(119.)

Fig. 35.

Watt first proposed to effect this by attaching to the end of the piston-rod a straight rack, faced with teeth, which should work in corresponding teeth raised on the arch head of the beam, as represented infig.35.If his improved steam engines required no further precision of operation and construction than the atmospheric engines, this might have been sufficient; but in these engines it was indispensably necessary that the piston-rod should be guided with a smooth and even motion through the stuffing-box in the top of the cylinder, otherwise any shake or irregularity would cause it to work loose in the stuffing-box, and either to admit the air, or to let the steam escape. Under these circumstances, the motion of[Pg195]the rack and toothed arch head were inadmissible, since it was impossible by such means to impart to the piston-rod that smooth and equable motion which was requisite. Another contrivance which occurred to Watt was, to attach to the top of the piston-rod a bar, which should extend above the beam, and to use two chains or straps, one extending from the top of the bar to the lower end of the arch head, and the other from the bottom of the bar to the upper end of the arch head. By such means the latter strap would pull the beam down when the piston would descend, and the former would pull the beam up when the piston would ascend. These contrivances, however, were superseded by the celebrated mechanism since called theParallel Motion, one of the most ingenious mechanical combinations connected with the history of the steam engine.

(119.)It will be observed that the object was to connect by some inflexible means the end of the piston-rod with the extremity of the beam, and so to contrive the mechanism, that while the end of the beam would move alternately up and down in part of a circle, the end of the piston-rod connected with the beam should move up and down in a straight line. If the end of the piston-rod were fastened upon the end of the beam by a pivot without any other connection, it is evident that, being moved up and down in the arch of a circle, it would be drawn to the left and the right alternately, and would consequently either be broken or bent, or would work loose in the stuffing-box. Instead of connecting the end of the rod immediately with the end of the beam by a pivot, Watt proposed to connect them by certain moveable rods, so arranged that, as the end of the beam would move up and down in the circular arch, the rods would so accommodate themselves to that motion, that the end connected with the piston-rod should not be disturbed from its rectilinear course.

To explain the principle of the mechanism called the parallel motion, let us suppose thatO P(fig.36.) is a rod or lever moveable on a centreO, and that the endPof this rod shall move through a circular archP P′ P″ P‴a vertical plane, and let its play be limited by two stopsS, which shall prevent its ascent above the pointP, and its descent below[Pg196]the pointP‴. Let the position of the rod and the limitation of its play be such that the straight lineA Bdrawn throughPandP‴, the extreme positions of the leverO P, shall be a vertical line.

Fig. 36.

Letobe a point on the other side of the vertical lineA B, and let the distance ofOto the right ofA Bbe the same as the distance ofoto the left ofA B. Leto pbe a rod equal in length toO P, moving likeO Pon the centreo, so that its[Pg197]extremitypshall play upwards and downwards through the archp p′ p″ p‴, its play being limited in like manner by stopss.

Now, let us suppose that the endsPpof these two rods are joined by a linkPp, the connection being made by a pivot, so that the angles formed by the link and the rods shall be capable of changing their magnitude. This link will make the motion of one rod depend on that of the other, since it will preserve their extremitiesPpalways at the same distance from each other. If, therefore, we suppose the rodO Pto be moved to the positionO P‴, its extremityPtracing the archP P′ P″ P‴, the link connecting the rods will at the same time drive the extremitypof the rodo pthrough the archp p′ p″ p‴so that when the extremity of the one rod arrives atP‴, the extremity of the other rod will arrive atp‴. By this arrangement, in the simultaneous motion of the rods, whether upwards or downwards, through the circular arches to which their play is limited, the extremities of the link joining them will deviate from the vertical lineA Bin opposite directions. At the limits of their play, the extremities of the link will always be in the lineA B; but in all intermediate positions, the lower extremity of the link will be to the right ofA B, and its upper extremity to the left ofA B. So far as the derangement of the lower extremity of the link is concerned, the matter composing the link would be transferred to the right ofA B, and so far as the upper extremity of the link is concerned, the matter composing it would be transferred to the left ofA B.

