Prof. Barnard on a modification of the Ericsson Engine. 239 
the case admits of. We shall find that, while the plan now pro- 
posed will materially reduce the pressure at the maximum point 
below that of the Ericsson engines at the same point, it in so do- 
ing only reserves a large amount of force, to be subsequently ex- 
pended upon a part of the stroke where the mechanical advantage 
attending its application is rea greater. ‘The minimum pres- 
sure in single engines, must, in the nature of things. be the same 
in both forms of constr spans but in double engines, the joint 
Jorce of the pair at minimum will be much superior in the form 
now proposed, to what it can be in the present. In comparing 
these joint ae sg in the expressions ae they have been treated 
as if they were exerted in the same straight line, instead of bein 
perpendicular to each other in mean direction. But this will not 
interfere with the object in view, which is merely to illustrate 
the difference between the two constructions, in regard to uni- 
formity of action. The maximum pressure, in a double engine, 
will ee occur when one of the pistons is commencing its 
stroke, the other one then in action being about at mid-stroke. 
In Ericsson’s engines, we have seen Fie the effective pressure on 
the first may be expressed by the 
P=at— 150, (1) 
while that on the second will be, 
P=at—amt—15(1-—m)a (ii) 
and that on both together is, 
= (2-—m)(t-15)a [I] 
In order to reduce to a corresponding expression the condition 
of one of our proposed engines at the same moment, we must 
first determine the cross-section to be given to the cylinder Bas B44 
in order that its capacity may be just equal to the bulk of the air 
in C’C’, reduced to the required density. Now this bulk, being 
that of the constant supply, must be also equal to the constant 
consumption, which we have seen to be = Of two equal but 
dissimilar cylinders, the bases must be inversely as the altitudes. 
Hence, ‘e nie :m/a 
in which m/ represents the ratio of the cross-section of C’C” to 
‘that of CC, and is obviously equal to- 
