(119.)

It will be observed that the object was to connect by some inflexible means the end of the piston-rod with the extremity of the beam, and so to contrive the mechanism, that while the end of the beam would move alternately up and down in part of a circle, the end of the piston-rod connected with the beam should move up and down in a straight line. If the end of the piston-rod were fastened upon the end of the beam by a pivot without any other connection, it is evident that, being moved up and down in the arch of a circle, it would be drawn to the left and the right alternately, and would consequently either be broken or bent, or would work loose in the stuffing-box. Instead of connecting the end of the rod immediately with the end of the beam by a pivot, Watt proposed to connect them by certain moveable rods, so arranged that, as the end of the beam would move up and down in the circular arch, the rods would so accommodate themselves to that motion, that the end connected with the piston-rod should not be disturbed from its rectilinear course.

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.

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.

By the combined effects of these contrary derangements of the extremities of the link from the vertical line, it might be expected that a point would exist, in the middle of the link, where the two contrary derangements would neutralise each other, and which point would therefore be expected to be disturbed neither to the right nor to the left, but to be moved upwards and downwards in the vertical line A B. Such is the principle of the parallel motion; and in fact the middle point of the link will move for all practical purposes accurately in the vertical line A B, provided that the angular play of the levers O P and o p does not exceed a certain [Pg198] limit, within which, in practice, their motion may always be restrained.

To trace the motion of the middle point of the link more minutely, let P P′ P″ P‴ be four positions of the lever O P, and let p p′ p″ p‴ be the four corresponding positions of the lever o p. In the positions O P o p, the link will take the position P p, in which the entire link will be vertical, and its middle point x will therefore be in the vertical line A B.

When the one rod takes the position O P′, the other rod will have the position o p′; and the link will have the position P′ p′. The middle point of the link will be at x′, which will be found to be on the vertical line A B. Thus one half of the link P′ x′ will be to the left of the vertical line A B; while the other half, p′ x′, will be to the right of the vertical line; the derangement from the vertical line affecting each half of the link in contrary directions.

Again, taking the one rod in the position O P″, the corresponding position of the other rod will be o p″, and the position of the link will be P″ p″. If the middle point of the link in this position be taken, it will be found to be at x″, on the vertical line A B; and, as before, one half of the link P″ x″ will be thrown to the left of the vertical line, while the other half p″ x″, will be thrown to the right of the vertical line.

Finally, let the one rod be in its lowest position, O P‴, while the other rod shall take the corresponding position, o p‴. The direction of the link P‴ p‴ will now coincide with the vertical line; and its middle point x‴ will therefore be upon that line. The previous derangement of the extremities of the rod, to the right and to the left, are now redressed, and all the parts of the rod have assumed the vertical position.

It is plain, therefore, that by such means the alternate motion of a point such as P or p, upwards and downwards in a circular arch, may be made to produce the alternate motions of another point x, upwards and downwards in a straight line.