By the combined effects of these contrary derangements of the extremities of the link from the vertical line, it might be expected that a point would exist, in the middle of the link, where the two contrary derangements would neutralise each other, and which point would therefore be expected to be disturbed neither to the right nor to the left, but to be moved upwards and downwards in the vertical lineA B. Such is the principle of the parallel motion; and in fact the middle point of the link will move for all practical purposes accurately in the vertical lineA B, provided that the angular play of the leversO Pando pdoes not exceed a certain[Pg198]limit, within which, in practice, their motion may always be restrained.

To trace the motion of the middle point of the link more minutely, letP P′ P″ P‴be four positions of the leverO P, and letp p′ p″ p‴be the four corresponding positions of the levero p. In the positionsO Po p, the link will take the positionPp, in which the entire link will be vertical, and its middle pointxwill therefore be in the vertical lineA B.

When the one rod takes the positionO P′, the other rod will have the positiono p′; and the link will have the positionP′p′. The middle point of the link will be atx′, which will be found to be on the vertical lineA B. Thus one half of the linkP′x′will be to the left of the vertical lineA B; while the other half,p′ x′, will be to the right of the vertical line; the derangement from the vertical line affecting each half of the link in contrary directions.

Again, taking the one rod in the positionO P″, the corresponding position of the other rod will beo p″, and the position of the link will beP″p″. If the middle point of the link in this position be taken, it will be found to be atx″, on the vertical lineA B; and, as before, one half of the linkP″x″will be thrown to the left of the vertical line, while the other halfp″ x″, will be thrown to the right of the vertical line.

Finally, let the one rod be in its lowest position,O P‴, while the other rod shall take the corresponding position,o p‴. The direction of the linkP‴p‴will now coincide with the vertical line; and its middle pointx‴will therefore be upon that line. The previous derangement of the extremities of the rod, to the right and to the left, are now redressed, and all the parts of the rod have assumed the vertical position.

It is plain, therefore, that by such means the alternate motion of a point such asPorp, upwards and downwards in a circular arch, may be made to produce the alternate motions of another pointx, upwards and downwards in a straight line.

(120.)Although the guidance of the air-pump rod in a true vertical line is not so necessary as that of the steam piston,[Pg199]and as the air-pump piston is always brought down by its own weight and that of its rod, the connection of the air-pump piston-rod with the beam, by any contrivance of the kind now described, was not so necessary. Nevertheless, by a slight addition to the mechanical contrivance which has been just described, Watt obtained the means of at once preserving the true rectilinear motion of both piston-rods.

Fig. 37.

Let the lever represented byO Pinfig.36.be conceived to be prolonged to twice its length, as represented infig.37., so thatO P′shall be twiceO P. Let the pointsPpbe connected by a link as before. Let a linkP′x′, equal in length to the linkPpbe attached to the pointP′, and let the extremityx′of this link be connected with the pointpby another link, equal in length toP P′, by pivots atx′andp, so that the figureP P′x′ pshall be a jointed parallelogram, the angles of which will be capable of altering their magnitude with every change of position of the rodso pandO P. Thus, when the rodO Pdescends, the angles of the parallelogram atPandx′will be diminished in magnitude, while the angles atP′andpwill be increased in magnitude. Now, let a line be conceived to be drawn fromOtox′. It is evident that that line will pass through the middle point of the linkpP, for the triangleO Pxis in all respects similar to the greater triangleO P′x′only on half the scale, so that every side of the one is[Pg200]half the corresponding side of the other. ThereforePxis half the length ofP′x′; butP′x′was made equal toPp, and thereforepxis half ofPp, that is to say,xis the middle point ofPp.

It has been already shown, that in the alternate motion of the rodso p,O Pin ascending and descending, the pointxis moved upwards and downwards in a true vertical line. Now since the triangleO Pxis in all respects similar toO P′x′, and subject to a similar motion during the ascent and descent of the rods, it is apparent that the pointx′must be subject to a motion in all respects similar to that which affects the pointsx, except that the pointx′will move through double the space. In fact, the principle of the mechanism is precisely similar to that of the common pantograph, where two rods are so connected as that the motion of the one governs the motion of the other, so that whatever line or figure may be described by one, a similar line or figure must be described by the other. Since, then, the pointxis moved upwards and downwards in a vertical straight line, the pointx′will also be moved in a vertical straight line of double the length.

