Chapter X: Part 10

In many cases the utility of the wedge depends on that which is entirely omitted in its theory, viz. the friction which arises between its surface and the substance which it divides. This is the case when pins, bolts, or nails are used for binding the parts of structures together; in which case, were it not for the friction, they would recoil from their places, and fail to produce the desired effect. Even when the wedge is used as a mechanical engine, the presence of friction is absolutely indispensable to its practical utility. The power, as has already been stated, generally acts by successive blows, and is therefore subject to constant intermission, and but for the friction the wedge would recoil between the intervals of the blows with as much force as it had been driven forward. Thus the object of the labour would be continually frustrated. The friction in this case is of the same use as a ratchet wheel, but is much more necessary, as the power applied to the wedge is more liable to intermission than in the cases where ratchet wheels are generally used.

(292.) When a road directly ascends the side of a hill, it is to be considered as an inclined plane; but it will not lose its mechanical character, if, instead of directly ascending towards the top of the hill, it winds successively round it, and gradually ascends so as after several revolutions to reach the top. In the same manner a path may be conceived to surround a pillar by which the ascent may be facilitated upon the principle of the inclined plane. Winding stairs constructed in the interior of great columns partake of this character; for although the ascent be produced by successive steps, yet if a floor could be made sufficiently rough to prevent the feet from slipping, the ascent would be accomplished with equal facility. In such a case the winding path would be equivalent to an inclined plane, bent into such a form as to accommodate it to the peculiar circumstances in which it would be required to be used. It will not be difficult to trace the resemblance between such an adaptation of the inclined plane and the appearances presented by the thread of a _screw_: and it may hence be easily understood that a screw is nothing more than an inclined plane constructed upon the surface of a cylinder.

This will, perhaps, be more apparent by the following contrivance: Let A B, _fig. 135._, be a common round ruler, and let C D E be a piece of white paper cut in the form of an inclined plane, whose height C D is equal to the length of the ruler A B, and let the edge C E of the paper be marked with a broad black line: let the edge C D be applied to the ruler A B, and being attached thereto, let the paper be rolled round the ruler; the ruler will then present the appearance of a screw, _fig. 136._ the thread of the screw being marked by the black line C E, winding continually round the ruler. Let D F, _fig. 135._, be equal to the circumference of the ruler, and draw F G parallel to D C, and G H parallel to D E, the part C G F D of the paper will exactly surround the ruler once: the part C G will form one convolution of the thread, and may be considered as the length of one inclined plane surrounding the cylinder, C H being the corresponding height, and G H the base. The power of the screw does not, as in the ordinary cases of the inclined plane, act parallel to the plane or thread, but at right angles to the length of the cylinder A B, or, what is to the same effect, parallel to the base H G; therefore the proportion of the power to the weight will be, according to principles already explained, the same as that of C H to the space through which the power moves parallel to H G in one revolution of the screw. H C is evidently the distance between the successive positions of the thread as it winds round the cylinder; and it appears from what has been just stated, that the less this distance is, or, in other words, the finer the thread is, the more powerful the machine will be.

(293.) In the application of the screw the weight or resistance is not, as in the inclined plane and wedge, placed upon the surface of the plane or thread. The power is usually transmitted by causing the screw to move in a concave cylinder, on the interior surface of which a spiral cavity is cut, corresponding exactly to the thread of the screw, and in which the thread will move by turning round the screw continually in the same direction. This hollow cylinder is usually called the _nut_ or _concave screw_. The screw surrounded by its spiral thread is represented in _fig. 137._; and a section of the same playing in the nut is represented in _fig. 138._

There are several ways in which the effect of the power may be conveyed to the resistance by this apparatus.

First, let us suppose that the nut A B is fixed. If the screw be continually turned on its axis, by a lever E F inserted in one end of it, it will be moved in the direction C D, advancing every revolution through a space equal to the distance between two contiguous threads. By turning the lever in an opposite direction, the screw will be moved in the direction D C.

If the screw be fixed, so as to be incapable either of moving longitudinally or revolving on its axis, the nut A B may be turned upon the screw by a lever, and will move on the screw towards C or towards D, according to the direction in which the lever is turned.

In the former case we have supposed the nut to be absolutely immoveable, and in the latter case the screw to be absolutely immoveable. It may happen, however, that the nut, though capable of revolving, is incapable of moving longitudinally; and that the screw, though incapable of revolving, is capable of moving longitudinally. In that case, by turning the nut A B upon the screw by the lever, the screw will be urged in the direction C D or D C, according to the way in which the nut is turned.

