The term gearing, which was once applied to wheels, shafts, and the general mechanism of mills and factories, has now in common use become restricted to tooth wheels, and is in this sense employed here. Gearing as a means of transmitting motion is employed when the movement of machines, or the parts of machines, must remain relatively the same, as in the case of the traversing screw of an engine lathe—when a heavy force is transmitted between shafts that are near to each other, or when shafts to be connected are arranged at angles with each other. This rule is of course not constant, except as to cases where positive relative motion has to be maintained. Noise, and the liability to sudden obstruction, may be reasons for not employing tooth wheels in many cases when the distance between and the position of shafts would render such a connection the most durable and cheap. Gearing under ordinary strain, within limited speed, and when other conditions admit of its use, is the cheapest and most durable mechanism for transmitting power; but the amount of gearing employed in machinery, especially in Europe, is no doubt far greater than it will be in future, when belts are better understood.

No subject connected with mechanics has been more thoroughly investigated than that of gearing. Text-books are replete with every kind of information pertaining to wheels, at least so far as the subject can be made a mathematical one; and to judge from the amount of matter, formul?, and diagrams, relating to the teeth of wheels that an apprentice will meet with, he will no doubt be led to believe that the main object of modern engineering is to generate wheels. It must be admitted that the teeth of wheels and the proportions of wheels is a very important matter to understand, and should be studied with the greatest care; but it is equally important to know how to produce the teeth in metal after their configuration has been defined on paper; to understand the endurance of teeth under abrasive wear when made of wrought or cast iron, brass or steel; how patterns can be constructed from which correct wheels may be cast, and how the teeth of wheels can be cut [52]by machinery, and so on.

A learner should, in fact, consider the application and operative conditions of gearing as one of the main parts of the subject, and the geometry or even the construction of wheels as subsidiary; in this way attention will be directed to that which is most difficult to learn, and a part for which facilities are frequently wanting. Gearing may be classed into five modifications—spur wheels, bevel wheels, tangent wheels, spiral wheels, and chain wheels; the last I include among gearing because the nature of their operation is analogous to tooth wheels, although at first thought chains seem to correspond more to belts than gearing. The motion imparted by chains meshing over the teeth of wheels is positive, and not frictional as with belts; the speed at which such chains may run, with other conditions, correspond to gearing.

Different kinds of gearing can be seen in almost every engineering establishment, and in view ............