the nut, then p will be large, and since we cannot cut the groove very deep owing to the weakening effect on the screw, the cylinder when one

spiral or thread had been cut would appear as in the upper figure of Fig. 33.

The screw would not, however, be used in this state, but the tool would be shifted to midway between the grooves, and a second groove cut, thus obtaining the shape shown in the lower figure. The screw appears at first sight like Fig. 32, so far as the edges are concerned, but on looking at the angle of the threads the difference is plain.

Fig. 33.

We have now practically two screws, each of pitch 2p, and two threads must be cut in the nut. The nut moves as it would do on each alone, but there is twice as much bearing surface and hence less wear.

The screw thus cut is said to have a double thread, and we may extend the process to three or more separate threads.

The velocity ratio is, as before,

the pitch being that of either spiral, i.e. in Fig. 33, 2p not p.

An important example is that of a screw propeller.

Screw Propeller. This consists of a very short piece of a screw, working, not in a solid nut, but in the water, which acts similarly to a nut, though with some important differences not needful here to consider.

If the propeller worked in an actual solid nut at an angular velocity A, then it, and consequently the ship to which it is attached, would advance at a speed V given by

But the water being yielding, it is as if the nut slipped back, and the actual speed is less than V by a certain amount, called the slip. This effect belongs to Hydraulics, so now we only mention it, but shall not take it into

account.

If now the engines be revolving at N revolutions per minute, and be the pitch, in feet, of the propeller, we have, neglecting slip,

a result which we can also obtain directly, since at each revolution the ship advances p feet.

The pitch being coarse, the propeller will, when the

W

B

ship is under sail and the engines not working, be revolved by its passage through the water if it be not held fast.

Another practical application of the screw is the Lifting Jack.

This is simply a screw, the nut A of which rests on the ground, and the screw B can be revolved by a handle passing through the head C, which is solid with B. When the handle is turned, B screws out and lifts a weight W placed on the top of the piece D, which moves longitudinally with B but does not turn with it, this being effected by cutting a circular groove in the end of B which fits in D, and of a small set screw into the groove. small compared to the circumference of the circle described by the end of the handle, the longitudinal

Fig. 34.

screwing the end The pitch being

motion is slow, which, as we shall see hereafter, implies that the screw can exert a heavy thrust.

As an example of the reversed action, we may take the common Archimedean Drill.

A screw of very long pitch is cut on the spindle of the drill, and the nut being moved alternately backward

Fig. 35.

and forward, the drill rotates alternately in opposite. directions.

EXAMPLES.

1. A train is running at 20 miles per hour. Find its velocity in f.s. Ans. 293.

2. If in (1) the train be stopped in 10 seconds, its velocity being decreased uniformly by the brake, at how many yards from the stopping point were the brakes applied ? Ans. 48.

3. The stroke of an engine is 2 ft. 3 ins., and it runs at 130 revolutions per minute. Find the mean speed of piston, and the angular velocity of the crank shaft (supposed uniform).

Ans. 585 ft. per min.; 13.6 per sec.

4. The piston speed of an engine is 850 feet per minute. Supposing the velocity curve (p. 24) during the time of one stroke be a semicircle, find the maximum speed of piston; and also the speed when of the time of a stroke from the commencement have elapsed. Ans. 1082 and 1067 ft. per minute.

5. The stroke of an engine is 4 ft., revolutions 96 per minute, diameter of crank shaft 14 ins. Determine the speed of rubbing of the main bearings, and compare it with the mean value of the rubbing velocity of the crosshead guide.

Ans. 5.87 f.s.; ratio, 11:24.

6. Cast-iron should be cut at from 12 to 16 feet per minute. The travel of a planing machine is 3 ft., and it makes the return stroke at twice the speed of the cutting one. How many strokes per minute should it make when planing cast-iron ?

Ans. 2 to 35.

7. Brass should be cut at 25, and wrought-iron at 22 feet per minute. Find the revolutions a lathe should turn at: Ist, when turning a brass plug 2 inches diameter; 2d, when turning a 1in. wrought-iron pin.

Ans. 48 per min. nearly; 168 per min. nearly.

8. A thread is being cut on a 1-inch brass screw. Find the proper angular velocity of the work, and also the velocity at which the tool should travel to cut the thread. If the saddle be moved by a screw of 4-inch pitch, how many revolutions should it revolve at?

Ans. 10; .2 ins. per sec. very nearly; 9. The pitch of screw in a screw jack is turned by a handle 19 ins. long. of the handle to that of lifting.

10. A ship moves at 17 knots.

in miles per hour.

2312 per minute.

ins., and it is Compare the speed of the end Ans. 273: I.

Find her speed in f.s. and
Ans. 28.7; 19 very nearly.
Find how many

II. If in (10) the propeller pitch be 16 ft. revolutions the engines run at, neglecting slip.

Ans. 107.3.

12. In (11) the thrust rings on the shaft are 2 ins. wide, 14 ins. external diameter. Find the maximum and mean rubbing velocities over the surface. Ans. 6.91 and 6.44 f.s.

CHAPTER II

EFFORTS AND RESISTANCES-FRICTION

THE relative motion of a pair is, in nearly all cases, resisted by some force, which we hence call the Resistance. And in order to produce the motion a force must be applied, which we call the Effort.

For example, consider the sliding pair consisting of the piston and cylinder of a steam engine.

Then the relative motion is resisted, the resistance being supplied by the connecting-rod end which bears. against the end of the piston rod. The relative motion then will not take place until a sufficient effort has been applied to the piston by the steam.

We therefore now inquire into the sources from whence we derive our Efforts and Resistances in nature, and also into the way in which we are going to measure these magnitudes.

A source of effort or energy must be capable of exerting a force and of following it up. Of such sources the principal is—

Elasticity of Fluids.-By fluids we must not be understood as meaning liquids, the term fluid including liquids, gases, and vapours. It is of the latter two we speak, and they may be spoken of as elastic fluids, in distinction to liquids.

The elasticity of a fluid is the name by which we denote the power it possesses of exerting pressure on the sides of the vessel in which it is contained. If this