The apparatus may, on the contrary, be so arranged, that the nut, though incapable of revolving, is capable of moving longitudinally; and the screw, though capable of revolving, is incapable of moving longitudinally. In this case, by turning the screw in the one direction or in the other, the nut A B will be urged in the direction C D or D C.

All these various arrangements may be observed in different applications to the machine.

(294.) A screw may be cut upon a cylinder by placing the cylinder in a turning lathe, and giving it a rotatory motion upon its axis. The cutting point is then presented to the cylinder, and moved in the direction of its length, at such a rate as to be carried through the distance between the intended thread, while the cylinder revolves once. The relative motions of the cutting point and the cylinder being preserved with perfect uniformity, the thread will be cut from one end to the other. The shape of the threads may be either square, as in _fig. 137._, or triangular, as in _fig. 139._

(295.) The screw is generally used in cases where severe pressure is to be excited through small spaces; it is therefore the agent in most presses. In _fig. 140._, the nut is fixed, and by turning the lever, which passes through the head of the screw, a pressure is excited upon any substance placed upon the plate immediately under the end of the screw. In _fig. 141._, the screw is incapable of revolving, but is capable of advancing in the direction of its length. On the other hand, the nut is capable of revolving, but does not advance in the direction of the screw. When the nut is turned by means of the screw inserted in it, the screw advances in the direction of its length, and urges the board which is attached to it upwards, so as to press any substance placed between it and the fixed board above.

In cases where liquids or juices are to be expressed from solid bodies, the screw is the agent generally employed. It is also used in coining, where the impression of a die is to be made upon a piece of metal, and in the same way in producing the impression of a seal upon wax or other substance adapted to receive it. When soft and light materials, such as cotton, are to be reduced to a convenient bulk for transportation, the screw is used to compress them, and they are thus reduced into hard dense masses. In printing, the paper is urged by a severe and sudden pressure upon the types, by means of a screw.

(296.) As the mechanical power of the screw depends upon the relative magnitude of the circumference through which the power revolves, and the distance between the threads, it is evident, that, to increase the efficacy of the machine, we must either increase the length of the lever by which the power acts, or diminish the magnitude of the thread. Although there is no limit in theory to the increase of the mechanical efficacy by these means, yet practical inconvenience arises which effectually prevents that increase being carried beyond a certain extent. If the lever by which the power acts be increased, the same difficulty arises as was already explained in the wheel and axle (254.); the space through which the power should act would be so unwieldy, that its application would become impracticable. If, on the other hand, the power of the machine be increased by diminishing the size of the thread, the strength of the thread will be so diminished, that a slight resistance will tear it from the cylinder. The cases in which it is necessary to increase the power of the machine, being those in which the greatest resistances are to be overcome, the object will evidently be defeated, if the means chosen to increase that power deprive the machine of the strength which is necessary to sustain the force to which it is to be submitted.

(297.) These inconveniences are removed by a contrivance of Mr. Hunter, which, while it gives to the machine all the requisite strength and compactness, allows it to have an almost unlimited degree of mechanical efficacy.

This contrivance consists in the use of two screws, the threads of which may have any strength and magnitude, but which have a very small difference of breadth. While the working point is urged forward by that which has the greater thread, it is drawn back by that which has the less; so that during each revolution of the screw, instead of being advanced through a space equal to the magnitude of either of the threads, it moves through a space equal to their difference. The mechanical power of such a machine will be the same as that of a single screw having a thread, whose magnitude is equal to the difference of the magnitudes of the two threads just mentioned.

Thus, without inconveniently increasing the sweep of the power, on the one hand, or, on the other, diminishing the thread until the necessary strength is lost, the machine will acquire an efficacy limited by nothing but the smallness of the difference between the two threads.

This principle was first applied in the manner represented in _fig. 142._ A is the greater thread, playing in the fixed nut; B is the lesser thread, cut upon a smaller cylinder, and playing in a concave screw, cut within the greater cylinder. During every revolution of the screw, the cylinder A descends through a space equal to the distance between its threads. At the same time the smaller cylinder B ascends through a space equal to the distance between the threads cut upon it: the effect is, that the board D descends through a space equal to the difference between the threads upon A and the threads upon B, and the machine has a power proportionate to the smallness of this difference.

Thus, suppose the screw A has twenty threads in an inch, while the screw B has twenty-one; during one revolution, the screw A will descend through a space equal to the 20th part of an inch. If, during this motion, the screw B did not turn within A, the board D would be advanced through the 20th of an inch; but because the hollow screw within A turns upon B, the screw B will, relatively to A, be raised in one revolution through a space equal to the 21st part of an inch. Thus, while the board D is depressed through the 20th of an inch by the screw A, it is raised through the 21st of an inch by the screw B. It is, therefore, on the whole, depressed through a space equal to the excess of the 20th of an inch above the 21st of an inch, that is, through the 420th of an inch.

