In the illustration a tooth has just passed under the "impulse face" b of P¹. The lever has been moved upwards at the right end; and its forked end has given an impulse to R, and through it to the balance-wheel. The spring winds up. The pin C prevents the lever dropping, because it no longer has the notch opposite to it, but presses on the circumference of R. As the spring unwinds it strikes the lever at the moment when the notch and C are opposite. The lever is knocked downwards, and the tooth, which had been arrested by the locking-face a of pallet P, now presses on the impulse face b, forcing the left end of the lever up. The impulse pin I receives a blow, assisting the unwinding of the spring, and C again locks the lever. The same thing is repeated in alternate directions over and over again.

COMPENSATING BALANCE-WHEELS.

The watchmaker has had to overcome the same difficulty as the clockmaker with regard to the expansion of the metal in the controlling agent. When a metal wheel is heated its spokes lengthen, and the rim recedes from the centre. Now, let us suppose that we have two rods of equal weight, one three feet long, the other six feet long. To an end of each we fasten a 2-lb. weight. We shall find it much easier to wave the shorter rod backwards and forwards quickly than the other. Why? Because the weight of the longer rod has more leverage over the hand than has that of the shorter rod. Similarly, if, while the mass of the rim of a wheel remains constant, the length of the spokes varies, the effort needed to rotate the wheel to and fro at a constant rate must vary also. Graham got over the difficulty with a rod by means of the compensating pendulum. Thomas Earnshaw mastered it in wheels by means of the compensating balance, using the same principle—namely, the unequal expansion of different metals. Any one who owns a compensated watch will see, on stopping the tiny fly-wheel, that it has two spokes (Fig. 206), each carrying an almost complete semicircle of rim attached to it. A close examination shows that the rim is compounded of an outer strip of brass welded to an inner lining of steel. The brass element expands more with heat and contracts more with cold than steel; so that when the spokes become elongated by a rise of temperature, the pieces bend inwards at their free ends (Fig. 207); if the temperature falls, the spokes are shortened, and the rim pieces bend outwards (Fig. 208).[39] This ingenious contrivance keeps the leverage of the rim constant within very fine limits. The screws S S are inserted in the rim to balance it correctly, and very fine adjustment is made by means of the four tiny weights W W. In ships' chronometers,[40] the rim pieces are sub-compensated towards their free ends to counteract slight errors in the primary compensation. So delicate is the compensation that a daily loss or gain of only half a second is often the limit of error.

KEYLESS WINDING MECHANISM FOR WATCHES.

The inconvenience attaching to a key-wound watch caused the Swiss manufacturers to put on the market, in 1851, watches which dispensed with a separate key. Those of our readers who carry keyless watches will be interested to learn how the winding and setting of the hands is effected by the little serrated knob enclosed inside the pendant ring.

There are two forms of "going-barrel" keyless mechanism—(1) The rocking bar; (2) the shifting sleeve. The rocking bar device is shown in Figs. 209, 210. The milled head M turns a cog, G, which is always in gear with a cog, F. This cog gears with two others, A and B, mounted at each end of the rocker R, which moves on pivot S. A spring, S P, attached to the watch plate presses against a small stud on the rocking bar, and keeps A normally in gear with C, mounted on the arbor of the mainspring.

To wind the watch, M is turned so as to give F an anti-clockwise motion. The teeth of F now press A downwards and keep it in gear with C while the winding is done. A spring click (marked solid black) prevents the spring uncoiling (Fig. 209). If F is turned in a clockwise direction it lifts A and prevents it biting the teeth of C, and no strain is thrown on C.

To set the hands, the little push-piece P is pressed inwards by the thumb (Fig. 210) so as to depress the right-hand end of R and bring B into gear with D, which in turn moves E, mounted on the end of the minute-hand shaft. The hands can now be moved in either direction by turning M. On releasing the push-piece the winding-wheels engage again.

