When pullies 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 as 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 pullies running on differ ent pivots, Mr. James White, a very able mechanic, invented the concentric pulley, (fig. 17.) for which he obtained a patent. 0 and R are two brass pullies in which grooves are cut ; round these a cord is passed, by which means the two 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 121b. 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 lind.er C will keep at rest on any part 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 it from descending. Let A B (fig. 10.) be a plane parallel to the horizon, and A I) a plane inclined to it ; and suppose the whole length A D to be four thnes as great as the perpendicular I) B. In this case the cylinder It will be supported up on the plane I) A, and kept from rolling, by a power equal to a fourth part of the weight of the cylinder ; therefore a weight may be rolled up this inclined plane, by a third part of the power which would be sufficient to draw it up by the side of an upright wall. It must also be evident, that the less the angle of eleva tion, or the gentler the ascent is, the greater will be the weight which a given potver can draw up ; for the steeper the inclined plane is, the less does it support of the weight ; and the greater the ten dency which the weight has to roll ; con sequently, the more difficult for the pow er to support it : the advantage gained by this mechanical power, therefore, is as great as its length exceeds its perpendi cular height. To the inclined plane may
be reduced all hatchets, chisels, and other edge-tools..
The inclined plane, when combined with other machinery, is often of great use in the elevation of weights: it has been likewise made use of in the late Duke of Bridgewater's canal. After this canal has extended about 40 miles on the same level, it is joined to a subterraneous na vigation about 12 miles long, by means of an inclined plane, and this subterraneous portion is again connected by an inclined plane with another portion 100 feet above rt. This plane is a stratum of stone which slopes one foot in four, and is about 450 feet long. The boats are conveyed from one level to another by means of a wind lass, so that a loaded boat descending along the plane turns the axis of the wind lass, and raises an empty boat.
The fifth mechanical power or machine is the wedge ; which may be considered as two equally inclined planes, joined to gether at their bases ; then D G (fig. 21.) is the whole thickness of the wedge at its back ABGD, where the power is applied ; ltF is the depth or height of the wedge ; BP the length of one of its sides ; and OF is its sharp edge, which is entered into the wood intended to be split, by the force of a hammer or mallet striking per pendicularly on its back. Thus, AB (fig. 22.) is a wedge driven into the cleft CED of the wood FG. When the wood does not cleave at any distance before the wedge, there will be an equilibrium be tween the power impelling the wedge downward and the resistance of the wood acting against the two sides of the wedge, when the power is to the resistance as half the thickness of the wedge at its tack is to the length of either of its sides ; be cause the resistance then acts perpendi cularly to the sides of the wedge. But when the resistance on each side acts pa rallel to the back, the power that balances the resistances on both sides will be, as the length of the whole back of the wedge is to double its perpendicular height.