12 |. Doolitile on the Steam Engine. 
cource to fluxions, with which I must own I'am not sufii- 
ciently conversant, and if I were, I should perhaps prefer 
employing a mechanical or graphic solution, because I be- 
lieve a greater number of persons will be able to understand 
me. The method I employ, though not mathematically 
exact, is nevertheless sufficiently so for all practical purpo- 
ses. 
The cylinder in its revolutions describes a circle A. B. 
A’. B’. Fig. I. about the center c. through which center 
the piston rod must continually pass, whatever may be the 
position of the cylinder in the circle; and the point of junc- 
tion of the pitman with the cross piece of the piston rod, 
describes, in the same time, the circle x. r. x’. (whose ra- 
dius is equal to the length of the pitman) about the center 
o. the distance between the two centers is equal to half the 
length of the stroke of the piston. 
When the cylinder, in its revolution arrives in A. or in A’. 
the two centres are in a line with its axis, and the whole 
force employed either to raise or depress the piston, is en- 
tirely lost, no part of it bemg employed to turn the machine 
—these points, in the common engine, working with a crank 
and fly wheel, are called the dead points. ‘The actuating 
force is here=o. 
If, about the centre c., and with a radius equal to half the 
stroke of the piston, we describe a circle o. n. n’. (fig. 2 and 
3.) and divide the circumference into any number of equal 
parts, and if we draw lines to represent the piston rod im its 
several positions, always passing through the centre of this 
circle, and the divisions of its circumference continuing them 
when necessary, until they strike the circumference of the 
circle r. d. f. described by the extremity of the pitman, that 
point will be the point of junction of the pitman with the 
piston rod; and a line drawn from the center of the latter 
circle to that point will represent the position of the pitman. 
One half of the circle, (taken in a line with the dead 
points) being an exact representation of the other half, it is 
unnecessary to occupy ourselves with a larger portion ; if, 
then we divide the semicircle o. n’. p. into eight equal parts, 
and find the quantity of force utilized at each of these 
points, we shall obtain a result sufficiently exact for our 
purpose. 
