SECT, iv.] AND PROPORTIONS OF ENGINES. 169 



and temperature (art. 122.) ; consequently this air must accumulate and fill half 

 the capacity of the condenser after a few strokes, and the capacity of the air pump 

 must be such as will remove 7$? of air, and 7^5 of vapour, or both together T^TJ, 

 in order to get rid of the air which enters at each stroke, when it is of such a 

 degree of density that its force is equal to the force of steam corresponding to the 

 temperature of the hot well. 



349. If it be assumed that the elastic force of the uncondensed vapour is equal 

 to 2 inches of mercury, and the air pump be equal to the condenser, then the 

 bulk of the air and vapour being shown above to be TJT, at the pressure of 30 

 inches, and the bulk being inversely as the pressure, we shall have 2 : 30 : : TT<J : ?g. 



Thus the air pump has to clear the engine of -jV of the volume of the cylinder of 

 air and vapour, and of ?V of its volume of water ; the sum of these is, in the 

 nearest fraction, -fa of the capacity of the cylinder, for each stroke. 1 



350. In a double engine the air pump makes only one stroke for each 

 cylinder of steam, but since the condenser receives a new quantity to replace 

 that taken by the pump, there is no expansion : hence TF part of the capacity 

 of the cylinder of a double engine is the least proportion for the air pump, so that 

 the engine may work effectively in the same manner as for a single engine. In 

 both cases the condenser and air pump are supposed to be of equal size to render 

 this proportion applicable, and it is also understood that river water is used. 



1 Let be the volume of air contained in the injection water and the steam, t' the tem- 

 perature of the condenser, and /' the force of steam corresponding to it,/ being the force in the 



cylinder. Then -^ . ( ^^ ) = the volume of air, and a = that of water for each stroke. 

 / \ oil / 



The condenser must contain both these quantities, and also what the pump leaves ; and with 

 an allowance of half for leakage and imperfect action of the valves, its least capacity must 

 obviously be 



When the pump ascends, the air will saturate with vapour, and become of twice its former 

 volume; hence if the air pump and condenser jointly contain it in this state, they will be of equal 

 size, and the quantity required will be removed at each stroke of the pump. Putting t' = 100, 

 /' = 2, and/= 30 inches, we have 



3 a ( - + '67 ] = capacity of air pump = condenser. 

 \ n J 



/ 



If n = 20, as for river water, then 4-48 a = capacity of pump. 

 If n = 14, as for well water, then 5-55 a = capacity of pump. 



Y 



