The wheel tooth drives the pinion by coming in contact with the straight flank of the leaf at the line of centers, that is a line drawn through the centers of the two wheels; centers of revolution. These curves are called “epicycloids,” and have the peculiar property that if a line be drawn through the generating point and the point of contact of the two circles, this will always be at right angles to a tangent of the curve at its point of intersection. It is this property to which it owes its value as a shape for the acting surface of a wheel tooth, for it is owing to this that a tooth whose acting surface is bounded by such a curve can impel a pinion leaf through the entire lead with little sliding action between the two surfaces. This, then, is the curve on which we will form the addenda of our wheel teeth. With such a depth the only friction would be from a slight adhesion of the surfaces in contact, a factor too small to be taken into consideration. 21 to 25, that a wheel and pinion are merely a collection of levers adapted to continuous work, that the teeth may be regarded as separate levers coming into contact with each other in succession; this brings up two points.

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• The eyes should all be in planes parallel to the plane of oscillation of the pendulum, otherwise the bob will take an elliptical path instead of oscillating in a plane.
• When the teeth are cut with the ordinary Swiss cutters, which, of course, cannot be epicycloidal, it is best to make the spaces one-seventh wider than the tooth.
• When a regulator case is known to have been made by an inexperienced person, which sometimes happens, or when we already have a case, it is always the safest course for those who make the clock to examine the case personally and see the exact accommodation there is for the clock.

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In chronometers, especially those measuring sidereal time, the hour hand is frequently suppressed, and the hours are indicated by a star wheel, or ring, with figures engraved on it, that show through a hole in the dial. The third system uses a weight on the end of a lever connected with a ratchet wheel on the center arbor and does away with springs. One type of each of these clocks will be described so that jewelers may comprehend the principles on which the three types are built.

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