438 TRANS. ST, LOUIS ACAD. SCIENCE. 



ofciit-oft'. The mean effective pressure would be less, and the 

 back pressure would be h. Increasing the boiler pressure, the 

 back pressure increases by a quantity which is proportional to 

 the speed. 



Measuring P\ from the atmospheric line, 



P'^ = cn-^ P.^E^bn (7) 



where en is the mean back pressure, Po the mean effective pres- 

 sure, E a function of the inverse expansion ratio, and bn is a 

 term applying to the entry port which is entirely analogous to 

 en. The constants c and b depend upon the size of the ports, b 

 also depending to a less extent upon the pipes connecting the 

 steam-chest and boiler. In a throttle governor, the value of b is 

 changed in order to change mean effective pressure. In a gov- 

 ernor which varies the cut-ofF. both E and b are changed by the 

 action of the governor. 



The action of any governor changes the inclination of the line 

 K, B in Fig. I. For a constant boiler pressure P\ if the cut-off' 

 comes earlier, or, if the steam is throttled, the line V^B becomes 

 less steep, and the points p' and f" sink to represent a smaller 

 output.* In Fig. 2, the action of the governor changes the posi- 

 tion of the line u'= c, and in fact the entire surface of IIP as func- 

 tion of P' . 



Making the indicated substitutions in (6) 



P'=-h+^^^^-^^{h + Po-\-E-\-{b + c)n) . ■ (8) 



Solving this equation for w, 



tt' = vLm-^p7+:e+(^ + c)« - (^^+^°)J • • (9) 



Multiplying (9) by " ^/^'' 

 33000 



33000 



r ih + P,) {k + P')n ,, , o^ ] , , 



♦ In an experimental engine the head of the screw which controls the steam should be 

 provided with a divided scale like a micrometer. 



