(263.) Toothed wheels are of three kinds, distinguished by the position which the teeth bear with respect to the axis of the wheel. When they are raised upon the edge of the wheel as in _fig. 105._, they are called _spur wheels_, or _spur gear_. When they are raised parallel to the axis, as in _fig. 107._, it is called a _crown wheel_. When the teeth are raised on a surface inclined to the plane of the wheel, as in _fig. 108._, they are called _bevelled wheels_. [Illustration: _H. Adlard, sc._ _London, Pubd. by Longman & Co._] If a motion round one axis is to be communicated to another axis parallel to it, spur gear is generally used. Thus, in _fig. 105._, the three axes are parallel to each other. If a motion round one axis is to be communicated to another at right angles to it, a crown wheel, working in a spur pinion, as in _fig. 107._, will serve. Or the same object may be obtained by two bevelled wheels, as in _fig. 108._ If a motion round one axis is required to be communicated to another inclined to it at any proposed angle, two bevelled wheels can always be used. In _fig. 109._ let A B and A C be the two axles; two bevelled wheels, such as D E and E F, on these axles will transmit the motion or rotation from one to the other, and the relative velocity may, as usual, be regulated by the proportional magnitude of the wheels. (264.) In order to equalise the wear of the teeth of a wheel and pinion, which work in one another, it is necessary that every leaf of the pinion should work in succession through every tooth of the wheel, and not continually act upon the same set of teeth. If the teeth could be accurately shaped according to mathematical principles, and the materials of which they are formed be perfectly uniform, this precaution would be less necessary; but as slight inequalities, both of material and form, must necessarily exist, the effects of these should be as far as possible equalised, by distributing them through every part of the wheel. For this purpose it is usual, especially in mill-work, where considerable force is used, so to regulate the proportion of the number of teeth in the wheel and pinion, that the same leaf of the pinion shall not be engaged twice with any one tooth of the wheel, until after the action of a number of teeth, expressed by the product of the number of teeth in the wheel and pinion. Let us suppose that the pinion contains ten leaves, which we shall denominate by the numbers 1, 2, 3, &c., and that the wheel contains 60 teeth similarly denominated. At the commencement of the motion suppose the leaf 1 of the pinion engages the tooth 1 of the wheel; then after one revolution the leaf 1 of the pinion will engage the tooth 11 of the wheel, and after two revolutions the leaf 1 of the pinion will engage the tooth 21 of the wheel; and in like manner, after 3, 4, and 5 revolutions of the pinion, the leaf 1 will engage successively the teeth 31, 41, and 51 of the wheel. After the sixth revolution, the