432 Messrs. Hartley, Ponder, Bowen, and Merton on an 



where the absorbing power is A , and K is a constant 

 appropriate to the mass of the particles and the temperature 

 of the gas. The absorbing power through each line can 

 thus be plotted as a probability curve, and it is at once 

 evident that if the maxima of absorption for the different 

 types of molecule are at a distance apart which is com- 

 parable with the "half-widths," the effectiveness of the 

 chlorine filter will be impaired. It can be seen, however, 

 that the filter is still operative, though less efficient, when 

 the difference between the maxima is less than the " half- 

 widths " of the lines, which it would then be impossible to 

 resolve so that they could be seen as separate lines in the 

 spectroscope; but in the absence of any data as to the sepa- 

 ration of the components, or their number, further discussion 

 would be redundant. 



From the foregoing considerations it is evident that, 

 according to theory, the success of the experiment should 

 be favoured by working at a low temperature, and that 

 the temperature of the reaction vessel should be equal to 

 or less than that of the filter ; but the probable gain in 

 efficiency is very small in comparison with the difficulties 

 of manipulation at low temperatures. 



Conditions for Maximum Efficiency. 



By the efficiency E we denote the ratio of the number of 

 atoms of the one kind to the number of atoms of the other 

 kind which, in a reaction vessel one molecule in depth, 

 combine with hydrogen to form hydrochloric acid under 

 the' influence of the light which has traversed the filter. 

 If the chlorine contains n kinds of isotopic atoms denoted 

 bv m u m 2 , m d ...m n , in the proportion a l5 a 2 , a 3 ...a n , 

 there will be \n(n + l) kinds of molecule in the gas, and the 

 proportions of the different kinds of molecule in the gas can be 

 found from the coefficients of [a 1 m 1 + a 2 m 2 + a 3 m 3 . . . + a 7l ??i n p, 

 where, for example, the coefficients of (mi 2 ) and (m 2 m n ) 

 denote the relative numbers of the molecules (m^m 2 ) and 

 O2, m n ) in the gas. In the present case we consider only 

 two kinds of isotopic atoms which are present in the ratio 

 (1— x)\3C, the three kinds of molecules being thus present 

 in the ratio (l-2x + x 2 ) : (2x-2x 2 ) : x 2 . If the absorption 

 coefficient is denoted by k and the length of the column 

 of gas in the filter by I, it can be easily shown that the 

 efficiency 



e - klx" -\-±- e - kl{2x-2x*) 

 = Ig—kl^x - 2x2) _j_ e - kl{ 1 -at + x2, ' 