The power of this machine will, therefore, be expressed by the number of times the 420th of an inch is contained in the circumference through which the power moves.

(298.) In the practical application of this principle at present the arrangement is somewhat different. The two threads are usually cut on different parts of the same cylinder. If nuts be supposed to be placed upon these, which are capable of moving in the direction of the length, but not of revolving, it is evident that by turning the screw once round, each nut will be advanced through a space equal to the breadth of the respective threads. By this means the two nuts will either approach each other, or mutually recede, according to the direction in which the screw is turned, through a space equal to the difference of the breadth of the threads, and they will exert a force either in compressing or extending any substance placed between them, proportionate to the smallness of that difference.

(299.) A toothed wheel is sometimes used instead of a nut, so that the same quality by which the revolution of the screw urges the nut forward is applied to make the wheel revolve. The screw is in this case called an endless screw, because its action upon the wheel may be continued without limit. This application of the screw is represented in _fig. 143._ P is the winch to which the power is applied; and its effect at the circumference of the wheel is estimated in the same manner as the effect of the screw upon the nut. This effect is to be considered as a power acting upon the circumference of the wheel; and its proportion to the weight or resistance is to be calculated in the same manner as the proportion of the power to the weight in the wheel and axle.

(300.) We have hitherto considered the screw as an engine used to overcome great resistances. It is also eminently useful in several departments of experimental science, for the measurement of very minute motions and spaces, the magnitude of which could scarcely be ascertained by any other means. The very slow motion which may be imparted to the end of a screw, by a very considerable motion in the power, renders it peculiarly well adapted for this purpose. To explain the manner in which it is applied--suppose a screw to be so cut as to have fifty threads in an inch, each revolution of the screw will advance its point through the fiftieth part of an inch. Now, suppose the head of the screw to be a circle, whose diameter is an inch, the circumference of the head will be something more than three inches: this may be easily divided into a hundred equal parts distinctly visible. If a fixed index be presented to this graduated circumference, the hundredth part of a revolution of the screw may be observed, by noting the passage of one division of the head under the index. Since one entire revolution of the head moves the point through the fiftieth of an inch, one division will correspond to the five thousandth of an inch. In order to observe the motion of the point of the screw in this case, a fine wire is attached to it, which is carried across the field of view of a powerful microscope, by which the motion is so magnified as to be distinctly perceptible.

A screw used for such purposes is called a _micrometer screw_. Such an apparatus is usually attached to the limbs of graduated instruments, for the purposes of astronomical and other observation. Without the aid of this apparatus, no observation could be taken with greater accuracy than the amount of the smallest division upon the limb. Thus, if an instrument for measuring angles were divided into small arcs of one minute, and an angle were observed which brought the index of the instrument to some point between two divisions, we could only conclude that the observed angle must consist of a certain number of degrees and minutes, together with an additional number of seconds, which would be unknown, inasmuch as there would be no means of ascertaining the fraction of a minute between the index and the adjacent division of the instrument. But if a screw be provided, the point of which moves through a space equal to one division of the instrument, with sixty revolutions of the head, and that the head itself be divided into one hundred equal parts, each complete revolution of the screw will correspond to the sixtieth part of a minute, or to one second, and each division on the head of the screw will correspond to the hundredth part of a second. The index being attached to this screw, let the head be turned until the index be moved from its observed position to the adjacent division of the limb. The number of complete revolutions of the screw necessary to accomplish this will be the number of seconds; and the number of parts of a revolution over the complete number of revolutions will be the hundredth parts of a second necessary to be added to the degrees and minutes primarily observed.

It is not, however, only to such instruments that the micrometer screw is applicable; any spaces whatever may be measured by it. An instance of its mechanical application may be mentioned in a steel-yard, an instrument for ascertaining the amount of weights by a given weight, sliding on a long graduated arm of a lever. The distance from the fulcrum, at which this weight counterpoises the weight to be ascertained, serves as a measure to the amount of that weight. When the sliding weight happens to be placed between two divisions of the arm, a micrometer screw is used to ascertain the fraction of the division.

Hunter’s screw, already described, seems to be well adapted to micrometrical purposes; since the motion of the point may be rendered indefinitely slow, without requiring an exquisitely fine thread, such as in the single screw would be necessary.

CHAP. XVII.

ON THE REGULATION AND ACCUMULATION OF FORCE.

