ON GASEOUS EXPLOSIONS* 219 



and composition should both vary directly as the pressure or density. 

 The value of the radiation from a layer of thickness 1 cm. at a pressure 

 of 10 atmos. would be the same as that from a layer of 10 cm. at 

 1 atmo., assuming that the quality of the radiation or the nature of 

 the combustion were not altered by the pressure. This effect is repre- 

 sented by increasing the absorption coefficient in proportion to the 

 pressure, leaving the limit for infinite thickness unaltered. 



The. effect of temperature is more difficult to estimate because the 

 radiation from a flame is very complicated and there is no means of 

 accurately measuring the temperature. Nernst, 1 from observations 

 by others on the cooling of an explosive gas mixture, maximum 

 pressure about 6 atmos., allowing for convection and conduc- 

 tion, finds the radiation to vary as the fourth power of the 

 temperature. The method is very uncertain, and his conclusion was 

 most severely criticised by Lummer, Bringsheim, and Schaefer, who 

 explained that the radiation was quite different from that of a black 

 body, and that the quality of the radiation was little, if at all, affected 

 by pressure up to 4 atmos. 



The principal maxima of emission and absorption in the Bunsen 

 flame spectrum are at 2 - 8/* and 4 - 4 /x. Taking a mean wave-length 

 of 3"5 /m, it is easy to estimate how the intensity should vary with 

 temperature by assuming Planck's equation. The following table gives 

 approximate relative values for comparison with the fourth-power law 

 of the Stefan for the radiation of a black body : — 



The rate of variation, according to Planck's formula for a single 

 wave-length, is much slower than the fourth-power law, and tends in 

 the limit to be directly proportional to the absolute temperature at high 

 temperatures. The actual rate of variation should lie between these 

 limits, but nearer to Planck, unless carbon begins to separate in rich 

 mixtures at high temperatures. 



Effect of Radiation TjOSs on the Thermal Efficiency. 



Although it is not possible to calculate the absolute magnitude of 

 the radiation-loss in a motor, or to deduce from it the relative loss 

 of thermal efficiency, it is not difficult to see in what manner this 

 loss should vary with flame temperature and with linear dimensions of 

 the cylinder. We may assume for this purpose that the cylinder at 

 the moment of maximum pressure is filled with practically homogeneous 

 flame and that the walls are practically non-reflecting. For similar 

 motors under similar conditions the heat-loss per explosion will vary 

 as the product ES of the intrinsic radiance E and the surface S. The 

 percentage heat-loss should vary as ES/V, where V is the volume of 

 the cylinder. This will vary as B/D, where D is the diameter, for 

 similar motors. Assuming a pressure of 20 atmos. in a cylinder of 

 x Proc. Inst. Aut. Eng., 1909, pp. 457-408. 



