the thread, but the strength is proportional to the area of its cross section. Now, if for any purpose requiring a rapid movement of the nut or of a screw, the pitch must be increased; and if the screw consisted of a single-threaded square one, where the depth, thickness of the thread, and the width of the groove are each equal to half the pitch, the strength of the shaft upon which the screw is cut would be unnecessarily reduced. If the groove be made shallower and narrower then two threads, with two spaces having the same pitch as the single one, can be cut upon it so as to present about the same area of bearing surface to the pressure and at the same time afford quite as great a shearing thickness without interfering with the velocity ratio. If a very great velocity ratio should be required, then three or more threads with corresponding grooves may be cut in the shaft and nut.

Backlash in Wheel and Screw-Gearings.-Backlash is the slackness between the teeth of wheels in gear or between a screw and its nut. Suppose that two wheels are in gear, and that you move one of them in a certain direction until it turns the other, and then reverse the motion; if you can now move the pitch circle through, say, inch, before the second wheel responds, this distance is the amount of backlash. In the same way, suppose you turn a screw in one direction until its nut moves, and then reverse the motion, the angle or proportion of a turn which you can now make before the nut responds, is the backlash of the screw and its nut. If a great amount of backlash be present in wheel-gearing, it causes vibration and a disagreeable rattling noise; and where severe stresses and sudden stoppages are common, the teeth are liable to be stripped. It can only be thoroughly prevented by cutting the teeth most accurately of the best rolling contact form by a tooth-cutting machine. All screws and nuts that are much worked are liable to backlash as they become worn, although when new they may have been very free from it, so that the best way of taking up the slack is to form the nut in two parts with flanges connected by screw-bolts, which may be tightened from time to time so as to take up the wear, and thus keep one side of the threads in one half of the nut, bearing hard against one side of the threads of the screw, and those in the other half against the other

side.

* Refer to the Index for the page where the figure of the Fly Press appears. The screw of that machine is a double-threaded one.

LECTURE XIV.-QUESTIONS.

1. Explain how a screw is a combination of the lever and inclined plane, and illustrate your remarks. Find the theoretical advantage or ratio of W to P in the case of a screw of 1 inch pitch and 3.2 inches diameter; if the lever or spanner key be 7 feet long. Ans. 528: 1.

2. Given a cylinder and a sheet of paper of sufficient size to cover the cylindrical surface, show how you would trace an evenly pitched spiral or screw line on the cylinder. Mark on your sketch the pitch, circumference, and angle of the screw-thread.

3. Trace a screw-thread line on a cylinder. Draw a triangle to represent the pitch, circumference and angle of the thread, and show the direction of all the forces on the supposition that there is a total pressure, Wlbs., on the end of the cylinder acting parallel to its axis and balanced by a force, P lbs., acting at its circumference in a plane at right angles to the axis, with a total friction of F lbs. on the screw-thread.

4. What are the essential characteristics of a screw-thread ? Upon which of these do (1) the efficiency, (2) the strength, (3) the durability of a screw depend?

5. Sketch and describe all the forms of screw-threads which you have seen in practice. State their representative advantages and disadvantages, and for which kind of work each kind is most suitable.

6. Define the pitch of a screw. In the Whitworth angular screw-thread, what is the angle made by opposite sides of the thread? To what extent is the thread rounded off at the top and bottom? Distinguish between a single and a double-threaded screw; in what cases should the latter be used? Why are holding down bolts made with angular threads?

7. Distinguish between a right-handed and a left-handed screw. Sketch the screw-coupling which is commonly used to connect two railway carriages, and explain the action of the combined screws. If the pitch of each screw is g inch and the lever-arm from the axis of the screw to the centre of the ball is 12 inches, with what force will the carriages be pulled together by a force of 50 lbs. applied to the ball on the end of the arm? Ans. 5028.5 lbs.

8. Draw a single, double, and treble square-threaded screw to a th scale, where the outside diameter of the screw-thread is 10 inches and the pitch 6 inches. Explain the advantages of using a double or treble thread instead of a single one for transmitting rapid motion against a considerable resistance.

9. Why is the angular-threaded Whitworth or Seller's screw better adapted than the square, rounded, or buttress thread for the bolts which are used to bind pieces of machines, &c., together?

10. What is meant by backlash? How may backlash be prevented in a screw, and in wheel gearing?

II. Sketch the screw-coupling commonly used to connect together the carriages of a railway train, and explain its action. With what force would the carriages be drawn together by the exercise of a pressure of 50 lbs. applied to the ball at the end of the arm, supposing the pitch of the screw to be §-inch, and that the centre of the ball measures 1 foot from the axis of the screw? Friction is to be neglected. (S. and A. Exam. 1893). Ans. 5026 56 lbs. (π=3*1416).

