24 Prof. W. M. Thornton on the 



When two atoms combine to form a molecule their energy 

 of combination is shared with surrounding inert molecules, 

 and the greater the proportion of inert gas the more com- 

 pletely the observed maximum should approach a maximum 

 calculated on an energy basis only, since whatever form the 

 energy of combination may for the moment take, it must be 

 shared equally with the neighbouring molecules and in the 

 end the translational or pressure energy is equalized. Thus 

 the ratio of observed to the calculated maximum pressure 

 would approach unity in the weakest mixtures if combination 

 were not checked by the insufficiency of energy, set free by 

 the molecules which are formed, to raise the whole mass of 

 gas to a temperature such that all the combustible portions 

 may unite. 



At the upper and lower limits of inflammability the ratio 

 expressing the " efficiency " of explosion is of course zero. 

 For coal-gas these limits are usually 29 and 6 per cent. 

 Straight lines drawn from the upper limit through the 

 curves cut the vertical axis at 0'94 and 0'98. [In the case 

 of hydrogen, for which only three points are available, a line 

 from the upper limit at 70 per cent, through two of the 

 points cuts the axis at 0'78.] From this it is seen that the 

 efficiency of explosion of the richer mixtures decreases to 

 zero at a uniform rate as the percentage of gas is raised. 

 In weaker mixtures, diluted with air, every atom of com- 

 bustible gas enters into combination and shares its energy 

 with the residue of the air. Thus the ratio of rotational to 

 translational energy is not at any moment abnormally great 

 for the whole volume, and the percentage of pressure 

 developed is higher than if there were no nitrogen present. 

 On the other hand, in richer mixtures with excess of com- 

 bustible gas, all the oxygen is taken up but less combustible 

 gas, and at the upper limit none of the latter. The efficiency 

 of explosion should, therefore, always diminish in mixtures 

 above the point of perfect combustion. 



Let N be the number of combustible gas molecules 

 entering into combination in unit volume of mixture, n of 

 " inert " molecules. The ratio rj of Table II. and the figure 

 is that of the translational energy of the whole mixture to the 

 energy of combustion in it. The translational energy is 

 directly proportional both to N, the combustion of which 

 gives rise to the heat, and to n which helps to transfer it as 

 pressure to the walls, and therefore to their product. As the 

 percentage is varied the sum N + w = M say remains constant, 

 and Nw = N(M — N). Thus we may write the translational 



