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 f 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. 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; for example, in No. 5. it is double on the first whip, and double on the sccond, 2 × 2=4, giving a fourfold advantage. In No. 16. it is double on runner, and quadrupled on the tackle; or 2 × 48, giving an eightfold advantage.

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.

answer.

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 Thus, in the thrcefold purchase No. 9, a power of 20' cwt. would balance a weight of 6 tons (friction not considered). The more precise rule is to divide the weight to be raised by the number of parts of rope leading to, from, or attached to the lower block; the quotient being the power required to produce equilibrium, provided friction did not exist. Thus in the case of a fourfold purchase, the standing part of the rope being fast to the lower block, the weight, 3000 lbs. would be balanced by the power of 330 lbs.

To ascertain the amount of purchase required to raise a given weight with a given power; divide the weight to be raised by the power to be applied, and the quotient will be the number of cords (or parts of ropes) which must be attached to the lower

block, thus: to balance a weight of 19 tons with a power of 43 cwt. nine parts of rope at the moving block would be necessary. And as, in working such a purchase, there would be much friction and consequent increase of strain, a 3-inch rope, which is equal to bearing a strain of nearly 60 cwt., should be used.

To ascertain what amount of weight given tackling will raise, the weight that the single rope will bear is multiplied by the number of its parts at the moving block.

The proper size of ropes and blocks to be used as tackling may be determined by reference to such Tables as those on pages 152 and 161; and the amount of allowance that should be made for the consequences of friction by considerations similar to those advanced on pages 118 and 158 of this work.

LIST OF TACKLES.

The figures on the tackles in the engraving denote the advantage; thus, in No. 5, it is 4 to 1; in 14, 16 to 1; that is to say, a weight of 1 lb. on the fall of No. 5. would balance a weight of 4 lbs. on the lower block—or in other words, one man with this tackle could suspend as great a weight as four could without it.

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 bartons. 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 yard, while the single man at his tackle must walk until he has shortened the 10 plies of rope of 1 yard each; that is, he must walk 10 yards, or ten times as far as the 10 men did. In both cases, therefore, we have just the same quantity of man's work

*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.