The shifting sleeve mechanism has a bevel pinion in the place of G (Fig. 209) gearing with the mainspring cog. The shaft of the knob M is round where it passes through the bevel and can turn freely inside it, but is square below. On the square part is mounted a little sliding clutch with teeth on the top corresponding with the other teeth on the under side of the bevel-wheel, and teeth similar to those of G (Fig. 209) at the end. The clutch has a groove cut in the circumference, and in this lies the end of a spring lever which can be depressed by the push-piece. The mechanism much resembles on a small scale the motor car changing gear (Fig. 49). Normally, the clutch is pushed up the square part of the knob shaft by the spring so as to engage with the bevel and the winding-wheels. On depressing the clutch by means of the push-piece it gears with the minute-hand pinion, and lets go of the bevel.

In one form of this mechanism the push-piece is dispensed with, and the minute-wheel pinion is engaged by pulling the knob upwards.

THE HOUR-HAND TRAIN.

The teeth of the mainspring drum gear with a cog on the minute-hand shaft, which also carries one of the cogs of the escapement train. The shaft is permitted by the escapement to revolve once an hour. Fig. 211 shows diagrammatically how this is managed. The hour-hand shaft A (solid black) can be moved round inside the cog B, driven by the mainspring drum. It carries a cog, C. This gears with a cog, D, having three times as many teeth. The cog E, united to D, drives cog F, having four times as many teeth as E. To F is attached the collar G of the hour-hand. F and G revolve outside the minute-hand shaft. On turning A, C turns D and E, E turns F and the hour-hand, which revolves ⅓ of ¼ = 1⁄12 as fast as A.[41]

LOCKS.

On these unfortunately necessary mechanisms a great deal of ingenuity has been expended. With the advance of luxury and the increased worship of wealth, it becomes more and more necessary to guard one's belongings against the less scrupulous members of society.

The simplest form of lock, such as is found in desks and very cheap articles, works on the principle shown in Fig. 212. The bolt is split at the rear, and the upper part bent upwards to form a spring. The under edge has two notches cut in it, separated by a curved excrescence. The key merely presses the bolt upwards against the spring, until the notch, engaging with the frame, moves it backwards or forwards until the spring drives the tail down into the other notch. This primitive device affords, of course, very little security. An advance is seen in the

TUMBLER LOCK.

The bolt now can move only in a horizontal direction. It has an opening cut in it with two notches (Figs. 213, 214). Behind the bolt lies the tumbler T (indicated by the dotted line), pivoted at the angle on a pin. From the face of the tumbler a stud, S, projects through the hole in the bolt. This stud is forced into one or other of the notches by the spring, S¹, which presses on the tail of the tumbler.

In Fig. 213 the key is about to actuate the locking mechanism. The next diagram (Fig. 214) shows how the key, as it enters the notch on the lower side of the bolt to move it along, also raises the tumbler stud clear of the projection between the two notches. By the time that the bolt has been fully "shot," the key leaves the under notch and allows the tumbler stud to fall into the rear locking-notch.

A lock of this type also can be picked very easily, as the picker has merely to lift the tumbler and move the bolt along. Barron's lock, patented in 1778, had two tumblers and two studs; and the opening in the bolt had notches at the top as well as at the bottom (Fig. 215). This made it necessary for both tumblers to be raised simultaneously to exactly the right height. If either was not lifted sufficiently, a stud could not clear its bottom notch; if either rose too far, it engaged an upper notch. The chances therefore were greatly against a wrong key turning the lock.

THE CHUBB LOCK

is an amplification of this principle. It usually has several tumblers of the shape shown in Fig. 216. The lock stud in these locks projects from the bolt itself, and the openings, or "gates," through which the stud must pass as the lock moves, are cut in the tumblers. It will be noticed that the forward notch of the tumbler has square serrations in the edges. These engage with similar serrations in the bolt stud and make it impossible to raise the tumbler if the bolt begins to move too soon when a wrong key is inserted.

