Chas
Reiss, are of a complex nature, and though positive, are difficult of application on account of the impracticability of determining the value of the elements on which we have to base our calculations. These elements are the main-spring or motive power, the hairspring representing the force of gravity on the pendulum, momentum and friction. The relation of the motive power, or the mainspring, to the subject under discussion lies first in the necessary proportion between it and the amount of tension of the spring to be overcome, according to extent and number of vibrations aimed at; and, second, to that of friction affecting motion of the balance and incidental to it. In an 18,000 train the main-spring has to overcome resistance of the hairspring for 432,000 vibrations daily. The hairspring, having its force established by the relative force of the motive power, circumscribes the proportions of the mass called balance and is a co-agent for overcoming friction.
Momentum overcomes some of the elastic force of the spring and friction. It is the force of a body in motion and is equal to the weight of the body multiplied by its velocity. Velocity in a balance is represented by its circumference, a given point in which travels a given distance in a given time. Weight is that contained in its rim. A balance is said to have more or less momentum, in proportion as it retains force imparted to it by impulsion. If a watch has a balance with which it has been brought to time, and this is changed to one-half the size, it requires to be four times as heavy, because its weight is then only half the distance from the center, and any given point in its circumference has only half the distance to travel. On the other hand, a balance twice the size, would have one-fourth the weight. In the first case the balance would have twice as much momentum as the original one, because if we multiply the weight by the velocity we have a product twice as great. In the latter case a like operation would give a product half as great as in the original balance.
It follows that the smaller and heavier a balance the more momentum, and, vice versa, the less momentum it has, always on condition that the hairspring controls both equally. Friction, affecting the vibration of the balance, is that of the pivots on which it moves and that of the escape, ment. It is in proportion to the force with which two surfaces are pressed together and their area. In a balance, weight is synonymous with pressure. Area is represented by the size of its pivots and the thickness of the pivot holes. The first, pivot friction, is continuous and incidental and is overcome by combined forces, the motive power, the elasticity of the hair-spring, and the momentum of the balance. The latter, or escapement friction, is intermitting and is overcome by contending forces, the hair-spring and the momentum of the balance on one side and the motive power on the other.
Having in our power, as shown above, to obtain the desired momentum of the balance by differing relative pressure and diameter, we can regulate pivot friction within certain limits and distribute the labor of overcoming it, among the co-operative forces, in such a manner that the proportions of such distributions shall not be disturbed during their (forces) increase or decrease. Incidental pivot friction is that caused by the unlocking on the impulse. The first causes retardation, the latter acceleration in the motion of the balance, regardless of isochronism. It is easy to comprehend that a heavy balance would, by its greater momentum, unlock the escapement with less retardation than a light one; but, on the other hand, the acceleration by the impulse would be less also; and with a varying motive power a disturbing element would be introduced by a change in the relative proportions of these forces, the momentum of the balance decreasing or increasing faster than the motive power, constituting as it does relatively a more variable force. In argument the reverse of this might be advanced in regard to a balance which is too light. Without, however, entering further into the subject it is plain how the rate of a watch under such conditions might be affected after being apparently adjusted in stationary positions, by being used on a locomotive or under conditions where external disturbances should lessen the extent of vibration, and making the contact between the balance and the escapement of less duration.
The almost universal abandonment of watches with uniform motive power and the introduction of stem-winders with going barrels, invest the subject with special interest; and, as stated in the beginning, applying rules for defining these desirable proportions being impracticable, the only solution of the problem which remains to us is the study, by observation of certain symptoms which do exist, to determine that which by other means cannot be done. During the progress of horology, similar difficulties had to be met in every kind of watch which happened to be in use. The old Verge watch had its balance proportioned thus: that it could lie inside in the main-spring barrel, and the watch, when set going without a balance spring, would indicate, by the hand on the dial, a progress of twenty-seven and one-half minutes during one hour running. It was said that under these circumstances it would be least affected by inequalities of the motive power, and the verge would not be cut by the escape wheel. The balance in the Cylinder watch was to be sized according to the proportion of the train, each successive wheel to be one-half smaller than the preceding one, and the balance to be twice the size of the escape wheel, the weight to be determined by the equal running of the watch during all the changes of an unequal motive power. The cutting of the steel pallets in Duplex watches or chronometers is caused more by too heavy balances than by any other defect in their parts. It might be well to note the following which is very important and too often neglected. That is the arrangement of the mainspring in the barrel so as to avoid coil friction. The smallest advantage of the old Fusee watch was not the facility of obtaining five turns of the fusee to three or three and one-half of the mainspring, but being enabled thereby to arrange the latter around a small arbor in such a manner that the coils never touched, insuring a smooth motive power and lessening the chances of breakage beyond estimation.