262 Mr. J. J. Thomson on the 



hence 



s 2 =— a — pm 2 



T 3 t 2 



(27) 



or substituting for p, m, r their values from (26), and 

 supposing that the number of free oxygen atoms is small 

 compared with the number of molecules of any kind, 



2 



t 2 2 h 



2 



_i^_ li (N- 5 -z/)(M-s) 5 



T 3 h J 



\ ■ ■ ■ (28) 



These two equations are sufficient to determine s and u, and 

 we see that, since the right-hand side of the equations contains 

 cubes of the number of molecules, while the left-hand side 

 only contains squares, the combination will be relatively 

 greater at high than at low pressures, at any rate when the 

 quantity of the gases which combine is small compared with 

 the quantity of them which is left free. 

 From equations (27) we see that 



/ h T z , 

 s/m = - rn/r, 



h T 2 



so that the ratio of the quantity of water formed to the quan- 

 tity of carbonic acid always bears a constant ratio to the 

 ratio of quantity of hydrogen left free to the quantity of free 

 carbonic oxide. The following account of Horstinann's 

 experiments on this reaction from Watts 's ' Dictionary of 

 Chemistry,' 3rd Supplement, p. 433, is of interest in connec- 

 tion with this result : — 



" The law according to which the oxygen is divided between 

 the combustible gases may be expressed thus : — The propor- 

 tion of the resulting water-vapour to the resulting carbon 

 dioxide is equal to the proportion of the unburnt hydrogen 

 to the unburnt carbon oxide, multiplied by a coefficient of 

 affinity which is independent of the proportion of the com- 

 bustible gases, but varies with the relative quantities of oxygen 

 added. This coefficient of affinity varies, according to Horst- 

 mann, between 4'0 and 6*4 when between 20 and 70 per cent. 

 of the combustible gases is burnt, the maximum coefficient- 

 coinciding with the combustion of 30-40 per cent, of the 