Fig. 217 is a Chubb key with eight steps. That nearest the head (8) operates a circular revolving curtain, which prevents the introduction of picking tools when a key is inserted and partly turned, as the key slot in the curtain is no longer opposite that in the lock. Step 1 moves the bolt.

In order to shoot the bolt the height of the key steps must be so proportioned to the depth of their tumblers that all the gates in the tumblers are simultaneously raised to the right level for the stud to pass through them, as in Fig. 218. Here you will observe that the tumbler D on the extreme right (lifted by step 2 of the key) has a stud, D S, projecting from it over the other tumblers. This is called the detector tumbler. If a false key or picking tool is inserted it is certain to raise one of the tumblers too far. The detector is then over-lifted by the stud D S, and a spring catch falls into a notch at the rear. It is now impossible to pick the lock, as the detector can be released only by the right key shooting the bolt a little further in the locking direction, when a projection on the rear of the bolt lifts the catch and allows the tumbler to fall. The detector also shows that the lock has been tampered with, since even the right key cannot move the bolt until the overlocking has been performed.

Each tumbler step of a large Chubb key can be given one of thirty different heights; the bolt step one of twenty. By merely transposing the order of the steps in a six-step key it is possible to get 720 different combinations. By diminishing or increasing the heights the possible combinations may be raised to the enormous total of 7,776,000!

THE YALE LOCK,

which comes from America, works on a quite different system. Its most noticeable feature is that it permits the use of a very small key, though the number of combinations possible is still enormous (several millions). In our illustrations (Figs. 219, 220, 221) we show the mechanism controlling the turning of the key. The keyhole is a narrow twisted slot in the face of a cylinder, G (Fig. 219), which revolves inside a larger fixed cylinder, F. As the key is pushed in, the notches in its upper edge raise up the pins A¹, B¹, C¹, D¹, E¹, until their tops exactly reach the surface of G, which can now be revolved by the key in Fig. 220, and work the bolt through the medium of the arm H. (The bolt itself is not shown.) If a wrong key is inserted, either some of the lower pins will project upwards into the fixed cylinder F (see Fig. 221), or some of the pins in F will sink into G. It is then impossible to turn the key.

There are other well-known locks, such as those invented by Bramah and Hobbs. But as these do not lend themselves readily to illustration no detailed account can be given. We might, however, notice the time lock, which is set to a certain hour, and can be opened by the right key or a number of keys in combination only when that hour is reached. Another very interesting device is the automatic combination lock. This may have twenty or more keys, any one of which can lock it; but the same one must be used to unlock it, as the key automatically sets the mechanism in favour of itself. With such a lock it would be possible to have a different key for every day in the month; and if any one key got into wrong hands it would be useless unless it happened to be the one which last locked the lock.

THE CYCLE.

There are a few features of this useful and in some ways wonderful contrivance which should be noticed. First,

THE GEARING OF A CYCLE.

To a good many people the expression "geared to 70 inches," or 65, or 80, as the case may be, conveys nothing except the fact that the higher the gear the faster one ought to be able to travel. Let us therefore examine the meaning of such a phrase before going farther.

The safety cycle is always "geared up"—that is, one turn of the pedals will turn the rear wheel more than once. To get the exact ratio of turning speed we count the teeth on the big chain-wheel, and the teeth on the small chain-wheel attached to the hub of the rear wheel, and divide the former by the latter. To take an example:—The teeth are 75 and 30 in number respectively; the ratio of speed therefore = 75⁄30 = 5⁄2 = 2½. One turn of the pedal turns the rear wheel 2½ times. The gear of the cycle is calculated by multiplying this result by the diameter of the rear wheel in inches. Thus a 28-inch wheel would in this case give a gear of 2½ × 28 = 70 inches.