If such an arrangement of mechanism as has been here described can be connected with the beam of the steam engine, so that while the pointx′is attached to the top of the steam piston, and the space through which it ascends and descends shall be equal to the length of the stroke of that piston, the pointxshall be attached to the rod of the air-pump piston, the stroke of the latter being half that of the steam piston, then the pointsx′andxwill guide the motion of the two pistons so as to preserve them in true vertical straight lines.

The manner in which these ideas are reduced to practice admits of easy explanation: let the pointObe the centre of the great working beam, and letO P′be the arm of the beam on the side of the steam cylinder. LetPbe a pivot upon the beam, at the middle point between its centreOand its extremityP′; and let the linksPp,P′x′, andPpbe jointed together, as already described. Let the point or pivotobe attached to some part of the fixed framing of the engine or engine house, and let the rodo p, equal to half the arm of the beam, be attached by a pivot to the corner of the parallelogram at[Pg201]p. Let the end of the steam piston-rod be attached to the corner of the parallelogramx′, and let the end of the air-pump be attached to the middle pointxof the linkPp; by which arrangement it is evident that the rectilinear motion of the two piston-rods will be rendered compatible with the alternate circular motions of the pointsP′andPon the beam.

Among the many mechanical inventions produced by the fertile genius of Watt, there is none which has excited such universal, such unqualified, and such merited admiration as that of the parallel motion. It is indeed impossible, even for an eye unaccustomed to view mechanical combinations, to behold the beam of a steam engine moving the pistons, through the instrumentality of the parallel motion, without an instinctive feeling of pleasure at the unexpected fulfilment of an end by means having so little apparent connection with it. When this feeling was expressed to Watt himself, by those who first beheld the performance of this exquisite mechanism, he exclaimed with his usual vivacity, that he himself, when he first beheld his own contrivance in action, was affected by the same sense of pleasure and surprise at its regularity and precision. He said, that he received from it the same species of enjoyment that usually accompanies the first view of the successful invention of another person.

"Among the parts composing the steam engine, you have doubtless," says M. Arago, "observed a certain articulated parallelogram. At each ascent and descent of the piston, its angles open and close with the sweetness—I had almost said with the grace—which charms you in the gestures of a consummate actor. Follow with your eye alternately the progress of its successive changes, and you will find them subject to the most curious geometrical conditions. You will see, that of the four angles of the jointed parallelogram, three describe circular arches, but the fourth which holds the piston-rod is moved nearly in a straight line. The immense utility of this result strikes mechanicians with even less force than the simplicity of the means by which Watt has attained it."

The parallel motion, of which there are several other varieties, depending, however, generally upon the same[Pg202]principle, formed part of a patent which Mr. Watt obtained in the year 1784, another part of which patent was for a locomotive engine, by which a carriage was to be propelled on a road. In a letter to Mr. Smeaton dated 22d October, in the same year, Watt says,—

"I have lately contrived several methods of getting entirely rid of all the chains and circular arches about the great levers of steam engines, and nevertheless making the piston-rods ascend and descend perpendicularly, without any sliding motions or right-lined guides, merely by combinations of motions about centres; and with this further advantage, that they answer equally well to push upwards as to pull downwards, so that this method is applicable to our double engines which act both in the ascent and descent of their pistons.

"A rotative engine of this species with the new motion which is now at work in our manufactory (but must be sent away very soon) answers admirably. It has cost much brain work to contrive proper working gear for these double engines, but I have at last done it tolerably well, by means of the circular valves, placed in an inverted position, so as to be opened by the force of the steam; and they are kept shut by the working gear. We have erected an engine at Messrs. Goodwyne and Co.'s brewery, East Smithfield, London."

Fig. 38.

(121.)By the contrivance which has been explained above, the force of the piston in ascending and descending would be conveyed to the working end of the beam; and the next problem which Watt had to solve was, to produce by the force exerted by the working end of the beam in ascending and descending a continuous motion of rotation. In the first instance he proposed to accomplish this by a crank placed upon the axle to which rotation was to be imparted, and driven by a rod connecting it with the working end of the beam. LetK(fig.38.) be the centre, to which motion is to be imparted by the working endHof the beam. On the axleKsuppose a short leverK Ito be fixed so that whenK Iis turned round the centreK, the axle must turn with it. Let an iron rod, the weight of which shall balance the piston and piston-rod at the other end of the beam, be connected by joints with the working endHof the beam, and the extremityIof the[Pg203]leverK I. As the endHof the beam is moved upwards and downwards, the leverK Iwill be turned round the centreK, taking successively the positions represented by faint lines in the figure; and thus a motion of continued rotation will be imparted to the axleK.

