to bear on the circumference of another on the same principle as that which obtains in a combination of levers, and the conditions of equilibrium are also similar.

The convenience of this combination will be comprehended by bearing in mind that if, for example, we want to raise or move a weight through the space of 100 feet with as small an exertion of force as 1 pound, that force must move through a space of 100 feet, by whatever kind of machine we may employ. Now it is more convenient to describe 50 circles of 2 feet in circumference with the arm, than to make one great vertical stroke of a lever of 100 feet, or move round a circle 100 feet in circumference with a horizontal one. Such a combination of wheels is called a Train. The cogs on the surface of the wheels are usually called teeth; those on the axle, leaves; and the axle having leaves, the pinion. When arranged, as in fig. 49., the power is said to be Concentrated.

If the diameter of all the axles be multiplied together, and also that of all the wheels be multiplied together, then the power

will be to the weight as the product of the axles is to that of the wheels. Or the conditions of equilibrium may be obtained by multiplying together the number of teeth on all the wheels,

and the number on all the pinions, the power being on the weight as the product of the latter is to the former.*

Leaves on the axle b of the first wheel a act on teeth on the circumference of the second wheel e; and as there are six times as many teeth as there are leaves, e is turned once for every six turns of a. In the same manner e, in turning six times, turns ƒ once; therefore, the first wheel turns 36 times for one turn of the last; and as the diameter of a (to which the power is applied) is 3 times as great as that of the axle d (which has the resistance), three times 36, or 108, is the difference of intensity between weights or forces that will balance here.

When great velocity is required, the circumference of a large cog wheel is made to act on that of the axle or rim of a smaller one, in which case the power is said to be Diffused. Were there 48 teeth on the rim of the larger wheel and 16 on the smaller, one revolution of the former would produce three of the latter, and in a train thus arranged, it is evident that the wheel farthest from the force would move with the greatest rapidity. The extent of motion that can thus be obtained, may be comprehended by studying the number of revolutions made by the second hands of a watch, or those of a driving wheel when used with the propeller shaft.

TACKLES.

Tackles (fig. 50.) are named according to the number of Blocks employed; and the arrangement and size of gear. The rope rove is the Fall; the part made fast, the Standing part: and the part hauled on, the running part, or end, or frequently also the fall.

Small tackles are usually called Jiggers; larger ones Bartons; still larger, Luffs; a heavy tackle or combination of such is a Purchase. A rope rove through a single fixed block is a Whip, as in fig. 50. No. 1. Rove through a single moveable block, a Double whip this on a large scale is a Runner, as in Nos. 2. and 16. Rove through two single blocks, the upper one being fixed, a double whip, as in No. 3. Rove through two single blocks, the upper one being moveable, a Gun tackle purchase, as in No. 11.

:

*Arnott's Physics.

Rove through a double and single block, the standing part being fast to the single block, a Luff-tackle, as in Nos. 8. 12, 13. Rove through two doubles, the standing part being fast to one of them, a Twofold Purchase, as in No. 6. Rove through two threefold blocks, the standing part being fast to one of them, a Threefold Purchase, as in No. 9. Rove through two fourfold blocks, the standing part being fast to one of them, a Fourfold Purchase, as in No. 10.

Combinations of tackles may be made variously; thus: No. 5. is a Whip upon whip. No. 16. is a Runner and tackle. Nos. 4. 6, 7. 14, 15. are Spanish Bartons. The increased advantage is found by multiplying their respective advantages into each other.

The general rule for ascertaining the power necessary to raise a weight with a tackle, is to divide the weight by twice the number of sheaves in the lower block, the quotient being the answer. Thus, in a threefold purchase, a power of 20 cwt. would balance a weight of 6 tons (friction not considered), but this only applies to particular reeves. Perhaps the theory of tackles will be best understood thus: - In No. 2. the strain is equally distributed between each part of the rope; and there being two parts employed in sustaining the weight, it is balanced by an exertion of power equal to one half of its weight; and the same principle applies to tackles of all kinds. Reeving the fall, as in No. 3., merely gives a more convenient lead; for the blocks which are fixed afford no mechanical advantage.

The figures on the falls, in the engraving, denote the advan

tage; thus, in No. 5. it is 4 to 1; in No. 14. 16 to 1.

The "Establishment" of spare disposable tackles of a ship

are

Four runners and tackles, with their respective lashing blocks. Four long tackles, the double blocks having a lashing eye. Two mizen burtons.

Four yard tackles; and, as there are great numbers of fitted blocks and spare ends of coils, any number of luffs may be rove when requisite.

It must be observed that too much attention cannot be paid to the maxim, that fixed blocks give no gain, for tackles admit of different applications. For instance, in No. 1. there is merely a lead; whereas in the runner in Nos. 16. and 2. with the same reeve of rope, but having a moveable block, a resistance of a certain amount would be overcome by about one half of its amount. Also in Nos. 12. and 8. the advantage is 3 to 1; whereas in 13. with the same kind of tackle it is 4 to 1.

In tackles, as in other machines, there is no increase of "Power; " for-the mechanical effects produced by any machine being measured by the work done in a given time, or by the product of the force exerted, and the distance gone through in a unit of time, in the direction of that force-whatever is gained in force is lost in time; and whatever is gained in time, is lost in force.* The convenience of a machine consists in enabling a small force working by a succession of efforts through a great space to raise a great weight, or to overcome a great resistance through a small space.

The ascent of a weight attached to a tackle is as many times less than the descent of the force as the weight itself is greater than the power; thus, in a twofold purchase the force being one, and the weight 4 cwt., and it being required to raise the weight 1 foot, each part of the rope must be shortened 1 foot, and the force descend through 4 feet.

One man may be able, with a tackle having 10 plies of rope, to raise a weight which it would require 10 men to raise at once, without a tackle. But if the weight is to be raised a yard, the 10 men will raise it, by pulling at a single rope, and walking 1

* Thus, the answering pendant is easily but slowly hauled down by one boy. Put a moveable block on the bight, as in No. 17., and to run away with it we shall require several boys. In the first case we economise force, but spend time; in the latter, we expend force but gain velocity.