(314.) By a continued rectilinear motion another continued rectilinear motion in a different direction may be produced, by one or more fixed pulleys. A cord passed over these, one end of it being moved by the power, will transmit the same motion unchanged to the other end. If the directions of the two motions cross each other, one fixed pulley will be sufficient; see _fig. 113._, where the hand takes the direction of the one motion, and the weight that of the other. In this case the pulley must be placed in the angle at which the directions of the two motions cross each other. If this angle be distant from the places at which the objects in motion are situate, an inconvenient length of rope may be necessary. In this case the same may be effected by the use of two pulleys, as in _fig. 158._ If the directions of the two motions be parallel, two pulleys must be used as in _fig. 158._, where P′ A′ is one motion, and B W the other. In these cases the axles of the two wheels are parallel. It may so happen that the directions of the two motions neither cross each other nor are parallel. This would happen, for example, if the direction of one were upon the paper in the line P A, while the other were perpendicular to the paper from the point O. In this case two pulleys should be used, the axle of one O′ being perpendicular to the paper, while the axle of the other O should be on the paper. This will be evident by a little reflection. In general, the axle of each pulley must be perpendicular to the two directions in which the rope passes from its groove; and by due attention to this condition it will be perceived, that a continued rectilinear motion may be transferred from any one direction to any other direction, by means of a cord and two pulleys, without changing its velocity. If it be necessary to change the velocity, any of the systems of pulleys described in chap. XV. may be used in addition to the fixed pulleys. By the wheel and axle any one continued rectilinear motion may be made to produce another in any other direction, and with any other velocity. It has been already explained (250.) that the proportion of the velocity of the power to that of the weight is as the diameter of the wheel to the diameter of the axle. The thickness of the axle being therefore regulated in relation to the size of the wheel, so that their diameters shall have that proportion which subsists between the proposed velocities, one condition of the problem will be fulfilled. The rope coiled upon the axle may be carried, by means of one or more fixed pulleys, into the direction of one of the proposed motions, while that which surrounds the wheel is carried into the direction of the other by similar means.