The axis to which rotation is to be given, or from which it is to be taken, is sometimes variable in its position. In such cases, an ingenious contrivance, called a _universal joint_, invented by the celebrated Dr. Hooke, may be used. The two shafts or axles A B, _fig. 167._, between which the motion is to be communicated, terminate in semicircles, the diameters of which, C D and E F, are fixed in the form of a cross, their extremities moving freely in bushes placed in the extremities of the semicircles. Thus, while the central cross remains unmoved, the shaft A and its semicircular end may revolve round C D as an axis; and the shaft B and its semicircular end may revolve round E F as an axis. If the shaft A be made to revolve without changing its direction, the points C D will move in a circle whose centre is at the middle of the cross. The motion thus given to the cross will cause the points E F to move in another circle round the same centre, and hence the shaft B will be made to revolve. [Illustration: _C. Varley, del._ _H. Adlard, sc._ _London, Pubd. by Longman & Co._] This instrument will not transmit the motion if the angle under the directions of the shafts be less than 140°. In this case a double joint, as represented in _fig. 168._, will answer the purpose. This consists of four semicircles united by two crosses, and its principle and operation is the same as in the last case. Universal joints are of great use in adjusting the position of large telescopes, where, while the observer continues to look through the tube, it is necessary to turn endless screws or wheels whose axes are not in an accessible position. The cross is not indispensably necessary in the universal joint. A hoop, with four pins projecting from it at four points equally distant from each other, or dividing the circle of the hoop into four equal arcs, will answer the purpose. These pins play in the bushes of the semicircles in the same manner as those of the cross. The universal joint is much used in cotton-mills, where shafts are carried to a considerable distance from the prime mover, and great advantage is gained by dividing them into convenient lengths, connected by a joint of this kind. (318.) In the practical application of machinery, it is often necessary to connect a part having a continued circular motion with another which has a reciprocating or alternate motion, so that either may move the other. There are many contrivances by which this may be effected.