It is first necessary to know how many beats per hour the balance is required to make. This varies according to the kind of watch. A Geneva or an American watch will beat 18,000 per hour; an English watch may beat 14,400, 16,200, 18,000, or some number between. In an English lever, if the fourth wheel has ten times as many teeth as the 'scape pinion has leaves, the train is 18,000; if nine times as many, it is 16,200; if eight times as many, it is 14,400. A watch with an 18,000 train beats 150 double vibrations per minute, and so on. The number of beats per minute of a watch balance when keeping correct time may be anything between 240 and 300. Watch trains are calculated as so many beats per hour. Thus, a watch beating 240 per minute is said to have a 11,400 train, and one beating 300 per minute has an 18,000 train. To ascertain the train of any watch, multiply together the numbers of the teeth in the centre, third, fourth, and 'scape wheels. Also multiply together the numbers of the leaves of the third, fourth, and 'scape pinions. Divide the first product by half of the second product, and the result is the number of beats per hour.

Thus, centre wheel has 60 teeth; third wheel, 60; fourth wheel, 51; 'scape wheel, 13; third pinion, 8; fourth pinion, 6; 'scape pinion, 6. Then 60 x 60 x 54 x 13 = 2,527,200; and 8 x 6 x 6 = 288. Therefore, the train = 2,527,200 /(288/2) = 17,550. Select a hairspriug of about the required diameter to suit the regulator pins, or a little larger, and lay it in position on the balance, pushing the brass hairspring collet down tightly upon it to hold it temporarily in position. Then hold the outer end of the spring in a pair of tweezers, and lift up the balance, just allowing the lower pivot to rest upon a watch glass. In this position, give it a rotary motion, as in the watch, holding it as steady as possible. When once started, the balance will continue to vibrate backwards and forwards for more than a minute. Have at hand a watch with a seconds hand, and carefully count the double vibrations in a minute, or, for a preliminary trial, in twenty or thirty seconds. If the! trial spring is too slow, try a stronger one; if too fast, try a weaker spring.

Be careful to hold the spring in the tweezers at the point where it must be pinned into its stud, as a spring that is too large for the watch must have several complete turns broken off before using, and in such a case must be held in the tweezers for counting several turns from the outside end. By repeated trials, select a spring that, when held at the required diameter, counts the correct number in a full minute. To pin it into its collet, put the collet on a broach and hold in the hand; cut out the inner coils of the spring until the collet will easily pass through; then bend the inner end sharply inwards to pin in the collet. To cut out the centre, lay the spring on a watch glass and, holding the inner coil with a fine pair of tweezers, break off about one-third of a turn at a time until it is correct. When properly cut out, and the end bent inwards, pass the hairspring over the broach upon which the collet was placed, and insert the bent-in end for pinning. File up a smooth brass pin to fit, flat it on one side (to go against the spring), try it in the hole before cutting off, and half cut it through with a knife; then insert it, and break off, afterwards pushing it home with the tweezers.

Then see that the spring is flat as it stands upon the broach, and revolve the broach in the fingers to test it. If flat, take it off the broach, lay it on a watch glass, and see that it is true to centre - that is, that the collet occupies the exact centre of the spring, and that the spring starts away from the collet freely, and does not " hug " it. Then put it on the balance, and again count it for a full minute, trying it repeatedly until a point is found at which, when held, it counts one beat per minute too slow. This is the point at which to pin it in its stud. Then try in the watch, and if too slow, as it will be a trifle, shorten it until correct. It is always best to pin them in a little slow at first, and shorten till right, as, if the spring is once made too short, it cannot again be lengthened. When finished and in the watch, be careful to see that the spring lies quite flat, and is free of the balance arms and the balance cock; that its outer coil passes freely between the curb pins of the regulator, and plays between them nicely: and that the second coil does not touch the stud or the inner curb pin, and in a Geneva watch be careful that the outer coil never touches the centre wheel.