Doolittle on the Steam Engine. 103 
If we suppose the cylinder arrived in E. (fig. 2.) or in 
E’. (fig. 3.) and if, from any scale of equal parts, we set off, 
from the point a., on the line representing the piston rod, a 
distance a. b. equal to two hundred, and consider this as 
the force constantly applied to drive the piston in the cylin- 
der, this force will resolve itself into two forces ; the one, a. 
e. parallel to the position of the pitman, which of course is 
entirely lost, being employed in fruitless endeavours to re- 
move the center piece, the other, a. m. in a line tangent to 
the circle r. d. f. at the point of contact, a.—by completing 
the parallelogram a. e. b. m. of which the primitive force a. 
‘b. is the diagonal, we have the measure of the forces re- 
spectively. 
But the force a. m. is oblique to the direction of the 
movement of the machine, and is therefore again decom- 
posed, the two forces resulting from this second decompo- 
sition, act, the one a. t. ina line parallel to the piston rod, 
and the other a. s. in the direction of the tangent to a circle 
whose radius is equal to that portion of the piston rod, com- 
prised between its junction with the pitman and the center 
c. of rotation, and parting from the point of junction ;—By 
completing the parallelogram a. s. m. t. of which a. m. is the 
diagonal, the side a. t. parallel to the piston rod, is the meas- 
ure of the force lost in the second decomposition, and the 
side a. s. represents the force virtually employed in this 
point in turning the machine. This force measured by the 
same scale of equal parts gives sixty-two. 
But it will at once be seen that the lever c. a. in fig. 2. is 
much longer than the lever c. a. in fig. 3. therefore, if the 
forces were equal, the effects must be different, in inverse 
proportion to the length of the levers. And, to compare 
the effect of this machine to that of one working in the or- 
dinary way, we must reduce all the forces to a length of 
lever equal to that where they could be applied if the cylin- 
der stood still and turned the crank, instead of turning itself 
around it=this lever is represented by the distance between 
the centre c of rotation and the circumference of the circle 
n. 0. n’. 
To find the equivalent of the force a. s. if applied at the 
point h. of the lesser circle (fig. 2.) say—force applied at 
the extremity of long lever c. a. is to length of short lever c. 
_h. as length of long lever c. a. is to force at the extremity of 
short lever ¢. h.—in this construction. 
