F. J. W. ROUGHTON 



terms can thus all be neglected. The kinetic equations for dissociation 

 then reduce to 



4 — — k C 3 — k C — k c 2 — Jr c — h c 



— — K^tt —j- ^4^4 ^3^39 ~r ^3^3 '<-2^2> 



— — = k 2 C 2 ~ f^v^ii —-j— — "ovi . . . .(2) 



This set of equations is mathematically identical with those obtaining 

 in a chain of radio-active changes, the general solution for which has 

 been given by H. Bateman 11 . He has shown that the concentration 

 of the n ,h intermediary product, C„ is given by 



C„ = C{P x e- klt + P 2 e"* 2 ' + P z e~ k3t + P^e~ kit ) .... (3) 



where the coefficients P l9 P 2 . . . are each functions of k l9 k 2 , /c 3 , k x of 

 given form, so that numerical values of P x etc can at once be worked 

 out when k l9 k 2 etc are known. 



The corresponding equations for the combination velocities are only 

 mathematically tractable, if 1, the back reaction velocity terms {i.e. 

 — k„C„ etc.) can be neglected (as in the case of the CO + Hb reaction 

 over almost its whole range) and 2, X is present in such large excess 

 that its concentration may be taken as constant. These simplifications 

 lead to a set of equations similar to (3), but with ki etc replaced by 

 k{ etc. For the exact form of the equations and of the coefficients 

 P l9 Pi etc and P/, P 2 ' etc (for the combination velocity), reference 

 should be made to the current paper by Roughton 12 . 



In attempting to apply the intermediate compound hypothesis to 

 the kinetics of the haemoglobin reactions with the aid of the equations 

 just given, we are again faced with the difficulty of having at our choice 

 a large number of unknown velocity constants, without any clue as 

 to the exact values to be assigned to these individual constants. The 

 only limitation imposed by the law of mass action is that k{\k x must 

 = K l9 k 2 '/k 2 — K 2 etc. A full kinetic investigation must therefore 

 wait until the determination of the values of K t , K 2 , K 3 and K^ has been 

 attempted in the way described in the previous section. In the present 

 section, however, we think it worth while to show that the further 

 development of one particular example of the intermediate theory, 

 namely that which formed the basis of case A of the previous section, 

 provides satisfactorily for most of the present known features of the 

 kinetic data. The latter are expressible by the equation 



^ [X , Hb] = fc'OTHb] - *[XHb] ... .(4) 



at 



with the limitation that k' is only constant below y = 50 per cent in 



90 



