This section is from the book "Cassell's Cyclopaedia Of Mechanics", by Paul N. Hasluck. Also available from Amazon: Cassell's Cyclopaedia Of Mechanics.
The vibrations of a watch balance occupy exactly equal times (with an average hairspring) only when they are exactly equal in extent. For instance, in a watch with an ordinary flat hairspring, the balance vibrating exactly one whole turn, and going to time lying down, if the power be increased so as to make the vibrations of the balance one and a quarter turns, the watch will no longer be quite on time, but will either lose or gain - probably the latter. In such a case it may be said that the short arcs (one turn) are slower 1 than the long arcs (one and a quarter turns). But in the case of a breguet hairspring (with an overcoil), the spring can be so manipulated as to render the long and short arcs of the balance isochronous - that is, performed in equal times. In such a watch it would not matter whether the balance vibrated one turn or one and a half turns; the time registered would be the same. The average good three-quarter-plate English lever watch, when lying down, has a balance arc of about one and a quarter to one and a half turns, and makes what are termed " long arcs." When hanging up it will make about a quarter of a turn less, say one turn to one and a quarter turns, on account of the greater friction at the balance pivots when in that position.
The balance then rests upon the sides of the two pivots instead of resting on the end of one, as in lying down. The watch then makes " short arcs." Obviously, if the short arcs are slow, the watch will go slower when worn in tb.3 pocket than when lying on the dressing table at night. But if the hairspring is isochronous, causing the long and short arcs to be performed in equal times, there would be no difference in the timekeeping, whether the watch was worn in the pocket or was kept lying down. Ordinary watches with hairsprings that have not been thus manipulated will lose about one minute per day in the pocket more than when lying down, the short arcs being then known as " sixty seconds slow." To test a watch for this error, set it on time by a regulator, noting its rate lying dial up for twenty-four hours. Then place it nine o'clock up for twelve hours and three o'clock up for twelve hours, and the sum of these two last positions will be its rate for the short arcs, while the first twenty-four hours' run will give its rate for the long arcs.
 
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