(301.) It is frequently indispensable, and always desirable, that the operation of a machine should be regular and uniform. Sudden changes in its velocity, and desultory variations in the effective energy of its power, are often injurious or destructive to the apparatus itself, and when applied to manufactures never fail to produce unevenness in the work. To invent methods for insuring the regular motion of machinery, by removing those causes of inequality which may be avoided, and by compensating others, has therefore been a problem to which much attention and ingenuity have been directed. This is chiefly accomplished by controlling, and, as it were, measuring out the power according to the exigencies of the machine, and causing its effective energy to be always commensurate with the resistance which it has to overcome.

_London, Pubd. by Longman & Co._]

Irregularity in the motion of machinery may proceed from one or more of the following causes:--1. irregularity in the prime mover; 2. occasional variation in the amount of the load or resistance; and, 3. because, in the various positions which the parts of the machine assume during its motion, the power may not be transmitted with equal effect to the working point.

The energy of the prime mover is seldom if ever regular. The force of water varies with the copiousness of the stream. The power which impels the windmill is proverbially capricious. The pressure of steam varies with the intensity of the furnace. Animal power, the result of will, temper, and health is difficult of control. Human labour is most of all unmanageable; hence no machine works so irregularly as one which is manipulated. In some cases the moving force is subject, by the very conditions of its existence, to constant variation, as in the example of a spring, which gradually loses its energy as it recoils. (255.) In many instances the prime mover is liable to regular intermission, and is actually suspended for certain intervals of time. This is the case in the single acting steam-engine, where the pressure of the steam urges the descent of the piston, but is suspended during its ascent.

The load or resistance to which the machine is applied is not less fluctuating. In mills there are a multiplicity of parts which are severally liable to be occasionally disengaged, and to have their operation suspended. In large factories for spinning, weaving, printing, &c. a great number of separate spinning machines, looms, presses, or other engines, are usually worked by one common mover, such as a water-wheel or steam-engine. In these cases the number of machines employed from time to time necessarily varies with the fluctuating demand for the articles produced, and from other causes. Under such circumstances the velocity with which every part of the machinery is moved would suffer corresponding changes, increasing its rapidity with every augmentation of the moving power or diminution of the resistance, or being retarded in its speed by the contrary circumstances.

But even when the prime mover and the resistance are both regular, or rendered so by proper contrivances, still it will rarely happen that the machine by which the energy of the one is transmitted to the other conveys this with unimpaired effect in all the phases of its operation. To give a general notion of this cause of inequality to those who have not been familiar with machinery would not be easy, without having recourse to an example. For the present we shall merely state, that the several moving parts of every machine assume in succession a variety of positions; that at regular periods they return to their first position, and again undergo the same succession of changes. In the different positions through which they are carried in every period of motion, the efficacy of the machine to transmit the power to the resistance is different, and thus the effective energy of the machine in acting upon the resistance would be subject to continual fluctuation. This will be more clearly understood when we come to explain the methods of counteracting the defect or equalising the action of the power upon the resistance.

Such are the chief causes of the inequalities incidental to the motion of machinery, and we now propose to describe a few of the many ingenious contrivances which the skill of engineers has produced to remove the consequent inconveniences.

(302.) Setting aside, for the present, the last cause of inequality, and considering the machinery, whatever it be, to transmit the power to the resistance without irregular interruption, it is evident that every contrivance, having for its object to render the velocity uniform, can only accomplish this by causing the variations of the power and resistance to be proportionate to each other. This may be done either by increasing or diminishing the power as the resistance increases or diminishes; or by increasing or diminishing the resistance as the power increases or diminishes.

According to the facilities or convenience presented by the peculiar circumstances of the case either of these methods is adopted.

The contrivances for effecting this are called _regulators_. Most regulators act upon that part of the machine which commands the supply of the power by means of levers, or some other mechanical contrivance, so as to check the quantity of the moving principle conveyed to the machine when the velocity has a tendency to increase; and, on the other hand, to increase that supply upon any undue abatement of its speed. In a water-mill this is done by acting upon the shuttle; in a wind-mill, by an adjustment of the sail-cloth; and in a steam-engine, by opening or closing, in a greater or less degree, the valve by which the cylinder is supplied with steam.

(303.) Of all the contrivances for regulating machinery, that which is best known and most commonly used is the _governor_. This regulator, which had been long in use in mill-work and other machinery, has of late years attracted more general notice by its beautiful adaptation in the steam-engines of Watt. It consists of heavy balls B B, _fig. 144._, attached to the extremities of rods B F. These rods play upon a joint at E, passing through a mortise in the vertical stem D D′. At F they are united by joints to the short rods F H, which are again connected by joints at H to a ring which slides upon the vertical shaft D D′. From this description it will be apparent that when the balls B are drawn from the axis, their upper arms E F are caused to increase their divergence in the same manner as the blades of a scissors are opened by separating the handles. These, acting upon the ring by means of the short links F H, draw it down the vertical axis from D towards E. A contrary effect is produced when the balls B are brought closer to the axis, and the divergence of the rods B E diminished. A horizontal wheel W is attached to the vertical axis D D′, having a groove to receive a rope or strap upon its rim. This strap passes round the wheel or axis by which motion is transmitted to the machinery to be regulated, so that the spindle or shaft D D′ will always be made to revolve with a speed proportionate to that of the machinery.

