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chine is in motion) when the pressure of steam in the cylinder 

 differs from that in the boiler only by a small fraction of the 

 latter. In this case a relation exists between the velocity of 

 the piston and the relative areas of the cylinder and steam 

 pipe, which is easily determined. When the velocity of the 

 engine is uniform we may assume that the pressures in the 

 boiler and cylinder are ponstant, and are equal to P and P 

 respectively ; at the same time also we shall have av = dv, 

 a and a being the areas of the cylinder and steam pipe, v and 

 v the velocities of the piston and of the steam issuing into 

 the cylinder. Hence, the value oiv* being 



»-/V(^,'»«^)- 



\qio ^ n+ qP\ 

 where/" is a constant depending on the form of the steam pipe, 

 we have 



-^ a^ \qu} ^ n + qPJ ^ ' 



If the difference of pressures P, P' be small, we may assume 

 that the densities vary as the pressures, which reduces (1) to 



^=/^\/(2Hog5), (2) 



in which k = g x the relative volume of steam under any pres- 

 sure X the height of a column of water whose weight equals 

 the same pressure. 



" Further, putting P'= P(l -n), n being a very small frac- 

 tion whose square may be neglected, we have 



v^f^Vi^hn). (3) 



* This is the expression for the velocity with which an elastic fluid issues 

 through a small orifice from a vessel in which the pressure is constant on a 

 given section at a distance from the orifice, and equal to P, and at the ori- 

 fice itself also constant and = P, g = 32-15 and lo = the weight of a cuhic foot 

 of water : the units of weight, space, and time, being the pound, foot, and 

 second. The density is expressed in terms of the pressure by De Pambour's 

 empiric formula, d = n + qp. 



