240 Prof. Barnard on a modification of the Ericsson Engine. 
At the commencement of the stroke of one of the pistons, the 
pressure on its surface will be at, as before. But this will be op- 
posed not only by 15a, (the pressure on its upper surface) as in 
the former case, but also by that of the air in cylinder C’C” at 
the other end of the working beam, whose cross-section is ah 
and tension ¢. The atmospheric pressure on the upper surface se 
the smaller piston favors the power, so that the expression for 
total effect contains these four terms, 
P=ai —1lda+-l5a , _ ae 
n n 
ferrae e Z mn — ‘ 
l n 
= 15a () 
’ For the simultaneous effective einai upon the ee in ac- 
tion in the companion engine, at mid-stroke, we hav 
Pressure on under surface of Spire piston a1 
Atmospheric resistance, upper surface =—15(1=—m)a 
- . . 30m? n 
Resistance, partially condensed air, on P’ =— a. 
LP y a mn+l 
. 30/m 
Favoring pressure of same, on P” sane a. 
j : tae ; l 
Resistance, condensed air, passing into reservoir = —at-. 
n 
The atmospheric pressures on the two pistons, P’, at opposite 
ends of the beam, balance each other 
The co-efficient of a, in the third term, rout is obtained as 
follows. At mid-stroke, the undergoing condensation half fills 
1 
cylinders C’C’ and C”C”. Its bulk is therefore equal to (m+, a. 
Let ¢’= the corresponding tension, and we have 
30mn 
: mn+l 
which tension, acting on the surface of P’=ma, gives the term 
bet Bg” eee’ 8 2 
z n 
as above. In like manner, ¢” acting on the surface, ted of BM, 
gives the next following term. 
All the expressions above, united and reduced, give 
(mn—1)\ 
P=15a("=—- ; —- a) 2) 
This, added to the last, gives, for she sali power of both 
engines, 
P=15e( 275 ol nee a) 
i no ~ mat+l “ 