One turn of the pedals on a machine of this gear would propel the rider as far as if he were on a high "ordinary" with the pedals attached directly to a wheel 70 inches in diameter. The gearing is raised or lowered by altering the number ratio of the teeth on the two chain-wheels. If for the 30-tooth wheel we substituted one of 25 teeth the gearing would be—

75⁄25 × 28 inches = 84 inches.

A handy formula to remember is, gearing = T/t × D, where T = teeth on large chain-wheel; t = teeth on small chain-wheel; and D = diameter of driving-wheel in inches.

Two of the most important improvements recently added to the cycle are—(1) The free wheel; (2) the change-speed gear.

THE FREE WHEEL

is a device for enabling the driving-wheel to overrun the pedals when the rider ceases pedalling; it renders the driving-wheel "free" of the driving gear. It is a ratchet specially suited for this kind of work. From among the many patterns now marketed we select the Micrometer free-wheel hub (Fig. 222), which is extremely simple. The ratchet-wheel R is attached to the hub of the driving-wheel. The small chain-wheel (or "chain-ring," as it is often called) turns outside this, on a number of balls running in a groove chased in the neck of the ratchet. Between these two parts are the pawls, of half-moon shape. The driving-wheel is assumed to be on the further side of the ratchet. To propel the cycle the chain-ring is turned in a clockwise direction. Three out of the six pawls at once engage with notches in the ratchet, and are held tightly in place by the pressure of the chain-ring on their rear ends. The other three are in a midway position.

When the rider ceases to pedal, the chain-ring becomes stationary, but the ratchet continues to revolve. The pawls offer no resistance to the ratchet teeth, which push them up into the semicircular recesses in the chain-ring. Each one rises as it passes over a tooth. It is obvious that driving power cannot be transmitted again to the road wheel until the chain-wheel is turned fast enough to overtake the ratchet.

THE CHANGE-SPEED GEAR.

A gain in speed means a loss in power, and vice versâ. By gearing-up a cycle we are able to make the driving-wheel revolve faster than the pedals, but at the expense of control over the driving-wheel. A high-geared cycle is fast on the level, but a bad hill-climber. The low-geared machine shows to disadvantage on the flat, but is a good hill-climber. Similarly, the express engine must have large driving-wheels, the goods engine small driving-wheels, to perform their special functions properly.

In order to travel fast over level country, and yet be able to mount hills without undue exertion, we must be able to do what the motorist does—change gear. Two-speed and three-speed gears are now very commonly fitted to cycles. They all work on the same principle, that of the epicyclic train of cog-wheels, the mechanisms being so devised that the hub turns more slowly than, at the same speed as, or faster than the small chain-wheel,[42] according to the wish of the rider.

We do not propose to do more here than explain the principle of the epicyclic train, which means "a wheel on (or running round) a wheel." Lay a footrule on the table and roll a cylinder along it by the aid of a second rule, parallel to the first, but resting on the cylinder. It will be found that, while the cylinder advances six inches, the upper rule advances twice that distance. In the absence of friction the work done by the agent moving the upper rule is equal to that done in overcoming the force which opposes the forward motion of the cylinder; and as the distance through which the cylinder advances is only half that through which the upper rule advances, it follows that the force which must act on the upper rule is only half as great as that overcome in moving the cylinder. The carter makes use of this principle when he puts his hand to the top of a wheel to help his cart over an obstacle.

Now see how this principle is applied to the change-speed gear. The lower rule is replaced by a cog-wheel, C (Fig. 223); the cylinder by a cog, B, running round it; and the upper rule by a ring, A, with internal teeth. We may suppose that A is the chain-ring, B a cog mounted on a pin projecting from the hub, and C a cog attached to the fixed axle. It is evident that B will not move so fast round C as A does. The amount by which A will get ahead of B can be calculated easily. We begin with the wheels in the position shown in Fig. 223. A point, I, on A is exactly over the topmost point of C. For the sake of convenience we will first assume that instead of B running round C, B is revolved on its axis for one complete revolution in a clockwise direction, and that A and C move as in Fig. 224. If B has 10 teeth, C 30, and A 40, A will have been moved 10⁄40 = ¼ of a revolution in a clockwise direction, and C 10⁄30 = ⅓ of a revolution in an anti-clockwise direction.

