234 Prof. Barnard on a modification of the Ericsson Engine. 
The consumption of air at each stroke, “rsipias equals al in 
bulk, it having been expanded times by hea 
: ; a 
Same, reduced to density of reservoir, ay 
i 
Which would fill the supply cylinder to the height, a 
Having a density = and a tension = ant 
Now, if /=1, or there be no cut-off, this expansion becomes 
5mn ;—hence, ¢t/=15mn. 
*, / 
But, if there is a cut-off, <= 5G . » and t/ =i. 
If there is a cut-off, the air works by the expansion due to its 
natural elasticity during the remainder of the stroke, and its ulti- 
mate tension =/¢, which, as above, =?’. Hence, the final tension 
of the air in the working-cylinder i is constant, wherever the cut- 
off be placed, and is the same as if no cut-off were use 
From these data it is easy to find an expression for the mean 
effective pressure during a single’stroke ; this being equal to the 
whole upward pressure on the working piston, minus the resist- 
ances divided by the length, which is unity. This expression, 
reduced to its simplest form is as aoa ee P to represent 
the mean effective pressure during the s 
P= 15a(an—1) + L5am ( Anus ht (oh mn). 
As nis necessarily greater and J less than 1, it is evident that, 
m and m remaining unchanged, the power will increase while Z 
diminishes, and this without limit. A different conclusion drawn 
by Prof. Norton, seems to have resulted from leaving out of view 
a portion of the resistance. 
Bat, while this is the mean pressure, it will be seen that the 
actual pressure exerted at different periods of the stroke is very 
variable. The maximum will occur in the beginning when the 
positive pressure is =a, and the resistance simply that of the at- 
mosphere = 1 he minimum occurs at the close, when the 
pressure is =at', and the resistances =amt + 15a (1—m). e 
have seen ¢/ to be constant, m and m remaining the same, what- 
ever may be the value of L But ¢ increases inversely as /, an 
pone Pi ; So that amt+15a(1—m) may soon be equal to, oF 
exce 
This cironmataele practically restricts the power of a single 
pair of cylinders within a moderate limit. But when two pairs 
are connected as in the “ Ericsson” ship, so that one may be at 
mid-stroke when the other is encountering the greatest resistance. 
each may help the other out. And this it may do, even when 
the resistance exceeds its own positive power at the moment; 