This simple and effectual expedient of producing a continued rotatory motion by a crank was abandoned by Watt, as already explained, by reason of a patent having been obtained upon information of his experiments surreptitiously procured. To avoid litigation, he therefore substituted for the crank the sun and planet wheel already described; but at the expiration of the patent, which restricted the use of the crank, the sun and planet wheel was discontinued in Watt's engine, and the crank restored.

(122.)Whether the crank or the sun and planet wheel be used, there is still a difficulty in the maintenance of a regular motion of rotation. In the various positions which the crank and connecting rod assume throughout a complete revolution, there are two in which the moving power loses all influence in impelling the crank. These positions are those which the crank assumes when the piston is at the top and bottom of the[Pg204]cylinder, and is just about to change the direction of its motion. When the piston is at the bottom of the cylinder, the pivotI(fig.38.), by which the connecting rodH Iis attached to the end of the crank, is immediately over the axleKof the crank, and under the pivotH, which joins the upper end of the connecting rod with the beam. In fact, in this position the connecting rod and crank are in the same straight line, extending from the end of the beam to the axle of the crank. The steam, on entering the cylinder below the piston, and pressing it upwards, would produce a corresponding downward force on the connecting rod atH, which would be continued along the connecting rod and crank to the axleK. It is evident that such a force could have no tendency to turn the crank round, but would expend its whole energy in pressing the axleKdownwards.

The other position in which the power loses its effect upon the crank is when the piston is at the top of the cylinder. In this case, the working end of the beam will be at the lowest point of its play, and the crank-pinIwill be immediately below the axleK; so thatKwill be placed immediately betweenHandI. When the steam presses on the top of the piston, it will expend its force in drawing the endHof the connecting rod upwards, by which the crank-pinIwill likewise be drawn upwards. It is evident that this force can have no effect in turning the crank round, but will expend its whole energy in producing an upward strain on the axleK.

If the crank were absolutely at rest in either of the positions above described, it is apparent that the engine could not be put in motion by the steam; but if the engine has been previously in motion, then the mass of matter forming the crank, and the axle on which the crank is formed, having already had a motion of rotation, will have a tendency to preserve the momentum it has received, and this tendency will be sufficient to throw the crankK Iout of either of those critical positions which have been described. Having once escaped these dead points, then the connecting rod forming an angle, however obtuse or acute, with the crank, the pressure or pull upon the former will have a tendency to produce rotation in the latter. As the crank revolves, however, the influence[Pg205]of the connecting rod upon it will vary according to the angle formed by the connecting rod and crank. When that angle is a right angle, then the effect of the connecting rod on the crank is greatest, since the force upon it has the advantage of the whole leverage of the crank; but according as the angle formed by the crank and connecting rod becomes more or less acute or obtuse in the successive attitudes which they assume in the revolution of the crank, the influence of the connecting rod over the crank varies, changing from nothing at the two dead points already described, to the full effect produced in the two positions where they are at right angles. In consequence of this varying leverage, by which the force with which the connecting rod is driven by the steam is transmitted to the axle on which the crank revolves, a corresponding variation of speed would necessarily be produced in the motion imparted to the crank. The speed at the dead points would be least, being due altogether to the momentum already imparted to the revolving mass of the crank and axle; and it would gradually increase and be greatest at the points where the effect of the crank on the connecting rod is greatest. Although this change of speed would not affect the actual mechanical efficacy of the machine, and although the same quantity of steam would perform the same work at the varying velocity as it would do if the velocity were regulated, yet this variation of speed would be incompatible with the purposes to which it was now proposed that the steam engine should be applied in manufactures. In these a regular uniform motion should be imparted to the main axle.

(123.)One of the expedients which Watt proposed for the attainment of this end was, by placing two cranks on the same axle, in different positions, to be worked by different cylinders, so that while one crank should be at its dead points, the other should be in the attitude most favourable for its action. This expedient has since, as we shall see, been carried into effect in steam vessels; but one more simple and efficient presented itself in the use of afly-wheel.

