by Diffusion and similar Processes. 



497 



since r is nearly equal to unity 

 1 1 



2-r 



Accordingly 

 = r nearly, 



so that approximately s and r are reciprocal operations. For 

 example, if starting with any proportions we collect the 

 transmitted half, and submit it to another operation of the 

 same sort, retaining the half not transmitted, the final 

 composition corresponding to the operations sr is the same 

 (approximately) as the composition with which we started, 

 and the same also as would be obtained by operations taken 

 in the reverse order, represented by rs. A complete scheme * 

 on these lines is indicated in the diagram. Representing the 



i 

 r s 



r2 I S* 



r s 



initial condition by unity, we may represent the result of the 

 first operation by 



ir + i«, or i(r + s), 



in which the numerical coefficient gives the quantity of gas 

 whose character is specified by the literal symbols. The 

 second set of operations gives in the first instance 



\r 2 + %sr + Irs + Js 2 , 

 or, after admixture of the second and third terms (which are 

 of the same quality), 



In like manner the result of the third set of operations may 



fr -I - s \ 

 be represented by ( — ^— j, and (as may be formally proved by 



* It differs, however, from that followed by Prof. Ramsay in his 

 recent researches (Proc. Roy. Soc. vol. lx. p. 210, 1896). 



