specific names to all such functions of simple elements , &c. 27 
with improvements chiefly in the fire place, which produce a 
more rapid combustion, with consequently increased tempera- 
ture, and a more complete absorption of the generated heat ; 
in addition to expansive working, and to the use of steam 
raised considerably above atmospheric pressure. 
Since therefore a machine is efficient in producing duty, or 
effect, in proportion to the force applied, multiplied into the 
space through which it acts, I propose to denominate this 
function (f x s) efficiency; retaining the word duty for a 
similar function indicative of the work performed. 
And it is obvious, that by a comparison of these two quan- 
tities, the efficiency expended on any machine, and the duty 
performed by it, an exact measure will be ascertained of its 
intrinsic worth. 
Having never seen a full investigation of the engine moved 
by recoil, I am partly, on that account, induced to take it as 
an example of the utility to be derived from the use of this 
new term ; and I am in part also induced to do so, by the cir- 
cumstance of a most respectable society having last year held 
out the properties of Barker’s mill to the public, as fit objects 
for inquiry. 
To investigate the Recoil engine. 
Let every thing be taken in the abstract, and after a 
manner most advantageous to the machine. Suppose friction 
to vanish, and that the perpendicular tube, and the arms, are 
so capacious as to allow of the fluid issuing with a velocity 
equal to what a body would acquire by falling in free space, 
through an elevation equal to that of the perpendicular tube, 
or through, what is usually termed, the head. See Principia, 
B. 2. § 7. 
