SECT. VII.] 
STEAM ENGINES. 
237 
and suppose G m now to represent the beam; then, inverting the figure, we shall 
have the usual motion by means of the vibrating pillar, and hence the pre 
ceding rules may be applied to the calculation of this motion. 
If A B be retained as a parallel bar, and B D as a connecting bar, the point E 
may then be employed for a pump rod, as in the particular case of Fig. 9. 
Figs. 12 and 13 exhibit a very simple motion, by which the number of parts 
is diminished, and two diagrams are given to show that any length of radius bar 
may be used for such motion, provided the link be properly apportioned. 
495. When the proportions to obtain parallel motion have been found by the 
preceding rules, the point for the air-pump rod in the link D B is easily found 
by drawing a line from G to A, as in several figures, and then the rod must be 
attached to the point of intersection. Its distance from the point B may be 
calculated by the proportion, 
AF: FG : : AB : BE = —? * F G . 
A F 
Thus if A F be 12 feet, F G 3 feet, and A B 7 feet; then = 175 
= BE. 
In like manner, for any complex case, as in Woolfs engine with two cylinders, 
the points of connexion for the piston rods must all be in the line A G, as is shown in 
some examples in the plates ; or the point for the air-pump rod being found by the 
rule, (art. 491.) the point for the piston rod may be ascertained by drawing a 
line through the points A E, Fig. 4. Plate x. (A) till it cuts the line in which 
the piston rod is to move at G ; then draw G F parallel to the link B D, and G H 
parallel to the beam, and B F G Ii are the moveable points of the parallelogram, 
and G the point to which the piston rod should be connected. The calculation 
and construction of the parallel motion adopted for steam boat engines, Figs. 1. 
may be conveniently solved by the methods before described. 
To fix the radius bar. The line of the piston must be first made to 
bisect the versed sine of the arc described by the end of the beam. Plumb the 
piston rod when at the top extremity of its stroke ; then the radius bar being 
moveable about D, with the other end C describe a circular arc. Bring the 
piston down to the lowest extremity of the stroke, again plumb the piston 
rod, and in the same manner describe another arc intersecting the former. 
The point of intersection will evidently be the centre upon which the end 
C of the radius bar is to move. 
The length as well as position of the radius bar may be similarly ascertained by 
geometrically finding the positions of the point D respectively at the top extremity, 
at half stroke, and at the bottom extremity ; and then describing a circle through 
the three points so found.