The face of the steel is then cleaned, and by proper appli cation of the mechanical means of turning, boring, and filing, the superfluous steel is taken away, and the balance is left, consisting of two, or sometimes three, radii, and a rim, the external part of which is of brass, and the internal part of steel, the former metal being about twice the thickness of the latter. In this state the arms of the rim are then cut through and diminished in their length, as in the figure ; and near that extremity of each arc which is farthest from its radius, is put on a piece or weight, which can be elided along the arm, so as to be adjusted at that distance which shall be found, upon trial, to produce a good performance under the different changes of temperature; the flexure of the arms by the change of temperature carrying the weights nearer to the centre in hot than in cold weather, and the more the greater the distance of the weights from the radius. The small screws near the ends of the radii afford an adjustment for time, as the balance will vibrate more quickly the further these are screwed in ; and the contrary will be the case if they be unscrewed or drawn further out.
The accompanying cut shows a balance according to the construction of Arnold, and specified by him to the com missioners of longitude. The expansion weights are cylindrical, and are adjusted upon the arms by screwing ; and there is an inner rim, upon which three weights are adjusted by sliding, which serve to regulate the going of the time-piece in different posi tions. The necessity of a different adjust ment of the balance, according as the balance is to vibrate with its axis vertical to the horizon, or parallel to it, will be obvious when we consider that the pivots of the axis bear very differently according to the position of the chronometer ; and it requires some management to make the frictions the same, whether the axis be turning upon one of its ends, or upon the two cylindrical faces of the pivots ; and still more than this, since the balance itself has a permanent figure com pared with the spring, which, in every part of its vibration, alters its distance from the axis, and in every part of its length has a different degree of rotatory motion ; it cannot be expected, nor does it happen, that a balance, which is found to be in poize along with its spring when out of the chronometer, will make equal vibrations, as to time, in all positions when in its place ; and in addition to these difficulties, there is one part of the vibration where the force of the spring and the inertia of the balance are not simply in opposition to each other, but are combined with the maintaining power, viz. during the action
of the escape. The remedy for all these difficulties, which is happily adopted in chronometers for use at sea, is to place the axis in a vertical position, by which means the balance itself is not affected by gravity ; but for pocket time pieces, the ingenuity of the artist is called upon for expedients of which it would not be easy to exhibit a complete theory. The general principle com monly used, is to consider the balance, when out of adjustment for position, as a pendulum when above and below the centre of suspension, acted upon by gravity, and, at the same time, urged to a quiescent point by the force of elas ticity. In these circumstances the vibrations will be quickest when the point of stable equilibrium is downward, and they will be slowest in the opposite positions of the machine. This leads to the remedy of diminishing either the radius or the weight on that side which is lowest when the rate is most quick. Thus, if one of the two adjusting screws in the first of the preceding balances were downwards in the position of quickest rate, that screw would require to be screwed a very little quantity inwards, and the opposite screw to be screwed a like quantity outwards, in order to remedy this imperfection without much alteration of the other adjustments. And if la like imperfection were found in the vibrations of the balance when tried in a vertical position, having the lowest point at rest in a line at right angles to a line passing through the radii, a similar alteration must be made in the expansion weights, either by a careful flexure of the circular arcs, or by altering the quantities of those weights ; or else by means of small circular screws to ed into the weights themselves, and directed towards the centre like the w • is at the extremities of the radii. By these, and other correspondent means, e balance may be made to keep time in all those positions wherein its plane shall be perpendicular to the horizon ; but even in these trials very great pains and labour may be required to produce a high degree of accuracy ; and, after all, as the quantity of action in the spring must alter the quantity of pendulous effect in this curious and delicate time measurer, it may be doubted whether the adjustments for position in the vertical balance can be effectual any longer than while the arcs of vibration remain the same. This consideration points to the necessity of an adjustment in the maintaining power, in order that the vibrations shall not fall off; the means of effecting this will be shown in treating of the different sorts of escape ments, to the consideration of which we shall now proceed.