Now, coming back to what actually does happen, we shall be able to understand how far A rotates round C relatively to the motion of B, when C is fixed and B rolls (Fig. 225). B advances ⅓ of distance round C; A advances ⅓ + ¼ = 7⁄12 of distance round B. The fractions, if reduced to a common denominator, are as 4:7, and this is equivalent to 40 (number of teeth on A): 40 + 30 (teeth on A + teeth on C.)

To leave the reader with a very clear idea we will summarize the matter thus:—If T = number of teeth on A, t = number of teeth on C, then movement of A: movement of B:: T + t: T.

Here is a two-speed hub. Let us count the teeth. The chain-ring (= A) has 64 internal teeth, and the central cog (= C) on the axle has 16 teeth. There are four cogs (= B) equally spaced, running on pins projecting from the hub-shell between A and C. How much faster than B does A run round C? Apply the formula:—Motion of A: motion of B:: 64 + 16: 64. That is, while A revolves once, B and the hub and the driving-wheel will revolve only 64⁄80 = ⅘ of a turn. To use scientific language, B revolves 20 per cent. slower than A.

This is the gearing we use for hill-climbing. On the level we want the driving-wheel to turn as fast as, or faster than, the chain-ring. To make it turn at the same rate, both A and C must revolve together. In one well-known gear this is effected by sliding C along the spindle of the wheel till it disengages itself from the spindle, and one end locks with the plate which carries A. Since B is now being pulled round at the bottom as well as the top, it cannot rotate on its own axis any longer, and the whole train revolves solidly—that is, while A turns through a circle B does the same.

To get an increase of gearing, matters must be so arranged that the drive is transmitted from the chain-wheel to B, and from A to the hub. While B describes a circle, A and the driving-wheel turn through a circle and a part of a circle—that is, the driving-wheel revolves faster than the hub. Given the same number of teeth as before, the proportional rates will be A = 80, B = 64, so that the gear rises 25 per cent.

By means of proper mechanism the power is transmitted in a three-speed gear either (1) from chain-wheel to A, A to B, B to wheel = low gear; or (2) from chain-wheel to A and C simultaneously = solid, normal, or middle gear; or (3) from chain-wheel to B, B to A, A to wheel = high gear. In two-speed gears either 1 or 3 is omitted.

AGRICULTURAL MACHINES.

THE THRESHING-MACHINE.

Bread would not be so cheap as it is were the flail still the only means of separating the grain from the straw. What the cream separator has done for the dairy industry (p. 384), the threshing-machine has done for agriculture. A page or two ought therefore to be spared for this useful invention.

In Fig. 226 a very complete fore-and-aft section of the machine is given. After the bands of the sheaves have been cut, the latter are fed into the mouth of the drum A by the feeder, who stands in the feeding-box on the top of the machine. The drum revolves at a very high velocity, and is fitted with fluted beaters which act against a steel concave, or breastwork, B, the grain being threshed out of the straw in passing between the two. The breastwork is provided with open wires, through which most of the threshed grain, cavings (short straws), and chaff passes on to a sloping board. The straw is flung forward on to the shakers C, which gradually move the straw towards the open end and throw it off. Any grain, etc., that has escaped the drum falls through the shakers on to D, and works backwards to the caving riddles, or moving sieves, E. The main blower, by means of a revolving fan, N, sends air along the channel X upwards through these riddles, blowing the short straws away to the left. The grain, husks, and dust fall through E on to G, over the end of which they fall on to the chaff riddle, H. A second column of air from the blower drives the chaff away. The heavy grain, seeds, dust, etc., fall on to I, J, and K in turn, and are shaken until only the grain remains to pass along L to the elevator bottom, M. An endless band with cups attached to it scoops up the grain, carries it aloft, and shoots it into hopper P. It then goes through the shakers Q, R, is dusted by the back end blower, S, and slides down T into the open end of the rotary screen-drum U, which is mounted on the slope, so that as it turns the grain travels gradually along it. The first half of the screen has wires set closely together. All the small grain that falls through this, called "thirds," passes into a hopper, and is collected in a sack attached to the hopper mouth. The "seconds" fall through the second half of the drum, more widely spaced, into their sack; and the "firsts" fall out of the end and through a third spout.

