26 Prof. W. M. Thornton on the 



the upper limit there are GU units, but the cooling or 

 retarding influence of the gas is greater than at the lower 

 limits and ignition again fails. The ratios 



VL_ TP_WU 

 FL~QP~ GU 



are those of gas to air for perfect combustion. 



Now the heat set free in combustion is directly propor- 

 tional to the number of combustible units in the mixture, 

 except at the limits where the inflammation suddenly ceases. 

 We may then write, for rich mixtures, from P to M, 



Q = Q c (l-aN), 



where Q c is the heat of combustion of unit volume of the 

 perfect mixture. For the part LP, 



Q = Q C 6N. 



The maximum pressure calculated from the heat liberated 

 is 



Pc=Pl.~ ' 



('♦£> 



where p 1 is the initial pressure, r , i\ the volumes before and 

 after explosion, Q the total heat of combustion, and a the 

 coefficient of expansion of the gas. Substituting the above 

 values for Q we have, since for the same gas Vi/v Q is 

 constant, 



above the point of perfect c Q c (l — aN)al 

 combustion P : ^ = ^ij 1+ — — q > , 



below P : p c = cp x (1 + ^ J. 



By definition y = p obg . \p c , so that 



(a) above P : p oba . = cpi??{l-f &(1— aN)}; 



and r] has been found to be of the form A — BN, 

 therefore in rich mixtures 



p obs> = c i ? l (A-BN){l + Z:(l-aN)}, 



which may be written 



