THE NATURE OF HEMOGLOBIN SOLUTION 75 



Let us take a single instance of the sort of difficulty which lies 

 before us. Suppose we consider the equilibrium of oxygen, hsemo- 

 globin and oxyhsemoglobin, all in solution in water, and supposing 

 the haemoglobin and oxyhsemoglobin are present as single molecules, 

 the simple reaction 



Hb + O2 :^ HbOa 



is represented mathematically by a rectangular hyperbola — a fact 

 which is shown in detail in Chapter x. If, on the other hand, the 

 haemoglobin and oxyhsemoglobin are conceived of as solids and in a 

 different phase from the oxygen, the law of mass action would indicate 

 that there should be a critical pressure of oxygen below which all 

 the haemoglobin would be reduced and above which it would all be 

 oxidised. That at least is what might be expected if a sufficiently 

 fine powder of crystalline haemoglobin were exposed to gaseous 

 oxygen. Now, if we are going to study the equilibrium of these 

 substances, which formula are we to adopt as being correct? The 

 dissociation curve cannot be both a continuous and a discontinuous 

 ascent. If the passage from a simple linimolecular solution to a 

 solid is a gradual one with no fundamental break in it, there should 

 be a corresponding gradual transition from the hyperbola to the 

 discontinuous curve. It may be so. At all events it may be worth 

 considering the matter if a certain assumption is made, namely, that 

 should molecules unite to form an aggregate that particular aggregate 

 is either completely oxidised or completely reduced. Under such 

 circumstances the reaction is represented by the formula 



y _ Kx"* 

 Too ~ \TK^ ' 



where y is the percentage of the haemoglobin which is oxidised, x is 

 the oxygen pressure, K is the equilibrium constant of the reaction, 

 and n is the average number of molecules, each capable of uniting 

 with two atoms of oxygen, which form an aggregate. \i n= 1, the 

 curve obtained from the above reaction is a hyperbola, if n is greater 

 than 1 , the curve becomes inflected and increasingly so with an increase 

 in the value oi n. In Fig. 14 a number of curves are drawn with 

 different values for n, it being assumed in each case that at 10 mm. 

 pressure of oxygen the haemoglobin is 50 per cent, saturated. In 

 the limiting case the inflection would be so great as to make the curve 

 vertical for most of its length, that is to say 10 mm. would be a 