On the main axle driven by the crank Watt placed a large wheel of metal, as represented infig.43., called afly-wheel. This wheel being well constructed, and nicely balanced on its[Pg206]axle, was subject to very little resistance from friction; any moving force which it would receive it would therefore retain, and would be ready to impart such moving force to the main axle whenever that axle ceased to be driven by the power. When the crank, therefore, is in those positions in which the action of the power upon it is most efficient, a portion of the energy of the power is expended in increasing the velocity of the mass of matter composing the fly-wheel. As the crank approaches the dead points, the effect of the moving power upon the axle and upon the crank is gradually enfeebled, and at these points vanishes altogether. The momentum which has been imparted to the fly-wheel then comes into play, and carries forward the axle and crank out of the dead points with a velocity very little less than that which it had when the crank was in the most favourable position for receiving the action of the moving power.

By this expedient, the motion of revolution received by the axle from the steam piston is subject to no other variation than just the amount of change of momentum in the great mass of the fly-wheel, which is sufficient to extricate the crank twice in every revolution from the mechanical dilemma to which its peculiar form exposes it; and this change of velocity may be reduced to as small an amount as can be requisite by giving the necessary weight and magnitude to the fly-wheel.

(124.)By such arrangements the motion imparted to the main axleKwould be uniform, provided that the moving power of the engine be always proportionate to the load which it drives. But in the general application of the steam engine to manufactures it was evident that the amount of the resistance to which any given machine would be subject must be liable to variation. If, for example, the engine drive a cotton-mill, it will have to impart motion to all the spinning frames in that mill. The operation of one or more of these may from time to time be suspended, and the moving power would be relieved from a corresponding amount of resistance. If, under such circumstances, the energy of the moving power remained the same, the velocity with which the machines would be driven would be subject to variation, being increased whenever the operation of any portion of the machines usually[Pg207]driven by it is suspended; and, on the other hand, diminished when any increased number of machines are brought into operation. In fine, the speed would vary nearly in the inverse proportion of the load driven, increasing as the load is diminished, andvice versâ.

On the other hand, supposing that no change took place in the amount of the load driven by the engine, and that the same number of machines of whatever kind would have to be continually driven, the motion imparted to the main axle would still be subject to variation by the changes inevitable to the moving power. The piston of the engine being subject to an unvaried resistance, a uniform motion could only be imparted to it, by maintaining a corresponding uniformity in the impelling power. This would require a uniform supply of steam from the boiler, which would further imply a uniform rate of evaporation in the boiler, unless means were provided in the admission of steam from the boiler to the cylinder to prevent any excess of steam which might be produced in the boiler from reaching the cylinder.

Fig. 39.

Fig. 40.

This end was attained by a contrivance afterwards called thethrottle-valve. An axisA B(figs.39, 40.) was placed across the steam pipe in a ring of cast-ironD E, of proper thickness. On this axis was fastened a thin circular plateT, of nearly the same diameter as the steam pipe. On the outer endBof this axle was placed a short lever or handleB C, by which it could be turned. When the circular plateTwas turned into such a position as to be at right angles to the length of the tube, it stopped the passage within the tube altogether, so that no steam could pass from the boiler to the engine. On the other hand, when the handle was turned through a fourth of a revolution from this position, then the circular plateThad its plane in the direction of the length of the tube, so that its edge would be presented towards the current of steam flowing from the boiler to the cylinder. In that position the passage within the tube[Pg208]would be necessarily unobstructed by the throttle-valve. In intermediate positions of the valve, as that represented infigs.39, 40., the passage might be left more or less opened, so that steam from the boiler might be admitted to the cylinder in any regulated quantity according to the position given to the leverB C.

A view of the throttle-valve taken by a section across the steam pipe is exhibited infig.40., and a section of it through the axis of the steam pipe is represented infig.39.The form of the valve is such, that, if accurately constructed, the steam in passing from the boiler would have no effect by its pressure to alter any position which might be given to the valve; and any slight inaccuracy of form which might give a tendency to the steam to alter the position would be easily counteracted by the friction of the valve upon its axle. The latter might be regulated at pleasure.

