MECHANICS. 



suspended to the ends of a rope passing 1 

 over it will balance each other, for tl*ey 

 stretch the rope equally, and if either ot 

 them be pulled down through any given 

 space, tiie other will rise through an 

 equal space in the same time ; and con- 

 sequently, as the velocities of 'both are 

 equal, they must balance each other. 

 Tiiis kind of pulley, therefore, gives no 

 mechanical advantage ; but its use con- 

 sists in changing the direction of the pow- 

 er, and sometimes enabling it to be ap- 

 plied with more convenience. By it, a 

 man may raise a weight to any point, as 

 the top of a building, without moving 

 fr)-n the place he is in ; whereas, other- 

 wise, he would have been obliged to as- 

 cend with the weight ; it also enables se- 

 veral men together to apply their strength 

 to the weight by means of the rope. 

 The moveable pulley represented at A 

 (fig. 12.) is fixed to the weight W, and 

 rises and falls with it. In comparing this 

 to a lever, the fulcrum must be consider- 

 ed as at A, the weight acts upon the cen- 

 tre c, and the power is applied at the ex- 

 tremity of the lever D. The power, 

 therefore, being twice as far from the 

 fulcrum as the weight is, the proportion 

 ,. between the power and weight, in order 

 to balance each other, must be as 1 to 2. 

 Whence it appears, that the use of this 

 pulley doubles the power, and that a man 

 may raise twice as much by it as by his 

 strength alone. Again, every moveable 

 pulley hangs by two ropes equally stretch- 

 ed, and which must, consequently, bear 

 equal parts of the weight ; but the rope 

 A B being made fast at B, half the weight 

 is sustained by it, and the other part of the 

 rope, to which the power is applied, lias 

 but half the weight to support ; conse- 

 quently, the advantage gained by this pul- 

 ley is as 2 to 1. When the upper and 

 fixed block contains two pullies, which 

 only turn upon their axis, and the lower 

 moveable block contains also two, which 

 not only turn on their axis, but rise with 

 the weight F (fig. 13.) the advantage 

 gained is as 4 to 1. For each lower pulley 

 will be acted upon by an equal part of 

 the weight ; and because in each pulley 

 that moves with the weight a double in- 

 crease of power is gained, the force by 

 which F may be sustained will be equal 

 to half the weight divided by the number 

 of lower pullies ; that is, as twice the 

 number of lower pullies is to 1, so is the 

 weight suspended to the power. But if 

 the extremity C (fig. 14.) be fixed to the 

 lower block, it will sustain half as much 

 as a pulley ; consequently, here tke rule 

 will bej as twice the number of pullies 



adding unity is to 1, so is the weig'ht to 

 the power. These rules hold good, what- 

 ever may be the number of pullies in the 

 blocks. If, instead of one rope going 

 round all the pullies, the rope belonging 

 to each pulley be made fast at top, as in 

 fig. 15, a different proportion between 

 the power and the weight will take place. 

 Here it is evident, that each pulley dou- 

 bles the power ; thus, if there are two 

 pullies, the power will sustain four times 

 tiie weight; if three pullies, eight times 

 the weight ; if four pullies, sixteen times; 

 and so on : that is, the power P, of lib, 

 will sustain a weight W of 16/6. 



When puilies in blocks are placed per- 

 pendicularly under each other, on sepa- 

 rate pins, they occupy considerable space, 

 and would not in general answer ; it is, 

 therefore, common to place all the pul- 

 lies in each block on the same pin, by the 

 side of each other, as in fig. 16. but the 

 advantage and rule for the power are the 

 same here us in fig. 13 and 14. A pair 

 of blocks with the rope fastened round 

 it, is commonly called a tackle. 



To avoid, in a great measure, the fric- 

 tion of several puilies running on differ- 

 ent pivots, Mr. James White, a very able 

 mechanic, invented the concentric pulley, 

 (fig. 17.) for which lie obtained a patent, 

 O and R are two brass pullies in which 

 grooves are cut ; round these a cord is 

 passed, by which means the Iwo answer 

 the same purpose of so many distinct 

 pullies as there are grooves ; and the ad- 

 vantage gained is found by doubling the 

 number of grooves in the lower block. 

 In this case the advantage gained is 12, 

 that is, a power of 12/. will balance a 

 weight of 144. The concentric pulley 

 removes very considerably the shaking 

 motion of the common pulley, as well as 

 the friction. 



The inclined plane is of very great use 

 in rolling up heavy bodies, such as casks, 

 wheel-barrows, &c. It is formed by plac- 

 ing boards, or earth, in a sloping direc- 

 tion. The force with which a body de- 

 scends upon an inclined plane is to the 

 force of its absolute gravity, by which it 

 would descend perpendicularly in free 

 space, as the height of the plane is to its 

 length. For suppose the plane A B (fig. 

 18.) to be parallel to the horizon, the cy- 

 linder C will keep at rest on any pai't of 

 the plane where it is laid. If the plane 

 be placed perpendicularly, as A B. (fig. 

 19.) the cylinder C will descend with its 

 whole force of gravity, because the plane 

 contributes nothing to its support or hin- 

 drance ; and therefore it would require 

 a power equal to its whole weight to keep 



