Table XII.—The Epicycloidal Pulley-Block.
Size adapted for lifting weights up to 5 cwt.; velocity ratio 12·5; mechanical efficiency 5; useful effect 40 per cent.; calculated formula P = 5·8 + 0·185 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs.. | Differences of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 56 | 15 | 16·2 | +1·2 |
| 2 | 112 | 27 | 26·5 | -0·5 |
| 3 | 168 | 40 | 36·9 | -3·1 |
| 4 | 224 | 47 | 47·2 | +0·2 |
| 5 | 280 | 56 | 57·6 | +1·6 |
| 6 | 336 | 66 | 68·0 | +2·0 |
| 7 | 392 | 78 | 78·3 | +0·3 |
| 8 | 448 | 88 | 88·6 | +0·6 |
| 9 | 504 | 100 | 99·0 | -1·0 |
| 10 | 560 | 110 | 109·4 | -0·6 |
The fourth column shows the calculated values of the powers derived from the formula. It will be seen by the last column that the formula represents the experiments with but little error.
227. Since 60 per cent. of energy is consumed by friction, this machine, like the differential pulley-block, sustains its load when the chains are free. The differential pulley-block gives a mechanical efficiency of 6, while the epicycloidal pulley-block has only a mechanical efficiency of 5, and so far the former machine has the advantage; on the other hand, that the epicycloidal pulley contains but one block, and that its lifting chain has two hooks, are practical conveniences strongly in its favour.
LECTURE VIII.
THE LEVER.
The Lever of the First Order.—The Lever of the Second Order.—The Shears.—The Lever of the Third Order.
THE LEVER OF THE FIRST ORDER.
228. There are many cases in which a machine for overcoming great resistance is necessary where pulleys would be quite inapplicable. To meet these various demands a correspondingly various number of contrivances has been devised. Amongst these the lever in several different forms holds an important place.
229. The lever of the first order will be understood by reference to [Fig. 38]. It consists of a straight rod, to one end of which the power is applied by means of the weight c. At another point b the load is raised, while at a the rod is supported by what is called the fulcrum. In the case represented in the figure the rod is of iron, 1" × 1" in section and 6' long; it weighs 19 lbs. The power is produced by a 56 lb. weight: the fulcrum consists of a moderately sharp steel edge firmly secured to the framework. The load in this case is replaced by a spring balance h, and the hook of the balance is attached to the frame. The spring is strained by the action of the lever, and the index records the magnitude of the force produced at the short end. This is the lever with which we shall commence our experiments.