102 Doolittle on the Steam Engine. 
eource to fluxions, with which I must own Iam not sufii- 
ciently conversant, and if I were, I should perhaps prefer 
employing a mechanical or graphic solution, because I be- 
oe greater number of persons will be able to understand 
"The method I employ, though not mathematically 
want is nevertheless sufficiently so for ilbvicantibat purpo- 
CSi52)> : 
The cylinder in its revolutions describes a circle A. B. 
A’. B’. Fig. I. about the center c. through which — 
the piston rod must continually pass, whatever may be t 
position of the cylinder in the circle ; and the point of j nak 
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 while 
force employed either to raise or depress the piston, is en- 
tirely lost, no one of it being 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 gentive e., and with a radius equal to half a 
stroke of the — we describe a circle o. n. n’. (fig. 
3.) and circumference into,any number of on 
parts, and if we des lines to represent the piston rod in 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. - 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 
ne half of the circle, (taken in a line with the dead 
points) being an — representation of the other half, it is 
unnecessary to occupy ourselves with a larger portion; 1, 
then we divide the semicircle o. n’. p. into eight equal ee 
and find the quantity of force utilized at each of the 
points, we shall nineee a result sufficiently exact for our 
purpose. 
pe NNN 
