To explain the principle of the mechanism called the parallel motion, let us suppose that O P (_fig._ 36.) is a rod or lever moveable on a centre O, and that the end P of this rod shall move through a circular arch P P′ P″ P‴ a vertical plane, and let its play be limited by two stops S, which shall prevent its ascent above the point P, and its descent below [Pg196] the point P‴. Let the position of the rod and the limitation of its play be such that the straight line A B drawn through P and P‴, the extreme positions of the lever O P, shall be a vertical line. [Illustration: _Fig._ 36.] Let _o_ be a point on the other side of the vertical line A B, and let the distance of O to the right of A B be the same as the distance of _o_ to the left of A B. Let _o p_ be a rod equal in length to O P, moving like O P on the centre _o_, so that its [Pg197] extremity _p_ shall play upwards and downwards through the arch _p p′ p″ p‴_, its play being limited in like manner by stops _s_. Now, let us suppose that the ends P _p_ of these two rods are joined by a link P _p_, the connection being made by a pivot, so that the angles formed by the link and the rods shall be capable of changing their magnitude. This link will make the motion of one rod depend on that of the other, since it will preserve their extremities P _p_ always at the same distance from each other. If, therefore, we suppose the rod O P to be moved to the position O P‴, its extremity P tracing the arch P P′ P″ P‴, the link connecting the rods will at the same time drive the extremity _p_ of the rod _o p_ through the arch _p p′ p″ p‴_ so that when the extremity of the one rod arrives at P‴, the extremity of the other rod will arrive at _p‴_. By this arrangement, in the simultaneous motion of the rods, whether upwards or downwards, through the circular arches to which their play is limited, the extremities of the link joining them will deviate from the vertical line A B in opposite directions. At the limits of their play, the extremities of the link will always be in the line A B; but in all intermediate positions, the lower extremity of the link will be to the right of A B, and its upper extremity to the left of A B. So far as the derangement of the lower extremity of the link is concerned, the matter composing the link would be transferred to the right of A B, and so far as the upper extremity of the link is concerned, the matter composing it would be transferred to the left of A B.