S

Fig. 62.

are convenient for altering the direction of the power. Thus, by means of a fixed pulley, and a rope passing over it, we can raise the weight by exerting a downward force. This arrangement is called a whip (fig. 62), and a force of 5 lbs. at B requires an equal force at A to balance it. It is the most common form of pulley and fall used, as may be seen in the crane, window blind, etc. It is evident that the strap of the block C bears a strain of 10 lbs; that is, a weight equal to the sum of the power and weight. Ignorance of this fact has led to many accidents, for a block calculated to bear a strain of one ton, will only be strong enough to lift half a ton. In theory, also, the fall need only be of such strength as will bear a little more than the power; but in practice the friction is found to be so great, that the hauling part of the fall has to sustain a considerably greater strain than the standing part; and this proportion increases with the number of the sheaves.

Movable Pulleys.-In the case of the movable pulley (fig. 63), the standing part, A, bears half the

weight of B; and consequently a power of 5 lbs. at C, will balance a weight of 10 lbs. at B. If the part C is rove through another fixed block, E (fig. 64), the part C bears a strain of 5 lbs., and so must the part D; and the only advantage of the fixed block, E, is that of changing an upward pull into a downward one. The weight 10, may be considered to be the resultant of the two equal parallel forces, A and C, and is therefore equal to their sum; and 10 ÷ 2 = 5, the strain of each point, A and C.

The combination of one whip with another (fig. 65), by connecting the fall of one whip, A B, with the block

B

D

Fig. 65.

Fig. 66.

Fig. 67.

Fig. 68. of another, F, is called a double whip, or whip and runner; the first whip in this case being called the runner. By this arrangement a force of 1 lb. applied to C, will balance a weight of 2 lbs. applied to E.

The standing part, D, of the whip, CD, bears a strain of one pound; hence, if we attach it to the weight, as in fig. 66, we gain an additional lifting force equal to the power. This arrangement is called a burton, and the weight is to the power as 3 to 1.

Another method of applying power by means of two single blocks, is the gun tackle (fig. 67). In this arrangement it is evident that a power of 1 lb. applied at A, will balance a weight of 3 lbs. applied at B, but only 2 lbs. at C. In all systems of pulleys, it is an advantage to apply the movable block to the weight; and in estimating the working efficiency, the weight of the movable block must be added to the weight to be raised.

A system consisting of a double and single block is called a luff tackle (fig. 68). Where the double block is movable, a power of 1 lb. applied to the hauling part will balance a weight of 4 lbs. applied to the block 4. Fig. 69 consists of two double blocks, and is called a twofold purchase: the power is to the weight as 1 to 5.1

1In figs. 67, 68, and 69, an advantage is gained by attaching the upper blocks to the weight. In Fig. 69, for example, if the weight is fixed to the upper block, the power is to the weight as 1 to 5; but if the lower block is attached, the proportion is as 1 to 4.

Long Tackle.-In blocks having the sheaves side by side, as double and treble blocks, it is difficult in heavy strains to prevent the blocks from tilting or canting on one side (fig. 70), owing to the power not being applied in a straight line with the centres

Fig. 69.

5

Fig. 70.

Fig. 71.

of the blocks. This endangers the splitting of the shells, besides causing additional friction of the sheaves against the sides of the shells. In order to obviate this danger, it is common to cross the fall in reeving it. This brings the standing and hauling parts in a line with the centres of the blocks; but the friction of the one part of the fall over the other is very great.

By reeving the fall through fiddle blocks (fig. 71), all the parts of the fall are in a line with the power and weight, and the larger size of the outer blocks keeps the parts of the fall clear of each other. This arrangement is called a long tackle. The only disadvantage here is, that when a number of blocks must be used, and the upper block can only be fixed at a limited height, the two blocks may come together before the weight is raised high enough.

Smeaton's Block.-Mr. Smeaton employed an ingenious invention when building the Eddystone lighthouse, to remedy this evil. A and B (fig. 72), are threefold fiddle-blocks. The fall is rove by fastening the standing part to the hook of the upper block 1, and reeving it through the sheaves 2, 3, etc., the haul

ing part coming out at 13 on the upper block. In this purchase the power is one-twelfth the weight.

a

Fig. 72. Smeaton's Block.

Jones's Block.-The great objection to the use of Smeaton's block is, that it requires a combination of at least twelve sheaves, and is therefore only adapted for very heavy work. The accompanying arrangement (fig. 73) can be applied to any number of sheaves from four upwards. The upper block, A, is attached to another block, B, whose sheave is at right angles to that of A; that is, A B is a shoe block. The lower block, C, has also two sheaves which diverge from each other, to allow the lower sheave of the shoe block to be of moderate dimensions. To reeve the fall, begin with the upper sheave of the shoe block, and reeve Jones's Block. through one of the sheaves of the lower block, then across the lower sheave of the shoe block, and through the opposite sheave of the lower block, and fasten the standing part to the shoe block.

Fig. 73.

77

Spanish Burton.-The mechanical advantage of a system of pulleys may be greatly augmented by increas ing the number of falls, the standing parts of which are connected with the movable blocks. This arrangement is called a Spanish burton (figs. 74-76). The tension of the part A equals the power; and the standing part B being attached to the weight, supports a part of it equal to the power. The hauling part, D, of the fall ECD, supports a weight equal to the tensions of A and B united, and the tensions of C and E being equal, the power is to the weight as 1 to 5.

Fig. 74.

Fig. 75.
Spanish Burton.

Fig. 76.

Another burton is represented in fig. 75; but by analysis of the application of the power, it will be seen that the weight is only four times the power. In both these systems the weight of the block of the whip assists the power. Thus, in fig. 74, if the weight of G be half that of K, it will exactly balance it; but in fig. 75, the weight of A must be equal to that of B to

balance it.

A powerful burton, having an efficiency of 9 to 1, is shown in fig. 76, the figures on each part of the rope showing the multiple of the power borne by each part.

Differential Sheaves.-It would appear that we possess unlimited means of increasing the difference