On the other hand, a very small force will move the teeth outwards from the line of centres, as the small inequalities, c, d, and a, b, may then slide over one another without being broken; for the teeth, when so working, are mutually receding from each other in their point of contact, and the wheels move on their centres with ease; and whereas, in the first case, they must have a tendency to force the centres, on which they turn outward, from their true position, in the second, they have no such tendency. Again, when the teeth are of metal, this unnecessary friction seems to arise principally after the teeth are in some degree worn (See the figure in page 58)-The teeth in that case have a kind of seat formed at their bottom, and the curve at the outward extremity is too much inclined to the radius, and very abrupt. In the action which takes place before the line of centres, the sliding of the teeth of the conducting wheel along those of the conducted, has a tendency to accumulate hardened grease, dust, sand, &c. at the bottom, which getting between the abrupt extremity of the tooth and the seat at the bottom, become like the key-stone of an arch, and must require often a considerable force to bruise the teeth in this situation past the line of centres. Thus it appears, that the friction of teeth, approaching the line of centres, is much greater than in receding from it. But in cases where the pinion is small, the action, in approaching to the line of centres, cannot be altogether prevented. M. Camus, in his "Cours de Mathematique," has demonstrated, that a wheel of 50 teeth cannot conduct a pinion of 7 leaves, without their acting partly before they arrive in the line of centres. He also proves the same with regard to 57 teeth and 8 leaves, 64 and 9, 72 and 10*. * See M. Camus. 7. From what I have already said, it will be evident, when the pinion consists of such a number of teeth, as to be conducted uniformly by the wheel in receding only from the line of centres, that except in small numbers, the epicycloid is necessary on the conductors only, whether it be a wheel or pinion. For instance, in p. 55, which represents two wheels of equal numbers, A is the conducting, and B the conducted wheel. But it is to be observed, when of two wheels acting on each other, sometimes the one, and sometimes the other, is the conductor, the teeth of both should be epicycloidal, as in p. 46. When the teeth of the conducted wheel or pinion, are acted upon by those of the conductor, in receding only, from the line of centres, it may be remarked, if they were perfectly made, and of durable materials, it would be unnecessary to extend the conducted teeth beyond their proportional circle. But these properties Conducted B Conductor being unattainable, and as the angles which terminate their sides, would be apt to cut the conducting teeth, and occasion an irregular motion, it is proper to form the extremity of the teeth of the conductor, in the manner represented in the figure by the dotted lines. 8. Sometimes it may be requisite to have but few teeth in the pinion. In such cases, in the conducted, whether wheel or pinion, I would prefer staves to teeth, properly so called, or to leaves, because a trundle or wheel, whose staves are cylindric, will be less acted upon in approaching the line of centres, and consequently have less friction than a pinion or wheel, the sides of whose teeth tend to the centre. This will appear by the figure, which represents a stave, a, of a trundle, and a leaf, b, of a pinion, turning round on the same centre, A, and a tooth adapted to each, turning on a common centre, B. The thickness of each of the teeth, and the proportional circle of both wheels, are the same, and the proportional circles of the pinions are also equal, and teeth are each made of the greatest length, which the intersection of the curves will admit, which turns out considerably greater in the tooth adapted to the stave. The shaded parts represent the teeth adapted to, and acting upon, the stave; and the dotted |