THE STEAM-ENGINE. 



play, the extremities of the link will always be in the line A B ; but in all in- 

 termediate 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 

 v 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 

 S 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 ex- 

 > ist, in the middle of the link, where the two contrary derangements would 

 ) neutralize each other, and which point would therefore be expected to be dis- 

 turbed neither to the right nor to the left, but to be moved upward and down- 

 ward 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 ac- 

 curately in the vertical line A B, provided that the angular play of the levers 

 P and op does not exceed a certain 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 p OS i t i ons O f t he lever O P, and let p p' p" p l " be the four 

 corresponding positions of the lever p 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 po- 

 sition o p' ; and the link will have the position P 7 p' . The middle point of 

 the link will be at a/, 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 de- 

 rangement 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, P x// , 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 1 " will there- 

 fore be upon that line. The previous derangement of the extremities of the 

 rod, to the right and to the left, ar<* 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, upward and downward in a circular arch, may be made to 

 produce the alternate motions of another point x, upward and downward in a 

 straight line. 



Although the guidance of the air-pump rod in a true vertical line is not so 

 necessary as that of the steam-piston, and as the air-pump piston is always 

 brought down by its own weight and that of its rod, the connexion of the air- 

 pump piston-rod with the beam, by any contrivance of the kind now described, 

 was not so necessary. Nevertheless, by a slight addition to the mechanical 

 contrivance which has been just described, Watt obtained the means of at once 

 preserving the true rectilinear motion of both piston-rods. 



Let the lever represented by O P, in fig. 17, be conceived to be prolonged 

 to twice its length, as represented in fig. 18, so that O P ; snail be twice O P. 



