THE UNION OF OXYGEN WITH HEMOGLOBIN 125 



as in Hiifner's theory. Hufner's theory is therefore included in and 

 is the simplest case of Hill's theory. The corresponding curve is, as 

 we have seen, a rectangular hyperbola. 



The above equation, expressed in djniamical terms, would be 



X[Hb][02]=[Hb02]; 



replacing [O2] by =^, where x is the pressure of oxygen, and a the 



solubihty, calling HbOg the percentage saturation y and Hb 100 — ?/, 

 and further remembering that a and 760 are constants and therefore 

 may be included in K, the above equation becomes 



K (100 - y) {X) = y, 



which may be written 



y _ Kx 

 l00~ 1 + Kx' 



That is if m = 1, but if m = 2 the equation would become 



100 ~ 1 + Kx"^' 

 or if m = n, Hill's well-known equation is obtained: 



y Ka 





100 1 + 



Among its merits is the fact that it contains but two variables, 

 K and n. In spite of this fact the equation, by suitable modifications 

 of these, can be made to yield curves which agree pretty closely to 

 those which have been determined experimentally. The idea of 

 aggregation is supported by the important work of Rona and 

 Yippo (13). 



The theory, however, only purports to be a first approximation, 

 because any curve drawn from the equation assumes that when the 

 oxygen pressure is varied the only effect on the haemoglobin is 

 to vary the quantity of oxygen with which the haemoglobin unites. 

 This is known now not to be so. To take a single factor: when the 

 oxygen pressure is reduced and a portion of the haemoglobin 

 changed from oxyhaemoglobin to reduced haemoglobin, the hydrogen- 

 ion concentration of the fluid is altered. This alteration in itself 

 influences the shape of the curve. If the haemoglobin were kept at 

 constant hydrogen-ion concentration (the condition to which Hill's 

 equation should rightly be applied) the curve would be somewhat 

 more inflected than the curve determined in the ordinary way and 



