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 at P will have a greater tendency to fall by gravitation towards o than it would have at p, because the acclivity of the arch descending towards o at P is greater than its acclivity at p. The gravitation, therefore, or tendency of the ball to fall towards the central axis being greater at P than at p it will be able to resist a greater centrifugal force. This increased centrifugal force, which the ball would have revolving at the distance P above what it would have at the distance p, 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 at p be greater than its velocity at p, 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 which P will have to travel over, as it will have to be

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

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 inchi 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 throttlevalve 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.

(127.) Having thus explained the principal mechanical contrivances provided by Watt for the maintenance and regulation of the rotatory motion to be produced by his double-acting steam engine, let us now consider the machine as a whole, and investigate the process of its operation. A section of this engine is represented in fig. 43.

Steam is supplied from the boiler to the cylinder by the steam pipe s. The throttle-valve T in that pipe, near the cylinder, is regulated by a system of levers connected with

the governor. The piston P is accurately fitted in the steam cylinder c by packing, as already described in the singleacting engine. This piston, as it moves, divides the cylinder into two compartments, between which there is no communication by which steam or any other elastic fluid can pass. The upper steam box в is divided into three compartments by the two valves. Above the upper steam valve v is a compartment communicating with the steam pipe; below the upper exhausting valve E is another compartment communicating with the eduction pipe which leads to the condenser. By the valves v and E a communication may be opened or closed between the boiler on the one hand, or the condenser on the other, and the top of the cylinder. The continuation s' of the steam pipe leads to the lower box B', which, like the upper, is divided into three compartments by two valves v' and E'. The upper compartment communicates with the steam pipe, and thereby with the boiler; and the lower compartment communicates with the eduction pipe, and thereby with the condenser. By means of the two valves v' and E', a communication may be opened or closed between the steam pipe on the one hand, or the exhausting pipe on the other, and the lower part of the cylinder. The four valves V, E, v', and E' are connected by a system of levers with a handle or spanner m, which, being driven downwards or upwards, is capable of opening or closing the valves in pairs, in the manner already described (116.). The condensers, the air-pump, and the hot-water pump, are in all respects similar to those already described in the single-acting engine, except that the condensing jet is governed by a lever 1, by which it is allowed to play continually in the condenser, and by which the quantity of water admitted through it is regulated. The cold-water pump N is worked by the engine as already described in the single-acting engine, and supplies the cistern in which the air-pump and condenser are submerged, so as to keep down its temperature to the proper limit. On the air-pump rod R are two pins properly placed, so as to strike the spanner m, upwards and downwards, at the proper times, when the piston approaches the termination of the stroke at the top or bottom of the cylinder. The pump L

conducts the warm water drawn by the air-pump from the condenser to a proper reservoir for feeding the boiler. The

vertical motion of the piston-rod in a straight line is rendered compatible with the circular motion of the end of the beam by the parallel motion already described. The point b, on the beam, moves upwards and downwards in a circular arch, of which the axis of the beam is the centre. In like manner the point d of the rod dc moves upwards and downwards, in a similar arch of which the fixed pivot c is the centre. The joint or bar db, which joins these two pivots, will be moved so that its middle point e will ascend and descend nearly in a straight line, as has been already explained (120.); op