as there are wheels: thus, two pulleys will have double the power of one, because half the weight is sustained by the frame to which one end of the cord is attached; but then it requires double the time to do the work. As the friction of the pulley is very great, particular attention must be paid that all the turns or kinks of a rope be taken out, before it is made use of, and it should enter easily into the grooves of the seaves.

Rule. Divide the weight to be raised by twice the number of pulleys in the lower block; the quotient will give the power necessary to raise the weight.

Example.-What power is required to raise 600 lb., when the lower block contains six pulleys?

600

= 50 lb. Ans.

6 × 2

COMBINATION OF PULLEYS.

A leading block is a fixed pulley, which alters the direction of the power, but does not increase it: Power Weight. On account of friction the power must exceed the weight a little, in order to raise it. Vide plate, Mechanics, Fig. 1.

A whip is one moveable pulley, which increases the power without altering the direction.

Power =

weight (or 2 to 1).-Vide Fig. 2.

A whip upon whip will afford the same purchase as a tackle having a single and double block, and with much less friction.

A gun tackle consists of two single blocks with fall fixed to the one, then rove through the other, and then through the first. Powerweight (or 2 to 1): or Power weight (or 3 to 1). Vide Fig. 3, and 4.

Two double blocks are generally used for very heavy guns.

A luff tackle, or half watch tackle, consists of one double and one single block: the fall is fixed to the single, then rove through first sheave of the double, then through sheave of single, and lastly through second sheave of double block. Powerweight (3 to 1): or Powerweight (4 to 1). Vide Fig. 5, and 6.

A runner tackle is the same as a luff tackle applied to the end of a large rope, called a runner, which is rove through a single block attached to a fixed point, or to a body that is to be moved, or raised; the standing end of the runner being secured to another point.

Power is either 6 to 1, or 7 to 1, or 8 to 1.

A gyn tackle consists of one triple and one double block: the fall is fixed to the double, then rove through first sheave of triple, then through first sheave of double, then through second sheave of triple, then through second sheave of double, and lastly through third sheave of triple block.

Power = Vide Fig. 7.

weight (5 to 1); or Power = weight (6 to 1).

If the moveable block of a tackle be strapped with a tail, it is called

a tail, or jigger block: and the tackle a tail, or jigger tackle: a block with a hook strapped to it, and attached to a selvage, answers the same purpose.

Two double blocks, with fall fixed to one of them, and then rove through the sheaves of both blocks, will either give Power (4 to 1): or Power weight (5 to 1). Fig. 8.

=

weight

Two triple blocks, with fall fixed to one of them, then rove through sheaves of both blocks, will either give power weight (6 to 1): or Power weight (7 to 1). Fig. 9.

In the system of pulleys (vide plate, Mechanics) the Power is shown at the hooks of the moveable blocks, which are to be applied to the bodies, or weights, requiring to be moved, or raised. The strain is also shown at the fixed blocks.

=

In Fig. 3, there are three parts of the rope engaged in supporting the weight-viz., the parts marked 1, 1, 1. Each of them, hence, sustains one-third of it, and the fall of the rope to which the power is to be attached requires the Power 1, if weight 3. The same principle of calculation is applicable to all systems of pulleys having one fixed block, any number of moveable wheels, and a single rope over all the wheels. Hence, in such a system of pulleys, gravity being applied, there will be an equilibrium, when the weight is as many times the power as there are portions of the rope employed in sustaining the weight. For example, in a system consisting of six moveable sheaves, the same rope going over them all, there will be 12 portions of the rope engaged; and to produce an equilibrium the power must be equivalent to the weight, no allowance being made for friction.

From the foregoing observations, and by referring to the plate, it will be seen that each tackle has two applications, differing in power one from the other; for example, if the double block of a luff tackle is fixed to a weight to be moved, and the single block to a picket, or other fastening, Fig. 6, then if one man haul on the fall, the power of four men will be applied to the weight (4 to 1), and the power of three men to the picket; but if the double block be fixed to the picket, Fig. 5, and the single block to the weight, then the force of only three men will be applied to the weight (3 to 1), and a power of four men to the picket, or fastening.

When the moveable block of one tackle is fixed to the fall of another tackle, their respective powers are to be multiplied into each other for the power of the combination: thus, if one luff tackle is fixed to the fall of another luff tackle (the double blocks of both tackles being moveable), the power will be 4 x 4 = 16 (16 to 1); in this, the men haul through 16 feet to move the weight one foot; therefore if the combination be increased until the men haul through 100 feet to move the weight one foot, then the power would be 100 to 1.

The foregoing powers are, however, only true in theory, and are, therefore, called theoretical powers: for owing to the great friction of the pulleys, the stiffness of the ropes, &c., the actual practical powers are far less; so much so, that with a combination giving power of 48

to 1, a 24-pr. (2 tons weight) suspended, can scarcely overhaul the fall, the friction being so very great.

THE INCLINED PLANE.

The inclined plane forms simply a gradual and sloping instead of a sudden and perpendicular ascent, by which heavy bodies may be raised to certain heights. The power necessary for raising a weight depends on the difference between the length of the plane, and the height to be ascended. If the height be one-third of the length, then one pound will lift three pounds. The force with which a rolling body descends on an inclined plane, is to the force of its absolute gravity, as the height of the plane, is to its length.

Parbuckling a gun on skids unites the advantage of one moveable pulley with that of the inclined plane.

Rule. As the length of the plane, is to its height, so is the weight, to the power.

Example.-Required the power necessary to raise 540 lb. up an inclined plane, five feet long, and two feet high.

As 52 540: 216 lb. Ans.

THE WEDGE.

The wedge may be considered as two equally inclined planes joined together at their bases. It has a great advantage over all the other powers, arising from the force of percussion, or blow, with which the back is struck; which is a force incomparably greater than any dead weight, or pressure, such as is employed in other machines. The largest masses of timber may by this means be riven, and vessels of war, weighing many thousand tons, are lifted from their supports by the power of a few men, exerted by blows of mallets on wedges inserted

for that purpose.

The power of the wedge increases in proportion as its angle is acute. In tools intended for cutting wood the angle is commonly about 30°; for iron from 50° to 60°; and for brass from 80° to 90°.

Case 1.-When two bodies are forced from one another, by means of a wedge, in a direction parallel to its back.

Rule. As the length of the wedge is to half its back, or head, so is the resistance, to the power.

Example. The breadth of the back, or head of the wedge, being 3 inches, and the length of either of its inclined sides 10 inches, required the power necessary to separate two substances, with a force of 150 lb.

As 10 1 150: 22 lb. Ans.

Case 2.-When only one of the bodies is moveable.

Rule.- -As the length of the wedge, is to its back, or head, so is the resistance, to the power.

Example.-The breadth, length, and force, the same as in the last