By this expedient, however the evaporation of water in the boiler might vary within practical limits, the supply of steam to the cylinder would be rendered regular and uniform. If the boiler became too active, and produced more steam than was necessary to move the engine with its load at the requisite speed, then the throttle-valve was shifted so as to contract the passage and limit the supply of steam. If, on the other hand, the process of evaporation in the boiler was relaxed, then the throttle-valve was placed with its edge more directed towards the steam. Independently of the boiler, if the load on the engine was lightened, then the same supply of steam to the cylinder would unduly accelerate the motion. In this case, likewise, the partial closing of the throttle-valve would limit the supply of steam and regulate the motion; and if, on the other hand, the increase of load upon the engine rendered necessary an increased supply of steam, then the opening of the throttle-valve would accomplish the purpose. By these means, therefore, a uniform motion might be maintained, provided the vigilance of the engine-man was sufficient for the due management of the leverB C, and provided that the furnace under the boiler was kept in sufficient activity to supply the greatest amount of steam which would be necessary[Pg209]for the maintenance of a uniform motion with the throttle-valve fully opened.

(125.)Watt, however, soon perceived that the proper manipulation of the leverB Cwould be impracticable with any degree of vigilance and skill which could be obtained from the persons employed to attend the engine. He, therefore, adapted to this purpose a beautiful application of a piece of mechanism, which had been previously used in the regulation of mill-work, and which has since been well known by the name of theGovernor, and has always been deservedly a subject of much admiration.

The governor is an apparatus by which the axle of the fly-wheel is made to regulate the throttle-valve, so that the moment that the axle begins to increase its velocity, it shifts the position of the throttle-valve, so as to limit the supply of steam from the boiler, and thereby to check the increase of speed. And on the other hand, whenever the velocity of the axle is diminished, the leverB Cis moved in the contrary direction, so as to open more fully the passage for the steam, and accelerate the motion of the engine.

A small grooved wheelA B(fig.41.) is attached to a vertical spindle supported in pivots or socketsCandD, in which it is capable of revolving. An endless cord works in the grooveA B, and is carried over proper pulleys to the axle of the fly-wheel, where it likewise works in a groove. When this cord is properly tightened the motion of the fly-wheel will give motion to the wheelA B, so that the velocity of the one will be subject to all the changes incidental to the velocity of the other. By this means the speed of the grooved wheelA Bmay be considered as representing the speed of the fly-wheel, and of the machinery which the axle of the fly-wheel drives.

Fig. 41.

It is evident that the same end might be attained by substituting for the grooved wheelA Ba toothed wheel, which might be connected by other toothed wheels, and proper shafts, and axles with the axle of the fly-wheel.

A ring or collarEis placed on the upright spindle, so as to be capable of moving freely upwards and downwards. To this ring are attached by pivots two short levers,E F, the[Pg210]pivots or joints atEallowing these levers to play upon them. AtFthese levers are joined by pivots to other leversF G, which cross each other atH, where an axle or pin passes through them, and attaches them to the upright spindleC D. These intersecting levers are capable, however, of playing on this axle or pinH. To the endsGof these levers are attached two heavy balls of metalI. The leversF Gpass through slits in a metallic arch attached to the upright spindle, so as to be capable of revolving upon it. If the ballsIare drawn outwards from the vertical axis, it is evident that the endsFof the levers will be drawn down, and therefore the pivotsElikewise drawn down. In fact, the anglesE F Hwill become more acute, and the angleF E Fmore obtuse. By these means the sliding ringEwill be drawn down. To this sliding ringE, and immediately above it, is attached a grooved collar, which slides on the vertical spindle upwards and downwards with the ringE. In the grooved collar are inserted the prongs of a forkK, formed at the end of the leverK L, the fulcrum or pivot of the lever being atL. By this arrangement, when the divergence of the ballsIcauses the collarEto be drawn down, the forkK, whose prongs are inserted in the groove of that collar, is likewise drawn down; and, on the other hand, when, by reason of the ballsIfalling towards the[Pg211]vertical spindle, the collarEis raised, the forkKis likewise raised.

The ascent and descent of the forkKnecessarily produce a contrary motion in the other endNof the lever. This end is connected by a rod, or system of rods, with the endMof the short lever which works the throttle-valveT. By such means the motion of the ballsI, towards or from the vertical spindle, produces in the throttle-valve a corresponding motion; and they are so connected that the divergence of the ballsIwill cause the throttle-valve to close, while their descent towards the vertical spindle will cause it to open.

