F. J. W. ROUGHTON 



particular equation the ratios of K x to K % to K 3 to AT 4 are those put 

 forward by the author but the absolute value of K x is, in each case, so 

 chosen that at p — 3 mm, y = 50 ± 0-05 per cent saturation. 



Figure 2 A to J shows graphically the size of the discrepancies 

 between the observed data of Table I, and the figures calculated accord- 

 ing to the respective equations, over the whole range of the dissociation 

 curve. 



A W. H. Forbes and F. J. W. Roughton assumed 2 that the 

 first three intermediate reactions take place on statistical principles, 

 the velocity constants of combination being proportional to the 

 number of uncombined Fe atoms, and the velocity constants of 

 dissociation to the number of combined Fe atoms. It then follows 

 that K x : K 2 : K 3 : : 4 : 3 / 2 : 2 / 3 . In the fourth and final reaction 

 (Hb 4 O e + 2 ^ Hb 4 8 ) it is assumed that there is a great increase 

 in K^ i.e. a large ' interaction ' in Pauling's sense 4 . With these 

 assumptions equation (1) can be shown to reduce to 



K iP (i+ K -fy+v 



100 ./. . K lP 



4(l +£?)*+ »P« 



where X = K X S KJ4 approximately. 



With K x = 0-32 and AT 4 = 8-8, Figure 2 A shows agreement of 

 calculated and observed values to within ±1-5 per cent over the whole 

 range. 



£ Forbes 5 tried the effect of assuming the concentrations of Hb 4 4 

 and Hb 4 O e were so slight as to be negligible. This, as he pointed out, 

 is an impossible assumption from the kinetic point of view, but it leads 

 to the equation 



y Kxp + v-p* 



100 4(1 + K lP ) + y.p* 



which, with K x = 0-544, and jj. = 0-0896, gives good agreement except 

 at the bottom of the curve, where the discrepancies exceed experimental 

 error. The equation must therefore be rejected both on theoretical and 

 experimental grounds. 

 C is based on the well-known equation of L. C. Pauling 4 



y K lP -f- (2a + l)*i 8 /? 2 + 3a 2 ^ 1 3 ^ 3 + a^V 



100 1 + 4K x p + (4a + 2)K x 2 p 2 + 4a 2 K 1 3 /? :r + a^ 4 / 4 ' 



In deriving this equation, Pauling assumed that when an 2 molecule 

 combines with a Fe atom adjacent to one already combined, there is 

 an ' interaction ' resulting in an increase of the equilibrium constant 



86 



