(257.) The manner in which the circumferences of the axles act upon the circumferences of the wheels in compound wheel-work is various. Sometimes a strap or cord is applied to a groove in the circumference of the axle, and carried round a similar groove in the circumference of the succeeding wheel. The friction of this cord or strap with the groove is sufficient to prevent its sliding and to communicate the force from the axle to the wheel, or _vice versa_. This method of connecting wheel-work is represented in _fig. 100._ Numerous examples of wheels and axles driven by straps or cords occur in machinery applied to almost every department of the arts and manufactures. In the turning lathe, the wheel worked by the treddle is connected with the mandrel by a catgut cord passing through grooves in the wheel and axle. In all great factories, revolving shafts are carried along the apartments, on which, at certain intervals, straps are attached passing round their circumferences and carried round the wheels which give motion to the several machines. If the wheels, connected by straps or cords, are required to revolve in the same direction, these cords are arranged as in _fig. 100._; but if they are required to revolve in contrary directions, they are applied as in _fig. 101._ One of the chief advantages of the method of transmitting motion between wheels and axles by straps or cords, is that the wheel and axle may be placed at any distance from each other which may be found convenient, and may be made to turn either in the same or contrary directions. (258.) When the circumference of the wheel acts immediately on the circumference of the succeeding axle, some means must necessarily be adopted to prevent the wheel from moving in contact with the axle without compelling the latter to turn. If the surfaces of both were perfectly smooth, so that all friction were removed, it is obvious that either would slide over the surface of the other, without communicating motion to it. But, on the other hand, if there were any asperities, however small, upon these surfaces, they would become mutually inserted among each other, and neither the wheel nor axle could move without causing the asperities with which its edge is studded to encounter those asperities which project from the surface of the other; and thus, until these projections should be broken off, both wheel and axle must be moved at the same time. It is on this account that if the surfaces of the wheels and axles are by any means rendered rough, and pressed together with sufficient force, the motion of either will turn the other, provided the load or resistance be not greater than the force necessary to break off these small projections which produce the friction.