These arrangements being comprehended, let us suppose that, either by reason of a diminished load upon the engine or an increased activity of the boiler, the speed has a tendency to increase. This would impart increased velocity to the grooved wheelA B, which would cause the ballsIto revolve with an accelerated speed. The centrifugal force which attends their motion would therefore give them a tendency to move from the axle, or to diverge. This would cause, by the means already explained, the throttle-valveTto be partially closed, by which the supply of steam from the boiler to the cylinder would be diminished, and the energy of the moving power, therefore, mitigated. The undue increase of speed would thereby be prevented.

If, on the other hand, either by an increase of the load, or a diminished activity in the boiler, the speed of the machine was lessened, a corresponding diminution of velocity would take place in the grooved wheelA B. This would cause the ballsIto revolve with less speed, and the centrifugal force produced by their circular motion would be diminished. This force being thus no longer able fully to counteract their gravity, they would fall towards the spindle, which would cause, as already explained, the throttle-valve to be more fully opened. This would produce a more ample supply of steam to the cylinder, by which the velocity of the machine would be restored to its proper amount.

Fig. 42.

(126.)The principle which renders the governor so perfect a regulator of the velocity of the machine is difficult to be[Pg212]explained without having recourse to the aid of the technical language of mathematical physics. As, however, this instrument is of such great practical importance, and has attracted such general admiration, it may be worth while here to attempt to render intelligible the mechanical principles which govern its operation. LetS(fig.42.) be the point of suspension of a common pendulumS P, and letP O P′be the arch of its vibration, so that the ballPshall swing or vibrate alternately to the east and to the west of the lowest pointO, through the archesO P′andO P. It is a property of such an instrument that, provided the arch in which it vibrates be not considerable in magnitude, the time of its vibration will be the same whether the arch be long or short. Thus, for example, if the pendulum, instead of vibrating in the archP P′, vibrated in the archp p′, the time which it would take to perform its vibrations would be the same. If, however, the magnitude of the arch of vibration be increased, then a variation will take place in the time of vibration; but unless the arch of vibration be considerably increased, this variation will not be great.

Now let it be supposed that while the pendulumP P′continues to vibrate east and west through the archP P′, it shall receive such an impulse from north and south as would, if it were not in a state of previous vibration, cause it to vibrate between north and south, in an arch similar to the archP P′. This second vibration between north and south[Pg213]would not prevent the continuance of the other vibration between east and west; but the ballPwould be at the same time affected by both vibrations. While, in virtue of the vibration from east to west, the ball would swing fromPtoP′, it would, in virtue of the other vibration, extend its motion towards the north to a distance from the lineW Eequal to half a vibration, and will return from that distance again to the positionP′. While returning fromP′toP, its second vibration will carry it towards the south to an equal distance on the southern side ofW E, and it will return again to the positionP. If the combination of these two motions or vibrations be attentively considered, it will be perceived that the effect on the ball will be a circular motion, precisely similar to the circular motion of the balls of the governor already described.

Now the time of vibration of the pendulumS Pbetween east and west will not in any way be affected by the second vibration, which it is supposed to receive between north and south, and therefore the time the pendulum takes in moving fromPtoP′and back again fromP′toPwill be the same whether it shall have simultaneously or not the other vibration between north and south. Hence it follows that the time of revolution of the circular pendulum will be equal to the time of similar vibrations of the same pendulum, if, instead of having a circular motion, it were allowed to vibrate in the manner of a common pendulum.

If this point be understood, and if it also be remembered that the time of vibration of a common pendulum is necessarily the same whether the arch of vibration be small or great, it will be easily perceived that the revolving pendulum or governor will have nearly the same time of revolution whether it revolve in a large circle or a small one: in other words, whether the balls revolve at a greater or a less distance from the central spindle or axis. This, however, is to be understood only approximately. When the angle of divergence of the balls is as considerable as it usually is in governors, the time of revolution at different distances from the axis will therefore be subject to some variation, but to a very small one.[Pg214]

The centrifugal force (which is the name given in mechanics to that influence which makes a body revolving in a circle fly from the centre) depends conjointly on the velocity of revolution, and on the distance of the revolving body from the centre of the circle. If the velocity of revolution be the same, then the centrifugal force will increase in the same proportion as the distance of the revolving body from the centre. If, on the other hand, the distance of the revolving body from the centre remain the same, the centrifugal force will increase in the same proportion as the square of the time of vibration diminishes, or, in other words, it will increase in the same proportion as the square of the number of revolutions per minute. It follows from this, therefore, that the greater is the divergence of the balls of the governor, and the more rapidly they revolve, the greater will be their centrifugal force. Now this centrifugal force, if it were not counterbalanced, would give the balls a constant tendency to recede from the centre; but from the construction of the apparatus, the further they are removed from the centre the greater will be the effect of their gravitation in resisting the centrifugal force.

