624 PRINCIPLES OF GENERAL PHYSIOLOGY 



may be, and usually is, fractional. The curve in both cases belongs to the 

 parabolic family, but, if we glance at those of Figs. 191 and 192, we see that, 

 in the presence of salts or acid, the experimental curve is S-shaped, that is, 

 more complex than either of these two possibilities alone. 



In the data given by A. V. Hill (1910, 2), we note at once that the values of 

 n are mostly fractional. The explanation given is that there are present a number 

 of aggregates of haemoglobin containing different numbers of molecules, so that the 

 net result is a combination of different orders of reaction above the unimolecular 

 one. But, as already pointed out, it is not clear that it is legitimate to assume 

 that the n of Hill's formula corresponds to that of the expression for the velocity 

 of reaction, where it refers to the number of kinds of molecules taking part. If 

 aggregation takes place, it would seem more likely to produce a change in the 

 effective concentration, rather than in the exponent ; that is, in C in the formula : 



$=*C, 



dt 



and therefore in the equilibrium constant, K, of Hill's formula. 



Put in another way, it is not obvious why the order of the reaction, 



Hb. 2 + 2O 2 =^= Hb.>O 4 , 

 should differ from that of 



Hb + O 2 :^= HbOo, 



unless Hb t , is a different chemical individual from Hb, and that it dissociates 

 differently. 



In the reaction : 



EtA + H 2 ^=^ EtOH + HA, 



although the association of water and of alcohol differs at different temperatures, 

 there is no evidence of a change in the order of the reaction, so far as I am aware. 



A. V. Hill, in a further note (1914, 3), shows how the same equation, 



can be obtained thermodynamically by consideration of osmotic pressures, without reference 

 to aggregation. But the applicability of mass action to the system is assumed, and the 

 difficulty lies here rather than in the hypothesis of aggregation, which is not improbable. It 

 is further suggested that the lowering of osmotic pressure required in this form of treatment 

 might be due to the unequal distribution of electrolytes, described above in relation to Congo- 

 red (page 160), but the electrolytic nature of oxyhsemoglobin is not yet demonstrated. The 

 situation of the membrane is not clear when none is provided by the experimenter, although 

 the boundary between the gas phase and the liquid phase may act as such. 



With reference to the constancy of n (about 2-5) in the presence of different 

 concentrations of carbon dioxide (see Barcroft's book, 1914, pp. 65 and 66), 

 it is scarcely necessary to add that, in itself, no proof is hereby given that it 

 is explicable as the order of a reaction. As Barcroft remarks, " since n remains 

 so constant, it is probably the expression of some definite physical fact," and 

 it seems to me that this is as far as we can go at present. 



The constancy of n with a particular acid leads Barcroft to make the statement 

 (1913, p. 490) that the action of acid does not lead to change in the number 

 of molecules in the aggregates, but to a change of the equilibrium constant. 

 But, as we have seen, it is not satisfactorily shown that n refers to the number of 

 molecules in the aggregates, and I might venture to point out that constancy 

 of the exponent is also a characteristic of adsorption. From the similarity of 

 the curves in the cases of the action of acids and of salts, one would infer that. 

 whatever the action may be, it differs only in degree in the two cases. It might 

 be thought that, as a part of the hsemoglobin molecule is of protein nature, 

 this would enter into combination with acid ; but, as we have seen (p. 103), 

 there is no evidence that proteins or ammo-acids, except the strongly basic ones, 

 combine with weak acids at all. Perhaps measurements of the electrical con- 

 ductivity of haemoglobin solutions, as changed by the action of acids, might throw 

 light on the question. Barcroft also suggests (1914, p. 316) that the H' ion 

 causes the globin molecule to aggregate, and itself enters into combination with 



