An improvement is to have the weights threaded on to the bar, like a nut on to a bolt, so that they may be moved outwards or inwards by being rotated on the bar, and they will remain where they are put however the direction of the bar may be changed. This second balance is applicable to portable clocks.

The modern form of balance is that of a relatively heavy wheel, or rather rim of a wheel, united to the hub by light spokes.

In all of these cases the balance may turn on its axis in one continuous direction, after the manner of a revolving wheel, and the only thing that prevents it from doing so is the action of the escapement which will be explained hereafter.

R

Now, a pendulum oscillates, when set in motion, by the action of gravity, altogether independently of the escapement, and one of the uses of the escapement is to overcome the friction and resistance of the atmosphere and keep up the motion.

And to accomplish the same thing with the balance, upon which gravity has no moving effect, a spring, called the hair spring, is made use of.

Hence it appears that the parts of the modern balance are 1, the pivoted axis supporting the bar or wheel, 2, the bar or wheel, and 3, the hair spring. Let us consider these in order.

1. The axis. The axis rotates on pivots at the ends so that there is always a certain amount of friction in the action of the balance. And although this friction can be reduced to a minimum by the use of small pivots turning in bearings made of some very hard material such as ruby or sapphire, yet it cannot be eliminated.

Also, to prevent undue wear oil must be used in the bearings, and as the best oil deteriorates with use and exposure the friction is not invariable. Hence the pendulum, which moves without friction in itself, must necessarily be superior to the balance as a governor.

2. The bar, or wheel, of the Balance. In all watches and marine clocks, as portable clocks are often called, the wheel form of balance is used, but in some of the best ship's chrono

meters a modified form of the bar is still employed, as it is believed to give better results along certain lines.

The wheel or rim of the balance is the analogue of the bob of the pendulum, and should therefore be relatively heavy as compared with spokes or arms which join it to the hub.

Any small section of the rim with a connecting spoke turns about a centre in the same way as a pendulum does in its oscillation, and has therefore a centre of oscillation. And these centres, for all the segments which make up the balance, lie on a circle which we may call the circle of oscillation. The radius of this circle is the effective radius of the balance.

With all other things remaining the same, if we increase the effective radius the balance will, under the same impulse, move more slowly; and if we diminish this radius the motion of the balance will be accelerated.

But if the small weights in the bar balance be moved outwards the effective radius is increased, and if inwards it is decreased. And hence regulation is effected by moving the weights outwards when the clock is gaining time, or going too fast, and inwards when the clock is going too slow.

This is the usual way of regulating a bar balance, but with a wheel balance other methods are commonly employed, and sometimes in conjunction with this.

3. The hair-spring. This is a long delicate spring coiled into a flat helix.

It is fastened at its inner end into a collar which fits on the shaft or axis with sufficient closeness to prevent it from shifting by any action of the spring, but so that its position

may be changed if necessary in order to adjust the spring. At its outer end it is pinned to a stud in the frame of the machine. This spring holds the balance in a position of rest, or a neutral position in relation to the frame. If the balance be moved from this position, in either direction, and let go, the tension of the spring brings it back to the neutral position; but the momentum of the balance carries it past this position nearly as far on the other side, and thus the balance oscillates back and forth, somewhat after the manner of the pendulum, until it is brought to rest by friction on the pivots and atmospheric resistance.

With the hair-spring the balance moves more definitely and is much less under the disturbing influence of the escapement than where no spring is present, so much so, in fact, that a portable clock without a hair-spring would at the present day be regarded as an ancient curiosity.

The force, which brings the pendulum back to the vertical after it has been displaced, is not quite proportional to the angle through which it has been displaced, and through which it must turn to reach the vertical again. And this is the cause of the circular error. But in the case of the balance, the tension of the hair-spring is exactly proportional to the amount of bending, or to the angle through which the balance has turned away from neutral position or, in other words, the force of restitution is exactly proportional to the angular displacement. So that in the balance there is nothing corresponding to the circular error in the pendulum, and the time of oscillation is independent of the angle through which the balance swings. In this one respect, and probably in this alone, the balance has a superiority over the pendulum.

