[sect. II. 
138. The quantity of steam generated may be considered to be equal to the 
quantity consumed in the same time, or that the boiler is of sufficient capacity to 
admit of its being taken at intervals without a sensible loss of elastic force ; and as 
these conditions are essential to a good engine, we shall consider them to be 
fulfilled. (See sect. hi. art. 210. for the proportion of space in boilers.) 
139. The volume of steam required in a second is equal to the area of the 
piston multiplied by its velocity in feet per second : and its density or elastic force 
must be as much less than that of the steam in the boiler, as to allow the same 
weight of steam to pass in a second through the steam passages; for if it passed 
through the steam passages with no greater velocity than that of the piston, those 
passages must be of the same area as the cylinder; but as they are less than the 
cylinder, the excess of velocity must be produced by a corresponding excess of force 
in the boiler. 
140. The steam, till it has passed the narrowest part of the passages, will have 
the same density as in the boiler, but in the cylinder it must expand till its density 
be so reduced as to cause the difference of pressure producing the velocity through 
the contracted passages; and as the density is as the elastic force, the force of the 
steam in the boiler multiplied by the velocity, and the area of the passage, must be 
equal to the elastic force on the piston multiplied by its area and velocity. 
That is, fa v = p A V, when f is the force of the steam in the boiler in inches of 
mercury ; a the area of the steam passages ; v the velocity ; p the force on the 
piston in inches, A its area, and V its velocity. 
From this we have 
P AY 
v = . 
J « 
But by the rule (art. 137.) 
v = 6*5 f 1*13 b (f—p); 
therefore = 6*5>/l , 136 (f—p)- 
f a 
If the area of the steam passage be required, we have 
pA V pAY 
® = 6-5 / VT43M7-J)' r ° “ G-5/ n /86 5«(!M+?) 5 
when nf=f—p = the loss of force, which should not be exceeded. 
141. In practice for low pressure engines it is usual to make the diameter of 
the passage about one-fifth of the diameter of the cylinder, and then its area is -¡ts 
of the area of the cylinder : and as this proportion is grounded upon the experience 
of the difficulties involved by making the passages larger, it ought not to be 
departed from without a sufficiently obvious advantage. 
142. This formula applies only to the case of a pipe without obstructions, and