As the shaft D D′ revolves, the balls B are carried round it with a circular motion, and consequently acquire a centrifugal force which causes them to recede from the axle, and therefore to depress the ring H. On the edge or rim of this ring is formed a groove, which is embraced by the prongs of a fork I, at the extremity of one arm of a lever whose fulcrum is at G. The extremity K of the other arm is connected by some means with the part of the machine which supplies the power. In the present instance we shall suppose it a steam-engine, in which case the rod K I communicates with a flat circular valve V, placed in the principal steam-pipe, and so arranged that, when K is elevated as far as by their divergence the balls B have power over it, the passage of the pipe will be closed by the valve V, and the passage of steam entirely stopped; and, on the other hand, when the balls subside to their lowest position, the valve will be presented with its edge in the direction of the tube, so as to intercept no part of the steam.

The property which renders this instrument so admirably adapted to the purpose to which it is applied is, that when the divergence of the balls is not very considerable, they must always revolve with the same velocity, whether they move at a greater or lesser distance from the vertical axis. If any circumstance increases that velocity, the balls instantly recede from the axis, and closing the valve V, check the supply of steam, and thereby diminishing the speed of the motion, restore the machine to its former rate. If, on the contrary, that fixed velocity be diminished, the centrifugal force being no longer sufficient to support the balls, they descend towards the axle, open the valve V, and, increasing the supply of steam, restore the proper velocity of the machine.

When the governor is applied to a water-wheel it is made to act upon the shuttle through which the water flows, and controls its quantity as effectually, and upon the same principle, as has just been explained in reference to the steam-engine. When applied to a windmill it regulates the sail-cloth so as to diminish the efficacy of the power upon the arms as the force of the wind increases, or _vice versâ_.

In cases where the resistance admits of easy and convenient change, the governor may act so as to accommodate it to the varying energy of the power. This is often done in corn-mills, where it acts upon the shuttle which metes out the corn to the millstones. When the power which drives the mill increases, a proportionally increased feed of corn is given to the stones, so that the resistance being varied in the ratio of the power, the same velocity will be maintained.

(304.) In some cases the centrifugal force of the revolving balls is not sufficiently great to control the power or the resistance, and regulators of a different kind must be resorted to. The following contrivance is called the _water-regulator_:--

A common pump is worked by the machine, whose motion is to be regulated, and water is thus raised and discharged into a cistern. It is allowed to flow from this cistern through a pipe of a given magnitude. When the water is pumped up with the same velocity as it is discharged by this pipe, it is evident that the level of the water in the cistern will be stationary, since it receives from the pump the exact quantity which it discharges from the pipe. But if the pump throw in more water in a given time than is discharged by the pipe, the cistern will begin to be filled, and the level of the water will rise. If, on the other hand, the supply from the pump be less than the discharge from the pipe, the level of the water in the cistern will subside. Since the rate at which water is supplied from the pump will always be proportional to the velocity of the machine, it follows that every fluctuation in this velocity will be indicated by the rising or subsiding of the level of the water in the cistern, and that level never can remain stationary, except at that exact velocity which supplies the quantity of water discharged by the pipe. This pipe may be constructed so as by an adjustment to discharge the water at any required rate; and thus the cistern may be adapted to indicate a constant velocity of any proposed amount.

If the cistern were constantly watched by an attendant, the velocity of the machine might be abated by regulating the power when the level of the water is observed to rise, or increased when it falls; but this is much more effectually and regularly performed by causing the surface of the water itself to perform the duty. A float or large hollow metal ball is placed upon the surface of the water in the cistern. This ball is connected with a lever acting upon some part of the machinery, which controls the power or regulates the amount of resistance, as already explained in the case of the governor. When the level of the water rises, the buoyancy of the ball causes it to rise also with a force equal to the difference between its own weight and the weight of as much water as it displaces. By enlarging the floating ball, a force may be obtained sufficiently great to move those parts of the machinery which act upon the power or resistance, and thus either to diminish the supply of the moving principle or to increase the amount of the resistance, and thereby retard the motion and reduce the velocity to its proper limit. When the level of the water in the cistern falls, the floating ball being no longer supported on the liquid surface, descends with the force of its own weight, and producing an effect upon the power or resistance contrary to the former, increases the effective energy of the one, or diminishes that of the other, until the velocity proper to the machine be restored.

