To accomplish this, he conceived the notion of connecting three rods in the following manner:--A B and C D (fig. 14.), are two rods or levers turning on fixed pivots or centres at A and C. A third rod, B D, is connected with them by pivots placed at their extremities, B and D, and the lengths of the rods are so adjusted that when A B and C D are horizontal, B D shall be perpendicular or vertical, and that A B and C D shall be of equal lengths. Now, let a pencil be imagined to be placed at P, exactly in the middle of the rod B D: if the rod A B be caused to move up and down like the beam of the steam engine in the arch represented in the figure, it is clear, from the mode of their connexion, that the rod C D will be moved up and down in the other arch. Now Watt conceived that, under such circumstances, the pencil P would be moved up and down in a perpendicular straight line. However difficult the first conception of this mechanism may have been, it is easy to perceive why the desired effect will be produced by it. When the rod A B rises to the upper extremity of the arch, the point B departs a little to the right; at the same time, the point D is moved a little to the left. Now the extremities of the rod B D being thus at the same time, carried slightly in opposite directions, the pencil in the middle of it will ascend directly upwards; the one extremity of the rod having a tendency to draw it as much to the right as the other has to draw it to the left. In the same manner, when the rod A B moves to the lower extremity of the arch, the rod C D will be likewise moved to the lower extremity of its arch. The point B is thus transferred a little to the right, and the point D to the left; and, for the same reason as before, the point P in the middle will move neither to the right nor to the left, but straight downwards.[17] [Footnote 17: In a strict mathematical sense, the path of the point P is a curve of a high order, but in the play which is given to it in the application used in the steam engine, it describes only a part of its entire locus; and this part extending equally on each side of a point of inflection, its radius of curvature is infinite, so that, in practice, the deviation from a straight line, when proper proportions are observed in the rods, and too great a play not given to them, is insignificant.] Now Watt conceived that his object would be attained if he could contrive to make the beam perform the part of A B in fig. 14., and to connect with it other two rods, C D and D B, attaching the end of the piston to the middle of the rod D B. The practical application of this principle required some modification, but is as elegant as the notion itself is ingenious.