60 Chapter V 



and acids to haemoglobin it may be profitable to give a brief sketch 

 of an attempt which has recently been made to find a physical expla- 

 nation of these facts. 



Any such explanation starts from the proven fact that the dis- 

 sociation curve is a rectangular hyperbola, representing a simple 

 reaction 



This reaction involves single molecules only, and has a definite 

 equilibrium constant. 



The equation for this curve may be written 



y Kx 



100 ~ = 1 + Kx ' 



where y = the percentage saturation of the haemoglobin with oxygen, 

 x = oxygen pressure, and K is the equilibrium constant of the curve. 



This curve, as I have said, assumes that the molecules of haemo- 

 globin are single ones. Hill <7) amplified this equation with the object 

 of ascertaining the shapes of the dissociation curves which would be 

 obtained on the assumption that the molecules of haemoglobin fall 

 into aggregates as the result of the addition of salts. At the end 

 of Chapter IV I pointed out that there was independent reason to 

 suppose that this was the case. 



If on the average there are n molecules in each aggregate, the 



equation becomes 



y Kx n 



100 ~1 +Kx n ' 



The solution is conceived of as containing haemoglobin in the various 

 degrees of molecular aggregation, the reactions of which would take 

 place in the following way : 



Hb + O 2 ^ 



Hb 3 + 3O 2 ^ Hb 3 O 6 , &c., &c. 



The equation however has certain limitations of which the only one 

 to be considered, so long as we are confining our attention to oxy- 

 haemoglobin, is that there is no considerable quantity of intermediate 

 oxides such as Hb,0 2 in the solution (8 '. The theory does not preclude 

 the formation of such substances. It is highly probable that Hb 2 2 

 for instance is a stage on the way to Hb 2 4 . But to make the 

 equation hold, the suboxides can only exist as stages in the reaction ; 

 in short the assumption is that if two molecules of Hb,O 2 met, they 