The sensibility of these regulators is increased by making the surface of water in the cistern as small as possible; for then a small change in the rate at which the water is supplied by the pump will produce a considerable change in the level of the water in the cistern.

Instead of using a float, the cistern itself may be suspended from the lever which controls the supply of the power, and in this case a sliding weight may be placed on the other arm, so that it will balance the cistern when it contains that quantity of water which corresponds to the fixed level already explained. If the quantity of water in the cistern be increased by an undue velocity of the machine, the weight of the cistern will preponderate, draw down the arm of the lever, and check the supply of the power. If, on the other hand, the supply of water be too small, the cistern will no longer balance the counterpoise, the arm by which it is suspended will be raised, and the energy of the power will be increased.

(305.) In the steam-engine the self-regulating principle is carried to an astonishing pitch of perfection. The machine itself raises in due quantity the cold water necessary to condense the steam. It pumps off the hot water produced by the steam, which has been cooled, and lodges it in a reservoir for the supply of the boiler. It carries from this reservoir exactly that quantity of water which is necessary to supply the wants of the boiler, and lodges it therein according as it is required. It breathes the boiler of redundant steam, and preserves that which remains fit, both in quantity and quality, for the use of the engine. It blows its own fire, maintaining its intensity, and increasing or diminishing it according to the quantity of steam which it is necessary to raise; so that when much work is expected from the engine, the fire is proportionally brisk and vivid. It breaks and prepares its own fuel, and scatters it upon the bars at proper times and in due quantity. It opens and closes its several valves at the proper moments, works its own pumps, turns its own wheels, and is only not alive. Among so many beautiful examples of the self-regulating principle, it is difficult to select. We shall, however, mention one or two, and for others refer the reader to our treatise on this subject.[3]

[3] Lardner on the Steam-Engine, Steam-Navigation, Roads, and Railways. 8th edition. 1851.

It is necessary in this machine that the water in the boiler be maintained constantly at the same level, and, therefore, that as much be supplied, from time to time, as is consumed by evaporation. A pump which is wrought by the engine itself supplies a cistern C, _fig. 145._, with hot water. At the bottom of this cistern is a valve V opening into a tube which descends into the boiler. This valve is connected by a wire with the arm of a lever on the fulcrum D, the other arm E of which is also connected by a wire with a stone float F, which is partially immersed in the water of the boiler, and is balanced by a sliding weight A. The weight A only counterpoises the stone float F by the aid of its buoyance in the water; for if the water be removed, the stone F will preponderate, and raise the weight A. When the water in the boiler is at its proper level, the length of the wire connecting the valve V with the lever is so adjusted that this valve shall be closed, the wire at the same time being fully extended. When, by evaporation, the water in the boiler begins to be diminished, the level falls, and the stone weight F, being no longer supported, overcomes the counterpoise A, raises the arm of the lever, and, pulling the wire, opens the valve V. The water in the cistern C then flows through the tube into the boiler, and continues to flow until the level be so raised that the stone weight F is again elevated, the valve V closed, and the further supply of water from the cistern C suspended.

In order to render the operation of this apparatus easily intelligible, we have here supposed an imperfection which does not exist. According to what has just been stated, the level of the water in the boiler descends from its proper height, and subsequently returns to it. But, in fact, this does not happen. The float F and valve V adjust themselves, so that a constant supply of water passes through the valve, which proceeds exactly at the same rate as that at which the water in the boiler is consumed.

