W A T C H It is almost impossible to move such a regulator little enough, and with sufficient accuracy, for a very small variation of rate. One way of obtaining greater accuracy, and probably the best, is to make the regulator movable by a tangent screw acting on its end, and capable of being j turned by the watch key. Another mode of giving a small motion to the regulator is by putting a portion of a wheel with teeth on it, and turning it by a small pinion with the index attached to it, so that the motion of the index exceeds that of the regulator itself as much as the radius of that wheel exceeds the radius of the pinion. Chronometers are regulated in a different way altogether. It is not expedient to alter the effective length of the spring after its length is once fixed. For it has long been ascertained that a spring does not give isochronous vibra tions at all lengths, but only at certain intervals ; and therefore it is necessary in an accurate timekeeper to use only one of those lengths of the spring which are found to be isochronous for different arcs of vibration ; and, that being fixed, the timing of the balance can only be done by altering its moment of inertia, and this is done in chrono meters by screws with heavy heads in the rim of the balance, set farther in or out as it is wanted to go faster or slower. In marine chronometers, where there is plenty of room for it, the balance-spring is generally made in a cylindrical form, with the coils all of the same diameter, instead of the flat spiral used in watches, though it does not seem to be quite clear that the cylindrical form is materially better than the other. The timing of a watch for position, as it is called, is a matter which requires some attention. If the balance is not exactly poised on its axis, it will have a tendency to take one position when the watch is carried vertically, as it always is in the pocket ; and the time of vibration will be affected by its disposition thus to act as a pendulum. The watch ought therefore to be tried with XII, IX, VI, and III successively upwards, and if it does not keep the same rate the balance is not properly poised. Marine chronometers, indeed, being set in gimbals (a ring with the two pivots into the box at right angles with the pivots which carry the chronometer), will remain horizontal, though not without some degree of motion under the motion of the ship ; and this gives the balance the further advantage of having its weight resting only on the end of the axis or verge, a position in which there is much less friction than that of a watch carried in the pocket ; but there it is not of so much consequence, because the balance is so much lighter than a chronometer balance. Compensated Balances. A pendulum requires scarcely any com pensation except for its own elongation by heat ; but a balance re quires compensation, not only for its own expansion, which increases its moment of inertia just like the pendulum, but far more on account of the decrease in the strength of the spring under increased heat. Dent, in a pamphlet on compensation balances, gave the following results of some experiments with a glass balance, which he nsed for the purpose on account of its less expansibility than a metal one : at 32 F. , 3606 vibrations in an hour ; at 66, 3598 5 ; and at 100, 3599. If therefore it had been adjusted to go right (or 3600 times in an hour) at 32, it would have lost 7i and 8i seconds an hour, or more than three minutes a-day, for each successive in crease of 34, which is about fifteen times as much as a common wire pendulum would lose under the same increase of heat ; and if a metal balance had been used instead of a glass one the ditl erence would have been still greater. The necessity for this large amount of compensation having arisen from the variation of the elasticity of the spring, the iirst attempts at correcting it were by acting on the spring itself in the manner of a common regulator. Harrison s compensation consisted of a compound bar of brass and steel soldered together, having one end fixed to the watch-frame and the other carrying two curb pins which embraced the spring, as was described at fig. 2. As the brass expands more than the steel, any increase of heat made the bar bend ; and so, if it was set the right way, it carried the pins along the spring, so as to shorten it. This contrivance is called a com pensation curb ; and it has often been reinvented, or applied in a Fi modified form. But there arc two objections to it : the motion of the curb pins does not correspond accurately enough to the varia tions in the force of the spring, and it disturbs the isochronism, which only subsists at certain definite lengths of the spring. The compensation which was next invented left the spring un touched, and provided for the variations of temperature by the construction of the balance itself. Fig. 3 shows the plan of the ordinary compensation balance. Each por tion of the rim of the balance is composed of an inner bar of steel with an outer one of brass soldered upon it, and carrying the weights b,b, which are screwed to it. As the temperature increases, the brass expanding must bend the steel inwards, and so carries the weights farther in, and diminishes the moment of inertia of the balance. The metals are generally soldered together by pouring melted brass round a solid steel disk, and the whole is afterwards turned and filed away till it leaves only the crossbar in the middle lying flat and the two portions of the rim standing edgeways. The first person who practised this method of uniting them appears to have been Thomas Earnshaw, who brought the chronometer to the state in which it has remained for the last century, with scarcely any alteration except more com plete compensation. The adjustment of a balance for compensation can only be done by trial, and requires a good deal of time. It must be done in dependently of that for time, the former by shifting the weights, because the nearer they are to the crossbar the less distance they will move over as the rim bends with them. The timing is done by screws with heavy heads (t,t, fig. 3), which are just opposite to the ends of the crossbar, and consequently not affected by the bend ing of the rim. The compensation may be done approximately by the known results of previous experience with similar balances ; and many watches are sold with compensation balances which have never been tried or adjusted, and sometimes with a mere sham compensation balance, not even cut through. Secondary Compensation. When chronometers had been brought to great perfection it was perceived that there was a residuary error, which was due to changes of temperature, but which no adjust ment of the compensation would correct. For, if the compensation was adjusted for two extreme temperatures, such as 32 and 100, then the chronometer gained at mean temperatures; and, if ad justed for any two mean temperatures, it would lose for all beyond them. This error was observed, and attempts were made to correct it before anybody had pointed out how it arose : this appears to have been first done in a paper in the Nautical Magazine by E. J. Dent in 1833 ; and he gave the following illustration of it. The variation of the force of the spring proceeds uniformly in proportion to the temperature, and therefore may be represented by a straight line inclined at some angle to another straight line divided into degrees of temperature. But the inertia of a balance of the common construction cannot be made to vary uniformly according to the temperature, but will vary more rapidly in cold than heat ; and con sequently its rate of variation can only be represented by a curve, and the curve can only be made to coincide with the straight line representing the rate of variation of the spring in two points, either two extremes, or two means, or one extreme and one mean point. The same thing may be shown mathematically, as follows. Let r be the distance of the compensation weights b, b, in fig. 3 (which we may assume for convenience to be the whole mass M of the balance) from the centre at some mean temperature, and let dr be their increase of distance due to a decrease of some given number of degrees of heat, under the action of the compensation bars. Then the new moment of inertia will be M (r" + 2rdr + dr-), and the ratio of the new to the old will be 1 + + ( ; and the term ( ) r r- / r J is now too large to be disregarded, as it might be in pendulums, where the compensation -7- is only required to be about ^th of the ( ) in a balance. It is found that an equal increase of temperature will produce an equal or rather a less motion ( - dr) of the weights towards the centre than from it at any given point ; but, calling it only equal, the ratio of the decreased moment of inertia to the original one will be 1 --- h ( ) , so that the r r J increase and the decrease from the mean amount differ by twice ) ; in other words, the moment of inertia of the balance varies less in passing from mean to hot temperature than from mean to cold ; and consequently if it is adjusted for mean and cold it will not have decreased enough at an equal increase from mean to hot, or the chronometer will lose, and if adjusted for the two extremes it will gain at mean temperatures.
The correction of this error is called the secondary compensation,