Fourier analyses of physiological pressure and flow signals are required to determine the complex fluid impedance at the various harmonics of the fundamental frequency. Digital computer programming is eased if a readily recognized event initiates the simultaneous recording of both pressure and flow signals. Digital switching elements in simple electronic circuits are used to synchronously initiate...

We use Hobson's definition of the associated Legendre functions [1]. Any product of non-negative powers of (x/r), (y/r), and (z/r) can be expanded as a linear combination of harmonics Pn(cos 0), PFm(cos 0) cos mp and Pnm(cos 0) sin m4 in which n and m take appropriate values. This expansion is given formally by Equation (2), which defines the coefficients a',,,. We consider only non-negative integer values of u, v, w.

By using carbon monoxide as a reagent for releasing oxygen from blood solutions (instead of the customary potassium ferricyanide) and by combining the techniques of the Van Slyke constant-volume gasometric apparatus and the Scholander gas analysis apparatus, a precise method has been devised of estimating oxygen content and carbon monoxide capacity simultaneously on one and the same sample of blood solution. The procedure eliminates various errors inherent in the determination of oxygen percentage saturation, when oxygen content and capacity are successively measured on separate samples. The method has been extensively tested on sheep blood solutions containing 3 to 4 g haemoglobin/100 ml. and is considered to give an accuracy of ± 0.5 in the oxygen percentage saturation of such solutions. In its present form the method is only applicable to solutions containing a negligible amount of dissolved nitrogen, but it is probable that this restriction could be removed by the simple addition to the technique suggested in the text. Modifications are also described in the usual tonometer technique for equilibrating blood solutions with various pressures of oxygen, and for transferring the equilibrated blood solution to the Van Slyke apparatus for analysis. The techniques of the present paper have been specially used for obtaining oxyhaemoglobin dissociation curve data of higher accuracy than hitherto available. From these improved data it has for the first time been possible to calculate directly, and in many cases with fair precision, the values o f the equilibrium constants of the four successive reactions of haemoglobin with oxygen.

It is now generally accepted that the equilibrium between oxygen (or carbon monoxide) and mammalian haemoglobin is expressible in terms of four intermediate reactions Hb 4 + O 2 ⇌ Hb 4 O 2 (equilibrium constant K 1 ), Hb 4 O 2 + O 2 ⇌ Hb 4 O 4 ( K 2 ), Hb 4 O 4 + O 2 ⇌ Hb 4 O 6 ( K 3 ) and Hb 4 O 6 + O 2 ⇌ Hb 4 O 6 ( K 4 ), as Adair first suggested about 30 years ago. Hitherto, experimental data on the oxyhaemoglobin dissociation curve have not been precise enough to permit the direct determination of the equilibrium constants, K 1 to K 4 , of the intermediate reactions. Recently, however, the accuracy of the observations at the top and at the bottom ends of the dissociation curve has been improved about 10-fold, i.e. to within ±0.05% saturation. From such measurements—together with 2- to 3-fold more accurate data over the main part of the curve—it has now proved possible to evaluate directly, by standard statistical procedure, the values of K 1 (± ca . 5%), K 2 ( ± ca . 25%), K 3 ( ± ca . 33%) and K 4 (± ca . 13.7%) for sheep haemoglobin solutions at alkaline pH (9.1). Unfortunately, it is not yet feasible to extend the attack fully to haemoglobin solutions at neutral pH, since the method for obtaining highly accurate data at the top of the dissociation curve breaks down at this pH. For 3 to 4% solutions of sheep haemoglobin at pH 9.1, K 1 , K 2 and K 3 are found to be of the same order, whereas K 4 is from 10 to 20 times greater, thus pointing to some marked internal change in the sheep haemoglobin molecule after three molecules of oxygen have combined therewith. From the effect of temperature on K 1 and K 4 , values are derived for the heats of all the intermediate reactions and for the entropies, Δ S 1 and Δ S 4 , of the first and last of the intermediate reactions. There are appreciable differences between the heats of the intermediate reactions, contrary to the old view that these heats are all equal. Preliminary, but very rough, data are also given on the effect of pH and dilution. In the discussion it is shown that the new and more accurate data on the dissociation curve are incompatible with previous special theories of the oxygen-haemoglobin equilibrium, which had been based on, and checked by, conventional but less accurate experimental data. Wyman’s recent symmetry theory is a striking example in the latter category and hence is given detailed consideration. The kinetic implications of the higher value of K 4 are briefly considered. It appears that the responsibility therefore is about equally borne by the relative increase in k' 4 , the velocity constant of the combination Hb 4 O 6 + O 2 → Hb 4 O 8 , and by the relative decrease in k 4 , the velocity constant of the dissociation Hb 4 O 8 → Hb 4 O 6 + O 2 .