(306.) In the same machine there occurs a singularly happy example of self-adjustment, in the method by which the strength of the fire is regulated. The governor regulates the supply of steam to the engine, and proportions it to the work to be done. With this work, therefore, the demands upon the boiler increase or diminish, and with these demands the production of steam in the boiler ought to vary. In fact, the rate at which steam is generated in the boiler, ought to be equal to that at which it is consumed in the engine, otherwise one of two effects must ensue: either the boiler will fail to supply the engine with steam, or steam will accumulate in the boiler, being produced in undue quantity, and, escaping at the safety valve, will thus be wasted. It is, therefore, necessary to control the agent which generates the steam, namely, the fire, and to vary its intensity from time to time, proportioning it to the demands of the engine. To accomplish this, the following contrivance has been adopted:--Let T, _fig. 146._, be a tube inserted in the top of the boiler, and descending nearly to the bottom. The pressure of the steam confined in the boiler, acting upon the surface of the water, forces it to a certain height in the tube T. A weight F, half immersed in the water in the tube, is suspended by a chain, which passes over the wheels P P′, and is balanced by a metal plate D, in the same manner as the stone float, _fig. 145._, is balanced by the weight A. The plate D passes through the mouth of the flue E as it issues finally from the boiler; so that when the plate D falls it stops the flue, suspending thereby the draught of air through the furnace, mitigating the intensity of the fire, and checking the production of steam. If, on the contrary, the plate D be drawn up, the draught is increased, the fire is rendered more active, and the production of steam in the boiler is stimulated. Now, suppose that the boiler produces steam faster than the engine consumes it, either because the load on the engine has been diminished, and, therefore, its consumption of steam reduced, or because the fire has become too intense; the consequence is, that the steam, beginning to accumulate in the boiler, will press upon the surface of the water with increased force, and the water will be raised in the tube T. The weight F will, therefore, be lifted, and the plate D will descend, diminish, or stop the draught, mitigate the fire, and retard the production of steam, and will continue to do so until the rate at which steam is produced shall be commensurate to the wants of the engine. If, on the other hand, the production of steam be inadequate to the exigency of the machine, either because of an increased load, or of the insufficient force of the fire, the steam in the boiler will lose its elasticity, and the surface of the water not sustaining its wonted pressure, the water in the tube T will fall; consequently the weight F will descend, and the plate D will be raised. The flue being thus opened, the draught will be increased, and the fire rendered more intense. Thus the production of steam becomes more rapid, and is rendered sufficiently abundant for the purposes of the engine. This apparatus is called the _self-acting damper_.

(307.) When a perfectly uniform rate of motion has not been attained, it is often necessary to indicate small variations of velocity. The following contrivance, called a _tachometer_[4], has been invented to accomplish this. A cup, _fig. 147._, is filled to the level C D with quicksilver, and is attached to a spindle, which is whirled by the machine in the same manner as the governor already described. It is well known that the centrifugal force produced by this whirling motion will cause the mercury to recede from the centre and rise upon the sides of the cup, so that its surface will assume the concave appearance represented in _fig. 148._ In this case the centre of the surface will obviously have fallen below its original level, _fig. 147._, and the edges will have risen above that level. As this effect is produced by the velocity of the machine, so it is proportionate to that velocity, and subject to corresponding variations. Any method of rendering visible small changes in the central level of the surface of the quicksilver will indicate minute variations in the velocity of the machine.

[4] From the Greek words _tachos_ speed, and _metron_ measure.

A glass tube A, open at both ends, and expanding at one extremity into a bell B, is immersed with its wider end in the mercury, the surface of which will stand at the same level in the bell B, and in the cup C D. The tube is so suspended as to be unconnected with the cup. This tube is then filled to a certain height A, with spirits tinged with some colouring matter, to render it easily observable. When the cup is whirled by the machine to which it is attached, the level of the quicksilver in the bell falls, leaving more space for the spirits, which, therefore, descends in the tube. As the motion is continued, every change of velocity causes a corresponding change in the level of the mercury, and, therefore, also in the level A of the spirits. It will be observed, that, in consequence of the capacity of the bell B being much greater than that of the tube A, a very small change in the level of the quicksilver in the bell will produce a considerable change in the height of the spirits in the tube. Thus this ingenious instrument becomes a very delicate indicator of variations in the motion of machinery.

(308.) The governor, and other methods of regulating the motion of machinery which have been just described, are adapted principally to cases in which the proportion of the resistance to the load is subject to certain fluctuations or gradual changes, or at least to cases in which the resistance is not at any time entirely withdrawn, nor the energy of the power actually suspended. Circumstances, however, frequently occur in which, while the power remains in full activity, the resistance is at intervals suddenly removed and as suddenly again returns. On the other hand, cases also present themselves, in which, while the resistance is continued, the impelling power is subject to intermission at regular periods. In the former case, the machine would be driven with a ruinous rapidity during those periods at which it is relieved from its load, and on the return of the load every part would suffer a violent strain, from its endeavour to retain the velocity which it had acquired, and the speedy destruction of the engine could not fail to ensue. In the latter case, the motion would be greatly retarded or entirely suspended during those periods at which the moving power is deprived of its activity, and, consequently, the motion which it would communicate would be so irregular as to be useless for the purposes of manufactures.

It is also frequently desirable, by means of a weak but continued power, to produce a severe but instantaneous effect. Thus a blow may be required to be given by the muscular action of a man’s arm with a force to which, unaided by mechanical contrivance, its strength would be entirely inadequate.

