The simplest of all the methods of regulating the velocity of the train, and one which certainly existed before De Vick’s time, is the fan fly, or a pair of arms with vanes which are resisted by the air. I think it by no means improbable, though it is never likely to be ascertained now, that some of those earlier clocks were trains of wheels with a fly to regulate their velocity, instead of a balance, which De Vick used in his going part, though he had a fly in the striking part, as the earlier English clocks have, and exactly as it is used to this day.
So long as the force and friction of the train are uniform the velocity of the fly will be uniform, as the variation of density of the air is too small to affect it materially; and it should be observed, that a long fly with a rather slow motion is less affected by variations of force than a short and quick one; but as far more accurate methods are now used, it is unnecessary to go further into this.
A fly wheel, which is either a wheel with a heavy rim or a pair of weighted arms at right angles to the axis which carries them, is another method; but not so good, because, not being resisted by the air nearly so much as fans, it is much more affected by a change of force, which in clock work nearly always means a change of friction in the train. It acts simply by its moment of inertia, which is constant, and therefore the velocity cannot be constant if the force varies.
In fact there is theoretically no limit to the velocity of a fly wheel driven by a weight, so long as the weight can go on falling, though practically a terminal velocity is soon reached, when the friction and the increasing resistance of the air balance the force; but of course this balance is disturbed and the velocity changes as soon as the force varies. Conical Pendulum. A pair of weighted arms attached to a revolving vertical axis by horizontal hinges, so that they can fly farther out as they go, will regulate the velocity more completely than a fly wheel or arms rigidly fixed, and still better if it has fans attached to it, but not completely enough to keep it uniform if the force varies much.
They are like the ‘governor’ of a steam engine in appearance, but no further; for the governor arms work a lever which opens more or less of the throttle valve of the steam pipe, according as the engine is going too slow or too fast.
A single ball or pair of balls hung in this way and driven by a clock train form what is called a conical pendulum, because each arm describes a cone, and the time of its revolution may easily be determined as follows, except so far as it is affected by friction and resistance of air:— Let l be the length of each arm, and the angle at which it happens to be inclined to the vertical axis, which of course depends on the rate of revolution or angular velocity, which is usually called !; then the centrifugal force of each ball = !2l sin ; and as that is the force which keeps the balls away from the vertical, it must balance the force which draws them to it, which is g tan (g being the usual symbol for the force of gravity, or twice the number of feet which a body falls in the first second of time, and g in this latitude is 32.2); therefore ! or the angular space moved over by the arms in one
Fig. 5: Revolving Pendulum
second = p g l cos , and the time of a complete revolution through 360 or 2, is 2 ! = 2 pl cos g . If you wish to know what that means in figures, you must express l in feet, as g is, and write the numerical value 3.14159 for , and take the numerical value of cos from a table of sines and cosines; and the result, after extracting the square root and dividing, is the number of seconds in which the revolution is performed. We shall see hereafter that it is just so much less than the time of a common vibrating pendulum of the same length as p cos is less than 1.
And as the cosine varies least when an angle is small, a clock of this kind will go better when the length of the arms and the weight of the balls are such that they make only a small angle with the axis when the clock weight is driving them. But again it must be remembered that these results are very much modified in actual working by the resistance of the air, which acts more strongly on the balls as they fly farther out, and thereby tends to regulate the velocity, as it does with a fan fly.
A clock of this kind is often used to turn the reflectors or coloured lenses of revolving lighthouses, and also for the more accurate purpose of driving large equatorial telescopes, to keep them pointed to a star notwithstanding the revolution of the earth.
For the earth does not move by jerks, as a clock with a vibrating pendulum and escapement necessarily does. A revolving pendulum alone will not do without some contrivance to equalise the force upon it, or to check the pendulum itself by friction.
The simplest form of it is setting the revolving balls within a conical ring, which they can graze slightly, and it is better if they are furnished with slight grazing springs. And if the cone is also made raisable by a handle within reach of the observer, so that he can regulate the friction, probably this is enough in all ordinary cases.
But for telescopes of great importance superior contrivances are used. The chronograph at Greenwich, which drives a barrel covered with paper, on which the times of various observations are pricked by galvanic communication from the observers, is an ordinary clock with a revolving pendulum, driven by an arm which also carries round a kind of spade, dipped a little into an annular trough of water; and the farther out the pendulum swings the deeper it pushes the spade into the water, by a simple lever arrangement which can easily be imagined.
The great equatorial telescope there has a similar pendulum and trough; but besides that, the clock is itself driven by a ‘Barker’s mill,’ or a pair of revolving horizontal arms on a vertical axis, all hollow and receiving water at the top of the axis. The arms have holes near their ends, on opposite sides, and the water flowing out there drives the arms the other way. The pendulum also works a throttle valve as the governor of a steam engine does, and so regulates the flow of water through the mill.
A revolving pendulum may be hung by a single wire, as there is no tendency to twist, and they are so made in bedroom clocks, which have the advantage of being silent.
But it is difficult to get a wire strong enough for a heavy pendulum which would not also be too stiff. The Greenwich ones are hung by a kind of universal joint, made of two pairs of suspension springs in stirrups, set across each other, one turned upwards and the other downwards, with a cross between.
We shall have to notice afterwards some other clocks for this purpose, in which a revolving continuous movement is combined with a vibrating pendulum and escapement; but I must describe escapements first.
It is perhaps worth mentioning that any point in a wheel revolving uniformly has always the same velocity in a horizontal direction as some point in a pendulum which makes a double vibration in the same time as the wheel revolves; and therefore, theoretically, a constant motion of a clocktrain might be got by connecting some point in a 1 sec. pendulum with a pin in a small disc revolving in 2 seconds, by a rod so long as to be practically horizontal. But it would probably be impracticable to keep the force constant enough to give just proper impulse to the pendulum; and if too much was given, there would be a jerk at the end of every beat, and if too little, the pendulum and the clock would stop.