It is evident that the ball atPwill have a greater tendency to fall by gravitation towardsOthan it would have atp, because the acclivity of the arch descending towardsOatPis greater than its acclivity atp. The gravitation, therefore, or tendency of the ball to fall towards the central axis being greater atPthan atpit will be able to resist a greater centrifugal force. This increased centrifugal force, which the ball would have revolving at the distancePabove what it would have at the distancep, is produced partly by the greater distance of the ball from the central axis, and partly by the greater velocity of its motion. But it will be evident that the time of its revolution may nevertheless be the same, or nearly the same, at both distances. If it should appear that the actual velocity of its motion of revolution atPbe greater than its velocity atp, in the same proportion as the circles in which they revolve, then it is evident that the time of revolution would be as much increased by the greater space whichPwill have to travel over, as it will have to be[Pg215]diminished by the greater speed with which that space is traversed. The time of revolution, therefore, may be the same, or nearly the same, in both cases.

If this explanation be comprehended, it will not be difficult to apply it to the actual case of the governor. If a sudden increase of the energy of the moving power, or a diminution of the load, should give the machine an increased velocity, then the increased speed of the balls of the governor will give them an increased centrifugal force, which for the moment will be greater than the tendency of their gravitation to make them fall towards the vertical axis. This centrifugal force, therefore, prevailing, the balls will recede from the axis; but as they recede, their gravitation towards the vertical axis will, as has been already explained, be increased, and will become equal to the centrifugal force produced by the increased velocity, provided that velocity do not exceed a certain limit. When the balls, by diverging, get such increased gravitation as to balance the centrifugal force, then they will continue to revolve at a fixed distance from the vertical axis. When this happens, the time of the revolution must be nearly the same as it was before their increased divergence; in other words, the proportion of the moving power to the load will be so restored by the action of the levers of the governor on the throttle-valve that the machine will move at its former velocity, or nearly so.

The principle on which the governor acts, as just explained, necessarily supposes temporary disarrangements of the speed. In fact, the governor, strictly speaking, does not maintain a uniform velocity, but restores it after it has been disturbed. When a sudden change of motion of the engine takes place, the governor being immediately affected will cause a corresponding alteration in the throttle-valve; and this will not merely correct the change of motion, but it will, as it were, overdo it, and will cause a derangement of speed of the opposite kind. Thus if the speed be suddenly increased to an undue amount, then the governor being affected will first close the throttle-valve too much, so as to reduce the speed below the proper limit. This second error will again affect the governor in the contrary way, and the speed[Pg216]will again be increased rather too much. In this way a succession of alterations of effect will ensue until the governor settles down into that position in which it will maintain the engine at the proper speed.

To prevent the inconvenience which would attend any excess of such variations, the governor is made to act with great delicacy on the throttle-valve, so that even a considerable change in the divergence of the balls shall not produce too much alteration in the opening of that valve: the steam in the boiler should have at least 2 lbs. per square inch pressure more than is generally required in the cylinder. This excess is necessary to afford scope for that extent of variation of the power which it is the duty of the throttle-valve to regulate.

The governor is usually so adjusted as to make thirty-six revolutions per minute, when in uniform motion; but if the motion is increased to the rate of thirty-nine revolutions, the balls will fly to the utmost extent allowed them, being the limitation of the grooves in which their rods move; and if, on the other hand, the speed be diminished to thirty-four revolutions per minute, they will collapse to the lowest extent of their play. The duty of the governor, therefore, is to correct smaller casual derangements of the velocity; but if any permanent change to a considerable extent be made either in the load driven by the machine or in the moving power supplied to it from the boiler, then a permanent change is necessary to be made in the connection between the governor and the throttle-valve, so as to render the governor capable of regulating those smaller changes to which the speed of the machine is liable.

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