Ward’s Steam- Engine. 99 
at these points of division, with the effects produced by a 
like number of impulsesat the circumference of the reduced 
circle. The pressure of the steam upon the piston being 
uniform throughout the stroke, it follows that the impulses 
at all points are equal to one another ; and this being the 
case, it is equally a matter of course, that the effects pro- 
duced at the several points of division of the quadrant, are 
as the perpendiculars respectively from those points to the 
line of force. The sum of the effects, then, will be equal 
io the sum of these perpendiculars: but these perpendicu- 
lars are as the sines of the angles at the several points of di- 
vision; and, if the reader will take the trouble of adding to- 
gether the natural sines for every degree in the quadrant, 
including radius, he will find their sum to be as nearly equal 
to ninety timies the radius of the reduced circle, as the im- 
perfection of our circulating decimals will admit. The for- 
mula would be this :— 
Let the radius of the circle described by the crank = 1. 
Ee Kae eh | 
Then 3.1415926 &c. =. 6366x90=the sum of the 
5 ve 
natural sines of the quadrant for every degree including ra- 
dius. 
As an objection particularly applicable to my engine, it 
has been suggested by some, who have seen the model, 
that the power is exerted at a disadvantage, from the cir- 
cumstance, that the centre of reaction is within the circle of 
motion. Nothing is easier than to show, however, that, sup- 
posing, as we must in all such comparisons, the length and 
diameter of the cylinder, and also the elastic force of the 
steam, to be equal in each, the effect produced in my en- 
zine is equal to that produced in the Lever Engine. _ 
Let the line DB (Plate III. Fig. 1.) represent the elastic 
force of the steam ; the point D be the point of reaction ; 
and the circle BKZ, the circle of motion. The force DB 
is resolvable into DE and EB, parallel and perpendicular 
respectively to the radius AB ; and that part of it, which is 
exerted in the direction of the tangent, will be represented 
by the line EB. This is the force exerted in the Lever 
Engine. ma 
Th my engine, B is the point of reaction, and LDM, the 