In all these cases, it is evident that the object to be attained is, an effectual method of accumulating the energy of the power so as to make it available after the action by which it has been produced has ceased. Thus, in the case in which the load is at periodical intervals withdrawn from the machine, if the force of the power could be imparted to something by which it would be preserved, so as to be brought against the load when it again returned, the inconvenience would be removed. In like manner, in the case where the power itself is subject to intermission, if a part of the force which it exerts in its intervals of action could be accumulated and preserved, it might be brought to bear upon the machine during its periods of suspension. By the same means of accumulating force, the strength of an infant, by repeated efforts, might produce effects which would be vainly attempted by the single and momentary action of the strongest man.

(309.) The property of inertia, explained and illustrated in the third and fourth chapters of this volume furnishes an easy and effectual method of accomplishing this. A mass of matter retains, by virtue of its inertia, the whole of any force which may have been given to it, except that part of which friction and the atmospheric resistance deprives it. By contrivances which are well known and present no difficulty, the part of the moving force thus lost may be rendered comparatively small, and the moving mass may be regarded as retaining nearly the whole of the force impressed upon it. To render this method of accumulating force fully intelligible, let us first imagine a polished level plane on which a heavy globe of metal, also polished, is placed. It is evident that the globe will remain at rest on any part of the plane without a tendency to move in any direction. As the friction is nearly removed by the polish of the surfaces, the globe will be easily moved by the least force applied to it. Suppose a slight impulse given to it, which will cause it to move at the rate of one foot in a second. Setting aside the effects of friction, it will continue to move at this rate for any length of time. The same impulse repeated will increase its speed to two feet per second. A third impulse to three feet, and so on. Thus 10,000 repetitions of the impulse will cause it to move at the rate of 10,000 feet per second. If the body to which these impulses were communicated were a cannon ball, it might, by a constant repetition of the impelling force, be at length made to move with as much force as if it were projected from the most powerful piece of ordnance. The force with which the ball in such a case would strike a building might be sufficient to reduce it to ruins, and yet such force would be nothing more than the accumulation of a number of weak efforts not beyond the power of a child to exert, which are stored up, and preserved, as it were, by the moving mass, and thereby brought to bear, at the same moment, upon the point to which the force is directed. It is the sum of a number of actions exerted successively, and, during a long interval, brought into operation at one and the same moment.

But the case which is here supposed cannot actually occur; because we have not usually any practical means of moving a body for any considerable time in the same direction without much friction, and without encountering numerous obstacles which would impede its progress. It is not, however, essential to the effect which is to be produced, that the motion should be in a straight line. If a leaden weight be attached to the end of a light rod or cord, and be whirled by the force of the arm in a circle, it will gradually acquire increased speed and force, and at length may receive an impetus which would cause it to penetrate a piece of board as effectually as if it were discharged from a musket.

The force of a hammer or sledge depends partly on its weight, but much more on the principle just explained. Were it allowed merely to fall by the force of its weight upon the head of a nail, or upon a bar of heated iron which is to be flattened, an inconsiderable effect would be produced. But when it is wielded by the arm of a man, it receives at every moment of its motion increased force, which is finally expended in a single instant on the head of the nail, or on the bar of iron.

The effects of flails in threshing, of clubs, whips, canes, and instruments for striking, axes, hatchets, cleavers, and all instruments which cut by a blow, depend on the same principle, and are similarly explained.

The bow-string which impels the arrow does not produce its effect at once. It continues to act upon the shaft until it resumes its straight position, and then the arrow takes flight with the force accumulated during the continuance of the action of the string, from the moment it was disengaged from the finger of the bow-man.

Fire-arms themselves act upon a similar principle, as also the air-gun and steam-gun. In these instruments the ball is placed in a tube, and suddenly exposed to the pressure of a highly elastic fluid, either produced by explosion as in fire-arms, by previous condensation as in the air-gun, or by the evaporation of highly heated liquids as in the steam-gun. But in every case this pressure continues to act upon it until it leaves the mouth of the tube, and then it departs with the whole force communicated to it during its passage along the tube.

(310.) From all these considerations it will easily be perceived that a mass of inert matter may be regarded as a magazine in which force may be deposited and accumulated, to be used in any way which may be necessary. For many reasons, which will be sufficiently obvious, the form commonly given to the mass of matter used for this purpose in machinery is that of a wheel, in the rim of which it is principally collected. Conceive a massive ring of metal, _fig. 149._, connected with a central box or nave by light spokes, and turning on an axis with little friction. Such an apparatus is called a fly-wheel. If any force be applied to it, with that force (making some slight deduction for friction) it will move, and will continue to move until some obstacle be opposed to its motion, which will receive from it a part of the force it has acquired. The uses of this apparatus will be easily understood by examples of its application.