98 Ward’s Steam-Engine. 
The first of these notions, I think I have already disproved ; 
and that the last is equally founded in error, I must be al- 
lowed the boldness to aver. 
Mathematicians have computed this loss at jy of the pow- 
er used. But, in estimating the effect produced, they seem 
to have lost sight of the power consumed. In comparing 
the effects produced, when the steam is made to act, at all 
points, wholly in the direction of the tangents at those points, 
that is, at right angles to the crank, with the effects produ- 
ced, when, as in the common mode of applying the crank, 
the direction of the force is at an angle to it, continually va- 
rying from a right angle to a coincident line, men of science 
appear never to have considered, that, where the force is al- 
ways applied, as in the first instance, at right angles to the 
crank, the distance passed over by the piston, that is, the 
length of piston-rod protruded, is equal to the semicircum- 
ference of the circle described by the crank; whereas, when 
applied, as in the last case, at a perpetually varying angle, 
the length of piston-rod protruded is equal to the dtameter 
only of the same circle. Now, all other things being equal, 
the power consumed is proportional to the length of piston-rod 
protruded; and thesemi-circumference of the circle being to 
its diameter, as 11 is to 7, it follows, that, when the power 
is applied wholly in the direction of the tangents, its quanti- 
ty is expressed by 11, while, when applied as in the com- 
mon crank, its quantity is expressed by 7 only. So that, if 
the effect produced, when the power is applied in the tan- 
gents, be four-elevenths greater than when applied by the 
crank, the reason is, not that, in the latter case, four-elevenths 
of power are lost, but that four-elevenths less power are 
consumed. 
The same truth may be demonstrated in another way. 
Suppose the force to be applied in the tangents of a circle, 
the semicircumference of which is equal to the diameter of 
that which is described by the crank. Then, of course, the 
length of piston-rod protruded, during the semi-revolution 
of this reduced circle, is equal to the length protruded, when 
tbe crank is used 3 and the quantities of power consumed in 
each will be equal. That the effects produced will also be 
equal, may be shown by taking a quadrant of the circle de- 
seribed by the crank,—dividing it into a number of equal 
parts,—and comparing the effects produced by the impulses 