Thermometric error. Change of temperature has no effect whatever upon the force of gravity under whose action a pendulum swings, but it has a decided influence over the hairspring of the balance, for a spring of any kind is somewhat weaker at a high temperature than at a low temperature. And other things being the same, the time of the oscillation of the balance varies with the strength of the hair-spring, so that the balance will swing more slowly in warm weather than it will in cold weather.

Also, when the balance expands, as it does under a rise of temperature, the rim is carried outwards by the expansion of the spokes, and the effective radius is thus increased, and the balance, on account of the increase in its momentum, swings more slowly; while the opposite effect follows a reduction of temperature.

On both of these accounts a watch, which keeps correct time at a mean temperature, will lose when the temperature rises, and gain when the temperature falls, or will lose in summer and gain in winter.

Compensation of the balance. We have seen that the effects of a change of temperature upon the hair-spring and upon the arms of the balance act in the same direction, that is

they both tend to make the watch gain, or to make it lose, as the case may be. And this is according to the natural and unchangeable order of things.

If these two sources of error could be so arranged as to oppose and neutralize one another, the variation due to change of temperature might be largely if not wholly overcome.

From the delicacy and nature of the hair-spring it is not easy to see how any effective change could well be made in it, so that if anything is to be done we must give our attention to the rim of the balance.

Brass
Steel

Let two thin strips of metal, one of brass and the other of steel, be soldered together throughout their whole length, and be bent into a semicircular form, with the brass on the outside, as in the figure where the dark part denotes steel and the light brass.

A

B

Now, under a rise of temperature brass expands more than steel in the proportion of 87 to 53, so that the outer side of the curved bar will expand more than the inner, and the bar will become more curved. On the other hand when the temperature falls the outside of the bar will contract more than the inside and the bar will become less curved, or will tend to straighten out.

And thus, if the end A be fixed, the end B will move inwards towards h under a rise of temperature, and will move outwards towards c under a fall of temperature.

with.

Now consider the balance figured here

The rim is formed of a compound bar of brass and steel, with the brass on the outside, and is cut through at opposite A points, close to the arm, as clearly shown in D the illustration.

B

C

These

The semicircular bar AB, when warmed, will increase its curvature and bring B inwards towards the centre. For similar reasons D will also move toward the centre. movements tend to diminish the effective radius of the balance and thus accelerate the oscillations.

On the other hand, with a reduction of temperature both B and D will move outwards thus tending to increase the effective radius of the balance and to retard the oscillations. And if matters be properly arranged, these changes, which are directly opposed to those of the hair-spring, may be made to correct the latter almost completely.

For greater effect the arcs of the balance carry small weights, and by shifting these weights, which must be so carefully done as not to disturb the equilibrium of the balance, the compensation may be varied at will between certain limits.

Where weights are not employed the arcs of the rim are usually loaded with heavy screws, as represented in the figure, and some little variation may be made in the compensation by screwing these inwards or outwards.

A steel hair-spring weakens, not in proportion to the rise in temperature, but at an increasing rate. So that an amount of compensation that would serve between 20°F. and 60°F. would not be sufficient for temperatures far above 60°F., such as 100°F. say, and probably no compensation that could be devised would be applicable to all temperatures.

For pocket watches these secondary sources of variation are usually ignored in the presence of greater sources arising from continual changes in position during the day, and a fixed position during the night. But in the chronometer, where change of position is avoided as much as possible by placing the machine in gimbals so as to have the dial upwards and horizontal, it is well to consider and correct every source of error in as far as it is possible to do so.

For this purpose glass hair-springs have sometimes been employed, as the weakening of a glass spring, under a rise of temperature, is more uniform in character than that of a steel one.

Mr. Dent, the celebrated chronometer maker of London, from his experiments with a glass hair-spring, arrived at the following results:

A balance that at 32°F. made 3606 swings in an hour, made 3598.5 swings at 66°F., and 3599 at 100°F. The irregularity, or seeming irregularity, of action is here very apparent, as the balance would naturally be supposed to swing more slowly at 100°F. than at 66°F., while the reverse is the case.