MOWING-MACHINES.

The ordinary lawn—mower employs a revolving reel, built up of spirally-arranged knives, the edges of which pass very close to a sharp plate projecting from the frame of the mower. Each blade, as it turns, works along the plate, giving a shearing cut to any grass that may be caught between the two cutting edges. The action is that of a pair of scissors (Fig. 227), one blade representing the fixed, the other the moving knife. If you place a cylinder of wood in the scissors it will be driven forward by the closing of the blades, and be marked by them as it passes along the edges. The same thing happens with grass, which is so soft that it is cut right through.

HAY-CUTTER.

The hay-cutter is another adaptation of the same principle. A cutter-bar is pulled rapidly backwards and forwards in a frame which runs a few inches above the ground by a crank driven by the wheels through gearing. To the front edge of the bar are attached by one side a number of triangular knives. The frame carries an equal number of spikes pointing forward horizontally. Through slots in these the cutter-bar works, and its knives give a drawing cut to grass caught between them and the sides of the spikes.

SOME NATURAL PHENOMENA.

WHY SUN-HEAT VARIES IN INTENSITY.

The more squarely parallel heat-rays strike a surface the greater will be the number that can affect that surface. This is evident from Figs. 228, 229, where A B is an equal distance in both cases. The nearer the sun is to the horizon, the more obliquely do its rays strike the earth. Hence midday is necessarily warmer than the evening, and the tropics, where the sun stands overhead, are hotter than the temperate zones, where, even in summer at midday, the rays fall more or less on the slant.

The atmospheric envelope which encompasses the earth tends to increase the effect of obliquity, since a slanting ray has to travel further through it and is robbed of more heat than a vertical ray.

THE TIDES.

All bodies have an attraction for one another. The earth attracts the moon, and the moon attracts the earth. Now, though the effect of this attraction is not visible as regards the solid part of the globe, it is strongly manifested by the water which covers a large portion of the earth's surface. The moon attracts the water most powerfully at two points, that nearest to it and that furthest away from it; as shown on an exaggerated scale in Fig. 230. Since the earth and the water revolve as one mass daily on their axis, every point on the circumference would be daily nearest to and furthest from the moon at regular intervals, and wherever there is ocean there would be two tides in that period, were the moon stationary as regards the earth. (It should be clearly understood that the tides are not great currents, but mere thickenings of the watery envelope. The inrush of the tide is due to the temporary rise of level.)

WHY HIGH TIDE VARIES DAILY.

The moon travels round the earth once in twenty-eight days. In Fig. 231 the point a is nearest the moon at, say, twelve noon. At the end of twenty-four hours it will have arrived at the same position by the compass, but yet not be nearest to the moon, which has in that period moved on 1⁄28th of a revolution round the earth.[43] Consequently high tide will not occur till a has reached position b and overtaken the moon, as it were, which takes about an hour on the average. This explains why high tide occurs at intervals of more than twelve hours.

NEAP TIDES AND SPRING TIDES.

The sun, as well as the moon, attracts the ocean, but with less power, owing to its being so much further away. At certain periods of the month, sun, earth, and moon are all in line. Sun and moon then pull together, and we get the highest, or spring tides (Fig. 232). When sun and moon pull at right angles to one another—namely, at the first and third quarters—the excrescence caused by the moon is flattened (Fig. 233), and we get the lowest, or neap tides.