2 Walker, The Poly tropic Curve 



The simple expression (2) gives a "double infinity " of 

 curves comprising- each infinite series of lines in which " n " 

 has some definite value, which may be any positive, negative, 

 integral or fractional number. Well known polytropic lines 



are, the adiabatic lines when n—^r =8, isothermal lines when 



K v 



n—i, constant volume lines when k=K vi constant pressure 



lines when k=K and straight lines radiating from the origin 



when n— — 1. 



For the purpose of the present investigation the thermo- 

 dynamic cycles shown in Figs. 1 and 2 have been chosen as 

 representing, perhaps, the most general types, limiting cases 

 of which may be taken to represent most of the various 

 thermodynamic cycles on which modern internal combustion 

 engines are operated. 



Cycles such as those shown in Figs. 1 and 2 have already 

 been termed by the writer " Dual Combustion Cycles," 2 on 

 account of the fact that heat is imparted to the working fluid 

 by internal combustion both at constant volume and constant 

 pressure. The only difference between the two cycles is, as 

 shown, that when the fluid is in the state P&Jl^ in either case, 

 the state p o v T o is arrived at in the one case, represented by 

 Fig. 1, by the same type of polytropic compression through- 

 out the whole of the stroke, while in the second cycle, repre- 

 sented by Fig. 2, the same state p v T is arrived at after two 

 types of polytropic compression, namely, constant pressure 

 compression for the first part of the stroke and then adiabatic 

 compression for the remainder of the stroke. 



Fig. 1 represents the type of cycle in which the value of 

 the index of • • F " in the compression curve is affected by 

 various factors, either accidental, such as heat conduction to 

 or from the cylinder walls, or intentional, such as the injection 

 of water spray for the purpose of keeping down the tempera- 

 ture during the stroke. 



The general efficiency expression for this type of cycle is 

 obtained as follows : — 



heat withdrawn 



2. Phil. Mag., Sept., 1917. 



(3) 



