fore presses more severely on the lower 

 bearer A. 



This may be proved experimentally by 

 providing two straight bars, A B, A'B', 

 (Jig. 15.) and attaching them to the sides 



of a block of wood C D, which is pierced 

 with three holes, in any of which may 