LECTURE XV.

CONTENTS.-Efficiency, &c., of a Combined Lever, Screw, and Pulley GearExample I. - Bottle Screw-Jack -- Example II. Traversing ScrewJack-Screw Press for Bales-Screw Bench Vice-Example IIIEndless Screw and Worm-Wheel--Combined Pulley, Worm, WormWheel and Winch Drum-Worm-Wheel Lifting Gear-Example IV.Questions.

Efficiency, &c., of a Combined Lever, Screw, and Pulley Gear.-Construct an apparatus of the following description, having a horizontal Whitworth V-screw of, say, p" pitch, with cylindrical ends and flanges supported by bearings, so that the screw cannot move longitudinally, but with a nut free to travel from one end of the screw to the other, along a slide or guide

which prevents it from turning round. Apply a force, P, to a rope passed over the V-grooved pulley of radius, R, keyed to the end of the screw shaft, until it moves the nut with the hook, rope, and weight, W, attached thereto, as shown by the accompanying side elevation, plan and end view of the apparatus.*

EXAMPLE I.-If the radius, R, of the turning-pulley be 12", the pitch, p, of the screw 1", and the gross pull, P, required to lift a weight of 100 lbs. be 4 lbs.: find (1) the velocity ratio; (2) the theoretical advantage; (3) the working advantage; (4) the work put in to lift WI foot; (5) the work got out; (6) the percentage efficiency.

ANSWER. We have got in this question all the necessary data required to find the various answers except n, the number of turns which the screw will have to make in order to lift W I foot. Since the pitch of the screw is I", each turn thereof will elevate or lower the weight 1", according as it is turned the one way or the other; consequently, if the screw makes 12 turns, the nut and the weight will move through 12", therefore n=12 turns.

* It is evident that, in addition to the friction between the screw and the nut, there is friction at the several bearings, at the nut slide, and in the bending of the ropes. Consequently, if the student were to place in succession weights at W of, say, 10, 20, 30, 40 lbs., &c., and ascertain by aid of a Salter's spring balance (hooked into the rope which passes round the turning-pulley), the corresponding pulls required to lift these several weights, and to plot down the results on squared paper with the weights as abscissæ and the pulls as ordinates, and then to draw a line through the intersections of the vertical and horizontal lines drawn through the corresponding values, he would obtain a characteristic curve for the friction of the machine as a whole. If he took the precaution to balance the initial friction of the machine (when there was no weight attached at W) by hanging such a small weight at P as would just move the nut towards the turning-pulley, he would find upon repeating the above experiments (keeping the small additional weight on all the time) and replotting the results as now recorded by the spring balance, that the second frictional curve would approach much nearer to a straight line than the former one. In fact, its deviation therefrom would simply prove that the friction of the movable bearing surfaces was not directly proportional to the load. To arrive at the characteristic friction curve for the screw alone, he would have to find out by trial the proportion of the several pulls applied, which were spent in overcoming friction at all other points except between the screw and the nut. To those students who have the time and opportunity for carrying out experiments in applied mechanics, the apparatus illustrated above will prove interesting and instructive. The figures are drawn from the machine constructed in the author's engineering workshop for the purpose of enabling his students to make similar tests to those suggested above. A square, or a rounded, or a buttress-thread may be substituted for the V-Whitworth one, and sound information may thus be obtained about different forms of screws, which will make a stronger and more lasting impression on some students than by merely studying books.

(2) The Theoretical Ad-Weight lifted if there were no friction

vantage

Pull applied

2TR 75'4

Ρ
100 lbs.

4 lbs.

= 2πRnP

=

1

25

1

2 X 22 X 12" X 12 × 4-301.56 ft.-lbs.

7 × 12"

Wx I'= = 100 lbs. x 1'=100 ft.-lbs.

(6) The Percentage Effi- | = Efficiency × 100

ciency

Bottle Screw-Jack. The importance of the screw as a simple machine for exerting great pressures, is very well exemplified by the screw-jack. This tool is used for replacing locomotives and railway carriages upon their rails, for elevating heavy girders into position, or for overcoming any great resistance through a small space which cannot be effected by a labourer and a lever. As will be seen from the accompanying figure it consists of a strong hollow bottle-shaped casting, with a projecting handle for facilitating the carrying of the tool from one place to another. In the upper end of the casting a square-threaded screw is cut

*It is evident that with such a low percentage efficiency the weight when hanging from the rope will not be able to overhaul the machine. The student can calculate what pitch of screw would be required with the same co-efficient of friction before overhauling could take place.