RESPIRA TION 623 



more oxygen. Each gas, in fact, assists to drive off the other, but we require 

 more knowledge of the relative lowering of surface energy at the haemoglobin- 

 plasma boundary effected by the two gases before we can make any calculations 

 on this basis. 



The form of the dissociation curve is very sensitive to the concentration of 

 hydrogen ions, so that it can be used as an indicator for changes in this direction 

 occurring in the blood, either as the result of muscular work, of want of oxygen, or 

 in pathological states of "acidosis." 



Now, what are the equations to the curves obtained in the presence of acid 

 or of salts 1 Since haemoglobin is in colloidal solution and, as we have seen 

 (page 91), electrolytes have a powerful effect in causing aggregation of colloidal 

 particles, this phenomenon would naturally be looked for as the explanation. 



A. V. Hill (1910, 2), on the hypothesis of the aggregation of molecules of 

 haemoglobin causing the reaction to become of a higher order than unimolecular, 

 arrived at an expression of the form : 



where y is the percentage saturation of haemoglobin with oxygen, x the oxygen 

 pressure. This formula, by proper choice of the constants, K and n, was found 

 to apply to the experimental data of several cases taken. 



In attempting to understand the meaning of this equation, it is well to point 

 out that Hill himself (p. vi) did not profess to attach any direct physical meaning 

 to the constants, although Barcroft (1913, p. 481) regards K as the equilibrium 

 constant and n as the average number of molecules of haemoglobin in each 

 aggregate. Hill subsequently adopts this view to a large extent (1913, 5). 



It must be confessed that it is a very difficult matter to grasp the conditions 

 under which the various states of equilibrium in a colloidal system are attained, 

 and any criticism that I may make as to the above-given interpretation must not 

 be misunderstood. It is, undoubtedly, an extremely valuable contribution to the 

 theory, but careful consideration has made it clear to me that some doubtful 

 assumptions are made, and that a satisfactory solutioa of the problem will only 

 be reached by taking account of the conditions prevailing at the boundary 

 surfaces of the phases of a heterogeneous system, micro-heterogeneous, it is true, 

 and that the law of mass action alone is insufficient. If the phase rule requires 

 special proof in its application to colloidal systems, so also does the simple law of 

 mass action. 



It is clear that Hill's formula applies to the curves obtained by experiment. 

 Looking at those of Figs. 191 and 192, we see at once that, under the influence of 

 electrolytes, the dissociation curve is no longer the rectangular hyperbola of a 

 unimolecular reaction. But why should mere aggregation of haemoglobin change 

 the order of the reaction ? As I understand the theory of velocity of reaction, as 

 based on mass action, the order would be changed only if molecules of a different 

 chemical kind came in to take part in the reaction. There seems no reason to 

 suppose that the various degrees of aggregation of haemoglobin result in change 

 of its chemical nature. With regard to oxygen, of course, no suggestion of this 

 kind is possible. On the face of it, then, there seems no clear reason why the 

 reaction ceases to obey the formula of a unimolecular reaction, since it ought 

 still to be capable of expression as a change in concentration of one kind of 

 molecules, namely those of haemoglobin, as they combine with oxygen to form 

 oxyhaemoglobin. 



There are two forms of equation already known to us in which we have an 

 exponent, which we have called n in both cases. The first is that expressing 

 the velocity of reaction, where it has the significance of the number of different 

 kinds of molecules taking part in the reaction, whose concentration may vary 

 independently, so that it is necessary to take account of the change in concen- 

 tration of each. In this case it must, naturally, be a whole number. The 

 second equation is that expressing the amount of a substance adsorbed by a 

 surface as a function of the concentration of the substance. In this case, n 



