A pinion as low as eleven leaves can be made so that the action of the tooth will begin at or beyond the line of centers; but as eleven is an inconvenient number to use in clockwork, we may with great propriety decide upon twelve as being a sufficient number of leaves for all the pinions used in a regulator having a Graham escapement.

In arranging the size of the wheels in a regulator, the diameters of the center and third wheels are determined by the distance between the center of the minute and the center of the seconds hand circle on the dial. As the dials of regulators are usually engraved after the dial plates have been fitted, and as the position of the holes in the dial for the center and scape wheel pivots to come through determines the size of the seconds circle, it may be well to mention here that, for a twelve-inch dial, two and a half inches is a good distance for the center of the minute circle to be from the center of the seconds circle. Consequently the center and third wheels must be made of such a diameter as will raise the scape wheel arbor two and a half inches from the center arbor, and the other wheels must be made proportionally larger, according to the number of teeth they contain.

We all know what a difficult matter it is to make a cutter that will cut a tooth of the proper shape; but when the cutter is once made and carefully used, we also know that it will cut or finish a great number of wheels without injury. For this reason, those who are contemplating making only one, or at most but a few regulators, will find the work will be greatly simplified by making the wheels of a diameter proportionate to the number of teeth they contain, and for all practical purposes the cutter that cuts or finishes the teeth of one wheel will be sufficiently accurate for the others. If we make all the pinions with the same number of leaves they will also all be nearly of the same diameter, and may be cut, or rather the cutting operation may without any great impropriety be finished with one cutter.

An opinion prevails among a certain class of workmen that the teeth of the great wheel and leaves of the center pinion should be made larger and stronger than the other wheels and pinions, because there is a greater strain upon them than on the other. However reasonable this idea may seem, a little consideration will show that in the case of a regulator, with a Graham escapement, where so little motive power is required to keep it in motion, an arrangement of this nature is altogether unnecessary. The smallest teeth ever used in any class of regulators are strong enough for the great wheel; and if there be a greater amount of strain on the teeth of the great wheel in comparison with the teeth of the third wheel, for example, then make the great wheel itself proportionately thicker, as is usually done, according to the extra amount of strain that it is to bear. The teeth of wheels and the leaves of pinions wear more from imperfect construction than from any want of a sufficient amount of metal in them.

If we assume the distance between the center of the minute and the center of the seconds circle to be 2½ inches, and also assume that the clock will have a seconds pendulum, and all the pinions have 12 leaves, and the barrel make one turn in 12 hours, then the following is the diameter the wheels will require to be, so that the teeth may all be cut with one cutter, and also the number of teeth for each wheel:

Great wheel 144 teeth.
Diameter 3.40 inches for the pitch circumference.

Hour wheel 144 teeth.
Diameter 3.40 inches for the pitch circumference.

Center wheel 96 teeth.
Diameter 2.26 inches for the pitch circumference.

Third wheel 90 teeth.
Diameter 2.11 inches for the pitch circumference.

Scape wheel 30 teeth.
Diameter 1.75 inches for the pitch circumference.