if an uniform ring, with two or more radii placed at equal regular distances, and in all other respects alike, were to be poised on its axis, as a balance, no part would preponderate ; but it would remain at rest in any position ; and if we suppose the axis itself to be a spring, such as a piece of stretched wire, and we over! aok the difference of tension in the wire, which might arise from the weight of the balance itself, in' different positions, it is obvious that all the vibrations of that ba lance, through equal arcs, would, be per formed in equal times, whether the ba lance were made to vibrate parallel to the horizon, or in any other position. But in the balance of a time-piece, the pivots of its axis bear very differently,. accord ing to the position of the chronometer ; and it requires some management to make the frictions the same, whether the axis be turning on one of its Ends, or upon the two cylindrical faces of the pivots. And still more than this, since the balance it self has a permanent figure, compared with the spring, which in every part of the 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 vibra tion, as to time, in all positions when in its place. And in addition to these diffi culties, there is one part of the arc of vi bration, 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 pow er: namely, during-the action of escape. The remedy for all these difficulties, which is happily adopted in chronome ters for use at sea, is to place the axis in a vertical position ; by which means the ba lance itself is not affected by gravity ; but for pocket time-pieces, the ingenuity of the artik is called upon for expedients, of which it would be not easy to exhibit a complete theory. The general principle commonly used, and also adapted by Ar nold and Barnshaw, as far as can be ga thered from the little they say in their specifications to the commissioners of longitude, is to consider the balance, when out of adjustment for position, as a pendulum weight above and below the centre of suspension, acted upon by gra vity,—and at the same time urged to a quiescent point by the force of elasticity. In these circumstances the vibrations will he quickest when the point of stable equi librium is downwards, and they will be slowest in the opposite position of the machine. This leads to the remedy of diminishing either the weight of the ra dius, or that side which is lowest when the rate is most quick. Thus, if one of the two adjusting screws, in fig. 7, 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 reme dy this imperfection without much change in the other adjustments And if a 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 the line pass ing 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 screws tapped into the weights themselves, and directed towards the centre, like the weights at the extremi ties of the radii.
By these, and other correspondent means, the balance may be made to keep time, in all those positions wherein its plane shall be perpendicular to that of the horizon ; but even in these trials, very great pains and labour may be required to produce a high degree of accuracy ; and in this course of operation, the skil ful workman may be under the necessity of preparing a great number of expansion weights and regulating screws, to 'be ap plied in trial, whenever the course of ad justment in one part shall carry him be yond the general conditions of the whole machine. And after all, as the quantity of action, in the spring, must alter the quantity of pendulous effect, in this cu rious and delicate time-measurer, it may be doubted, whether the adjustments for position in the vertical balance can he ef fectual any longer than while the arcs of vibration continue permanent. This con sideration leadi us to the necessity of an adjustment in the maintaining power, in order that the vibrations shall not fall off; at the same time that it affords one of the strongest arguments in favour of a re montoire, notwithstanding the experi ment of Arnold, which showed that a sea-chronometer (face up) kept the same rate, when those arcs were greatly va ried.
When the balance has been adjusted for position in the vertical situation, it does not follow, as a matter of course, that it will keep the same time with its plane ho rizontal, or face up and face down. In the former cases, the effect of gravity still ap pears to be combined with that of elasti city, though under circumstances of ad justment; in the latter, gravity seems to be out of the question. If the rate should demand adjustment with the axis vertical, M order to make it agree with that which obtains when the balance is- vertical, it appears necessary, that either the inertia or the elastic force should be altered. The former seems to demand such changes of the screws or weights, as may alter the effective radius of the balance ; the latter requires a change of the spring itself. The artists, with whom the writer of this article has conferred, did not seem to have clear notions of any direct me thod for effecting the purpose here point ed out. It appeared, that they have re course to several expedients ; but that, in general, the rate, face up, of a time piece, which has been well adjusted in other respects, does not require much ad ditional adjustment.
From all these considerations, with others, into which brevity forbids us to enter, together with those which relate to the choice and preparation of materials, and the delicacy and truth of workman ship, the reader will be able to form some judgment of the intelligence and skill, with which, chiefly under the sanction of the British government, this important manufacture has been pursued, and like of the ample field for improvement, which remains for the exertions of future artists. See PENDITLUX, CLOCK, TRAIN, and WATCII-WORK.