Mr. W. J. M. Rankine on the Mechanical Action of Heat. 179 



nor less than 4, and the temperature not lower than 100^ Cen- 

 tigrade, nor higher than 171° Centigrade (which correspond to 

 212° and 340° Fahrenheit). 



The most convenient and expeditious mode, however, of com- 

 puting the pressure from the volume, or vice versa, is by inter- 

 polation from the table given in the sequel. 



(29.) The resistance denoted by R may be divided into two 

 parts; that which arises from the useful ivork performed, and 

 that which is independent of it, being, in fact, the resistance of 

 the engine when unloaded. Now it is e\'ident that the maximum 

 useful effect of the steam has been attained, as soon as it has 

 expanded to a pressure which is in equilibrio with the pressure 

 of the waste steam added to the resistance of the engine when 

 unloaded; for any further expansion, though increasing the total 

 effect, diminishes the useful effect. Therefore if we make 



R = R'+/, 

 R' being the resistance arising from the useful work, and / the 

 resistance of the engine when unloaded, both expressed in the 

 form of pressure on the piston, the expansion corresponding to 

 the maximum of useful effect will take place when 



the corresponding ratio of expansion being [_ . . . (53) 



The maximum useful effect with a given pressure on the 

 safety-valve has been so fully discussed by M. de Pambour, that 

 it is unnecessary to do more than to state that it takes place 

 when the initial pressure in the cylinder is equal to that at the 

 safety-valve ; that is to say, when it and the useful resistance 

 are the gi-eatest that the safety-valve will permit. 



(30.) Annexed is a table of the values of some of the quan- 

 tities which enter into the preceding equations in the notation 

 of the Count de Pambour's works. 



