Prof. Barnard on a modification of the Ericsson Engine. 233 
it may easily be shown, that when the cut-off is at a little short of 
¥, the driving power will be reduced nearly or quite to zero, at the 
points where the component of negative pressure directed against 
the power of the companion engine is near its maximum; and, 
with a two-thirds cut-off, which has been recommended by Prof. 
Norton, and which is larger than that sometimes or usually em- 
ployed in fact on the “ Ericsson,” the balance of positive power 
at these points will become but little more than one pound to the 
square inch. This indeed, is true only when there is no leak- 
age :—which, however, is simply saying that the disadvantage 
fails to become serious only in proportion as the advantage sought 
is unattained. 
In speaking of the possible modes of improving the performance 
of the engine, it is taken for granted that the safe limits o 
have already been experimentally found; and that consequently 
there is no room to look for improvement in this direction. And 
it is also admitted that the performance of the engines of the 
Ericsson will very possibly and even probably, be improved, if it 
shall be found practicable to save the large amount of power, now 
evidently lost by leakage. But it seems not at all difficult to 
show that these engines, with their present dimensions and form, 
can never develop the amount of power which has been estimated 
for them by their ingenious inventor, even if all leakage should 
€ stopped ; unless the heat imparted to the air should be made 
greater than we are told it has yet been. 
Whether any modification of the form of the engine can be 
effectual to remove the difficulties in the way of its improvement, 
or even partially to remove them, is a question which deserves 
examination. Apparently the hope of a favorable solution is not 
desperate ; and the object of the present paper is to offer a 
single suggestion looking in that direction. In order that it may 
be intelligibly presented, it will be necessary to throw the condi- 
tions of the problem into mathematical form. The symbols em- 
ployed by Maj. Barnard, in the article above alluded to, will be 
adopted so far as they serve. 
Put a= cross section of working cylinder. 
ma = the same.of supply cylinder. 
'= the tension of the air in reservoir, when working with 
any adjustment of the cut-off. 
t’ = the same, when working without cut-off. 
1= length of stroke; /=fractional part of stroke up to 
cut-off. 
n== ratio of expansion by heat referred to a unit-volame at 
the density of the air in reservoir. : 
15 lbs. = pressure of the atmosphere to the square inch. 
1= density of the external air, relatively to that in re- 
: servolr. 
Sxrconn Srrims, Vol. XVI, No. 47.—Sept., 1853. 30 
