Balance Vibrations

From The American Horologist magazine, November 1941

Balance Vibrations
By W. H. Samelius

"All pocket watches and most all wrist watches are so constructed that the balance vibrates 18,000 times per hour. This is usually known as a quick train. There are a few extremely small watches made in which the balance vibrates 19,800 per hour and some, 21,600 per hour. In vibrating hairsprings to the balance for the 18,000 beat watch, the count must be 300 vibrations per minute. It is customary when vibrating a balance, to count each alternate vibration, doubling the result for the actual count. The actual count is more easily controlled in this way. In selecting a hairspring, its diameter should be just one half the diameter of the balance rim. A hairspring of such diameter will usually be proper length for isochronism. The following table shows the time lost or gained for each count the balance makes over or under 300 per minute. For instance, if we count the vibrations of the balance and find it vibrates 298 per minute, it indicates that the balance is losing two vibrations, or 2/5th second per minute. 2/5 minute per hour would be 24 seconds and for 24 hours, the watch would lose 576 seconds or 9 minutes, 36 seconds per day.


"To determine the number of vibrations the balance makes per hour, multiply the number of teeth by themselves, taking the center wheel, 3rd, 4th, and escape wheel, multiply this result by 2 as each tooth of the escape wheel delivers two impulses; first on the receiving stone and then on the discharge.  Divide the results by the number of leaves multiplied by themselves, contained in the 3rd, 4th and escape pinion, thus:


64 x 75 x 60 x 15 x 2
--------------------------   =  18,000 beats per hour
        8 x 10 x 6


"If the watch or clock carries a second hand, then it would only be necessary to count the teeth in the 4th wheel, multiplying the number of teeth in the 4th wheel by the number of teeth in the escape wheel by two and dividing by the number of leaves in the escape pinion, the results then would be the number of vibrations the balance would make per minute.


Vibrations      Seconds  Seonds    Minutes & Seconds
per minute     per min.  per hour  per day
310                2             120         48
309                1 4/5       108         43.12
308                1 3/5       96           38.24
307                1 2/5       84           33.36
306                1 1/5       72           28.48
305                1             60           24
304                4/5          48           19.12
303                3/5          36           14.24 
302                2/5          24             9.36
301                1/5          12             4.48
300                On time  On time  On time
299                1/5          12             4.48
298                2/5          24             9.36
297                3/5          36           14.24
296                4/5          48           19.12
295                1             60           24
294                1 1/5       72           28.48
293                1 2/5       84           33.36
292                1 3/5       96           38.24
291                1 4/5       108         43.12
290                2             120         48


"When selecting a hairspring, it is essential to select a spring to vibrate correctly.  If a spring is fitted that is too weak to too strong, adding or deducting weight from the balance is necessary and if too much weight is either removed or placed on the balance, it will change the arc of the balance, which would show in the final results.  Care must be taken that a correct count is made, bearing in mind that we are fitting the hairspring to the balance rather than altering the balance to suit the hairspring."