adair's equation 263 



since it has been shown to be incompatible with the kinetic data {cf. 

 Section 6.), but his equation is still widely used, since it is convenient 

 and has been shown to be formally related to the more modern 

 theories. Hill assumed that the reaction could be described by the 

 equation : 



[Hb„] [o,Y 



from which the equation: 



1 + Kp'' 



y = 



may be obtained, where n is the average number of molecules in the 

 polymer, and the remaining symbols are the same as before. It can 

 be seen that, if n = 1, the equation becomes identical with that of 

 Hiifner. 



A convenient method for deciding which of these two equations 

 best fits a given set of data is by expressing the equation logarithmi- 

 cally. Hill's equation becomes: 



[HbJ 



— log K = w log [Oo] + log 



[Hb„02j 



and values for n and K may thus be obtained from a plot of the 

 values of log [Hb„]/[Hb„02n] against log po,. For the dissociation 

 of oxyhemoglobin in blood n =f 2.5. It should be noted that as far 

 as fitting a curve to a number of points is concerned, Hill's equation 

 with two constants gives more flexibility than does Hufner's with one. 

 Between 10 and 90% saturation, a very good fit can be obtained with 

 Hill's equation. 



The development of these empirical equations facilitated the com- 

 parison of results obtained by different workers. This, in turn, 

 accelerated the recognition of the importance of many of the factors 

 discussed above, and between the years 1900 and 1925 the effects of 

 salt concentration on pH were recognized and controlled. 



5.1.4. Adair's Equation. The equations so far described differ in 

 the mean size of the unit of hemoglobin assumed to be present in 

 solution. Hufner's equation assumed a molecular weight of 16,800, 

 while Hill's equation suggested that the most frequently found par- 

 ticle contained between two and three Hiifner units. By showing 

 that four atoms of iron were present in a molecule of hemoglobin, 



